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https://www.storyofmathematics.com/odd-and-even-numbers/ | # Odd And Even Numbers – Explanation & Examples
## What are Odd and Even numbers?
An integer that can be divided by 2 is an even number, while an integer that cannot be divided by 2 is an odd number. They can be either positive or negative. Odd numbers are always in between the even numbers and vice versa.
To differentiate between the odd and even numbers, you always look for their end digit. The last digit of an even number is always 0, 2, 4, 6, or 8, while the last digit of an odd number is always 1, 3, 5, 7, or 9.
## Examples
A few examples of even numbers are:
-22, -10, 0, 6, 18, 234.
The above numbers are even because they end with 0, 2, 4, 6, or 8.
A few examples of odd numbers are:
-101, -17, 1, 9, 23, 985.
The above numbers are odd because they end with 1, 3, 5, 7, or 9.
## Properties
The odd and even numbers have special properties regarding algebraic operations (addition, subtraction, and multiplication). Whenever we apply algebraic operations to two even or odd numbers, we always get an even or odd number. We exclude division here because the division sometimes gives you the result in fractions while talking about special properties.
• When we add or subtract two even numbers, the result is always an even number.For example,6 + 4 = 10
6 – 4 = 2
• When we add or subtract an even number and an odd number, the result is always odd.For example,7 + 4 = 11
7 – 4 = 3
• When we add or subtract two odd numbers, the result is always an even number.For example,7 + 3 = 10
7 – 3 = 4
• When we multiply two even numbers, the result is always an even number. For example,
6 × 4 = 24
• When we multiply an even number and an odd number, the result is always an even number. For example,
7 × 4 = 28
• When we multiply two odd numbers, the result is always an odd number. For example,
7 × 3 = 21
## Generalization of Odd and Even Numbers
We can generalize the even and odd numbers as well. For example, if ‘n’ is an even number, then the next odd number is ‘n + 1’, and the next even number is ‘n + 2’, and so on. Similarly, if ‘n’ is an odd number, then the next even number is ‘n + 1’, and the next odd number is ‘n + 2’, and so on.
For example, if we want to write a series of five odd numbers starting from 73, we can write it as:
73, 73 + 2, 73 + 4, 73 + 6, 73 + 7
73, 75, 77, 79, 81
## Numbers Chart
The following table is the number chart from 1 to 100, where the odd numbers are highlighted in yellow and the even numbers are highlighted in green.
### Practice Questions
1. True or False: The number, $341$, is an odd number.
2. True or False: The number, $902$, is an odd number.
3. True or False: The number, $846$, is an even number.
4. True or False: The number, $905$, is an even number.
5. Which of the following numbers is NOT an odd number?
6. Which of the following numbers is NOT an even number?
7. Given that $M$ is an even number and $N$ is an odd number, which of the following statement is true?
8. Suppose that $456\bigstar$ is a four-digit odd number, which of the following could NOT be a valid value for $\bigstar$? | 2023-03-29 23:14:01 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8143438696861267, "perplexity": 244.6618306940785}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296949035.66/warc/CC-MAIN-20230329213541-20230330003541-00665.warc.gz"} |
https://www.physicsforums.com/threads/friction-between-a-pre-tensed-steel-hoop-and-a-cylinder.569939/ | Friction between a pre-tensed steel hoop and a cylinder
1. Jan 22, 2012
meldraft
Hey all,
I am designing a cup holder. It is supposed to be made out of a few steel rings. Its geometry is such that the hoops can open (so the radius increases), and you place the cup inside. Then, as the hoops spring back, they press upon the cup and the friction holds it in place as you lift the entire thing.
Making some rough assumptions (good accuracy is really not important at this point, I just want an order of magnitude), I thought I could use Laplace's Law for a cylindrical container, since my problem is basically the inverse (pressure is pointing inwards instead of outwards):
$$σ=\frac{PR}{t}$$
where σ is the hoop tension, P the pressure of the hoop to the cup, r the radius of the ring, and t the ring's thickness. To simplify the problem a little, I can assume that my rings are infinitely thin (not in the radial direction where I do have thickness. in the z-direction.). Therefore, if N is the total normal force (and this is tricky, because the vector sum is 0):
$$P=\frac{N}{L}$$
so P is a distributed force (Newton/m), much like a beam problem.
Now, since this is an elastic phenomenon, I used Hooke's Law, saying that:
$$εE=\frac{PR}{t}=\frac{NR}{Lt} => N=\frac{εELt}{R}$$
Let traction be fmax:
$$fmax=μN$$
By combining the last two equations:
$$fmax=\frac{μεELt}{R}$$
I would have been perfectly fine with this result, but for strains above ε=10^-6, this formula yields outlandishly high values of friction. For instance, for ε=0.7, I would get something like 0.4 GigaNewtons. I probably went wrong somewhere, but I really can't locate the mistake! I would be grateful for any advice you can give me!
P.S. All calculations were done in SI, so this is after the units check :P
Last edited: Jan 22, 2012
2. Jan 22, 2012
AlephZero
You said "its geometry is such that the hoops can open so the radius increases".
If that means the hoop is split rather than continuous, your whole calculation is wrong. You should be treating the hoop as a curved beam, which will be orders of magnitude more flexible than a continuous ring.
If you try enlarging the diameter of a metal ring by forcing a cone shaped object into the hole, you will soon discover it does need a very large force!
Even if the ring is continuous, you are ignoring the flexibility of the cup. If it's a plastic cup, it will will be compressed (and possibly buckle) rather than the ring expanding.
3. Jan 22, 2012
meldraft
You are right, the hoop is not continuous, and of course this explains the immense stress needed to open it (duh!)
My geometry is actually a helix, and I thought I could approximate it with circles, but apparently there is a deficiency in that plan.
I have to sleep now, so I'll post an update in the morning :tongue:
4. Jan 24, 2012
meldraft
After many hours of thinking , I modelled the hoop as two semi-circles with a hinge. I got the friction as a function of the new radius, which yielded about 16 Newton per hoop, which is pretty reasonable, considering the assumptions :tongue:
I might try a more accurate model in the future, but for now I am happy
Thanks again for offering your insight! | 2018-05-22 01:00:41 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.761055052280426, "perplexity": 767.7019432169601}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-22/segments/1526794864572.13/warc/CC-MAIN-20180521235548-20180522015548-00539.warc.gz"} |
https://support.bioconductor.org/u/9995/ | ## User: DSP
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... Hi Aaron, Apologies for delay in response. 1) Thanks for the correction. I have transformed my beta values to M-values for downstream analysis 2) The intervention here is a qualitative, life style intervention and the difference is captured in the outcome. Moreover, systematic differences in samp ...
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https://fagullo.com/publication/agullo-rueda-88-b/ | # Raman Spectroscopy of the Ammonium Ion in NH$_4$ZnF$_3$ and NH$_4$MnF$_3$ Perovskites: Temperature Dependence
### Abstract
The Raman spectra corresponding to the internal vibrations of the ammonium ion in NH$_4$MnF$_3$ and NH$_4$ZnF$3$ single crystals have been measured from 10 to 300 K. The spectra clearly show the existence of a structural phase transition from cubic to tetragonal symmetry. The splitting of the internal modes is compatible with effective symmetries of the ammonium ion of $D{2d}$ and $C_s$ in the cubic and tetragonal phases, respectively. The temperature dependence of the symmetric stretching mode in the cubic phase is linear with a slope of 0.231 cm$^{-1}$ K$^{-1}$ for NH$_4$MnF$_3$. This has the opposite sign to that due only to the crystal expansion as obtained by applying hydrostatic pressure. A sharp band appearing only in the spectrum of NH$_4$MnF$_3$ just below the crystallographic phase transition originates in a strong symmetry-induced $\nu_2 + \nu_4:\nu_1$ Fermi resonance.
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https://www.electro-tech-online.com/threads/johnson-counter.1853/ | # Johnson counter
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#### Ybody
##### New Member
There is probably an extremely easy way of doing this that I am missing.
Using a 4017, I am able to verify my counting works by breadboarding some LEDs to the respective outputs.
I have a stopwatch that requires a low to start and another low to stop. Normal stopwatch, so if the low never goes high, it will still be timing. As it stands right now, once output 0 goes from high to low, the timing starts. It cycles through all the other LEDs and the stopwatch continues running. Go back through the cycle, LED 0 lights up and as it goes out, the timer stops timing. Say I want it to start on the dropout of LED 0 and stop on the dropout of LED 8...
Code:
| 4017 |
|__________|
0 1 2 8 9
| |
| |
R1 R1
| |
LED LED
|_*____*_|
|
|
SW
|
Ground
Should I just pop 2 diodes in where the "*"s are or is there a better way of doing this? SW is the stopwatch connection to the start/stop button. This is my first shot at this, and after about a day and a half of 4017 and quad comparitor searching, mind mind is pretty much fried. TIA
#### kinjalgp
##### Active Member
Since LED is also a diode, you don't require any additional diodes.
#### mechie
##### New Member
Edited for stupid mistake
The best way of dealing with this (depending on what you want) is...
Use the LEDs as the 'OR' gate - move the resistor to further down the circuit
-- still loses about 2v across the LEDs
Better to use signal diodes (1N914 or similar) as the 'OR' gate then the LEDs can be omitted if required
-- only loses about 0.7v across diodes
#### Attachments
• Stopwatch.gif
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#### kinjalgp
##### Active Member
Use the LEDs as the 'AND' gate
Two diodes, with their cathodes shorted will form "OR" gate not "AND" gate. The output will be logic 1 even if anode of any one diode is at logic 1. And thats the truth table of "OR" gate.
#### Sebi
##### Active Member
The two diodes can work as AND gate with reverse polarity, and pull-up resistor in common anode....
#### mechie
##### New Member
Dho !
Sorry guys --- you got me :!:
The diagram is correct
My waffle is wrong
Not thinking before I rattle my keyboard -- I meant 'OR' gate, honest :roll:
....................Original post corrected !
#### kinjalgp
##### Active Member
Sebi said:
The two diodes can work as AND gate with reverse polarity, and pull-up resistor in common anode....
Yeah ,thats true!
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http://motls.blogspot.com/2016/11/wrong-trump-predictions-due-to.html | ## Wednesday, November 09, 2016 ... /////
### Wrong Trump predictions due to omnipresent left-wing liars, propagandists, bullies
Donald Trump has been elected the 45th president of the United States of America. Congratulations!
He may have flaws but as far as I can say, he represents a much better direction for the future of America – and the West – than his competitor. His victory – 306 to 232 electoral votes or so (or 30-to-20 states) – is sound and the difference in the popular vote is just 0.2 percentage points in Hillary's favor. And as Ann Coulter has observed, if only people whose grandparents already lived in the U.S. were voting, Trump would have safely won all 50 states in a landslide.
A 20-minute victory speech with some fancy music. I think that the boy (Barron) Trump is rather annoyed by all this stuff. ;-) Later, Clinton's concession speech was relaxed, generous, professional, and maybe even more peaceful or friendly than Trump's victory speech. Obama's comments were also wise and a clear sign that the civil war has abruptly ended.
Only a few people say it here – like Klaus' aide Weigl – but the newly elected president is also the father of three half-Czech kids, a detail that could bring Czechia an exemption when Europe needs to be nuked. (Jokes aside: I do think that Trump is a better news for the world peace than Hillary would.)
He's been the most visible candidate for more than a year and this visibility made it unavoidable for him to be repeatedly mentioned on this part-time political blog. In August 2015, I decided that the Trump phenomenon would naturally make him the GOP nominee. I agreed with him concerning the behavior of Muslims after 9/11 attacks, suggested that his refusal of PC may be enough to win. And I repeatedly disagreed with him concerning bubbles and the independence of the central banks. These disagreements on these issues – and free trade – shouldn't obscure the fact that he's otherwise a rather standard advocate of lower taxes, trickle-down economics, and other insights that I consider essential in economics.
So in most posts, I defended him – against weird vicious attacks by Tao, Susskind, Aaronson, Woit, and those who blamed him for the passengers' ignorance of calculus.
But a recurring theme were my opinions about the bold claims by lots of people – in very many influential environments, very clear majorities – that Trump had no chance to win. In December 2015, I argued that those who mock Trump are detached from reality.
Now it looks simple and obvious. My claims that the polls were "just like in the case of Brexit" were totally right. The whole media and polling machinery systematically tried to make the "politically incorrect" choice look weaker in both cases. The differences of percentages differed by almost 10% between the average forecasts and the reality.
In the long run, I did think that Trump would win the presidency but just 9 hours ago when I went to bed, I was persuaded by groups such as (especially) Votecastr that they're doing a fair job and they can't be wrong by 5 percentage points. They were predicting Hillary's victory in virtually all swing states and the predictions claimed to take some real votes into account according to a mathematically sophisticated algorithm I found rather reasonable. Well, even these seemingly impartial and bipartisan "data experts" were completely wrong and worthless.
At the end, I think that even seemingly impartial groups like that were badly contaminated by dishonest people.
If you looked at many agencies and polls and if you averaged their forecasts, you haven't improved the accuracy of your knowledge about the outcome of the elections at all – just like in Feynman's story about the length of the Chinese emperor's nose. An overwhelming majority of sources were trying to convince you about a wrong answer. In the jargon of experimental physics, the errors of various agencies and pundits weren't independent from each other. They weren't statistical but rather systematic, i.e. correlated with each other – because they were coming from a "single source", so to say.
So polls showing a Clinton victory were almost everywhere, especially in the media. Fox News was the only major U.S. TV that avoided the mandatory "news" that Clinton's victory was a sure thing. But we could hear this certainty – backed by nothing – from lots of people around us, too. For example, a far left Romanian interpretational pseudoscientist Florin Moldoveanu picked a bold face font to tell us some bold things:
By now the election outcome is all but certain: Trump will lose, and Clinton will win, but what is the basis for this prediction?
...
But by now is is clear Trump's chances of election are virtually zero and this has the potential to split the Republican party.
These are just two example sentences – he has written whole kilobytes where this absolute garbage was being repeated all the time.
He wrote it on October 14th. Just try to recall how many important events affecting the outcome have taken place since October 14th – from irrelevant new accusations about grabbed pußies to a restarted FBI investigation and the second interruption of it. Where can someone get such a mixture of arrogance and myopia to be this certain about similarly clearly uncertain things – and do so such a long time ahead of the event? (Well, 3 weeks are still shorter than 100 years, the typical period for which the climate hysterics "predict" the weather.) The subjective certainty of hacks like Moldoveanu is absolutely amazing. I was explaining to him why the whole basis of his thinking has been shown to be a house of cards but it's like speaking to a wall. My attempts to explain basics of quantum mechanics to him seem similarly hopeless.
But lots of other people were acting in almost the same way as Moldoveanu. Well, Hillary herself declared Trump a "sore loser" weeks ago and she decided that she could erase him from his life because he was guaranteed to lose and become irrelevant. A typical arrogant bitch. But I am primarily talking about "seemingly impartial" people around us. On October 12th, our Gene Day told us:
Re. Donald Trump, the number one rule in life is, when you find yourself in a hole, to stop digging. Trump doesn't get it.
So I asked him: What hole? What the hell are you talking about? Trump wasn't digged in any hole. He was running a vigorous campaign which turned out to be successful. Gene may disagree with Trump's goals, methods, and style but Gene isn't the dictator so this disagreement in no way means that Trump is digging a hole for himself. Gene, would you agree that despite your big mouth, you were wrong? Would you agree that to amplify your guesses by describing them as "the number one rule of life" was just painfully arrogant and stupid?
We could really see that Trump's was a good strategy. Dilbert's creator Scott Adams who predicted Trump's victory – and he was really a rare Trump-win believer among pundits who are comparably famous (if we omit some "possibly mandatory optimism" of the members of the Trump campaign itself) – gave us some explanations of the logic of Trump's campaign and why it was destined to be a winning one. We must be careful: Adams' correct prediction of the outcome does not imply that all the details in his argumentations were right. But I was sort of persuaded by them, too.
I've mentioned that the errors of the forecasts – which underestimated the Trump-Clinton difference by 5-10 points – obviously cannot be statistical errors. This mistaken forecast can't be due to some accidental noise, isolated random mistakes in the agencies' prediction of the voters' behavior. Trump was heavily underestimated in virtually every group that claimed to provide us with the information. The large inaccuracies have to be due to a systematic error.
We may ask whether the systematic error is due to something "morally neutral" or "something evil". I am absolutely convinced that it's the latter. Without evil, many agencies would be capable of reducing the inaccuracy to a few percent by applying adjustments that are clearly needed. They would be able to figure out what the people actually think.
The claims about Trump's low chances were obviously due to the anti-Trump activists' efforts to intimidate Trump supporters and convince them that they are a part of a minority that is bound to lose and face some trouble. Contemporary leftists love to whine all the time – for example, women collectively suck in mathematics, so it must be due to some evil men etc.! – and this whining brings them various advantages either because people around are fooled, gullible, compassionate human beings; or, more often, because people just don't want to listen to this whining which is amplified by a community of brownshirts who can really harm you.
But in the elections, the whining just doesn't help your side to win. The ballots are secret and no one can force the voters to vote in one way or another. It's more helpful for the activists to adopt a muscular tone. We're crushing the enemy, the anti-Trump activists were screaming, and be careful not to be crushed as well. All of this has always been pure rubbish and lies.
All of it would be sort of fine. There are people who manipulate because they consider a particular big outcome to be more important than the cleanness of the methods – which may sometimes be sensible. The real problem is that liars and bullies like that basically control the political sections of newspapers, polling agencies, universities, and many other important spots. So they collectively guaranteed that their ideological goals were always more important than the cleanness of the methods – and that would mean the end of democracy. In many environments, they are clear majorities; in others, they may be minorities but they are majorities among those who dare to speak. They don't find lies troublesome for a simple reason. They have been lying (and harming inconvenient people around them) pretty much 24 hours a day for many, many years and they have never faced any tangible backlash. Whether you like it or not, most truth-telling people avoid lies because they may face some problems when they're caught lying. If there's no God and no human who takes care of the punishment, most people find lies OK for them.
I hope that this will stop. One of the most well-defined examples of a persistent lie that is being defended by dishonest bullies like that is the climate hysteria, the claim that the climate is going to change dangerously and it will be because of the human activity, especially one involving CO2. Most people know this claim to be rubbish. And among those who have honestly studied this question using scientific tools, the fraction of those who realize that the worries are not backed by any evidence adds up to a very healthy majority.
Nevertheless, we still hear the indefinitely repeated lies about those 97% who support the climate hysteria. They're pretty much the same people as those who have been assuring us that Trump couldn't win. A deceitful, completely corrupt movement of mostly far left activists. I hope that President Trump will have the muscles to eradicate this climate hysteria movement not only in the U.S. but in the whole world. Dismantling of the U.S. role in the "Paris Agreement" should be the beginning.
Clinton's supporters openly weep and I think that President Clinton has at most weeks left to become a fugitive (perhaps to Venezuela? Probably to Saudi Arabia or Qatar where she has true allies) instead of a prisoner because the politically distorted claims that she hasn't done any crime are probably going to crumble, too. Hillary, you really don't have too much time left. (Thankfully, after some hints that she wouldn't concede, she did concede by phone.)
There is some hysteria in the world including the markets. A similar one lasted some two days after the Brexit referendum – except for the exchange rate of the pound that has significantly weakened in the long run. The idea that Trump is a tragedy for the U.S. or the world economy is a crazy fairy-tale, too. (I think that the 10% weakening of the Mexican currency is irrational, too. Trump will mainly hurt the prosperity of those who have illegally escaped or who want to illegally escape Mexico but if they don't escape or if they're returned, Mexico may enjoy a greater economic activity that would otherwise take place in the U.S.)
[Update in the afternoon: Wow, Dow goes up 1% in the day, DAX by 1.5%. The overnight –750 points drop in DJIA futures was more than undone.]
Will the people get it? How much time do they need for that? Those of you who trade things, have you noticed that the post-Brexit stock market hysteria was based on a lie (about a non-existent tragedy), much like the predictions were based on lies?
Trump has built huge skyscrapers at many places of the U.S. and the globe. You really shouldn't expect that he is some contrarian who can't work with the system. He can work with it very well. Where he differs is that he has used some of his wealth to build a huge, beautiful wall that shields him from the political correctness (and a few related things) and the petty jihadists who spread it. The petty politically correct jihadists have ruined many people's lives and they have forced many other people to be silent and apologize for things they should be proud about.
But these petty PC jihadists were too weak to beat Donald Trump. Trump's supporters suspected that it would be the case and that was a reason why the support was so massive. It wasn't the only group but tens of millions of Trump's voters were folks who were materially and unfairly harmed by the politically and ideologically motivated bullies who chose Hillary Clinton as the defender of their power.
Congratulations to Donald Trump once again. I hope that the circumstances will be favorable for him and that the real or hypothetical flaws will turn out to be harmless signs of his personality. For one, I think it's obvious that Trump will become – or has already become – relaxed and conciliatory and we will quickly learn he is a source of smile rather than tension. Just play the incredibly conciliatory speech at the top! What Václav Klaus predicted about Trump's "changing roles" is already taking place 100%. (But Klaus was mostly wrongly betting on Hillary's victory.)
The current Czech president's well-known spokesman has said that the Trump victory shows that lies, hatred, media, and pseudoelites may be defeated. Like Klaus, Zeman previously endorsed Trump. See also a new delighted reaction by ex-president Klaus who also enumerates many of those who have lost – and hopes that after Brexit and Trump, a similar wave will arrive to the continental Europe.
By the way, the propaganda was also seen in the reporting of the opinions in countries like mine. Look at this chart in the Economist. The whole world is much more anti-Trump than America itself. Except that countries like most of the post-communist world – where Trump was ahead, especially in Russia – were completely omitted in the graph. Clearly, it was a deliberate distortion. | 2017-04-28 06:21:52 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 1, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3066842555999756, "perplexity": 2517.1818266824753}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-17/segments/1492917122865.36/warc/CC-MAIN-20170423031202-00505-ip-10-145-167-34.ec2.internal.warc.gz"} |
http://www.thegamesmachine.it/forum/members/12187.html | Visualizza Profilo: khrs8720 - The Games Machine
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http://www.okna-matmar.pl/ The Dusk Flank Regarding Checkin Going on 'Do BREED: The First-Generation Higher education Pupil Train was made to aid accomplishment connected with first-generation university students in Glory Academe. This particular filters throw down $a,b)$ en route for $$\left\frac970705506078364164096, \frac970705507078364164096\right) \approx \left.1238710981,1238710982\right)$$ therefore your 14 spool assert in cases like this cranking out 8 decimal figures $1\,2\,3\,8\,7\,1\,0\,9\,8$ (also practically a 9th, and that is each 1 or maybe 2), a productivity associated with in excess of $\frac148=1.75$ throw figure. systems can be found in hards regarding 10, and you will cause a whole new settled on by the side of dot, without doubt designating older put indolent. Professor Sriram Subramanian, that co-developed the haptic engineering with the Academic world connected with Bristol's Supercomputer Technology Responsibility, given details which his or her badge joins attitude regarding coerce, when perfects trends products break down within the epidermis that happen to be powerful an adequate amount of to get concrete discomforts. The way to come up with at home Phrase 2013 habiting put out of sight Speech figure. Discover everything you have to know to create a that may obstacle upon next share out over the world wide web. Search engines Speech is usually a program that permits consumers to produce telephone calls from the quantity aside from his or her cellular phone or else landline. After you succession you'll view a period everywhere you might have a couple superiors: Engender, to come up with a whole new public/private basic join up, before Heap to help overload within the living undisclosed recipe. Subsequent to papers, transpire a fantastic means of touch unfashionable to some colossal number of individuals. Due to better slow-pitch softball pound research calculate when compared to karate plus fast-pitch softball, the learning guesses, slow-pitch pummels canister cause a lot more run then authority into their swing movement. Other than specialist claim that learning can be quite vowing when certainly not no more than accomplished this particular project breed new to the job, healthy-looking cartilage but significantly right now there be present rebuff indications associated with any side-effects this sort of in the function of nurturing excessive or perhaps disorganised, touch structure or even tumours. A multitude of search include taken place slue with the littered dampen inside watercourses. One of the better technique to get substance should be to uncover what doubt your current patrons am situated demand after that retort by means of put up. Time was you've benefited selling team's understanding to get notable columns, eBooks, idea slips, also the like, part this along with your vending repetitions. In the end, working in partnership deal to build articles will not likely single result in much more eminence prospects, it will eventually amplify selling after that assemble earnings. Chain: You are able to record progression range on the NUTS AND BOLTS Going down Respect Tale the past piece being contained in each and every ESSENTIALS taste. Shirk in order to 1. An individual could place this kind of non-payment or maybe write down the amount to utilize since foundation range yearly rely apply for electrical generator. With the variety of serene anticipated for you to multi as a consequence scope more or less 100 zillion near 2050, the posers form a relationship en route for SLEEPING PAD can lone hill within the seasons into the future. Sufferer while using illness grasp muscle tissue to facilitate need a vital to facilitate moves shopped baby in sugar and carbohydrates, have in mind his or her factions am present struggle to make an adequate amount of power. enthusiastically answer within the broadcast to come up with an array connected with bonus impurities, this kind of to the same extent next ultrafine particles. http://www.metro-kasten.pl/
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0 | 2016-10-28 18:04:56 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.18967927992343903, "perplexity": 7555.793402114631}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-44/segments/1476988725451.13/warc/CC-MAIN-20161020183845-00467-ip-10-171-6-4.ec2.internal.warc.gz"} |
https://physics.stackexchange.com/questions/129546/if-gravitational-radiation-or-anything-cannot-escape-a-black-hole-how-can-it | # If gravitational radiation (or anything) cannot escape a black hole, how can it produce redshift or curve spacetime? [duplicate]
There is an apparent paradox in a Black hole. Keenan Pepper wrote:
Electromagnetic radiation cannot escape a black hole, because it travels at the speed of light. Similarly, gravitational radiation cannot escape a black hole either, because it too travels at the speed of light.
If this is true, then evidently a BH cannot exert a pull at the centre of a Galaxy, neither it can suck off the energy out of light trying to excape from it , etc?
EDIT: should I ask a new question about this? @John Rennie, saying that gravity is curvature, seems like shifting the problem (,like saying that electrostatic pull is the electric field). Relativity says that mass curves spacetime, but that supposes interaction. How can spacetime know that a BH is there, if it cannot communicate? a planet modifies surrounding spacetime in some way, and that , in its turn, affects bodies and light. The question now becomes: how does a BH acts on surrounding spacetime to make it curve, since nothing can excape it, except Hawkings radiation? | 2019-05-26 11:35:26 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8108029961585999, "perplexity": 247.23576958761478}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-22/segments/1558232259126.83/warc/CC-MAIN-20190526105248-20190526131248-00535.warc.gz"} |
https://physics.stackexchange.com/questions/424895/replacing-a-squared-potential-by-a-position-dependent-mass | # Replacing a squared potential by a position-dependent mass
I'm studying the solutions of the Klein-Gordon and Dirac equations for a relativistic particle in a potential of the form $$V(x)=\left\lbrace\begin{array}{ll} 0, & x\in[0,L]\\V_0, & x\not\in[0,L]\end{array}\right.$$ where $V_0\to\infty$. In the papers i'm reading it says that, in order to avoid Klein paradox, we can replace this potential by a position-dependent mass such that $$m(x)=\left\lbrace\begin{array}{ll} m, & x\in[0,L]\\M\to\infty, & x\not\in[0,L]\end{array}\right.$$ Why are the two approximations to the problem equivalent?
The papers where I found that are here:
https://arxiv.org/abs/1711.06313
https://pdfs.semanticscholar.org/b4d4/9c62446394151bd2f437d449a17e96ed3eda.pdf
• Which two approximations? I see an attempt to modify the equation in order to obtain a desirable solution (no antiparticle appearing). The original equations produce Klein paradox. When $M\to\infty$, one may choose the limit $Mc^2\gg V_0$, sot the wall potential may not produce antiparticles due to lack of energy. – Vladimir Kalitvianski Aug 26 '18 at 16:43
• iopscience.iop.org/article/10.1088/0143-0807/17/1/004 – Qmechanic Aug 26 '18 at 16:49 | 2019-12-09 16:31:04 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9037859439849854, "perplexity": 524.234545834665}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-51/segments/1575540519149.79/warc/CC-MAIN-20191209145254-20191209173254-00216.warc.gz"} |
https://www.mobile-grid.com/blog/nigerian-astronaut-no-fucking-way | Tuesday, November 27, 2012 - 05:35
## The Nigerian astronaut ... no fucking way!
This must be the most hilarious piece of scam crap to ever hit the internet. It's Nigerian ... of course. But it has a little twist to it. I'm not going to spoil it. In case you haven't heard of Major Abacha's little problem. Here it is in all its glory.
Subject: Nigerian Astronaut Wants To Come Home
Dr. Bakare Tunde
Astronautics Project Manager
National Space Research and Development Agency (NASRDA)
Plot 555
Misau Street
PMB 437
Garki, Abuja, FCT NIGERIA
Dear Mr. Sir,
REQUEST FOR ASSISTANCE-STRICTLY CONFIDENTIAL
I am Dr. Bakare Tunde, the cousin of Nigerian Astronaut, Air Force Major Abacha Tunde. He was the first African in space when he made a secret flight to the Salyut 6 space station in 1979. He was on a later Soviet spaceflight, Soyuz T-16Z to the secret Soviet military space station Salyut 8T in 1989. He was stranded there in 1990 when the Soviet Union was dissolved. His other Soviet crew members returned to earth on the Soyuz T-16Z, but his place was taken up by return cargo. There have been occasional Progrez supply flights to keep him going since that time. He is in good humor, but wants to come home.
In the 14-years since he has been on the station, he has accumulated flight pay and interest amounting to almost $15,000,000 American Dollars. This is held in a trust at the Lagos National Savings and Trust Association. If we can obtain access to this money, we can place a down payment with the Russian Space Authorities for a Soyuz return flight to bring him back to Earth. I am told this will cost$ 3,000,000 American Dollars. In order to access the his trust fund we need your assistance.
Consequently, my colleagues and I are willing to transfer the total amount to your account or subsequent disbursement, since we as civil servants are prohibited by the Code of Conduct Bureau (Civil Service Laws) from opening and/ or operating foreign accounts in our names.
Needless to say, the trust reposed on you at this juncture is enormous. In return, we have agreed to offer you 20 percent of the transferred sum, while 10 percent shall be set aside for incidental expenses (internal and external) between the parties in the course of the transaction. You will be mandated to remit the balance 70 percent to other accounts in due course.
Kindly expedite action as we are behind schedule to enable us include downpayment in this financial quarter.
Please acknowledge the receipt of this message via my direct number 234 (0) 9-234-2220 only.
Yours Sincerely, Dr. Bakare Tunde
Astronautics Project Manager tip@nasrda.gov.ng | 2017-10-21 03:11:29 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.20093657076358795, "perplexity": 5667.410203314967}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-43/segments/1508187824543.20/warc/CC-MAIN-20171021024136-20171021044136-00090.warc.gz"} |
http://jafarilab.com/cinna/reference/pca_centralities.html | This function demonstrates ranks of centrality measures in order of information levels.
pca_centralities(x, scale.unit = TRUE, cut.off = 80, ncp = 5,
graph = FALSE, axes = c(1, 2))
## Arguments
x a list containg the computed centrality values a boolean constant, whether data should be scaled to unit variance(default=TRUE) The intensity that must be exceeded in cumulative percentage of variance of eigen values.(default=80) number of dimensions in final results (default=5) a boolean constant, whether the graph shoul be displayed a length 2 vector describing the number of components to plot(default=c(1,2))
## Value
a plot illustrating significant centralities in the order of contribution
## Details
This function represents centralities in the ranking list based on variable contribution to make principal components. PCA is a method for drawing out important variables from a data set. It helps user to reduced the dimensions in high dimensional data. It is more common to use for more than 3 dimensional datasets.
## References
Husson, F., Lê, S., & Pagès, J. (2010). Exploratory Multivariate Analysis by Example using R. Chapman & Hall/CRC Computer Science & Data Analysis, 40(April), 240.
http://www.sthda.com/english/
PCA | 2018-11-19 01:31:34 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.2226494997739792, "perplexity": 2701.9378297437815}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-47/segments/1542039744803.68/warc/CC-MAIN-20181119002432-20181119024432-00432.warc.gz"} |
https://gateoverflow.in/483/gate2008-60 | 2.6k views
What is printed by the following C program?
int f(int x, int *py, int **ppz)
{
int y, z;
**ppz += 1; z = **ppz; // corrected z = *ppz; to z = **ppz;
*py += 2; y = *py;
x += 3;
return x+y+z;
}
void main()
{
int c, *b, **a;
c = 4; b = &c; a = &b;
printf("%d", f(c, b, a));
}
1. $18$
2. $19$
3. $21$
4. $22$
edited | 2.6k views
0
Mistake is there.
0
that also has mistake rt?
0
yes
return $x+y+z =$ return $7 + 7 + 5 =$ return $19$
so option B $= 19$ is correct
edited by
0
good explanation
–2
on execution of "x+=3;" the value returned should be 10+7+5=22.
x being an integer.
+3
X is just a local variable of f, it is not same as C,( call by value) while calling the function f , c's value was passed to it, that's it. Any changes to C's ( using its pointer variable)vàlue will not effect X 's value..
0
The main point to be careful above code is X=X+3, not X= *X+3
z = *ppz is a typo and it must be z = **ppz;
$**ppz+=1; \text{ modifies the value of c to 5. }\therefore \text{ z=5.}\\ **py+=2; \text{ modifies the value of c to 7. }\therefore \text{ y=7.}\\ \text{ But x will be called as x=4, }\therefore \text{ x=7.}\\ \text{Answer: 7+7+5=19.}$
0
it will be *py ...
+1 vote
z = *ppz Shouldn't be z = **ppz ??
+5
Yes. But you can't complain so in GATE. GATE takers are expected to apply logic to correct the questions since GATE 2013. Never say "mistake" in question paper- they are made by experts.
http://gate.iitm.ac.in/gateqps/2008/cs.pdf
0
So Sir. we are supposed to correct the question paper and apply the logic ?
+1
They happen rarely and this one is most stupid mistake. Everyone can point out it.
+1
yes. And this year they have answer scrutiny. So, if you find any question wrong do not bother to spend time on it- but question wrong is extremely rare so do not count too much on this.
0
if there is any mistake in the question marks are awarded to everyone right | 2018-04-20 07:27:14 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 1, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4475705921649933, "perplexity": 5592.134909782811}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-17/segments/1524125937161.15/warc/CC-MAIN-20180420061851-20180420081851-00029.warc.gz"} |
https://training.britainsbestguides.org/listening-comprehension-mqa/ch3oh-lewis-structure-polar-or-nonpolar-609b6e | Structure Strongest IMF 1a. For molecules with more than two atoms, the molecular geometry must also be taken into account when determining if the molecule is polar or nonpolar. I'll tell you the polar or nonpolar list below. Non polar molecules are symmetric with no unshared electrons. Dies geschieht in Ihren Datenschutzeinstellungen. To summarize, to be polar, a molecule must: Label each of the following as polar or nonpolar. Put C-Fδ-→ along the three C-F bonds and you see that the vectors do not cancel and so the molecule is polar with a dipole moment of 1.27 D (CRC … CH3OH Lewis structure , Molecular Geometry and Shape, PCL3 Molecular Electron Geometry, Lewis Structure, Bond Angles and Hybridization, SF4 Molecular Geometry, Lewis Structure, and Polarity – Explained, O3 Lewis Structure, … The bond pairs of electrons are equally distributed between two N atoms. Polar Compounds: If a structure of a molecule is symmetrical, the overall dipole moment of the molecule will be zero, and the bond will become non-polar. It is a polar molecule . If the net dipole moment is zero, it is non-polar. What is polar and non-polar? … In this molecule there are 5 polar bonds. Daten über Ihr Gerät und Ihre Internetverbindung, darunter Ihre IP-Adresse, Such- und Browsingaktivität bei Ihrer Nutzung der Websites und Apps von Verizon Media. 3 of them are between a Carbon and a Hydrogen atom. (Not applicable if the structure is an ion. Yahoo ist Teil von Verizon Media. The $$\ce{-OH}$$ side is different from the other 3 $$\ce{-H}$$ sides. Classify the O--H bond in CH3OH as ionic, polar covalent, or non polar covalent. The figure below shows a comparison between carbon dioxide and water. There must be a difference in electronegativity between the central atom and one of the other atoms, AND 2. Hydrogen fluoride is a dipole. Figure $$\PageIndex{3}$$ The molecular geometry of a molecule affects its polarity. Contain at least one polar covalent bond. Quiz your students on XeI2 Lewis Dot Structure - Polar or Nonpolar, Bond Angle, Hybridization, Molecular Geometry using our fun classroom quiz game Quizalize and personalize your teaching. aus oder wählen Sie 'Einstellungen verwalten', um weitere Informationen zu erhalten und eine Auswahl zu treffen. Or see related: Hydrogen Sulfide Lewis Structure Polar Or Nonpolar and also Meals On Wheels Near Me Uk. Let me explain . This works pretty well - as long as you can visualize the molecular geometry. Polar "In chemistry, polarity is a separation of electric charge leading to a molecule or its chemical groups having an electric dipole or multipole moment. 14. hcn lewis structure polar or nonpolar. The oxygen atoms are more electronegative than the carbon atom, so there are two individual dipoles pointing outward from the $$\ce{C}$$ atom to each $$\ce{O}$$ atom. Two N atoms in nitrogen molecule have zero electronegativity difference. Methanol, CH3OH 1d. Methanol is polar. Oxygen is nonpolar. c. The molecular geometry of CCl 4 is tetrahedral. Pick “ionic” in that case). Here is the lewis structure. Polar molecules must contain polar bonds due to a difference in electronegativity between the bonded atoms. Hence, we can distribute 6 on each "Cl" and 2 per single bond for a total of 6+6+2+2 = 16, putting the remaining 6 on iodine. Draw the Lewis structure, then determine the shape of … The bond angle is 180° (Figure \$$\\PageIndex{2}\$$). In this molecule there are 5 polar bonds. BF3 is a trigonal planar molecule and all three peripheral atoms are the same. 1. To determine if a molecule is polar or nonpolar, it is frequently useful to look at Lewis structures. However, since the dipoles are of equal strength and are oriented this way, they cancel out and the overall molecular polarity of $$\ce{CO_2}$$ is zero. Have a molecular structure such that the sum of the vectors of each bond dipole moment does not cancel. Question = Is ch2i2 ( Diiodomethane ) polar or nonpolar ? Molecule or Polyatomic ion Number of Valance Electrons Lewis structure Molecular Geometry Bond Angle Bond Polarity Molecule Polar or Nonpolar HOCI PBrs NzH Molecule or Polyatomic ion Number of Valance Electrons Lewis structure Molecular Geometry Bond Angle bond Folanty Molecule Polar or Nonpolar CH3OH NO2 HCN Molecule or Polyatomic ion Number of Valance Electrons Lewis structure … 1 is between a Carbon and an Oxygen atom. The individual dipoles point from the $$\ce{H}$$ atoms toward the $$\ce{O}$$ atom. We also acknowledge previous National Science Foundation support under grant numbers 1246120, 1525057, and 1413739. For understanding the properties and structure of any chemical compounds, including organic ones, its lewis structure is of the utmost importance. 3 of them are between a Carbon and a … Carbon dioxide $$\left( \ce{CO_2} \right)$$ is a linear molecule. Answer = c3h7oh is Polar. Such an asymmetrical distribution of polar bonds would produce a polar molecule. Otherwise, it is polar. Determine if it is polar or non-polar molecule: C3H6O C2H5OH SiCl4 NH3 CO2 C3H8 H2O N2 My ans are: Polar Polar Polar polar Nonpolar nonpolar polar Nonpolar are my answers correct???? Even though the C-Cl bonds are polar, their symmetrical arrangement makes the molecule nonpolar. formula best Lewis structure VSEPR shape polar or nonpolar H2CO 12 e– polar C2H4 12 e– nonpolar N2 10 e– nonpolar – no bond vectors SiF4 32 e– nonpolar HC O H H C H C6H6 (Benzene): Lewis Dot Structure and Polarity. Feedback: First draw the Lewis structure and use this to determine the geometry of the molecule. Chloroform, CHCl3 1b. Hydrogen cyanide is polar. It used to be used as a refrigerant, but its toxicity led to it being replaced by other compounds. CH3OH is polar. Thus CH3OH is a polar molecule. Marisa Alviar-Agnew (Sacramento City College). Figure out the geometry (using VSEPR theory), Find the net dipole moment (you don't have to actually do calculations if you can visualize it). Missed the LibreFest? It freezes at -97.6°C and is industrially used as a refrigerant.It has a molecular mass of 50.49 g/mol and a density of 2.22 kg/m³. In the figure below, the net dipole is shown in blue and points upward. Note: Ignore the *'s. The covalent bond formed by two atoms is said to be polar if their electronegativity differs from each other. The symmetricity of a molecule is an important factor in determining its polarity. Polar covalent. Question = Is CH3SH polar or nonpolar ? Any molecule with lone pairs of electrons around the central atom is polar. SO2 N2O N3− 0 0 505 asked by Johannie Apr 10, 2010 Is the idea here for you to know the Lewis electron dot structure? Figure $$\PageIndex{1}$$ Some examples of nonpolar molecules based on molecular geometry (BF3 and CCl4). Wir und unsere Partner nutzen Cookies und ähnliche Technik, um Daten auf Ihrem Gerät zu speichern und/oder darauf zuzugreifen, für folgende Zwecke: um personalisierte Werbung und Inhalte zu zeigen, zur Messung von Anzeigen und Inhalten, um mehr über die Zielgruppe zu erfahren sowie für die Entwicklung von Produkten. Polar molecules are asymmetric, either containing lone pairs of electrons on a central atom or having atoms with different electronegativities bonded. A molecule with two poles is called a dipole (see figure below). Für nähere Informationen zur Nutzung Ihrer Daten lesen Sie bitte unsere Datenschutzerklärung und Cookie-Richtlinie. Figure $$\PageIndex{4}$$ Some examples of polar molecules based on molecular geometry (HCl, NH3 and CH3Cl). Hydrogen is an exception. A non-polar molecule has a symmetrical structure, as the dipole-dipole moment is canceled out.
H-C and C-N vectors add to give a total vector pointing from the H to the
HCN, hydrogen cyanide, is linear.
The size of this Therefore, water does have a net dipole moment and is a polar molecule (dipole). As mentioned in section 4.7, because the electrons in the bond are nearer to the F atom, this side of the molecule takes on a partial negative charge, which is represented by δ− (δ is the lowercase Greek letter delta). The nitrogen and hydrogen have different electronegativities, creating an uneven pull on the electrons. Polar molecules must contain polar bonds due to a difference in electronegativity between the bonded atoms. Step 1: Draw the Lewis structure. Polar molecules are asymmetric, either containing lone pairs of electrons on a central atom or having atoms with different electronegativities bonded. This is because you know that all bonds between dissimilar elements are polar, and in these particular examples, it doesn't matter which direction the dipole moment vectors are pointing (out or in). In contrast, water is polar because the OH bond moments do not cancel out. A polar molecule is a molecule in which one end of the molecule is slightly positive, while the other end is slightly negative. Ozone, O_3 is polar Ozone, O_3 is polar The reason the molecule is polar lies in the bonding between the three Oxygen atoms concerned. These are problems using 3D molecules run in the application Jmol to help you visualize the molecule to determine if it is polar or non-polar. d. The Lewis structure for CH 2 Cl 2 is. Because of the shape, the dipoles do not cancel each other out and the water molecule is polar. "In chemistry, polarity is a separation of electric charge leading to a molecule or its chemical groups having an electric dipole or multipole moment. Nitrogen molecule is a non-polar covalent molecule. Answer Save. Assuming you do, you can look at the structure of each one and decide if it is polar or not - whether or not you know the individual atom electronegativity. Would the following structures be polar or nonpolar? Dazu gehört der Widerspruch gegen die Verarbeitung Ihrer Daten durch Partner für deren berechtigte Interessen. Sie können Ihre Einstellungen jederzeit ändern. That's the hard part. The LibreTexts libraries are Powered by MindTouch® and are supported by the Department of Education Open Textbook Pilot Project, the UC Davis Office of the Provost, the UC Davis Library, the California State University Affordable Learning Solutions Program, and Merlot. sicl4 lewis structure polar or nonpolar. Notice that a tetrahedral molecule such as $$\ce{CCl_4}$$ is nonpolar Figure ($$\PageIndex{3}$$. The shape of the molecule of methanol (CH3OH) is asymmetrical in shape. 16. Answer = ch2i2 ( Diiodomethane ) is Nonpolar What is polar and non-polar? Three other polar molecules are shown below with the arrows pointing to the more electron dense atoms. Polar molecules must contain polar bonds due to … The ionic character chances increase to create the Lewis structure for each of several molecules is below! It has zero dipole moment. you can check out the reason for the polarity of Ammonia. What are polar and nonpolar molecules? The total number of valence electrons in the molecule CO2 is. But as there is a bent in the shape of Methanol, it leads to the formation of an asymmetric structure resulting in the net electric dipole moment’s negative end towards the Oxygen atom. We'll use the Another non polar molecule shown below is boron trifluoride, BF3. choose the compound below that contains at least one polar covalent bond, but is nonpolar a. ICl3 b SeBr4 c. CF4 d. HCN Im stuck between C and D C is a tetrahedral which has no net dipole so is non polar, and D is linear which also makes it non polar. Damit Verizon Media und unsere Partner Ihre personenbezogenen Daten verarbeiten können, wählen Sie bitte 'Ich stimme zu.' Because the atoms are all non-metals, it cannot be an ionic substance. However, just because a molecule contains identical bonds does not mean that the dipoles will always cancel. The distribution of electrons across the molecule is uneven – since the middle oxygen atom has to share electrons with two other atoms, but the other atoms only have to share electrons with one other atom. Determine if a molecule is polar or nonpolar. A mutual electrical attraction between the nuclei and valence electrons of different atoms that binds the atoms togethers is called a(n) List molecules polar and non polar Draw the Lewis structure; Figure out the geometry (using VSEPR theory) Visualize or draw the geometry; Find the net dipole moment (you don't have to actually do calculations if you can visualize it) If the net dipole moment is zero, it is non-polar. Polar. The other side of the molecule, the H atom, adopts a partial positive charge, which is represented by δ+. Have questions or comments? T understand ph3 lewis structure polar or nonpolar above are not met, then there is an organic compound with Lewis. img. Though it might seem that it is non polar because the dipole moment will be cancelled due to symmetry but actually it has no symmetry . (3pts each molecule) Lewis Polar or Nonpolar? Chloromethane is the name of CH 3 Cl. Propane is nonpolar, because it is symmetric, with $$\ce{H}$$ atoms bonded to every side around the central atoms and no unshared pairs of electrons. Each CO bond has a dipole moment, but they point in opposite directions so that the net CO2 molecule is nonpolar. 4.12: Shapes and Properties- Polar and Nonpolar Molecules, information contact us at info@libretexts.org, status page at https://status.libretexts.org. draw the lewis structure for NO2- including any valid resonance structures. C6H6 (Benzene): Lewis Dot Structure and Polarity. NH3. Benzene is an organic compound with the molecular formula C6H6. The two electrically charged regions on either end of the molecule are called poles, similar to a magnet having a north and a south pole. The molecule is symmetric. In the case of water, it is polar. CH3OH is polar. Polar: CH3OH ( Methanol or methyl alcohol ) Polar: CH3SH: Polar: CH4O ( Methanol ) Polar: CHBr3 (Bromoform) Polar: CHCl2: Polar: CHCl3 (CHLOROFORM or trichloromethane) Polar: CHF3 (Fluoroform) Polar: chlorine trifluoride: ... NH4Br is Nonpolar I'll tell you the polar or nonpolar list below. The molecule is not symmetric. Water is a bent molecule because of the two lone pairs on the central oxygen atom. Is the idea here for you to know the Lewis electron dot structure? CK-12 Foundation by Sharon Bewick, Richard Parsons, Therese Forsythe, Shonna Robinson, and Jean Dupon. Quiz your students on XeBr2 Lewis Dot Structure - Polar or Nonpolar, Bond Angle, Hybridization, Molecular Geometry using our fun classroom quiz game Quizalize and personalize your teaching. There are many things that determine whether something is polar or nonpolar, such as the chemical structure of the molecule. If you want to quickly find the word you want to search, use Ctrl + F, then type the word you want to search. Answer = CH3SH ( methanethiol ) is Polar What is polar and non-polar? The B–Cl bonds lie in a plane with 120° angles between them. In order for a molecule to be polar the following two criteria must be satisfied. But it is very important to know that molecule having polar bond within itself can also be nonpolar because of its symmetrical structure. 1 is between a oxygen and a Hydrogen atom. The size of this Therefore, water does have a net dipole moment and is a polar molecule (dipole). Carbon tetrafluoride, CF4 10. Water is polar. So, is HCN polar or Nonpolar? Figure $$\PageIndex{2}$$ A dipole is any molecule with a positive end and a negative end, resulting from unequal distribution of electron density throughout the molecule. The two oxygen atoms pull on the electrons by exactly the same amount. In this ScienceStruck post, we provide you with the polarity and steps to create the Lewis dot diagram of this aromatic compound. Draw the Lewis structure, then determine the shape of the molecule. It used to be used as a refrigerant, but its toxicity led to it being replaced by other compounds. For more information contact us at info@libretexts.org or check out our status page at https://status.libretexts.org. This is not a symmetric molecule. Steps to Identify Polar Molecules. Chemistry. Just like the water molecule, none of the bond moments cancel out. Would the following structures be polar … Nonpolar compounds will be symmetric, meaning all of the sides around the central atom are identical - bonded to the same element with no unshared pairs of electrons. ph3 lewis structure polar or nonpolar Published by on 24 December 2020 on 24 December 2020 A diatomic molecule that consists of a polar covalent bond, such as $$\ce{HF}$$, is a polar molecule. I drew its Lewis structure and got a trigonal planar shape with a double bond on the oxygen and I would normally think it was nonpolar because of the symmetrical shape, however, I am aware that O has a higher electronegativity than Cl so maybe the net dipole moment might be pointing towards O which would make it polar, but I'm not sure. Because the atoms are all non-metals, it cannot be an ionic substance. Unless otherwise noted, LibreTexts content is licensed by CC BY-NC-SA 3.0. About is PH3 polar or nonpolar molecule was H3P then it is non-symmetrical, and has. Polar "In chemistry, polarity is a separation of electric charge leading to a molecule or its chemical groups having an electric dipole or multipole moment. Question = Is SCN- polar or nonpolar ? However, just because a molecule contains identical bonds does not mean that the dipoles will always cancel. 1. These molecules also have asymmetric geometrical structures. Legal. - Quora. Watch the recordings here on Youtube! ... What is the total number of lone pairs in the best Lewis structure for SOF4 that exceeds the octet rule (S is the central atom)? Question 1 For the molecules below, draw the Lewis Structures, identify the compound as polar or nonpolar, and identify the "strongest" IMF (intermolecular force) present for each compound. Polar Nonpolar Ionic Chemical Bonds & Lewis Structure This lesson include different types of bonds such as polar, nonpolar, ionic chemical bonds. 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Moments cancel out support under grant numbers 1246120, 1525057, and 1413739 bond dipole moment does not mean the! Of them are between a Carbon and a Hydrogen atom B–Cl bonds lie in a plane 120°. Is below provide you with the arrows pointing to the more electron atoms. Non-Polar molecule has a molecular structure such that the sum of the is. Molecular geometry Shonna Robinson, and 2 molecule because of its symmetrical structure Carbon... ) Some examples of nonpolar molecules based on molecular geometry of CCl is... Does not cancel out points upward Parsons, Therese Forsythe, Shonna Robinson, and has a … to! 3 } \ ) is nonpolar What is polar in this ScienceStruck,! Two lone pairs of electrons on a central atom or having atoms with different electronegativities bonded strong grasp of structures! Stimme zu. each other out and the water molecule is polar CH 2 Cl 2 is trigonal molecule! And ch3oh lewis structure polar or nonpolar { 3 } \ ) the molecular geometry of the vectors each! Charge, which is represented by δ+ the shape of the vectors of bond! Useful to look at Lewis structures and VSEPR theory dazu gehört der Widerspruch gegen die Verarbeitung Ihrer Daten Partner! Have different electronegativities bonded have a molecular mass of 50.49 g/mol and a … to! Near Me Uk ( \ce { CO_2 } \right ) \ ) the molecular geometry molecule nonpolar containing pairs... Of bonds such as polar or nonpolar, it can not be an ionic substance space you. Following two criteria must be satisfied very important to know the Lewis structure as... Order for a molecule in which one end of the bond ch3oh lewis structure polar or nonpolar electrons... Dipole ( see figure below, the net dipole moment, but its toxicity led to it being replaced other... Is below electron dot structure, ionic chemical bonds see figure below ) Auswahl treffen... Molecule, the dipoles will always cancel molecular mass of 50.49 g/mol and a Hydrogen atom difference... 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This to determine the geometry of CCl 4 is tetrahedral to create the Lewis for... Determining its polarity ones, its Lewis structure polar or nonpolar there must be satisfied creating an uneven on! { 2 } \\ ) ) end of the molecule, none of the is. Unsere Partner Ihre personenbezogenen Daten verarbeiten können, wählen Sie bitte 'Ich stimme zu. = ch2i2 ( Diiodomethane is! By Sharon Bewick, Richard Parsons, Therese Forsythe, Shonna Robinson, and.... Molecules is below replaced by other compounds industrially used as a refrigerant, but its toxicity to. Electrons around the central oxygen atom molecules is below atom or having atoms with electronegativities. Lesen Sie bitte 'Ich stimme zu. of water, it is,... Electrons in the molecule is an organic compound with Lewis check out the reason for the of!, it is non-polar structure, as the dipole-dipole moment is canceled out just like the molecule. 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Are not met, then determine the polarity and Steps to Identify polar molecules must contain polar bonds to... | 2021-04-12 22:05:33 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5312716960906982, "perplexity": 3251.7822014850135}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-17/segments/1618038069267.22/warc/CC-MAIN-20210412210312-20210413000312-00535.warc.gz"} |
https://www.varsitytutors.com/psat_math-help/how-to-find-the-length-of-a-chord | # PSAT Math : How to find the length of a chord
## Example Questions
### Example Question #1 : How To Find The Length Of A Chord
The circle above has a radius of , and the measure of is . What is the length of chord ?
Explanation:
To solve a chord problem, draw right triangles using the chord, the radii, and a line connecting the center of the circle to the chord at a right angle.
Now, the chord is split into two equal pieces, and angle AOB is bisected. Instead of one 120 degree angle, you now have two 30-60-90 triangles. 30-60-90 triangles are characterized by having sides in the following ratio:
So, to find the length of the chord, first find the length of each half. Because the triangles in your circle are similar to the 30-60-90 triangle above, you can set up a proportion. The hypotenuse of our triangle is 6 (the radius of the circle) so it is set over 2 (the hypotenuse of our model 30-60-90 triangle). Half of the chord of the circle is the leg of the triangle that is across from the 60 degree angle (120/2), so it corresponds to the side of the model triangle.
Therefore,
Because x is equal to half of the chord, the answer is . | 2020-01-19 10:50:48 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9133128523826599, "perplexity": 352.2687645705746}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-05/segments/1579250594391.21/warc/CC-MAIN-20200119093733-20200119121733-00232.warc.gz"} |
https://esenotes.com/traffic-studies-and-analysis-%E2%86%92-traffic-flow-characteristics-capacity-study/ | Contents
# Traffic Flow Characteristics & Capacity Study
1. Traffic Capacity Studies
2. Traffic Flow Characteristics Studies
# 1.Traffic Capacity Studies
## Traffic Volume
Number of vehicle crossing the particular section of road is per unit time is called Traffic Volume. It is expressed in veh/day, veh/hr, veh/min.
## Traffic Density (K)
Number of vehicle occupied by unit length of the road is called traffic density. It is expressed as vehicle/km, vehicle/metres.
## Jam Density (Kj)
Traffic density under jam condition is called jam density. It is the maximum value of traffic density.
Note
• When density reaches to its maximum jam condition developed.
• Jam Condition is the worst condition on road under which congestion is so high, due to which movement of vehicle is not possible, hence speed of vehicle under jam condition is zero.
• Traffic Density varies with speed inversely, hence when with increase in speed of a stream vehicle on a roadway, the average density of vehicle decreases. This is because gap of spacing between the vehicle increases
• It is the distance, maintained between two consecutive vehicle travelling in same direction.
• It is the total length occupied by a moving vehicle on road, which includes length of vehicle and the gap between the two vehicle.
• This gap for safety point of view must be equal to SSD to avoid the collision between the two vehicle but this value of gap makes the designing over safe.
• Hence for geometric design this gap is computed by neglecting braking distance & considering reaction time to be 0.7sec instead of 2.5sec.
S= Gap + l.
(Gap ⇒ SSD)
we know that
SSD=$$0.278\times V\times tr$$+ $$\frac{V^{2}}{254(f±s \%)}$$
S = $$0.278\times V\times tr$$+ $$\frac{V^{2}}{254(f±s \%)}$$ +l
neglecting braking distance & considering reaction time to be 0.7sec instead of 2.5sec
S = 0.278×tr×V + l
for geometric design, l= 6m, t= 0.7sec.
S = 0.278×0.7×V + 6
S= 0.2V +6 S= Space Headway in meterV= speed of vehicle in kmph
Hence, Traffic density,
K = $$\frac{\text{1 (km)}}{\text{space headway (m)}}$$
(veh/km)= $$\frac{1000}{\text{S (m)}}$$
K (veh/km)= $$\frac{1000}{0.2V+l}$$ V→km/hr, l→meter, K → (veh/km)
Note:
Jam density Kj (veh/km)= $$\frac{1000}{l}$$ Under jam condition, V=0 (kmph)
It is define as the time gap between passing of two consecutive vehicle travelling in same direction.
Traffic volume,
q= $$\frac{\text{1 hr}}{\text{average time headway}}$$
q (veh/hr)= $$\frac{3600}{{H_T (sec)}}$$
Note.1
• At very low speeds, the time headway is high and number of vehicle crossing a section on the road is also low. As speed of stream gradually increase, the minimum time headway decreases up to a lowest value at a certain speed.
• The speed at which the value of time headway is lowest represent the optimum speed corresponding max flow or capacity flow.
• If speed of traffic stream is further increased the minimum time headway starts increasing resulting in decrease of traffic flow.
Note.2
Relationship between traffic volume (q), Traffic density (K), and Traffic speed (V).
It is difficult to measure traffic density directly in practical situation, hence the relationship between traffic volume, traffic density and speed is used.
K (veh/km)= $$\frac{\text{q (veh/hr)}}{\text{V (km/hr)}}$$
q= KV Traffic volume = Traffic Density × Traffic speed
q (veh/hr) = $$\frac{1000}{\text{S (m)}}$$ × V (km/hr) we know thatK (veh/km)= $$\frac{1000}{\text{S (m)}}$$
also
q (veh/hr)= $$\frac{\text{3600}}{H_T (sec)}$$
From above two equation of q
$$\frac{3600}{H_T }$$=$$\frac{1000V}{\text{S }}$$
## Traffic Capacity
Maximum value of traffic volume, which a road can accommodate is called Traffic Capacity. It is expressed as vehicle per hour per lane. (Traffic Volume ≤ Traffic Capacity).
## Basic Capacity
This Traffic Capacity under most ideal condition is termed as Basic Capacity/Theoretical Capacity.
Note: Two road having the same physical features will have the same basic capacity irrespective of traffic condition, as they are assumed to be ideal.
## Practical capacity
It is the maximum number of vehicle that can pass a given point on a roadway during one hour, without traffic density being so great, as to cause unreasonable delay, hazard or restriction to the driver’s freedom to maneuver under the prevailing roadway and traffic conditions.
Note:
• Sometimes practical capacity is also called as design capacity.
• For design purpose we neither use basic capacity or possible capacity as they represents the two extreme cases of roadway and traffic condition. Hence we have another type of capacity called Practical capacity.
## Calculation of Theoretical Maximum Capacity
1. Max Theoretical Capacity from Space Headway
2. Max Theoretical Capacity from Time Headway
### Max Theoretical Capacity from Space Headway
qmax = $$\frac{1000 V}{S}$$
Max Theoretical Capacity of lane,
C = $$\frac{1000 V}{S}$$
where,
C= Capacity of single lane (vehicle per hour)
V= speed of vehicle (kmph)
S= 0.2V +6 = Space Headway in meter
### Max Theoretical Capacity from Time Headway
qmax= $$\frac{3600}{H_T}$$
Max Theoretical Capacity of lane,
C = $$\frac{3600}{H_T}$$
HT = Minimum time headway in seconds.
# 2.Traffic Flow Characteristics Studies
Traffic flow characteristics are divided under two categories:
1. Macroscopic Characteristics
2. Microscopic Characteristics
## Macroscopic Characteristics
It represents how the behavior of one parameter of traffic flow changes with respect to another. There are many types of macroscopic models but we discuss only Green Shield’s Stream Model.
### Green Shield’s Stream Model
Green shield’s assumed a linear speed- density relationship to derive this model.
The equation for the relationship can be derived as
y= mx +c
V =mK +Vf
m = $$\frac{0-V_f}{Kj-0}$$
m = $$\frac{-V_f}{Kj}$$
V= Vf – $$\frac{V_f}{Kj}$$K
$$V=V_f\left ( 1-\frac{K}{K_j} \right )$$
This equation is referred as “Green Shield’s Stream Model”
now,
q= KV from previous relationship
q = $$V_f\left ( 1-\frac{K}{K_j} \right )$$K
q = $$V_f\times K-\frac{V_f\times K^{2}}{K_j}$$
using the above relationship, density can be found at which max flow occurs as follows
$$\frac{dq}{dK}=0$$
$$V_f-\frac{V_f\times (2K)}{K_j}$$=0
K= Kj/2
Density at which max flow occurs is denoted as optimum density,
KO= Kj/2
For qmax, put K=KO=Kj/2 in q
qmax = $$V_f\times \frac{K_j}{2}-V_f\times( \frac{K_j}{2})^{2}\cdot \frac{1}{K_j}$$
qmax = $$\frac{V_f\times K_j}{4}$$
since,
q = $$V_f\times K-\frac{V_f\times K^{2}}{K_j}$$
q= KV ⇒ K=q/V
q = $$V_f\times \frac{q}{V}-V_f\frac{q^{2}}{V^{2}K_j}$$
1 = $$\frac{V_f}{V}-\frac{V_f\times q}{V^{2}\times K_j}$$
$$V^{2}\times K_j=\frac{V_f\times V^{2}\times K_j}{V}-V_f\times q$$.
$$q= K_j\times V-\frac{K_j}{V_f}V^{2}$$
to find the speed at which flow is max put K=KO=Kj/2
V= Vf – $$\frac{V_f}{Kj}$$K
at optimum speed V=VO, q=qmax
VO= Vf – $$V_f\frac{K_j}{2}\frac{1}{K_j}$$
VO= V/2
# Delay & Queue Analysis at Signalized Intersection
## Delay (D)
• It is defined as the time a vehicle is stopped in queue while waiting to pass through signalized Intersection.
• It begins when the vehicle is fully stopped & end when the vehicle begin to accelerate.
• It is mathematically difference departure time & arrival time.
• Average delay is the average for all vehicle during the specified time period.
## Queue (Q)
• It is the difference of total no of vehicle arrival & total number of vehicle departure at any instant of time.
Note:
Average Delay Per Vehicle = {Area between cumulative arrival & cumulative departure curve for one cycle time } ÷ {Cumulative number of vehicle arrival per cycle time}
• Vehicle arrive & departure at uniform rate. (hence cumulative Arrival & cumulative departure curve with time is linear.)
• No pre existing queue is there at intersection.
• Arriving vehicle departs instantaneously when the signal is green.
• The departure of vehicle takes place at it max rate termed as Saturated Flow / Service Rate.
• The departure curve catches up with arrival curve before the next red interval begins.
Note: Queue length v/s Time Graph can be converted into cumulative arrival & departure v/s time graph.
1. Cumulative departure matches cumulative arrival exactly at the end of one cycle.
2. Cumulative departure matches cumulative arrival before the completion of cycle time.
3. Cumulative departure does not matches cumulative arrival even at the end of one cycle time. | 2023-03-22 12:52:41 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4485872685909271, "perplexity": 5070.362087535208}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296943809.76/warc/CC-MAIN-20230322114226-20230322144226-00216.warc.gz"} |
https://zbmath.org/?q=an:0868.57024 | # zbMATH — the first resource for mathematics
Pushing arcs and graphs around in handlebodies. (English) Zbl 0868.57024
Johannson, Klaus (ed.), Low-dimensional topology. Proceedings of a conference, held May 18-26, 1992 at the University of Tennessee, Knoxville, TN, USA. Cambridge, MA: International Press. Conf. Proc. Lect. Notes Geom. Topol. 3, 163-171 (1994).
An oriented 3-manifold obtained by attaching a finite collection of 1-handles to the 3-ball is called a handlebody. This work deals with the problem of moving arcs and graphs in handlebodies and planarity of graphs.
Particularly graphs in 3-space and arc families in $$F\times I$$ where $$F$$ is a surface, are discussed. This is a continuation of the work of Y.-Q. Wu on planar graphs in 3-manifolds and of N. Robertson, P. D. Seymour and R. Thomas on linkless embeddings of graphs in 3-space. In analogy to the families of arcs in $$F\times I$$, a graph $$\Gamma$$ in $$S^3$$ in taken and called cycle-trivial if every imbedded cycle in it bounds a disc having disjoint interior from $$\Gamma$$. Then it is proven that if $$\Gamma$$ is finite and is the disjoint union of two subgraphs $$B$$ and $$C$$, then the necessary and sufficient conditions for it to be made cycle-trivial over $$C$$ is $$S^3-\eta (B' \cup C)$$ is a connected sum of handlebodies for every $$B' \subset B$$. It is also proven that this is still true when $$\Gamma$$ is a graph in a connected sum of handlebodies.
For the entire collection see [Zbl 0816.00026].
##### MSC:
57N35 Embeddings and immersions in topological manifolds 57M99 General low-dimensional topology
##### Keywords:
3-manifold; handlebody; graphs; embeddings | 2021-03-03 15:32:39 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6340213418006897, "perplexity": 730.8182950522404}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178366969.45/warc/CC-MAIN-20210303134756-20210303164756-00327.warc.gz"} |
http://clay6.com/qa/34060/an-ac-source-gives-a-voltage-of-v-20-cos-2000-t-it-is-connected-in-a-circui | Browse Questions
# An AC Source gives a voltage of $V= 20\; \cos \;(2000 \;t)$. It is connected in a circuit as shown. The voltmeter reading is
$(a)\;4\;V \\ (b)\;4 \sqrt 2\;V \\(c)\;2 \sqrt {3} \\(d)\;3\sqrt {2} V$
For the given circuit the resonance frequency
$w=\large\frac{1}{\sqrt {LC}} =\frac{1}{\sqrt {5 \times 10^{-3} \times 50 \times 10^{-6}}}$
$\qquad= 2000\;rad/s$
Given AC source has $V=20 \;\cos (2000 t) \;V$
Since the frequency of the ac source is also $2000\;rad/s$ it running under resonance conditions.
$I=\large\frac{V}{R} =\frac{20/\sqrt 2}{6+4}$
$\qquad= \sqrt 2 A$
$V=I \times 4= 4 \sqrt 2 \;V$
Hence b is the correct answer.
edited Sep 24, 2014 | 2016-12-09 17:43:00 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7995477914810181, "perplexity": 1046.2923205342645}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-50/segments/1480698542714.38/warc/CC-MAIN-20161202170902-00442-ip-10-31-129-80.ec2.internal.warc.gz"} |
https://physicsoverflow.org/34814/proving-killing-contractions-geodesics-constants-motion?show=34818 | # Proving that Killing form contractions with geodesics are constants of motion
+ 3 like - 0 dislike
2630 views
I want to prove the fundamental theorem of Killing forms, namely that
$$\frac{d}{d \lambda} \Big( \frac{d P^{\mu}}{d \lambda} \xi_{\mu}(P(\lambda)) \Big) = 0$$
If $P(\lambda)$ is a Geodesic curve, which implies that $\dot{P}^{\mu} \xi_{\mu}(P(\lambda))$ are constants of geodesic motion
This should be straightforward to prove, basically expanding the derivative expression
\begin{align*} \frac{d}{d \lambda} \Big( \frac{d P^{\mu}}{d \lambda} \xi_{\mu}(P(\lambda)) \Big) &= \\ &=\frac{d^2 P^{\mu}}{d \lambda^2}\xi_{\mu}(P(\lambda))+\frac{d P^{\mu}}{d \lambda}\partial_{;\nu} \xi_{\mu}(P(\lambda)) \frac{d P^{\nu}}{d \lambda} \\ \end{align*}
We now use the fact that $\xi_{\nu}$ is a Killing form, that is:
$$\partial_{;\nu} \xi_{\mu}(P(\lambda)) = - \partial_{;\mu} \xi_{\nu}(P(\lambda))$$
And we expand the covariant derivative:
\begin{align*} \frac{d}{d \lambda} \Big( \frac{d P^{\mu}}{d \lambda} \xi_{\mu}(P(\lambda)) \Big) &= \\ &=\frac{d^2 P^{\mu}}{d \lambda^2}\xi_{\mu}(P(\lambda))-\frac{d P^{\mu}}{d \lambda}\partial_{;\mu} \xi_{\nu}(P(\lambda)) \frac{d P^{\nu}}{d \lambda} \\ &= \frac{d^2 P^{\mu}}{d \lambda^2}\xi_{\mu}(P(\lambda))-\frac{d P^{\mu}}{d \lambda} \Big[ \partial_{\mu} \xi_{\nu}(P(\lambda)) - \Gamma^{\theta}_{\mu \nu} \xi_{\theta}(P(\lambda)) \Big] \frac{d P^{\nu}}{d \lambda} \\ &= \frac{d^2 P^{\mu}}{d \lambda^2}\xi_{\mu}(P(\lambda))+ \Gamma^{\theta}_{\mu \nu} \xi_{\theta}(P(\lambda))\frac{d P^{\mu}}{d \lambda}\frac{d P^{\nu}}{d \lambda} - \partial_{\mu} \xi_{\nu}(P(\lambda)) \frac{d P^{\mu}}{d \lambda} \frac{d P^{\nu}}{d \lambda} \end{align*}
But
$$\Gamma^{\theta}_{\mu \nu}\frac{d P^{\mu}}{d \lambda}\frac{d P^{\nu}}{d \lambda}= - \frac{d^2 P^{\theta}}{d \lambda^2}$$
Since the curve is a geodesic, which means that the expression simplifies:
\begin{align*} \frac{d}{d \lambda} \Big( \frac{d P^{\mu}}{d \lambda} \xi_{\mu}(P(\lambda)) \Big) &= \\ &= \frac{d^2 P^{\mu}}{d \lambda^2}\xi_{\mu}(P(\lambda))- \frac{d^2 P^{\theta}}{d \lambda^2} \xi_{\theta}(P(\lambda)) - \partial_{\mu} \xi_{\nu}(P(\lambda)) \frac{d P^{\mu}}{d \lambda} \frac{d P^{\nu}}{d \lambda} \\ &= - \partial_{\mu} \xi_{\nu}(P(\lambda)) \frac{d P^{\mu}}{d \lambda} \frac{d P^{\nu}}{d \lambda} \end{align*}
So, I am able to get rid of those two terms, but there is still an uncancelled term with the coordinate derivative of the $\xi$ form. I don't know how to proceed next
Suggestions?
This post imported from StackExchange Physics at 2015-12-31 08:11 (UTC), posted by SE-user lurscher
Suggestion to the question (v1): Replace the word Killing form with Killing vector field.
This post imported from StackExchange Physics at 2015-12-31 08:11 (UTC), posted by SE-user Qmechanic
In the very last expression if you change $\mu$ and $\nu$ the expression will be the same (since there is a summation over them). On the other hand $\xi$ is Killing so it will change sign. Thus the expression is equal to its negative, so it must be zero.
This post imported from StackExchange Physics at 2015-12-31 08:11 (UTC), posted by SE-user MBN
And all the calculation, from where you expanded the covarient derivative till the end, are unnecessary.
This post imported from StackExchange Physics at 2015-12-31 08:11 (UTC), posted by SE-user MBN
@Qmechanic, the reason to call it a form is that symmetrization of indices with the covariant index of a derivative ought to be a covariant index as well. But I agree that it might lead to confusion with the other Killing form used in Lie algebras
This post imported from StackExchange Physics at 2015-12-31 08:11 (UTC), posted by SE-user lurscher
@MBN, no, you are missing the $\frac{d^2 P^{\mu}}{d \lambda^2} \xi_{\mu}$ term
This post imported from StackExchange Physics at 2015-12-31 08:11 (UTC), posted by SE-user lurscher
+ 3 like - 0 dislike
Your $d/d\lambda$ should be understood in terms of parallel transport $$\frac{d}{d\lambda}\equiv \frac{dP^\mu}{d\lambda}\partial_{;\mu}$$ It is not an ordinary derivative when it acts on a vector.
So writing your third line in more transparent notation: $$\frac{d}{d \lambda} \Big( \frac{d P^{\mu}}{d \lambda} \xi_{\mu} \Big) =\left(\frac{dP^\nu}{d\lambda}\partial_{;\nu} \frac{dP^\mu}{d\lambda}\right)\xi_{\mu}+\left(\frac{dP^\nu}{d\lambda}\partial_{;\nu} \,\xi_{\mu}\right)\frac{dP^\mu}{d\lambda}$$ The second term vanishes since $\partial_{;\mu}\xi_\nu$ is antisymmetric in the indices as MBN points out in his comment (although it only applies to the covariant derivative). The first term vanishes by the geodesic equation, as should be clear in this notation.
This post imported from StackExchange Physics at 2015-12-31 08:11 (UTC), posted by SE-user octonion
answered Dec 29, 2015 by (145 points)
A few observations: 1) your expression has the index $\mu$ repeated four times, which might be confusing
This post imported from StackExchange Physics at 2015-12-31 08:11 (UTC), posted by SE-user lurscher
2) What is the point of using two notations for the covariant derivative? $\nabla_{\mu}=\partial_{;\mu}$
This post imported from StackExchange Physics at 2015-12-31 08:11 (UTC), posted by SE-user lurscher
3) $\partial_{;\nu} \frac{d P^{\mu}}{d\lambda}$ is not meaningful since $P^{\mu}$ is not a function of coordinates but of $\lambda$, so there is no point in complicating things here; $\frac{d}{d\lambda}( \frac{d P^{\mu}}{d \lambda})$ is just $\frac{d^2 P^{\mu}}{d \lambda^2}$
This post imported from StackExchange Physics at 2015-12-31 08:11 (UTC), posted by SE-user lurscher
I copy pasted your answer and made clear the part where I think your notation is confusing you. By all means change the indices or use semicolons, I am just trying to communicate where the error is to you. It is not just a complication, to use the product rule over a contraction like you did you need to use the covariant derivative. Since you are dotting the index with the tangent vector it does not matter if $dP^\mu/d\lambda$ is only defined on the path.
This post imported from StackExchange Physics at 2015-12-31 08:11 (UTC), posted by SE-user octonion
How do you evaluate the expression $\partial_{;\nu} \frac{dP^\mu}{d\lambda}$? (or $\nabla_{\nu} \frac{dP^\mu}{d\lambda}$ in your previous notation)
This post imported from StackExchange Physics at 2015-12-31 08:11 (UTC), posted by SE-user lurscher
You can only evaluate it in the tangent direction. That's ok because it is contracted with the tangent vector, and $P^\mu_{,\lambda}\partial_\mu = \partial_\lambda$. Expand it out in terms of the Christoffel symbols and you'll recognize the geodesic equation and see why the first term is zero.
This post imported from StackExchange Physics at 2015-12-31 08:11 (UTC), posted by SE-user octonion
ok that makes sense
This post imported from StackExchange Physics at 2015-12-31 08:11 (UTC), posted by SE-user lurscher
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Something interesting about Taylor series bo198214 Administrator Posts: 1,389 Threads: 90 Joined: Aug 2007 06/29/2010, 06:32 AM (This post was last modified: 06/29/2010, 06:42 AM by bo198214.) (06/24/2010, 08:23 PM)tommy1729 Wrote: http://mathworld.wolfram.com/PowerTower.html formula ( 6 ) , ( 7 ) and ( 8 ). a classic. Hm, that is a development in $\ln(x)$, Not really a Taylor devlopment of x^^n at some point $x_0$. I wonder whether we have formulas for the powerseries development of $x\^\^n$ at $x_0=1$ (and not at 0 because the powertower is not analytic there). And indeed Andrew pointed it out in his tetration-reference formula (4.17-4.19) (or in the Andrew's older Tetration FAQ 20080112: (4.23-25)): $\begin{equation} {}^{n}{x} = \sum^\infty_{k=0} t_{n,k} (x-1)^k \end{equation}$ where: $\begin{equation} t_{n,k} = \begin{cases} 1 & \text{if } n \ge 0 \text{ and } k = 0, \\ 0 & \text{if } n = 0 \text{ and } k > 0, \\ 1 & \text{if } n = 1 \text{ and } k = 1, \\ 0 & \text{if } n = 1 \text{ and } k > 1, \end{cases} \end{equation}$ otherwise: $\begin{equation} t_{n,k} = \frac{1}{k} \sum^k_{j=1} \frac{1}{j} \sum^k_{i=j} i {(-1)^{j-1}} t_{n,k-i} t_{n-1,i-j} \end{equation}$ I think it has convergence radius 1 because the substituted logarithm has convergence radius 1 and also because of the singularity at 0. « Next Oldest | Next Newest »
Messages In This Thread Something interesting about Taylor series - by Ztolk - 03/13/2010, 10:55 PM
Possibly Related Threads... Thread Author Replies Views Last Post Perhaps a new series for log^0.5(x) Gottfried 3 714 03/21/2020, 08:28 AM Last Post: Daniel Interesting commutative hyperoperators ? tommy1729 0 218 02/17/2020, 11:07 PM Last Post: tommy1729 Very interesting topic Ansus 0 616 10/01/2019, 08:14 PM Last Post: Ansus Taylor series of i[x] Xorter 12 13,390 02/20/2018, 09:55 PM Last Post: Xorter Taylor series of cheta Xorter 13 14,422 08/28/2016, 08:52 PM Last Post: sheldonison Taylor polynomial. System of equations for the coefficients. marraco 17 18,242 08/23/2016, 11:25 AM Last Post: Gottfried [integral] How to integrate a fourier series ? tommy1729 1 2,787 05/04/2014, 03:19 PM Last Post: tommy1729 regular tetration base sqrt(2) : an interesting(?) constant 2.76432104 Gottfried 7 10,135 06/25/2013, 01:37 PM Last Post: sheldonison (MSE): Comparision of powertowers -.Possibly interesting thread in MSE Gottfried 0 2,065 05/22/2013, 07:02 AM Last Post: Gottfried Iteration series: Series of powertowers - "T- geometric series" Gottfried 10 17,817 02/04/2012, 05:02 AM Last Post: Kouznetsov
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http://ftp.hillcrestanimalrescue.org/slug/fa1638-is-syria-safe | # is syria safe
In simplest term, it is the volume of a box - 1 ft long, 1 ft wide, and 1 ft … This was part of a multi-sheet project for the complete design of an A-frame wood structure. You can use the Wood&Armer method (the European code supplement [ENV 1992-1-1 EC2 Design of Concrete Structures - Appendix 2, point A.2.8 Reinforcement in Slabs]). The volume calculations for these individual frustums of trunk segments can be further refined by considering the overall shape of the trunk. Here is a series of "Wood Doctor Approved" calculators to make your lumber and timber related estimating a little easier. But if you want to know the exact formula for calculating cord then please check out the "Formula" box above. But if you want to know the exact formula for calculating cord then please check out the "Formula" box above. Maximum Volume volume. But it comes at a cost of the designer having to perform more calculations and designs to follow the load path through all of the headers, jambs, sills, etc., and their connections. This autumn I’ll be constructing a rather large white oak built-in at my home. A cubic foot is the space occupied by a cube with 1 foot width, length and height. M = maximum bending moment, in.-lbs. K. WOOD CONSTRUCTION CONNECTOR: SIMPSON Strong-Tie or Approved Equal L. TRUSS CALCULATIONS: Provided by: _____ It is the full intention of the Engineer that these calculations conform to the International Building Code, 2003 edition. Re: Wood Weight Calculations The volume of a linear foot of wood, in cubic inches, is the width x the height x 12 inches (the length). Calculation. I was also thrilled to find … Ft. $$Board\,Feet\,(bf) = {Thickness\,(in) \times Width\,(in) \times Length\,(ft) \over 12}$$. Cft or Cubic feet or ft3 is a unit of measurement of volume in imperial unit. Note: You can give measurements in imperial units (inches, feet, yards) or metric units (centimeters, meters). Wood volume calculation using taper models. Surprisingly, the calculations are extremely easy! Connection Calculator available for the iPhone. Accurate calculations of wood beam strength are essential in construction. Dimensional Change Coefficient::A number that reflects how much a certain species of wood will change in width. Create an Excel file report that can easily be imported into Excel and other spreadsheet applications. 1,250 millimeter * 100 millimeter * 25 millimeter = 3,125,000 cubic millimeter You can then convert cubic millimeter to cubic meter on the Volume conversion page, or just divide by 1,000,000,000. Hardwood flooring instantly upgrades the look and feel of any home. I want to estimate the total board feet and cost for this landscaping project. Details concerning the method can be found, for instance, in R.H.Wood, "The reinforcement of slabs in accordance with a pre-determined field of … 6. Instructions: Wood Shrinkage Calculator Width: Enter the actual measured width of the lumber, in inches and fractions of an inch (centimeters, if metric). Our calculator works out the board feet of standard three dimensional wood material based on the measurements you provide. I don’t know the price per board foot, but I can purchase 20 board feet for a cost of $60. The optimum depth of the cut, and thus remaining minimum thickness of wood to obtain the curve cannot be calculated. How much is 1 cft or ft 3? 3 Methods Same Result. Wood expands and contracts the most across the width. All calculations are according to the NDS code. For general description of the module, end fixity, loads, and load combinations click here. Thickness uses the rough sawn dimension, not your final net dimension. Minimum Volume volume. So 1 ft * 1 ft * 1 ft = 1 ft3. For our second example let’s imagine I need to lay down two planks of wood each measuring 12 feet in length, 5 inches wide and 2 inches deep for a construction build. You can also calculate the volume of lumber by measuring the length, width, and thickness in inches and multiplying them together. The Board Foot Formula. Create an Excel file report that can easily be imported into Excel and other spreadsheet applications. Wood Section Properties: Calculate the section properties for a wood beam, joist, plank or decking. Given here is an online wood density calculator to calculate density of wooden block in mass per unit volume. Calculate timber volume in cubic metre, cubic foot volume (CFT), board feet (CBF) from a diameter or circumferences (girth) and length, create a wood log and share it over email, other sharing apps and cloud storage services for free. How to Calculate Cord. A board foot is actually a measure of volume. To calculate trunk volume, the tree is subdivided into a series of segments with the successive diameters being the bottom and top of each segment and segment length being equal to the difference in height between the lower and upper diameters, or if the trunk is not vertical, the segment length can be calculated using the limb length formula above. There are several ways to solve this problem and several "correct" answers. In addition, you can calculate the price per board foot/linear foot for the wood you have purchased using the formula: $$Price\,Per\,Board\,Foot = {Total\,Cost\,of\,Wood \over Total\,Board\,Feet\,of\,Wood}$$, $$Price\,Per\,Linear\,Foot = {Total\,Cost\,of\,Wood \over Total\,Linear\,Feet\,of\,Wood}$$. Volume = Length * Width * Height They just all need to be in the same base unit, as yours already are. This unit is very commonly used in wood industry for pricing wooden planks/ lumbers. However, where any discrepancies occur between these calculations and the … I would then enter the measurements into the calculator to calculate the total board feet and linear feet. Share. At present, the Wood Shear Wall module implements the Individual Full-Height Wall Segment Shear Walls method. Tue May 12, 2015: Post #1: JAI PRAKASH Join date: May 2014: It should be calculated in running feets, For a door frame of 7*3, total would be 7+7+3 = 17 feets. please can you tell how to calculate wood for door frames{chowkath} ? Formula works only when wood is between 6 percent and 14 percent moisture, but this is a fair range for furniture. Calculating for Wood Movement. On another end, multiply the wood value (based on the wood type) with 100. Pay special attention to the units! All calculations are according to the NDS code. The first size is 1" x 5.5" and the second is 1.5" x 5.5". Select dimensions of lumber. ByExample.com provides an instant geodesic dome calculator to simplify dome formulas. Since your density figure is metric, inches are the wrong unit. Enter the length, breadth and depth of your requirement, and the volume of wood required will be presented to you. This calculator calculates the volume in cubic meters from unit sizes and number of units and vice versa. Calculator - Log volume calculator - Wood log volume calculation - Logs - Volume m³ BF - - Wood calculators A formula developed by Hiram Hallock, retired, U.S. Forest Service, can be used to determine horsepower requirements. The calculators "remember" previous calculations, and generate a running report of entries and subtotals. This calculator finds the spacing of the cuts (at entered dimensions), so when the piece is bent, the inside edges of each cut touch together to form the correct curve. The beam calculator uses these equations to generate bending moment, shear force, slope and defelction diagrams. On this page, you can calculate the volume of wood/ lumber in cubic feet (Cft). Calculate timber volume in cubic metre, cubic foot volume (CFT), board feet (CBF) from a diameter or circumferences (girth) and length, create a wood log and share it over email, other sharing apps and cloud storage services for free. Step 1: Given that, Length of the wood = 10 ft Width of the wood = 4 ft Thickness of the wood = 3 ft Step 2: Applying the values in the formula, CFT of Wood = 10 ft x 4 ft x 3 ft CFT of Wood = 120 ft 3 Quality, the inside edges of the cuts so when bent, the wood column module,. Linear foot for several different sizes number of units and vice versa published the! Price\, Per\, Linear\, foot \times Linear\, feet$.! Implements the individual Full-Height Wall Segment shear Walls method frames { chowkath } say that out! Chart are adapted from the design standpoint MC ) our Free online calculator! Through C5 are a set of examples that illustrate the elevation of a vintage Delmhorst G-22 moisture that. Meters ( three times, because you have cubic inches ) would then enter percentage! To play around with all of my sizes to quickly validate forces in beams a board foot is a... Like a tank the look and feel of any home will change in width close! Inches ) into Excel and other spreadsheet applications the design process, the wood Handbook, by. Of these calculators different initial criteria inside edges of the cuts join to create the curve a measure of in... The cells include NDS 2005 code calculations and specifications of an A-frame wood structure takes into account the load... The trunk accurate calculations of wood beam, joist, plank or decking slope and diagrams... Conditions are more consequential are the elements required to optimize the Forest value chain elevation of a home! 2005 code calculations and specifications not be calculated two types of formulas to calculate wood for door frames { }... Flooring with hardwoods and not sure where to start make your measurements and... Everyday use three times, because you have cubic inches by 1,728 to find … Woodworkers double wardrobe with... Was also thrilled to find … Woodworkers double wardrobe calculator with shelves Forest are the unit... The log length ( feet ) with the constant value 0.5454 Excel and spreadsheet... Rate, local market conditions are more consequential, wood and concrete beams under various loading conditions bearing the. Calculations for these individual frustums of trunk segments can be determined full screen for wood column.. Elements required to optimize the Forest value chain net dimension, width, length and height with! - 770 kg/m3 a residential setting definition, a board foot is actually a of. Wood shear Wall module implements the individual Full-Height Wall Segment shear Walls method Properties: calculate the of! Location of wood of measurement of volume and is known as the section modulus been... Elevation of a floodwall in a Forest are the elements required to the! Are automatically determined and applied for the complete design of an A-frame wood structure online will... Thickness in inches and multiplying them together create an Excel file report that can easily be into. Series of wood Doctor ) during development of these calculators with all of my sizes you... Will change in width and iOS for you the obtained value by log diameter ( inches ), and not... Centimeters, meters ) or other component bearing on the wood log expand and contract more than 120 species wood... Of any roofing or other component bearing on the beam should already have been calculated calculating. Formula correctly to obtain a valid Result or region reflect the typical rate, local market conditions more! Live load and dead load on the wood log built-in at my home and construction a. Worked closely with Gene Wengert ( the wood shear Wall module implements individual... Forces in beams Forest are the wrong unit … all calculations are according to the value! { chowkath } to limit any material waste and in doing so save!, plank or decking, U.S. Forest Service, can be determined and multiplying them together 1! Dimensional wood material based on linear board-feet and so works only when wood is between 6 percent and percent. Or region reflect the typical wood calculation formula, local market conditions are more.... That will affect the dimensional change Coefficient::A number that reflects how much wood your next project. ( and remaining wood … all calculations are according to the Forest Products Laboratory website the of... Weight of the working drawings and location of wood required will be in ft3 ) word .! Reflects how much wood your next landscaping project determining equivalent moment is authored by wood and.! At an angle to the NDS code close but somewhat different from projected! To generate bending moment, shear force, slope and defelction diagrams wood for door frames chowkath... This is a fair range for furniture I 'd like to play around all... And defelction diagrams K F and phi are automatically determined and applied for the LRFD method a! Imperial units ( centimeters, meters ) used for calculating cord then check. The working drawings U.S. Forest Service, can be determined find the volume of wood beam strength are in! Calculating volume of a multi-sheet project for the complete chart listing more than 120 species of beam. Compromise the safety of the word attempts. techniques for elevation, dry floodproofing,.... Easy the calculator to simplify dome formulas and read about the disadvantages of living in a Forest are the unit! Dry floodproofing, and generate a running report of entries and subtotals, and... 1 '' x L '' ÷ 144 = Bd the screen capture below shows the screen.
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North Texas, USA | 2022-05-26 18:40:42 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3412802815437317, "perplexity": 3546.556162900523}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662619221.81/warc/CC-MAIN-20220526162749-20220526192749-00196.warc.gz"} |
https://www.ideals.illinois.edu/handle/2142/8903/browse?rpp=20&order=ASC&sort_by=1&etal=-1&type=title&starts_with=Z | # Browse College of Liberal Arts and Sciences by Title
• (1984)
Zeolites are characterized as structural templates for light-induced electron transfer reactions. The main emphasis is on factors affecting loading of Ruthenium tris(bipyridine) (Ru(bpy)(,3)('+2)) into the lattice and ...
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• (1980)
A prime p is said to be irregular if it divides the numerator of the Bernoulli number B(,i) for some even integer i between 1 and p-2. For every irregular pair (p,i) with p < 125,000 it is known that the corresponding ...
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• (1995)
A classical result of Jentzsch states that, for a power series with radius of convergence one, every point on the unit circle is a limit point of zeros of partial sums of the power series. In this thesis, the relationship ...
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• (1990)
Zeta functions have been of major importance in algebraic number theory for many years. They are useful (along with L-functions) in obtaining results concerning the asymptotic distribution of ideals in a given class. In ...
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• (1984)
The thesis deals with the theory of two-sided ideals in arithmetic orders. The theory and techniques developed by Bushnell and Reiner are used.
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• (1996)
This thesis details how Zimbabwean stone sculpture has been creatively conceived in terms of a "tribal" renaissance by the first director of the National Gallery in Harare, Zimbabwe, Frank McEwen. Despite the complexity ...
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My dissertation is dedicated to the symbolist-critic Zinaida Vengerova. I focus not only on the work of Vengerova as a critic, her primary public role, but also on her writing which demonstrates her conception and dedication ...
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In the first part of the thesis, reactions of zinc powder with solutions of elemental sulfur in various donor solvents are described. Complexes of the type $\rm ZnS\sb6$(N-donor)$\sb2$ are obtained for the ligands ...
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Alkylation of ZrCl$\sb4$ with phenyllithium affords the new d$\sp0$ complex $\rm\lbrack Li(Et\sb2O)\rbrack\sb2\lbrack ZrPh\sb6\rbrack ;$ the $\rm\lbrack ZrPh\sb6\sp{2-}$) anion adopts a trigonal prismatic geometry. Despite ...
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PDF (26Mb) | 2015-04-01 03:10:07 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4945191442966461, "perplexity": 3476.8301229323315}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-14/segments/1427131302478.63/warc/CC-MAIN-20150323172142-00182-ip-10-168-14-71.ec2.internal.warc.gz"} |
https://codegolf.stackexchange.com/questions/192641/parallel-resistance-in-electric-circuits/192661 | # Parallel resistance in electric circuits
### Introduction:
Two resistors, R1 and R2, in parallel (denoted R1 || R2) have a combined resistance Rp given as:
$$R_{P_2} = \frac{R_1\cdot R_2}{R_1+R_2}$$ or as suggested in comments:
$$R_{P_2} = \frac{1}{\frac{1}{R_1} + \frac{1}{R_2}}$$
Three resistors, R1, R2 and R3 in parallel (R1 || R2 || R3) have a combined resistance (R1 || R2) || R3 = Rp || R3 :
$$R_{P_3} = \frac{\frac{R_1\cdot R_2}{R_1+R_2}\cdot R_3}{\frac{R_1\cdot R_2}{R_1+R_2}+R_3}$$
or, again as suggested in comments:
$$R_{P_3} = \frac{1}{\frac{1}{R_1} + \frac{1}{R_2}+ \frac{1}{R_3}}$$
These formulas can of course be extended to an indefinite number of resistors.
### Challenge:
Take a list of positive resistor values as input, and output the combined resistance if they were placed in parallel in an electric circuit. You may not assume a maximum number of resistors (except that your computer can handle it of course).
### Test cases:
1, 1
0.5
1, 1, 1
0.3333333
4, 6, 3
1.3333333
20, 14, 18, 8, 2, 12
1.1295
10, 10, 20, 30, 40, 50, 60, 70, 80, 90
2.6117
Shortest code in each language wins. Explanations are highly encouraged.
• I think it would be much clearer to write $R_p = \frac{1}{\frac{1}{R_1} + \frac{1}{R_2}$, which extends more easily to the case of an arbitrary number of resistors. – flawr Sep 11 at 14:56
• There are a few other challenges that refer to the harmonic mean (1 2 3) but I don't think there is a duplicate. In line with what flawr suggested, I think this challenge body should have that phrase listed somewhere so we can close a future dupe more easily. – FryAmTheEggman Sep 11 at 15:17
• Obligatory XKCD – Mast Sep 12 at 6:25
• "You may not assume a maximum number of resistors." May we at least assume the amount fits in a 32-bit int? – Mast Sep 12 at 6:29
• Better hope the resistor list fits in memory.... – Jacco van Dorp Sep 12 at 6:56
# Japt v2.0a0, 7 bytes
1÷Ux!÷1
Try it
# OCaml, 50 bytes
fun l->1./.(List.fold_left(fun a e->a+.1./.e)0. l)
Try it online!
New contributor
Saswat Padhi is a new contributor to this site. Take care in asking for clarification, commenting, and answering. Check out our Code of Conduct.
# Stax, 5 bytes
{u+Fu
Run and debug it at staxlang.xyz!
{ F For each:
u Invert
u Invert
Implicit print as fraction
# Perl 5 (-p), 17 bytes
$a+=1/$_}{$_=1/$a
Try it online!
# [MATLAB], 15 bytes
One more byte than flawr excellent answer, but I had to use other functions so here goes:
@(x)1/sum(1./x)
It's rather explicit, it sums the inverse of the resistances, then invert the sum to output the equivalent parallel resistance.
# Scala, 15 bytes
1/_.map(1/).sum
Try it online!
# expl3 (LaTeX3 programming layer), 65 bytes
The following defines a function that prints the result to the terminal (unfortunately expl3 has very verbose function names):
\def\1#1{\fp_show:n{1/(\clist_map_function:nN{#1}\2)}}\def\2{+1/}
A complete script which can be run from the terminal including all the test cases as well as the setup to enter expl3:
\RequirePackage{expl3}\ExplSyntaxOn
\def\1#1{\fp_show:n{1/(\clist_map_function:nN{#1}\2)}}\def\2{+1/}
\1{1, 1}
\1{1, 1, 1}
\1{4, 6, 3}
\1{20, 14, 18, 8, 2, 12}
\1{10, 10, 20, 30, 40, 50, 60, 70, 80, 90}
\stop
If run with pdflatex <filename> the following is the console output:
This is pdfTeX, Version 3.14159265-2.6-1.40.20 (TeX Live 2019) (preloaded format=pdflatex)
restricted \write18 enabled.
entering extended mode
(./cg_resistance.tex
LaTeX2e <2018-12-01>
(/usr/local/texlive/2019/texmf-dist/tex/latex/unravel/unravel.sty
(/usr/local/texlive/2019/texmf-dist/tex/latex/l3kernel/expl3.sty
(/usr/local/texlive/2019/texmf-dist/tex/latex/l3kernel/expl3-code.tex)
(/usr/local/texlive/2019/texmf-dist/tex/latex/l3backend/l3backend-pdfmode.def))
(/usr/local/texlive/2019/texmf-dist/tex/latex/l3packages/xparse/xparse.sty)
(/usr/local/texlive/2019/texmf-dist/tex/generic/gtl/gtl.sty))
> 1/(\clist_map_function:nN {1,1}\2)=0.5.
l.3 \1{1, 1}
?
> 1/(\clist_map_function:nN {1,1,1}\2)=0.3333333333333333.
l.4 \1{1, 1, 1}
?
> 1/(\clist_map_function:nN {4,6,3}\2)=1.333333333333333.
l.5 \1{4, 6, 3}
?
> 1/(\clist_map_function:nN {20,14,18,8,2,12}\2)=1.129538323621694.
l.6 \1{20, 14, 18, 8, 2, 12}
?
> 1/(\clist_map_function:nN
{10,10,20,30,40,50,60,70,80,90}\2)=2.611669603067675.
l.7 \1{10, 10, 20, 30, 40, 50, 60, 70, 80, 90}
?
)
No pages of output.
Transcript written on cg_resistance.log.
## Explanation
\fp_show:n : evaluates its argument as a floating point expression and prints the result on the terminal, every expandable macro is expanded during that process.
\clist_map_function:nN : takes two arguments, a comma separated list and a function/macro, if called like \clist_map_function:nN { l1, l2, l3 } \foo it expands to something like \foo{l1}\foo{l2}\foo{l3}. In our case instead of \foo the macro \2 is used, which expands to +1/ so that the expression expands to +1/{l1}+1/{l2}+1/{l3} | 2019-09-16 04:48:32 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 2, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 4, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.43277424573898315, "perplexity": 4565.041130640685}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-39/segments/1568514572484.20/warc/CC-MAIN-20190916035549-20190916061549-00162.warc.gz"} |
http://openstudy.com/updates/5013a1f9e4b0fa2467305823 | ## Callisto 4 years ago Just for practice
1. Callisto
(A) Four basic operations (i) Addition => + $$+$$ (ii) Subtraction => - $$-$$ (iii) Multiplication => \times $$\times$$ or \cdot $$\cdot$$ (iv) Division => \div $$\div$$ or / $$/$$ ** (v) plus / minus => \pm $$\pm$$ ** (vi) minus/plus => \mp $$\mp$$
2. Callisto
(B) ''Equal'' signs (i) Equal => = $$=$$ (ii) Not equal to => \ne $$\ne$$ (iii) Approximately equal to => \approx $$\approx$$ (iv) Similar to => \sim $$\sim$$ (v) Congruent to => \cong $$\cong$$
3. Callisto
(C) Inequality signs (i) less than => < $$<$$ (ii) less than or equal to => \le $$\le$$ (iii) greater than => > $$>$$ (vi) greater than or equal to => \ge $$\ge$$
4. Callisto
(D) Exponent and logarithm (i) power => x^{n} $$x^{n}$$ (ii) base => x_{n} $$x_{n}$$ (iii) square root => \sqrt{x} $$\sqrt{x}$$ (iv) nth root => \sqrt[n]{x} $$\sqrt[n]{x}$$ (v) common log => \log x $$\log x$$ (vi) common log with base n => \log_{n}x $$\log_{n}x$$ (vii) natural log => \ln x $$\ln x$$
5. Callisto
(E) Binomial expansion (i) summation => \sum_{}^{} $$\sum_{n=0}^{\infty}$$ (ii) combination => _{n}C_{r} $$_{n}C_{r}$$
6. Callisto
(F) Probability (i) Combination => _{n}C_{r} $$_{n}C_{r}$$ (ii) Permutation => _{n}P_{r} $$_{n}P_{r}$$ (iii) A∪B => A\cup B $$A\cup B$$ (iv)
7. Callisto
(F) Probability (i) Combination => _{n}C_{r} $$_{n}C_{r}$$ (ii) Permutation => _{n}P_{r} $$_{n}P_{r}$$ (iii) A∪B => A\cup B $$A\cup B$$ (iv) A∩B => A \cap B $$A \cap B$$
8. Callisto
$\int_{-2}^{2}\sqrt{4-x^2}dx$ Using trigo substitution: Let x = 2sinθ , dx = 2cosθ dθ When x = 2, θ = π/2 When x = -2, θ = -π/2 The integral becomes $\int_{-\frac{π}{2}}^{ \frac{π}{2}}\sqrt{4-(2\sin\theta)^2}(2\cos\theta d\theta)$$=4\int_{-\frac{π}{2}}^{ \frac{π}{2}}\cos^2\theta d\theta$$=4\int_{-\frac{π}{2}}^{ \frac{π}{2}}\frac{\cos(2\theta)+1}{2} d\theta$$=2\int_{-\frac{π}{2}}^{ \frac{π}{2}}(\cos(2\theta)+1)d\theta$$=2(\frac{1}{2}sin(2\theta)+\theta|_{-\frac{π}{2}}^{ \frac{π}{2}})$$=2(\frac{\pi}{2}-(-\frac{\pi}{2}))$$= 2\pi$ This is not really I want to show LOL! Suppose $$y=f(x)=\sqrt{4-x^2}$$ |dw:1383399191453:dw| It's clear that integrating the function y=f(x) from -2 to 2 is the same as finding the area of the semi-circle with radius = 2. So, immediately, we get $\int_{-2}^{2}\sqrt{4-x^2}dx=\pi(2^2) /2 = 2\pi$ Geometry has its role here :D | 2016-10-01 22:25:08 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9858719110488892, "perplexity": 6750.6949955139025}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-40/segments/1474738663308.86/warc/CC-MAIN-20160924173743-00143-ip-10-143-35-109.ec2.internal.warc.gz"} |
http://rosettacode.org/wiki/Literals/Floating_point | CloudFlare suffered a massive security issue affecting all of its customers, including Rosetta Code. All passwords not changed since February 19th 2017 have been expired, and session cookie longevity will be reduced until late March.--Michael Mol (talk) 05:15, 25 February 2017 (UTC)
Literals/Floating point
Literals/Floating point
You are encouraged to solve this task according to the task description, using any language you may know.
Programming languages have different ways of expressing floating-point literals.
Show how floating-point literals can be expressed in your language: decimal or other bases, exponential notation, and any other special features.
You may want to include a regular expression or BNF/ABNF/EBNF defining allowable formats for your language.
Real literals contain decimal point. The exponent part is optional. Underline may be used to separate groups of digits. A literal does not have sign, + or - are unary operations. Examples of real literals:
3.141_592_61.0E-120.13
Aime
3.145.08r # without the "r"(eal) suffix, "8" would be an integer.125
ALGOL 68
# floating point literals are called REAL denotations in Algol 68 ## They have the following forms: ## 1: a digit sequence followed by "." followed by a digit sequence ## 2: a "." followed by a digit sequence ## 3: forms 1 or 2 followed by "e" followed by an optional sign ## followed by a digit sequence ## 4: a digit sequence follows by "e" followed by an optional sign ## followed by a digit sequence ## ## The "e" indicates the following optionally-signed digit sequence is ## the exponent of the literal. ## If the implementation allows, a "times ten to the power symbol" ## can be used to replace "e" - e.g. a subscript "10" character ## ## spaces can appear anywhere in the denotation ## Examples: #REAL r;r := 1.234;r := .987;r := 4.2e-9;r := .4e+23;r := 1e10;r := 3.142e-23;r := 1 234 567 . 9 e - 4;
ALGOL W
begin real r; long real lr; % floating point literals have the following forms: % % 1 - a digit sequence followed by "." followed by a digit sequence % % 2 - a digit sequence followed by "." % % 3 - "." followed by a digit sequence % % 4 - one of the above, followed by "'" followed by an optional sign % % folloed by a digit sequence % % the literal can be followed by "L", indicating it is long real % % the literal can be followed by "I", indicating it is imaginary % % the literal can be followed by "LI" or "IL" indicating it is a long % % imaginary number % % an integer literal ( digit sequence ) can also be used where a % % floating point literal is required % % non-imaginary examples: % r := 1.23; r := 1.; r := .9; r := 1.23'5; r := 1.'+4; r := .9'-12; r := 7; lr := 5.4321L;end.
Applesoft BASIC
All numeric literals are treated as floating point. (In the Apple II world, Applesoft was sometimes called "floating-point BASIC" to contrast it with Integer BASIC.)
0
19
-3
29.59
-239.4
1E10
1.9E+09
-6.66E-32
AWK
With the One True Awk (nawk), all numbers are floating-point. A numeric literal consists of one or more digits '0-9', with an optional decimal point '.', followed by an optional exponent. The exponent is a letter 'E' or 'e', then an optional '+' or '-' sign, then one or more digits '0-9'.
22..345e645e+678e-91.2E34
Other implementations of Awk can differ. They might not use floating-point numbers for integers.
This Awk program will detect whether each line of input contains a valid integer.
Nemerle
3.14f // float literal
3.14d, 3.14 // double literal
3.14m // decimal literal
Formally (from the Reference Manual):
<floating_point_literal> ::=
[ <digits_> ] '.' <digits_> [ <exponent> ] [ <suffix> ]
| <digits_> <exponent> [ <suffix> ]
| <digits_> <suffix>
<exponent> ::=
<exponential_marker> [ <sign> ] <digits>
<digits> ::=
{ <digit> }
<digits_> ::=
<digits> [ { '_' <digits> } ]
<exponential_marker> ::=
'e'
| 'E'
<sign> ::=
'+'
| '-'
<digit> ::=
<decimal_digit>
<suffix> ::=
<floating_point_suffix>
<floating_point_suffix> ::=
'f'
| 'd'
| 'm'
NetRexx
NetRexx supports decimal and exponential notation for floating point constants. A number in exponential notation is a simple number followed immediately by the sequence "E" (or "e"), followed immediately by a sign ("+" or "-"), followed immediately by one or more digits.
NetRexx supports floating point number notation in the primitive float and double types, it's built in Rexx object and any other Java object that supports floating point numbers.
/* NetRexx */options replace format comments java crossref symbols nobinary numeric digits 40 -- make lots of space for big numbersnumeric form scientific -- set output form for exponential notation say 'Sample using objects of type "Rexx" (default):'fv = 1.5; say '1.5'.right(20) '==' normalize(fv).right(20) -- 1.5fv = -1.5; say '-1.5'.right(20) '==' normalize(fv).right(20) -- -1.5fv = 15e-1; say '15e-1'.right(20) '==' normalize(fv).right(20) -- 1.5fv = 3e-12; say '3e-12'.right(20) '==' normalize(fv).right(20) -- 3E-12fv = 3e+12; say '3e+12'.right(20) '==' normalize(fv).right(20) -- 3000000000000fv = 17.3E-12; say '17.3E-12'.right(20) '==' normalize(fv).right(20) -- 1.73E-11fv = 17.3E+12; say '17.3E+12'.right(20) '==' normalize(fv).right(20) -- 17300000000000fv = 17.3E+40; say '17.3E+40'.right(20) '==' normalize(fv).right(20) -- 1.73E+41fv = 0.033e+9; say '0.033e+9'.right(20) '==' normalize(fv).right(20) -- 33000000fv = 0.033e-9; say '0.033e-9'.right(20) '==' normalize(fv).right(20) -- 3.3E-11say say 'Sample using primitive type "float":'ff = floatff = float 15e-1; say '15e-1'.right(20) '==' normalize(ff).right(20) -- 1.5ff = float 17.3E-12; say '17.3E-12'.right(20) '==' normalize(ff).right(20) -- 1.73E-11ff = float 17.3E+12; say '17.3E+12'.right(20) '==' normalize(ff).right(20) -- 17300000000000ff = float 0.033E+9; say '0.033E+9'.right(20) '==' normalize(ff).right(20) -- 33000000ff = float 0.033E-9; say '0.033E-9'.right(20) '==' normalize(ff).right(20) -- 3.3E-11say say 'Sample using primitive type "double":'fd = doublefd = 15e-1; say '15e-1'.right(20) '==' normalize(fd).right(20) -- 1.5fd = 17.3E-12; say '17.3E-12'.right(20) '==' normalize(fd).right(20) -- 1.73E-11fd = 17.3E+12; say '17.3E+12'.right(20) '==' normalize(fd).right(20) -- 17300000000000fd = 17.3E+40; say '17.3E+40'.right(20) '==' normalize(fd).right(20) -- 1.73E+41fd = 0.033E+9; say '0.033E+9'.right(20) '==' normalize(fd).right(20) -- 33000000fd = 0.033E-9; say '0.033E-9'.right(20) '==' normalize(fd).right(20) -- 3.3E-11say return /** * Convert input to a Rexx object and add zero to the value which forces NetRexx to change its internal representation * * @param fv a Rexx object containing the floating point value * @return a Rexx object which allows NetRexx string manipulation methods to act on it */method normalize(fv) private constant return fv + 0
Output:
Sample using objects of type "Rexx" (default):
1.5 == 1.5
-1.5 == -1.5
15e-1 == 1.5
3e-12 == 3E-12
3e+12 == 3000000000000
17.3E-12 == 1.73E-11
17.3E+12 == 17300000000000
17.3E+40 == 1.73E+41
0.033e+9 == 33000000
0.033e-9 == 3.3E-11
Sample using primitive type "float":
15e-1 == 1.5
17.3E-12 == 1.73E-11
17.3E+12 == 17300000000000
0.033E+9 == 33000000
0.033E-9 == 3.3E-11
Sample using primitive type "double":
15e-1 == 1.5
17.3E-12 == 1.73E-11
17.3E+12 == 17300000000000
17.3E+40 == 1.73E+41
0.033E+9 == 33000000
0.033E-9 == 3.3E-11
Nim
var x: floatx = 2.3x = 2.0x = 0.3x = 123_456_789.000_000_1x = 2e10x = 2.5e10x = 2.523_123E10x = 5.2e-10 var y = 2'f32 # Automatically a float32var z = 2'f64 # Automatically a float64
Objeck
3 + .141593.14159314.159E-2
OCaml
In the OCaml manual, the chapter lexical conventions describes floating-point literals, which are:
float-literal ::= [-] (0…9) { 0…9∣ _ } [. { 0…9∣ _ }] [(e∣ E) [+∣ -] (0…9) { 0…9∣ _ }]
Here are some examples:
0.51.01. (* it is not possible to write only "1" because OCaml is strongly typed, and this would be interpreted as an integer *)1e-103.14159_26535_89793
Oforth
A literal floating point number is written with a . and with or without an exponential notation :
3.141.0e-120.131000.0.22
PARI/GP
Similar to C, but allowing only decimal. Also, GP allows a trailing decimal point:
[+-]?((\d*\.\d+\b)|(\d+(\.\d*)?[Ee][+-]?\d+\b)|-?(\.\d+[Ee][+-]?\d+\b)|(\d+\.))
PARI t_REAL numbers have a maximum value of
32-bit 64-bit ${\displaystyle 2^{2^{29}}(1-\epsilon )}$ 161,614,249 decimal digits ${\displaystyle 2^{2^{61}}(1-\epsilon )}$ 694,127,911,065,419,642 decimal digits
where ${\displaystyle \epsilon }$ is the machine epsilon at the selected precision. The minimum value is the opposite of the maximum value (reverse the sign bit).
Pascal
1.345
-0.5345
5.34e-34
Perl
# Standard notations:.5;0.5;1.23345e10;1.23445e-10;# The numbers can be grouped:100_000_000; # equals to 100000000
Perl 6
Floating point numbers (the Num type) are written in the standard 'e' scientific notation:
2e2 # same as 200e0, 2e2, 200.0e0 and 2.0e26.02e23-2e481e-91e0
A number like 3.1416 is specifically not floating point, but rational (the Rat type), equivalent to 3927/1250. On the other hand, Num(3.1416) would be considered a floating literal though by virtue of mandatory constant folding.
Phix
Phix does not require any distinction between integers and floats: 5 and 5.0 are exactly the same. A variable declared as atom can hold an integer or a floating point value.
Division and other operators do what a sensible language should, eg 1/3 is 0.333333, not 0. [for the latter use floor(1/3)]
Floats cannot be expressed in any base other than decimal. They may optinally include a sign for mantissa and/or exponent.
It is not necessary for a digit to precede a decimal point, but one must follow it. Upper or lower e/g may be used.
In the 32-bit version, integers outside -1,073,741,824 to +1,073,741,823 must be stored as atoms. In the 64-bit version the limits of integers are -4,611,686,018,427,387,904 to +4,611,686,018,427,387,903.
On a 32-bit architecture floats can range from approximately -1e308 to +1e308 with 15 decimal digits, and on a 64-bit architecture they can range from approximately -1e4932 to +1e4932 with 19 decimal digits.
The included bigatom library allows working with extremely large integers and floats with arbitrary precision. In the following, '?x' is the Phix shorthand for 'print(1,x)', plus \n
?1e+12 -- (same as 1e12)?1e-12?5 -- (same as 5.0)--?1. -- (illegal, use 1 or 1.0)?.1 -- (same as 0.1)?1/3 -- 0.333333printf(1,"%g %G\n",1e-30)
Output:
1e+12
1e-12
5
0.1
0.3333333333
1e-30 1E-30
PHP
.120.12341.2e37E-10
Formal representation:
LNUM [0-9]+
DNUM ([0-9]*[\.]{LNUM}) | ({LNUM}[\.][0-9]*)
EXPONENT_DNUM [+-]?(({LNUM} | {DNUM}) [eE][+-]? {LNUM})
PicoLisp
PicoLisp does not support floating point literals in the base language, only fixed point (scaled) decimal integers of unlimited size and precision. See Numbers in the reference.
PL/I
1.2345e-4 decimal floating-point7e5 decimal floating-point1.234_567_89e0 decimal floating-point.1.0s0 decimal floating-point (single precision)1.0d0 decimal floating-point (double precision)1.34q0 decimal floating-point (quadruple/extended precision) 111.0101e7b binary floating-point equals 111.0101 * 2**7 or 7.3125 * 2**71e5b binary floating-point equals 1 * 2**5
PureBasic
Floating point literals do not need a decimal point if an exponent is used. They may also include a sign for the number or exponent.
-1.0 1.0 1.0E2 1.0E+2 1.0E-2 -1E2
Python
Works with: Python version 2.3.3
This is an excerpt of an ANTLR grammar for python obtained from here.
FLOAT : '.' DIGITS (Exponent)? | DIGITS '.' Exponent | DIGITS ('.' (DIGITS (Exponent)?)? | Exponent) ; DIGITS : ( '0' .. '9' )+ ; Exponent : ('e' | 'E') ( '+' | '-' )? DIGITS ;
Examples
2.3 # 2.2999999999999998.3 # 0.29999999999999999.3e4 # 3000.0.3e+34 # 2.9999999999999998e+33.3e-34 # 2.9999999999999999e-352.e34 # 1.9999999999999999e+34
Racket
#lang racket.22.2.+0i ; zero imaginary part2e0#x10.8 ; hex float#o1e2 ; oct float2.0f0 ; single float1.0t0 ; extended 80-bit float (when available on platform)
Output:
0.2
2.0
2.0
2.0
16.5
64.0
2.0f0
1.0t0
REXX
All values in REXX are character strings, so a value could hold such things as these (decimal) numbers:
something = 127something = '127' /*exactly the same as the above. */something = 1.27e2something = 1.27E2something = 1.27E+2something = ' + 0001.27e+00000000000000002 '
To forcibly express a value in exponential notation, REXX has a built-in function format that can be used.
Note that a value of 0 (zero) in any form is always converted to
0
by the format BIF.
something = -.00478say somethingsay format(something,,,,0)
output
-0.00478
-4.78E-3
The last invocation of format (above, with the 5th parameter equal to zero) forces exponential notation, unless the exponent is 0 (zero), then exponential notation won't be used.
There are other options for the format BIF to force any number of digits before and/or after the decimal point, and/or specifying the number of digits in the exponent.
Ruby
A Float literal is an optional sign followed by one or more digits and a dot, one or more digits and an optional exponent (e or E followed by an optional sign and one or more digits). Unlike many languages .1 is not a valid float.
Underscores can be used for clarity: 1_000_000_000.01
Rust
2.3 // Normal floating point literal3. // Equivalent to 3.0 (3 would be interpreted as an integer)2f64 // The type (in this case f64, a 64-bit floating point number) may be appended to the value1_000.2_f32 // Underscores may appear anywhere in the number for clarity.<lang rust> =={{header|Scala}}=={{libheader|Scala}}As all values in Scala, values are boxed with wrapper classes. The compiler will unbox them to primitive types for run-time execution.<lang Scala>1. //Double equal to 1.01.0 //Double, a 64-bit IEEE-754 floating point number (equivalent to Java's double primitive type) 2432311.7567374 //Double1.234E-10 //Double1.234e-10 //Double758832d //Double728832f //32-bit IEEE-754 floating point number (equivalent to Java's float primitive type)1.0f //Float758832D //Double728832F //Float1.0F //Float1 / 2. //Double1 / 2 //Int equal to 0 // ConstantsFloat.MinPositiveValueFloat.NaNFloat.PositiveInfinityFloat.NegativeInfinity Double.MinPositiveValueDouble.NaNDouble.PositiveInfinityDouble.NegativeInfinity
Values that are outside the bounds of a type will give compiler-time errors when trying to force them to that type.
Scheme
.2 ; 0.22. ; 2.02e3 ; 20002.+3.i ; complex floating-point number ; in Scheme, floating-point numbers are inexact numbers(inexact? 2.); #t(inexact? 2); #f
Seed7
The type float consists of single precision floating point numbers. Float literals are base 10 and contain a decimal point. There must be at least one digit before and after the decimal point. An exponent part, which is introduced with E or e, is optional. The exponent can be signed, but the mantissa is not. A literal does not have a sign, + or - are unary operations. Examples of float literals are:
3.141592653589791.0E-120.1234
The functions str and the operators digits and parse create and accept float literals with sign.
Original source: [1]
Sidef
say 1.234;say .1234;say 1234e-5;say 12.34e5;
Output:
1.234
0.1234
0.01234
1234000
Smalltalk
2.0 45e6 45e+6 78e-9 1.2E34
base 2 mantissa:
2r1010.0 -> 10.0 2r0.01 -> 0.25 2r1010e5 -> 320.0
base 2 mantissa and base 2 exponent:
2r1010e2r0101 -> 320.0
Swift
let double = 1.0 as Double // Double precisionlet float = 1.0 as Float // Single precisionlet scientific = 1.0E-12 // Swift does not feature type coercion for explicit type declarationlet sum = double + float // Error let div = 1.1 / 2 // Doublelet div1 = 1 / 2 // 0
Tcl
Floating point literals in Tcl always contain either “.” or “e” (of any case), if not both, or are references to either one of the IEEE infinities or NaN. Formally, they are values that (case-insensitively) match one these regular expressions:
Normal values
[-+]?[0-9]*\.[0-9]+(e[-+]?[0-9]+)?
[-+]?[0-9]+\.?e[-+]?[0-9]+
Infinite values
[-+]?inf(inity)?
NaN values
[-+]?nan($$[0-9a-f]+$$)?
Note also that NaN values usually result in checked exceptions; they are supported mainly so that they can be handled when parsing and generating external binary data. All other floating-point literals are fully legal values. (Also note that this excludes the definition of integer literals; for details see this TIP document, which explains the whole state machine.)
Ursa
Cygnus/X Ursa (the standard Ursa interpreter) is written in Java and supports Java style floating-point literals.
1.1.0 2432311.75673741.234E-101.234e-10758832d728832f1.0f758832D728832F1.0F
Vim Script
There are two ways to write floating point literals:
• [-+]?[0-9]+\.[0-9]+
• [-+]?[0-9]+\.[0-9]+[eE][-+]?[0-9]+
Examples: 12.34 +0.34 -1.0 12.34e5 0.99e-2 -1.0E+4
Note that there must always be at least one digit before and after the period (and for the exponent).
XPL0
0..11e3123.456E-300-123_456_789e+123
zkl
zkl requires something on both sides of the dot for a thing to be a float
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http://www.powerguru.org/super-capacitors-the-unknown-capacity-giants/ | ### Categorized |2014, April, Bodo's Power, Capacitors, Devices and Components
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Posted on 03 April 2019
# Super Capacitors, the Unknown Capacity Giants
The unit of capacitance farad (F) has been known only in combination with the prefixes micro, nano, and pico for a long time. Nowadays, however, kilofarads have become possible. How do these new super capacitors work, which base on a principle that was discovered 160 years ago?
By Wolf-Dieter Roth, HY-LINE Power Components
Super capacitors have become known by the name of gold caps after their market launch. These were capacitors that were capable of carrying only low voltages but providing sufficient capacity to replace backup batteries of RAM retention or real time chips. They were also used for LED tail lights of bicycles and astonished people seeing a bicycle stopping at a traffic light whose tail light was still shining for minutes and no battery to be seen. Initially, these super capacitors featured only a low peak current but a relatively high equivalent serial resistance.
In the mean time, however, their technology has been very much advanced. Today, even mass produced super capacitors up to 7,000 F are offered (figure 1). With respect to their storage capacity they can compete with smaller accumulators. The physics of super capacitors, however, differs from the one of accumulators. That is why they have a completely different electrical behaviour.
To begin with, super capacitors are basically capacitors: their capacity is determined by two opposing conductive surfaces. The larger the surface, the smaller the clearance between the surfaces and the higher the dielectric constant – the higher is the capacity. The formula for that is:
where C = capacitance, A = area, d = distance and ε = dielectric constant.
### Increasing capacitance values
So an air or vacuum capacitor has a lower capacitance value, because d is high whereas ε and A are low. But a high dielectric strength is achieved.
A film capacitor, however, has a markedly higher capacity because it has a larger surface and a higher dielectric constant. In addition to that the film allows for reducing clearance without compromising dielectric strength. Depending on the dielectric constant of the materials used, ceramic capacitors feature even higher capacities but accompanied by a possibly reduced voltage persistance and capacitance stability.
E capacitors have an even increased capacity because there is no mechanically manufactured dielectric but a thin chemically generated oxide layer instead. A rough base material results in a larger surface and higher capacity. Dielectric strength is lower and the capacitor requires the user to observe the correct polarity. Improper handling such as reverse polarity, overvoltage, overcurrent, and overtemperature can lead to capacitor failure.
Super capacitors are double layer capacitors whose working principle bases on the Helmholtz double layers and has been known for more than 130 years. These layers have a thickness of only a few molecules, that is to say in the nanometer range, which results in an increased capacity compared with E capacitors of up to factor 10,000 and a lower dielectric strength which, in comparison with the stateof-the-art technology, ranges for individual cells under 3 V. For higher voltages the cells may be connected in series as it is the case with batteries. More than two cells which reach a peak operating voltage of 5 up to 5.5 V require that measures for a symmetrical voltage division are to be taken.
### The alternative to accumulators
Electrochemical reactions as they occur in batteries and accumulators lead to wear and tear of the electrode material. They only play a minor part with double layer capacitors and contribute to the capacity of state-of-the-art super capacitors in the percent range.
What is of some relevance, however, is ionic shift and the formation of ions in the double layer. That is why super capacitors are also known as electrochemical capacitors and the reason for the exceptionally high field strengths of up to 5,000 kV/mm in the double layer which would lead to electrical breakdown in a normal dielectric.
Charge and discharge currents of double layer capacitors can be very high, whereas deep discharge is no problem. 100,000 charge and discharge cycles and even more are possible which means a life of more than 20 years. The capacities already lie at 1/10 of those of accumulators. Consequently, super capacitors have a far better performance in cyclic operations than accumulators. Even racing cars or means of public transport such as electric buses, which are being recharged during a short stop at the bus stop, can be powered by these capacitors. The Fraunhofer Institute, for instance, had hybrid buses manufactured in Dresden, which after having been recharged for 15 seconds at the bus stop were able to reach the next charging station 2 km away with this charge.
The principles of E and super capacitors were discovered almost at the same time: in 1875 by Eugène Adrien Ducrete (E capacitor) and even some time before in 1853 by Hermann von Helmholtz (Supercap) who also detected the double layer effect in 1879. But while the aluminium E capacitor was industrially used from 1892 and from 1931 onwards manufactured in the known technology of today, the super capacitor was ignored for many years. The first patents occurred in 1957 and in 1962 a canoe of Standard Oil powered by a super capacitor, which had the size of a car battery, made a demonstration for ten minutes on a lake in Ohio. Standard Oil, however, decided that there was no market chance for the capacitor and sold the patents to NEC. At the time even the developers of super capacitors did not know the difference from the principle of E capacitors. Thus Standard Oil regarded them as E capacitors. In 1971 NEC launched the first market-ready products and in 1978 they were followed by Panasonic’s 10 F “Goldcap” versions. Since 1992 capacities of 1,000 F have been available.
Epcos went out of the super capacitor business at the end of 2006. Super capacitors have a higher temperature resistance (see figure 3) and a much better performance at low temperatures than accumulators. Certain limit values, however, must not be exceeded lest the electrolyte evaporates. At the end of its life there is a 30% loss of capacity or a doubling of the internal resistance. When used properly total failure of a super capacitor is seldom.
### Combination with batteries
Besides the extremely thin insulation layer the high capacity of super capacitors is gained by the fact that super capacitors use carbon electrodes. They are very porous and rough – mostly active coal is used. With only one gram carbon powder a surface of 3,000 square metres can be realised.
Super capacitors are no filters like normal and E capacitors – they are primarily energy storages. The internal resistance at higher frequencies makes them unsuitable for sieving especially with switched-mode power supplies and converters – already at 10 Hz only a fraction of the super capacitor’s capacity is effective. This is due to the fact that the ions of the double layer do not move fast enough and the internal resistance is generally higher than the one of E capacitors. As a consequence the use of super capacitors as filter and smoothing capacitor is far from satisfactory and may even result in overheating and failure of the capacitor. However, in uninterruptible power supplies they are capable of bridging a potential power failure for several seconds without the need for permanent maintenance and inspection as is the case with a battery-powered UPS. They can even be used as starters of cars because in contrast to conventional starter batteries their capacity does not drop at low temperatures. Only the price for their use in these applications is still too high and therefore not yet competitive.
Likewise super capacitors are suitable for use as backup (see figure 4) if the device such as an optical smoke detector, despite the fact that it is supplied by batteries, draws current rather discontinuously. In this case the ESR of the batteries becomes too high, especially during the continuous discharge of the batteries.
With a super capacitor connected in parallel, however, these batteries can be used much longer before transients are able to cause undervoltages. Alternatively, long term high capacity lithium ion batteries can be used instead of the high current alkaline batteries.
### Electrical characteristics
Super capacitors are used exclusively as secondary storage components. Even though they feature high capacity and a low self-discharge, they are not suited for use as an independent power supply of equipment for several months. Their self-discharge, however, is low enough for bridging days and even weeks.
For safety reasons, super capacitors are not delivered charged like accumulators, and are not mounted as plug-in or replaceable components. Peak currents caused by improper handling (short-circuit) would be very high and could do some serious damage. Unlike batteries or accumulators, super capacitors do not supply voltage which is chemically defined and constant for some time, and rapidly drops at discharge end, but like every capacitor supply constantly decreasing voltage at constant current drain. By using voltage regulators the output voltage of a UPS powered by super capacitors can be kept constant. However, when the capacitor voltage drops to half of its initial value, three quarters of the stored energy will be discharged. Consequently it is not worth while using wide range converters for discharging further.
Deep discharge is principally no problem for super capacitors, and you need not be afraid of a sudden failure when the electrical storage component has reached the discharge voltage.
### Calculating super capacitor arrays
The end of life of a super capacitor is defined by a reduction of capacity to 70 per cent of the initial capacity and/or an increase of ESR to 200 per cent. Thus a circuit designed to supply a certain voltage and capacity by means of a super capacitor array is to be dimensioned with sufficient reserve capacities. If a discharge within seconds instead of hours is planned, the internal resistance will result in a drop of voltage which has to be compensated by a higher charging voltage and several super capacitors connected in series. The series circuitry, however, will lead to a reduction of capacity. A correct dimensioning of the individual capacitors will be calculated with end-of-life parameters instead of parameters of a brand new super capacitor. Only this way the long term operation of the circuit within its working limits is ensured.
The rule of thumb is that the life of a super capacitor is increased by a factor of 2.2 when:
• the operating voltage is reduced by 0.2 V
• the ambient temperature drops by 10 °C
Consequently, if you want the capacitor to have an especially long life, it is best to use it at reduced voltage and not too high temperatures. Likewise, it is necessary to prevent overvoltages and incorrect polarity, since this will cause decomposition of the electrolyte as well as capacitor gassing as it is the case with E capacitors.
When used within a wide temperature range, it is to be taken into consideration that the ESR will increase considerably below 0 °C whereas the capacity will be slightly reduced (see figure 5), however not to a level as it is usual with common accumulators.
### Applications for super capacitors
There are mainly four fields of application (see figure 5):
Low – internal resistance – high (verticle axis in figure 5)
Low – capacity – high (horizontal axis in figure 5)
Class 1
Data preservation
Class 2
For energy storage
Class 3
For power applications
Class 4
For instantaneous power
IEC 62576
Automotive applications
DIN EN 61881-3
Railway applications
Class 1: Characterized by low capacities and slow discharge. This type is designed for storage retention and uninterruptible power supply of real-time chips. They feature 0.1 up to 1 F capacity and low leak current values. Typical of this category are the Powerstor B, HB, and K series as well as the SPSCAP-SCV series.
Class 2: Characterized by low to medium capacities and slow discharge. This type is used for energy storage and power supply of torch lights, toys, emergency exit lights, small electrical tools, tail lights of bicycles, solar lamps, and for shutting down machines in case of a blackout. They come with capacities from 5 to 400 F. Typical for this category are the Powerstor XB and XV series as well as the SPSCAP-SCE series.
Class 3: This type of capacitor is marked by high capacities and strong discharge. They are typically used for electric vehicles (energy recovery, starting aid, start-stop systems), renewables (wind turbines and PV installations), x-ray devices and construction machines. They come with capacities from 100 to 5,000 F. Typical of this category is the SPSCAP-SCP series.
Class 4: These capacitors feature only low capacities but short transients. Their capacity ranges from 1 to 22 F and their ESR values are low. Typical of this category are the Powerstor HV and M series.
The first super capacitors introduced to the market belonged to class 1, whereas under class 3 fell all capacitors that were used for all kinds of vehicles. Class 2 capacitors are much cheaper if there is no need for the extremely high current ratings of class 3 capacitors, whereas class 4 capacitors are only poorly represented in the market.
With some applications it is difficult to see the possibilities they open up for capacitors as, for instance, their use in wind turbines: Here they are used among other things to quickly move the blades out of the wind in the event of a mains failure, before they get damaged. Other most obvious applications such as energy recovery during elevator operation have not been realised yet because of the aging of accumulators. With super capacitors, however, this has become possible.
Even a combination of different application modes is possible. One such example is the emergency power supply whose first task is to immediately shut down a high-power installation and after that to ensure its storage retention by way of supplying low current for long periods of time. Contrary to conventional battery-supported backup systems, there is no need for maintenance and the regular replacement of batteries with super capacitors and the temperature dependence of the installation is much lower. This is highly beneficial for traffic lights, data centres, telecommunications systems, or one-armed bandits, where a failure due to grid perturbations does not endanger lives but, nevertheless, can cause a lot of annoyance. A further advantage is that, after returning of the power supply, a super capacitor UPS system can be rapidly recharged and is capable of handling disturbances occurring anew.
More generally, it should be noted that some parameters increase the capacitor’s capacitance density and others its energy density. High capacitance density is required for class 3 and 4 applications, whereas high energy density is important to class 2 and 3 applications. Thus porous active carbon layers, for instance, ensure a higher capacity but the expanded surface area and the resulting longer ways will increase the ESR and thus reduce the capacitor’s energy density.
Choosing the right electrolyte
Today’s customary super capacitors use either propylene carbonate or acetonitrile as electrolytes. The formula of propylene carbonate is C4H6O3. It is a water-soluble carbon acid ester which becomes liquid at -48.8 °C and boils at 242 °C. Although falling under the German Ordinance on Hazardous Substances it is regarded as an unproblematic and environmentally friendly material – as a solvent it has replaced more hazardous substances. Super capacitors using it as an electrolyte can be operated without limitation at temperatures ranging from -25 °C to +70 °C. There are, however, limitations at temperatures up to +85 °C (due to voltage and power derating). At temperatures below -25 °C the capacitors cannot be operated any longer because the electrolyte freezes. Powerstor A, B, HB, P, K and XB capacitor series use propylene carbonate as electrolyte. There are series, however, where you have a choice as for SCV-P (propylene carbonate) or SCVA (acetonitrile).
The formula of acetonitrile is C2H3N. It has a higher conductivity, so capacitors using it as electrolyte have a somewhat lower ESR. It is, however, highly flammable. It becomes liquid at -45 °C and boils at +82 °C. It is deemed more critical in environmental terms and might cause poisoning because it undergoes decomposition and finally forms hydrogen cyanide (HCN) in case of fi re or when swallowed. The small quantity of acetonitrile in the enclosure of the super capacitor, however, does not pose a threat to anybody. The formerly existing dangerous goods regulations related to super capacitors fi lled with acetonitrile no longer apply except for certain limitations or transport regulations with regard to the generally high capacitance density of super capacitors, as is the case with lithium batteries.
The Powerstor HV, PHV and XV series use actonitrile as electrolyte, whereas the M and PM series use a mixture of 50% propylene carbonate and 50% acetonitrile. Super capacitors filled with acetonitrile can already be used at -40 °C but not above +65 °C, because this is not far from boiling point. With 2.7 V instead of 2.5 V the permissible voltage might be slightly higher, which is not due to the electrolyte but to the upper limiting temperature. If it is limited at +65 °C the 2.7 V can also be realized with propylene carbonate. Which of the two electrolytes is more appropriate for a certain application must be assessed case by case. In most cases, however, propylene carbonate is the more cost-effective solution.
### Round or square?
In order to exploit a specified volume to the maximum square capacitors seem to be more beneficial at first. No different from fi lm capacitors, round windings have a superior performance and are cheaper to produce in the case of super capacitors. Compared with dense packed square capacitors, arrays are much easier to cool. Although square designs for special applications such as the SPP series from SPSCAP (see figure 6) are available, round designs are principally the better choice.
For further reference
Double layer (interfacial) http://en.wikipedia.org/wiki/Double_layer_%28interfacial%29
Excel spread sheet for calculating super capacitor UPS http://www.hy-line.de/supercapcalc
SPSCAP super capacitors http://www.hy-line.de/spscapPowerstor super capacitors http://www.hy-line.de/powerstor
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https://www.aimsciences.org/article/doi/10.3934/eect.2020011?viewType=html | # American Institute of Mathematical Sciences
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doi: 10.3934/eect.2020011
## Null-controllability properties of a fractional wave equation with a memory term
1 DeustoTech, University of Deusto, 48007 Bilbao, Basque Country, Spain, Facultad de Ingeniería, Universidad de Deusto, Avenida de las Universidades 24, 48007 Bilbao, Basque Country, Spain 2 University of Puerto Rico, Rio Piedras Campus, Department of Mathematics, Faculty of Natural Sciences, 17 University AVE. STE 1701 San Juan PR 00925-2537 (USA)
* Corresponding author: Umberto Biccari
Received January 2019 Revised May 2019 Published August 2019
Fund Project: The work of the first author is supported by the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreement NO: 694126-DyCon), by the Grant MTM2017-92996-C2-1-R COSNET of MINECO (Spain), and by the ELKARTEK project KK-2018/00083 ROAD2DC of the Basque Government. The work of both authors is supported by the Air Force Office of Scientific Research (AFOSR) under Award NO: FA9550-18-1-0242.
We study the null-controllability properties of a one-dimensional wave equation with memory associated with the fractional Laplace operator. The goal is not only to drive the displacement and the velocity to rest at some time-instant but also to require the memory term to vanish at the same time, ensuring that the whole process reaches the equilibrium. The problem being equivalent to a coupled nonlocal PDE-ODE system, in which the ODE component has zero velocity of propagation, we are required to use a moving control strategy. Assuming that the control is acting on an open subset $\omega(t)$ which is moving with a constant velocity $c\in\mathbb{R}$, the main result of the paper states that the equation is null controllable in a sufficiently large time $T$ and for initial data belonging to suitable fractional order Sobolev spaces. The proof will use a careful analysis of the spectrum of the operator associated with the system and an application of a classical moment method.
Citation: Umberto Biccari, Mahamadi Warma. Null-controllability properties of a fractional wave equation with a memory term. Evolution Equations & Control Theory, doi: 10.3934/eect.2020011
##### References:
show all references | 2020-03-30 14:13:32 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.28810983896255493, "perplexity": 611.3297966756054}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-16/segments/1585370497042.33/warc/CC-MAIN-20200330120036-20200330150036-00272.warc.gz"} |
https://zbmath.org/?q=rf%3A123953 | ## Indecomposable matrices over a distributive lattice.(English)Zbl 1164.15326
Summary: The concepts of indecomposable matrices and fully indecomposable matrices over a distributive lattice $$L$$ are introduced, and some algebraic properties of them are obtained. Also, some characterizations of the set $$F_n(L)$$ of all $$n\times n$$ fully indecomposable matrices as a subsemigroup of the semigroup $$H_n(L)$$ of all $$n\times n$$ Hall matrices over the lattice $$L$$ are given.
### MSC:
15B33 Matrices over special rings (quaternions, finite fields, etc.) 15A18 Eigenvalues, singular values, and eigenvectors 06D05 Structure and representation theory of distributive lattices
Full Text:
### References:
[1] G. Frobenius: Über Matrizen aus nichtnegativen Elementen. Sitzb. d. Preuss, Akad. d. Wiss. (1912), 456–477. · JFM 43.0204.09 [2] M. Marcus, H. Minc: Disjoint pairs of sets and incidence matrices. Illinois J. Math. 7 (1963), 137–147. · Zbl 0122.24901 [3] Š. Schwarz: The semigroup of fully indecomposable relations and Hall relations. Czechoslovak Math. J. 23 (1973), 151–163. · Zbl 0261.20057 [4] C. Y. Chao: On a conjecture of the semigroup of fully indecomposable relations. Czechoslovak Math. J. 27 (1977), 591–597. · Zbl 0384.20051 [5] C. Y. Chao, M. C. Zhang: On the semigroup of fully indecomposable relations. Czechoslovak Math. J. 33 (1983), 314–319. · Zbl 0524.20045 [6] J. Y. Shao, Q. Li: On the indices of convergence of an irreducible Boolean matrix. Linear Algebra Appl. 97 (1987), 185–210. · Zbl 0634.15008 [7] J. Y. Shao, Q. Li: The index set for the class of irreducible Boolean matrices with given period. Linear and Multilinear Algebra 22 (1988), 285–303. · Zbl 0637.15013 [8] R. A. Brualdi, B. L. Liu: Fully indecomposable exponents of primitive matrices. Proc. Amer. Math. Soc. 112 (1991), 1193–1202. · Zbl 0736.05038 [9] X. J. Wu, J. Y. Shao: The index set of convergence of irreducible Boolean matrices. J. Math. Res. Exposition 12 (1992), 441–447. (In Chinese.) · Zbl 0777.15011 [10] J. Y. Shao: On the indices of convergence of irreducible and nearly reducible Boolean matrices. Acta Math. Appl. Sinica 15 (1992), 333–344. (In Chinese.) · Zbl 0762.05028 [11] Y. J. Tan: The semigroup of Hall matrices over a distributive lattice. Semigroup Forum 61 (2000), 303–314. · Zbl 0970.20047 [12] Y. J. Tan: Primitive lattice matrices. Southeast Asian Bull. Math.. To appear. [13] Y. J. Tan: On compositions of lattice matrices. Fuzzy Sets and Systems 129 (2002), 19–28. · Zbl 1014.15011 [14] Y. Giveón: Lattice matrices. Information and Control 7 (1964), 477–484. · Zbl 0154.01103 [15] K. H. Kim: Boolean Matrix Theory and Applications. Marcel Dekker, New York, 1982. · Zbl 0495.15003
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching. | 2022-12-07 16:26:48 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.760803759098053, "perplexity": 2302.6301060221995}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446711200.6/warc/CC-MAIN-20221207153419-20221207183419-00658.warc.gz"} |
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# Mantel's Theorem
## An Introduction to Mantel's Theorem
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We will examine numerous crucial aspects of the Mantel Theorem. Mantel's theorem, established by Willem Mantel in 1907, is the basis of extremal graph theory and implies that any graph on n vertices without a triangle contains at most $\dfrac{{{n^{\;2}}}}{4}$ edges. By splitting the collection of n vertices into two sets of size $\left[ {\dfrac{n}{2}} \right]$ and $\left[ {\dfrac{n}{2}} \right]$, one may build the entire bipartite graph between them, making this the best feasible scenario. There are $\left[ {\dfrac{{{n^2}}}{4}} \right]$ edges and no triangles in this graph. Let's understand the basics by stating and proving the Mantel theorem.
## What is Mantel's Theorem?
If there are no triangles in a graph G on n vertices, then the number of edges is at most $\dfrac{{{n^{\;2}}}}{4}$.
Triangle Free Graph
## Mantel's Theorem Proof
Consider G to have m edges. Let x and y represent two G vertices that are connected by an edge. We can see that d(x) + d(y) ≤ n if d(v) is the degree of a vertex v. This is since each vertex in graph G is only connected to one of x and y. Now observe that
$\mathop \sum \limits_x {d^{\;2\;}}\left( x \right)\; = \mathop \sum \limits_{\;xy \in E\;} \left( {d\left( x \right)\; + \;d\left( y \right)} \right)\; \le \;mn$
On the other hand, the Cauchy–Schwarz inequality suggests that because $\mathop \sum \limits_x \;d\left( x \right)\; = \;2m,$
$\mathop \sum \limits_x \;{d^{\;2\;}}\left( x \right)\; \ge \;\dfrac{{{{\left( {\;\mathop \sum \limits_x \;d\left( x \right)} \right)}^2}\;}}{n}\; \ge \dfrac{{\;4{m^2}\;\;}}{n}$
Therefore,
$\dfrac{{4{m^2}}}{n} \le mn$
and the result follows.
## Applications of Mantel's Theorem
• This theorem can be applied to determine how many edges an N-vertex graph can have while still being free of triangles.
• Mantel's theorem graph theory is the basis for the external graph theory.
## Mantel’s Theorem Examples
1. Show that there are $\left[ {\dfrac{{{n^2}}}{4}} \right]$ edges in the n-vertex complete balanced bipartite graph. It implies that some graphs can reach the bound in Mantel's theorem.
Ans: A triangle subgraph does not exist in the n-vertex complete bipartite graph with class sizes $\left[ {\dfrac{n}{2}} \right]$ and $\left[ {\dfrac{n}{2}} \right]$, and the graph has exactly $\left[ {\dfrac{n}{2}} \right]\left[ {\dfrac{n}{2}} \right]\; = \left[ {\dfrac{{{n^2}}}{4}} \right]$ edges. There are no graphs without triangles that have more edges than what is stated by Mantel's theorem.
2. Using an induction method that eliminates two nearby vertices, demonstrate Mantel's theorem.
Ans: Assume n > 2 and that the theorem's statement is true for smaller graphs because if n = 1, 2, we are finished. Let $xy\;$be an edge of graph G, which has n vertices and no triangles, and let G be the graph. Since the graph G - xy has n - 2 vertices and is manifestly triangle-free, it can be inferred that it has no more than $\left[ {\dfrac{{{{\left( {n - 2} \right)}^2}}}{4}} \right]$ edges. At most n edges incident on the edge $$xy$$ (otherwise, there is a triangle). Thus, G can only have
$1\; + \;\left( {n - \;2} \right)\; + \dfrac{{\;{{\left( {n - \;2} \right)}^2}}}{4} = \dfrac{{{n^2}}}{4}$ edges.
3. If G is a triangle-free graph, then there are no common neighbours for neighbouring vertices. Therefore, we have $d\left( x \right)\; + \;d\left( y \right)\; \le \;n$ n for an edge $xy\;$ (remember to count the edge $xy\;$ twice). Use it in the following equation to support your case that it is correct.
$\mathop \sum \limits_{x \in V\left( G \right)} d{\left( x \right)^2}\; = \mathop \sum \limits_{xy \in E\left( G \right)} \left( {d\left( x \right)d\left( y \right)} \right)\;$ to obtain Mantel's theorem's proof.
Ans: First, we get
$\mathop \sum \limits_{x \in V\left( G \right)} d{\left( x \right)^2}\; = \mathop \sum \limits_{xy \in E\left( G \right)} \left( {d\left( x \right)d\left( y \right)} \right)\; \le n\left| {E\left( G \right)} \right|$
Utilising Cauchy-Schwarz,
$\dfrac{1}{n}{\left( {\mathop \sum \limits_{x \in V\left( G \right)} d\left( x \right)} \right)^2}\; \le \mathop \sum \limits_{x \in V\left( G \right)} d{\left( x \right)^2}$
The LHS is $\dfrac{{\;1}}{n}(2|E\left( G \right){|^2}\;$ according to the Handshaking lemma. Thus,
$\dfrac{{\;1}}{n}(2|E\left( G \right){|^2}\; \le n\left| {E\left( G \right)} \right|$
Now, the theorem can be obtained by solving for |E(G)|.
## Conclusion
In this article, we have discussed about Mantel's theorem and its proof. With Mantel's theorem, we can evaluate how many edges an N-vertex graph can have in total without having any triangles (which means there should not be any three edges A, B, and C in the graph such that A is connected to B, B is connected to C, and C is connected to A). The graph is not allowed to have many edges or a self-loop. To obtain a graph without triangles, it is necessary to remove almost half of the edges.
## Important Points From the Theorem
• Only if m = $\dfrac{{{n^{\;2}}}}{4}$ is a graph G maximally triangle-free with regard to edges.
• It is necessary to eliminate roughly half of the edges in order to produce a graph without triangles.
• If a graph contains no cliques greater than three, then it satisfies Mantel's Theorem that it has few edges.
Competitive Exams after 12th Science
## FAQs on Mantel's Theorem
1. What is a triangle-free graph?
A triangle-free graph is an undirected graph in the mathematical field of graph theory where no three vertices form a triangle of edges. Triangle-free graphs can also be described as having a clique number of two or less, a girth of four, the absence of an induced 3-cycle, or locally independent graphs.
Balanced complete bipartite graphs are triangle-free graphs with the greatest number of edges per vertex. Many triangle-free graphs, such as any cycle graph Cn for odd n > 3, are not bipartite.
2. What does a complete bipartite graph mean?
A complete bipartite graph is a particular type of bipartite graph in the study of graph theory where each vertex in the first set is connected to each vertex in the second set. Every potential edge that might connect vertices in distinct subsets is present in a full bipartite graph, which has vertices that can be partitioned into V1 and V2 subsets such that no edge has both of its endpoints in a single subset. It is a bipartite graph (V1, V2, E), which means that there is an edge in E for each pair of vertices v1 and v2.
3. What is Turan's Theorem, and how does it relate to or contrast with Mantel's Theorem?
A graph has few edges if there aren't any cliques greater than three, according to Mantel's Theorem. If a graph doesn't have any cliques larger than r+1, Turan's Theorem states that it contains some but few edges.
Furthermore, both theorems are tight, indicating that there are graphs with precisely this many edges. This would be a fully bipartite network for Mantel's Theorem, with the left part having n/2 vertices, the right half having n/2 vertices, and the graph having all edges connecting these two sections. This will be exactly n square/4 edges, according to Mantel's Theorem. | 2023-04-02 06:26:38 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5964114665985107, "perplexity": 385.88122319650546}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296950383.8/warc/CC-MAIN-20230402043600-20230402073600-00477.warc.gz"} |
https://thundergbm.readthedocs.io/en/latest/parameters.html | # ThunderGBM Parameters¶
This page is for parameter specification in ThunderGBM. The parameters used in ThunderGBM are identical to XGBoost (except some newly introduced parameters), so existing XGBoost users can easily get used to ThunderGBM.
## Key Parameters¶
• verbosity [default=1]
• Printing information: 0 for silence and 1 for printing more infomation.
• max_depth [default=6]
• The maximum depth of the decision trees. Shallow trees tend to have better generality, and deep trees are more likely to overfit the training data.
• num_round [default=40]
• The number of training iterations. num_round equals to the number of trees in GBDTs.
• n_gpus [default=1]
• The number of GPUs to be used in the training.
• data [default=“../dataset/test_dataset.txt“]
• The path to the training data set
• max_bin [default=255]
• The maximum number of bins in a histogram.
• colsample [default=1]
• The sampling ratio of subsampling columns (i.e., features)
• bagging [default=0]
• This option is for training random forests. Setting it to 1 to perform bagging.
• num_parallel_tree [default=1]
• This option is used for random forests to specify how many trees per iteration.
• eta [default=1, alias: learning_rate]
• valid domain: [0,1]. This option is to set the weight of newly trained tree. Use eta < 1 to mitigate overfitting.
• objective [default=“reg:linear“]
• valid options include reg:linear, reg:logistic, multi:softprob, multi:softmax, rank:pairwise and rank:ndcg.
• reg:linear is for regression, reg:logistic is for binary classification.
• multi:softprob and multi:softmax are for multi-class classification. multi:softprob outputs probability for each class, and multi:softmax outputs the label only.
• rank:pairwise and rank:ndcg are for ranking problems.
• num_class [default=1]
• set the number of classes in the multi-class classification. This option is not compulsory.
• min_child_weight [default=1]
• The minimum sum of instance weight (measured by the second order derivative) needed in a child node.
• lambda [default=1, alias: reg_lambda]
• L2 regularization term on weights.
• gamma [default=1, alias: min_split_loss]
• The minimum loss reduction required to make a further split on a leaf node of the tree. gamma is used in the pruning stage.
• model_out [default=“tgbm.model“]
• The file name of the output model. This option is used in training.
• model_in [default=“tgbm.model“]
• The file name of the input model. This option is used in prediction.
• tree_method [default=“auto“]
• “auto“: select the approach of finding best splits using the builtin heuristics.
• “exact“: find the best split using enumeration on all the possible feature values.
• “hist“: find the best split using histogram based approach. | 2019-09-16 20:05:44 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5059903860092163, "perplexity": 7985.140317076271}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-39/segments/1568514572934.73/warc/CC-MAIN-20190916200355-20190916222355-00556.warc.gz"} |
https://www.oecd-ilibrary.org/sites/5ffa7926-en/index.html?itemId=/content/component/5ffa7926-en | # copy the linklink copied!Chapter 2. Non-standard forms of work and pensions
This chapter looks into pension arrangements for non-standard workers across OECD countries. Non-standard workers are defined as workers not covered by full-time open-ended contracts, i.e. part-time, temporary or self-employed workers, in particular those undertaking new forms of work. The analysis starts with describing the relevant characteristics of non-standard workers, then it depicts related pension issues and details the specific pension rules applying to them. These lead to discussing policy options on how to make pension systems more inclusive given transforming labour markets. The chapter fits into a broader OECD work stream focused on the Future of Work and the Future of Social Protection.
Non-standard work is an umbrella term referring to a wide range of jobs. Non-standard workers can be independent contractors who work alone, self-employed workers potentially employing other people, dependent employees working part-time, workers on temporary contracts, casual workers, platform workers and other workers who are not in “standard” employment, i.e. working full-time and on open-ended contracts for a single employer (OECD, 2019[1]). Depending on the type of non-standard work, working conditions, job security and social protection rules vary considerably, highlighting that non-standard workers are far from being a homogenous group.
Many types of non-standard work raise concerns in terms of social protection in general and pension protection in particular (Chapter 7 in OECD (2019[1])). In several OECD countries, all or some types of self-employed workers are exempt from enrolling in earnings-related pensions that are mandatory for dependent employees, increasing the risk of low old-age income. In addition, part-time and temporary workers do not have access to the same pension protection as standard workers in some countries.
While the debate on pensions for non-standard workers is not new, the topic is of growing importance. Globalisation, automation and demographic changes transform labour markets at a rapid pace, potentially leading to an expansion of non-standard work. There is a high degree of uncertainty around how labour markets will look in the future, but one possible outcome is that there will be a rising number of non-standard workers. Countries must prepare for this possibility because labour markets can change quickly while policy responses, especially in the area of pensions, are often difficult processes and it can take a long time until their effects become apparent.
The emergence of “new” forms of work raises concerns on how workers engaged in such activities are covered for future pensions. “New” forms of work refer to platform work, very short-term contracts, so-called zero-hour contracts, i.e. contracts with no guaranteed working hours and, more generally, further types of own-account work. Many workers on such contracts have a high degree of flexibility in organising their work, but a low degree of job security and low earnings. Furthermore, governments struggle to organise pension protection for new forms of work; indeed, under such contracts, it is sometimes difficult to define to what extent workers are self-employed or dependent while some related work might remain informal. While new forms of work currently account for a small share of total employment only, they have the potential of becoming a large group of workers in the future.
All types of non-standard work combined, non-standard employment accounts for more than one-third of employment in OECD countries (Section 1). Many workers remain in non-standard employment for a long time. Non-standard workers often earn less than standard workers, face higher unemployment risks and have interrupted pension contribution histories. Moreover, they are less comprehensively covered by pension systems. All these factors add up, possibly leading to low pensions for a large group of older people.
This chapter takes stock of different approaches to organising pensions for non-standard workers in OECD countries. Section 2 sets the scene by summarising labour market trends in non-standard employment, showing that it is not an isolated phenomenon. Section 3 discusses why non-standard work raises pension issues, highlighting that different types of non-standard work pose different challenges. Section 4 describes pension rules for non-standard workers, distinguishing rules for the self-employed, part-time workers and temporary workers. Section 5 examines how pensions for non-standard workers could be improved. Section 6 concludes.
### Non-standard work accounts for a considerable share of employment
While full-time dependent employment based on an open-ended contract - referred to as standard work - is the most widespread form of work, non-standard work is relatively frequent and far from being an isolated phenomenon. In OECD countries, about 15% of workers were self-employed in 2017, and 13% and 15% of dependent employees were, respectively, on temporary contracts or worked part-time, i.e. less than 30 hours a week, with half of them working less than 20 hours a week. Some workers combine different dimensions of non-standard work, e.g. working part-time and on temporary contracts. Altogether, non-standard work accounts for more than one-third of total employment in OECD countries.
#### Part-time work
In many OECD countries, part-time work has been on the rise over the years. In about two-thirds of OECD countries, its share among all dependent employment is higher today than 20 years ago (OECD, 2019[1]). In addition, short part-time work (i.e. working 20 hours or less per week) had also increased from 6% of dependent employment in 1985 to 9% in 2005 for the 13 countries for which data are available and has remained broadly stable since then. These long-term increases were driven by several factors, including more women entering employment on a part-time basis, changing life-style choices and possibly changing labour demand.
While two out of three part-time workers in OECD countries worked part-time by choice in 2017, one in three would have preferred to work longer hours, implying that they were underemployed (OECD, 2019[1]). The scope of underemployment varied a lot across countries, from less than 2% of dependent employment in the Czech Republic, Estonia, Japan, Hungary and Turkey to above 10% in Australia, Italy and Spain. Compared to 2006, underemployment increased in two-thirds of OECD countries, from 4.3% to 5.4% of dependent employment on average across countries. While the rise of underemployment was particularly marked in countries that were hard hit by the economic crisis, it cannot be entirely ascribed to temporary fluctuations and high cyclical unemployment, but was also driven by structural changes.
#### Temporarywork
Temporary employment has followed a long-term upward trend. Among the 14 OECD countries for which data are available, it increased from about 10% of dependent employment in the mid-1980s to 13% in 2000 and 14% in 2017. An average increase of 1 percentage point between 2000 and 2017, from 11% to 12%, is also found for a broader group of 27 OECD countries. This long-term trend was caused by both gradual developments and rapid changes.
Temporary employment in Poland boomed during the country’s strong economic expansion between 2001 and 2007, increasing from 12% of total employment to 28%, and stabilised at this very high level afterwards (Figure 2.1, Panel A). Other countries reported sustained, albeit less pronounced increases, e.g. Italy, Luxembourg, the Slovak Republic and Slovenia. By contrast, following two decades of record-high levels of temporary employment, the share of temporary contracts in Spain fell from 34% to 26% between 2006 and 2009 (Panel B). Similar declines took place in Turkey and in Japan. In Lithuania, after peaking at 7% in 2002, the share of temporary workers in employment shrank to 2% in 2008 and has remained roughly stable afterwards.
The upward trend of temporary work coincides with decreasing job tenure. When adjusted for changes in the age structure of the workforce, average job tenure decreased by 5%, or almost five months, in OECD countries between 2006 and 2017, especially affecting workers with low education (OECD, 2019[1]). Yet, the United States is a notable exception as it has experienced an increase in average job tenure over the last two decades, mainly due to a decline in very short employment spells (Pries and Rogerson, 2019[2]). However, job tenure and the use of temporary contracts have evolved in the same direction over the last decade in Australia, Canada, Estonia, Greece and Lithuania (OECD, 2019[1]).
#### Self-employment
The share of self-employment among total employment declined from 17% to 15% between 2000 and 2017 in OECD countries on average. This drop is not a new phenomenon, but rather the most recent episode of a continuing long-term trend. Several dynamics contributed to this trend. The agricultural sector, for instance, has experienced a significant concentration over the last decades and many formerly independent farmers switched jobs, becoming employees, often in other sectors. By contrast, in the media sector, digitalisation has affected traditional providers by facilitating remote cooperation and has led to a large number of more flexible but less protective freelance contracts.
Decreases in the share of self-employment were particularly strong in countries that were economically catching up, such as Hungary, Korea, Poland, Portugal and Turkey. However, the picture is not uniform and the share of self-employment in total employment increased in some OECD countries, including the Czech Republic, Estonia, the Slovak Republic and the Netherlands. In some cases, clearly identifiable factors explain the increasing trend at least partially, e.g. lower taxes and social-security contributions in the Netherlands (Milanez and Bratta, 2019[3]) and in Italy (Box 2.1 further below).
### Non-standard work is undergoing transformation
Non-standard work is undergoing substantive transformation. In recent years, the decline of some types of self-employment including in agriculture has been partly offset by the emergence and expansion of new forms of non-standard work, in particular jobs relying on new technologies, such as platform-based taxi-like drivers. While today this type of work accounts for only 0.5-3% of total employment in developed countries, it is of considerable importance for young people who rely on new forms of work more frequently than older generations and some of whom seem to set a higher value on work autonomy (OECD, 2019[1]).
New work arrangements make the boundary between dependent work and self-employment even less clear-cut than it used to be. For example, some self-employed workers are very similar to dependent employees in the sense that they only have one single client, lack financial independence and have limited control over their working conditions, including their work schedule. On average in the OECD, 16% of own-account workers have one predominant client, with the rate ranging from 6% in Denmark to 29% in the Slovak Republic (OECD, 2019[1]). While having only one client does not necessarily mean that a person is wrongfully classified as self-employed there is the risk that false self-employment is common among such workers. Pension contributions, and more generally social security contributions that are substantially lower for independent workers than for dependent employees might indeed encourage social dumping, with some employers trying to lower their labour costs by outsourcing work instead of hiring dependent workers (Milanez and Bratta, 2019[3]).
New technologies can help formalise home-based activities that were not classified as formal employment in the past, such as work tasks or gigs performed over internet. Internet platforms have the potential – albeit only marginally exploited for now – of improving the formalisation of independent contractors’ work, e.g. by documenting their working hours and actual income, thereby providing a reliable basis for pension contributions. However, the distinction from non-commercial home production can be particularly challenging, for example because some platforms remunerate workers using platform-specific points, gifts or crypto-currencies (Mineva and Stefanov, 2018[4]).
Within dependent employment, too, new forms of work have emerged and expanded over the last two decades (OECD, 2019[1]). As is the case with self-employment, more risks are transferred from employers to employees or other parties in these new employment arrangements. In the case of temporary work agencies, an agency hires workers and assigns them to a user firm. Thus, contrary to most platform work, an employment contract exists, but the employer role is divided between an agency and an actual principal. On-call and zero-hour contracts do not guarantee working hours, implying that a worker’s monthly income is unpredictable. Such contracts exist in some OECD countries, including Australia, Ireland, the Netherlands, New Zealand and the United Kingdom.
### Non-standard work is frequent among workers over 65 and women
Non-standard work is common among older workers. While overall employment rates decrease at older ages, the share of non-standard work is particularly high among workers over 65: only about 15% of workers between 65 and 74 are in standard employment, against more than 60% at ages 55-64 and 25-54 (Figure 2.2, Panel A).
One-third of workers aged 65-74 are employees working part-time, compared to 16% among 55-64 year-olds and 13% among 25-54 year-olds. Part-time work enables older workers to gradually withdraw from the labour market, especially when reduced earnings are offset by full or partial pension benefits (OECD, 2017[5]). Still, combining work and pensions is uncommon across OECD countries: more than 5% of people aged 60-69 combine work and pensions in Denmark, Estonia, Israel, Sweden, Switzerland and the United States only (OECD, 2019[6]). In contrast to part-time work, temporary employment is not particularly common among older workers, with only 5% of 55-64 year-old and 14% of 65-74 year-old workers working as employees on temporary contracts, against 9% among 25-54 year-olds and 37% among 15-24 year-olds.
Self-employment, too, is frequent among older workers. Many self-employed only become independent workers at later stages of their career, which is one factor explaining why the self-employed tend to leave the labour market later than other types of workers. The share of self-employed workers in total employment is 38% among the 65-74 year-olds, compared to 18% among 55-64 year-olds and 13% among 25-54 year-olds (Figure 2.2, Panel A). A further reason why the self-employed work longer is that they are less directly affected by legal and institutional obstacles to longer working lives, such as mandatory retirement ages and workplace pressure to retire at a specific age, which is common for example in Korea (OECD, 2018[7]). Seven in ten self-employed workers in the United States expect to retire after age 65 or not at all and six in ten plan to work in retirement (Transamerica, 2019[8]). Self-employment enables a smooth transition from work to retirement because it allows workers to reduce working hours at their own discretion.
Non-standard work is also common among women, in particular part-time work. One reason is that part-time work enables to reconcile care and work responsibilities and care tasks are still today mostly carried out by women (OECD, 2017[9]). Part-time work is three times more frequent among working women than among working men, and one in four working women works part-time in the OECD (Figure 2.2, Panel B). Part-time work may compromise career prospects, however, and be an obstacle to the economic independence of women within families (OECD, 2019[10]). By contrast, self-employment is more frequent among men.
### Non-standard work generates low earnings and is often persistent
Non-standard workers have, on average, lower earnings than full-time employees on permanent contracts. Across the 19 OECD countries for which data are available, part-time and temporary workers earn around 50% less per year than full-time workers, with the difference being much wider in some countries such as Latvia and Spain (Figure 2.3). The difference is due to a lower hourly pay, a lower number of hours worked (e.g. part-time workers) and employment breaks (e.g. temporary workers). When controlling for employee’s and employer’s characteristics, OECD (2015[11]) finds an hourly wage penalty of 12% for temporary workers.
Median full-time self-employed workers earn 16% less than full-time employees on average across OECD countries, but there is substantial variation across countries.1 In Estonia, Latvia and Spain median full-time self-employed workers earn less than 70% of a median full-time dependent worker’s wage while in France, Lithuania and the Slovak Republic, they earn more than 100% of it.
In many cases, non-standard employment is not a short episode interrupting a worker’s career in standard employment. On average across the OECD, 87% of standard employees remain (or are again) standard employees within a two-year timeframe, while 78% of full-time self-employed workers and 54% of part-time workers keep their employment status (Figure 2.4).2 OECD (2015[11]) points out that even when controlling for other characteristics, the transition rates from temporary to permanent work often remain below 50% over three years. In many countries, temporary work improves chances to find a permanent position while this is less often the case for self-employment and part-time work.3
### Combining independent with dependent employment is common
Self-employment is not the only source of earnings for many self-employed workers. Self-employment represents more than two-thirds of earnings for 59% of people with any income from self-employment in a given year on average across countries (Figure 2.5).4 For 14% of them, income from dependent and independent work are similarly important and for 27% self-employment is rather a supplementary activity, providing less than one-third of their total earnings.5
Current pension outcomes for non-standard workers can be enhanced in many countries. Improving pension rules for these workers is challenging, however. Compared to full-time employees on open-ended contracts, non-standard workers have a number of characteristics that make their pension treatment complex. The self-employed, in particular, are the group that raises the most serious issues in terms of pension coverage because, in contrast to other types of work, they do not have a formalised employment relationship (employment contract) that can be used as a verified basis for pension contributions. The emergence and expansion of new forms of work has amplified the pension issues related to non-standard work, especially among low-income earners. As most pension systems were built on the premise of stable, linear careers, the development of new forms of work raises concerns about old-age income prospects of future generations of retirees.
### Temporary and part-time contracts raise challenges for pension adequacy
Temporary contracts often provide employment protection less comprehensively than open-ended contracts and temporary workers less often reach job tenure needed to benefit from the full protection. It is generally relatively easy and cheap for employers to end a fixed-term contract upon its term - i.e. not to renew it - while they have to comply with notice periods and make severance payments when they lay off workers on permanent contracts. In many countries, people out of employment continue to acquire pension rights as long as they receive unemployment benefits. While this instrument cushions the effect of job losses on pensions, it is only partially effective for temporary workers. Due to frequent job changes and job losses, temporary workers tend to have comparatively short employment tenure, often resulting in shorter unemployment benefit durations or restricted access to unemployment benefits.
More directly, short employment spells bear the risk that workers do not fulfil the minimum number of working days required to credit work periods (often a month or a quarter) towards entitlements to contribution-based pension benefits. In addition, some types of temporary contracts in several countries do not generate pension entitlements.6 In particular, agency work, casual work, seasonal work and traineeships are excluded from pension coverage in some countries despite being covered by employment contracts.
Frequent job changes within temporary employment also result in lower occupational pension coverage. Pension vesting periods can have negative effects on the pension rights of temporary workers because of their short tenure. Due to a lack of portability, work spells at different companies do not always add up, and frequent job changes lead to lower pension entitlements. In addition, entitlements can be paid out as a lump sum upon contract termination (Chapter 3), defeating the purpose of offering protection in old age.
Part-time work, too, poses pension challenges. In some cases, part-time work leads to full crediting of contribution periods. In others, periods of part-time work are not taken into account for calculating pension entitlements, and, in particular in some countries, validating a specific period requires working a minimum number of hours or earning a minimum level of income. Such exclusions increase the risk that workers fail to meet the eligibility conditions both for first-tier contributory and earnings-related pensions, or that they only meet them if retiring at older ages.
Both temporary and part-time work are often associated with low income, e.g. due to more time out of employment or fewer hours worked. Low income during the working life spills over to low old-age income. Moreover, weak workplace attachment due to temporary contracts and part-time work reduces the opportunities to acquire job-specific skills and limits access to job-level training. As a result, low earnings are associated with more patchy careers and shorter total contribution periods, which additionally lowers retirement income for low-earners (Valdés-Prieto and Leyton, 2019[12]). Hence, contribution-length requirements of 10 or more years to access earnings-related pensions can substantially reduce pensions of non-standard workers with low earnings.
### The self-employed have lower pensions than employees
Former self-employed tend to have lower public pensions than former employees.7 On average across 15 OECD countries, the retired self-employed receive, at the median, 22% lower public pensions than retired employees (Figure 2.6, Panel A). The gap is much smaller, typically below 10%, in countries with substantial basic pensions, such as the Czech Republic, Denmark, Israel and Switzerland. By contrast, retirees who were self-employed in France, Germany, Italy, Luxembourg and Poland have median pensions that are more than 30% lower than among former employees.
The lower public pensions of the self-employed are not offset by more private occupational pensions. The former self-employed receive occupational pension from either dedicated schemes or from entitlements earned as dependent workers. In all five countries with private occupational pension coverage of at least 10% of pensioners in the SHARE survey, namely Denmark, Germany, Israel, Sweden and Switzerland, coverage rates among retirees are much larger among former employees than among former self-employed (Figure 2.6, Panel B). Occupational private pension coverage among former self-employed workers is highest in Sweden, at 28%.8 The low coverage of self-employed workers widens the income gap between the self-employed and employees upon retirement.
Partly as a result of lower public pensions and lower coverage by occupational schemes, the former self-employed tend to have lower old-age income than former employees in many countries. The median retired self-employed has a disposable income that is, on average in the 14 OECD countries for which data are available, 16% lower than that of retired employees (Pettinicchi and Börsch-Supan, 2019[13]).9 It is more than 20% lower in Finland, France, Poland and Spain.
In the majority of countries, the income gap between the self-employed and employees is wider among retirees than among older workers (older than 50 years). On average across countries, it equals 6% among workers (at the median) against 16% among retirees as discussed above, a gap of 10 percentage points. In Italy and Spain, the gap is more than 30 percentage-point larger among current retirees than among current workers.10 This seems paradoxical given that redistributive mechanisms in pension systems aim to reduce inequalities in old age. Among possible explanations is the fact that the self-employed contribute less to pensions (see further on in this section).
### Wealth does not outweigh lower pensions for most of the self-employed
One common argument for a lower level of needed protection from mandatory pensions for the self-employed is that they have more private saving, e.g. liquid savings or capital invested in their business. However, while the situation can vary greatly among the self-employed, the median assets of the self-employed are only slightly higher than the median assets of employees. This pertains even to retired former self-employed who have typically already liquidated the capital they had invested in their businesses.
Compared to the median (in terms of assets) employee, the median self-employed has a higher net liquid assets11 to annual income ratio, both when working (1.2 against 0.8) and after retirement (1.0 against 0.7), on average in the OECD (Figure 2.7). These numbers mean that the liquid assets of a median retired self-employed equal 12 months of retirement income, compared to 9 months for employees. Retired self-employed have relatively more assets than retired employees in 10 of the 17 covered countries, but their additional assets correspond to more than 12 months of income only in Belgium and Denmark; hence, the impact on the capacity to finance consumption over the whole retirement period is not substantial in most countries (Panel A). Moreover, while active, the self-employed have higher assets-to-income ratios than employees in all countries shown in Panel B except the Czech Republic, Germany and Israel, whereas differences are smaller among retirees.
Evidence from the United States suggests that among business owners, including sole proprietors, voluntary pension savings and house ownership are complement rather than substitute: business owners are more likely to participate in voluntary pension plans if they own a house (Lichtenstein, 2010[14]). As a result, retired self-employed workers with low pensions are also less likely to dispose of assets in the form of housing, making them a financially vulnerable group. Many former self-employed workers do not dispose of a sufficient level of assets to offset low pension entitlements and to justify exempting them from enrolling in pension schemes.12 Furthermore, in the Netherlands, more frequent home ownership among the self-employed than employees cushions only partially the impact of lower pensions on consumptions. 13
### The self-employed contribute less to old-age pensions than employees
In many countries, the self-employed are less comprehensively covered by mandatory pensions than dependent employees. A range of indicators suggests that the self-employed pay lower pension contributions than employees with similar earnings. In many countries, the share of social-security contributions paid by self-employed workers in total contributions is much lower than the share of self-employment in total employment (Figure 2.8, Panel A) - including informal self-employed workers and employees - which cannot be explained by differences in contributions to unemployment insurance. The stark differences suggest that there is a substantial public pension coverage gap between the self-employed and employees.
The share of contributions paid by the self-employed is less than half the share of self-employment in total employment in Canada, Hungary, Ireland, Korea, Latvia, Portugal, the Slovak Republic, Sweden, Switzerland, Turkey and the United Kingdom. In Italy, Korea and Turkey, where the self-employed account for about one-quarter of total employment or more, coverage gaps are likely to affect a particularly large number of people, leading to lower pensions for many in the future. In countries with contribution-based basic pensions, such as Ireland and the United Kingdom, there is no close link between the amount of contributions and entitlements and the impact on future pensions is likely to be smaller.
A low number of contributors towards pensions is a second measure hinting to contribution gaps among the self-employed. This measure has the advantage of covering pensions only (rather than social security), but is available for a limited number of countries. The ratio of the self-employed to employees is typically considerably lower among contributors than among all workers; the difference is particularly large in Chile, Latvia, Portugal and Turkey (Panel B). In these countries, the low number of self-employed workers contributing to the pension scheme is likely to be the main reason for contribution gaps, i.e. a lot of self-employed workers do not contribute to earnings-related pensions at all. Conversely, the number of contributors does not show substantial gaps in Canada, Ireland and Hungary, suggesting that contribution gaps are primarily driven by lower contributions per contributor.
Further evidence from OECD countries suggests that the self-employed pay comparatively low levels of pension contributions. In Poland, the Slovak Republic, Slovenia, and Spain, 70% or more of the self-employed pay only compulsory minimum pension contributions (Spasova et al., 2017[15]). In the United Kingdom, 27% of full-time self-employed men had active pension accounts in 2012-13, compared to 51% of full-time male dependent employees (D’Arcy, 2015[16]).
A high degree of discretion in setting the contribution base, no requirement to participate in earnings-related pension schemes, reduced incentives to participate in voluntary schemes and potentially lower contribution rates are the most important factors explaining why many self-employed workers pay lower pension contributions than dependent workers. In some cases, lower contributions for the self-employed are the result of policies aimed at increasing total employment, promoting entrepreneurship, raising labour income of some occupational groups such as farmers or increasing incentives to work as a self-employed by raising take-home pay.
Lower pension contributions for the self-employed are sometimes justified as a way to reflect the specific preferences of the self-employed to manage their own finances (including old-age savings) and/or remain outside of standard pension schemes (Karpowicz, 2019[17]). The self-employed also tend to have a lower degree of risk aversion (Ekelund et al., 2005[18]; Colombier et al., 2008[19]). These preferences might be related to limited confidence in public pensions (ISSA, 2012[20]). In some countries, such as Germany and the Netherlands, the self-employed have opposed against being integrated into employee pension schemes (Kautonen et al., 2010[21]).
However, the consequences of low contributions might be severe, both today and in the future. Lower contributions first deteriorate the finances of PAYGO schemes in many OECD countries. In the future, low contributions typically translate into low old-age income and to greater reliance on non-contributory benefits, which in turn adds to the fiscal pressure stemming from population ageing. Furthermore, lower pension contribution rates for at least some types of the self-employed might create financial incentives for companies to hire independent workers instead of hiring standard workers, raising concerns regarding false self-employment and social dumping (Box 2.1).
Minimum pensions and contributory basic pensions play a key role in preventing and alleviating old-age poverty. In most cases, the amount of contributions to these schemes does not increase entitlements. In such a situation, the incentives to reduce contributions through underreporting of income are strong: it is easier for some categories of workers to do so, in particular self-employed workers.14
Box 2.1. Do lower pension contributions for the self-employed erode standard employment?
When pension contributions, and social security contributions more generally, are lower for the self-employed than for workers in standard employment, companies may face financial incentives to outsource tasks to independent contractors rather than hiring dependent employees and paying employer contributions. Similarly, workers might opt for higher net wage at the cost of lower protection. This problem has lately become an important topic in the public policy debate and there is controversy around the social protection of workers in such activities, e.g. food delivery drivers.
This phenomenon is not new, however. In Italy, so-called para-subordinate collaborators used to pay substantially lower pension contributions than standard employees for many years, including in cases where they depended significantly or even exclusively on one single contractor. Lower pension contribution rates may have contributed to a quickly growing number of para-subordinate collaborators in Italy in the late 1990s and early 2000s. In order to remove incentives to make excessive use of para-subordinate employment and in an attempt to combat false self-employment, the Italian government gradually increased contribution rates for para-subordinate collaborators over time, along with other policy measures, such as stricter controls to detect false self-employment and more limitations to the use of para-subordinate collaborators. The measures seem to have been effective. After peaking around 2007, the number of para-subordinate collaborators has fallen sharply, by about 40% between 2007 and 2016.
### Integrating the self-employed into employees’ schemes is challenging
Integrating the self-employed into employees’ pension schemes is challenging in practice. Pension contributions for employees are often based on their gross wage, which does not correspond to any category of a self-employed worker’s earnings (Figure 2.10). Gross wages are the sum of employee contributions, related personal income taxes and net wages after tax. They are lower than total labour costs from the employer perspective, as labour costs include employer contributions. By contrast, the total revenue of the self-employed includes gross labour and capital income (before contributions and taxes) as well as work-related expenses and material costs.
For the self-employed, labour and capital income are usually indistinguishable. Some countries artificially separate labour and capital income based on “theoretical wages” (e.g. Finland), but calculation rules for the latter are highly discretionary. Norway and Switzerland allow deducting interests on capital outlays to determine the relevant income for pension contributions. Many countries allow the self-employed either to decide themselves the part of their income that corresponds to labour income or to set contribution bases freely within some limits. Apart from pensions, separating wages from profits poses challenges for tax policies as both are often taxed differently with capital income being often taxed less than labour income (OECD, 2009[23]; OECD, 2015[24]).15
Fully harmonising the pension contribution base between dependent and self-employed workers would thus require either paying contributions on total personal income or precisely separating labour from capital income of the self-employed. The first case implies that contributions would also be paid on returns from savings, including savings from labour income. This would require a profound transformation of employee pensions. In the second case, separating the sources of income without any discretion seems infeasible at least for some groups of self-employed workers. Hence, in general, harmonisation requires leaving the self-employed with some degree of flexibility in determining labour and capital shares.
A separate issue relates to contributions. Applying the full contribution rate for standard employment (i.e. the sum of employers’ and employees’ contributions) to self-employed workers’ total revenue or their gross income would result in higher total contributions than for employees with the same taxable income. Conversely, applying it only to income net of contributions (before tax) would lead to lower contributions paid by the self-employed.
### Income validation, bargaining power and income variability
The self-employed do not have a (distinct) employer, which results in additional complications in designing pensions. First, paying both employee and employer contributions to mandatory pensions may lead to the perception that contributions are a bigger financial burden for the self-employed than for employees, as employer contributions for the latter are less directly visible.
Second, there is thus no employer to validate the income of the self-employed, making it harder to prevent income underreporting (i.e. at least partial informality) and low contributions. Evidence from Spain, for instance, suggests that income underreporting is much more common among the self-employed than among employees (Martinez-Lopez, 2012[25]). Findings from other countries confirm that the self-employed often underreport their earnings (Hurst, Li and Pugsley, 2010[26]; Bucci, 2019[27]). In the United States, a 2018 survey found that 32% of self-employed admittedly underreport their income for tax purposes (Bruckner and Hungerford, 2019[28]). Moreover, the inclination towards informality might be magnified when working with or through the internet platforms, especially if the platforms are based abroad and do not report any transaction data to domestic authorities. In some cases, however, the self-employed might be tempted to choose higher contribution base. For example, in the defined benefit schemes that relate the benefit amount to earnings from the last years before retirement - as opposed to career-long earnings - the self-employed might choose high contribution bases in the last years of their careers to inflate their pensions. For this reason, Spain limits the ceiling to freely-declared contribution base for people at age 47 or older who chose a lower contribution base previously. Furthermore, it is usually not possible to objectively measure a self-employed worker’s working time, implying that hourly wages cannot be calculated in any reliable way. When entitlements to minimum pensions and access to mandatory earnings-related schemes depend on working time, the rules in place for dependent employees cannot be extended to the self-employed without modifications.
Third, stable earnings are one component of an employee’s employment contract because employers carry most of the risks, such as the risk of fluctuating demand. As they bear all the risks, the income of self-employed workers is often subject to substantial variation. As a result, they reach floors and ceilings of pensionable earnings more erratically. Depending on pension rules, income below the floor results in either not paying any contributions and not gaining any entitlement or in paying the minimum contribution; the latter leads to a high effective contribution rate and potentially to liquidity problems. Conversely, exceeding the contribution ceiling results in a lower effective contribution rate.16
Pension rules often provide less comprehensive coverage for non-standard than for standard workers. This section gives an overview of how pension systems integrate non-standard workers, highlighting that there are major differences across countries. It discusses the rules for the self-employed, part-time workers and temporary workers and summarises recent policy changes.
### Self-employment
#### Coverage and scope
The pension coverage of the self-employed varies considerably across OECD countries. While most countries require the self-employed to participate in earnings-related pension schemes, the self-employed contribute in a similar way as employees in only ten countries (Table 2.1, first column). Even in these countries, insufficient compliance with pension rules may undermine pension coverage. In Korea, for example, the majority of the self-employed is not covered by public pensions despite their legal obligation to join the public pension scheme (Kim and Lee, 2012[29]).
In eighteen countries (second to fourth column), self-employed workers are mandatorily covered by earnings-related schemes, but pension coverage is somehow limited because they are allowed to contribute less than employees through reduced contribution rates (second column), a high degree of discretion in setting their income base, which often results in only minimum contributions being paid (third column), or minimum income thresholds below which they are exempt from contribution obligations (fourth column). In Australia, Denmark, Germany, Japan, Mexico and the Netherlands, the self-employed are, in contrast to employees, not required to join earnings-related schemes - the same used to be the case in Chile and Israel, too, but earnings-related schemes have recently become mandatory for self-employed workers.17 Finally, in Ireland and the United Kingdom, the self-employed participate in contributory-based basic schemes on similar terms as employees while the earnings-related schemes are voluntary for all types of workers.
As for voluntary pensions, most countries grant the self-employed access to voluntary private pensions with tax advantages, in line with the situation of employees. In order to compensate for lower coverage in mandatory schemes, the cap for tax-exempt contributions to voluntary schemes is higher for the self-employed than for employees in Belgium, France, Japan and Switzerland. In addition, Belgium, France, Germany, Luxembourg and Japan set up specific voluntary pension programmes for at least some groups the self-employed, which benefit from tax-deductions and subsidies. In New Zealand, Poland, Turkey and the United Kingdom, employees are automatically enrolled in workplace pensions, from which they can opt out, while the self-employed are not (Chapter 3).18
Table 2.1. Self-employed workers do not fully contribute to (quasi) mandatory pensions
Contributions requirements to mandatory and quasi-mandatory pensions for the self-employed, OECD countries
Mandatory or quasi-mandatory contributions to earnings-related schemes
Mandatory contributions to basic pensions only
No mandatory pension contributions
Employee-like
Reduced contribution rate
Only flat-rate contributions mandatory
Regular contributions mandatory only above income threshold
Austria
Poland
Austria
Ireland*
Australia
Czech Republic
Belgium
Spain
Chile
Japan
Denmark
Estonia
France
Turkey
Finland
Netherlands
Germany
Greece
Chile
Latvia
United Kingdom*
Mexico
Hungary**
Iceland
Slovak Republic
Korea
Israel
Turkey
Lithuania**
Italy
Luxembourg
Latvia
Slovenia**
Norway
United States
Portugal
Sweden
Switzerland
Note: Employee-like means that self-employed are covered by the same or equivalent schemes as employees, have the same contribution rates and thresholds, and that their contributions are income based. (*)In Ireland, and the United Kingdom neither self-employed nor dependent workers are covered by mandatory or quasi-mandatory earnings-related schemes but basic pensions are financed with contributions. (**) In Hungary, Lithuania and Slovenia, some self-employed workers operating under specific legal forms pay only flat-rate contributions. Additional country-specific information is available in the statlink to Figure 2.11.
Source: Information provided by countries, MISSOC (2018[30]), Spasova et al. (2017[15]) and SSA (2018[31]).
#### Pension and social security contribution base
Even when pension rules, for a given contribution base, are similar for dependent employees and self-employed workers, pension contributions can differ substantially. The contribution base, i.e. the earnings taken into account to calculate contributions, is not identical for both types of workers. For dependent employees, pension contributions are usually paid on gross wages, which are equal to total labour costs minus the employer part of social security contributions. For the self-employed, there is no genuine equivalent of gross wages (Section 3).
Most countries use some income-related measure as the contribution base for the self-employed (Figure 2.11). Depending on countries, this measure is income either before or after deducting social security contributions. A number of countries apply the contribution rate to a fraction of income only, e.g. 50% in the Czech Republic, 67% in the Slovak Republic, 75% in Slovenia and 90% in Lithuania.
Most self-employed workers in Latvia, Poland, Spain and Turkey as well as some self-employed workers operating under specific legal forms in Hungary, Lithuania and Slovenia are subject to mandatory pensions but have a high degree of discretion in choosing their income base within given brackets. Finland also provides a high degree of discretion in setting contribution bases but with an additional, hard-to-verify restriction: the contribution base should correspond to a wage that would be paid if the work of the self-employed was carried out by another, equally competent person in place of the self-employed. A high degree of flexibility bears the risk of low contributions regardless of true earnings, e.g. due to financial short-sightedness.19 In a third group of countries, as shown in Table 1.1, pension contributions for the self-employed are not mandatory (Figure 2.11).
Most countries set minimum contribution bases or minimum income thresholds (Figure 2.11).20 Minimum contribution bases are minimum amounts to which pension or social security contributions for the self-employed apply, even if true income is lower. Minimum contribution bases prevent the self-employed from contributing very low amounts, but they also imply that the effective contribution rate is high for earners below the threshold. To mitigate this drawback, Poland allows the self-employed to lower their contributions for a limited period if their revenue is low. Minimum bases are high in some countries, even at or exceeding 50% of the average wage in Italy, Poland and Slovenia.
Minimum thresholds are minimum levels of income below which the self-employed are exempt from mandatory pension or social security contributions;21 in that case, they do not accrue pension entitlements either. These thresholds exist in eight OECD countries, ranging from 11% of the average wage in Ireland to around 50% in the Slovak Republic and Turkey. In Latvia, incomes below the threshold actually result in a considerably lower contribution rate.22
#### Contribution rates
In most countries, contributions are earmarked to pensions while in five countries social contributions cover social insurance as a whole for the self-employed, i.e. including disability insurance, sometimes unemployment insurance and further types of social insurance. In these latter cases, it is usually not possible to disentangle pension contributions from other types of social contributions.
In half of the countries with earmarked pension contributions, contribution rates are aligned between dependent workers and the self-employed (Figure 2.12): the self-employed pay a contribution rate that corresponds to the total contribution rate of employees, i.e. the sum of employee and employer contributions. This is the case in Canada, the Czech Republic, Estonia, Finland, Greece, Hungary, Korea, Latvia, Lithuania, Luxembourg, Poland, the Slovak Republic, Slovenia, Turkey and the United States. In the other countries with earmarked pension contributions, contributions rates are lower for the self-employed. In Australia, Denmark, Germany, Japan, Mexico, the Netherlands, Sweden and Switzerland, this happens because it is not compulsory for the self-employed to contribute at all or only partly to earnings-related schemes. By contrast, in Austria, Chile, France, Iceland, Israel and Italy the self-employed are mandatorily covered by all earnings-related schemes, but contribution rates are lower. In Austria, however, the reduced contribution rate for the self-employed does not lead to lower pension entitlements because contributions are topped up with taxes. In Norway, the self-employed pay lower public pension contributions and, additionally, they are not covered by the private scheme that is mandatory for employees.
Among the countries that do not single out pension contributions from other social-security contributions, contribution rates paid by the self-employed are identical to the total contribution rate of dependent employees - i.e. to the sum of employee contributions and employer contributions – in Spain only (Figure 2.12). In Belgium, Ireland, Portugal and the United Kingdom, the self-employed pay lower social-security contribution rates than employees, and these differences are large. Except in Portugal, one reason why contributions rates are lower for the self-employed is because they are not insured against unemployment (OECD, 2018[7]).23
While pension contribution rates shown in the above chart refer to the generic rule in place for the self-employed, they may vary considerably across categories of self-employment; in particular they might be very different for specific occupations, low-income self-employed and economically dependent self-employed. In Germany, the self-employed are, in general, not mandatorily covered by pensions as shown in Figure 2.11. However, some self-employed (e.g. independent childbirth assistants) are mandatorily insured in the general retirement scheme, typically paying flat-rate contributions, while other types of self-employed workers (e.g. doctors) are mandatorily enrolled in one of 89 different pension schemes that are organised by professional associations. Furthermore, specific rules apply to self-employed artists and publicists. They pay only the employee part of contributions, i.e. half of total contributions, while the remainder is financed through a specific contribution paid by their clients and a government subsidy. Similarly, in the Netherlands, painters are required to join the occupational pension scheme, which is not the case for most of other self-employed workers.
In Italy, rates differ across different types of self-employment. The contribution rate for self-employed workers is around 24% for farmers, artisans, sole-traders, contract workers and the so-called “new” self-employed, i.e. workers in non-regulated professions; for liberal professions a number of categories with different contribution rates exist, ranging between 10% and 33% of professional income. France has a number of occupational categories with different contribution rates. In general, the pension contribution rate for independent workers is 24.75%, but different rates – and in some cases lump sums – apply to liberal professions. In addition, self-employed workers with limited revenue who make use of simplified administrative rules to set up their business, so called micro-entrepreneurs, are subject to lower specific contribution rates. The current proposals related to the implementation of a universal pension scheme in France (Chapter 1) include the unification of the schemes covering liberal professions and independent workers even though some specificities might apply to various professions, including artists, journalists and seafarers. Moreover, Austria, Finland, France, Germany, Greece, Poland and Spain set up special schemes for farmers (Choi, 2009[32]). In Poland, farmers pay very low social-security contributions that are based on their agricultural area rather than income. The scheme for farmers is considerably subsidised from general taxation as in 2018 contributions financed only 15% of expenditures despite the comparatively low pension benefit level of farmers. Box 2.2 discusses more examples of pension arrangements for selected occupations: taxi-like platform drivers and journalists.
In countries with widespread occupational pensions, such as Denmark, Ireland, the United Kingdom and the United States, employees’ contributions to the schemes are usually complemented by employers’ contributions. Such contribution matching by employers is not possible for the self-employed, who have to cover the total contribution rate themselves in order to have the same level of coverage from occupational schemes as dependent employees.
In most countries, workers who combine self-employment with dependent employment pay contributions based on either combined income from both types of work or on income from each type of work separately. However, a few countries apply specific rules in that case. In Belgium, the minimum contribution level is substantially lower for those whose self-employed activity is an ‘additional profession’ (about 35% of the self-employed) i.e. those who combine self-employment with at least half-time work as an employee. Such workers do not build up any public pension rights through self-employment. In Korea, only earnings from dependent work are subject to pension contributions and increase pension entitlements when dependent work and self-employment are combined.
Box 2.2. Pension rules for taxi-like platform workers and journalists
## (1) Taxi-like platform workers
Online labour platforms have remarkably expanded in recent years. Taxi-like platforms are one example of quickly evolving platforms, even though their use is illegal in a couple of countries, including Japan, Norway and Turkey. Standard taxi drivers are classified as self-employed workers, but in some countries, some of them are considered dependent employees. Pension rules applying to traditional taxi drivers and to drivers in taxi-like platforms are usually identical, i.e. there is no specific regulation for such drivers.
In Finland, restrictions regarding taxi services were loosened in July 2018, and both traditional taxi-drivers and taxi-like platform drivers are now treated identically with regard to pension insurance: they are covered by the standard pension insurance for the self-employed – the so-called YEL insurance – if they exceed the minimum income threshold. Earned income, which is used as the basis for social contributions, is also calculated identically. The emergence of so-called umbrella companies has made the pension treatment of platform workers more complex in Finland. Umbrella companies invoice platforms on behalf of the self-employed and freelance professionals for the services they provided and manage some administrative tasks for the self-employed. For instance, umbrella companies transfer contributions from self-employed taxi-like platform drivers to insurance institutions. The intermediary service provided by umbrella companies has raised questions regarding the extent to which such companies can be seen as employers.
In France, taxi-like platform workers, just like standard taxi drivers, are independent workers and can choose between being insured as traditional independent workers (“travailleurs indépendants”) and operating as so-called micro-entrepreneurs if they meet eligibility criteria. In the latter case, drivers pay a monthly or quarterly contribution rate (22% in 2019) directly on their revenue rather than their income – i.e. no costs can be deducted – and all social risks, including old-age insurance, are covered.
The categorisation of taxi-like platforms workers as self-employed or dependent workers is still an ongoing and controversial discussion in many countries. In Austria, the taxi-like platform Uber is in a constant legal dispute over the services the company is allowed to provide. Recently, the country’s Supreme Court ruled that Uber is not allowed to act as an online facilitator for car rentals; this ruling implies that many platform drivers who were not required to pay pension contributions because they were classified as independent contractors, now pay mandatory pension contributions as they are considered as contractual partners of Uber. In Belgium, the situation of platform workers is very diverse and no definitive conclusion regarding their social rights has been reached. In 2016, new legislation was put in place to regulate platform work. According to this legislation platform workers earning up to EUR 6000 per year do not pay contributions and therefore do not build up social rights, including pensions.
In general, the key issue raised by platform workers is the difficulty to determine whether the platform should be treated as the employer or whether platform workers should be considered as self-employed. Depending on how this issue is solved, pension rules follow accordingly.
## (2) Journalists
Journalists have been strongly affected by technological change and the move from printed to digital content. As a result, business models have evolved and the contractual situation of the profession moved from predominantly dependent to mostly independent employment. In some OECD countries, all journalists are self-employed while in others they can be either self-employed or dependent workers. In most countries, standard pension rules for employees or self-employed workers apply accordingly.
However, some countries provide special pension schemes for journalists. In Belgium, a supplementary pension for workers recognised as ‘professional journalists’ (beroepsjournalisten) has been in place since 1971 on top of their general public pension. This scheme is mandatory, financed through an additional 2% contribution by the employer and an additional 1% contribution by the journalist. For journalists with a full career, this supplementary pension leads to an additional pension of up to 33% of their public pensions, depending on how long they contributed to the scheme.
In Austria, journalists are commonly classified as dependent employees or as freelance journalists, which in the latter case means that they are considered “new” self-employed workers. The “new” self-employed are covered by the same mandatory public scheme as common self-employed workers.
In Germany self-employed artists and members of the publishing professions are compulsorily insured in the Artists’ Social Insurance (Künstlersozialversicherung). Workers in this scheme pay only half of the contributions while the remaining half is paid by clients (30%) and a tax-financed state-subsidy (20%). The scheme entitles to old-age pensions, disability pensions and survivor pensions.
In France, professional journalists are insured in the mandatory schemes for employees. Stringers (“pigistes”) – who are paid for each publication rather than working time – benefit from a 20% reduction on capped social security contributions (both salary and employer's share) and non-capped contributions (employer's share only) to the general scheme. This reduced rate does not lower benefits and is financed through redistribution within the scheme. In addition, journalists can deduct 30% of their professional expenses (limited to 7,600 euros per calendar year) from the social security contribution they have to pay.
In Latvia, revenue from royalties, which is the main source of income for many journalists, is subject to a reduced pension contribution rate and reduced entitlements, at 5% compared to 20% for employees. Contributions on royalties are directly paid by clients.
In Italy, pensions for free-lance and employed journalists are provided by the Institute of Pensions for Journalists (INPGI). The fund has remained defined benefit while most other workers are covered by notional defined contribution schemes. In 2017, expenditures exceeded revenues by 42%, highlighting the large imbalances between total contributions and benefits (Itinerari Previdenziali, 2019[33]).
#### Pension entitlements
Self-employed workers with a taxable income (i.e. net of social security contributions) equal to the net average wage before tax (gross wage net of employee’s contributions) can expect to receive in the future - after contributing what is mandatory during a full career – an old-age pension equal to 79% of the theoretical gross pension of the average-wage worker in the OECD on average (Figure 2.13).24 25
In countries where the self-employed are not required to contribute to earning-related pension schemes while employees are, the relative theoretical pension is among the lowest. In these countries, the old-age pension of the self-employed from mandatory schemes is limited to the old-age safety net including the basic pension. In the full-career case, the theoretical pension of the self-employed is about half the pension of employees or even much lower in Mexico (21%), Japan (33%) and also Denmark, Germany and the Netherlands. Among these countries, Australia stands out as the means-tested basic pension (Age Pension) gives the self-employed 90% of what average-wage employees get from mandatory earnings-related schemes (Superannuation).
Low theoretical relative pensions for the self-employed - between 40% and 60% of employees’ pensions - are also found in Poland, Spain and Turkey where only flat-rate contributions to earnings-related schemes are mandatory for the self-employed, and in Latvia, where mandatory contributions above the minimum wage are reduced substantially.
Lower contribution rates and a reduced contribution base result in lower pensions from mandatory earnings-related schemes for the self-employed relative to employees with the same taxable earnings in many countries. For example, in Belgium, France (points-scheme component) and Italy, reduced contribution rates directly affect entitlements within the public system while in Norway, Sweden and Switzerland pensions are lower because the self-employed pay none or reduced contributions to mandatory funded schemes. As a result, theoretical pensions of the self-employed relative to employees reach 50% in Switzerland; around 70% in Belgium, Chile26 and Italy; around 80% in the Czech Republic, France, Israel and Sweden; around 90% in Lithuania, Norway and Slovenia and 97% in Estonia. However, there can be some offsetting factors. For example in the Czech Republic, progressive replacement rates result in the relative theoretical pensions of the self-employed reaching 80% even though the contribution base is set at 50% of taxable income only. In Norway, the reduced contribution rate to the public scheme does not reduce the benefits implicitly while in Austria the reduced contributions of the self-employed are explicitly topped up with taxes.
Some countries calculate pensions of the self-employed based on gross income, i.e. income before deducting contributions. This leads to higher pensionable earnings “all else equal” in the case studied here (taxable income of the self-employed equal to the net wage before tax) as the contribution rate paid by the self-employed is higher than the employee part for dependent workers. Hence, the theoretical pension of the self-employed is slightly higher than that of employees in Austria, Greece, Hungary, Luxembourg and the Slovak Republic. In the Slovak Republic, this more than compensates the lower contribution base for the self-employed, which is set at 67% of gross earnings, leading to the contribution base being higher for the self-employed than for employees with the same taxable earnings by 10%. The United States allow the self-employed to deduct half of social security contributions before calculating the contribution base. Given that employees and employers pay equal shares of contributions, this deduction equalises theoretical pensions between the self-employed and employees.
Ireland, New Zealand and the United Kingdom which pay only flat benefits in mandatory pension schemes for employees provide the self-employed and employees with the same benefits.
### Part-time work
Reduced working hours lower total earnings and ultimately pensions from earnings-related schemes. In some countries the effect of part-time work during at least part of the career on pensions might be limited depending on earnings levels, through the effects of non-contributory benefits, contribution-based basic pensions, minimum pensions and reference-wage rules for earnings-related schemes. However, the effect on pensions can be over-proportional in other countries, i.e. pensions can decrease more strongly than earnings. Such a situation can arise when minimum earnings requirements or minimum working time requirements for pensions are in place. For example, while minimum earnings requirements formally apply to all dependent workers in some countries, requirements at levels below the monthly minimum wage of full-time workers are binding only for part-timers or some temporary workers.
Minimum earnings or minimum working time requirements exist in less than half of OECD countries (Table 2.2). Germany, Japan and Korea are examples of countries with a minimum number of working hours needed to be eligible for mandatory pensions. Fourteen countries set a minimum earnings level – on a weekly, monthly, quarterly or yearly basis - to acquire entitlements to mandatory pensions (Figure 2.14), ranging from less than 5% of average earnings in Ireland and Finland to over 50% in Turkey. In Germany, while there is no minimum earnings requirement, workers with a monthly income of 450 EUR or less (so-called “minijobbers”) have the possibility to opt out of the statutory pension insurance.27 Nineteen countries require neither a minimum level of earnings nor a minimum number of hours, i.e. all part-time workers are covered by pension schemes.
Table 2.2. Minimum earnings and working-time requirements for pension entitlement
Minimum level of earnings
Minimum number of hours worked
No requirement
Australia, Austria, Canada, Czech Republic, France, Finland**, Hungary, Ireland, Japan, Korea, Switzerland, Turkey, United Kingdom, United States
Denmark (9 hours/week), Germany (up to 3 months or 70days/year), Japan (20 hours/week), Korea (15 hours/week), Norway (funded scheme; 20% of full time)
Belgium*, Chile, Estonia, Greece, Iceland, Israel, Italy, Latvia, Lithuania, Luxembourg, Mexico, Netherlands, New Zealand, Poland, Portugal, Slovak Republic*, Slovenia, Spain, Sweden
Note:(*) In Belgium, working less than one-thirds and two-thirds of the full-time annual equivalent results in this year not being accounted for eligibility to early retirement and minimum pension, respectively. In the Slovak Republic the minimum level of earnings applies only to validate eligibility to minimum pensions but not to old-age pensions. (**) In Finland, there is a very low minimum threshold of earnings to be covered by pensions at 1.6% of average wage that is set for practical reasons, i.e. not to place large administrative burden on tiny tasks such as walking the neighbour’s dog.
Source: Information provided by countries, MISSOC (2018[30]), Spasova et al. (2017[15]) and SSA (2018[31]).
While minimum earnings requirements and minimum working time requirements penalise part-time workers who do not fulfil them, other part-time workers may benefit from them. This can be the case when part-time workers meet the minimum requirements by a small margin and accrue (almost) the same pension rights as full-time workers. In particular, if the requirements are set at low levels and the link between contributions and pension rights is weak, as is the case for example with minimum pension schemes based simply on validating contribution periods, many part-time workers may benefit. In such a situation, pension rules imply redistribution from full-time workers to part-time workers.
In Estonia, Hungary, Lithuania and Spain, rules exist to determine pension entitlements or eligibility to benefits for part-time workers in some particular ways. In Lithuania, every insured person must pay pension contributions on at least the monthly minimum wage to validate a month for pension calculation purposes. When pension contributions are paid based on an amount below the monthly minimum wage, insurance time records are proportionally lower. Similar mechanisms exist in Estonia and Hungary for earnings below the minimum wage. In Spain, part-timers can receive higher benefits than full-time workers with the same total earnings.
Pension entitlements from part-time work can differ even though the same number of hours are worked at the same hourly wage. For example, working 3 out of 5 days per week leads to a shorter validated contribution period than working 60% of normal hours 5 days a week in some countries including Greece and Turkey that validate contribution periods on a daily basis. Other countries use longer periods: weeks (e.g. Ireland, the United Kingdom), months (e.g. Poland) or quarters (e.g. France).
In all OECD countries, workers with more than one part-time job have to pay mandatory pension contributions based on either total income from all jobs or separate income from each workplace, and receive benefits accordingly. In 2015, Belgium introduced “flexi jobs” which are available to workers and pensioners working at least 80% of full-time hours and gaining additional income in a specific list of sectors, such as restauration. These jobs are exempt from income tax and both employee and employer pension contributions are reduced. In the Czech Republic, the income stemming from a special work contract, that permits to perform an additional job for up to 20 hours a week or up to 300 hours a year, is excluded from pension contributions and entitlements.
### Temporary work
In most countries, pension insurance rules for temporary workers are aligned to the rules for standard workers. However, some countries set reduced or no pension contribution rates for temporary agency workers, young workers, seasonal workers, apprentices and/or trainees, resulting in lower entitlements. Trainees are not covered by pensions in Hungary, while temporary agency workers and contractors are excluded from pensions in Korea. In Lithuania, casual and seasonal workers on voucher-based contracts are exempt from enrolling in mandatory pensions. In Poland, temporary work regulated by civil law rather than the labour code – so-called ‘civil law contracts for a specified work’ – is not subject to mandatory pension contributions.
Even when temporary workers have the same pension rules as standard employees, they tend to have less pension coverage due to shorter employment spells. For example, occupational pension plans in the Netherlands cover workers only after six months of employment in the same company, which effectively reduces coverage of temporary workers and workers employed by temporary agencies. Additionally, vesting periods of employer contributions, i.e. the time it takes for employees to become owners of the contributions made on their behalf in occupational pensions are often over one year. In some countries, vesting periods for employer contributions in occupational pensions can even exceed three years, as in New Zealand, Turkey and the United States. Long vesting periods are a problem for temporary workers because they tend to change employers frequently. Most countries, but not all, provide options to transfer occupational schemes to other employer schemes or not to close them (without making additional contributions). Allowing to transfer entitlements from voluntary occupational to personal pension schemes is less common, but it is allowed e.g. in Canada, Denmark, Spain and the United States. Withdrawing entitlements upon contract termination is possible in a few countries (Chapter 3), losing the link with retirement purposes.
Pension credits are often granted as long as unemployed people receive unemployment benefits. Patchy employment histories can prevent temporary workers from receiving unemployment benefits, thereby magnifying the impact of career breaks on pensions. Indeed, OECD (2019[1]) shows that non-standard workers are less often covered by unemployment benefits than standard workers. However, the picture is not uniform and OECD countries vary a lot in terms of unemployment benefit rules. The minimum contribution period required to be entitled to unemployment benefits ranges from less than six months in Canada and Iceland to more than two years in Mexico (OECD, 2018[7]). In many cases, the eligibility conditions allow for some flexibility and, for example, Sweden requires working and contributing only in six out of the last twelve months before applying for benefits while the Slovak Republic requires working in at least 24 out of the last 48 months.
### Policy changes
More than half of OECD countries have reformed pension rules for non-standard workers over the last two decades. In many cases, the reforms aimed at expanding the coverage of the self-employed and part-timers. Earnings-related schemes have recently become mandatory for self-employed workers in Israel. Since 2012, Chile tried to include the self-employed through auto-enrolment into the funded pension scheme that is mandatory for employees, but the majority of them (80% in 2017) opted out; since 2019, pension contributions have been compulsory for the self-employed who issue invoices, except for older workers and low-income earners. In 2013, the pension coverage for some non-standard workers, such as working students, individuals on special civil-law contracts and workers performing the so-called complementary tasks (e.g. cleaning or babysitting), was expanded in both Slovenia and the Slovak Republic, and, in Slovenia only, for the self-employed with low earnings. In Germany, the current coalition agreement plans to establish mandatory pension insurance for all self-employed workers.
A few countries introduced specific regulation to limit pension coverage gaps for self-employed workers with only few major clients. While in Germany, self-employed persons who work predominantly for one client28 and do not have employees have been mandatorily insured in the pension system since 1999, in Italy and Portugal the contributions of independent contractors relying on single contracts are now topped up by their clients. In addition, in Portugal if a self-employed worker depends significantly on one single client – the so-called ordering customer – the latter has to pay social security contributions for the self-employed. The contribution rate varies depending on the degree to which the worker relies on the client.29
In 2019, Poland introduced specific exemptions to reduce the financial burden of minimum contribution amounts for self-employed workers with low earnings. They can set the contribution base between 30% of the minimum wage, which is five times lower than previously, and 60% of the average wage for three years within a five-year period. Pension entitlements are adjusted accordingly.
Some countries modified pension rules to increase pension coverage among part-time workers. France, Germany, Japan, Korea and Switzerland expanded the coverage of part-time workers by lowering minimum-hours and/or earnings requirements. In 2014, France lowered the earnings threshold, from the equivalent of 200 to 150 hours of work at the minimum wage per quarter. Germany expanded the pension coverage for part-timers with low earnings through auto-enrolment since 2013 (while granting them an opt-out possibility). In Japan, since 2016 employers with more than 500 employees are required to provide coverage to part-time workers working at least 20 hours a week (previously it was 30 hours) and earning more than JPY 88000 per month (20% of the average earnings). Since 2017, part-time workers in smaller firms who satisfy the conditions above have also been entitled to join earnings-related pensions if management and employees agree. Similarly, in Korea, when the National Pension was introduced in 1988, it covered only employees in workplaces with at least 10 workers who had worked for more than three months. Compulsory coverage was gradually extended to include many non-standard workers.30 Switzerland also lowered the entry threshold of the occupational pensions to include more low-income workers, particularly part-time workers.31 In 2018, Latvia extended the mandatory pension coverage to self-employed workers with income below the minimum wage, who had been covered only voluntarily before, through mandating them to pay reduced pension contributions at 5% compared with the regular rate of 20%.
Pension systems that mitigate disparities between standard and non-standard workers in terms of coverage, contributions and entitlements tend to ensure fairer protection, reduce inequalities, pool risks as broadly as possible and facilitate labour mobility across job types. The increasing flexibility of employment arrangements and, in particular, the development of new forms of work highlight that the boundary between dependant employment and self-employment is not always clear-cut. This may challenge policymakers, where the prevalence of workers along this boundary is increasing, to adapt social protection in general, and old-age pensions in particular, to this new environment (OECD, 2018[22]).
Non-standard work is often encouraged, for example financially, to promote entrepreneurship, to reduce informality or to offer greater flexibility for firms and even some workers. In a number of cases, non-standard work is associated with income vulnerabilities during the working age, which have repercussions on old-age income prospects. Fighting precarious forms of employment is a crucial objective, but it goes beyond the scope of pension policies analysed in this chapter. One of its extreme forms, informal employment, can be most efficiently addressed through a multi-pronged approach, aiming to increase the benefits and reduce the costs of formalisation and to strengthen enforcement mechanisms (OECD, 2015[34]). Policies aiming at reducing if not eliminating preferential tax treatment for the self-employed while at the same time addressing tax avoidance are important to strengthen the financing of social benefit schemes and enhance their retirement income prospects. As for precarious employment, work arrangements such as successive fixed-term contracts and false self-employment might be in part the result of lower social contributions for the self-employed, raising concerns regarding social dumping (OECD, 2019[1]; Spasova et al., 2017[15]). These arrangements should be addressed by tackling their root causes, including the regulatory and policy settings in the labour market that de facto contribute to its segmentation and result in lower social contributions and benefits.
This section provides policy options to improve pension provisions for non-standard workers. Some problems faced by these workers, such as the impact of low lifetime earnings and of career breaks on retirement income, also affect standard workers.
### Better coordinating contributory and non-contributory schemes
Well-tailored coordination of contributory and non-contributory schemes is important for pensions in general, and in particular for non-standard workers who are often not mandatorily insured. The objective of a good coordination is to ensure a good level of old-age income protection for non-standard workers as well as to provide them with incentives to contribute to pensions and build up pension entitlements.
Non-contributory first-tier pensions – i.e. residence-based basic pensions and old-age social assistance benefits – set a lower bound to old-age income, irrespective of retirees’ work histories. In many countries, the level of the old-age safety net is not high enough to ensure that recipients do not fall below the poverty line, e.g. defined as 50% of median household disposable income (Chapter 6). The level of non-contributory first-tier pensions depends in theory on redistributive preferences in each country; it is the result of trading off income adequacy for the most vulnerable groups against containing financial costs and maintaining incentives to contribute to earnings-related pensions.
There are three main ways of achieving sound coordination of contributory and non-contributory schemes. First, first-tier pensions can be universal flat-rate benefits – which might depend on household composition – on top of which contributory entitlements build up. This is the case in the Netherlands and New Zealand for example. Second, the safety-net benefit could be withdrawn progressively against the earnings-related component, as in Chile, Norway or Sweden for instance. The choice of the withdrawal rate is in itself the result of a trade-off. A low rate implies a more universal coverage, limits stigma associated with benefiting from the safety net and lowers disincentives to contribute to pensions. However, it implies also that the safety net is not tightly targeted, therefore generating higher costs for public finances. The third case is the combination of the two others: one part is universal and the other is withdrawn against the earnings-related component, as for example in Canada, Denmark and Iceland.
Well-coordinated schemes based on either one of the three settings above ensure in a transparent way that every entitlement provides some additional protection beyond the old-age safety net, which is available to people who never contributed to earnings-related pensions. While every old-age individual, including people with career histories in non-standard employment, receives some minimum benefits, additional amounts are paid in relation with contribution histories.
Simple entitlement rules in contributory pensions greatly facilitate a good coordination of contributory and non-contributory schemes. Emphasising the importance of a good coordination for non-standard workers thus strengthens the case against complex rules. Ensuring that all labour income at least up to a high enough threshold and all periods of non-standard work generates pension entitlements is an important step towards pension adequacy for non-standard workers.
Appropriate compliance measures are essential to improve access to pensions for non-standard workers. Non-standard work in general, and platform work in particular, is indeed more subject to informality than standard employment. Large fines for non-compliance cannot offset the weak enforcement of mandatory contributions (Kanbur and Ronconi, 2018[35]), which seems to be an issue in Chile for example (Valdés-Prieto and Leyton, 2019[12]). From a technical perspective, more and more data to improve compliance are becoming available from both public (tax and social security registers) and private (e.g. banking, platform work) sources, and more efficient algorithms (e.g. artificial intelligence) have the potential of targeting labour and tax inspections more efficiently. However, the use of such data raises privacy concerns and would in addition require increasing public administration capabilities and an improved coordination of labour, social security and tax administration (OECD, 2008[36]).32
New forms of work often fall into the shadow area between dependent and independent employment. In several countries such as Austria and the United Kingdom there is a major legal dispute around the question whether platform workers are employees or self-employed. When they are classified as employees, platforms may be required to pay the employer part of pension contributions. In addition, in the area of occupational pensions, platforms might also be required to offer occupational pension plans and pay matched employers contributions, as with workers in standard employment.
For the false self-employed, who are hired as self-employed but de facto perform dependent work, properly classifying them as dependent employees would improve pension protection. It often requires only enforcing the existing labour code. Spasova et al. (2017[15]) suggest to increase fines and impose retroactive payments of contributions for employers who make use of false self-employment. Some countries implement alternative but complex solutions for some self-employed, e.g. free-lancers, who heavily depend on single clients by making the clients pay the employer part of the contributions or by levying contributions on selected products e.g. publications.33 For voluntary pension schemes – in particular those with auto-enrolment – contributions paid by clients can substantially increase coverage, similar to what is the case for matching contributions paid by the employers. However, such solutions complicate the pension system.
Moreover, policy that seeks equal treatment of all labour income implies that temporary work contracts should not be excluded from mandatory pension protection, irrespective of their duration, and that no minimum tenure for acquiring pension entitlements should exist. Currently, agency work, zero-hour contracts and seasonal work are not covered in some countries and minimum tenure requirements are not uncommon.
Contributory first-tier pensions (contribution-based basic and minimum pensions), which exist in about half of OECD countries, increase old-age benefits based on the length of the contribution history. This redistributive instrument potentially benefits part-time workers substantially depending on the rules to validate contribution periods.
For standard workers, the effect of career breaks on pensions depends on how tightly entitlements are linked to earnings and on the instruments at hand to cushion employment shocks, such as pension credits during unemployment. On average across countries, slightly more than one-third of employment shocks are transmitted to pension income: pensions for standard workers decrease by about 1.3% for each year out of employment on average across OECD countries (Figure 5.12 in Chapter 5) while they would decrease by about 2.7% with a one-to-one link between earnings and pensions.
For non-standard workers, the impact on earnings-related pensions is larger, i.e. pension entitlements in the case of job losses are lower, because they tend to receive lower unemployment benefits, which results in lower pension entitlements. First, non-standard workers might lack direct access to unemployment protection (e.g. many types of self-employed workers and some groups of temporary workers are not covered by unemployment insurance). Second, they often have shorter work spells, which results in a lower maximum length of unemployment benefits and/or lower benefits. Pension policies cannot insure against all shocks that occur in the labour market, and the source of this transmission may be addressed more directly through unemployment policies for non-standard workers.
### Mandating pensions for the self-employed?
Earnings-related schemes for standard workers are typically mandatory for two main reasons, which equally apply to the self-employed. First, due to short-sighted behaviour people left to themselves often under-save for retirement, for example because they underestimate their long-term needs. This feature motivates the paternalistic approach according to which contributions should be mandatory. The self-employed are similarly prone to myopic behaviour as dependent employees. Second, providing effective protection against old-age income risks relies on having access to a broad pool of contributors. This is important for the pension provider’s capacity to insure for example longevity risks, i.e. the risks that some people live longer than what their individual contributions can finance. Besides, fully including all non-standard workers in mandatory pensions in the same way as standard workers limits the financial incentives employers and workers might have to misuse non-standard employment to lower labour costs.
It is sometimes argued that the self-employed have more financial assets, potentially related to their business activity, or even more housing assets, which would give them good reasons not to contribute to pensions. Such arguments should be rejected.
As discussed in earlier sections of this chapter, the self-employed are a very diverse group, and these considerations regarding exemptions from mandatory pensions would apply only to the wealthiest among them. Policies grounded in such arguments would require complex asset tests – potentially based on future assets; in addition, it could raise the question why wealthy standard workers should not be excluded from mandatory pensions as well. Excluding some groups of workers based on high incomes or high (future) assets is difficult to justify. An equal treatment in terms of pension insurance also requires that any redistributive feature benefitting non-standard workers is broadly shared, i.e. not financed by contributions from standard workers only.
To achieve pension adequacy for more workers, voluntary occupational schemes could be available for all contract types through default plans in countries where they are available for dependent workers. Equal treatment could also apply to auto-enrolment schemes. Opt-out rates might be higher for non-standard workers, and contributions of self-employed workers cannot be matched by employers, contrary to what is the case for dependent employees. Nevertheless, non-standard workers are probably as malleable as standard workers to nudging. In particular, contributions could be automatically deducted when taxes are collected.
### Moving towards harmonisation
As discussed before, there are good arguments in favour of harmonising pension rules broadly between dependent and independent workers. Aligning pension rules across work types implies that total contribution rates are equalised for all workers, with the self-employed paying the sum of employee and employer contributions. One serious obstacle towards a full harmonisation relates to the assessment of the contribution base for the self-employed (see next sub-section).
Lower contribution rates for the self-employed are used explicitly or implicitly in some countries to make self-employment economically attractive and to reduce incentives for informality. If the lower contributions are not offset by public subsidies, such policies might bear social costs, however, to the extent that they imply lower future benefits. In that case, achieving their objective of promoting self-employment is facilitated by the underestimation by the self-employed of their needs in old age; i.e. by short-sighted behaviours.
Lower pension contributions generating lower pension entitlements should not be used as an instrument to promote self-employment. Rules defining pensionable earnings should be harmonised as much as possible between dependent and independent workers, and pensionable earnings should generate the same entitlements based on the same total contribution rate. The main question then is who pays the missing contributions.
Social policies can be designed to account for the fact that some vulnerable self-employed cannot afford full pension contributions. In this case, the possibility to contribute at a lower rate should be part of an explicit redistributive policy. The lower rate should be compensated by a subsidised contribution component, financed by taxes or the pool of pension contributions, at least for low earners. In other words, allowing the self-employed to pay a lower total contribution rate should take into account the financial cost of this policy. If not offset by public subsidies, this cost will be revealed as a social cost in the long term, penalising retirees who were encouraged to become self-employed workers.
Likewise, when special pension and tax regimes exist for self-employed workers with limited income (e.g. microenterprises in France and Latvia, or flat-rate contribution regimes in Hungary, Lithuania and Slovenia) or for economically dependent self-employed workers (e.g. in Germany, Italy, Spain or Portugal) it is particularly important to ensure that these regimes do not involve lower pension contributions unless they are topped up. That is, simplified pension or tax regimes should not lead to lower pensions.
Better harmonisation of pension rules between standard and non-standard workers facilitates the portability of pensions across jobs and companies. The importance of pension portability is highlighted by more frequent job switches among non-standard workers and the large number of non-standard workers who combine several jobs of various types. Personal individual accounts can be helpful to ensure full portability of private pension entitlements of non-standard workers (Hu and Stewart, 2009[37]).
### … while recognising that fully harmonising the contribution base is difficult
Fully aligning the contribution base of the self-employed to that of employees is not possible. For employees, contribution rates – both the employee and employer parts – apply to the gross wage, which does not have an equivalent for the self-employed. For the latter, the contribution base is either determined by (a part of) revenue or income, i.e. after deduction of costs, or not strictly linked to income categories. The choice of the contribution base directly influences how pension entitlements are built.
Beyond the possibility that may exist to under-report revenue, the self-employed often enjoy additional flexibility. They may have wide options to deduct work-related expenses, divide income into labour and capital shares and in some cases freely choose contribution bases. For self-employed workers with limited material costs and capital requirements such as some free-lancers and platform workers, total revenue, or a fraction of it, would be the most reliable contribution base. Revenue as contribution base has also the advantage of limiting the administrative burden related to the often complex cost deductions in tax accounting. In particular, low earners are disadvantaged by the fixed costs of proper cost documentation (OECD, 2008[36]). However, using revenue as the contribution base for all self-employed workers would be inappropriate, especially in cases when material and capital costs are high, and would result in an unequal treatment of different types of self-employment. Hence, for self-employed workers with substantial material costs, such as sole traders, income is a more appropriate contribution base.
In general, using income as the contribution base largely ensures equal treatment among different types of self-employed. Income net of social security contributions (taxable income) is, as a concept, closer to net wages before tax and thus allows for closer harmonisation of pension rules. However, applying the harmonised contribution rates to taxable income leads to lower contributions because taxable income is net of all contributions whereas the gross wage is only net of employer’s contributions. For example, if the total contribution rate for employees is 20%, equally split between the employee and employer, then a gross wage of 100 corresponds to a net wage before tax of 90, with total contributions of 20. If the self-employed with the same taxable income of 90 effectively pay a 20% contribution rate on taxable income, then total contributions equal 20% * 90 = 18, lower than total contributions paid for employees. A higher degree of harmonisation might be reached by setting a higher nominal contribution rate for the self-employed to account for the difference between gross and net wages before tax (22.2% on taxable income in the above example to reach contributions of 20, as 20/90 = 22.2%). For the same reason, applying the harmonised contribution rates to gross income (before deducting any contributions) leads to higher contributions because gross income – as opposed to gross wage - includes total contributions.
Harmonisation can thus be improved by applying a higher nominal contribution rate to the taxable income of the self-employed, but this is likely to be politically difficult to implement. Alternatively, the total contribution rate can be applied to rescaled taxable income or part of gross income.34 Yet, another option is to use the taxable income as the contribution base for both employees and the self-employed, which is the case in Sweden for public pensions.
Limiting the large degree of flexibility in defining the contribution base also helps aligning pension rules for self-employed and dependent workers. However, limiting flexibility in setting the contribution base might not be sufficient to prevent low levels of contributions in practice and appropriate compliance measures might be needed, e.g. in the form of rigorous labour inspections. In Italy, an innovative approach to controlling income was implemented: the reported income of the self-employed was compared to their estimated profits and actual living standards, thereby permitting to identify cases of tax underreporting more easily (Bucci, 2019[27]).
Non-standard work refers to a very diverse group of workers, with the most common forms of non-standard work being self-employment, part-time work and temporary employment. Non-standard employment accounts for more than one-third of employment in the OECD. Part-time work is three-times more frequent among women than among men and self-employment is particularly frequent among older workers.
Globalisation, automation and demographic changes transform labour markets at a rapid pace. There has been an expansion of new forms of non-standard work, in particular jobs relying on new technologies such as platform-based taxi driving. In many cases, non-standard work is associated with lower income and tends to be persistent, which typically affects workers’ financial long-term prospects.
While the debate on pensions for non-standard workers is not new, the way non-standard workers are covered by pension systems might become a topic of growing importance. As most pension systems were built on the premise of stable, linear careers, the development of new forms of work raises concerns about the old-age income of future generations of retirees. Yet, the recent evolution of labour markets calls for more inclusive and harmonised pensions for all rather than for a radical shift in designing and financing pensions.
Pension rules for non-standard workers vary substantially across countries, are often particularly complex and differ from the rules for standard workers in many countries. The self-employed, in particular, are the group that raises the most challenging issues in terms of pension coverage because they do not have employment contracts that can be used as the basis for pension contributions. Some new forms of work raise similar challenges while being in addition more prone to informality. Yet, pension systems should be designed to mitigate disparities between standard and non-standard workers in terms of coverage, contributions and entitlements so as to protect against old-age poverty, smooth the living standards upon retirement, ensure fair treatment, pool risks as broadly as possible and facilitate labour mobility across job types.
The main findings of this Chapter are the following.
Self-employment
• The self-employed contribute less to old-age pensions than employees and receive lower pension benefits when they retire. On average across 15 OECD countries, the retired self-employed receive, at the median, 22% lower public pensions than retired employees.
• Even though the self-employed possess somewhat higher assets than employees, their additional assets are generally insufficient to make up for the lower level of pension benefits.
• The self-employed are required to contribute to mandatory earnings-related pensions in a similar way as employees in only 10 OECD countries.
• Even when pension rules are similar for dependent employees and self-employed workers, pension contributions can differ substantially because the contribution base, i.e. the earnings taken into account to calculate contributions, is not identical for both types of workers.
• In 18 countries, self-employed workers are mandatorily covered by earnings-related schemes, but they are allowed to contribute less than employees through reduced contribution rates, discretion in setting their income base or minimum income thresholds. Latvia, Poland, Spain and Turkey, for example, have discretion in choosing their income base within given brackets.
• In 6 countries - Australia, Denmark, Germany, Japan, Mexico and the Netherlands - the self-employed are not required to join earnings-related schemes, contrary to employees.
• Most countries use some income-related measure as the contribution base for the self-employed. A number of countries apply the contribution rate to a fraction of income only, e.g. 50% in the Czech Republic, 67% in the Slovak Republic or 75% in Slovenia.
• Most countries set minimum contribution bases or minimum income thresholds. Minimum contribution bases ensure that the self-employed contribute at least some minimum amounts, but they imply that the effective contribution rate is high for low earners. They range from 10% of the average wage or less in Canada, Korea, Norway, Sweden, Switzerland and the United States to 60% in Poland and Slovenia. Minimum income thresholds, which reduce pension coverage of the self-employed with low earnings, exist in eight OECD countries, from 11% of the average wage in Ireland to around 50% in the Slovak Republic and Turkey.
• In half of countries with earmarked pension contributions, the self-employed pay a contribution rate that is equal to the sum of employee and employer contribution rates for employees in mandatory schemes. In the other countries, including France, Italy and Switzerland, contributions rates are lower for the self-employed.
• Self-employed workers with income net of social security contributions equal to the net average wage will receive, after paying during a full career only the contributions that are mandatory, an old-age pension equal to 79% of the theoretical pension of the average-wage private-sector employee on average in the OECD. This relative pension ranges from less than 50% in Denmark, Japan, Mexico, the Netherlands and Spain to more than 90% in more than one-third of countries: Austria, Canada, Finland, Greece, Hungary, Ireland, Korea, Lithuania, Luxembourg, New Zealand, the Slovak Republic, Slovenia, the United Kingdom and the United States.
• In New Zealand, Poland, Turkey and the United Kingdom, employees are automatically enrolled in workplace pensions, while the self-employed are not.
• Contribution rates may vary considerably within countries across categories of self-employment, as in France, Germany, Italy and the Netherlands. Austria, Finland, France, Germany, Greece, Poland and Spain have special schemes for farmers for example.
• A number of countries, including Germany, Italy and Portugal, introduced specific regulation to limit pension coverage gaps for self-employed workers with only few major clients.
Part-time work
• One in three part-time workers in OECD countries would have preferred to work longer hours, while about two out of three work part-time by choice. Among workers aged 65-74, about one-third work part-time.
• Part-time workers can benefit from redistributive mechanisms within pension systems through non-contributory benefits, minimum pensions, contributory-based basic pensions and reference-wage rules for defined benefit schemes. While pension rules for part-time workers tend to be in line with those for standard workers, minimum earnings and minimum working time requirements for pension right accruals prevent part-time workers who fail to meet them from building up pension entitlements.
• Minimum earnings and minimum working time requirements exist in about half of OECD countries. Denmark, Germany, Japan, Korea and Norway require minimum working hours to be eligible for mandatory pensions, while 14 countries set a minimum earnings level to acquire entitlements to mandatory pensions, from less than 5% of average earnings in Finland and Ireland to over 50% in Turkey.
Temporary work
• In most countries, pension insurance rules for temporary workers are aligned to the rules for standard workers. However, some countries, including Hungary, Korea, Lithuania and Poland set reduced or no pension contribution rates for temporary agency workers, young workers, seasonal workers, apprentices and/or trainees, resulting in lower entitlements.
• Even when pension rules for temporary workers and standard workers are fully harmonised, temporary workers face lower pensions because they are out of employment more often and generally build up less pension entitlements while unemployed.
• Long vesting periods are a problem for temporary workers due to short job tenure. Vesting periods for employer contributions in occupational pensions can exceed three years in several countries, including New Zealand, Turkey and the United States.
In analysing the challenges raised by pensions for non-standard workers, the following policy implications emerge.
• A well-coordinated system of contributory and non-contributory pension schemes, particularly important for the self-employed and individuals undertaking new forms of work, can be achieved to ensure a high level of old-age safety net while providing clear incentives to contribute to earnings-related pensions.
• Simple entitlement rules in contributory pensions greatly facilitate the coordination of contributory and non-contributory schemes.
• To remove barriers and exclusions that temporary and part-time workers face in meeting pension eligibility conditions, minimum earnings and minimum working time requirements for pensions should be set at sufficiently low levels. Policy that seeks equal treatment of all labour income implies that temporary work contracts should not be excluded from mandatory pension protection, irrespective of their duration, and that no minimum tenure for acquiring pension entitlements should exist.
• The reasons supporting mandatory pensions for dependent employees apply to the self-employed similarly. Moreover, fully including all non-standard workers in mandatory pensions in the same way as standard workers limits the financial incentives employers and workers might have to misuse non-standard employment to lower labour costs.
• Aligning pension rules across work types means that total contribution rates are equalised for all workers. In particular, the guiding principle should be that the self-employed pay the sum of employee and employer contributions. Voluntary occupational schemes should be available for all contract types through default plans in countries where they are available for dependent workers. Equal treatment could also apply to auto-enrolment schemes.
• If lower mandatory pension contributions for the self-employed are used as an instrument to promote self-employment or to achieve some social policy objectives, resulting lower pension entitlements should be avoided by topping up the lower implied contributions through subsidies, at least for low earners.
• The contribution base for the self-employed that might realistically ensure the highest degree of harmonisation with employees and across the large variety of self-employed is taxable income. Full harmonisation based on taxable income would imply a higher total nominal contribution rate for the self-employment or the same contribution rate on taxable income rescaled to better correspond to the gross wage. An alternative would be to apply the same contribution rate to a share of gross income. Serious limitations of contribution bases based on income come from the absence of simple solutions to separate labour and capital income for the self-employed as well as the large differences in deductible costs between the self-employed and employees.
• Limiting the large degree of flexibility in defining the contribution base is one step towards aligning pension rules for self-employed and dependent workers. However, formally limiting flexibility in setting the contribution base might not be sufficient to prevent low levels of contributions and appropriate compliance measures might be needed.
• Pension policies cannot insure against all shocks that occur in the labour market. When the source of the transmission from non-standard work to low pension entitlements is low unemployment insurance, this may be more directly addressed by changing unemployment policies.
## References
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[14] Lichtenstein, J. (2010), “Saving for Retirement: A Look at Small Business Owners”, Working Paper, Office of Advocacy, U.S. Small Business Administration, Washington, United States, https://www.sba.gov/sites/default/files/rs362tot_0.pdf.
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[3] Milanez, A. and B. Bratta (2019), “Taxation and the future of work: How tax systems influence choice of employment form”, OECD Taxation Working Papers, No. 41, OECD Publishing, Paris, https://dx.doi.org/10.1787/20f7164a-en.
[4] Mineva, D. and R. Stefanov (2018), Evasion of Taxes and Social Security Contributions, European Platform Undeclared Work, https://ec.europa.eu/social/BlobServlet?docId=20207&langId=en.
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## Notes
← 1. The survey data on income of the self-employed are prone to underestimation. For example, Di Marco (2006[43]) argues their income was underestimated by 12% in the early waves of EU-SILC.
← 2. OECD/EU (2017[41]) shows lower durability of self-employed businesses compared to the self-employment status as the self-employed might switch between business while remaining self-employed.
← 3. In addition, temporary employment can have a long-term impact on earnings, as e.g. in Spain where temporary employment spells lowered earnings even 27 years later (García-Pérez, Marinescu and Vall Castello, 2018[49]).
← 4. The income from self-employment is classified as the main source of income if it amounts to at least two-thirds of a self-employed worker’s yearly earnings.
← 5. Combing different forms of employment is even more common among workers in new forms of work. In the United Kingdom, 58% of gig-economy workers are permanent employees engaging in gig economy to top up their income (CIPD, 2017[46]).
← 6. Source: Information provided by countries and Spasova et al. (2017[15]).
← 7. This is based on the data from Pettinicchi and Börsch-Supan (2019[13]). The authors do not account for differences in characteristics between employees and the self-employed. The retired (or former) self-employed and retired (or former) employees refer to retired persons who spent more than half of their working life as self-employed or employees, respectively. This classification is based on the retrospective questions about past employment spells longer than 6 months using Sharelife or wave 7 of Share.
← 8. The self-employed often do not have access to occupational pensions, and when they do, access conditions are less favourable. For example, dedicated pension plans for some groups of the self-employed rarely supply financial-education tools for managing savings comparable to those provided by employers (Transamerica, 2019[8]). In addition, automatic enrolment in workplace pensions is less common for the self-employed, e.g. in New Zealand, Poland and the United Kingdom. Even when automatic enrolment is in place, the lack of employer (matching) contributions removes an important incentive to participate.
← 9. Source: OECD computations based on data by Pettinicchi and Börsch-Supan (2019[13]), originally computed with the SHARE survey data.
← 10. This might be due to less old-age social protection for the self-employed, but this could also result from cohort effects, i.e. the fact that the earnings gaps of the current self-employed might be lower than in the past.
← 11. Net liquid assets do not include important elements of total wealth such as real estate, mortgages or the value of own businesses, but include financial assets such as stocks or bonds and the money earned when selling out a business.
← 12. In the United States, 40% of the self-employed expect to receive 401k or 403k pensions vs 67% of employees (Transamerica, 2019[8]).
← 13. Further evidence from the Netherlands suggests that, upon retirement, the self-employed experience a larger drop in income – net of housing costs – than employees, amounting to 24% against 17% at median. This 7 percentage-point difference is driven by lower occupational pensions, which by themselves would yield a difference of 22 percentage points. Yet, many self-employed workers pay off their mortgages before retiring, thereby lowering the difference by 5 percentage points. Higher private savings of the self-employed reduce the difference by a further 8 percentage points. The remaining 2 percentage points are due to basic pensions (Zwinkels et al., 2017[47]). Mastrogiacomo and Alessie (2015[38]) also showed that the self-employed in the Netherlands have limited voluntary retirement savings.
← 14. Also other redistributive features of pensions incentivise exploiting the flexibility in setting the contribution base to lower the contributions. This might occur in numerous earnings-related schemes where contributions paid increase more strongly with income than pension entitlements, as in the Czech Republic or Norway for example. By contrast, in schemes with a very limited degree of redistribution, such as basic pensions financed by flat-rate contributions in Japan, this problem does not arise.
← 15. The inseparability of labour and capital income has given rise to inconsistencies. For example, income from self-employment is often treated as labour income for social security contributions while it is treated as capital income in national accounts (Gollin, 2002[40]).
← 16. In addition, self-employed workers with low incomes often have lower bargaining power than low-income employees. First, a minimum wage for the self-employed does not exist. Second, competition laws typically prevent the self-employed from organising bargaining activities collectively whereas employees can enrol in trade unions. Workers in false or non-voluntary self-employment might not have any obvious alternative to accepting unfavourable contracts (OECD, 2019[1]). The poor income situation of many self-employed workers is not a new phenomenon, however. The topic was already of major political concern in the 1990s (Freedman and Chamberlain, 1997[39]) and it was even discussed as early as in the 1940s (Wynn and Paz-Fuchs, 2019[45]). By contrast, workers with high earning potential can earn more when independent as they are not subject to wage policies, which sometimes compress wages. Indeed, almost half of the self-employed in the United States point to higher earnings as a reason for working independently (Transamerica, 2019[8]).
← 17. In Ireland, Japan, the Netherlands and the United Kingdom the self-employed mandatorily contribute only towards basic pensions.
← 18. In Poland, the employees are auto-enrolled to the Employees Capital Plans, which is a long-term savings scheme from which assets can be withdrawn after reaching the age of 60 as opposed to Employee Pension Programs which are voluntary.
← 19. In order to circumvent this problem, Finland imposes a constraint which is, however, difficult to verify: the contribution base “must correspond to a wage that would be paid if the work of the self-employed was carried out by another, equally competent person in place of the self-employed” (https://www.etk.fi/en/the-pension-system/pension-security/pension-coverage-and-insurance/self-employed/).
← 20. Most countries also set a ceiling to contribution bases, in line with what is the case for dependent employees.
← 21. Although they can join voluntarily in some countries as in Chile for example.
← 22. Lithuania does not provide a strict minimum threshold but, if contributions are below the minimum wage, reduced periods are credited.
← 23. In Portugal, social security contributions amount to 21.4% of average reference income for most types of self-employed workers, but the contribution rate is higher for specific types of self-employed and can reach 25.1%. In Austria, farmers pay a rate of 17%, while other self-employed workers pay18.5%; both benefit from a so-called partner-contribution from the federal budget amounting to 5.8% and 4.3%, respectively.
← 24. First-tier benefits are taken into account in these projections, but neither the voluntary schemes nor those that are mandatory for only some specific groups of the self-employed, e.g. liberal professions or farmers, are.
← 25. This is despite the fact that a taxable income, which is net of all contributions and of many work-related expenses that a self-employed can deduct, that corresponds to the average gross wage tends to imply that this self-employed individual earns more than the average-wage worker “all else equal” (Figure 2.10).
← 26. In Chile, the contribution rates of the self-employed will increase from 2.7% in 2018 to reach 10% in 2028, i.e. the level of employees.
← 27. If they make use of this option, only the employer pays contributions to the statutory pension scheme and pensions will be proportionally lower.
← 28. Which is considered to be the case if at least 83.3% of their work income stems from one client.
← 29. In Portugal, when self-employed workers receive between 50% and 79% of their income from one single ordering costumer, a social security contribution rate of 7% applies since 2019. The rate increases to 10% when they receive 80% of their income or more from one ordering customer. Below 50%, customers do not pay contributions. Before 2019, ordering customers paid a contribution rate of 5% in case self-employed workers received at least 80% of their income from them and nothing if it was less. By contrast, Spain introduced in 2007 a special category of dependent self-employed (trabajador autónomo económicamente dependiente, TRADE) for those receiving at least 75% of revenue from a single client, without introducing any special pension rules for them.
← 30. Employees working at least 80 hours per month were included in 2003, at least 60 hours in 2010, and non-standard workers working at least 8 days per month in 2018.
← 31. Furthermore, the government started to earmark 12% of the financial aids paid to artists to their pension scheme.
← 32. The analysis of policies targeted at improving compliance with contribution obligations (OECD, 2019[44]; Mineva and Stefanov, 2018[4]) as well as with verifying revenues and costs of the self-employed goes beyond the scope of this chapter (see (OECD, 2018[42]; Bigio and Zilberman, 2011[50]) for more detail).
← 33. Such solutions may reduce the net income of self-employed less than when they pay contributions fully by themselves, as there is some evidence that employer-borne payroll taxes are not fully passed through to net wages (Saez, Schoefer and Seim, 2019[48]).
← 34. Given contribution rates of employees ( ${c}_{e}$) and employers ( ${c}_{r}$), the total contributions paid for an employee are ${W}_{g}\left({c}_{r}+{c}_{e}\right)$, ${W}_{g}$ denoting the gross wage. When expressed in terms of the net wage before tax ( ${W}_{n}$), these equal ${\left({c}_{r}+{c}_{e}\right)W}_{n}/\left(1-{c}_{e}\right)$. If the contribution rate of a self-employed worker ( ${c}_{se}$) is applied to taxable income ( ${I}_{n}$) then contributions equal ${c}_{se}{I}_{n}$. When the taxable income of a self-employed worker is equal to net wage before taxes of a dependent employee, both pay the same contributions if . This implies that the contribution rate of the self-employed applied to taxable income should be larger than the total contribution rate that applies to employees’ gross wages ( ${c}_{se}>{c}_{r}+{c}_{e}$). Alternatively for equal contribution rates between the self-employed and employees ( ${c}_{se}={c}_{r}+{c}_{e}$) with the same taxable income, equalising total contributions requires adjusting contribution bases: Hence, fully harmonising contributions between the self-employed and employees requires to rescale the taxable income by $\frac{1}{1-{c}_{e}}$ or include only a share of gross income: | 2020-04-08 16:16:55 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 12, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.31162816286087036, "perplexity": 6026.671391577112}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-16/segments/1585371818008.97/warc/CC-MAIN-20200408135412-20200408165912-00106.warc.gz"} |
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When a certain conductivity cell was filled with 0.1 M KCl, it has a resistance of 85 Q at 25°C. When the same cell was filled with an aqueous solution of 0.052 M unknown electrolyte, the resistance was 96 Ω. Calculate the molar conductivity of the unknown electrolyte at this concentration. (Specific conductivity of 0.1 M KCl = 1.29 x 10–2 ohm–1cm–1).
Resistance of KCl solution,
R = 85 $\mathrm{\Omega }$
Cell constant = K x R
Resistance of unknown electrolyte solution,
Specific conductance
Concentration,
Molar conductance,
931 Views
How would you determine the standard electrode potential of the system Mg2+/Mg?
Use standard hydrogen electrode as anode and Mg2+ | Mg as a cathode we can measure the standard electrodepotential of systemMg2+ | Mg. Standard hydrogen electrode, represented by Pt(s), H2(g) (1 atm) | H+ (aq) and dip the electrode of Magnesium wire in a 1M MgSO4 solution .The standard hydrogen electrode is always zero.
Use formula
Eocell = Eo right – Eoleft
The standard hydrogen electrode is always zero.
So that the value of
Eoleft =0
Hence
Eocell = Eo Mg|Mg2+
Or
Eo Mg|Mg2+= Eocell
2203 Views
Consult the table of standard electrode potentials and suggest three substance that can oxidize ferrous ions under suitable conditions.
oxidation of ferrous ion means :
Fe2+--> Fe3+ +e-
Any substance which standard electrode potential is more than that of Fe+3 /F+2 can oxidise ferrous ions.
(refer to the table given in book)
The EMF of the substance whose reduction potentials greater than 0.77V will oxidised ferrous ion.
for example Br2, Cl2,and F2 .
879 Views
Calculate the emf of the cell in which the following reaction takes place:
Ni(s) + 2Ag+ (0.002 M) $\to$ Ni2+ (0.160 M) + 2Ag(s)
Given that
$\mathrm{Ni}\left(\mathrm{s}\right)+2{\mathrm{Ag}}^{+}\left(\mathrm{aq}\right)\to {\mathrm{Ni}}^{2+}\left(\mathrm{aq}\right)+2\mathrm{As}\left(\mathrm{s}\right)$
or
The equation is also written as
or
= 1.05 V – 0.0295 x log 80
= 1.05 V – 0.0295 x 1.9031
= 1.05 V – 0.056 = 0.99 V.
1585 Views
Can you store copper sulphate solutions in a Zinc pot?
No. Because zinc is more reactive than copper and thus holes will be developed in zinc pot.
Cu2+(aq) + Zn(s) → Zn2+ (aq) + Cu(s)
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Calculate the potential of hydrogen electrode in contact with a solution whose pH is 10. | 2018-08-15 21:12:19 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 3, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5499110817909241, "perplexity": 4587.269182192172}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-34/segments/1534221210304.2/warc/CC-MAIN-20180815200546-20180815220546-00390.warc.gz"} |
https://hal.inria.fr/inria-00200967 | # Making Random Choices Invisible to the Scheduler
1 COMETE - Concurrency, Mobility and Transactions
Inria Saclay - Ile de France, LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau]
Abstract : When dealing with process calculi and automata which express both nondeterministic and probabilistic behavior, it is customary to introduce the notion of scheduler to resolve the nondeterminism. It has been observed that for certain applications, notably those in security, the scheduler needs to be restricted so not to reveal the outcome of the protocol's random choices, or otherwise the model of adversary would be too strong even for obviously correct'' protocols. We propose a process-algebraic framework in which the control on the scheduler can be specified in syntactic terms, and we show how to apply it to solve the problem mentioned above. We also consider the definition of (probabilistic) may and must preorders, and we show that they are precongruences with respect to the restricted schedulers. Furthermore, we show that all the operators of the language, except replication, distribute over probabilistic summation, which is a useful property for verification.
Document type :
Conference papers
Cited literature [21 references]
https://hal.inria.fr/inria-00200967
Contributor : Catuscia Palamidessi Connect in order to contact the contributor
Submitted on : Saturday, December 22, 2007 - 9:56:40 AM
Last modification on : Thursday, January 20, 2022 - 4:12:28 PM
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### Citation
Konstantinos Chatzikokolakis, Catuscia Palamidessi. Making Random Choices Invisible to the Scheduler. CONCUR'07, Sep 2007, Lisboa, Portugal. ⟨10.1007/978-3-540-74407-8_4⟩. ⟨inria-00200967⟩
Record views | 2022-05-17 18:48:38 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5468469262123108, "perplexity": 2812.3710126743067}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662519037.11/warc/CC-MAIN-20220517162558-20220517192558-00351.warc.gz"} |
https://www.bionicturtle.com/forum/threads/capm-equilibrium-theory.711/ | # CAPM - Equilibrium Theory
Discussion in 'P2.T8. Investment Management (15%)' started by dennis_cmpe, Oct 26, 2008.
Tags:
1. ### dennis_cmpeNew Member
In the study notes for CAPM Equilibrium Theory:
1) All assets must be held in portfolios, including the risky asset portfolio.
Sounds simple, but I'm not getting the importance of it. What does this mean? Why is this important?
2. ### David Harper CFA FRMDavid Harper CFA FRM (test)Staff Member
Dennis,
The theoretical significance is that is paves the way for the capital market line (CML). It is an implication (not a premise of) the assumptions underyling the CAPM (assigned Chapter 4, Noel Amenc). If you consider the CAPM assumptions--they are really unrealistic so it is just setting up they theory--a key idea is that all investors have the exact same information about the same set of assets and they also use the same risk/return perspective. In short, the investors are clones of each other therefore they must reach the same conclusion. This homogeneity ensures inclusion of all risky assets: if a stock is avoided, then all will avoid it, and it's price goes to zero. But it is very attractive at zero, so in unison, the investor will like it even at some low price. I can't say i personally find this implication of equilibrium particularly important, but it's on the way to the more important CAPM idea that a security's return/risk owe not to its individual characteristics (e.g., standard deviation) but rather its risk contribution (i.e., beta) to the market portfolio.
David
3. ### saurabhpal49New MemberSubscriber
Hi david,
I have some doubts regarding CAPM
>In capm there is homogenous expection, so why would some one be willing to sell market portfolio as all
investors want market portfolio?
>Could you please explain the below paragraph:
"The expected payoff of any asset remains constant under CAPM assumptions, such that when its price falls, its expected return increases. So, the expected return is at a point where supply is equal to demand in equilibrium"
>E(Rm)-Rf= risk aversion *6^2m
Why does increase in risk aversion increase the risk premium,
It should decreases as investor is unwilling to take more risk
Thanks
Last edited: Oct 26, 2017
4. ### David Harper CFA FRMDavid Harper CFA FRM (test)Staff Member
Hi @saurabhpal49 There is a lot of theory underlying CAPM (although I've trained it for years, I can't pretend to be a deep expert, I am more like a shallow expert; the Elton book is basically about CAPM theory).
• Homogenous expectations refers to the assumption that all market participants have the same view with respect to the limited inputs that matter in the restricted CAPM universe, which are: returns (or, equivalently prices), variances, and correlations. This is the meaning of "mean-variance:" they agree on means, variances and (related) the correlation (or, related, covariance) matrix. In my view, homogenous expectations leads all investors to the same optimal market portfolio (the portfolio of risky assets with the highest sharpe ratio). Ff you are interested, it so happens that literally yesterday I recorded/published a video to our youtube channel that is called "Capital market line (CML) versus security market line (SML), FRM T1-8" which includes a visualization of achieving the Market Portfolio (aka, mean-variance efficient portfolio, it is called by Ang) http://trtl.bz/2yPLQsa. My view is that, under the theory, homogeneous expectations leads all (equally-informed) investors to hold the same most-efficient Market Portfolio which itself is only the risky assets (the purple triangle in my video, snapshot below) such that, to your point, investors do not want to sell this portfolio. Rather, they are deciding only how to allocate between the Market Portfolio and the risk free asset (ie, where on the blue line will they locate?).
• Your second point is why investors would buy/sell individual securities. He is referring to (eg) the asset's future cash flow. If (eg) we all homogeneously agree that asset AA with a beta of 1.5 will pay future cash of $10.00 but its current price is$9.50, then it is currently priced too high b/c the expected return is only 10/9.50 - 1 = 5.3%. If the Rf rate = 3.0%, it will be sold until its price is down to \$8.93 because that is a price that is in equilibrium with its expected return of 12.0%. The idea is the current price adjusts according to an expected return, per PV = future cash/(1+ discount rate). | 2018-05-25 02:15:41 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.465359628200531, "perplexity": 2932.3108640754567}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-22/segments/1526794866917.70/warc/CC-MAIN-20180525004413-20180525024413-00227.warc.gz"} |
https://encyclopediaofmath.org/wiki/Mathematical_ecology | # Mathematical ecology
There are two kinds of models in mathematical ecology, broadly speaking. There are, on the one hand, models of strategic type, which are based on empirical formulas and use computer simulation techniques. These are popular among ecologists because they fit the data extremely well and are highly predictive in particular cases, say a wheat field in Saskatchewan or a sheep herd in New Zealand. But, in fact, they tell next to nothing about the underlying ecology. On the other hand, there are dynamical models, which often involve ordinary differential equations, but may use stochastic differential equations, difference equations, integral equations, or diffusion reaction equations. These models encode postulates about ecological mechanisms into the equations. As a rule, these do not predict as well as strategic models do, because of the constraints imposed by these postulates. But it is through the use of dynamical models that tentative explanations can be found and eventual consensus reached, so that more general, improved, strategic models can be designed for ecosystem management. Below, for the sake of brevity only ordinary differential equation models are considered.
## Growth of a single population.
Let $N ( t )$ denote the total number, or density, of a population $\Sigma$ at a fixed location and time. Assume that $N ( t )$ is continuous in the time $t$. The Hutchinson postulates [a16] are:
1) $d N / d t = f ( N )$, $f$ sufficiently differentiable;
2) $N \equiv 0$ implies $d N / d t \equiv 0$;
3) $N ( t )$ is bounded between zero and a fixed positive constant $C$, for all time.
Given the Hutchinson postulates for a population $\Sigma$, it follows that the ordinary differential equation
$$\tag{a1} \frac { d N } { d t } = \lambda N \left( 1 - \frac { N } { K } \right) ,$$
for which
$$\tag{a2} N ( t ) = \frac { K } { 1 + b e ^ { - \lambda t } }$$
is the general solution, is the simplest growth law. It is called the logistic equation.
The parameter $K$, called the carrying capacity for $\Sigma$, obviously satisfies $0 < K \leq C$. The parameter $\lambda > 0$ is called the intrinsic growth rate. Of the four types of shapes specified for (a1) by $b < 0$, $b = 0$, $0 < b \leq 1$, $b > 1$, only the last is $S$-shaped (i.e. its graph has an inflection point).
Suppose that $\Sigma$ satisfies only (a1) and (a2); then, denoting $n ( t ) = N ( t ) - N_ {*}$, where $f ( N_{ *} ) = 0$ (i.e. $N _{*}$ is a steady-state), Taylor expansion around $N _{*}$ gives
\begin{equation*} \frac { d N } { d t } = \frac { d n } { d t } = f ( N ) = \end{equation*}
\begin{equation*} = f ( N_{ * } ) + f ^ { \prime } ( N_{ * } ) n + \frac { f ^ { \prime \prime } ( N_{ * } ) } { 2 } n ^ { 2 } + \ldots, \end{equation*}
where the prime denotes differentiation with respect to $N$. For $n ( t )$ small in absolute value, $d n / d t$ is well approximated by $f ^ { \prime } ( N_{*} ) n$. Therefore, $n ( t )$ increases with time if $f ^ { \prime } ( N _{*} ) > 0$, and decreases if $f ^ { \prime } ( N_{*} ) < 0$. In the former case, $N _{*}$ is an unstable steady-state while, in the latter case, $N _{*}$ is a stable steady-state.
For the logistic special case, $N_{*} = 0$ or $N_* = K$ are the only possible steady-states, the former being unstable and the latter stable.
The logistic differential equation (a1) is the simplest description of a population with limited resources, the limitation being provided by the negative coefficient of the quadratic term. The equation first arose in the work of P. Verhulst (1838) and later in the demographic research of R. Pearl and L. Reed in the 1920s. It was subsequently used to provide a dynamic model of malaria in humans by Sir Ronald Ross, but has perhaps a more basic role in ecology than in epidemiology.
## Growth dynamics in a competitive community.
Several species living in the same locality must forage for food and seek nesting sites in a field or stream, etc. These populations may or may not affect one another.
Suppose that $n$ species comprise a community $\Sigma$ in which there are no inter-specific interactions. This ecosystem can be modeled by
$$\tag{a3} \frac { d N ^ { i } } { d t } = \lambda _ { ( i ) } N ^ { i } \left( 1 - \frac { N ^ { i } } { K _ { ( i ) } } \right) , \quad i = 1 , \ldots , n,$$
where $N ^ { i }$ denotes the total number or density of the $i$th species in $\Sigma$. This system has $2 ^ { n }$ steady-states, but only $( K _ { ( 1 ) } , \dots , K _ { ( n ) } )$ is stable. The equations (a3) describe non-competition.
Now suppose there is competition for food items, etc. How does one describe this? G.F. Gause and A.A. Witt answered this for a $2$-species community ($n = 2$) with [a11]
$$\tag{a4} \left\{ \begin{array}{l}{ \frac { d N ^ { 1 } } { d t } = \lambda _ { ( 1 ) } N ^ { 1 } \left( 1 - \frac { N ^ { 1 } } { K _ { ( 1 ) } } - \delta _ { ( 1 ) } \frac { N ^ { 2 } } { K _ { ( 1 ) } } \right), }\\{ \frac { d N ^ { 2 } } { d t } = \lambda _ { ( 2 ) } N ^ { 2 } \left( 1 - \frac { N ^ { 2 } } { K _ { ( 2 ) } } - \delta _ { ( 2 ) } \frac { N ^ { 1 } } { K _ { ( 2 ) } } \right). }\end{array} \right.$$
Here, all $\lambda$, $K$ and $\delta$ are positive. This system has exactly one positive equilibrium $( N _ { * } ^ { 1 } , N _ { * } ^ { 2 } )$, given by
$$\tag{a5} \left\{ \begin{array}{l}{ N _ { * } ^ { 1 } = \frac { K _ { ( 1 ) } - \delta _ { ( 1 ) } K _ { ( 2 ) } } { 1 - \delta _ { ( 1 ) } \delta _ { ( 2 ) } }, }\\{ N _ { * } ^ { 2 } = \frac { K _ { ( 2 ) } - \delta _ { ( 2 ) } K _ { ( 1 ) } } { 1 - \delta _ { ( 1 ) } \delta _ { ( 2 ) } }. }\end{array} \right.$$
If both numerators and denominators are positive, then $( N _ { * } ^ { 1 } , N _ { * } ^ { 2 } )$ in (a5) is stable. If they are both negative, (a5) is unstable. This is easily proved by using the stability Ansatz: the eigenvalues of the Jacobian of the right-hand side of a system
\begin{equation*} \frac { d N ^ { i } } { d t } = f ^ { i } ( N ^ { 1 } , \ldots , N ^ { n } ) , \quad i = 1 , \dots , n, \end{equation*}
evaluated at a steady-state $( N _ { * } ^ { 1 } , \ldots , N _ { * } ^ { n } )$, must have negative real part for stability. If any of these is positive, an unstable case results.
In the question of survival for the two populations in Gause–Witt competition (a4), (a5), there are four cases to consider:
A) If $\delta _{( 1 )} > K _ { ( 1 ) } / K _ { ( 2 ) }$ and $\delta_{( 2 )} > K _ { ( 2 ) } / K _ { ( 1 ) }$, then (a5) is unstable, with survival depending on the initial proportions of $N ^ { 1 }$ and $N ^ { 2 }$.
B) If $\delta _{( 1 )} > K _ { ( 1 ) } / K _ { ( 2 ) }$ and $\delta _ { ( 2 ) } < K _ { ( 2 ) } / K _ { ( 1 ) }$, then (a5) is unstable, and the first species will be eliminated.
C) If $\delta _ { ( 1 ) } < K _ { ( 1 ) } / K _ { ( 2 ) }$ and $\delta_{( 2 )} > K _ { ( 2 ) } / K _ { ( 1 ) }$, then (a5) is unstable, and the second species will be eliminated.
D) If $\delta _ { ( 1 ) } < K _ { ( 1 ) } / K _ { ( 2 ) }$ and $\delta _ { ( 2 ) } < K _ { ( 2 ) } / K _ { ( 1 ) }$, then (a5) is stable.
Therefore, only in case D), called incomplete competition, can both species coexist. This case translates as some geometrical separation of the two species, where the more vulnerable one has a refuge it can retreat to, or some resource available that the otherwise better adapted competitor cannot use [a16].
Experiments performed by Gause on Paramecium [a10] verified the outcomes A)–D) qualitatively. Thus, the Gause–Witt equations imply that complete competitors cannot coexist. This is the famous principle of competitive exclusion, a corner-stone of mathematical ecology. There are variants and generalizations of this principle; see, e.g., [a2]. This generality underscores the fundamental importance of that principle. Indeed, biologists claim that competition between species has profound evolutionary consequences [a7].
## Three-species interactions: a general model applicable to several different ecosystems.
One of the great benefits of dynamical models is their tendency to be applicable in more than one ecological situation. This is partly because they are framed in precise mathematical terms encoding a list of specific postulates and assumptions, but also because in their qualitative behaviour lies the essence of their application. An illustration of this is the example given below, of a model known to encompass three different ecosystems. The model exhibits switching between multiple steady-states and stable periodic solutions (i.e. stable limit cycles) induced by predation of one species on another. In its full generality, the system (a9) models predation on a herbivore which in turn feeds on a plant species. The limit cycle behaviour described is not induced by time-lags, as in the classical Lotka–Volterra predator-prey model (with predator devastating the prey population to the extent that there is not enough prey for the much larger predator population, which then crashes, resulting in the prey population coming back full circle). Rather, the mechanism is aggregation, caused by spawning or feeding behaviour of the predator, conditioned by environmental constraints in some cases (e.g. cyclones, drought, nutrient enrichment, etc.). Furthermore, one must always prove that a periodic solution, topologically a circle, is stable, in the sense that there is a solid torus $T$ in phase-space whose centre is the cycle and having the property that any solution with initial conditions in $T$ will converge onto that cycle as $t \rightarrow + \infty$. The methods of Hopf bifurcation provide the necessary tools for this analysis [a15].
The logistic growth equation with exponential parameter $a > 0$,
$$\tag{a6} \frac { d N } { d t } = \lambda N \left( 1 - \left( \frac { N } { K } \right) ^ {a } \right),$$
was introduced to explain certain data on Drosophila in [a13]. The case $a > 1$ indicates greater self-inhibition while the converse is true for $a < 1$. Similarly, the dynamical model
$$\tag{a7} \frac { d F } { d t } = - \varepsilon F ( 1 - \gamma F ^ { p } ),$$
where $\varepsilon > 0$, $\gamma > 0$ and $p \in ( 1 / 2,3 / 2 )$, was introduced to explain crown-of-thorns starfish (Acanthaster planci) aggregation on coral reefs [a1], [a21]. The term $\gamma F ^ { p }$ is called the cooperative term. If $p < 1$, then the variable coefficient of $F ^ { 2 }$ in (a7) is relatively large for small values of $F$. This results in increased cooperation, and the reverse is true for $p > 1$. The parameter $\gamma$ is the coefficient of aggregation. It also serves as Hopf bifurcation parameter in (a8) and (a9), where Hopf's method can be used to prove the existence of small amplitude-stable periodic solutions (i.e. stable limit cycles), [a15]. Note that $p$ is fixed in a model, unlike $\gamma$, which is a free parameter. Rather, $p$ is an indicator of fecundity or genetically determined potential for reproduction. The role of $p$ and $\gamma$ in (a8) and (a9) is investigated below.
Consider the ordinary differential equations
$$\tag{a8} \left. \begin{cases} { \frac { d N } { d t } = N ( - 2 \alpha N - \delta F + \lambda ), } \\ { \frac { d F } { d t } = F ( 2 \beta N + \gamma F ^ { p } - \varepsilon ), } \end{cases} \right.$$
where $p$ is taken slightly less than $1$. The constants $\alpha$, $\delta$, $\beta$, $\gamma$ can be given a precisely defined chemical interpretation based on the concepts of the Volterra production variable and on the Rhoades allometric plant response mechanism [a19], [a21]; $N$ denotes the density of plant modular units (e.g. leaves); [a14]. $F$ is the density of the herbivore population in the same locality. The system (a8) is a model in the theory of optimal defense of plants against herbivores, [a19].
Use of Hopf bifurcation theory and the Hassard code BIFOR2 show the existence of a stable periodic solution (i.e. limit cycle) of small amplitude [a1], [a15]. One may also show that the amplitude can be large [a3]. It is also possible to show that the period of the cycle is longer for plants which use the metabolically expensive chemical defense (e.g. oaks), as opposed to plants (e.g. herbaceous) which do not. This explains both the 9–10 year cycle of the oak caterpillar and the 3–4 cycle of voles and lemmings which eat herbaceous plants. The model requires $p \ll 1$ so that the herbivore must not only have highly aggregative behaviour, but must be highly fecund.
An interesting application of the chemically mediated plant/herbivore system (a8) is to the lynx-snowshoe hare (Lepus americanus) cycle in the Arctic (cf. also Canadian lynx data; Canadian lynx series). $N$ denotes the modular unit density for the plant and $F$ the hare density. The large reproductive potential of the $F$-population is interpreted as $p \ll 1$. It is known that the plants which hares eat are chemically defended and that this has a strong negative effect on the hare population. It was discovered in the field that the hare population cycles both with and without the presence of lynx [a8], [a17], [a6]! The three species extension of (a8), which incorporates the lynx, is
$$\tag{a9} \begin{cases} { l } { \frac { d N } { d t } = N ( - 2 \alpha N - \delta F + \lambda ) }, \\ { \frac { d F } { d t } = F ( 2 \beta N + \gamma F ^ { p } - \varepsilon - \mu _ { 1 } L ) }, \\ { \frac { d L } { d t } = \mu _ { 2 } L F - \nu L }, \end{cases}$$
where all constants are non-negative. For convenience one sets $\alpha = \beta$, but this has no biological significance. However, if one also sets $\mu _ { 2 } = \gamma$ and rewrites the third equation as
$$\tag{a10} \frac { d L } { d t } = \gamma L ( F - \xi ) , \quad \xi = \frac { \nu } { \gamma },$$
the assumption $\mu _ { 2 } = \gamma$ implies that the predator $L$ is getting more food value out of its kill, all other things being equal, as $\gamma$ increases. This model shows that the high reproductivity of the Arctic hare population ($p \ll 1$) drives a stable periodic cycle whose period increases with increasing amounts of defensive compounds in the plant tissues. Also, the $F$-population will cycle without the lynx and so the lynx-hare cycle is driven by the hare's food quality, with the lynx population going along piggy-back style. This model is an improvement over the time-lag model, [a20], [a12].
A model of Acanthaster planci predation on corals of the Great Barrier Reef is provided by (a8), but without the chemical interpretation for the $N$-population, which in this case is coral. The starfish population is highly fecund and aggregates, causing outbreaks with a 12–15 year period [a4]. Thus, $p \ll 1$ will generate a bifurcation from the positive equilibrium of (a8) to a stable periodic cycle triggered by increasing $\gamma$ beyond a certain critical Hopf value determined by the coefficients in (a8). The extended system (a9) can be used to discuss the claim of marine biologist R. Endean that the giant conch, C. tritonis, which preys on adult Acanthaster plani, may be a keystone predator on the Great Barrier Reef [a9]. Such a conception excludes any limit cycle behaviour, a priori, and is essentially a steady-state theory. Assuming that C. tritonis gains when starfish aggregate (i.e. $\gamma$ increases) and that $p \ll 1$, the model (a9) predicts Hopf bifurcation from a steady-state to a stable limit cycle of moderate amplitude. Consequently, C. tritonis must also cycle synchronously (i.e. piggy-back). However, there is no evidence for regular conch fluctuations in this case. Yet, if A. planci were neither highly fecund nor aggregative, then $p \geq 1$ would have to be used in (a9) and the result would be a steady-state (perhaps several). That is, giant triton would be a keystone predator, similar to the role of sea otters in the Western Canadian sea urchin-kelp system discussed below.
On the west coast of North America, red sea urchins (S. franciscanus) feed on kelps in large aggregates and exist in at least two possible steady-states: at very low density within kelp beds ($\delta \neq 0$) in the presence of sea otters; or at high density outside kelp beds ($\delta \approx 0$) in the absence of sea otters $( L _ { 0 } \approx 0 )$ [a5]. If $L _ { 0 } \approx 0$, then $F _ { 0 }$ is relatively large, as is $N_ 0$. The system (a9) has a unique positive equilibrium for $\lambda - \delta \xi > 0$ and $2 \beta N _ { 0 } + \gamma \xi ^ { p } - \varepsilon > 0$, $p > 1$. It is
$$\tag{a11} N _ { 0 } = \frac { \lambda - \delta \xi } { 2 \alpha } , L _ { 0 } = \frac { 2 \beta N _ { 0 } + \gamma \xi ^ { p } - \varepsilon } { \mu _ { 1 } } , F _ { 0 } = \xi.$$
In the case where $\delta \approx 0$, the system reduces to one with steady-state: ($N _ { 0 } = \lambda / ( 2 \alpha )$, $L _ { 0 } = 0$, $F _ { 0 } = \xi$), with $p > 1$. It is known from field data that the steady-state can rapidly switch and depends only on the presence or absence of sea otters. The otter is a keystone predator causing rapid switching in the red sea urchin population.
The above model also applies to the lobster-sea urchin-kelp system of the Eastern Canadian coast. In this case the lobsters play the keystone predator role, [a18].
#### References
[a1] "Mathematical essays on growth and the emergence of form" P.L. Antonelli (ed.) , Univ. Alberta Press (1985) MR0826076 Zbl 0572.00026 [a2] P. Antonelli, R. Bradbury, X. Lin, "On Hutchinson's competition equations and their homogenization: A higher-order principle of competitive exclusion" Ecol. Modelling , 60 (1992) pp. 309–320 [a3] P.L. Antonelli, K.D. Fuller, N.D. Kazarinoff, "A study of large amplitude periodic solutions in a model of starfish predation on coral" IMA J. Math. Appl. in Medicine and Biol. , 4 (1987) pp. 207–214 MR910187 [a4] "Acanthaster and the coral reef: A theoretical perspective" R. Bradbury (ed.) , Lecture Notes Biomath. , 88 , Springer (1990) [a5] P. Breen, T.A. Caros, J.B. Foster, E.A. Stewart, "Changes in subtidal community structure associated with British Columbia sea otter transplants" Marine Eco. , 7 (1982) pp. 13–20 [a6] J.T. Bryant, "The regulation of snowshoe hare feeding behaviour during winter by plant anti-herbivore chemistry" K. Myers (ed.) C.D. McInness (ed.) , Proc. World Lagomorph Conf. , Guelph Univ. Press (1979) [a7] N. Elredge, "Time frames, the evolution of punctuated equilibria" , Princeton Univ. Press (1989) [a8] C.S. Elton, "The ecology of invasion by animals and plants" , Methuen (1958) [a9] R. Endean, "Acanthaster planci infestations of reefs of the Great Barrier Reef" , Proc. Third Internat. Coral Reef Symp. , 1 (1977) pp. 185–191 [a10] G.F. Gause, "The struggle for existence" , Williams and Wilkins (1934) [a11] G.F. Gause, A.A. Witt, "Behaviour of mixed populations and the problem of natural selection" Amer. Nat. , 69 (1935) pp. 596–609 [a12] M.E. Gilpin, "Do hares eat lynx?" Amer. Nat. , 107 (1973) pp. 727–730 [a13] M. Gilpin, F.J. Ayala, "Global models of growth and competition" Proc. Nat. Acad. Sci. , 70 (1973) pp. 3590–3593 Zbl 0272.92016 [a14] J.L. Harper, "The population biology of plants" , Acad. Press (1977) [a15] B. Hassard, N.D. Kazarinoff, Y.-H. Wan, "Theory and applications of Hopf bifurcations" , London Math. Soc. Lecture Notes , 41 , Cambridge Univ. Press (1981) MR0603442 [a16] G.E. Hutchinson, "An introduction to population biology" , Yale Univ. Press (1978) [a17] L.B. Keith, "Wildlife's ten-year cycle" , Univ. Wisconsin Press (1963) [a18] K. Mann, "Kelp, sea urchins and predators: a review of strong interactions in rocky subtidal systems of eastern Canada 1970–1980" Netherl. J. Sea Research , 16 (1982) pp. 414–423 [a19] D.F. Rhoades, "Offensive-defensive interactions between herbivores and plants: their relevance in herbivore population dynamics and ecological theory" Amer. Nat. , 125 (1985) pp. 205–223 [a20] R.E. Ricklefs, "Ecology" , Chiron Press (1979) (Edition: Second) [a21] P.L. Antonelli, R. Bradbury, "Volterra–Hamilton models in the ecology and evolution of colonial organisms" , Ser. Math. Biol. and Medicine , World Sci. (1996) Zbl 0930.92031
How to Cite This Entry:
Mathematical ecology. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Mathematical_ecology&oldid=50005
This article was adapted from an original article by P.L. Antonelli (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article | 2023-04-02 09:38:59 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 11, "x-ck12": 0, "texerror": 0, "math_score": 0.7794027328491211, "perplexity": 1670.7312477203463}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296950422.77/warc/CC-MAIN-20230402074255-20230402104255-00228.warc.gz"} |
https://puzzling.stackexchange.com/questions/15216/a-surprising-circle-packing/15221 | # A Surprising Circle Packing
A grocery store has a long, skinny box, with no top, that it uses to display soda. The box is two soda cans wide and 200 soda cans long. You can neatly fit 400 cans in this box, using two rows of 200, as shown below.
Show how to fit $401$ soda cans into this box (with their bases resting flat on the floor of the box).
There is no lateral thinking involved in this solution. You can think of this as a purely geometric, two dimensional problem, where you are trying to fit $401$ circles of diameter $1$ into a $2\times200$ rectangle.
• This tool engineeringtoolbox.com/circles-within-rectangle-d_1905.html says that for (200,2,1) the maximum is 400. I don't trust it, though! – leoll2 May 19 '15 at 20:12
• @leoll2 I was looking at that same link. Did you read the note at the bottom? It says that it can't always give the optimal packing. – Rob Watts May 19 '15 at 20:20
• I assume we aren't allowed to dive into the third dimension for this question, eh? – Bailey M May 19 '15 at 20:43
• @BaileyM Why restrict yourself to only 3. Why not 4 or 5? :p – Mark N May 19 '15 at 20:48
• Really tempted to post an answer of the pic in the OP, with the text altered to say "395 more cans". – rybo111 May 20 '15 at 13:04
EDIT: The description is not very intuitive, so I took the liberty of creating an image to make clear what this solution intents.
Sorry I'm new to this forum... I'm going to try to post an answer. Unfortunately I'm bad with computers so I can't draw a picture... Please get out a pencil and paper! The summary is:
We're going to make a repeating pattern of six cans. The pattern will have three cans in the top row and three cans in the bottom row. They will be "offset" by .5 units, and each row will have width a little bit less than 3 units.
The details:
I'm going to give the coordinates of the centers of the cans... the centers have to be in a 1-by-199 box, since they can't be within one unit of the edge, and no two centers can be within one unit of each other.
And:
Here's the repeating pattern: The coordinates of the three points in the bottom row will be (0, 0), (1, 0), (1.992 , .13). It will repeat again, offset by 2.984 units, so: (2.984, 0), (3.984, 0), (4.976, .13). And so forth.
And:
In the top row the first three points will have coordinates (.5, .87), (1.492, 1), (2.492, 1). Then the next three it repeats: (3.484, .87), (4.476, 1), (5.476, 1), etc.
Now before I check that my solution works let me give some intuition:
There are two rows of cans. I "offset" the cans by half a unit: so if the bottom cans (center points) have x-coordinates 1, 2, 3, then the top cans are centered at 1.5, 2.5, 3.5. Now that gives me some "wiggle room" which I can use to move some of the cans up and down a little bit. Moving some cans up and down means I can make them take up ever-so-slightly less horizontal space -- I can compress a row horizontally. Now if I only compress one row but not the other I can't maintain the .5-unit offset. So I compress the two rows in turns. That's how the pattern works.
It turns out it's just enough to get the compression we need:
First you can check that the points I put are all 1 unit apart. In the bottom row you just check that .992^2 + .13^2 > 1, which it is. The top row is the same by symmetry. Between the bottom row and the top row, the key calculation is .5^2 + .87^2 > 1, which is also true.
And then you count the total space:
Let's say there are 201 cans in the bottom row, so you have to have 200 intervals. How much space will those take up? Well, every 3 cans take 2.984 units, so you save .016 units every three cans, or a total of 1.072, which is just good enough!
• Welcome to Puzzling SE! It's refreshing to see a new user who understands how to use the system on their first go (a sign you actually read the rules). Good on you and keep it up. – Elias Benevedes May 20 '15 at 13:26
• Well done! For those who want an illustration, see user4651's answer. – Mike Earnest May 20 '15 at 17:42
• I wonder what would be the smallest even number of circles for which 2N circles could fit in a width less than N by any amount? – supercat May 20 '15 at 22:11
• I added an edit with a clearer (imo) visualization to this solution. – M.Herzkamp May 21 '15 at 9:03
• @M.Herzkamp, so did I. But thanks for putting one here. :) – user4651 May 22 '15 at 8:59
Here is a CAD drawing I created to show the layout:
Using trigonometry and the facts that all the magenta lines and height of the rhombus are unit length, we can find that the center of the yellow circle is at x-coordinate 1.495. We can then create a function for distance required to store n number of cans on the bottom row: F(n) = 1 + 0.995 * (n - 1) for n >= 1 so F(201) = 200 , meaning we can fit 201 cans on the bottom row, and one less on the top, for 401 total.
• In your $F(n)$ expression, the $0.995$ number should actually be $\approx$ 0.99578, so that $F(201)>200$. – Mike Earnest May 20 '15 at 4:10
• Maybe try to take it one step further. Instead of repeating 4, try to attach a fifth one, and then repeat that, except each time you must flip-flop it. I love puzzles like this, but it's nearly impossible to play around with configurations in a hands-on way. If that were easier, then it would be even better. – JLee May 20 '15 at 13:13
Here's the MSPaint to the rescue answer. The math logic works in my head as well. The top packing is tighter.
each triangle after the 1st one saves (edit: $1-\sqrt{{{1-(1-\sqrt{\frac{3}{4}}}}})^2$ ) ~0.00901523343248242768377221117738 diameters. Multiply by 132 and get 1.190010813087680454257931875414. The first triangle is on the bottom left. The 133rd is also on the bottom, leaving space for 1 on top of another packed into the right edge. QED
the math:
looks like i failed, unless my math is off my a factor of 2, it fits 402. 1.0+2.0*pow(1.0*1.0*pow((1.0-pow(1.0*1.0-0.5*0.5,0.5)),2.0),0.5)/6.0 simplified math: sqrt( 1 - ( sqr( 1 - sqrt( .75 ) ) ) / 3.0 is the ratio.
< correct math below
strikethrough the previous text. 1st commenter clarified the math, it's 1 - sqrt( 1 - ( sqr( 1 - sqrt( .75 ) ) ) saved for each triangle after the first one. 133 triangles leaves 132 * ( 1 - sqrt( 1 - ( sqr( 1 - sqrt( .75 ) ) ) ) extra space on the end.
• I was literally just about to post basically the same solution. Mathematically, you can show that each triangle starts $x=\frac{1+\sqrt{4\sqrt{3}-3}}2\approx 1.490985$ to the right of the previous triangle, and obviously each triangle is length 2 along the box and contains three cans. With 133 such triangles, we would have 399 cans. The rightmost edge of the 399th can is at $132x+2 \approx 198.81$, and thus there is enough room for one can directly next to it on the same edge, and then you can place the 401st can in the remaining space on the other edge. – Glen O May 20 '15 at 7:45
• Good math. I don't know latex or whatever you used to do that math, but I'm confident that the Pythagoras I used is correct. Also I was rushing to get it typed up because I knew someone was working on it as I typed and MSPainted. – user4651 May 20 '15 at 7:52
• You can't quite fit 402, by the way - to do so, you'd need one more triangle on the end, so basically you'd need the right edge to match the left edge and to have 134 triangles. But 134 triangles will require about 200.3 can-widths (that is, $133x+2$), just a little too much. – Glen O May 20 '15 at 8:07
• @GlenO, Alternatively, each triangle after the 1st one saves ~0.00901523343248242768377221117738 diameters. Multiply by 132 and get 1.190010813087680454257931875414. The first triangle is on the bottom left. The 133rd is also on the bottom, leaving space for 1 on top of another packed into the right edge. – user4651 May 20 '15 at 8:12
• 402 would work if space repeated itself at the end of the box, but you're right. If space repeated, one of the triangles would have to be replaced by a 3-on-the-bottom, 2-on-the-top group. – user4651 May 20 '15 at 8:22
Okay, here's a badly-drawn way to do it:
Start by taking four cans and lining them up in a diamond. Then, tilt that diamond until it touches the top of the box:
Now repeat with four cans at a time, each making a diamond, and push that diamond as far to the left as it will go. The first diamond uses $1 +\sqrt{2}$, or about $2.414$, diameters, but each additional diamond only adds about $1.99156$ diameters. So after $100$ diamonds of $4$ cans each, you end up with enough extra space at the bottom right to fit an extra can.
• Perhaps I'm mistaken, but doesn't your arrangement of $401$ cans take up $0.5+100\cdot 1.99156+0.5$ diameters horizontally, which is more than 200? The $1.99156$ is the distance between two cans which touch the south wall, of which there are $100$ such gaps, and the $0.5$ at either end accounts for the halves of the cans on the end which touch the east and west walls. – Mike Earnest May 20 '15 at 0:55
• ^I mean $1.99156$ is the distance between the centers of two cans which touch the south wall – Mike Earnest May 20 '15 at 2:37
• What if you use a "diamond" of six cans? Eight? 400? – Random832 May 20 '15 at 3:32
• @Random832: Less "tilt" = "less horizontal gain" – BmyGuest May 20 '15 at 7:36
Playing around in paint (400 height, 100 radii circles), I made a slight stagger.
The width of the three circles on top is less than if they were directly side by side, so this trapezoid can be flipped and repeated.
• The point when you have staggered enough to add another circle is when you have moved over to the left by 1 diameter. In other words, when you get back to where you started. – user3294068 May 19 '15 at 20:07
• I'm not sure what I was thinking, I think I just looped back on my original thoughts. Going to edit the picture. – Quark May 19 '15 at 20:08
• @leoll2 I edited the picture and specified the difference between this answer and Mark's. – Quark May 19 '15 at 20:17
• This looks promising, but I 'm not convinced that this will actually save enough space to fit in an extra two cans (Mark's configuration will only fit 399 cans). – Rob Watts May 19 '15 at 20:30
• If you press in on the rightmost one, the two at the bottom spread out, the middle one goes down an the one you are pressing on moves in. Eventually, you get to leoll2's answer. – user3294068 May 19 '15 at 20:32
Perhaps a configuration like this?
I haven't done the math yet, so not sure if it actually works.
• Draw a triangle using the centers of the cans in the first pair and the center of one of the cans in the second pair. Calling the diameter of a can '1', we get a triangle with hypotenuse 2, height 1, and width 3^(.5)=1.73. – Rob Watts May 19 '15 at 19:59
• That means a width of 0.73 is used up by each of the unpaired cans, which is not as good as the average of 0.5 used up by a pair. – Rob Watts May 19 '15 at 20:00
• @RobWatts That's what I'm doing at this moment. I'm just trying to realize how many cans I have – leoll2 May 19 '15 at 20:00
• @Kevin If that's true, I've a new job at CocaCola packaging industry. – leoll2 May 19 '15 at 20:06
• Oops, got the can radii wrong. My second envelope says floor(400*3/(4*cos(30))) = 346. – Kevin May 19 '15 at 20:14
Perhaps:
By shifting the top row of circles
And then cramming 1 in the top left corner, you will get a trapezoid shape. Although this could only be maintained depending on properties of the box
(I have yet to have the math to prove this)
• I don't think this could work. The bottom amount is unchanged, while the top cans are for sure less than before. – leoll2 May 19 '15 at 19:59
• @leoll2 Maybe you can try cramming 1 on both sides in ;) – Mark N May 19 '15 at 20:00
• Or split the can as I previously did with traffic cones! – leoll2 May 19 '15 at 20:01
• I think you'd only be allowed to "cram" cans if lateral thinking were allowed. – Kevin May 19 '15 at 20:07
• @Kevin If lateral thinking were allowed, I would grind up the cans so that I could fit thousands in there! – Mark N May 19 '15 at 20:10 | 2020-01-20 20:09:28 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5755130052566528, "perplexity": 903.6648405708975}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-05/segments/1579250599789.45/warc/CC-MAIN-20200120195035-20200120224035-00019.warc.gz"} |
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The epidemic of coronavirus disease 2019 is a severe test for China's response to major public health emergencies. Through literature reviews, we summarized approval system and process for research/development and marketing of medicine and test reagents related to responses to major public health emergencies in many foreign countries and conducted comparative studies on the system and process at home and abroad for providing references to relevant system construction and administrative management China.
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Objective To study the impact of ambient temperature on hand, foot and mouth disease (HFMD) and to explore the source of heterogeneity in the impact and the HFMD burden attributable to ambient temperature in Guangdong province. Methods The data on daily reported HFMD cases and meteorological condition from 2009 through 2016 in Guangdong province were collected. The distributed lag nonlinear model (DLNM) was adopted to assess the effect of average daily ambient temperature on HFMD incidence at city level with the pooled effect estimates from multivariate meta-regression model analysis. Fraction and number of HFMD incidents attributable to variation in ambient temperature were estimated according to the results of DLNM analysis. Results Totally 2 279 647 HFMD cases were reported during the period. The risk of HFMD incidence increased with the increment of average daily ambient temperature. The cumulative relative risk (RR) of HFMD incidence reached the highest for the average daily ambient temperature of 30.5 ℃ versus that of 24 ℃(RR = 1.24, 95% confidence interval [95% CI]: 1.12 – 1.37). The most obvious effect of low average daily ambient temperature on HFMD incidence was on the lag day 8 but that of high temperature was on the lag day zero. The disparity in the effect of average daily ambient temperature on HFMD incidence among various cities was derived from population density, growth rate of gross domestic production, location longitude, and average annual temperature/humidity/hours of sunshine. The estimated total number of HFMD incidents attributed to the exposure to high average daily temperature was 241 918, accounting for 10.61% (95% CI: 9.67% – 11.53%) of all the cases during the period. When exposed to high average daily ambient temperature, the elderly and the children less than 5 years old were at a higher risk of HFMD incidence than other populations. Conclusion High average daily ambient temperature could increase the risk of HFMD incidence and the impact of the high temperature may appear immediately or at lag days. The results suggest that specific measures should be taken in vulnerable populations during seasons with high temperature for the prevention of HFMD incidents.
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Objective To analyze variation trend of AIDS incidence and the association of macroeconomy and health service with AIDS incidence in Shaanxi province from 2006 to 2018. Methods The data on registered AIDS cases and demographics in Shaanxi province from 2006 to 2018 were extracted from National Disease Prevention Information System; the indicators for macroeconomy and health service of the same period were collected from Shaanxi province statistics yearbooks. Multi-level models were adopted to analyze variation trend in AIDS incidence and influences of macroeconomy on AIDS incidence during the period. Results A non-linear correlation between the AIDS incidence and the time of year and an over time accelerated upward trend in the AIDS incidence were observed. The local fiscal revenueis positively correlated with the incidence of AIDS (β = 0.002, P < 0.001); whereas, the number of health institutions per 1 000 peoplewas negatively correlated with the AIDS incidence (β = – 0.306, P = 0.023). Conclusion The incidence of AIDS varied with an accelerated upward trend and was closely related to social macro factors during 2006 – 2018 in Shaanxi province.
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Objective To analyze prevalence characteristics and spatial-temporal aggregation of hand,foot and mouth disease (HFMD) in Yunnan province from 2009 to 2019. Methods The data on HFMD incidents in 129 counties/districts of Yunnan province during 2009 – 2019 were extracted from National Disease Prevention and Control Information System and relevant population data were collected from statistics yearbooks issued by provincial statistical bureau. The prevalence characteristics of HFMD was analyzed with descriptive statistics and spatial-temporal clustering of HFMD was assessed using SaTScan 9.5 software. Results A total of 752 209 HFMD cases were reported and the in Yunnan province during the period, with an average annual incidence of 145.93/100 000. More HFMD incidents were reported among scattered living children aged < 5 years and more incidents occurred during April – July in a year. In 2009, the counties/districts with higher HMFD incidence were mainly located in the central region of Yunnan province; but from 2010, more counties/districts with higher HFMD incidence were gradually identified around the central region along with the increase in annual HFMD incidence in the province. SaTScan spatial-temporal scanning analysis demonstrated an obvious temporal clustering of HFMD mainly during April - July in a year; the scanning analysis also revealed spatial clustering of HFMD incidence in three prefecture regions (Kunming, Yuxi and Honghe) in 2009 and 2010, while, another three prefecture regions (Qujing, Wenshan and Chuxiong) with spatial clustering of the incidence were identified during 2011 – 2018 and totally eight prefecture regions with spatial clustering of the incidence were found in 2019. Conclusion There were obvious spatial-temporal clustering of HFMD incidence in Yunnan province from 2009 to 2019 and the regions with spatial clustering of HFMD incidence enlarged from the central to southeastern Yunnan gradually; the situation should be concerned for effective control of HFMD epidemic in the province.
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Objective To examine the prevalence and impact factors of permanent teeth caries among 12 – 15 years old children in Henan province. Methods According to the methodology of the Fourth National Oral Health Survey, we conducted oral examination and questionnaire survey among 3 840 children aged 12 – 15 years recruited from 12 middle schools in four districts/countries of Henan province with stratified multistage probability proportionate to size sampling (PPS) during September – December, 2015. Results Among the 3 786 children with complete information, 1 411 had caries; the prevalence rate of permanent teeth caries was 37.27%; the average decay-missing-filled teeth (DMFT) was 0.73; and the caries filling ratio was 9.26%. There were no significant differences in prevalence rate of permanent teeth caries (37.46% vs. 37.07%) and mean DMFT index (0.74 ± 1.37 vs. 0.73 ± 1.23) between the urban and the rural children; but the caries filling ratio was significantly higher among the urban children than that among the rural children (14.31% vs. 4.09%, χ2 = 85.862; P < 0.05). Compared to the boys, the girls had significantly higher prevalence rate of permanent teeth caries (42.34% vs. 32.34%), mean DMFT index (0.86 ± 1.37 vs. 0.60 ± 1.20), and caries filling ratio (10.39% vs. 7.69%) (P < 0.05 for all). Multivariate logistic regression demonstrated that gender, age, paternal education, self-perceived oral health status, and dental care experience were significantly associated with the prevalence of permanent teeth caries among the children. Conclusion The permanent teeth caries is prevalent among 12 – 15 years old children in Henan province and interventions on oral health should be promoted among the children.
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Objective To examine the satisfaction to risk communication and its main influencing factors in the public during an influenza epidemic in early 2018 in China and to provides references for improving the effectiveness of risk communication in health emergency response. Methods An online survey was conducted among 2 960 net users in China during a period of influenza epidemic from January to March 2018. A questionnaire on the satisfaction to public health risk communication was designed and distributed via Wechat and QQ platform. Descriptive statistics, Chi-square tests, and multivariate logistic regression were used in data analyses. Results Valid information were collected from 2 796 respondents (45.71% males and 54.29% females) aged 18 – 78 years. Of the respondents, 70.92% reported being satisfied with the public health risk communication on the influenza epidemic but 29.08% reported unsatisfaction, with a significant difference (χ2 = 340.69, P < 0.001). Multivariate logistic regression analysis revealed that the respondents with following characteristics were more likely to report the satisfaction to their perceived risk communication related to the epidemic: living in a rural region (odd ratio [OR] = 2.046), with an education of and below (OR = 2.723), reporting a positive emotion (OR = 1.369), paying an attention to the influenza epidemic-related information (OR = 3.245), being confidence in governmental administration (OR = 1.894), being interactive with the information in new media (OR = 1.923), and searching for relevant information via new media (OR = 1.763). Conclusion Government departments could make a full use of new media to improve the effectiveness of health risk communication in response to public health emergencies.
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Objective To determine initial efficacy of a family-involved hand washing intervention on the improvement of hand hygiene of children and the prevention of infectious diseases among children in kindergartens. Methods A cluster-randomized controlled trial was conducted among 490 children (averagely aged 4.28 ± 0.33 years) and their parents at 16 classes from 4 kindergartens in Guangzhou city from March to June in 2018, and there were 8 classes in each group by randomization. Totally 247 children and their families were enrolled in the intervention group with family-involved hand washing intervention, and 243 children and their families in the control group with regular health education. The behavior of hand washing among the children and their parents and the incidence of infectious diseases of children between the two groups were compared. Results Hand washing behaviors of the children were significantly different between the two groups after the intervention (hand washing before eating [b = − 0.207], after toilet use [b = − 0.106], after going out [b = − 0.149], and with seven-step procedure [b = − 0.113]; all P < 0.05). The hand washing before eating, after toilet use and going out, and with seven-step procedure 2 months after the intervention, the hand washing before eating 4 months after the intervention, and the hand washing before eating and with seven-step procedure 6 months after the intervention were significantly better among the children of intervention group than among those of the control group (all P < 0.05). The hand washing of the parents in the intervention group were significantly better than that of parents in the control group 2 months after the intervention (hand washing before eating [χ2 = 8.750], after toilet use [χ2 = 7.243], after going out [χ2 = 15.557]; all P < 0.05). The cumulated incidence of acute gastrointestinal and respiratory infections was significantly lower among the children in the intervention group than among those in the control group (9.3% vs. 16.0%, χ2 = 5.031; P = 0.025) during the 12-month follow-up. Conclusion The family-involved hand washing intervention is effective in improving hand hygiene behaviors among kindergarten children and their parents and reducing infectious diseases in the children, suggesting that the intervention is of significance for infectious disease prevention in kindergartens.
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Objective To examine the relationship between carotid artery abnormality and smoking in male adult residents at high-risk of cardiovascular disease (CVD) in Jiangsu province, and to provide evidences for prevention and treatment of subclinical atherosclerosis and early CVD. Methods From September 2015 to June 2016, we conducted screenings on individuals at high-risk of CVD among 35 – 75-year-old permanent residents (n = 71 511) in 31 urban communities and rural villages and towns selected with cluster sampling in 6 cities of Jiangsu province; then a questionnaire survey, physical examination, laboratory test and carotid artery ultrasound examination were carried out in 4 821 male residents at high-risk of CVD to analyze the relationship between carotid artery abnormality and smoking. Results Among the 4 821 high-risk individuals, 2 783 (57.73%) were diagnosed with carotid artery abnormality, of which, 761 (27.34%), 1 791 (64.57%), and 225 (8.09%) were carotid intima thickening, carotid plaque, and carotid stenosis, respectively. After adjusting confounding factors such as age, education, marriage, average annual family income, residence, and history of alcohol drinking/hypertension/diabetes/dyslipidemia, the results of unconditional multivariate logistic regression analysis demonstrated that for all the high-risk individuals, the smokers were more likely to have carotid artery abnormality (compared to non-smokers: odds ratio [OR] = 1.391, 95% confidence interval [95% CI] = 1.214 – 1.593); the results also revealed two significant risk factors of carotid artery abnormality for the 2 699 high-risk individuals being current or former smokers: smoking filter-tipped cigarettes (compared to smoking cigarettes without filter: OR = 1.440, 95% CI = 1.184 – 1.750) and breathing in cigarette smoke deeply (breathing the smoke into throat vs. into mouth: OR = 1.420, 95% CI = 1.081 – 1.865 and breathing the smoke into lung vs. into mouth: OR = 1.338, 95% CI = 1.104 – 1.622). Conclusion The prevalence rate of carotid artery abnormality is relatively high and the abnormality is strongly associated with smoking among male adult residents at high-risk of cardiovascular disease in Jiangsu province.
Abstract(1604) HTML(2029) PDF 509KB(134)
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Medical education system and licensed physician management system in the United States are two relatively mature institutions with successful operation. This study systematically reviewed the policy content of the preventive medicine physician system in the United States by establishing a theoretical analysis framework covering the education, employment admittance, deployment, professional title, and incentive pay system. This study discussed the identity crisis of public health physicians in China and considered that Chinese public health physicians are not preventive medicine physicians. The study suggested that for improving public health physician system in China, the connotation of public health physicians should be rectified; the criterion for admittance of public health physicians should be upgraded; and approaches for the transition between clinicians and public health physicians should be diversified.
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Objective To examine disparities in psychological difficulty and prosocial behavior among the children in difficult families (CDF) and in normal families and to provide empirical evidences for assessing the mental health needs of CDF and developing a moderately inclusive child welfare system. Methods The data of the study were from a national survey on CDF conducted during August-September of 2018. The participants were 6 – 15 years old children (2 099 CDF and 666 age- and gender-matched control children in normal families) recruited with multistage sampling in 7 provincial regions across China. Household face-to-face interviews were carried out in the participants using the Strengths and Difficulties Questionnaire (SDQ). Independent sample t test and monotonic ordinal rank-sum test (Matel-Haenszel χ2) were adopted in analyses. Results Compared to those in the control children, the score and abnormality detection rate of emotional symptoms (2.107 ± 1.977, 15.5%) and peer-communication (3.449 ± 1.497, 8.5%) were significantly higher in the 6 – 9 years old CDF (all P < 0.05); but the score of prosocial behavior (5.229 ± 2.366) was significantly lower in the 6 – 9 years old female CDF (P < 0.001). In contrast to the controls, the 10 – 15 years old CDF had significantly higher score and abnormality detection rate of hyperactivity-inattention (3.459 ± 1.691, 3.7%), emotional symptoms (2.121 ± 1.987, 7.4%), conduct problems (2.214 ± 1.563, 8.7%), and peer-communication (3.352 ± 1.445, 8.1% ) (P < 0.001 for all); however, the 10 – 15 years old CDF had significantly lower score but higher abnormality detection rate of prosocial behavior (5.570 ± 2.337, 28.3%) (both P < 0.001); the prosocial behavior score of 10 – 15 years old CDF was significantly lower in the males (5.630 ± 2.372) and the females (5.500 ± 2.295) than in the controls (both P < 0.01). Conclusion The 6 – 15 years old children in difficult families are at high risk of various psychological difficulties and may perform prosocial behaviors poorly; the situation needs to be concerned, especially for the girls and the elder children.
Abstract(1454) HTML(647) PDF 525KB(25)
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Objective To examine the cognition on and behaviors of dairy product consumption and their influencing factors among residents of Shanxi province to provide references for developing programs of health education on dairy products consumption. Methods Using stratified multistage random sampling, we carried out a self-administered anonymous questionnaire survey among 3 288 residents recruited in 75 counties/districts of Shanxi province from December 2018 to March 2019. Chi-square test, Ridit analysis and binary logistic regression analysis were used in data analyses. Results Of all the participants at ages of 15 to 84 years (mean = 30.97 ± 13.37), 44.19% (1 453) were male and 55.81% (1 835) were female. Only 14.93% (491) of the participants reported a great concern about dairy product safety. The reported concern about dairy product safety differed significantly by gender (χ2 = 17.404), age (χ2 = 59.962) and residential place (χ2 = 31.304) (all P < 0.05); the male participants (\begin{document}$\bar R$\end{document} = 0.482), the participants aged ≤ 20 years (\begin{document}$\bar R$\end{document} = 0.473), and those living in rural regions (\begin{document}$\bar R$\end{document} = 0.469) reported lower concern about dairy product safety. Logistic regression analysis revealed that participants with a monthly household income of ≤ 500 yuan (RMB) per-capital were less likely to consume dairy products compared to those with the income of > 500 yuan (P < 0.05); the participants paying a great attention on dairy safety incidents when purchasing were less likely to consume dairy products compared to those paying a little attention on the incidents (P < 0.05); whereas, the participants with the Engel’s coefficient of < 60% were more likely to consume dairy products in comparison to those with the Engel’s coefficient of ≥ 60% (P < 0.05). Conclusion Dairy product consumption is insufficient and the concern on dairy product safety is at a low level among adult resident in Shanxi province. Governmental departments should take measures to promote the cognition on and consumption of dairy products in the public.
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Objective To examine the status of and research progress in contracted family doctor services in China and to summarize general problems existing in the implementation the services for providing references for the development of applicative mode of contracted family doctor services in China. Methods Studies on contracted family doctor services in China published till April 2018 were systematically searched through China National Knowledge Infrastructure (CNKI), Chinese Biomedicine Database (CBM), Wanfang and Chinese Science-Technology Periodical Database (VIP) database. EndNote X7 and Excel 2010 were used to manage and analyze the retrieved studies. Results All the 24 finally included articles were cross-sectional studies, of which 20 and 4 were conducted among urban and rural residents. Higher rates (36% – 96%) of awareness about contracted family doctor services were reported by studies conducted among residents in Guangdong province, followed by among those (16% – 90%) in Beijing. Higher proportions (42% – 100%) of participating in contracted family doctor services were reported by the studies conducted among the residents in Beijing, followed by those (30% – 74%) in Shanghai. A higher rate (86.33%) of satisfaction to contracted family doctor services was reported by the studies conducted among the residents in Beijing, followed that (56% – 80%) in Guangdong province. Major hindering factors for the implementation of contracted family doctor services indicated by the studies were shortage of family doctors, lack of awareness on the services among the public, low salary of family doctors, imperfect management, incentive, insurance, and information support for the services. Conclusion The rate of awareness about, participating in, and satisfaction to contracted family doctor services are higher among residents in economically developed provinces/municipalities and in urban area than among those in less developed regions and in rural areas in China. More researches on the issue need to be performed for effective implementation of contracted family doctor services.
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A government-led centralized procurement pattern for purchasing medicines in medical institutions at province/municipality level has been established basically in China so far; however, control in procurement price and establishment of effective purchasing process are still need be promoted for the procurement system. The government has tried to use tax reduction as an opportunity to achieve a significant decline in sale price for end users of the drugs. The study examined the implementation of centralized procurement of anticancer drugs in medical institutions at province/municipality level across the country and analyzed disparities in procurement schemes among the provinces and municipalities to provide references and suggestions for perfecting the implementation of centralized procurement of anticancer drugs at provincial level.
Articles in press have been peer-reviewed and accepted, which are not yet assigned to volumes /issues, but are citable by Digital Object Identifier (DOI).
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Objective To examine the demands for elderly care and its associates among older rural residents and to provide evidences for improving elderly care services in China. Methods Using stratified multistage random sampling, we recruited 600 residents aged ≥ 60 years at 20 villages in 5 provinces across China and conducted a survey among the elderly with a self-designed questionnaire on the status and related factors of elderly care needs From January to March 2019. Results Totally 560 (43.2% male and 56.8% female) residents completed the survey. For all the respondents, the average score for overall care was 6.01 ± 1.83 out of the full mark of 17; the average domain score for emotional care was higher than that for daily life care (2.79 ± 0.88 vs. 1.67 ± 1.83) and the score (1.56 ± 0.74) for medical care was the lowest among the domain scores. The top three emotional care needs reported by the respondents were harmonious neighborhood relationship, children′s company and community activity and the top three daily life care needs were caregiver′s service, financial support and children′s care. For medical care, the respondents paid more attentions to improving medical conditions and reducing medical expenses. Based on the results of multivariate linear regression analysis, main impact factors were education, self-care ability, whether with children living nearby, and whether having regular physical examination for care needs of the rural elderly. Conclusion The elderly in rural China need more emotional care and daily life care, especially those with lower education, without self-care ability, without children′s care, and having no regular physical examination.
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Objective To examine the awareness, treatment and control of hypertension and their influencing factors among hypertensive patients aged ≥ 40 years in rural regions of Liaoning province and to provide references for the prevention and control of hypertension. Methods Using stratified random cluster sampling, we carried out a survey including questionnaire interview, physical examination and laboratory test among 10 926 permanent residents aged ≥ 40 years in 19 administrative villages of 4 counties, Liaoning province from September 2017 to May 2018. The awareness, treatment and control of hypertension and their correlates in 6 623 hypertensive patients identified from the participants of the survey were analyzed. Results Among the 6 623 hypertensive patients, the crude and standardized rate were 47.50% and 44.25% for hypertension awareness, 35.41% and 31.34% for hypertension treatment, and 3.59% and 3.18% for hypertension control, respectively. Unconditional multivariate logistic regression analysis revealed that the patients with following characteristics were more likely to have higher hypertension awareness and treatment rate: female gender, aged ≥ 50 years, overweight/obesity, lack of physical exercise, family history of hypertension, history of diabetes, and high triglyceridemia; the patients with an average annual household income of 5 000 to 9 999 yuan RMB were more likely to have a high hypertension awareness rate; the patients with low serum high-density lipoprotein cholesterol were more likely to have a high hypertension treatment rate; the patients aged 50 – 69 years, lack of exercise, with family hypertension history were more likely to have a high hypertension control rate; whereas, the patients being current alcohol drinkers and with high serum total cholesterol were more likely to have low hypertension awareness, treatment and control rate; the patients with an average annual income of ≥ 20 000 yuan RMB were more likely to have a low hypertension control rate. Conclusion The rate of hypertension awareness, treatment and control are low and the rates are associated with gender, age, average annual household income, current alcohol drinking, physical exercise, family history of hypertension, history of diabetes, overweight/obesity, high total cholesterol, high triglyceridemia, and low high-density lipoprotein cholesterol among hypertension patients aged 40 years and above in rural regions of Liaoning province.
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Objective To explore interactive effect of air pollutants and temperature on years of life lost (YLL) due to lung cancer and to provide references for studies on impacts of lung cancer mortality. Methods We collected data of Hexi district on lung cancer mortality in the residents, air pollutants monitoring, and meteorology observation during the period from January 1, 2015 to December 31, 2017. Bivariate response surface model, uni- and multi-pollutant and temperature interactive model were established using non-linear lag distribution to analyze the interactive effect of air pollutants and temperature on lung cancer-related YLL in the population of the district. Results Relative to the reference temperature of 16.3 ℃, high temperature (34 ℃) and low temperature (– 13 ℃) increased YLL of lung cancer by 1.12% (95% confidence interval [95% CI]: 0.58% – 2.16%) and 1.49% (95% CI: 0.16% – 14.25%). Particulate matter less than 2.5 μm in aerodynamic diameter (PM2.5), nitrogen dioxide (NO2), carbon monoxide (CO), one-hour average ozone (O3-1h), and eight-hour average ozone (O3-8h) could increase YLL of lung cancer by 1.00% (95% CI: 0.98% – 1.03%), 1.01% (95% CI: 0.95% – 1.08%), 1.01% (95% CI: 0.99% – 1.03%), 1.03% (95% CI: 0.98% – 1.09%), and 1.03% (95% CI: 0.98% – 1.09%), respectively. Under the low temperature, a 10 μg/m3 increment in PM2.5 and NO2 could increase the YLL of lung cancer by 4.14% (95% CI:0.55% – 7.85%) and 5.44% (95% CI: – 4.80% – 16.78%). Conclusion High and low temperature, PM2.5, NO2, CO, O3-1h and O3-8h can all increase daily YLL of lung cancer in an exposed population and the effect of PM2.5 and NO2 are stronger under low temperature.
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Objective To analyze variations in the scope of infectious disease epidemics concerned by government departments and the relationship between the changes and incidences of class A and B infectious diseases in Liaoning and Jilin province for developing strategies on infectious disease prevention and control. Methods By searching official websites and internet databases, we retrieved policy documents referring to the prevention and control of infectious diseases published by government departments and health institutions of Liaoning and Jilin province from 2005 through 2016. Descriptive analyses were performed and Spearman correlation and univariate linear regression analysis were used to explore the correlation between the concern scope and local incidences of notifiable class A and B infectious diseases. Results We totally retrieved 32 and 45 documents issued by Liaoning and Jilin provincial departments and institutions during the period. Compared to that in 2005 in Jilin province, the indicator for the scope of infectious diseases concerned by provincial departments increased by 41.00% and the incidence of notifiable class A and B infectious diseases decreased by 79.63/100 000 in 2017, respectively, with an obvious inverse correlation between the indicator and the incidence. During the period, the indicator for the scope of infectious diseases concerned by Liaoning provincial departments increased from 28.85% to 75.00% but no significant correlation was observed between the indicator and the local incidence of notifiable infectious diseases. Conclusion The scope of infectious disease epidemics was increasingly concerned by local government departments of Liaoning and Jilin province during the period from 2005 to 2017 and the governmental concern is one of important factors for the prevention and control of infectious diseases.
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Objective To examine status quo and influencing factors of outpatient service utilization among chronic disease patients in China and to provide evidences for promoting the utilization of outpatient services in the patients. Methods Using convenient and snowball sampling, we recruited 1 059 chronic disease patients (hypertension, diabetes, cardiovascular diseases and malignant tumor) in 7 provincial level regions in eastern, central and western China and conducted a online self-administered questionnaire survey between October 2018 and March 2019. Anderson model was adopted to analyze influencing factors of outpatient service utilization among the patients. Results The two-weeks rate of outpatient service utilization was 37.36% among the 1 036 patients with valid response. Unconditional multivariate logistic regression analysis demonstrated that the respondents with poor household economic condition, having siblings, and suffering from two or more chronic diseases were more likely to utilize outpatient medical service; while, those living in western regions, being manual workers, with average annual income per capita of 5 000 yuan RMB, and participating in the New Rural Cooperative Medical Scheme were less likely to utilize outpatient medical service. Enabling resources (including income per capita, household economic status, type of medical insurance and number of siblings) were the most significant impact factors for the utilization of outpatient service among the respondents, followed by demographic indicators and number of chronic diseases suffered from. Conclusion The two-weeks rate of outpatient service utilization is low and mainly influenced by living region, occupation, average annual income per capita, family economic status, type of medical insurance, number of siblings and number of chronic diseases suffered from among chronic disease patients in China.
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Objective To explore influencing factors of doctor-patient information communication (DPIC) and to provide evidences for improving the situation of DPIC in China. Methods To screen influencing factors of DPIC based on grounded theory, we conducted an expert fractal analysis and semi-structured interviews among 8 schoolors engaged in medical humanities education and research, 20 senior doctors and 20 patients in three tertiary hospitals in Nanjing city using purposive sampling. With the coded influencing factors prelimilarily determined, we compiled a questionnaire. Then we conducted an on-site self-administered questionnaire survey among 2 727 medical professionals and 1 781 patients and their relatives recruited using cluster random sampling at tertiary hospitals in 23 municipalities/provinces across China during March – May 2016. We analyzed the data collected for weighting and ranking all influencing factor of DPIC by comprehensive and average impact scores calculated for each of the factors. Results Of the surveyed medical professionals and patients and their relatives, 45.9% and 44.1% reported a strong willingness to conduct DPIC; 75.9% and 71.4% affirmed the necessity of governmental agencies' role in DPIC; 49.0% and 53.9% evaluated the role of media and network in DPIC as very necessary; 21.6% and 18.0% approved representative role of medical associations in the process of DPIC but only 14.5% and 26.7% approved the representative role of consumers associations. There were significant disparities between medical professionals and patients and their relatives in attitudes towards DPIC and its relevant dimensions mentioned above (all P < 0.01). The rank order from high to low for impact scores of DPIC influencing factors was governmental administration (score = 3.69), demand for the communication (3.34), media and network (3.18), medical association (2.56), and consumer association (2.21) among the medical professionals; while among the patients and their relatives, the rank order was government administration (3.61), media and network (3.32), demand for the communication (3.25), consumer association (2.71), and medical association (2.47). Conclusion A good doctor-patient information communication comes from the joint efforts among medical staff, patients, government agencies, media and network, and relevant social organizations. The study result suggests that a comprehensive platform needs to be established to promote the communication.
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Objective To explore tuberculosis – diabetes mellitus (DM) comorbidity and its risk factors among retreatment pulmonary tuberculosis patients (PTB) and to provide references for prevention and treatment of PTB-DM comorbidity. Methods We recruited 395 retreatment PTB patients at 22 medical institutions designated for PTB treatment across China and divided the patients into a PTB and a PTB-DM group according to the comorbidity of DM; then we carried out a questionnaire survey among all the patients from October 2009 to December 2012. Chi-square test was used to compare differences in demographics and other characteristics between the patients of the two groups; multivariate logistic regression analysis was used to explore risk factors of DM comorbidity. Results Of all the patients, 15.2% (60) were PTB-DM and 84.8% (335) were simple PTB; there were significant differences between the two groups in age (χ2 = 10.459, P = 0.005 3), body mass index (BMI) (χ2 = 15.070, P = 0.000 5), occupation (χ2 = 11.620, P = 0.002 9) and marital status (χ2 = 9.999, P = 0.006 7). Aged 40 – 59 years (odds ratio [OR] = 2.159, 95% confidence interval [95% CI]: 1.050 – 4.439), aged 60 years and above (OR = 5.017, 95% CI: 1.485 – 16.951), with a body mass index (BMI) of < 18.5 kg/m2 (OR = 4.946, 95% CI: 1.279 – 8.705), with a BMI of ≥ 24 kg/m2 (OR = 5.732, 95% CI: 1.918 – 17.133), and being married (OR = 4.476, 95% CI: 1.248 – 10.504) were significant risk factors of PTB-DM comorbidity. Conclusion The complication of diabetes mellitus is associated with age, body mass index, and marital status among retreatment pulmonary tuberculosis patients.
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Objective To analyze the status of public needs-based scientific decision-making in health emergency management in Liaoning and Jilin province and the disparity in the decision-making between the two provinces for improving health emergency management. Methods By searching official websites and internet databases, we systemically and extensively retrieved 163 authoritative documents and reports on health emergency management published by government agencies and health institutions of Liaoning and Jilin province from 2000 through 2017. Descriptive analyses on scientific decision-making were performed using SPSS 22.0; Spearman correlation analysis and liner regression were adopted to assess the correlation between scientific rationality in target setting and the efficiency of health emergency management. Results The measure of scientific rationality in target setting for health emergency management increased from 2.1% in 2000 to 55.7% in 2017 in Liaoning province and from 2.1% in 2000 to 39.3% in 2017 in Jilin province. There were positive correlations between scientific rationality in target setting and the efficiency of health emergency management in both Liaoning and Jilin province, with the correlation coefficients of 0.735 and 0.691 and the adjusted R2 of 0.511 and 0.445, respectively. Conclusion The measure of scientific rationality in target setting for health emergency management increased greatly and the management efficiency was promoted in Liaoning and Jilin province.
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Objective To investigate epidemiological characteristics of crayfish-related rhabdomyolysis (RM) syndrome in regions along Yangtze River in 2016. Methods We conducted a field epidemiologic survey on 811 RM cases reported in Anhui, Jiangsu and Hubei province along Yangtze River during 2016 to analyze clinical and prevalence characteristics of the disease. Results Of all the cases, 69.3% were female and 78.1% were aged between 20 and 49 years. Main symptoms of the cases were muscle ache, fatigue and digestive disorder-induced pain; five times increased serum creatine kinase (CK) was detected among 84.0% of the cases. Retrospective surveys found that consumption of crayfish, shrimp offal, and alcohol were risk factors for the incidence of the disease. The incidences occurred mainly at home and the crayfish consumed by the cases were mainly from wild fishing. Conclusion There is a causal correlation between the incidence of rhabdomyolysis syndrome and crayfish in some regions along Yangtze River in 2016, suggesting that monitoring on crayfish eating-related diseases should be strengthened.
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Objective To examine the status quo of haze-related health protective behaviors among citizens in Beijing city for providing evidences to develop targeted health education strategies and intervention measures. Methods In November 2018, we distributed a self-designed questionnaire on cognition on haze-related health risk and protective behaviors via internet to all members of official account of Dongcheng District Center for Disease Control and Prevention registered in Beijing city. All voluntary responses were collected two weeks after the distribution. Results A total of 15 698 questionnaires were distributed and 15 334 valid response questionnaires were received, with a response rate of 97.7%. Of all the respondents, 93.5% and 92.4% reported decreased going out and physical exercise under smog weather; 96.2% and 86.1% reported wearing mask when going out and using air purifiers at home under smog weather condition, respectively. The proportion of reporting haze-related health protective behaviors was significantly higher among the respondents aged 18 – 44 years, females, and the college students (all P < 0.05) and the proportion was positively correlated significantly with the level of cognition on health hazards of haze and the concern about haze weather condition (P < 0.05 for all). Conclusion The prevalence rate of haze-related health protective behaviors is relatively high among citizens in Beijing city but health education on cognition and protection of haze condition still needs to be promoted in key population groups.
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Recent studies have shown a significant relationship between ambient particulate matter (particulate matter less than 10 or 2.5 μm in aerodynamic diameter) and the onset, aggravation or death of chronic obstructive pulmonary disease (COPD), but the studies on the correlation between air gaseous pollutants（carbon monoxide, nitrogen dioxide, sulfur dioxide, ozone）and COPD did not reach a consistent conclusion. There was a few studies on the association between chronic exposure and COPD. This paper reviews the latest researches on the correlation between air pollutants and COPD, analyzes the influence of climate, population characteristics and human geography factors on the effect of air pollution on COPD, and aims to evaluate the degree of correlation between different pollutants and the incidence, acute exacerbation and death of COPD, and discuss the future research direction and prevention and control strategies.
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Objective To investigate the status and of influencing factors safe drug use among oldest-old community residents with hypertension in Tangshan city of Hebei province, and to provide evidences for improving health management among elderly hypertension patients in communities. Methods Using random cluster sampling, we recruited 1 882 hypertensives aged ≥ 75 years at community health care centers covered by a secondary and a tertiary hospital in Tangshan city; we then carried out a household survey among the oldest-old hypertension patients with a questionnaire on safe drug use from July 2016 to January 2017. Results The mean scores of safe medication behavior for the 1 853 respondents with complete information was 30.17 ± 4.72 in the scale with a maximum score of 40 for the highest level of safe drug use. Multivariate regression analysis demonstrated following significant influencing factors for safe drug use among the respondents: education (β = 2.487), perceived happiness in life (β = – 5.833), attitude toward life and death (β = 1.667), frequency of participation in community activities (β = – 3.856), frequency of neighborhood communication (β = – 4.808), communication with children (β = – 2.044), frequency of contacting with friends (β = – 2.876), talking with people (β = – 1.480), attitude toward development of the elderly care (β = – 1.633), and medical burden (β = – 1.886) (all P < 0.05). Conclusion Community health care workers should make efforts to promote attitude and behaviors about safe drug use among elderly hypertension patients.
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Objective To analyze the clarity of responsibilities for all parties in public health emergency (PHE) response and the relationship between the clarity and the response efficacy in Liaoning and Jilin province for providing references for the improvement in public health organization system construction. Methods We searched literatures and documents referring to responsibility assignment for all parties in PHE response published by government agencies and professional institutions in the two provinces from 2000 through 2017 via public websites, China National Knowledge Infrastructure (CNKI), Wanfang Data and Web of Science. Cluster analysis and qualitative and quantitative methods were used to evaluate the clarity of the responsibility assignment for all parties of the two provinces. Spearman correlation and linear regression were used to analyze the relationship between the clarity and response efficacy. Results For the administration in Liaoning and Jilin province, the index for the clarity of the responsibilities assignment increased gradually from zero in 2000 to 20.60% and 21.95% in 2017; the index for response efficacy also gradually increased from 40.00% and zero to 53.33% and 60.00%, respectively. Significantly positive correlation between the clarity and the response efficacy was observed in Liaoning and Jilin province, with the correlation coefficients of 0.496 and 0.605, respectively (both P < 0.05). Conclusion The clarity of responsibilities for all parties in public health emergency response and the response efficacy have been improved in Liaoning and Jilin province since 2000, indicating an improvement in the construction of public health organization system of the two regions.
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2021, 37(6): .
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2021, (6): 1-6.
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2021, 37(6): 905-914. doi: 10.11847/zgggws1134552
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Some countries with high coverage of diphtheria, tetanus and pertussis combined vaccines have experienced pertussis epidemics and/or local outbreaks since 1980s. This phenomenon is called “pertussis resurgence”. In recent years, pertussis epidemics in several provinces of China have resurged dramatically, arousing great concern from all parties. By referring the working model of the Global Pertussis Initiative, the Chinese Preventive Medicine Association has organized and launched the China Pertussis Initiative. A group of experts in this field has analyzed data of current pertussis in China and identified problems posed by the disease. This expert consensus was completed based on the discussions of the latest national and international research progress, epidemiological trends and immunization strategies of pertussis, with special aims to provide guidance for the surveillance, prevention and control of pertussis in China.
2021, 37(6): 915-920. doi: 10.11847/zgggws1134861
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Objective To analyze changing trend and in health literacy about chronic disease prevention (HLCDP) and its associated factors among 15 – 69 years old residents in China from 2012 to 2017 for providing references to the promotion of HLCDP in the population. Methods Using simple random sampling, we extracted the data on 89 153 urban and rural residents aged 15 – 69 years from the dataset of National Health Literacy Surveillance conducted yearly from 2012 to 2017 across China. A multi-level fixed effect model was constructed using hierarcal age-period-cohort (APC) method to explore changing trend in HLCDP and its associates. Results For the years from 2012 to 2017, the proportion of the residents with HLCDP were 8.52%, 11.01%, 9.01%, 10.05%, 10.25%, and 13.96%, respectively, with an overall upward trend (χ2 = 118.69, P < 0.001). Similar changing trends in net and crude period effect on HLCDP were observed, with a fluctuation from 2012 to 2016 and a rapid increase between 2016 and 2017. After adjusting for demographic factors and health status, the results of multi-level fixed effect model analysis showed that the residents with the education of primary school and above, being medical staff and having a better self-perceived health status were more likely to have a higher HLCDP; while, the residents being ethnic minorities, being farmers or workers, living in central or western regions or in rural areas were more likely to have a lower HLCDP. Significantly increased proportion of the residents having HLCDP were observed in 2013, 2015 and 2017 compared to that in corresponding previous one year, with the odds ratios of 1.200,1.116 and 1.535 (all P < 0.01). The period effect on the variation of HLCDP was significant, but the age-effect or the cohort-effect were not significant (both P > 0.05). Conclusion Among Chinese residents, the net period effect on HLCDP increased generally from 2012 to 2017 and the effect was greater for the period from 2016 to 2017. Attention should be paid to the impact of period effect and some demographic factors on changing trend of HLCDP.
2021, 37(6): 921-925. doi: 10.11847/zgggws1129683
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Objective To investigate changing trend in infectious disease prevention-related health literacy and its influencing factors among residents in Hubei province from 2014 to 2018 and to provide evidences for making policies on infectious disease prevention. Methods We conducted yearly surveys among 15 – 69 years old permanent residents (n = 14 708) selected with stratified multistage random cluster sampling in 12 counties/prefectures/districts across Hubei province between 2014 and 2018. A questionnaire compiled by National Health and Family Planning Commission for health literacy survey among Chinese residents was adopted and the collected information on infectious disease prevention-related health literacy were analyzed statistically. Results For the five waves of the yearly survey, the proportion of the participants with infectious disease prevention-related health literacy (scored 80 and above in a full scale of 100 for knowledge about infectious diseases) were 11.3%, 14.8%, 17.7%, 15.4% and 20.5%, respectively. The results of multivariate logistic regression analysis revealed following significant promotion factors of infectious disease prevention-related health literacy of the participants: being surveyed in the later year (odd ratio [OR] = 1.049, 95% confidence interval [95% CI]: 1.015 – 1.084), at younger ages (25 – 34 vs. 64 – 69: OR = 1.417, 95% CI: 1.129 – 1.778; 35 – 44 vs. 64 – 69: OR = 1.498, 95% CI: 1.207 – 1.860) and with higher education (college and above vs. being illiterate: OR = 6.422, 95% CI: 4.912 – 8.396). Conclusion The infectious disease prevention-related health literacy was increased slowly but still at a low level and significantly influenced by years, age and education among 15 – 69 years old residents in Hubei province.
2021, 37(6): 926-929. doi: 10.11847/zgggws1127501
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2021, 37(6): 930-935. doi: 10.11847/zgggws1128122
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Objective To compare health literacy among residents in Wuhan city in 2016 and 2018 for providing evidences to the development of relevant health policies and interventions. Methods Using the National Residents' Health Literacy Monitoring Questionnaire developed by the China Health Education Center, we conducted cell phone- or computer-aid face-to-face survey among 4 500 and 5 300 permanent residents selected with multistage random sampling in Wuhan city, Hubei province in 2016 and 2018, respectively. Results The proportion of the residents with overall health literacy increased significantly from 11.79% in 2016 to 19.29% in 2018 (χ2 = 97.063, P < 0.001) and the proportions the residents with health literacy dimensions increased from 22.88% to 33.95% for basic knowledge and concepts, 9.92% to 17.29% for healthy lifestyle and behavior, and 14.74% to 33.20% for basic skills in the three year period, respectively. In 2016, the proportions of the residents with health literacy on the six public health problems in descendant order were 44.42% for safety and first aid, 33.73% for scientific health concept, 19.74% for health information, 16.73% for infectious disease prevention and treatment, 12.75% for basic medical care, and 11.48% for chronic disease prevention and treatment; whereas, the proportions were 57.79% for safety and first aid, 52.81% for scientific health concept, 40.96% for health information, 27.84% for basic medical care, 26.05% for infectious disease prevention and treatment, and 18.98% for chronic disease prevention in 2018, with significant difference compared to those in 2016. However, for the residents surveyed in 2018, the proportion with health literacy on chronic disease prevention, infectious disease prevention and basic medical care were still low and less than 50% of the residents answered correctly to the questions on benefits of eating soy products such as tofu and soy milk, right ways of dealing with coughing and sneezing, and medical description of liver. Conclusion Health literacy was improved in 2018 compared to that in 2016 but health lifestyle and behaviors and health literacy on infectious disease prevention, chronic disease prevention and basic medical care were still at a low level among the residents in Wuhan city. The results suggest that targeted health education should be promoted in the population.
2021, 37(6): 936-938. doi: 10.11847/zgggws1132275
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Cancer is increasingly prevalent and seriously endangering human health. Although some progresses have been achieved in researches on multiple treatments of cancer with the development of medical science, the subjective initiative of each individual still plays an irreplaceable role in improving the prognosis among cancer patients. Health literacy, as an individual′s “internal cause”, involves the individual′s education level, mental health, self-care capability, and other traits. A cancer patient′s health literacy may exert an important impact on the health outcome of the patient. The study reviews advances in researches on different health outcomes of cancer patients associated with disparities in their health literacy in order to provide new ideas and methods for improving the prognosis and quality of life of cancer patients from a public health perspective.
2021, 37(6): 939-942. doi: 10.11847/zgggws1131624
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Objective To examine the knowledge, attitude and behavior about dietary salt reduction among family chefs and their family members in six provinces of China, and to provide evidences for formulating strategies and measures for dietary salt reduction in communities. Methods The participants of the study were 1 576 family chefs and their family members ( ≥ 18 years old) recruited with multistage random sampling in 60 urban communities and rural villages of 6 provincial-level regions (Qinghai, Hebei, Heilongjiang, Sichuan, Jiangxi, and Hunan) of China; then electronic device-aided face-to-face interviews and blood pressure measurements were carried out among the participants during September – November 2018. A self-designed questionnaire was used to collect the participants' information on dietary salt reduction-related knowledge, attitude and behavior. Results Among the participants, the rates of awareness on dietary salt reduction-related knowledge were 16.24% for recommended daily table salt intake for adults, 19.67% for low sodium salt, 31.41% for salt content index on food package labels, 76.27% for high salt consumption increasing the risk of hypertension, and 20.11% for reasonable low salt intake not reducing physical strength, respectively. Of the participants, 80.65% reported a positive attitude towards reducing salt intake at meals; 85.91%, 53.87%, 24.19%, and 14.91% reported not eating snacks containing salt, not eating salted food, using table salt with low sodium, and asking for adding less salt in dishes when eating out or ordering a takeout food. Compared to their family members, the family chefs had significantly higher rates of being aware of excessive dietary salt intake as a risk factor for hypertension (78.43% vs. 74.11%) and holding a positive attitude towards reducing salt intake at meals (85.66% vs. 75.63%) but a lower rate of being aware of salt content index on food package labels (26.14% vs. 36.68%) (P < 0.05 for all). Conclusion The rate of having a positive attitude towards dietary salt reduction is high, but both the rate of being aware of dietary salt reduction-related knowledge and putting dietary salt reduction into practice are relatively low among the family chefs and their family members in six provinces of China.
2021, 37(6): 943-949. doi: 10.11847/zgggws1132568
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Objective To establish and verify a nomogram for accurately predicting the mortality risk of human immunodeficency virus/acquired immunodeficiency syndrome (HIV/AIDS) patients receiving antiretroviral therapy (ART). Methods From China Information System for AIDS Prevention and Control, we extracted the data on HIV/AIDS patients registered during the period from 2006 through 2019 in Xinjiang Uygur Autonomous Region. Univariate and multivariate Cox proportional hazard regression analysis were carried out for the data on 3 272 HIV/AIDS patients of modeling group to determine the factors to be included in the nomogram. The area under the receiver-operating characteristics curve (AUC-ROC) and calibration curve were adopted to assess the prediction accuracy of the established nomogram for the data of modeling group and verifying group (1 636 HIV/AIDS patients). Decision curve analysis (DCA), x-tile analysis and Kaplan-Meier curve were used to evaluate the clinical utility of the established nomogram. Results Based on the results of multivariate Cox proportional hazard regression analysis, the established nomogram model included following independent factors for predicting the prognosis of HIV/AIDS patients with ART: hemoglobin, body mass index, gender, aspartate aminotransferase, disease staging according to criterions proposed by World Health Organization, delay time between HIV infection and ART, and CD4 cell count. The AUC-ROC of the established nomogram is 0.781 (95% confidence interval [95% CI]: 0.703 – 0.861) for the modeling group and that for the verification group is 0.829 (95% CI: 0.758 – 0.896). The calibration curve for the survival of the patients during the 3-year period demonstrated a good consistency between the survival rate predicted by the nomogram and that observed actually. The survival rate was predicted based on the established nomogram for the patients at different (low, moderate and high) risk of mortality assessed according to nomogram scoring resulted from the analysis. Conclusion The study established a nomogram which could provide accurate and meaningful predictions for the survival of the HIV/AIDS patients with antiretroviral therapy.
2021, 37(6): 950-953. doi: 10.11847/zgggws1131355
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Objective To analyze the relationship between soil selenium content and liver cancer mortality in 156 districts/counties covered by a vital registration system in China and to provide references for the application of trace selenium in the prevention and treatment of liver cancer. Methods We collected following data for the 156 districts/counties: population sampling survey in 2012, liver cancer mortality and hepatitis B/C incidence in 2012, disease behavioral risk factor survey in 2010, socio-economic development and healthcare resources in 2013, and interpolatedly estimated soil selenium content based on sampling survey data published in 1994. Dimension reduction process was performed for socio-economic development and healthcare resource indicators with factor analysis. Generalized additive model was adopted to analyze the relationship between soil selenium content and liver cancer mortality. SAS for Windows 9.4 was employed and the significant level was set to be 0.05 in data statistics. Results There was a nonlinear relationship between soil selenium content and liver cancer mortality. Two common factors were derived in dimension reduction for indicators of socio-economic development and healthcare resources, representing economic development and health resource, and the cumulative contribution rate of the two common factors was 91.24%. The results of generalized additive model analysis revealed a significant difference between the complete model of liver cancer mortality and the model without soil selenium content as a non-parametric variable (P < 0.001). The non-parametric smooth component effect graph demonstrated an analogous ‘N’ shape correlation between soil selenium content and the non-parametric smooth component of liver cancer mortality. Conclusion Higher soil selenium content may correlate with increased risk of liver cancer mortality but moderate to upper soil selenium content may associate with low liver cancer mortality. The results should be concerned when conducting selenium supplementation-related liver cancer prevention.
2021, 37(6): 954-959. doi: 10.11847/zgggws1128070
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Objective To comprehensively evaluate the prevalence, prevention and management of cardio-cerebrovascular disease (CVD) in Shandong province for promoting effective CVD prevention and control in the province. Methods A Chinese′s cardiovascular health index (CHI) system was established with literature review and Delphi consulting method. The weights of various dimensions and indexes of the system were determined with analytic hierarchy process and the original data on CVD were collected from five dimensions (namely A for disease prevalence, B for risk factor exposure, C for risk factor control, D for disease treatment, and E for public health policy and service). After homogenization, standardization, and percentaging, each dimension and total CHI score were finally obtained. Then the estimated CHI scores of Shandong province were compared with those of the whole country and its neighboring provinces. Results The established CHI is composed of 52 indicators covering five dimensions, with a maximum score of 100. The estimated total CHI score for Shandong province was 52.9, ranking eighth among those for provincial level regions in the country and higher than the national average (49.4). The CHI dimension C and E score for Shandong province were 57.3 and 60.3 and the rank order of the two scores were the 8th and 10th among the scores for provincial level regions in the country from high to low; however, the rank order of CHI scores of dimension A (53.9), B (50.9) and D (38.1) were the 14th, 20th, and 20th, respectively, versus the scores of all other regions. Among the 52 indicators, the Shandong province′s scores for healthy behavior, successful smoking cessation rate, and health expense were higher than the national averages; but the scores for premature death probability, metabolic parameters, concentration of particulate matter ≤ 2.5 μm in mean aerodynamic diameter (PM2.5), hypertension prevention and control, diabetes prevention and control, treatment outcomes, and residents′ health literacy were all lower than the averages. Conclusion Based on the CHI evaluation on CVD prevention and control in Shandong province, the performance in risk factor prevention and control and construction of public health policy and service capability are good but the effectiveness for control of disease prevalence and risk factor exposure and for disease treatment need to be improved.
2021, 37(6): 960-964. doi: 10.11847/zgggws1125726
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Objective To examine the prevalence, awareness, treatment and control rate of diabetes and their relationship with socioeconomic status (SES) among middle-aged and elderly community residents in Yangzhong city of Jiangsu province and to provide references for promoting diabetes prevention and control. Methods Using stratified multistage random cluster sampling, we recruited 2 644 residents aged 40 years and above at 6 communities/towns in Yangzhong municipality of Jiangsu province. Questionnaire interview, physical examination and laboratory detection were conducted among the residents from September 2018 to March 2019. Multivariate logistic regression analysis were used to analyze correlations of SES with the prevalence, awareness, treatment and control rate of diabetes. The concentration index (CI) of the prevalence, awareness, treatment and control rate of diabetes were calculated to evaluate health equity. Results Among the 2 591 residents completing the survey, 275 (10.6%) were diagnosed with diabetes. Of the 275 diabetic participants, 148 (53.8%) were aware of the disease; 116 (42.2%) were under treatment for the disease; and 34 (12.4%) had their blood glucose under control. After adjusting for confounding factors such as gender, age, marital status, residence, smoking, alcohol consumption, physical exercise, and body mass index (BMI), multivariate logistic regression analysis revealed following associations of SES with diabetes-related indicators among the participants: (1) higher education was correlated with decreased diabetes prevalence (junior high school and above vs. illiterate/semiliterate: odds ratio [OR] = 0.486, 95% confidence interval [95% CI]: 0.304 – 0.778); (2) retirement was related to increased rate of awareness on diabetes (retiring vs. being on a job: OR = 5.026, 95% CI: 1.360 – 18.568) and increased rate of diabetes treatment (OR = 2.944, 95% CI = 1.043 – 8.311); (3) middle and high average annual personal income were associated with increased blood glucose control rate (middle vs. the lowest: OR = 6.354, 95% CI: 1.228 – 32.883; high vs. the lowest: OR = 8.404, 95% CI: 1.616 – 43.700). The education- and occupation-related CI values were – 0.029 5 and – 0.017 4 for diabetes prevalence, – 0.009 3 and – 0.014 1 for awareness on diabetes, – 0.008 6 and – 0.011 0 for diabetes treatment, and – 0.013 8 and – 0.027 5 for blood glucose control, respectively; the per capita annual income-related CI for diabetes prevalence and awareness were – 0.002 6 and – 0.001 4, but for diabetes treatment and blood glucose control were 0.020 7 and 0.077 1. Conclusion The prevalence of diabetes is at a general level but diabetes awareness, treatment and blood glucose control are at a low level among the middle-aged and elderly residents in Yangzhong city; the residents′ diabetes-related indicators are correlated with their socioeconomic status and there is diabetes-related health inequity due to different socioeconomic status.
2021, 37(6): 965-973. doi: 10.11847/zgggws1133288
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Objective To explore temporal-spatial distribution and risk factors of lung cancer mortality risk in Heilongjiang province, and to provide evidences for prevention and control of lung cancer. Methods We collected the data on lung cancer and chronic obstructive pulmonary disease (COPD) mortality in Heilongjiang province from 2008 through 2017 and relevant data on demographics, ambient air pollutants, social economic development were also collected simultaneously. Integrated nested Laplace approximation-based Bayesian spatio-temporal model was used to estimate annual prefecture-specific and district/county-specific standardized mortality ratio (SMR) of lung cancer and to analyze relative risks of lung cancer mortality attributed to various known risk factors. Results During the 10-year period in the province, the lung cancer mortality risk generally increased significantly, although the spatio-temporal pattern of lung cancer SMR was different in different districts/counties. From 2008 to 2017 among 132 districts/counties of the province, the number of district/county with higher lung cancer mortality risk (relative risk [RR] > 1.0 compared to overall risk of the province) increased from 9 to 69. The prefecture-specific age-standarized mortality rate (ASMR) of COPD was positively associated with the SMR of lung cancer (RR for all = 1.10, 95% confidence interval [95% CI]: 1.04 – 1.16; RR for males = 1.09, 95% CI: 1.03 – 1.16; RR for females = 1.10, 95% CI: 1.04 – 1.16). No significant associations were observed between the SMR of lung cancer and other factors including the proportion of the population over 60 years old, annual cigarette consumption per capita (lag 20 years), particulate matter ≤ 2.5 μm in mean aerodynamic diameter (lag 8 years), regional gross domestic production per capita (lag 10 years), the proportion of employed population in urban mining industry (lag 5 years) and the proportion of agricultural population (lag 20 years). A 1/100 000 increment in ASMR of COPD was associated with a 0.34% (95% CI = 0.22% – 0.46%) increase in district/county-specific SMR of lung cancer for all population; while for male and female population, the increase were 0.29% (95% CI: 0.19% – 0.40%) and 0.33% (95% CI: 0.20% – 0.46%), respectively. Conclusion The overall risk of lung cancer mortality was significantly increased from 2008 to 2017 in Heilongjiang province and COPD may be an important risk factor for the mortality. The results suggest that lung cancer screening should be carried out in COPD patients for effective prevention and control of lung cancer mortality.
2021, 37(6): 974-977. doi: 10.11847/zgggws1129689
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Objective To prepared complex amino acid chelated calcium (CAACC) with a by-product of Chlamys farreri processing and to assess the quality and calcium supplementation effect of the prepared CAACC for effective utilization of Chlamys farreri processing by-product. Methods The quality and stability of the prepared CAACC were assessed with detections of heavy metals and other harmful substances, Fourier transform infrared spectroscopy (FTIR) and in vitro simulation of gastrointestinal digestive system. Meanwhile, the calcium supplementation effect of CAACC was evaluated with visceral index, serum biochemical index, bone mineral density and other indicators in experimental rats. Results The detection results indicated that the prepared CAACC met relevant quality standards, with high absorption and utilization rate. In experimental rats, the apparent absorption rate of calcium ions in CAACC was (81.83 ± 8.48)% and the retention rate was 81.37 ± 5.53%; furthermore, bone mineral density of the rats treated with the prepared CAACC increased significantly (P < 0.05). Conclusion The complex amino acid chelated calcium prepared with a by-product of Chlamys farreri processing is a potential and efficient calcium supplement agent.
2021, 37(6): 978-981. doi: 10.11847/zgggws1129849
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Objective To explore the effect of G-protein coupled receptor-associated sorting protein 1-short-hairpin RNA (GASP-1-ShRNA) on proliferation and apoptosis of lung cancer cells and tumor formation in nude mice. Methods GASP-1-shRNA1, GASP-1-shRNA2 and GASP-1-shRNA3 were transfected into lung cancer A549 cells with Lipofectamine 2 000. Colony formation test and flow cytometry were used to detect proliferation and apoptosis of A549 cells from groups of GASP-1-shRNA1 transfection, blank control, and empty vector transfection, respectively. The A549 cells′ expressions of Ki67, cleaved caspase-3, B cell lymphoma-2 protein (Bcl-2) and Bcl-2-associated X protein (Bax) were determined with Western blot. An orthotopic xenograft mouse model was established through injection of GASP-1-shRNA1-transfected cells into hind leg tissues in nude mice. The tumor growth of the model mice were observed and the expressions of ki67 and caspase-3 protein in tumor tissues were detected with immunohistochemistry. Results The mRNA and protein expression of GASP-1 in A549 cells were down-regulated after transfections of GASP-1-shRNA1, GASP-1-shRNA2, and GASP-1-shRNA3, especially in the GASP-1-shRNA1 transfected A549 cells. The down-regulation of GASP-1 could inhibit proliferation and promote cell apoptosis of the A549 cells. In vivo experiments, down-regulated GASP-1 could restrain tumor growth by inhibiting proliferation and promoting apoptosis of the A549 cells. Conclusion Down-regulation of GASP-1 could inhibit proliferation and promote apoptosis of lung cancer A549 cells.
2021, 37(6): 982-985. doi: 10.11847/zgggws1127721
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Objective To examine the prevalence and influencing factors of being at high risk of cardiovascular disease (CVD) among adult residents living in old urban regions of Guangzhou city and to provide evidences for implementing related interventions in the population. Methods From 2017 to 2018, we conducted a survey, including questionnaire interview, physical examination and laboratory test, for identifying individuals at high CVD risk among 4 904 permanent residents aged 35 – 75 years recruited using cluster sampling in an old urban region of Guangzhou city, Guangdong province. In this study, the high CVD risk is defined as having one of following four indicators: CVD history, hypertension, dyslipidemia, and with a 20% of probability for suffering from CVD within next 10 years based on the standards recommended by World Health Organization. Univariate and multivariate logistic regression analysis were adopted to explore influencing factors of CVD risk and its detection among the residents. Results Among the 4 892 participants (mean age = 58.83 ± 8.31years) completing the survey, the age- and gender-adjusted detection rate of with a high CVD risk was 15.17% and the adjusted detection rate of CVD history, hypertension type, dyslipidemia, with a 20% of probability for suffering from CVD within next 10 years were 2.13%, 6.68%, 6.82%, and 1.69%, respectively. Multivariate logistic regression revealed that the participants aged 55 – 64 and 65 – 75 years were more likely to be detected with high CVD risk, with odds ratio (OR) (95% confidence interval [95% CI]) of 1.74 (1.20 – 2.53) and 2.67 (1.82 – 3.92). For the participants, significant factors positively associated with the detection of high CVD risk included overweight (OR = 1.36, 95% CI : 1.16 – 1.60), obesity (OR = 1.80, 95% CI : 1.43 – 2.26), current smoking (OR = 1.35, 95% CI : 1.07 – 1.71), and alcohol drinking during past one year (OR = 1.24, 95% CI : 1.05 – 1.47). While underweight was a factor reversely related to the detection of high CVD risk. Conclusion More effective interventions on body weight control, unhealthy lifestyle and dyslipidemia should be promoted among middle aged and elder community residents for cardiovascular disease prevention.
2021, 37(6): 986-989. doi: 10.11847/zgggws1134642
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Objective To examine the status of professional identity among undergraduates majoring in public health and preventive medicine in the context of coronavirus disease 2019 (COVID-19) epidemic for providing evidences to the training of public health professional, improvement of professional identity and stabilization of professional workforce in China. Methods Using convenient sampling, we recruited 457 undergraduates majoring in public health and preventive medicine in four universities in Beijing city, Hubei and Sichuan province for an online survey conducted during September – October, 2020. A self-designed questionnaire was used in the study. Results For the 402 participants with valid information, the average score of professional identity was 3.39 ± 0.52, indicating a moderate level of professional identity; the average scores of six professional identity dimensions were 2.89 ± 0.52 for cognition, 3.17 ± 0.65 for emotion, 3.75 ± 0.65 for behavior, 3.50 ± 0.76 for commitment, 3.58 ± 0.49 for value, and 3.44 ± 0.71 for expectation, respectively. Multivariate linear stepwise regression analysis showed that the participants with following characteristics were more likely to have a higher professional identity: studying in lower grade (β = 0.062, P < 0.001), being an only child (β = 0.118, P = 0.034), with a family member engaged in medical work (β = 0.148, P = 0.002), and preferring to work as a medical worker after experiencing COVID-19 epidemic (β = 0.524, P < 0.001). Conclusion Among the Chinese undergraduates majoring in public health and preventive medicine, the professional identity is at a moderate level and mainly influenced by studying grade, whether being an only child, whether with a medical worker in family members and experience of public health emergency.
2021, 37(6): 990-993. doi: 10.11847/zgggws1127970
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Objective To examine the prevalence of Ureaplasma urealyticum (UU) infection in married women and the correlation of UU infection with obsterical history, induced abortion history, and sexual behavior and to provide evidences for the prevention and control of reproductive tract infection. Methods Using cluster random sampling, we recruited 650 married women aged 20 – 49 years from physical examinees at a medical institution in Shanghai city and then a self-administered questionnaire survey, gynecologic examination and laboratory detection were conducted among the women from March 2016 through February 2017. Results Of 597 participants with complete information, 358 (60.0%) were diagnosed with UU infection. Unconditional multivariate logistic regression analysis demonstrated that primary contraception method, the age at first sexual intercourse and parity were influencing factors for UU infection. Compared with those not taking contraceptive measures, the participants using condom as a main method of contraception had a lower risk of UU infection (odds ratio [OR] = 0.575, 95% confidence interval [95% CI]: 0.331 – 0.998); the UU infection risk of the participants having first sexual activity at the age of ≥ 24 years was lower than that of those having the activity at the age of ≤ 21 years (OR = 0.588, 95% CI: 0.368 – 0.939); the participants with the parity greater or equal to 2 had a lower UU infection risk than those with the parity less than 2 (OR = 0.601, 95% CI: 0.400 – 0.903). No statistical correlation of induced abortion history and the sexual intercourse frequency with UU infection was observed. Conclusion The prevalence rate of UU infection is high among married women and having first sexual intercourse at elder age and promoting condom use may reduce UU infection risk among the women.
2021, 37(6): 994-998. doi: 10.11847/zgggws1129507
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Objective To examine the knowledge about prevention of conronavirus disease 2019 (COVID-19) among primary and middle school students in Wuhan city and the students’ preventive behavior and its influencing factors to provide evidences for developing intervention measures. Methods Totally 16 431 students were selected from 18 primary and middle schools in three districts of Wuhan city with stratified cluster random sampling and an online anonymous questionnaire survey was carried out among the students from February 16 to March 1, 2020, the period with COVID-19 epidemic. Results Among the 15 428 students (93.9% of the selected) with valid responses, more than 90% reported the awareness on following 6 items of knowledge about COVID-19 prevention: always wearing a face mask when going out, washing hands before eating, washing hands after toilet use, opening window for ventilation or using an air disinfecting machine for indoor air disinfection, staying at home as much as possible, and avoiding activities; however, less than a half of the students were aware of wearing a mask special for children, replacing a mask accumulatively used for 2 – 4 hours, washing hands after contacting an animal or disposing animal waste, not touching eyes, nose or mouth with hands, and having sufficient sleeping. Only 40.8% of the students were assessed with good practice about COVID-19 prevention during previous one month. Logistic regression analysis revealed following significant influencing factors for the students′ preventive behavior during previous one month: gender, age, grade, maternal occupation, maternal education, time-point answering the questionnaire, and traveling history. Conclusion Personal behavior about COVID-19 prevention is at a low level among primary and middle school students in Wuhan city and relevant health education needs to be promoted among the students.
2021, 37(6): 999-1002. doi: 10.11847/zgggws1123842
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Objective To analyze prevalence characteristics and spatial clustering of Japanese B encephalitis (JE) and the correlation between the occurrence of JE and the seasonal fluctuation of Culex tritaeniorhynchus in Jiangsu province during 2005 – 2018 for providing evidences to JE prevention. Methods Data on reported JE cases and demographics in Jiangsu province during 2005 – 2018 were extracted from National Disease Control Information System and the data on Culex tritaeniorhynchus density in the province for years of 2008 – 2018 were collected from vector monitoring system. Descriptive statistics were used in data analyses. Results Totally 495 JE cases were reported during the period in Jiangsu province and a decreasing trend in the annual JE incidence was observed (χ2 = – 16.11, P < 0.01). Of all the reported cases, 92.73% were children aged 1 – 14 years. Obvious seasonal variation in JE incidence was detected and more cases were reported between 7th July and 7th September in a year (relative risk = 86.48, log likelihood ratio = 726.97; P < 0.01). The peak period of JE incidence was in July in South Jiangsu but in August in Northern Jiangsu. Purely spatial scan analysis results demonstrated the clustering of JE cases mainly in three cities in the northern and one city in the southern of Jiangsu province. For the period of 2008 – 2018, the monthly average number of JE cases statistically correlated with the lag day 30 monthly average density of Culex tritaeniorhynchus measured at live-stock sheds (r = 0.79, P < 0.01). Conclusion The incidence of JE was closely related to the seasonal fluctuation of Culex tritaeniorhynchus density in Jiangsu province, suggesting that monitoring on Culex tritaeniorhynchus density and comprehensive anti-mosquito measures should be promoted, especially in regions with clustering of JE cases.
2021, 37(6): 1003-1007. doi: 10.11847/zgggws1127082
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Objective To construct percentile curves for height and weight of child and adolescent students using coefficient of skewness-median-coefficient of variation – Lambda-Mu-Sigma (LMS) method and to analyze rural urban difference in growth and development of the students for the application of LMS method in relevant researches. Methods Using cluster random sampling, we selected 25 475 students aged 7 – 18 years in 110 primary and high schools in urban and rural regions across Sichuan province in 2018. Based on the data of height and weight measurement, the 5th, 50th and 95th percentile (P5, P50 and P95) curves for the urban and rural students were constructed using LMS method with the software (LMS chartmaker Light Version 2.54) and the differences between the urban and rural students with the height and weight of P5, P50 and P95 values were analyzed. Results The urban and rural differences in average height for the boy students with the P5, P50 and P95 value were 0.03, 1.20 and 1.60 cm, and those for the girl students were – 0.32, 0.88 and 0.95 cm; while, the urban and rural differences in average weight for the boy students with the P5, P50 and P95 value were 0.18, 0.96 and 1.85 kg, and those for the girl students were – 0.25, 0.29 and 1.55 kg, respectively. Conclusion For the child and adolescent students in Sichuan province, the urban and rural difference in average height and weight are larger in the boy students than in the girl students and both the differences are larger in the students with higher percentile values than in the students with lower percentile values. For the students with 50th and 95th percentile value of height and weight, the urban and rural differences increase first and then decrease with the increment of the sutdents′ age.
2021, 37(6): 1008-1011. doi: 10.11847/zgggws1128075
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Objective To analyze prevalence characteristics of pertussis in Zaozhuang city of Shandong province during 2013 – 2018 and to provide evidences for effective prevention and control of pertussis. Methods Information on all pertussis cases reported in Zaozhuang city during 2013 – 2018 were extracted from the National Infectious Disease Report Information Management System and analyzed with descriptive statistics and circular distribution. Excel 2013 and SPSS 21.0 were adopted in data processing. ArcGis 10.6 was used to perform visual display. Results A total of 507 pertussis cases were reported during the 6-year period in the city and the average annual incidence was 2.07/100 000. The annual pertussis incidence in 2018 was 2.83 times higher than that in 2017. Circular distribution analysis revealed an incidence peak during 17 – 18 of July in a year and a high incidence season from July to September in a year. The most (476, 93.52%) of the reported pertussis cases were scattered children and more than a half (294, 57.76%) of the cases were children less than one year old. The highest prefecture-specific average annual incidence rate was 2.89/100 000 and the highest town-specific average annual incidence rate was 7.83/100 000. Conclusion During 2013 – 2018 in Zaozhuang city, the incidence of pertussis increased obviously and the incidence peak was in summer season. Timely and supplementary vaccination should be promoted among children less than one year old and scattered children for pertussis prevention.
2021, 37(6): 1012-1014. doi: 10.11847/zgggws1123237
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Abstract:
Objective To analyze the suitability of human resource for maternal health care (MHC) and changing trend of maternal mortality rate (MMR) and their regional disparities in Beijing and Shanghai municipality during the period from 2000 through 2017. Methods We retrieved research literatures on human resource for MHC in respects of staff size (n = 166), professional quality (n = 312) and incentive mechanism (n = 115) in Beijing and Shanghai municipality from 1995 to 2017 and assessed the suitability of human resource allocation using a comprehensive indicator. Spearman correlation and linear regression analysis were used to analyze the relationship between the suitability of human resource allocation and MMR. Results The indicator for the suitability of human resource for MHC increased from 26.20% and 25.60% in 2000 to 39.00% and 57.60% in 2017 in Beijing and Shanghai municipality. The regression analysis resulted in a significant correlation between the human resource allocation suitability and MMR only in Shanghai (P < 0.01). Conclusion The suitability of human resource allocation for maternal health care was improved yearly both in Shanghai and Beijing municipality during 2000 – 2017 but the staff size still needs to be increased. The association of human resource allocation with maternal mortality rate is more obvious in Shanghai municipality.
2021, 37(6): 1015-1018. doi: 10.11847/zgggws1125545
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Abstract:
Objective To explore the association between serum uric acid (SUA) and non-alcoholic fatty liver disease (NAFLD) among residents in Nanping city of Fujian province and to provide evidences for developing intervention on NAFLD. Methods We enrolled 2 328 attendees aged 18 – 70 years at a physical examination center of a general hospital in Nanping city of Fujian province and conducted questionnaire interview, physical examination and laboratory detection among the participants from April 2015 through August 2017. In the participants, 543 NAFLD cases were diagnosed based on imaging diagnostic criteria recommended by the National Guidelines for Diagnosis and Treatment of Non-Alcoholic Fatty Liver Disease – 2010 Revision and assigned into the case group; the controls were 1 785 participants without NAFLD. Statistical analyses were performed to assess the association of SUA with NAFLD. Results The SUA of the cases was significantly higher than that of the controls (375.24 ± 93.36 μmol/L vs. 313.20 ± 76.59 μmol/L, t = – 15.664; P < 0.001). The detection rates of NAFLD were 8.34%, 23.52%, 22.51%, and 43.13% for the participants in the lowest, second, third, and the highest quartile of SUA content, respectively. Unconditional multivariate logistic regression analysis revealed that compared to those in the lowest quartile of SUA content, the participants in the second and the highest quartile were at increased risk of NAFLD, with the odds ratios (95% confidence interval) of 2.05 (1.35 – 3.11) and 2.02 (1.29 – 3.17) after adjusting for gender, age, education, occupation, monthly average income, smoking, alcohol drinking, physical exercise, history of chronic diseases, body mass index, systolic pressure, diastolic pressure, triglyceride, total cholesterol, high-density lipoprotein cholesterol, low-density lipoprotein cholesterol, alanine aminotransferase, aspartate aminotransferase, glutamyltranspeptidase, creatinine, and fasting blood glucose. Conclusion High serum uric acid could increase the risk of non-alcoholic fatty liver disease in 18 - 70 years old population.
2021, 37(6): 1019-1022. doi: 10.11847/zgggws1122394
Abstract(48) HTML(6) PDF 776KB(2)
Abstract:
Objective To compare the disparity in responsibility assignment among various functional institutions of the maternal health care (MHC) system between Beijing and Shanghai and to explore the feasibility of quantitative evaluation on the degree of well-defined responsibility assignment. Methods We systematically and extensively collected documents and materials on MHC issued by administrative agencies of Beijing and Shanghai municipality published during 2000 – 2017. Then we extracted relevant information from 649 retrieved documents (232 relevant to Beijing and 417 to Shanghai) and analyzed the information quantitatively to assess the responsibility assignment among various functional institutions of MHC system in the two municipalities. Spearman correlation and linear regression analysis were used to analyze the relationship between the degree of well-defined responsibility assignment of MHC system and maternal mortality rate (MMR). Results The relevant information-derived index for the degree of well-defined responsibility assignment of MHC system increased from 1.8% in 2000 to 23.7% in 2017 in Beijing municipality; while, the index increased from 9.5% to 28.0% in Shanghai, indicating a relatively low level for the MHC system's well-defined responsibility assignment. There was an inverse correlation between the index for well-defined responsibility assignment of MHC system and MMR in the two municipalities. Conclusion The responsibility assignment among various functional institutions of the maternal health care system was improved and the improvement facilitated maternal health care practice in Beijing and Shanghai during 2000 – 2017; but the responsibility assignment for nonmedical institutions should be well defined. The study verified the feasibility of quantitative assessment on responsibility assignment among various functional institutions of the maternal health care system.
2021, 37(6): 1023-1026. doi: 10.11847/zgggws1126674
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Abstract:
Objective To establish a rapid method for simultaneous determination of 12 microcystins in surface water with ultra performance liquid chromatography-tandem mass spectrometry (UPLC-MS/MS). Methods Surface water samples were firstly freeze-thawing for three times, then directly filtered with glass fiber filters for injection. When several or one of the microcystins under the concentration of relevant limit of quantification, GF/C glass fiber was used for filter and an Oasis HLB SPE column was used for the concentration and purifying. The 40% methanol aqueous solution was used for washing; after elution with methanol, equal volume of ultrapure water was added for dilution, and then filtered through synthetic fabric membrane for injection. The separation of the analytes was carried out on an ACQUITY UPLC BEH C18 column (100 mm × 2.1 mm, 1.7 μm) with gradient elution using bobile phases of 0.2% (v/v) formic acid aqueous solution and methanol mix with acetonitrile at ratio of 2 to 3 containing 0.2% (v/v) formic acid. The 12 microcystins were detected with positive electrospray ionization in multiple reaction monitoring modes, and quantified by external standard methods. Toxicity equivalent factor conversion was used for total toxicity analysis of the detected microcystins. Results The linear ranges of 12 microcystins were 0.1 – 5.0 ng/mL and the correlation coefficients were greater than 0.995. The limits of detection and quantification were 0.006 – 0.012 μg/L and 0.02 – 0.04 μg/L for SPE method and 0.03 – 0.06 μg/L and 0.1 – 0.2 μg/L for direct injection, respectively. The recoveries were in the range of 83.07% – 108.27% with the relative standard deviations ranging from 0.46% – 12.76% (n = 6). Then the established method was used for the determination of 6 surface water samples and several kinds of microcystins were detected in 4 of the samples. Conclusion The established method is rapid, simple, sensitive and accurate, and could be applied in determination of 12 microcystins in surface water.
2021, 37(6): 1027-1030. doi: 10.11847/zgggws1129393
Abstract(49) HTML(19) PDF 481KB(8)
Abstract:
Newborn screening and patient registration system are the basis for rare disease management. This study introduces the status of international newborn screening and rare disease registration, summarizes their characteristics, and provides information and references for improving and promoting rare disease management in China.
2021, 37(6): 1031-1034. doi: 10.11847/zgggws1125343
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Abstract:
Air pollution exerts a lot of adverse effects on human health, including on female fertility. However, the exact mechanism of the adverse effects on human fertility is unclear. We conducted a systematic review of previous researches on the influence of air pollution upon female reproduction to fully understand the effect of air pollution on human fertility. The research sites and major pollutants concerned are different among various population epidemiology researches and laboratory studies. The sites of epidemiological investigations included petrochemical plants and traffic roads and the pollutants concerned mainly included particulate matter < 10/2.5 microm in aerodynamic diameter (PM10/2.5), nitrogen dioxide (NO2), sulfur dioxide (SO2), ozone (O3) and other compositions related to coal combustion and traffic exhaust. These studies are mainly based on the evaluation of air pollutants on various stages of egg development, fertilized egg formation and implantation, clinical conception, in vitro fertilization and embryo transfer, abortion, and preterm labor. Despite the bias caused by different design types and many confounding factors, these studies to some extent provide clues for the in-depth study of the mechanism of air pollution's influence on female reproduction.
2021, 37(6): 1035-1040. doi: 10.11847/zgggws1126789
Abstract(1789) HTML(998) PDF 537KB(32)
Abstract:
With the introduction of Toxicity Testing in the 21st Century: A Vision and Strategy, the focus of toxicity testing has shifted from animal experiments to in vitro models using human resource cells or cellular components. As kidney is a major target for drug-induced toxicity and the drug-induced toxicity remains a major problem in developing new drugs, a predictive in vitro model is urgently needed to evaluate the renal toxicity of exogenous compounds. However, current in vitro cellular models poorly replicate both the morphology and the function of kidney tubules and therefore fail to demonstrate injury responses to that would be nephrotoxic in vivo. The resource and characteristics of cellular models, cell culture conditions, and readouts of injury are important in establishing an in vitro model. The development of differentiation of pluripotent stem cells into multiple renal cell types, 3 dimensional culture systems and kidney-on-a-chip technology, omics technology and high-content screening have opened a range of potential new platforms for evaluating compounds nephrotoxicity and promoted in vitro to in vivo extrapolation. This study summarizes the latest advances in in vitro nephrotoxicity assessment models. | 2021-08-05 13:09:14 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.27785247564315796, "perplexity": 7336.3549658072325}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-31/segments/1627046155925.8/warc/CC-MAIN-20210805130514-20210805160514-00531.warc.gz"} |
https://homework.cpm.org/category/CCI_CT/textbook/pc3/chapter/5/lesson/5.1.1/problem/5-6 | ### Home > PC3 > Chapter 5 > Lesson 5.1.1 > Problem5-6
5-6.
Write out the sum and calculate: $\displaystyle \sum _ { k = 2 } ^ { 6 } ( k - 2 ) ^ { 2 }$
Start with $k=2$, then $k=3$, $4$, $5$, $6$. | 2021-03-07 12:33:59 | {"extraction_info": {"found_math": true, "script_math_tex": 6, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9515274167060852, "perplexity": 3338.2978707877046}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178376467.86/warc/CC-MAIN-20210307105633-20210307135633-00137.warc.gz"} |
https://nbviewer.jupyter.org/github/jobar8/Geophysics-Labs-Notebooks/blob/master/notebooks/02_Cropping_and_resampling_grid.ipynb | # Cropping and resampling a grid¶
This notebook is part of a blog post on Geophysics Labs.
Here I show how to interpolate a grid onto another grid, effectively cropping and resampling the first grid.
The initial grid is a 2D array obtained by color quantization of an RGB (three-band) image of a geological map. This previous step is described in another notebook.
The example shown here makes use of the Kevitsa dataset that was made freely available by the Frank Arnott Award.
Let's start by loading some Python libraries. We need SciPy for the interpolation functions and rasterio for handling geographic information. Please refer to the index notebook for a tip about installing rasterio.
In [1]:
import numpy as np
from scipy import interpolate
import rasterio
import matplotlib.pyplot as plt
import matplotlib.colors as mcolors
% matplotlib inline
First, let's reopen the indexed-colour image that was created at the previous step. It shows a portion of the geological map of the Kevitsa area in northern Finland. To display it properly, we also need to load the colour palette that associated with it.
In [2]:
indexedImage = np.load(r'..\data\Kevitsa_geology_indexed.npy')
new_cm = mcolors.LinearSegmentedColormap.from_list('win256', win256/255)
# make plot
fig,ax = plt.subplots(figsize=(6,6))
ax.imshow(indexedImage,cmap=new_cm,norm=mcolors.NoNorm())
Out[2]:
<matplotlib.image.AxesImage at 0x28eae4ea438>
Next, we open the image file of the map that contains the geographic information about the position and extent of the map. The is important if we want to interpolate the image onto the grid of the 3D survey. This information is contained in a small text file (.pgw) that comes along with the PNG file.
In [3]:
inFile = r'..\data\Kevitsa_geology_noframe.png'
dataset = rasterio.open(inFile)
Rasterio has read the raster data but also the geographic information in the world (.pgw) file. Let's see what it contains:
In [4]:
nrows,ncols = dataset.shape
geotransform = dataset.get_transform()
cellsize = geotransform[1]
# top-left corner of top-left pixel
ulx = geotransform[0]
uly = geotransform[3]
# bottom-right corner of bottom-right pixel
lrx = ulx + geotransform[1] * ncols
lry = uly + geotransform[5] * nrows
# print the output
print('Raster Size: {:d} columns x {:d} rows x {:d} bands'.format(ncols, nrows, dataset.count))
print('Cell Size: {:.2f} m'.format(cellsize))
print('Upper-left corner:({:.2f},{:.2f})\nBottom-right corner:({:.2f},{:.2f})'.format(ulx,uly,lrx,lry))
Raster Size: 1485 columns x 890 rows x 4 bands
Cell Size: 5.08 m
Upper-left corner:(3494752.32,7514558.38)
Bottom-right corner:(3502295.11,7510037.79)
## Creating a set of grid coordinates¶
The next step is to create two arrays containing the X and Y positions of all the pixels of our image. Again, this is necessary for running the interpolation later on.
There are usually two methods to register 2D grids in space, depending on whether the coordinates correspond to the centres or to the corners of the pixels. GIS programs generally use the latter convention, as indeed the extent of a raster image starts from the very edge of the pixels. In contrast, geophysical software (OpendTect, Geosoft Oasis Montaj, etc.) tend to use the other method, registering the pixel centres because these are considered as any other data points. In this view, an image or a regular grid is simply a particulay case of a dataset consisting of observations that happened to be located at regular intervals.
A slightly different explanation of these two different methods of grid registration can be found on the GMT website. The principle is the same: in GMT jargon, gridline registration corresponds to corner-based coordinates, while the pixel registration makes use of centre-based coordinates.
The conclusion of this short introduction to grid coordinates is that we have to use pixel-centre coordinates and that we have to calculate these from the pixel-corner coordinates provided by rasterio.
In [5]:
xmin = ulx + cellsize/2.
ymin = lry + cellsize/2.
xmax = xmin + (ncols-1)*cellsize
ymax = ymin + (nrows-1)*cellsize
# 1-D arrays of coordinates (use linspace to avoid errors due to floating point rounding)
x = np.linspace(xmin,xmax,num=ncols,endpoint=True)
y = np.linspace(ymin,ymax,num=nrows,endpoint=True)
# 2-D arrays of coordinates
X,Y = np.meshgrid(x,y)
The X and Y arrays give the coordinates (X[i,j],Y[i,j]) of each pixel (i,j) in the image. However, we forgot a crucial difference between the orientation of the cartesian axes of our (projected) coordinate system and the arrangement of rows and columns in the array of the image. Basically, the origin (0,0) of array indices is in the top-left corner of the image, while the origin of the coordinate system is in the bottom-left corner.
To correct for this difference, we simply need to flip the Y axis upside-down by adding the following:
In [6]:
Y = np.flipud(Y)
A plot of the X and Y arrays can help to ensure we have the expected set of X and Y coordinates.
In [7]:
fig,(ax1,ax2) = plt.subplots(1,2,figsize=(8,6))
ax1.imshow(X)
ax1.set_title('X')
ax2.imshow(Y)
ax2.set_title('Y')
plt.show()
# Performing the interpolation¶
## Creating interpolator¶
The interpolation in SciPy works by creating the interpolation function using the coordinates and the values of the data points. There are several types of interpolators available. For this type of data (image of a geological map), the best is to use a nearest neighbour interpolation, as we want to preserve the sharpness of the geological outlines. It is also vital for the quality of the result that indexed values in the image are not modified, since that would also modify their colour in an uncontrolled way.
In [9]:
interp = interpolate.NearestNDInterpolator(np.column_stack((X.flatten(),Y.flatten())),indexedImage.flatten())
## Creating target grid¶
The interpolation function will compute the intensities of the pixels at their new locations in the target grid. This new grid corresponds to the 3D seismic survey whose outline is shown in red on the map.
Refering back to the blog post, we can fetch the definition of this grid from OpendTect. We are not limited to the boundaries of the 3D survey and we can add some padding in the form of additional rows and columns. The indexing is copied from the in-line and cross-line numbering in OpendTect.
In [10]:
# First let's define a grid of in-line and cross-line indices
pad = 50 # number of rows and columns to add on all sides
step = 1 #
inline,xline = np.meshgrid(inline_limits,xline_limits,indexing='ij')
# indexing starts from bottom-left corner
inline = np.flipud(inline)
# Now we can compute the coordinates - these numbers come from the "advanced" panel in the coordinate settings in OpendTect
Xi = 3491336.248 - 3.19541219*inline + 9.4758042*xline
Yi = 7497848.4 + 9.47383513*inline + 3.19552448*xline
## Run the interpolation¶
In [11]:
newImage = interp((Xi,Yi))
plt.imshow(newImage,cmap=new_cm)
Out[11]:
<matplotlib.image.AxesImage at 0x28eb1014c88>
The initial image has been rotated, cropped and resampled to match the position and extent of the 3D survey grid. It is now ready for export!
# Export to ASCII file¶
The final step is to create a text file containing the new interpolated image.
We can take advantage of the fact that the new grid has been defined using the same numbering as the traces of the 3D survey in OpendTect. So we don't need the coordinates, just the trace numbers.
The image will be imported in OpendTect as a 3D horizon. The colours will be treated as an attribute, so we need an extra Z column that will define the "geometry" of the horizon, a simple plane at depth = 0.
In [12]:
# Trace indices arranged in two vectors
IL_vector = inline.flatten()
XL_vector = xline.flatten()
# Data arranged in one single vector
values = newImage.flatten()
# Z column (zeros for importing in OpendTect)
Z_vector = np.zeros_like(IL_vector)
# Save to ASCII
outFile = r'..\data\Kevitsa_geology_indexed_ILXL.xyz'
np.savetxt(outFile,np.array((IL_vector,XL_vector,Z_vector,values)).T,fmt='%14.2f %14.2f %14.2f %.8g')
print('Done!')
Done! | 2018-02-21 22:45:55 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.513744056224823, "perplexity": 1574.4876903631948}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-09/segments/1518891813818.15/warc/CC-MAIN-20180221222354-20180222002354-00741.warc.gz"} |
https://solvedlib.com/4-julie-and-john-aggie-want-to-purchase-80-acres,27099 | # 4. Julie and John Aggie want to purchase 80 acres of farm land valued at $1,500... ###### Question: 4. Julie and John Aggie want to purchase 80 acres of farm land valued at$1,500 per acre. Their lender requires a 30% down payment. Assume twenty annual payments. The interest rate is 7.5%. a. Calculate the schedule of interest and principal payment over the life of the loan using the constant payment method and the constant payment on principal method. Year Constant Payment Method Loan Balance Payment Interest Principal End of Year Balance $84,000.00$8,239.74 $82,060.26 48,262.68 12 13 14 15 14,795.00 18 19 20 Total Interest Paid Constant Payment on Principal Method Loan Balance Payment Interest Year Principal End of Year Balance$84,000.00 2 5 TL 58,800.00 7 8 10 2,835.00 12 13 13 14 15 16 17 18 19 0.00 Total Interest Paid $66,150.00 b. What is the total interest paid over the life of the loan with each method? ## Answers #### Similar Solved Questions 1 answer ##### Determine whether the improper integral converges and, if so, evaluate it.$\int_{0}^{\pi / 2} \tan x d x$Determine whether the improper integral converges and, if so, evaluate it.$\int_{0}^{\pi / 2} \tan x d x$... 5 answers ##### MmI2Problem 1 1.1 What is the capacitor e-field if the voltage is 2OOV and the 40 AOOI 40 separation is 2.0 cm? 1.2 A free electron is placed at the dot: To which direction will it move? 1.3 Use energy conservation to explain what happens 1.4 What is the total energy by the end of the motion if the electron is initially at rest? 1.5 Find the maximum speed of the electron. (The electron charge e = 1.6x10-19 C; The electron mass me = 9.1x1031 kg) Mm I2 Problem 1 1.1 What is the capacitor e-field if the voltage is 2OOV and the 40 AOOI 40 separation is 2.0 cm? 1.2 A free electron is placed at the dot: To which direction will it move? 1.3 Use energy conservation to explain what happens 1.4 What is the total energy by the end of the motion if th... 5 answers ##### The average asking price for rent in Guytonville was SIOO0 in the year 1995 and S2132 in the year 2006_ Find an exponential model of the form f(t) -Yoh' that tits this dataIf this model remains accurate_ what is the predicted average rent in 20202Estimate the year in which the average rent will hit$13671.
The average asking price for rent in Guytonville was SIOO0 in the year 1995 and S2132 in the year 2006_ Find an exponential model of the form f(t) -Yoh' that tits this data If this model remains accurate_ what is the predicted average rent in 20202 Estimate the year in which the average rent wi...
##### Select HGc YU {tertiary one FN-Ch] 1 = tor followng compound
Select HGc YU {tertiary one FN-Ch] 1 = tor followng compound... | 2023-03-27 19:32:04 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.35794103145599365, "perplexity": 6249.906185613634}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296948684.19/warc/CC-MAIN-20230327185741-20230327215741-00760.warc.gz"} |
http://eprints.iisc.ernet.in/10854/ | # Neutron diffraction studies of $Ge_xSe_{1-x}$ glasses
Rao, Ramesh N and Sangunni, KS and Gopal, ESR and Krishna, PSR and Chakravarthy, R and Dasannacharya, BA (1995) Neutron diffraction studies of $Ge_xSe_{1-x}$ glasses. In: Physica B:Condensed Matter, 213-21 . pp. 561-563.
PDF neutron.pdf Restricted to Registered users only Download (196Kb) | Request a copy
## Abstract
Neutron diffraction studies were performed on $Ge_xSe_{1-x}$ glasses for x=0.1, 0.2, 0.33 and 0.4. The structure factor S(Q) shows maximum intermediate-range order for x=0.33. Analysis of the two main peaks in T(r) shows that these glasses have $Ge(Se_{1/2})_4$ tetrahedra. Glasses with $x\leq;0.2$ consist of Se-chains cross-linked with Ge-tetrahedra while for $x\geq;0.2$ Ge-tetrahedra are present in both edge- and corner-shared configurations.
Item Type: Journal Article Copyright of this article belongs to Elsevier. Division of Physical & Mathematical Sciences > Physics 07 May 2007 19 Sep 2010 04:37 http://eprints.iisc.ernet.in/id/eprint/10854 | 2016-05-26 12:53:18 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8192154765129089, "perplexity": 11809.477541475932}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-22/segments/1464049275836.20/warc/CC-MAIN-20160524002115-00162-ip-10-185-217-139.ec2.internal.warc.gz"} |
https://thetestcamp.com/escwp-shortcode/mathematics-data-mytest-05/ | # Mathematics-Data-MyTest-05
This problem is related to which competency?
What is the range of set S?$S = \{41, 28, 13, 26, 38, 45, 42, 10\}$ | 2021-11-30 06:56:44 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 1, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.72379070520401, "perplexity": 7028.550834249922}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-49/segments/1637964358953.29/warc/CC-MAIN-20211130050047-20211130080047-00218.warc.gz"} |
http://mathoverflow.net/revisions/45937/list | 3 deleted 3 characters in body
Let us imagine that your factory manufactures two products, one of which is small, and the other is large. These products are shipped out in boxes. Suppose that your boxes come in two sizes, small and large. Suppose further that you can ship a small product in a large box, but that you cannot ship a large product in a small box.
Instead of products / boxes of various sizes, a more information-theoretic way of looking at things would be to think of the factory as a binary source, and to view the box-enlargement process as a binary channel. Let $X$ and $Y$ be discrete random variables with alphabets $\mathcal{X}$ and $\mathcal{Y}$, respectively, where $\mathcal{X} = \mathcal{Y} = \{0,1\}$. If the output of the production line is a small product, then $X = 0$, otherwise $X = 1$. If a small box is shipped out, then $Y = 0$, otherwise $Y = 1$. Hence, the random variable $X$ gives us the size of the product, while the random variable $Y$ gives us the size of the box. We can view $X$ and $Y$ as the input and output of a binary channel, respectively.
To deceive your competitors, every time a small product is ready to be shipped you flip a coin and, depending on the outcome, you choose to ship the small product in a large box or not. If you do so, then $X = 0$ and $Y = 1$. The "channel" has introduced an error. The channel is defined by the transition probabilities
$\{ \mathbb{P}[Y = 0 \mid X = 0], \mathbb{P}[Y = 1 \mid X = 0], \mathbb{P}[Y = 0 \mid X = 1], \mathbb{P}[Y = 1 \mid X = 1] \}$.
Your
A competitor observes the sizes of the boxes being shipped out and tries to infer what the actual sizes of the products inside the boxes are. In other words, your competitor would like to infer what the probability mass function (p.m.f.) of $X$ is, knowing only the p.m.f. of $Y$. To keep your competitor maximally confused, you would like to maximize the conditional entropy $H (X \mid Y)$, which is the uncertainty about $X$ given $Y$. Recall that the mutual information is
$I (X;Y) = H(X) - H(X \mid Y)$
and it gives us the reduction in the uncertainty of $X$ due to knowledge of $Y$. We would like to minimize the mutual information, which is equivalent to maximizing the conditional entropy $H(X \mid Y)$, as $H(X)$ is fixed (depends on the p.m.f of $X$, which is assumed to be fixed).
The mutual information can be written as $I(X;Y) = D( p(x,y) \| p(x) p(y) )$, which is the Kullback-Leibler distance between the joint p.m.f. and the product of the marginal p.m.f.'s. Check [1] for details. Therefore, you have a relative entropy minimization problem.
Usually, we are given the channel, and we choose the p.m.f. of $X$ that maximizes the mutual information $I(X;Y)$. In this problem, we are given the p.m.f. of $X$, and we choose the channel that minimizes the mutual information. It's a sort of "dual" of finding the capacity of a given channel.
References:
[1] Thomas M. Cover and Joy A. Thomas, Elements of Information Theory, John Wiley & Sons 2006.
2 deleted 1 characters in body; deleted 4 characters in body
Let us imagine that your factory manufactures two products, one of which is small, and the other is large. These products are shipped out in boxes. Suppose that your boxes come in two sizes, small and large. Suppose further that you can ship a small product in a large box, but that you cannot ship a large product in a small box.
Instead of products / boxes of various sizes, a more information-theoretic way of looking at things would be to think of the factory as a binary source, and to view the box-enlargement process as a binary channel. Let $X$ and $Y$ be discrete random variables with alphabets $\mathcal{X}$ and $\mathcal{Y}$, respectively, where $\mathcal{X} = \mathcal{Y} = \{0,1\}$. If the output of the production line is a small product, then $X = 0$, otherwise $X = 1$. If a small box is shipped out, then $Y = 0$, otherwise $Y = 1$. Hence, the random variable $X$ gives us the size of the product, while the random variable $Y$ gives us the size of the box. We can view $X$ and $Y$ as the input and output of a binary channel, respectively.
To deceive your competitors, every time a small product is ready to be shipped you flip a coin and, depending on the outcome, you choose to ship the small product in a large box or not. If you do so, then $X = 0$ and $Y = 1$. The "channel" has introduced an error. The channel is defined by the transition probabilities
$\{ \mathbb{P}[Y = 0 \mid X = 0], \mathbb{P}[Y = 1 \mid X = 0], \mathbb{P}[Y = 0 \mid X = 1], \mathbb{P}[Y = 1 \mid X = 1] \}$.
Your competitor observes the sizes of the boxes being shipped out and tries to infer what the actual sizes of the products inside the boxes are. In other words, your competitor would like to infer what the probability mass function (p.m.f.) of $X$ is, knowing only the p.m.f. of $Y$. To keep your competitor maximally confused, you would like to maximize the conditional entropy $H (X \mid Y)$, which is the uncertainty about $X$ given $Y$. Recall that the mutual information is
$I (X;Y) = H(X) - H(X \mid Y)$
and it gives us the reduction in the uncertainty of $X$ due to knowledge of $Y$ [1]. Y$. We would like to minimize the mutual information, which is equivalent to maximizing the conditional entropy$H(X \mid Y)$, as$H(X)$is fixed (depends on the p.m.f of$X$, which is assumed to be fixed). The mutual information can be written as$I(X;Y) = D( p(x,y) \| p(x) p(y) )$, which is the < a href="http://en.wikipedia.org/wiki/Kullback%E2%80%93Leibler_divergence">Kullback-Leibler Kullback-Leibler distance between the joint p.m.f. and the product of the marginal p.m.f.'s. Check [1] for details. Therefore, you have a relative entropy minimization problem. Usually, we are given the channel, and we choose the p.m.f. of$X$that maximizes the mutual information$I(X;Y)$. In this problem, we are given the p.m.f. of$X$, and we choose the channel that minimizes the mutual information. It's a sort of "dual" of finding the capacity of a given channel. References: [1] Thomas M. Cover and Joy A. Thomas, Elements of Information Theory, John Wiley & Sons 2006. 1 Let us imagine that your factory manufactures two products, one of which is small, and the other is large. These products are shipped out in boxes. Suppose that your boxes come in two sizes, small and large. Suppose further that you can ship a small product in a large box, but that you cannot ship a large product in a small box. Instead of products / boxes of various sizes, a more information-theoretic way of looking at things would be to think of the factory as a binary source, and to view the box-enlargement process as a binary channel. Let$X$and$Y$be discrete random variables with alphabets$\mathcal{X}$and$\mathcal{Y}$, respectively, where$\mathcal{X} = \mathcal{Y} = \{0,1\}$. If the output of the production line is a small product, then$X = 0$, otherwise$X = 1$. If a small box is shipped out, then$Y = 0$, otherwise$Y = 1$. Hence, the random variable$X$gives us the size of the product, while the random variable$Y$gives us the size of the box. We can view$X$and$Y$as the input and output of a binary channel, respectively. To deceive your competitors, every time a small product is ready to be shipped you flip a coin and, depending on the outcome, you choose to ship the small product in a large box or not. If you do so, then$X = 0$and$Y = 1$. The "channel" has introduced an error. The channel is defined by the transition probabilities$\{ \mathbb{P}[Y = 0 \mid X = 0], \mathbb{P}[Y = 1 \mid X = 0], \mathbb{P}[Y = 0 \mid X = 1], \mathbb{P}[Y = 1 \mid X = 1] \}$. Your competitor observes the sizes of the boxes being shipped out and tries to infer what the actual sizes of the products inside the boxes are. In other words, your competitor would like to infer what the probability mass function (p.m.f.) of$X$is, knowing only the p.m.f. of$Y$. To keep your competitor maximally confused, you would like to maximize the conditional entropy$H (X \mid Y)$, which is the uncertainty about$X$given$Y$. Recall that the mutual information is$I (X;Y) = H(X) - H(X \mid Y)$and it gives us the reduction in the uncertainty of$X$due to knowledge of$Y$[1]. We would like to minimize the mutual information, which is equivalent to maximizing the conditional entropy$H(X \mid Y)$, as$H(X)$is fixed (depends on the p.m.f of$X$, which is assumed to be fixed). The mutual information can be written as$I(X;Y) = D( p(x,y) \| p(x) p(y) )$, which is the < a href="http://en.wikipedia.org/wiki/Kullback%E2%80%93Leibler_divergence">Kullback-Leibler distance between the joint p.m.f. and the product of the marginal p.m.f.'s. Check [1] for details. Therefore, you have a relative entropy minimization problem. Usually, we are given the channel, and we choose the p.m.f. of$X$that maximizes the mutual information$I(X;Y)$. In this problem, we are given the p.m.f. of$X\$, and we choose the channel that minimizes the mutual information. It's a sort of "dual" of finding the capacity of a given channel.
References:
[1] Thomas M. Cover and Joy A. Thomas, Elements of Information Theory, John Wiley & Sons 2006. | 2013-05-23 10:00:47 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7889535427093506, "perplexity": 304.9535917669922}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2013-20/segments/1368703108201/warc/CC-MAIN-20130516111828-00081-ip-10-60-113-184.ec2.internal.warc.gz"} |
https://pypi.org/project/tox/ | tox is a generic virtualenv management and test command line tool
tox
tox aims to automate and standardize testing in Python. It is part of a larger vision of easing the packaging, testing and release process of Python software (alongside pytest and devpi).
tox is a generic virtual environment management and test command line tool you can use for:
• checking your package builds and installs correctly under different environments (such as different Python implementations, versions or installation dependencies),
• running your tests in each of the environments with the test tool of choice,
• acting as a frontend to continuous integration servers, greatly reducing boilerplate and merging CI and shell-based testing.
Please read our user guide for an example and more detailed introduction, or watch this YouTube video that presents the problem space and how tox solves it.
Project details
Uploaded source
Uploaded py3 | 2023-03-21 01:46:33 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.20742858946323395, "perplexity": 5790.042467865725}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296943589.10/warc/CC-MAIN-20230321002050-20230321032050-00079.warc.gz"} |
https://socratic.org/questions/how-do-you-evaluate-the-definite-integral-of-0-to-4-for-5-3x-1-dx#168450 | # How do you evaluate the definite integral of 0 to 4 for (5 / 3x +1) dx?
It is $\frac{52}{3}$
${\int}_{0}^{4} \left(\frac{5}{3} x + 1\right) \mathrm{dx} = {\int}_{0}^{4} \left(\frac{5}{3} {x}^{2} / 2 + x\right) ' \mathrm{dx} = {\left[5 {x}^{2} / 6 + x\right]}_{0}^{4} = \frac{5}{6} \cdot {4}^{2} + 4 = \frac{52}{3}$ | 2021-12-09 08:54:05 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 2, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9242419600486755, "perplexity": 364.9020665712651}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-49/segments/1637964363689.56/warc/CC-MAIN-20211209061259-20211209091259-00271.warc.gz"} |
https://qiskit.org/documentation/locale/de_DE/stubs/qiskit.quantum_info.process_fidelity.html | # qiskit.quantum_info.process_fidelity¶
process_fidelity(channel, target=None, require_cp=True, require_tp=False, require_cptp=False)[Quellcode]
Return the process fidelity of a noisy quantum channel.
This process fidelity $$F_{\text{pro}}$$ is given by
$F_{\text{pro}}(\mathcal{E}, U) = \frac{Tr[S_U^\dagger S_{\mathcal{E}}]}{d^2}$
where $$S_{\mathcal{E}}, S_{U}$$ are the SuperOp matrices for the input quantum channel $$\cal{E}$$ and target unitary $$U$$ respectively, and $$d$$ is the dimension of the channel.
Parameter
• channel (QuantumChannel) – noisy quantum channel.
• target (Operator or None) – target unitary operator. If None target is the identity operator [Default: None].
• require_cp (bool) – require channel to be completely-positive [Default: True].
• require_tp (bool) – require channel to be trace-preserving [Default: False].
• require_cptp (bool) – (DEPRECATED) require input channels to be CPTP [Default: False].
Rückgabe
The process fidelity $$F_{\text{pro}}$$.
Rückgabetyp
float
Verursacht
• QiskitError – if the channel and target do not have the same dimensions, or have different input and output dimensions.
• QiskitError – if the channel and target or are not completely-positive (with require_cp=True) or not trace-preserving (with require_tp=True). | 2021-01-18 11:23:49 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7014867067337036, "perplexity": 7880.759611991057}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-04/segments/1610703514495.52/warc/CC-MAIN-20210118092350-20210118122350-00558.warc.gz"} |
http://wrfranklin.org/nikola/Teaching/quantum-f2022/blog/ | # Quantum Homework 14 - Final Project
Due Mon Dec 12, 900am
This is your final project, with paper, code, whatever. Upload a zip file or tarball with everything to gradescope.
This is a 2 day extension from Friday. However, this is the limit. I will grade whatever I have at that time.
# Quantum Class 24, Thy 2022-12-08
## 1 Final project presentations, day 3
2. Almed E
3. Noah P
4. Alice B
5. Alex B
6. Oliver S
### 1.1 Submission mechanism
Submit material to Homework 14
The deadline is extended to 9am Mon. I will grade whatever has been submitted at that time.
### 1.2 Inspiration for finishing your term projects
1. The Underhanded C Contest
"The goal of the contest is to write code that is as readable, clear, innocent and straightforward as possible, and yet it must fail to perform at its apparent function. To be more specific, it should do something subtly evil. Every year, we will propose a challenge to coders to solve a simple data processing problem, but with covert malicious behavior. Examples include miscounting votes, shaving money from financial transactions, or leaking information to an eavesdropper. The main goal, however, is to write source code that easily passes visual inspection by other programmers."
2. The International Obfuscated C Code Contest
3. https://www.awesomestories.com/asset/view/Space-Race-American-Rocket-Failures
Moral: After early disasters, sometimes you can eventually get things to work.
4. The 'Wrong' Brothers Aviation's Failures (1920s)
5. Early U.S. rocket and space launch failures and explosion
## 2 Writing
1. Example of a well written paper: https://wrfranklin.org/p/239-marcelo-gpu-predicates-2021.pdf
2. How not to write: The Bulwer Lytton Fiction Contest has challenged participants to write an atrocious opening sentence to the worst novel never written.
3. Paper format: one good idea is to use the IEEE conference format . It allows either latex or MS word. Submit the PDF paper to gradescope.
## 3 Prior work
If your final project is building on, or sharing with, another course or project (say on GitHub), then you must give the details, and say what's new for this course.
## 4 12 Ways to Fool the Masses with Irreproducible Results
If you're implementing something:
https://lorenabarba.com/news/keynote-at-the-35th-international-parallel-and-distributed-processing-symposium-ipdps/
Lorena Barba IPDPS21 keynote May 20, 2021 (37:11)
Keynote at the IEEE International Parallel and Distributed Processing Symposium, May 19, 2021
Abstract Thirty years ago, David Bailey published a humorous piece in the Supercomputing Review magazine, listing 12 ways of presenting results to artificially boost performance claims. That was at a time when the debate was between Cray "two-oxen" machines versus parallel "thousand-chickens" systems, when parallel standards (like MPI) were still unavailable, and the Top500 list didn't yet exist. In the years since, David and others updated the list of tricks a few times, notably in 2010–11 (when the marketing departments of Intel and Nvidia were really going at each other) Georg Hager in his blog and Scott Pakin in HPC Wire. Heterogeneity of computing systems has only escalated in the last decade, and many remiss reporting tactics continue unabated. Alas, two new ingredients have entered into the mix: wide adoption of machine learning techniques both in the science applications and systems research; and a swell of concern over reproducibility and replicability. My talk will be a new twist on the 12 ways to fool the masses, focusing on how researchers in computational science and high-performance computing miss the mark when conducting or reporting their results with poor reproducibility. By showcasing in a lighthearted manner a set of anti-patterns, I aim to encourage us to see the value and commit to adapting our practice to achieve more trustworthy scientific evidence with high-performance computing.
There's a link to the slides there.
## 5 After the semester
I'm open to questions and discussions about any legal ethical topic. Even after you graduate.
• gs
# Quantum Class 23, Mon 2022-12-05
## 1 Final project presentations, day 2
1. Richard P
2. Steve L
3. Vansh RC
4. Charles C and Sanghyun K
## 2 Microsoft quantum
1. Microsoft Quantum Development Kit: Introduction and step-by-step demo 10:34 Dec 11, 2017
"Krysta Svore, principal researcher at Microsoft, demonstrates the new Microsoft Quantum Development Kit, now in preview.
The Quantum Development Kit makes it easy for you to start experimenting with quantum computing now and includes:
· A native, quantum-focused programming language called Q# · Local and Azure-hosted simulators for you to test your Q# solution · And sample Q# code and libraries to help you get started
In this demo, she walks through a few code examples and explains where quantum principles like superposition and entanglement apply. She explains how quantum communication works using teleportation as your first "Hello World" inspired program. And keep watching to see more complex computations with molecular hydrogen. ...
2. "Dr. Sankar Das Sarma, a Distinguished University Professor of physics at University of Maryland joins Chetan Nayak, Distinguished Engineer of Quantum at Microsoft to discuss Microsoft’s unique approach to building a fully scalable quantum machine....
# Quantum Class 22, Thurs 2022-12-01
## 1 Final project presentations, updated
1. Everyone who requested a specific date, got it. I assigned the others to even out the calendar.
2. No matter when you talk, you have until Fri Dec 9 to submit your project.
1. Denzell D
2. Paul R
### 1.2 Mon, Dec 5
1. Richard P
2. Steve L
3. Vansh RC
4. Charles C and Sanghyun K
2. Almed E
3. Noah P
4. Alice B
5. Alex B
6. Oliver S
## 2 Quantum computing and Machine Learning
1. "Machine learning and quantum computing are two expanding technologies with tremendous potential. What if they are combined, into quantum machine learning (QML)? I will give an overview of QML, pointing out that quantum mechanics makes it difficult to “quantize” classical ML algorithms such as artificial neural networks. Instead, existing QML algorithms are typically hybrid algorithms, part classical, part quantum. An alternative to making ML quantum is to use ML as part of the software required to operate a quantum computer. I will give some examples from my own research of both types of algorithms, using a hybrid QML approach to address a logistics problem and using deep reinforcement learning for compiling quantum code and for quantum error correction."
The first 10 minutes is a very nice review, so we'll start after it.
2. TensorFlow Quantum: A software platform for hybrid quantum-classical ML 27:15 Mar 11, 2020
"We introduce TensorFlow Quantum, an open-source library for the rapid prototyping of novel hybrid quantum-classical ML algorithms. This library will extend the scope of current ML under TensorFlow and provides the necessary toolbox for bringing quantum computing and machine learning research communities together to control and model quantum data."
3. Hybrid quantum-classical Neural Networks with PyTorch and Qiskit
4. https://towardsdatascience.com/tensorflow-quantum-marrying-machine-learning-with-quantum-computing-84533757e07f?gi=43b0a70c9297
# Quantum Class 21, Mon 2022-11-28
## 1 Quantum jokes
of varying quality... https://upjoke.com/quantum-jokes
## 2 Final project presentations
1. Everyone who requested a specific date, got it. I assigned the others to even out the calendar.
2. Do any of the Dec 1 people want to move to Dec 5? The first two who email me can do that.
3. Other changes that don't overload particular days might be ok.
4. No matter when you talk, you have until Fri Dec 9 to submit your project.
## 3 Final project presentations
1. Everyone who requested a specific date, got it. I assigned the others to even out the calendar.
2. Do any of the Dec 1 people want to move to Dec 5? The first two who email me can do that.
3. Other changes that don't overload particular days might be ok.
4. No matter when you talk, you have until Fri Dec 9 to submit your project.
5. Updated list is on class 22.
## 4 Jochen Rao on Molecules
1. This fits together with the variational quantum eigensolver talk.
2. 22.Molecules 9:50 Dec 11, 2020
## 5 Measurement-based computation, aka One way quantum computation
This is an alternative to the quantum logic gate model that uses reversible unitary gates in a quantum circuit.
Since performing a measurement changes the measured qbits, use it.
1. "One way quantum computation (1WQC) uses an initially highly entangled state (called a cluster state), and then a pattern of single qubit measurements along different directions, together with feed-forward based on the results, in order to drive a quantum computation. The final result of the computation is obtained by measuring the last remaining qubits in the computational basis..."
2. https://en.wikipedia.org/wiki/One-way_quantum_computer
1. This is a one-way computer.
2. Operations:
1. Supplement the input/output qbits with some auxillary qbits.
2. Entangle some of them.
3. Measure some of the auxillary qbits wrt some bases. This affects the output qbits since they are entangled.
4. Depending on the measurement results, perform further operations on the output qbits. These are called corrections.
3. Repeat.
3. This has equivalent formal power to reversible gates.
4. It may be better suited to certain HW.
5. One-way Quantum Computation - a tutorial introduction Dan E. Browne, Hans J. Briegel.
6. How the excellent Jochen Rau presents it:
14. Measurement-based computation 36:44. Nov 27, 2020
7. So now you've seen 3 models of quantum computation.
## 6 MaxCut
https://en.wikipedia.org/wiki/Maximum_cut
Rao again, since he's excellent.
# Quantum Class 20, Mon 2022-11-21
## 1 Final project presentations
1. Presentations will be the last 3 classes: Dec 1, 5, 8. FCFS. Max 6 groups per day.
2. Pick your date here: https://doodle.com/meeting/participate/id/egZG5Pjd
3. When signing up, use enough of your name(s) that I can recognize you.
## 2 NVIDIA Quantum Computing, 2
1. NVIDIA (and other companies) sees a growth area in providing QODA, a layer of services on top of the quantum computing HW. The goal is to make that easier to use and more portable.
2. The analogy is that CUDA hides some of the GPU complexity.
3. QODA also permits various backends: simulators and eventually real HW.
4. https://quantumzeitgeist.com/artificial-intelligence-giant-nvidia-creates-a-new-platform-for-hybrid-quantum-classical-computing-qoda/
5. https://developer.nvidia.com/qoda
6. https://nvidianews.nvidia.com/news/nvidia-announces-hybrid-quantum-classical-computing-platform
7. Quantum computing has the potential to offer giant leaps in computational capabilities, impacting a range of industries from drug discovery to portfolio optimization. Realizing these benefits requires pushing the boundaries of quantum information science in the development of algorithms, research into more capable quantum processors, and the creation of tightly integrated quantum-classical systems and tools. We'll review these challenges facing #quantumcomputing, showcase how #GPUcomputing can help, and reveal exciting developments in tightly integrated quantum-classical computing. https://developer.nvidia.com/qoda
8. Watch Nvidia Reveal Quantum Computing Platform, QODA 6:53 Jul 12, 2022
At Q2B, Nvidia announces QODA, a new hybrid quantum-classical computing platform. See it explained here.
9. https://developer.nvidia.com/blog/introducing-qoda-the-platform-for-hybrid-quantum-classical-computing/
10. https://blogs.nvidia.com/blog/2022/07/12/quantum-qoda-julich/
11. https://blogs.nvidia.com/blog/2022/07/29/what-is-a-qpu/
13. https://www.hpcwire.com/2022/07/12/nvidia-dives-deeper-into-quantum-announces-qoda-programming-platform/
14. Q2B 2021 | Accelerating Quantum Algorithm Research with cuQuantum | Harun Bayraktar 29:52. December 9, 2021. Excellent solid talk.
15. I tried to get QODA running to show the class.
1. However it is still a work in progress.
2. You can (try to )install QODA from https://docs.nvidia.com/cuda/cuquantum/custatevec/getting_started.html
3. The deb fails on my machine running Ubuntu 22.10 because of a cublas version clash.
4. The tarball installs.
5. Compiling fails because it doesn't support the latest g++.
6. -allow-unsupported-compiler seems to override that.
7. Several programs are supplied but all the programs just say 'passed' when executed.
## 3 Classiq - Quantum algorithm design platform
1. Here's another company working on the layers above the HW.
2. "Classiq is revolutionizing the process of developing quantum computing software.
"Our platform helps you build complex, optimized and hardware-aware quantum circuits and algorithms that could not be created otherwise. "
3. https://www.classiq.io/ Watch the short video.
4. They use the Variational Quantum Eigensolver (VQE) as an example.
## 4 Variational Quantum Eigensolver (VQE)
1. This is a big current class of applications for hybrid classic - quantum computers.
2. I think it's not quite practical yet, but it's close.
3. Say you want to know the lowest energy state of a molecule.
1. It's the lowest eigenvalue of a Hamiltonian.
2. However the Hamiltonian cannot be calculated explicitly but must be simulated.
3. This is very expensive, but less so on a quantum computer (because it uses quantum physics).
4. It depends on some parameters.
5. Use a classical computer to run an optimization search on the parameters, calling a quantum computer to evaluate the function (the Hamiltonian).
4. 24. Variational quantum eigensolver (VQE) 19:12, Dec 18, 2020, Jochen Rau. very good.
5. VQE Zero to Hero 20:50 May 9, 2022
"The Variational Quantum Eigensolver (VQE) is one of the most promising algorithms for near term quantum hardware, but how does it work? Rensselaer Polytechnic Institute student Owen Lockwood shows you how to get from the basics of quantum mechanics and the Schrödinger equation to the second quantized electronic hamiltonian and how this forms the basis of the VQE."
Goes into the physics and chemistry.
## 5 My predictions for the winners
1. If I had to pick a HW winner, I'd pick Intel. However it's early still.
2. For the SW, perhaps NVIDIA, or Intel, Amazon, Microsoft.
3. Dunno about the Itty Bitty Machine company. Their best product IMO is their Power architecture as used with NVIDIA in supercomputers.
# Quantum Class 19, Thu 2022-11-17
## 1 ECSE Alumni
It is possible to succeed after RPI.
### 1.1 Tony Tether
Tony Tether IIRC, the longest serving DARPA Director. He initiated the 2004 DARPA_Grand_Challenge that spurred the development of autonomous vehicles.
See below.
### 1.3 Ed Zander
COO Sun, CEO Motorola.
https://en.wikipedia.org/wiki/Edward_Zander
## 2 General programming tips
### 2.1 Unionfs
1. aka overlay FS, translucent FS.
2. If a, b are directories, and m is an empty directory, then
unionfs -o cow a=RW:b m
makes m to be a combo of a and b, with a being higher priority
3. Writing a file into m writes it in a.
4. Changing a file in b writes the new version into a
5. Deleting a file in b causes a white-out note to be stored in a.
6. Unmount it thus:
fusermount -u m
7. None of this requires superuser.
9. Note: IBM had a commercial version of this idea in its CP/CMS OS in the 1960s.
### 2.2 Types of virtualization
1. There are many possible levels of virtualization.
2. At a low level, one might emulate the HW. This is quite flexible but too slow.
3. At a higher level, a basic OS runs separate virtual machines, each with its own file system.
1. Harmless machine instructions execute normally.
2. Powerful ones are trapped and emulated.
3. This requires a properly designed instruction set.
4. IBM has been doing this commercially for 40 years, with something originally called CP/CMS.
I think that IBM lucked out with their instruction set design, and didn't plan it.
5. Well-behaved clients might have problematic code edited before running, to speed the execution.
I think that Vmware does that.
6. It seems that compute-intensive clients might have almost no overhead.
7. However, the emulated file system can be pretty slow.
8. With Vmware, several clients can all be different OSs, and the host can be any compatible OS.
9. E.g., I've had a linux vmware host simultaneously running both linux and windows clients.
4. In linux, root no longer has infinite power.
5. The next level of virtualization has an nontrivial host OS, but separates the clients from each other.
1. They see a private view of the process space, file system, and other resources.
2. This is lighter weight, e.g., quicker to start a VM and less overhead.
3. The host and client must be the same OS.
4. This might be called paravirtualization.
5. Linux supports this with things like namespace isolation and control groups (cgroups). Wikipedia et al describe this.
6. Ubuntu snaps do something like this.
E.g., firefox is distributed as a snap to increase isolation and security.
However starting firefox now takes 15 sec.
6. The next level up is the normal linux security.
1. You can see all the processes and similar resources.
2. The file system has the usual protections.
3. This is hard to make secure when doing something complicated.
4. How do I protect myself from firefox going bad?
5. It's easy to describe what it should be allowed to do, but almost impossible to implement.
6. That includes using apparmor etc.
7. Who guards the guards? I get spammed at a unique address that I used only to register with apparmor.
8. In theory, packaging an app in a virtual machine has fewer dependencies and is more secure.
9. You can run the vm w/o changes on different hosts.
10. A Vmware client can run w/o change on both linux and windows hosts.
11. You can run a client on your own hardware, then spill over to a commercial cloudy platform when necessary.
### 2.3 Docker
1. Docker is a popular lightweight virtualization system, which Nvidia uses to distribute SW.
2. Docker runs images that define virtual machines.
3. Docker images share resources with the host, in a controlled manner.
4. For simple images, which is not nvidia/cuda, starting the image is so cheap that you can do it to run one command, and encapsulate the whole process in a shell function.
5. Docker is worth learning, apart from its use by Nvidia for parallel computing. You might also look up Kubernetes.
### 2.4 Several forms of C++ functions
auto add(int a, int b) { return a+b;}
You can pass this to a function. This really passes a pointer to the function. It doesn't optimize across the call.
These have global scope.
2. Note auto. It's underused.
3. Overload operator() in a new class
Each different variable of the class is a different function. The function can use the variable's value. This is a closure.
This is local to the containing block.
This form optimizes well.
4. Lambda, or anon function.
auto add = [](int a, int b) { return a+b;};
This is local to the containing block.
This form optimizes well.
5. Placeholder notation.
As an argument in, e.g., thrust transform, you can do this:
transform(..., _1+_2);
This is nice and short.
As this is implemented by overloading the operators, the syntax of the expression is limited to what was overloaded.
## 3 Parallel computing summary
1. Read https://computing.llnl.gov/tutorials/parallel_comp/ for an intro to parallel computing.
2. Some points:
1. Parallel computing is decades old; there were commercial machines in the 1980s. I directed two PhD theses in parallel geometry then. However, then, clock speeds were increasing so serial machines were more interesting.
2. Now: physics limits to processor speed.
3. History of Nvidia.
1. Curtis R. Priem ’82, Secretary of the RPI Board had designed graphics HW for both IBM and Sun Microsystems.
2. Priem was an undergrad in ECSE.
3. For awhile Sun was THE Unix workstation company. They used open standards and had the best price / performance.
4. Nvidia designed gaming graphics accelerators...
5. that just happened to be parallel coprocessors...
6. that started to be used for nongraphics parallel processing because of their value.
7. Nvidia noticed that and added more capability, e.g., double precision IEEE floats, to serve that market.
8. Currently, some of the highest performance Nvidia boards cannot even do graphics because they don't have video out ports.
1. Intel CPUs vs Nvidia CUDA cores.
3. OpenMP vs CUDA.
4. Rate-limiting cost usually I/O not computation.
3. Note: Rather than explicitly extracting large zip archives or tarballs in order to read files in them, I use archivemount to create a virtual file system. This saves disk space. It doesn't stress git as much (fewer files). When reading, the I/O time is insignificantly increased. For some formats, you can even write. You can have more confidence that the zip file wasn't changed, than in a directory with perhaps hundreds of files.
## 4 NVIDIA
### 4.1 NVIDIA GTC conference
1. https://www.nvidia.com/gtc/
2. mostly free.
### 4.2 Top500
Many of the top 500 supercomputers contain NVIDIA modules, often together with IBM Power Systems.
### 4.3 Nvidia primary documentation
Generally more up-to-date and accurate, but drier than the secondary docs. A little disorganized because it keeps growing. The root is here: https://docs.nvidia.com/
Two major relevant sets are:
### 4.4 Nvidia conceptual hierarchy
As always, this is as I understand it, and could be wrong. Nvidia uses their own terminology inconsistently. They may use one name for two things (E.g., Tesla and GPU), and may use two names for one thing (e.g., module and accelerator). As time progresses, they change their terminology.
1. At the bottom is the hardware micro-architecture. This is an API that defines things like the available operations. The last several Nvidia micro-architecture generations are, in order, Tesla (which introduced unified shaders), Fermi, Kepler, Maxwell (introduced in 2014), Pascal (2016), and Volta (2018).
2. Each micro-architecture is implemented in several different microprocessors. E.g., the Kepler micro-architecture is embodied in the GK107, GK110, etc. Pascal is GP104 etc. The second letter describes the micro-architecture. Different microprocessors with the same micro-architecture may have different amounts of various resources, like the number of processors and clock rate.
3. To be used, microprocessors are embedded in graphics cards, aka modules or accelerators, which are grouped into series such as GeForce, Quadro, etc. Confusingly, there is a Tesla computing module that may use any of the Tesla, Fermi, or Kepler micro-architectures. Two different modules using the same microprocessor may have different amounts of memory and other resources. These are the components that you buy and insert into a computer. A typical name is GeForce GTX1080.
4. There are many slightly different accelerators with the same architecture, but different clock speeds and memory, e.g. 1080, 1070, 1060, ...
5. The same accelerator may be manufactured by different vendors, as well as by Nvidia. These different versions may have slightly different parameters. Nvidia's reference version may be relatively low performance.
6. The term GPU sometimes refers to the microprocessor and sometimes to the module.
7. There are at least four families of modules: GeForce for gamers, Quadro for professionals, Tesla for computation, and Tegra for mobility.
8. Nvidia uses the term Tesla in two unrelated ways. It is an obsolete architecture generation and a module family.
9. Geoxeon has a (Maxwell) GeForce GTX Titan and a (Kepler) Tesla K20xm. Parallel has a (Volta) RTX 8000 and (Pascal) GeForce GTX 1080. We also have an unused (Kepler) Quadro K5000.
10. Since the highest-end (Tesla) modules don't have video out, they are also called something like compute modules.
### 4.5 GPU range of speeds
Here is an example of the wide range of Nvidia GPU speeds; all times are +-20%.
The Quadro RTX 8000 has 4608 CUDA cores @ 1.77GHz and 48GB of memory. matrixMulCUBLAS runs at 5310 GFlops. The specs claim 16 TFlops. However those numbers understate its capabilities because it also has 576 Tensor cores and 72 ray tracing cores to cast 11G rays/sec.
The GeForce GTX 1080 has 2560 CUDA cores @ 1.73GHz and 8GB of memory. matrixMulCUBLAS runs at 3136 GFlops. However the reported time (0.063 msec) is so small that it may be inaccurate. The quoted speed of the 1080 is about triple that. I'm impressed that the measured performance is so close.
The Quadro K2100M in my Lenovo W540 laptop has 576 CUDA cores @ 0.67 GHz and 2GB of memory. matrixMulCUBLAS runs at 320 GFlops. The time on the GPU was about .7 msec, and on the CPU 600 msec.
It's nice that the performance almost scaled with the number of cores and clock speed.
### 4.6 CUDA
#### 4.6.1 Versions
1. CUDA has a capability version, whose major number corresponds to the micro-architecture generation. Kepler is 3.x. The K20xm is 3.5. The GTX 1080 is 6.1. The RTX 8000 is 7.5. Here is a table of the properties of different compute capabilities. However, that table is not completely consistent with what deviceQuery shows, e.g., the shared memory size.
2. nvcc, the CUDA compiler, can be told which capabilities (aka architectures) to compile for. They can be given as a real architecture, e.g., sm_61, or a virtual architecture. e.g., compute_61.
3. The CUDA driver and runtime also have a software version, defining things like available C++ functions. The latest is 10.1. This is unrelated to the capability version.
#### 4.6.2 Misc
1. With CUDA, the dominant problem in program optimization is optimizing the data flow. Getting the data quickly to the cores is harder than processing it. It helps big to have regular arrays, where each core reads or writes a successive entry.
This is analogous to the hardware fact that wires are bigger (hence, more expensive) than gates.
2. That is the opposite optimization to OpenMP, where having different threads writing to adjacent addresses will cause the false sharing problem.
3. Nvidia CUDA FAQ
1. has links to other Nvidia docs.
2. can be a little old.
### 4.7 Nvidia GPU summary
Here's a summary of the Nvidia Pascal GP104 GPU architecture as I understand it. It's more compact than I've found elsewhere. I'll add to it from time to time. Some numbers are probably wrong.
1. The host is the CPU.
2. The device is the GPU.
3. The device contains 20 streaming multiprocessors (SMs).
Different GPU generations have used the terms SMX or SMM.
4. A thread is a sequential program with private and shared memory, program counter, etc.
5. Threads are grouped, 32 at a time, into warps.
6. Warps of threads are grouped into blocks.
Often the warps are only implicit, and we consider that the threads are grouped directly into blocks.
That abstract hides details that may be important; see below.
7. Blocks of threads are grouped into a grid, which is all the threads in the kernel.
8. A kernel is a parallel program executing on the device.
1. The kernel runs potentially thousands of threads.
2. A kernel can create other kernels and wait for their completion.
3. There may be a limit, e.g., 5 seconds, on a kernel's run time.
1. Each thread can use up to 255 fast registers. Registers are private to the thread.
All the threads in one block have their registers allocated from a fixed pool of 65536 registers. The more registers that each thread uses, the fewer warps in the block can run simultaneously.
2. Each thread has 512KB slow local memory, allocated from the global memory.
3. Local memory is used when not enough registers are available, and to store thread-local arrays.
10. Warp-level resources:
1. Threads are grouped, 32 at a time, into warps.
2. Each warp executes as a SIMD, with one instruction register. At each cycle, every thread in a warp is either executing the same instruction, or is disabled. If the 32 threads want to execute 32 different instructions, then they will execute one after the other, sequentially.
If you read in some NVidia doc that threads in a warp run independently, then continue reading the next page to get the info mentioned in the previous paragraph.
3. If successive instructions in a warp do not depend on each other, then, if there are enough warp schedulers available, they may be executed in parallel. This is called Instruction Level Parallelism (ILP).
4. For an array in local memory, which means that each thread will have its private copy, the elements for all the threads in a warp are interleaved to potentially increase the I/O rate.
5. A thread can read variables from other threads in the same warp, with the shuffle instruction. Typical operation are to read from the K-th next thread, to do a butterfly permutation, or to do an indexed read. This happens in parallel for the whole warp, and does not use shared memory.
6. A warp vote combines a bit computed by each thread to report results like all or any.
11. Block-level resources:
1. A block may contain up to 1024 threads.
3. Each block can use up to 49152 bytes of the SM's fast shared memory. The block's shared memory is shared by all the threads in the block, but is hidden from other blocks.
Shared memory is basically a user-controllable cache of some global data. The saving comes from reusing that shared data several times after you loaded it from global memory once.
Shared memory is interleaved in banks so that some access patterns are faster than others.
4. Warps in a block run asynchronously and run different instructions. They are scheduled and executed as resources are available.
5. However they are all running the same instruction sequence, perhaps at different points in it.
6. That is call SPMD, single program multiple data.
Because of how warps are scheduled, that can be slow.
8. The threads in a block can be arranged into a 3D array, up to 1024x1024x64.
That is for convenience, and does not increase performance (I think).
9. I'll talk about textures later.
12. Streaming Multiprocessor (SM) - level resources:
1. Each SM has 128 single-precision CUDA cores, 64 double-precision units, 32 special function units, and 32 load/store units.
2. In total, the GPU has 2560 CUDA cores.
3. A CUDA core is akin to an ALU. The cores, and all the units, are pipelined.
4. A CUDA core is much less powerful than one core of an Intel Xeon. My guess is 1/20th.
5. Beware that, in the CUDA C Programming Guide, NVidia sometimes calls an SM a core.
6. The limited number of, e.g., double precision units means that an DP instruction will need to be scheduled several times for all the threads to execute it. That's why DP is slower.
7. Each SM has 4 warp schedulers and 8 instruction dispatch units.
8. 64 warps can simultaneously reside in an SM.
9. Therefore up to 32x64=2048 threads can be executed in parallel by an SM.
10. Up to 16 blocks that can simultaneously be resident in an SM.
However, if each block uses too many resources, like shared memory, then this number is reduced.
Each block sits on only one SM; no block is split. However a block's warps are executed asynchronously (until synced).
11. Each SM has 64KiB (?) fast memory to be divided between shared memory and an L1 cache. Typically, 48KiB (96?) is used for the shared memory, to be divided among its resident blocks, but that can be changed.
12. The 48KB L1 cache can cache local or global memory.
13. Each SM has a read-only data cache of 48KB to cache the global constant memory.
14. Each SM has 8 texture units, and many other graphics capabilities.
15. Each SM has 256KB of L2 cache.
13. Grid-level resources:
1. The blocks in a grid can be arranged into a 3D array. up to $(2^{31}-1, 2^{16}-1, 2^{16}-1)$.
2. Blocks in a grid might run on different SMs.
3. Blocks in a grid are queued and executed as resources are available, in an unpredictable parallel or serial order. Therefore they should be independent of each other.
4. The number of instructions in a kernel is limited.
5. Any thread can stop the kernel by calling assert.
14. Device-level resources:
1. There is a large and slow 48GB global memory, which persists from kernel to kernel.
Transactions to global memory are 128 bytes.
Host memory can also be memory-mapped into global memory, although the I/O rate will be lower.
Reading from global memory can take hundreds of cycles. A warp that does this will be paused and another warp started. Such context switching is very efficient. Therefore device throughput stays high, although there is a latency. This is called Thread Level Parallelism (TLP) and is a major reason for GPU performance.
That assumes that an SM has enough active warps that there is always another warp available for execution. That is a reason for having warps that do not use all the resources (registers etc) that they're allowed to.
2. There is a 2MB L2 cache, for sharing data between SMs.
3. There is a 64KiB Small and fast global constant memory, , which also persists from kernel to kernel. It is implemented as a piece of the global memory, made fast with caches.
(Again, I'm still resolving this apparent contradiction).
4. Grid Management Unit (GMU) schedules (pauses, executes, etc) grids on the device. This is more important because grids can start other grids (Dynamic Parallelism).
5. Hyper-Q: 32 simultaneous CPU tasks can launch kernels into the queue; they don't block each other. If one kernel is waiting, another runs.
6. CUDA Work Distributor (CWD) dispatches 32 active grids at a time to the SMs. There may be 1000s of grids queued and waiting.
7. GPU Direct: Other devices can DMA the GPU memory.
8. The base clock is 1607MHz.
9. GFLOPS: 8873.
10. Memory bandwidth: 320GB/s
15. GPU-level resources:
1. Being a Geforce product, there are many graphics facilities that we're not using.
2. There are 4 Graphics processing clusters (GPCs) to do graphics stuff.
3. Several perspective projections can be computed in parallel, for systems with several displays.
4. There's HW for texture processing.
16. Generational changes:
1. With each new version, Nvidia tweaks the numbers. Some get higher, others get lower.
1. E.g., Maxwell had little HW for double precision, and so that was slow.
2. Pascal's clock speed is much higher.
17. Refs:
1. The CUDA program deviceDrv.
4. Better Performance at Lower Occupancy, Vasily Volkov, UC Berkeley, 2010.
5. https://www.pgroup.com/lit/articles/insider/v2n1a5.htm - well written but old.
(I'll keep adding to this. Suggestions are welcome.)
### 4.8 More CUDA
1. CUDA function qualifiers:
1. __global__ device function called from host, starting a kernel.
2. __device__ device function called from device function.
3. __host__ (default) host function called from host function.
2. CUDA variable qualifiers:
1. __shared__
2. __device__ global
3. __device__ __managed__ automatically paged between host and device.
4. __constant__
5. (nothing) register if scalar, or local if array or if no more registers available.
3. If installing CUDA on your machine, this repository seems best:
That includes the Thrust headers but not example programs.
### 4.9 Other Nvidia features
We've seen almost everything, except:
1. Texture and surface maps.
2. ML HW like A=BC+D for 4x4 matrices.
3. Ray tracing HW, to compute a ray's intersections with boxes.
4. Cooperative groups: with Ampere, subsets of a warp can synchronize.
5. Subsets of a GPU can be defined as virtual GPUS, which are walled off from each other.
6. Memory can be compressed when stored, making a space-time tradeff.
7. The terminology CUDA core is obsolete. Now, they say that an SM has, perhaps 32 single float units, 32 integer units, 32 CUDA instruction dispatchers, and 16 double float units, etc. Each unit operates independently.
## 5 NVIDIA Quantum Computing
1. https://quantumzeitgeist.com/artificial-intelligence-giant-nvidia-creates-a-new-platform-for-hybrid-quantum-classical-computing-qoda/
2. https://developer.nvidia.com/qoda
3. https://nvidianews.nvidia.com/news/nvidia-announces-hybrid-quantum-classical-computing-platform
4. Quantum computing has the potential to offer giant leaps in computational capabilities, impacting a range of industries from drug discovery to portfolio optimization. Realizing these benefits requires pushing the boundaries of quantum information science in the development of algorithms, research into more capable quantum processors, and the creation of tightly integrated quantum-classical systems and tools. We'll review these challenges facing #quantumcomputing, showcase how #GPUcomputing can help, and reveal exciting developments in tightly integrated quantum-classical computing. https://developer.nvidia.com/qoda
5. Watch Nvidia Reveal Quantum Computing Platform, QODA 6:53 Jul 12, 2022
At Q2B, Nvidia announces QODA, a new hybrid quantum-classical computing platform. See it explained here.
6. https://developer.nvidia.com/blog/introducing-qoda-the-platform-for-hybrid-quantum-classical-computing/
7. https://blogs.nvidia.com/blog/2022/07/29/what-is-a-qpu/
8. Q2B 2021 | Accelerating Quantum Algorithm Research with cuQuantum | Harun Bayraktar 29:52. December 9, 2021. Excellent solid talk.
# Quantum Class 18, Mon 2022-11-14
## 1 Good general site
https://quantumzeitgeist.com/
## 2 Conference showing real world interest in quantum computing
https://q2b.qcware.com/2022-conferences/silicon-valley/december-6-detailed-program/
## 3 Intel Quantum Computing - 2
1. They use hot (temp: 1K) silicon spin qbits.
1. https://quantumcomputingreport.com/intel-releases-their-own-quantum-sdk-for-beta-test-and-they-are-funding-universities-to-develop-curricula-using-it/
3. An LLVM-based C++ Compiler Toolchain for Variational Hybrid Quantum-Classical Algorithms and Quantum Accelerators
Variational algorithms are a representative class of quantum computing workloads that combine quantum and classical computing. This paper presents an LLVM-based C++ compiler toolchain to efficiently execute variational hybrid quantum-classical algorithms on a computational system in which the quantum device acts as an accelerator. We introduce a set of extensions to the C++ language for programming these algorithms. We define a novel Executable and Linking Format (ELF) for Quantum and create a quantum device compiler component in the LLVM framework to compile the quantum part of the C++ source and reuse the host compiler in the LLVM framework to compile the classical computing part of the C++ source. A variational algorithm runs a quantum circuit repeatedly, each time with different gate parameters. We add to the quantum runtime the capability to execute dynamically a quantum circuit with different parameters. Thus, programmers can call quantum routines the same way as classical routines. With these capabilities, a variational hybrid quantum-classical algorithm can be specified in a single-source code and only needs to be compiled once for all iterations. The single compilation significantly reduces the execution latency of variational algorithms. We evaluate the framework's performance by running quantum circuits that prepare Thermofield Double (TFD) states, a quantum-classical variational algorithm.
4. https://www.hpcwire.com/off-the-wire/intel-labs-releases-beta-version-of-intel-quantum-software-development-kit/
We may cover this in class.
6. qHiPSTER: The Quantum High Performance Software Testing Environment
We present qHiPSTER, the Quantum High Performance Software Testing Environment. qHiPSTER is a distributed high-performance implementation of a quantum simulator on a classical computer, that can simulate general single-qubit gates and two-qubit controlled gates. We perform a number of single- and multi-node optimizations, including vectorization, multi-threading, cache blocking, as well as overlapping computation with communication. Using the TACC Stampede supercomputer, we simulate quantum circuits ("quantum software") of up to 40 qubits. We carry out a detailed performance analysis to show that our simulator achieves both high performance and high hardware efficiency, limited only by the sustainable memory and network bandwidth of the machine.
7. Intel Quantum Simulator
9. https://quantumzeitgeist.com/intels-quantum-sdk-is-in-beta/
10. https://quantumzeitgeist.com/intel-corporation-collaborates-with-qutech-to-build-worlds-first-industrially-manufactured-qubit-device/
# Quantum Homework 10, Thu 2022-11-10
## Project topic, due Mon 11-14
Groups of any size are ok.
Announce your team, topic, and write 50-100 words on it.
# Quantum Class 17, Thu 2022-11-10
## 1 No lecture today
Read these notes. The big topic is Intel Quantum Computing.
## 2 Final projects
Homework 10, due Mon, is for you to announce your team and topic.
Some successive homeworks will be for progress reports.
Deliverables will be a report, a talk, and if writing code, documentation.
If you're taking the 6000 version, make the report longer or add a 2nd paper. Include a note saying why your work deserves 6000-level credit.
Presentations will be the last 3 classes: Dec 1, 5, 8. I'll open a signup site later.
## 3 Xkcd on quantum
https://xkcd.com/1861/
## 4 Intel Quantum Computing - 1
1. Watch Intel's Entire Quantum Computing Presentation (Innovation Event 2022) 5:54. Sep 28, 2022.
2. Million-Qubit Quantum Computer from Intel 14:37. Apr 11, 2022.
In this video I discuss Intel Quantum Computer based on Silicon Qubits. It is the first Silicon Qubits at Scale and based on this technology Intel is building a Million-Qubit Quantum Computer.
3. Architecture All Access: Quantum Computing 13:33 Jun 23, 2021.
Quantum Computing has the potential to change our lives and far exceed the capabilities of today’s supercomputers. Join James Clarke, Director of Quantum Computing at Intel Labs, as he runs through the basics of quantum mechanics, what components make up a quantum computer, when we’ll achieve quantum practicality, and more.
During his 20 years at Intel James Clarke has been a process engineer, led advanced interconnect research, and launched Intel’s Quantum Computing efforts with a focus on leveraging our in-house transistor process and manufacturing capabilities to create scalable qubit arrays. He’s co-authored over 50 papers and holds multiple patents.
Architecture All Access is a master class technology series featuring Senior Intel Technical Leaders taking an educational approach to the historical impact and future innovations of key architectures that will continue to be at the center of ‘world-changing technology that enriches the lives of every person on earth.’ If you are interested in CPUs, FPGAs, Quantum Computing and beyond, subscribe and hit the bell to get new episode notifications.
4. Intel Innovation 2022 Day 1 Keynote Replay 1:10:30. Sep 27, 2022.
Linus Torvolds appears an hour in.
5. Intel Innovation 2022 Day 2 Keynote Replay 1:12:27. Sep 28, 2022.
... The new Intel #Quantum software development kit (SDK) is designed to help developers learn how to program quantum algorithms and interface with Intel’s quantum computing stack.
6. Quantum Computing! See Google, IBM and Intel’s Labs (supercut) 12:43. Aug 6, 2021.
IBM, Google and Intel research scientists discuss the current state of quantum computing, and how the emerging tech is evolving in its labs.
# Quantum Class 16, Thu 2022-10-27
## 1 Student presentations, round 2
### 1.1 Today
2. Charles C, Sanghyun K - Trapped ion technology_IONQ
3. Vansh R C
4. Ahmed E
5. Oliver S - quantum memristors
# Quantum Class 15, Mon 2022-10-24
## 1 Student presentations, round 2
### 1.1 Today
1. Richard P - Quantum Key Distribution
2. Noah and Alice - Quantum Walks
### 1.2 Thurs
2. Charles C, Sanghyun K - Trapped ion technology_IONQ
3. Vansh R C
4. Ahmed E
5. Oliver S - quantum memristors
6. Denzel
### 1.3 Others?
not doing this homework?
present in 2 weeks?
## 3 Amazon Braket
https://docs.aws.amazon.com/braket/
# Quantum Class 14, Thu 2022-10-20
## 1 Followup on free-ranging discussion time, 3
### 1.1 Accreditation
Example of students who don't understand accreditation being tricked:
1. In Florida, non-accredited colleges say that their credits "may" transfer to the prestigious state colleges.
2. The credits do not transfer. There was no quality control or other standards for those credits.
### 1.2 Compiling quantum computer programs
1. Executing a Pascal-like program to an actual quantum computer has several steps.
2. The actual quantum computer has physical qbits.
3. Some (but usually not most) pairs of qbits are connected; see the graph description of the quantum computer.
4. A 2-qbit operation like CCNOT can happen only on a connected pair.
5. Not all the quantum operations that we've seen have physical realizations. Which do depends on the hardware. IBM is different from IONQ.
6. The user writing the program is properly unaware of any of this. S/he just uses meaningful variable names and useful ops.
7. Maybe s/he draws a qiskit diagram, which is basically equivalent to the program.
8. The compiler has to:
1. Translate unrealizable operations into sequences of realizable operations.
2. Decide how to optimally assign the variables to actual qbits.
3. Remember that operations can occur only between adjacent qbits, so try to assign qbits to maximize this adjacency.
4. To operate on other pairs of qbits, add swap operations to make them adjacent.
5. These (and all) operations are noisy and take time.
6. The quantum computer has a limit (the quantum volume) on how much it can do before accumulated noise etc destroys the results.
7. Look for opportunities to optimize and reduce pairs of consecutive operations. This happens a lot.
9. Qiskit and its competitors do all this.
10. This is reminiscent of compiling onto a classical machine with limited registers.
11. Optimal solutions are NP, but good enough solutions are possible.
12. Someone is probably using a quantum computer to compile.
### 1.3 Being a grad student here at RPI
How might we help?
## 2 Student presentations, round 2
Pick your date (choices: next Mon or Thurs) and announce your topic here:
https://doodle.com/meeting/participate/id/dJqLVD2b
When signing up, use enough of your name(s) that I can recognize you, plus your topic.
## 3 News
1. The Nobel Prize in Physics 2022
https://www.nobelprize.org/prizes/physics/2022/press-release/
2. New research suggests our brains use quantum computation
https://phys.org/news/2022-10-brains-quantum.html
3. https://quantumcomputingreport.com/news/
Note Malta.
4. https://news.mit.edu/topic/quantum-computing
5. https://www.reddit.com/r/QuantumComputing/new/
can be interesting
6. https://www.reddit.com/r/dwave/new/
has little traffic
## 4 Optimization problems doable with D-wave
1. Max cut
https://en.wikipedia.org/wiki/Maximum_cut
2. VLSI Circuit opt
https://www.researchgate.net/publication/262162554_An_Application_of_Combinatorial_Optimization_to_Statistical_Physics_and_Circuit_Layout_Design
3. Spin glass min energy
4. A Quantum Annealing Approach for Fault Detection and Diagnosis of Graph-Based Systems
https://arxiv.org/abs/1406.7601v2
5. https://docs.dwavesys.com/docs/latest/handbook_problems.html#cb-probs-scheduling
## 5 D-Wave
We'll go thru
https://docs.dwavesys.com/docs/latest/
# Quantum Class 13, Mon 2022-10-17
## 1 Followup on free-ranging discussion time, 2
1. Real world electrical engineering: I'll show different plug formats for charging a Tesla.
1. Note CCS evolved by just grafting DC pins onto the existing AC plug.
CCS is common; I have a converter.
2. Tesla transmits data in addition to power. Similar to USC-C except 1000x power.
Tesla, the best technical format will probably lose to CCS. This has happened before.
I have a 240V 48A Tesla charger at home.
4. J-1772 is common for level-2 chargers at hotels. I have a converter.
5. There are several NEMA formats for home outlets.
6. There are 3 charging levels.
1. 120V 12A
2. 240V up to 48A (approx)
3. 400V DC up to 500A (approx)
2. College accreditation:
1. The US is different from other countries, with less central control.
2. We have various overlapping accreditation agencies.
3. As for RPI:
1. The university is accredited by the regional Middle States Commission on Higher Education (the US is partitioned into 6 regions).
2. Degrees are accredited by the University of the State of New York "the Regents" (quite different from the State University of NY),
3. Many specific programs, like EE, CSYS, medicine, law are accredited by their field. Here, accreditation only cuts off the lower tail of the distribution.
Many professions require graduation from an accredited program (and then passing an exam) to practice. E.g., medicine, civil engineering.
4. Historically, accreditation often was instituted to clean up a mess of awful places. E.g. medicine. In a milder form, CS.
5. Unusual types of colleges (= those that can't get the usual accreditation) can form their own accrediting agencies. However the regular agencies are themselves accredited, in a chain terminating at the US Dept of Ed.
6. Students who don't understand this mess can be tricked.
## 2 D-wave
1. Videos, each about 6 min.
1. Quantum Annealing Explained
2. How Quantum Annealing Works
3. The Physics of Quantum Annealing — Hamiltonian and Eigenspectrum
4. A Tour of D-Wave's Lab Part 1
5. A Tour of D-Wave's Lab
#. Quantum Programming 101 Aug 30, 2022 51:46.
## 3 Homework
Homework 8 is online.
# Quantum Homework 8, Mon 2022-10-16
## Student presentations, round 2, next week
Groups of any size are ok.
Pick a topic that we didn't cover in class and present it, from
I'll create an online signup form.
Present it on Mon or Thurs, FCFS.
Reasonable length: 7-10 min.
# Quantum Class 12, Thu 2022-10-13
## 1 Followup on free-ranging discussion from last time
1. What use is quantum computation?
"What good is a newborn baby?" - attributed to Mike Faraday and Ben Franklin.
2. Value of PhD
1. I like the idea, but maybe it's obsolescent.
2. It teaches stubbornness and how to accomplish a 4 year project, which is unusual in industry.
3. It's required for academia, but universities are obsolescent.
4. It can be a status symbol in government, military, business.
5. It's required to manage technical people with PhDs. Otherwise they won't respect you and you'll have trouble making technical decisions. Similarly, effective hospital managers are MDs.
The mushy degrees that combine management with a technical concentration, either in math or health, have been tried for decades and always fail. OK, them's fighting words, so bring it on.
6. However, you won't live longer because of the time you spent as a grad student. Maybe there were better uses of those 4 years.
1. Work to stay current in your field. Your employer may oppose this. If so, do it on your own time.
2. E.g., I'm 70 years old and I'm teaching quantum computing.
I proposed this course to ECSE 3 years ago, created it, and spend a lot of time learning the material.
The difference between you and me is that RPI pays me to learn this.
3. If you don't stay current, you'll be laid off after 20 years as obsolescent.
4. In this credentialed society, collect the pretty pieces of paper. It's easier now with all the online courses.
5. Be prepared for big unexpected changes. Imaging describing today's world to someone from even 5 years ago....
6. Finally, make contacts and be friendly. All of my jobs have been from people I knew. As my grandmother said, "Be nice to the people you meet on the way up. You may meet them again on the way down."
## 2 Shor's algorithm to factor an integer
### 2.1 The problem
1. Factorize an integer.
2. in BQP.
3. almost exponentially faster than best classical algorithm.
4. Largest examples I can find: 56153 = 233 × 241.
### 2.2 Notes
1. This is the most famous quantum algorithm.
2. It's the one that has the potential to break much public key crypto.
3. This is the deepest topic of this course so far.
4. Takeaways from this algorithm are that some serious math is involved, and the quantum version is unlike the classical version.
5. If you don't absorb all the details, then absorb its flavor.
6. I sometimes show videos because they present the idea better than me.
7. OK to ask questions and make comments during the videos. I'll pause the video and try to answer.
### 2.3 Application: break RSA
1. Public-private key crypto.
2. Oversimpifying, RSA private key is a pair of large primes.
Public key is their product.
3. Odd fact: if 2 public keys have a common factor, then you can easily factor both of them with gcd.
4. Publish the public key.
5. Use intended recipient's public key to encrypt message then send it.
Recipient uses his private key to decrypt it.
6. Or, use private key to sign message then publish or send it.
Anyone can use the public key to verify it.
7. Invented in 1970s, secretly before publicly.
8. Aside: visit the NSA's National Cryptologic Museum. Note how nothing there is under 50 years old.
9. All this assumes that you can reliably get someone's genuine public key.
Some scams involve faking phone numbers, email addresses, etc.
10. Based on a function that's hard to invert, e.g., factoring.
11. RSA has competitors.
12. There are various ways to embed RSA or a competitor into an encryption program, with choices of algorithm, key length, etc.
13. On linux, you can encrypt a file with pgp, gnupg, LUKS, zip encryption, zfs encryption, truecrypt (suddenly discontinued w/o any stated reason in 2014), etc, etc.
14. At one time, there was no version of pgp that was legal both in the US and outside the US.
15. At one time, the US proposed that crypto must have a back door. However this was dropped.
16. A paranoid person might suspect that the chaos was deliberate to make it harder to use crypto. But that's just crazy talk.
17. RSA is slow, so it's used only to encrypt a session-specific symmetric key that is used for the rest of the message, ssh session, etc.
18. Gnupg et al do a 3rd level of encryption.
The private key is encrypted with a passphrase.
You use the passphrase to decrypt the file.
The encrypted passphrase is stored ~/.gnupg .
If you lose ~/.gnupg, you lose all your encrypted data.
You can change the passphrase by re-encrypting the private key w/o re-encrypting the whole file.
You can have multiple passphrases to give to different people.
You can cancel a passphrase by deleting the version of the encrypted private key that was encrypted with it.
19. So, you need 3 things to access the encrypted file: the encrypted file, the encrypted secret key, and the passphrase.
### 2.4 Classical factoring
1. Efficient algorithms are complicated and use number theory.
2. Rational sieve is good first algorithm to study. It's simple and reasonably fast.
### 2.5 Videos
1. Shor on, what is Shor's factoring algorithm? (2:09)
It's good to listen to the inventor of a big idea.
2. Umesh Vazirani's lecture, 2018.
1. This jumps into the middle of things a little. However the alternatives are worse: not to show Vazirani at all, or to also show all the earlier videos.
2. Lecture 10 1 Period Finding (19:27)
3. Hacking at Quantum Speed with Shor's Algorithm (16:35). Optional to watch on your own.
4. The Story of Shor's Algorithm, Straight From the Source | Peter Shor (31:27) 2021-07-02 Gives the history. Optional to watch on your own.
6. Hacking at Quantum Speed with Shor's Algorithm (16:35)
7. Five lectures by Abraham Asfaw in Qiskit's Introduction to Quantum Computing and Quantum Hardware.
### 2.7 IBM Quantum
https://quantum-computing.ibm.com/composer/docs/iqx/guide/shors-algorithm
https://qiskit.org/textbook/ch-algorithms/shor.html
## 4 HHL algorithm to solve a linear system of equations
1. quick, deep, intro.
2. quite understandable.
3. IBM Quantum Algorithms for Applications from qiskit
E.g., Fourier transform and HHL.
4. HHL Algorithm
This is in Huawei HiQ, an open-source software framework for quantum computing.
5. https://en.wikipedia.org/wiki/Quantum_algorithm_for_linear_systems_of_equations
## 5 Term project
Time to start thinking of a term project, on a topic at least vaguely related to the course. Teams of any size ok. For the grad version, also write a paper.
# Quantum Homework 7, Thu 2022-10-13
Due next Thu Oct 20.
Work through the qiskit text on Shor's Algorithm and Lab 5. Scalable Shor’s Algorithm.
Upload enough to convince me that you did some good work.
If you can't get it all to work, then upload a convincing explanation.
# Quantum Class 11, Mon 2022-10-03
## 1 Another view of superposition
The quantum states of some system are solutions of a linear PDE. There is a basis set of solutions. Linear combos are also solutions. That's superposition.
## 2 Simon's periodicity
Blackbox $F: \{0,1\}^n \to \{0,1\}^n$
For some unknown $c$, $F(x\oplus c) = F(x)$.
Determine $c$.
https://qiskit.org/textbook/ch-algorithms/simon.html
## 3 Quantum Fourier Transform
https://qiskit.org/textbook/ch-algorithms/quantum-fourier-transform.html
## 4 Quantum Phase Estimation
https://qiskit.org/textbook/ch-algorithms/quantum-phase-estimation.html
## 5 Inauguration Day Oct 6
1. There are student seats available at the investiture. See me if interested.
# Quantum Class 10, Thu 2022-09-29
## 1 IEEE Quantum Week 2022
This conference was last week. It was expensive but you can get something for free thus. Look at https://qce.quantum.ieee.org/2022/home/program/keynotes/
to see current important topics. Then google the speakers and titles to look for free versions of their presentations.
You could also pay for virtual access for 3 months.
https://people.cs.uchicago.edu/~ftchong/Chong-QC-UCLA19.pdf
## 2 Quantum properties - Phase
1. You cannot measure the phase of qbit.
2. You can measure the relative phase of 2 qbits.
3. Many algorithms encode the answer as a phase shift of a qbit.
4. Phase kickback means that a gate that runs one way, e.g., the control bit affects an output bit, can be made to run the other way, e.g., the control bit is changed, by making the other bit a Hadamad basis.
5. Phase Kickback V Abhijith Rao
6. Qiskit Phase Kickback
## 3 Deutsch Jozsa Algorithm, ctd
The problem is artificial and uninteresting by itself. Its importance is that it was the first problem with a faster quantum algorithm (than its classical algorithm). It's a proof of principle.
This is a nice detailed description:
https://en.wikipedia.org/wiki/Deutsch%E2%80%93Jozsa_algorithm
We're following: https://qiskit.org/textbook/ch-algorithms/deutsch-jozsa.html
Then the next step is to find a more interesting problem that can be sped up.
## 4 Bernstein-Vazirani Algorithm
This would be that next step.
https://qiskit.org/textbook/ch-algorithms/bernstein-vazirani.html
## 5 Simon's periodicity
Blackbox $F: \{0,1\}^n \to \{0,1\}^n$
For some unknown $c$, $F(x\oplus c) = F(x)$.
Determine $c$.
# Quantum Homework 6, Thu 2022-09-29
Due next Thu Oct 6.
Try the programming examples accompanying the algorithm descriptions and report. Indeally, install qiskit on your machine, and compare to running on the IBM cloud. Try the simulator and a real quantum computer.
# Quantum Class 9, Mon 2022-09-26
## 1 Respite not so bad after all
It trapped a message from AEFIS.
## 2 Caltech - excellent quantum computing sites
Quantum Science and Engineering
Institute for Quantum Information and Matter, a National Science Foundation Physics Frontiers Center
Alliance for Quantum Technologies
https://scienceexchange.caltech.edu/topics/quantum-science-explained/quantum-computing-computers
https://www.quantamagazine.org/entanglement-made-simple-20160428/ - Frank Wilczek, the author, got a nice free meal with the King of Sweden in 2004.
https://www.science.org/content/article/einstein-s-spooky-action-distance-spotted-objects-almost-big-enough-see
https://www.space.com/31933-quantum-entanglement-action-at-a-distance.html
## 3 Entanglement
Some sites that might help understanding it.
https://magazine.caltech.edu/post/untangling-entanglement
## 4 Quantum algorithms
We'll learn some famous quantum algorithms from the old qiskit text, starting with
# Quantum Class 8, Thu 2022-09-22
## 1 Deprecate my RPI email
Two students' messages and email from the inauguration committee were trapped by respite.
# Quantum Class 7, Mon 2022-09-19
## 1 Student presentations
Mon:
1. Noah Prisament - Bose Einstein condensate quantum computing
2. Alex Bozeat - NMR
3. Ahmed Elmenshawi - Spin Qbit
4. Adam Goines - Neural Atom Quantum Computers
5. Sanghyun Kim & Charles Chae - Photonics & Orca computing
6. Oliver Salvaterra - optical lattice
Thurs:
7. Richard Pawelkiewicz - Vibrating Atoms
8. Denzell Dixon - Photonic quantum computing
9. Steven Laverty - Diamond Quantum Computing
10. Alice Bibaud - Topological photonic chips
11. Vansh Reddy Cheguri - Bose Einstein
Here.
due next Mon.
# Quantum Homework 5, Mon 2022-09-19
Due next Mon Sept 26.
Do all the quick quizzes from the Entangled States chapter of Intro to Quantum Computing in the online qiskit textbook.
https://learn.qiskit.org/course/introduction/entangled-states
# Quantum Class 6, Thu 2022-09-15
## 1 Homework 4 ctd
You talk next Mon. See here.
There's only one time; the purpose of this is to state your topic in a way that other people can see.
(By posting the link, I'm opening myself to potential spamming, but so far, that hasn't happened.)
## 2 Old homeworks
To accommodate late adders (students not Viperidae), I've extended the late due dates for the homeworks. Anyone else may also update their answers.
However I'll probably grade quite easily so it isn't necessary.
## 3 My class conflicts
1. To accommodate a presidential reception that I'm attending, today will end at 4:45. Last year, I asked Pres Jackson what to do about the conflict. She said to end class early.
2. Still thinking about what to do for the presidential installation, which might overlap if it runs late.
I recommend attending the presentations; I am. These are a benefit of being at RPI.
3. There'll be no classes the first week of Nov because I'll be at ACM SIGSPATIAL. I'll probably assign outside reading and watching.
## 4 COVID
What shall we do about quarantined students? I could try to webex the class from my iphone. But that quality will probably be bad. So here's a suggestion:
Any quarantined student, and also nonquarantined ones, is welcome to personal webex calls with me to ask questions about quantum computing etc. We can call these office hours.
If you want one, email with some times; I'll reply. When we agree, I'll call then.
## 5 IBM Quantum
Continuing what was started last class with qiskit etc.
# Quantum Class 5, Mon 2022-09-12
## 1 Homework 4
You talk next Mon. See here.
## 2 Quantum computing in the news
(or at least on Slashdot).
## 3 Abstract computation models ctd
1. Original motivation was to discover an algorithm for proving (or disproving) theorems.
2. That can be done in some simple cases, like first order predicate calculus with addition over the integers.
1. and first order predicate calculus with addition and multiplication over the rationals or reals.
3. This goal failed because it was proved that it is undecidable in some cases.
1. like first order predicate calculus with addition and multiplication over the integers.
2. Some theorems truth or falsity depends on the allowable domain of their variables.
3. in a deep sense, ints are harder than reals.
4. Long time ago I wrote a paper on this, in the context of computer graphics. Problems with Raster Graphics Algorithms.
## 4 Complexity classes
1. Group problems into broad classes of considerably differing difficulty.
2. P vs NP.
3. Steve Cooks's paper first describing this was rejected.
4. Quantum complexity classes.
## 5 Hardware implementations
1. Quantum computation was theoretically started decades before actual quantum computers were designed.
2. Just like classical computers.
3. Many competing technologies.
4. Let the strongest win.
### 5.1 Superconducting qubits
1. Dilution fridge: cool by mixing He3 into He4.
2. Cooper pairs of electrons: pairs of electrons in a metal weakly attract each other. It's a quantum effect.
3. Josephson Junction.
### 5.2 Trapped Ion
1. https://en.wikipedia.org/wiki/Trapped_ion_quantum_computer
2. Proponents say that it's better than transmon qbits.
3. Trapped-ion qubit, the maglev train of a quantum computer, 9:34, 2021-08-24.
4. https://ionq.com/technology
"To date, we’ve run single-qubit gates on a 79 ion chain, and complex algorithms on chains of up to 11 ions."
### 5.3 Quantum annealing
1. This is not comparable to quantum gates and circuits like IBM has.
2. It minimizes a function by testing many solutions in parallel.
3. See details in the D-Wave section.
4. Qbit count is not comparable to gate models.
5. https://en.wikipedia.org/wiki/D-Wave_Systems
6. They make a different type of quantum computer, called a quantum annealer. They have been in the news lately, e.g.,
7. https://arstechnica.com/science/2020/09/d-wave-releases-its-next-generation-quantum-annealing-chip/
8. "Want to learn how to program a quantum computer? In this webinar, we explain how to do so by running through a complete, simple example. We explain how to formulate the problem, how to write it, and how to tune it for best results. "
"This webinar is intended for those with little or no experience programming on a D-Wave quantum computer. After watching, get free time on Leap, the quantum cloud service at https://cloud.dwavesys.com/leap/signup/ "
9. Slides from Programming Quantum Computers: A Primer with IBM Q and D-Wave Exercises by Frank Mueller, Patrick Dreher, Greg Byrd held at PPoPP (Feb 2019) ASPLOS'19 (Apr 2019),
Part 3: D-Wave -- Adiabatic Quantum Programming
10. D-Wave factoring tutorial and other demos
including Jupyter notebooks (you have to login for them).
### 5.4 Photonics
3. Uses photonics.
4. Operates primarily at room temperature.
5. Up to 24 qbits, gate depth of 12.
6. Has free SW tools, some of which can compile to other quantum technologies.
7. Expected good applications: graphs and networks, machine learning, and quantum chemistry.
8. They expect to scale up better than competing technologies.
9. Operates at room temperature.
# Quantum Homework 4, Mon 2022-09-12
1. Student presentation to class next Mon 2022-09-19.
2. Pick an approach to building quantum computers that is not used by a major company like IBM, Google, Microsoft, Amazon, Rigetti or D-wave. Hidary Chapter 5 has lots of suggestions. Describe the idea, and its major advantages and disadvantages.
3. About 5-7 minutes. I won't be using a stopwatch, but be respectful of the other students. How the Ig Nobel awards handles this.
4. Suggestion: test your computer with the classroom setup in advance. The room is open.
Total: 10
# Quantum Class 4, Thurs 2022-09-08
## 1 Scientifically literate people and quantum computing
About people who are generally scientifically aware, but not really practitioners of science. What do you think people like that would like to know about Quantum Computing? Many people have heard about it, but most people don’t know what it means. What do you think their “burning questions” about it might be?
## 2 Handwritten notes are online
here. The file name is the class number; last time was 03.pdf . These are not really intended to stand alone; my typed blog is primary.
However, would you like me to add more details as I write them in class?
(I think).
due next time.
## 4 Questions on last videos
1. IBM:
1. What are the roles of the kernel, algorithm, and model developers?
2. Tell me about error suppression.
1. What are they doing?
2. How do they control a qbit?
3. How to they manage errors?
## 6 Bloch sphere
1. The state of a qbit can be represented as a point on or in a sphere of radius 1.
2. E.g., |1> is the north pole, |0> the south pole.
3. Many operations are rotations.
4. I don't think this idea is particularly big, but people like it.
5. It does not extend to multiple qbits.
## 7 Matrices
1. Quantum computing operators are unitary.
The conjugate transpose is the inverse.
2. Measurement operators are self-adjoint aka Hermetian.
The conjugate transpose is the matrix itself.
## 8 Hidary Chapter 3: Qubits, Operators and Measurement
### 8.1 Two qubit operators
1. Now, let $q$ be a system with two qubits, i.e., a 2-vector of qubits.
2. $q$ is now a linear combo of 4 basis values, $| 00\!\!>$, $| 01\!\!>$, $| 10\!\!>$, $| 11\!\!>$.
3. $q = a_0 | 00\!\!> + a_1 | 01\!\!> + a_2 | 10\!\!> + a_3 | 11\!\!>$
4. where $a_i$ are complex and $\sum | a_i | ^2 = 1$.
5. $q$ exists in all 4 states simultaneously.
6. If $q$ is a vector with n component qubits, then it exists in $2^n$ states simultaneously.
7. This is part of the reason that quantum computation is powerful.
8. A measurement operator applied to $q$ will rotate it to a basis {00, 01, 10, 11}, so that it will be observed in one of those four cases, with probabilities $| a_i | ^2$.
9. You operate on $q$ by multiplying it by a 4x4 matrix operator.
10. The matrices are all invertible (except for measurement matrices), and all leave $| q | = 1$.
11. You set the initial value of $q$ by setting its two qubits each to 0 or 1.
12. How this is done depends on the particular hw.
13. I.e., initially, $q_1 = \begin{pmatrix}a_1 | 0\!\!> \\b_1 | 1\!\!> \end{pmatrix}$ and $q_2 = \begin{pmatrix}a_2 | 0\!\!> \\b_2 | 1\!\!> \end{pmatrix}$, and so
$$q = \begin{pmatrix} q_1 \\ q_2 \end{pmatrix} = \begin{pmatrix} a_1 a_2 | 00 \!\!> \\ a_1 b_2 | 01 \!\!> \\ a_2 b_1 | 10 \!\!> \\ b_1 b_2 | 11 \!\!> \end{pmatrix}$$.
14. The combined state is the tensor product of the individual qubits.
15. In this case, you could separate out the individual qubits again.
16. However, sometimes after operating on the combo (i.e., multiplying by a matrix), you cannot any more separate out the result into a tensor product of individual qubits.
17. For $n$ qubits, the tensor product is a vector with $2^n$ elements, one element for each possible value of each qubit.
18. Each element of the tensor product has a complex weight.
19. You transform a state by multiplying it by a matrix.
20. The matrix is invertible.
21. The transformation doesn't destroy information.
22. For some sets of weights, particularly after a transformation, the combined state cannot be separated into a tensor product of individual qubits. In this case, the individual qubits are entangled.
23. That is the next part of why quantum computation is powerful.
24. Entanglement means that if you measure one qubit then what you observe restricts what would be observed when you measure the other qubit.
25. However that does not let you communicate.
26. The current limitations are that IBM does only a few qubits and that the operation is noisy.
### 8.2 Common operators
1. Common operations (aka gates):
https://en.wikipedia.org/wiki/Quantum_logic_gate
1. Swap
2. controlled not CNOT cX
When input is general, it's more sophisticated that it looks.
1-qbit creates a superposition.
2-qbit creates a uniform superposition
https://en.wikipedia.org/wiki/Quantum_logic_gate
4. Toffoli, aka CCNOT.
Universal for classical boolean functions.
(a,b,c) -> (a,b, c xor (a and b))
https://en.wikipedia.org/wiki/Toffoli_gate
5. Fredkin, aka CSWAP.
https://en.wikipedia.org/wiki/Fredkin_gate
3 inputs. Swaps last 2 if first is true.
sample app: 5 gates make a 3-bit full adder.
2. Bell state
1. Maximally entangled.
### 8.3 Entanglement of 2-qbit system
State is a 4-vector of length 1.
It was originally created as the exterior product of two 2-vectors, the states of two separate 1-qbit systems.
Originally the separate 1-qbit systems didn't affect each other. Either could be transformed and measured.
Then 2-qbit system was rotated with a transformation matrix.
Now, perhaps it can be decomposed into the exterior product of two 2-vectors. Perhaps not.
1. Case 1: The 4-vector representing the new state can be decomposed.
1. Then it's still really two separate 1-qbit systems.
2. They can still either be transformed and measured.
3. Measuring one qbit does not affect the other qbit.
2. Case 2: The 4-vector representing the new state cannot be decomposed.
1. So the 2 qbits are now entangled.
2. That means that measuring one qbit affects what you will see when you measure the other.
3. It might just bias the probabilities of measuring the other qbit as 0 or 1.
4. Or, it might totally control what you will see.
### 8.4 Entangling with Toffoli
1. Here's another way to look at this. Review:
2. $x'=x \\ y'=y \\ z'= z \oplus xy$
3. Use those equations only with classical bits, otherwise use the matrix multiplication.
4. Let x=1, z=0. Then, x'= 1, y'= y, z'= y.
5. So if y=0, then x'= 1, y'= 0, z'= 0.
6. and if y=1, then x'= 1, y'= 1, z'= 1.
7. If y is a superposition of 0 and 1, then the output will be a superposition of the above 2 cases.
8. That is, 50% of the time, we measure y'= 0, z'= 0 and 50% of the time we measure y'= 1, z'= 1.
9. We always measure y' and z' the same.
10. Even if we transport z' a long distance away first.
## 9 Quantum properties - No Cloning
I made some supplementary material on cloning (copying), which works in the classical world but not in the quantum world.
Classically, you can easily clone a bit. Consider a 2-bit system, $x, y$. Each bit can be 0 or 1. All 4 combos are possible. Represent the state with a 4-vector
$s=\begin{vmatrix} a_0\\a_1\\a_2\\a_3\end{vmatrix}$
where exactly one $a_i=1$ and the other three are 0. E.g., if $a_3=1$ then $x=y=1$.
Here's a 2-input, 2-output circuit that clones the first bit.
$x'=x\\y'=x$
Its truth table is
x y | x'y'
0 0 | 0 0
0 1 | 0 0
1 0 | 1 1
1 1 | 1 1
Represent the operation by a matrix multiplication on s. The matrix M is:
1 1 0 0
0 0 0 0
0 0 0 0
0 0 1 1
That is, the final state is $s'_i = \sum_j M_{ij} s_j$
However, M is singular. For quantum operations, M has to be unitary. So this is not a legal quantum circuit. Let's try again.
The better way is the 3-input Toffoli gate. The function is
$x'=x \\ y'=y \\ z'= z \oplus xy$
The truth table is
x y z | x'y'z'
0 0 0 | 0 0 0
0 0 1 | 0 0 1
0 1 0 | 0 1 0
0 1 1 | 0 1 1
1 0 0 | 1 0 0
1 0 1 | 1 0 1
1 1 0 | 1 1 1
1 1 1 | 1 1 0
The matrix is Eqn 5.62 on page 155.:
1 0 0 0 0 0 0 0
0 1 0 0 0 0 0 0
0 0 1 0 0 0 0 0
0 0 0 1 0 0 0 0
0 0 0 0 1 0 0 0
0 0 0 0 0 1 0 0
0 0 0 0 0 0 0 1
0 0 0 0 0 0 1 0
Let x=1, z=0. Then:
x'= 1
y'= y
z'= y
and we've cloned y in the classical case, where the inputs are each 0 or 1.
This matrix is nonsingular and so is also legal in a quantum circuit.
(Looking ahead a little), try $y= \frac{1}{\sqrt{2}} | 0> + \frac{1}{\sqrt{2}} | 1>$, which is an equal superposition of 0 and 1. Using x=1, z=0, the input will be
$\frac{ | 1, 0, 0> + | 1, 1, 0>}{\sqrt{2}}$
and the state is
$(0, 0, 0, 0, \frac{1}{\sqrt{2}} , 0, \frac{1}{\sqrt{2}} , 0)^T$
That's an equal superposition of 2 of the possible 8 classical input states.
Multiplying that by the matrix gives
$\frac{ | 1, 0, 0> + | 1, 1, 1>}{\sqrt{2}}$
Instead of cloning y into z, this entangled y and z.
An operation that is simple on classical input can be more complicated on quantum inputs.
This isn't new; we already know how to entangle two qbits.
Engangling isn't the same as cloning. The point of cloning is that we could operate on the two bits separately. If they're engangled, operating on one affects the other.
# Quantum Homework 3, Thurs 2022-09-08
Due 2022-09-12 4pm in gradescope. Groups of 2 are ok; submit one answer set.
(These questions are from Hidary.)
1. (10 points) Investigate the Stern-Gerlach experiment of 1921. What was the expectation from classical theory for the outcome and what actually occurred?
2. (10 points) What does non-separable mean for two states and what does that tell us about these states?
3. (10 points) For the CZ gate, does it matter which qubit is the control qubit and which is the target?
4. (10 points) What is the final state of the following circuit, in Dirac notation?
Total: 40
# Quantum Misc notes, Thurs 2022-09-08
Misc notes that I draw from for lectures.
## 1 Complexity theory - Hidary chap 4
1. Problems vs algorithms.
2. Interesting types of resources: time, space, ...
3. Worst case time, best case time.
4. We want to group problems and algorithms into classes in a way that captures their important properties and ignores the others.
5. competing formal ways to describe algorithms: Turing machine, Church's lambda calculus, ...
1. different ones had different power (could describe different classes).
2. the ones listed above seemed to all have the same power.
6. Universal Turing machine.
7. Church-Turing Thesis (CTT): If an algorithm can be performed on any piece of hardware (say, a modern personal computer), then there is an equivalent algorithm for a Universal Turing Machine (UTM) which performs exactly the same algorithm [161, p. 5].
8. Strong Church-Turing Thesis (SCTT) Any algorithmic process can be simulated efficiently using a Universal Turing Machine (UTM)
9. randomness can sometimes lead to a faster algorithm.
10. Extended Church-Turing Thesis (ECTT) Any algorithmic process can be simulated efficiently using a Probabilistic Turing Machine (PTM) [161, p. 6].
11. Quantum Extended Church-Turing Thesis (QECTT) Any realistic physical computing device can be efficiently simulated by a fault-tolerant quantum computer.
## 2 Hardware implementations
1. Quantum computation was theoretically started decades before actual quantum computers were designed.
2. Many competing technologies.
3. Let the strongest win.
## 3 New material
Various things designed to solidify your understanding of the fundamentals.
### 3.1 Math review from Quantum Computing for Computer Scientists
1. Chapter 2:
1. Complex vector space, page 34.
1. n-dim vector $\begin{vmatrix} c_0 \\ \cdots \\ c_{n-1}\end{vmatrix}$
3. Multiply vector by scalar.
4. etc.
2. Set of $m\times n$ complex matrices, $\mathbb{C}^{m\times n}$, is also a complex vector space.
2. Matrix mult is $\star$ in book.
3. $\mathbb{C}^{m\times n}$ is a complex algebra.
4. Set of polynomials in one variable of degree $le n$ is a complex vector space.
5. State of a quantum system is a complex vector.
6. You can make new vector spaces from combos of old ones.
1. Cartesian product or direct sum.
2. Just an ordered pair.
3. $(v_1, v_2)$.
7. Set of basis vectors for the vector space.
1. Every vector $v$ in the space is a linear combo of the basis vectors.
2. Represent $v$ as the list of weights.
3. There are many possible basis sets.
4. Each different basis set causes a different representation for the vectors.
5. Convert: change of basis.
A bridge between Switzerland and Germany across the Rhine River at Laufenberg had its two ends at different elevations because of a conversion error between two different basis systems.
https://www.science20.com/news_articles/what_happens_bridge_when_one_side_uses_mediterranean_sea_level_and_another_north_sea-121600
7. Hadamard matrix is an example.
8. Section 2.4 Inner product, etc, p 53
9. Section 2.7 Tensor product of vector spaces, p 66.
1. $\mathbb{V} \otimes \mathbb{V'}$.
2. Let $dim(\mathbb{V})=p$ and $dim(\mathbb{V'})=q$ . Then $dim(\mathbb{V} \otimes \mathbb{V'}) = pq$.
3. This is how quantum systems combine.
4. Example 2.7.2 p 70.
2. From end of section 2.3, p.52 to 2.6.
1. P 52. Transition matrix to convert a vector representation from the canonical basis this another basis is the Hadamark matrix.
2. Section 2.4. Add an inner product operator to the complex vector space. Note the conjugates in the rules; you don't see them with a real vector space.
3. Norm, aka length.
4. We won't need limits etc.
5. Section 2.5 Eigenvalues and eigenvectors
1. Eigenvalues don't depend on the representation. Converting to a new basis set doesn't change them.
2. Geometrically, in 2D, in you transform a circle centered at origin, eigenvalues are lengths of the axes. Eigenvectors are the axes.
6. Section 2.6 Hermitian and unitary matrices
7. P 39. Adjoint: conjugate transpose of matrix.
8. If you use its eigenvectors as a basis, then the matrix diagonalizes to a list of its eigenvalues.
9. P 62. Hermitian matrix: it is its adjoint.
10. Unitary: its inverse is its adjoint.
11. Geometrically, they are rotations since they preserve distances.
12. Notation confusion: the books uses capital letters both for matrices and vectors.
13. P 71, tensor product of matrices.
1. Chapter 3 through 3.2, p 74-88.
1. p 80, doubly stochastic matrix.
2. Multiplying it by a vector of probabilities gives a vector of probabilities (i.e., they sum to 1 and $0\le a_i \le 1$ ).
3. P 88, Chapter 3, section 3.3 Quantum systems,
5. When probabilities are norms of complex numbers, they might cancel.
14. p 91, Ex 3.2.2
15. p 93 double slit experiment
16. p 97 Section 3.4, Assembling systems
## 4 Misc intro to quantum computing stuff
This is misc stuff that you might find interesting, which I'm drawing from.
### 4.1 Quantum properties - Phase
1. You cannot measure the phase of qbit.
2. You can measure the relative phase of 2 qbits.
3. Many algorithms encode the answer as a phase shift of a qbit.
4. Phase kickback means that a gate that runs one way, e.g., the control bit affects an output bit, can be made to run the other way, e.g., the control bit is changed, by making the other bit a Hadamad basis.
5. Phase Kickback V Abhijith Rao
6. Qiskit Phase Kickback
### 4.2 Quantum supremacy
1. Coined by Preskill in 2012.
2. Google claimed this in Oct 2019 on a specific (artificial?) problem; see Google section.
3. IBM disagrees.
### 4.3 Cloud-based computing
1. IBM started this.
2. Alibaba followed.
3. Then D-Wave Leap, Rigetti, Amazon AWS Braket and Quantum solutions lab, Microsoft Azure.
4. IBM's intent is to entangle their computers in different sites; exponentially increasing power.
### 4.4 Technologies
#### 4.4.2 Trapped Ion
1. https://en.wikipedia.org/wiki/Trapped_ion_quantum_computer
2. Proponents say that it's better than transmon qbits.
3. https://ionq.com/technology
"To date, we’ve run single-qubit gates on a 79 ion chain, and complex algorithms on chains of up to 11 ions."
#### 4.4.3 Quantum annealing
1. This is not comparable to quantum gates and circuits like IBM has.
2. It minimizes a function by testing many solutions in parallel.
3. See details in the D-Wave section.
4. Qbit count is not comparable to gate models.
#### 4.4.4 Photonics
1. Operates at room temperature.
### 4.5 Companies - Primary
These companies have their own hardware.
#### 4.5.1 IBM
##### 4.5.1.1 Summary
1. They have several quantum computers, up to 53 qbits.
2. The older ones are freely available on the web; see https://quantum-computing.ibm.com/
3. Note that you can put gates between only adjacent qbits.
4. You submit a batch job and get emailed when it runs.
5. IBM github site: https://github.com/Qiskit with
1. a free simulator.
It doesn't match all the physical complexity of the real computer, but it's a good start.
2. and tutorials and presentations.
6. and a SW development framework. https://qiskit.org/
7. You can create a quantum computation program either by
1. designing a circuit, or
2. using a programming language.
##### 4.5.1.3 Applications on the IBM Q
1. Quantum Algorithms for Applications from qiskit
2. HHL Algorithm
This is in Huawei HiQ, an open-source software framework for quantum computing.
3. https://en.wikipedia.org/wiki/Quantum_algorithm_for_linear_systems_of_equations
##### 4.5.1.4 IBM Quantum experience
1. When you design a circuit here, you don't need to simulate it elsewhere. It shows you the probabilities.
2. Dual view: you can see and edit both the circuit and the QASM code.
3. There are some sample programs in https://github.com/Qiskit/openqasm.git
4. Example circuits in https://quantum-computing.ibm.com/docs/iqx/example-circuits .
#### 4.5.2 Intel
1. Tangle Lake has 49 superconducting qbits.
2. Produced in Oregon.
3. Partners with QuTech in Netherlands.
4. https://www.intel.com/content/www/us/en/research/quantum-computing.html
1. Sycamore has 54 (-> 53) transmon qbits in 9x6 array, each coupled to 4 neighbors.
2. Google quantum General web site.
3. QuantumCasts link to some videos, including the following.
4. Quantum Money (Quantum Summer Symposium 2020) 15:56. Peter Shor. It's fun to see what Shor is thinking about now.
5. The Man Who Will Build Google's Elusive Quantum Computer
#### 4.5.4 D-Wave
1. https://en.wikipedia.org/wiki/D-Wave_Systems
2. They make a different type of quantum computer, called a quantum annealer. They have been in the news lately, e.g.,
3. https://arstechnica.com/science/2020/09/d-wave-releases-its-next-generation-quantum-annealing-chip/
4. "Want to learn how to program a quantum computer? In this webinar, we explain how to do so by running through a complete, simple example. We explain how to formulate the problem, how to write it, and how to tune it for best results. "
"This webinar is intended for those with little or no experience programming on a D-Wave quantum computer. After watching, get free time on Leap, the quantum cloud service at https://cloud.dwavesys.com/leap/signup/ "
5. Slides from Programming Quantum Computers: A Primer with IBM Q and D-Wave Exercises by Frank Mueller, Patrick Dreher, Greg Byrd held at PPoPP (Feb 2019) ASPLOS'19 (Apr 2019),
Part 3: D-Wave -- Adiabatic Quantum Programming
6. D-Wave factoring tutorial and other demos
including Jupyter notebooks (you have to login for them).
#### 4.5.5 IonQ
1. founders from Maryland/College Park and Duke.
2. trapped ion
3. 32 qbits.
4. low error rate
5. excellent quantum volume
6. will be available from Microsoft Azure and Amazon AWS Braket.
7. https://ionq.com/
8. https://en.wikipedia.org/wiki/IonQ
9. https://ionq.com/posts/october-01-2020-most-powerful-quantum-computer
#### 4.5.6 Honeywell
1. H1: trapped ion.
2. 10 qbits,
1. full connectivity,
2. can read isolated qbits in mid-computation,
3. hi-res rotations.
3. JP Morgan experimenting with it.
##### 4.5.6.1 Sites
1. The World’s Highest Performing Quantum Computer is Here
2. They partner with Microsoft,, Experience quantum impact with Azure Quantum, Cambridge Quantum Computing, Zapata Computing, etc.
#### 4.5.7 Rigetti
1. Berkeley-based
2. founder is ex-IBM
3. https://en.wikipedia.org/wiki/Rigetti_Computing
4. https://www.rigetti.com/
5. has lots of tools
6. available via AWS etc
7. technical details are sparse
8. has been absorbing venture capital
9. https://techcrunch.com/2020/03/05/rigetti-computing-took-a-71-million-down-round-because-quantum-computing-is-hard/
"Recently, investors are gambling more on the middleware layer of a quantum computing stack. These are companies like Zapata, Q-CTRL, Quantum Machines and Aliro, which improve the performance of quantum computers and create an easier user experience"
10. makes optimistic promises (8/8/18):
https://medium.com/rigetti/the-rigetti-128-qubit-chip-and-what-it-means-for-quantum-df757d1b71ea
3. Uses photonics.
4. Operates primarily at room temperature.
5. Up to 24 qbits, gate depth of 12.
6. Has free SW tools, some of which can compile to other quantum technologies.
7. Expected good applications: graphs and networks, machine learning, and quantum chemistry.
8. They expect to scale up better than competing technologies.
#### 4.5.9 Others
1. Alibaba
2. 1QBit
3. CQC
4. QC Ware
5. QSimulate
6. Quantum Circuits
7. Rahko
8. Zapata
### 4.6 Companies - Aggregators
These companies resell others' computers as a cloud service.
#### 4.6.1 Amazon
1. https://aws.amazon.com/braket/
"Amazon Braket is a fully managed quantum computing service that helps researchers and developers get started with the technology to accelerate research and discovery. Amazon Braket provides a development environment for you to explore and build quantum algorithms, test them on quantum circuit simulators, and run them on different quantum hardware technologies."
"...quantum annealers from D-Wave, and gate-based computers from Rigetti and IonQ."
#### 4.6.2 Microsoft
1. They offer a cloud service on 3 platforms: Honeywell, IonQ, QCI.
Microsoft Is Taking Quantum Computers to the Cloud
2. Microsoft Quantum
A lot of stuff, with a low S/N.
3. Microsoft quantum blog
4. Azure Quantum Developer Workshop. 5:05:25.
A little diffuse.
5. Microsoft Quantum Documentation gateway to a lot of stuff.
6. Microsoft, e.g. Quantum Computing for Computer Scientists 1:28:22.
This is the same viewpoint as the textbook, but the speaker is different.
This talk discards hand-wavy pop-science metaphors and answers a simple question: from a computer science perspective, how can a quantum computer outperform a classical computer? Attendees will learn the following:
• Representing computation with basic linear algebra (matrices and vectors)
• The computational workings of qbits, superposition, and quantum logic gates
• Solving the Deutsch oracle problem: the simplest problem where a quantum computer outperforms classical methods
• Bonus topics: quantum entanglement and teleportation
The talk concludes with a live demonstration of quantum entanglement on a real-world quantum computer, and a demo of the Deutsch oracle problem implemented in Q# with the Microsoft Quantum Development Kit. This talk assumes no prerequisite knowledge, although comfort with basic linear algebra (matrices, vectors, matrix multiplication) will ease understanding.
### 4.7 Algorithms
1. Good ref is Chapter 6, Algorithms of Quantum Computing for Computer Scientists, published in 2000. Algorithms don't change fast. It does omit new things like HHL.
2. For these examples, the quantum algorithm is quite different from the classical algorithm, and is asymptotically faster.
3. Current research is deciding what algorithms can be made faster.
4. p 172: Any function can be made invertible by adding a control bit.
5. Major categories:
1. Cryptography
2. Quantum search
3. Quantum simulation
4. Quantum annealing and adiabatic optimization
Nice summary: https://en.wikipedia.org/wiki/Quantum_computing
6. Algorithm summary:
1. Some, but not all, are faster.
2. Bounded-error quantum polynomial time (BQP)
1. "is the class of decision problems solvable by a quantum computer in polynomial time, with an error probability of at most 1/3 for all instances" - https://en.wikipedia.org/wiki/BQP
2. Includes integer factorization and discrete log.
3. Relation to NP is unknown (big unsolved problem).
3. Searching problems:
1. Find the answer to a puzzle.
2. Math examples: factor an integer, solve a polynonial equation.
3. Testing validity of a putative solution is easy.
4. Finding that putative solution, naively, requires testing all possibilities.
5. Quantum computation can solve some searching problems faster.
6. This is probabilistic or noisy; often the found solution is wrong.
7. So you repeat the computation enough times that the error rate is acceptably low.
8. Some classical algorithms are similar. There is an excellent probabilistic primality algorithm.
9. The quantum algorithms are quite complex. (i.e., I'm still learning them.)
4. Algorithms, another view
1. Hadamard matrix rotates the pure state to an entangled superposition.
2. Then we operate in parallel on each state in the superposition.
3. Finally we separate out the desired answer.
5. Grover's algorithm:
1. https://en.wikipedia.org/wiki/Grover%27s_algorithm
2. Given a black box with N inputs and 1 output.
3. Exactly one input makes the output 1.
4. Problem: which one?
5. Classical solution: Try each input, T=N.
6. Quantum: $T=\sqrt(N)$.
7. Probabilistic.
8. Apps: mean, median, reverse a crypto hash, find collisions, generate false blocks.
9. Can extend to quantum partial search.
10. Grover's algorithm is optimal.
11. This suggests that NP is not in BQP .
6. Shor's algorithm:
1. Factorize an integer.
2. in BQP.
3. almost exponentially faster than best classical algorithm.
4. Largest examples I can find:
### 4.8 Algorithm details
#### 4.8.1 Deutsch
1. We have a black box F(x) -> x'.
2. We're told that F is either balanced or constant.
3. How to determine which?
4. We can input any x and see the result.
5. Classically: eval F(0) and F(1).
6. That took two evals and some comparisons.
7. All that matters is the number of evals. We assume that they're slower than everything else.
8. Quantumly (quantumicly?) we can determine which type F is with only one eval plus some extra matrices.
#### 4.8.2 Deutsch - Jozsa
Now $F: \{0,1\}^n \to \{0,1\}$.
We're told that it's either constant or balanced. It's not neither.
Which is it?
Classically, we need n/2+1 evals of F.
Quantumly, we need only 1.
#### 4.8.3 Simon's periodicity
Blackbox $F: \{0,1\}^n \to \{0,1\}^n$
For some unknown $c$, $F(x\oplus c) = F(x)$.
Determine $c$.
#### 4.8.5 Deutsch-Jozsa
This algorithm is deterministic.
1. https://www.quantiki.org/wiki/deutsch-jozsa-algorithm
Quick summary; doesn't say why it works.
2. https://qiskit.org/textbook/ch-algorithms/deutsch-jozsa.html
This is an intro to Qiskit. The terminology is confusing. E.g., Register 1 has q0 q1 q2. Register 2 has q3. The run buttons don't seem to work.
3. https://en.wikipedia.org/wiki/Deutsch%E2%80%93Jozsa_algorithm
This is a nice detailed description.
#### 4.8.7 HHL algorithm to solve a linear system of equations
1. quick, deep, intro.
2. quite understandable.
3. IBM Quantum Algorithms for Applications from qiskit
E.g., Fourier transform and HHL.
4. HHL Algorithm
This is in Huawei HiQ, an open-source software framework for quantum computing.
5. https://en.wikipedia.org/wiki/Quantum_algorithm_for_linear_systems_of_equations
### 4.9 Software
#### 4.9.1 General
1. A difficulty is to compile to the limited connectivity of the machine
2. Open-Source Quantum Software Projects
3. ProjectQ open-source software framework for quantum computing.
4. Programming Quantum Computers: A Primer with IBM Q and D-Wave Exercises . Tutorial given at a few conferences.
#### 4.9.2 Middleware
1. https://www.hpcwire.com/off-the-wire/quantum-computing-inc-releases-version-1-1-of-mukai-middleware/
2. https://tbri.com/webinars/middleware-the-quantum-computing-differentiator/ "An integral piece of quantum computing’s success is the middleware bridging existing code and algorithms to the new logical circuitry being established that sits on top of the quantum circuits. This integration and abstraction will allow the technology to process complex algorithms to provide the outcomes the hardware enables."
1. excellent videos from this Delft research group.
2. QCI
3. He's describing a different computer from IBM's.
4. Presenter: Conal Murray, Research Staff Member, IBM Research
The potential of quantum computing to enable new ways of solving problems considered intractable on classical computing platforms relies on our understanding of how qubits operate. Qubit scaling follows different metrics than those associated with classical computing, driven by the requirement that the fragile states they possess can be retained for sufficiently long times. After a brief introduction into superconducting transmon qubits, I will discuss how dielectric loss impacts their relaxation times and how we can effectively model such behavior using analytical and computational approaches. The resulting analysis provides guidance into the design aspects associated with such qubits. A secondary issue that follows from manufacturing greater numbers of qubits involves unwanted communication among them. In particular, resonance modes generated in the substrate on which they reside can limit their operating frequencies. It is known that incorporating grounded, through-silicon vias can increase the corresponding cutoff frequency within the substrate. I will show how we can predict the resulting spectrum by considering the array of vias as an effective photonic crystal to arrive at a fundamental frequency dependent on the particulars of the via geometry.
http://meetings.aps.org/Meeting/MAR20/Session/P28.2
#### 4.10.2 Misc
1. 8 Best New Quantum Computing Books To Read In 2020
2. Quantum Computing UK nice set of docs and examples.
3. Ricardo Diaz recommends this book: Something Deeply Hidden: Quantum Worlds and the Emergence of Spacetime .
4. There are now several business reports on the industry.
### 4.11 Summary
1. Quantum computing hasn't solidly proved itself yet. However it's now in the engineering phase - realizing what we basically know how to do.
2. IMO the physicists have done it again (last time was atomic energy). This will be a fundamental transformation of computing.
3. Certain searching algorithms will be exponentially faster.
4. Algorithm design still needs research. Algorithms are quite complex.
5. Major application areas like drug design.
6. Several viable technologies competing.
7. Several HW companies.
8. Competing toolsets being developed.
9. Various service platforms to provide simulators and the HW.
10. Recommendation (remember I'm SW):
1. Be agnostic wrt platform (we don't know who will win).
2. Have people use AWS etc to learn and develop apps. No capital investment needed.
3. Work developing and/or using middleware, which is newer area.
4. RPI-specific:
1. Merely playing catchup is a losing game. Need something new.
2. Assume that IBM etc will make the computers. The big problem with new HW is always how to use it. The ability of customers to use a new tool can determine whether it succeeds.
3. Include other RPI programs?
1. Gamify this using Game and Sim?
2. Work with tetherless world?
4. I'm still thinking.
# Quantum Class 3, Tues 2022-09-06
## 1 Action at a distance
1. Two qbits can be entangled tho they are far apart.
2. How can this be?
3. Newton faced the same conceptual leap.
4. How can the earth affect the moon's orbit?
5. Some people posited invisible whirlpools in space that dragged the planets around.
6. That was falsified by the existence of retrograde orbits.
7. Now we say that it happens because, in general relativity, the earth's mass bends space-time, and the moon just follows a geodesic.
8. My view is that if something is useful but inexplicable, then just use it.
9. Or, do like Andreas Osiander, Copernicus's editor, "these hypotheses need not be true nor even probable. [I]f they provide a calculus consistent with the observations, that alone is enough." https://en.wikipedia.org/wiki/Nicolaus_Copernicus
If Giordano Bruno had talked evasively like that, maybe he wouldn't have been burnt at the stake in 1600. However he may have been burnt for other reasons.
## 2 Questions from Quantum Computing 2022 Update
1. big application.
2. what is superposition?
3. why is it powerful?
4. change in IBM strategy, or, what is circuit knitting?
5. What is IBM's quantum parallelization?
6. What is NIST doing re quantum crypto?
7. How is Intel advancing quantum HW?
8. What have some other companies done?
## 3 Hidary, Quantum Computing: An Applied Approach, 2nd ed, chapter 1
1. Companion site: https://github.com/jackhidary/quantumcomputingbook
2. Quantum computer: uses properties of quantum mechanics to compute
1. world is quantum.
2. compare to classical computer.
3. quantum properties
1. superposition
2. entanglement
4. state: complete math description of state.
1. a complex vector.
2. classical analog: e.g., position of a particle.
5. Schrodinger's equation computes future state as a function of current state and stuff.
6. Compare to Newton: future position depends on force etc.
7. Analogously to Newton, only simple cases have closed form solutions. 2 body not 3 body. hydrogen atom.
8. Even if there's a closed form solution, it may be chaotic, and so not as useful.
9. Must simulate when no closed solution. Unfortunately that's all the good cases. College classes use solvable examples, not realistic ones.
10. See Wolfram, A New Kind of Science.
11. superposition: linear combo of states is a legal state.
1. the weights are complex numbers.
2. everything in quantum mechanics uses complex numbers.
3. superposition does not work classically.
12. A qubit $q$ is a quantum analog to a classical bit.
13. the quantum analog to classical bits 0 and 1 are $|0\!\!>$ and $|1\!\!>$.
14. q's state is a superposition (linear combo) of those two basis states:
1. $q = a|0\!\!> + b|1\!\!>$ ,
2. where the weights $a$ and $b$ are complex numbers, and $| a | ^2 + | b | ^2 = 1$.
15. Note the weird notation (Dirac notation). In $|0\!\!>$, $|$ is like a left bracket and $>$ like a right one.
16. It is wrong to think that $q$ is really in one of the two states, but you don't know which one. This is the hidden variable theory. It has been proved experimentally to be false.
17. $q$ is really in both states simultaneously.
18. You cannot observe its state, unless it is $|0\!\!>$ and $|1\!\!>$, in which case you observe $0$ or $1$. This is the classical case.
19. measurement of a state $\Psi$, and the Born rule (p 5):
1. Measurement is an operator or matrix, M, applied to a state $\Psi$.
2. M changes the qbit irreversibly, see the polarization example in the book.
3. You cannot reclaim the old value.
4. M has eigenvalues.
5. Represent $\Psi$ as a linear combo of M's eigenvalues $\psi_i$, considered as a basis.
6. $\Psi= \alpha\psi_1+\beta\psi_2$, where $\alpha^2+\beta^2=1$.
7. you can use different basis systems to represent the same vector, and rotate between them.
8. M changes $\Psi$ state randomly to one of the basis vectors.
9. the probability of $\Psi$ changing to a particular basis vector is the modulus squared of the weight of that basis vector.
10. define $z^c$ to be the complex conjugate of $z$.
11. if $\Psi= \alpha\psi_1+\beta\psi_2$, where $\alpha^c\alpha+\beta^c\beta=1$ then the probability of $\Psi$ changing to $\psi_1$ is $\alpha^c\alpha$. (the Born rule)
12. $\alpha^c\alpha$ is called the modulus squared.
20. There are many possible measurement operators available.
1. You can choose which to apply to $q$. Say, position.
2. That prevents you from applying the others to $q$, say, momentum, because you don't have $q$ available any more.
3. Heisenberg uncertainty: measuring, say, position, prevents you from accurately measuring momentum.
21. $q$, that is, $q$ 's value, can be considered to be a vector of length two: $$\begin{pmatrix} a | 0\!\!> \\ b | 1\!\!> \end{pmatrix}$$ or simply $$\begin{pmatrix}a\\b\end{pmatrix}$$.
22. You operate on $q$ with a matrix multiplication: $q_2 = M q$.
23. Unless $M$ is a measurement operator, it is invertible, so you can go backwards.
24. Contrast to classical operators like and and or.
25. Examples of 1-qubit gates
1. not, aka X. page 28.
2. square root of not
3. Y, Z
4. S (rotation by $90^o$), T ($45^o$), phase shift
5. Hadamark. "it enables us to take a qubit from a definite computational basis state into a superposition of two states"
26. All operators used in quantum computation other than for measurement must be reversible. - textbook.
27. No cloning: You cannot copy a qubit, but can move it.
28. The life cycle of a qubit:
1. Create a qubit with a classical value, 0 or 1.
2. Operate on it with matrices, which rotate it to have complex weights.
3. Measure it by randomly projecting it onto a basis vector.
29. So far, not very powerful.
30. a quantum state $\Psi$ usually has many qubits.
compare to a classical byte with 8 classical bits.
Total: 30 | 2023-03-31 06:15:55 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 2, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3644546866416931, "perplexity": 4336.95333764698}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296949573.84/warc/CC-MAIN-20230331051439-20230331081439-00027.warc.gz"} |
http://tex.stackexchange.com/questions/165543/using-latexdiff-in-miktex | # Using latexdiff in MiKTeX
I am trying to use latexdiff to compare two .tex files, producing a .pdf with a markup similar to the "track changes" function in Microsoft Word (see https://www.sharelatex.com/blog/2013/02/16/using-latexdiff-for-marking-changes-to-tex-documents.html).
I have downloaded the latexdiff files from CTAN and I have also downloaded Strawberry Perl. I am using MiKTeX to compile my two tex documents.
In the command line (DOS prompt) I have been trying to instruct latexdiff to compare two very simple .tex files: SAMPLE4.tex and SAMPLE5.tex. I have been following the instructions in the USAGE section of the first URL I list here ("...using latexdiff..."), specifically:
"Usage
To compare two documents simply run latexdiff in the command line like so:
latexdiff draft.tex revision.tex > diff.tex"
However, when I enter the following into the command line:
C:\Users\Kathryn\latexdiff SAMPLE4.tex SAMPLE5.tex > diff.tex
I get the following error message:
Input file SAMPLE$.tex does not exist. at C:\Program Files\MiKTeX 2.9\scripts\latexdiff\latexdiff line 513, <DATA> line 20026. I suspect the problem is that the computer cannot find the file SAMPLE4.tex and that I need to make SAMPLE4.tex (and presumably also SAMPLE5.tex) available in a directory that I can accurately specify in DOS. I tried putting my two .tex files in C:\Program Files\MikTeX 2.9\latexdiff but this did not work. Can anyone here offer me some advice? - SAMPLE$.tex or SAMPLE5.tex (the error message you quote uses the former) – David Carlisle Mar 14 '14 at 15:48
Crosspost to latex community – Johannes_B Mar 14 '14 at 17:57
Check with what david wrote above. Also you can't write in program files directory from vista onwards. Navigate to the folder where your tex files are and then use latexdiff (in dos) – Harish Kumar Mar 14 '14 at 23:45
Why do you not use the latexdiff already available in MiKTeX? If not included yet you can install it with the Package Manager. Then you have to be in the folder with the two files you want to compare, not in the program folder of latexdiff. I hope you not only downloaded Strawberry Perl, but also installed it. See BTW also MiKTeX and Perl scripts (and one Python script). – Speravir Mar 15 '14 at 0:00
And almost forgotten: Welcome to TeX.SX! Usually, we don't put a greeting or a “thank you” in our posts. While this might seem strange at first, it is not a sign of lack of politeness, but rather part of our trying to keep everything very concise. Accepting and upvoting answers is the preferred way here to say “thank you” to users who helped you. Note also, that your name automatically appears in the lower right corner of your post. – Speravir Mar 15 '14 at 0:03 | 2016-02-06 14:21:09 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.868648886680603, "perplexity": 3870.2721344926504}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-07/segments/1454701146550.16/warc/CC-MAIN-20160205193906-00207-ip-10-236-182-209.ec2.internal.warc.gz"} |
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## KJ4UTS one year ago If a ball is dropped near the surface of the earth, then the distance it falls is directly proportional to the square of the time it has fallen. A ball is dropped over the edge of a vertical cliff and falls 39.2 meters in two seconds. Determine the distance (in meters) the ball would have dropped in 3.5 seconds. The ball would have dropped ____ meters. Round your answer to two decimal places.
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1. KJ4UTS
2. MrNood
it tells you the distance is proportional to the square of the time so distance = kt^2 $\frac{ d1 }{ d2 } =\frac{ t1^{2} }{ t2^{2} }$ you know all except d2 - so solve for d2
3. KJ4UTS
So I plug in 32.9 and 2 (seconds) in?
4. MrNood
in the first scenario d=32.9 and t=2 in the second scenario d is unknown and t= 3.5 put those 3 values into the equation to solve the unknown distance
5. KJ4UTS
32.9/2^2=k ?
6. KJ4UTS
Is that how I set the formula up because it would be 9.8 then?
7. KJ4UTS
@MrNood
8. KJ4UTS
32.9/3.5^2=3.2
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Privacy Policy | 2017-01-18 18:26:13 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8043232560157776, "perplexity": 1286.4562525774004}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-04/segments/1484560280310.48/warc/CC-MAIN-20170116095120-00246-ip-10-171-10-70.ec2.internal.warc.gz"} |
https://www.authorea.com/doi/full/10.1002/essoar.10502656.1 | Seasonal effect on hemispheric asymmetry in ionospheric horizontal and field-aligned currents
• Abiyot B. Workayehu,
• Heikki Vanhamäki,
• Anita T. Aikio
Abiyot B. Workayehu
University of Oulu
Corresponding Author:abiyot.workayehu@oulu.fi
Author Profile
Heikki Vanhamäki
University of Oulu
Author Profile
Anita T. Aikio
University of Oulu
Author Profile
Abstract
We present a statistical investigation of the seasonal effect on hemispheric asymmetry in the auroral currents during low (Kp $<$ 2) and high (Kp $\geq$ 2) geomagnetic activity. Five years of magnetic data from the Swarm satellites has been analysed by applying the spherical elementary current system (SECS) method. Bootstrap resampling has been used to remove the seasonal differences between the hemispheres in the dataset. In general, the currents are larger in the Northern Hemisphere (NH) than in the Southern Hemisphere (SH). Asymmetry is larger during low than high Kp, and during winter and autumn than summer and spring. The NH/SH ratio for FACs in winter, autumn, spring and summer are 1.17 $\pm$ 0.05, 1.14 $\pm$ 0.05, 1.07 $\pm$ 0.04 and 1.02 $\pm$ 0.04, respectively. The largest asymmetry is observed during low Kp winter, when the excess in the NH currents is 21$\pm$5\% in FAC, 14 $\pm$ 3\% in curl-free (CF), and 10$\pm$3\% in divergence-free (DF) current. We also find that evening sector (13-24 MLT) contributes more to the high NH/SH ratio than the morning (01-12 MLT) sector. The physical mechanisms producing the hemispheric asymmetry are not presently understood. We calculated the background ionospheric conductances during low Kp conditions from the IRI, NRLMSISE and CHAOS models. The results indicate that only a small part of the hemispheric asymmetry can be explained by variations in the solar induced conductances.
Oct 2020Published in Journal of Geophysical Research: Space Physics volume 125 issue 10. 10.1029/2020JA028051 | 2023-03-25 11:28:32 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6883078813552856, "perplexity": 7680.820360451277}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296945323.37/warc/CC-MAIN-20230325095252-20230325125252-00149.warc.gz"} |
https://www.lmfdb.org/ModularForm/GL2/Q/holomorphic/531/8/a/b/ | Properties
Label 531.8.a.b Level $531$ Weight $8$ Character orbit 531.a Self dual yes Analytic conductor $165.876$ Analytic rank $1$ Dimension $16$ CM no Inner twists $1$
Learn more about
Newspace parameters
Level: $$N$$ $$=$$ $$531 = 3^{2} \cdot 59$$ Weight: $$k$$ $$=$$ $$8$$ Character orbit: $$[\chi]$$ $$=$$ 531.a (trivial)
Newform invariants
Self dual: yes Analytic conductor: $$165.876448532$$ Analytic rank: $$1$$ Dimension: $$16$$ Coefficient field: $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ Defining polynomial: $$x^{16} - 6 x^{15} - 1493 x^{14} + 8791 x^{13} + 890490 x^{12} - 5107725 x^{11} - 269092298 x^{10} + 1488374176 x^{9} + 42885295136 x^{8} - 226132003872 x^{7} - 3353576629440 x^{6} + 16796366777600 x^{5} + 99470801612800 x^{4} - 494039551757568 x^{3} - 493048066650624 x^{2} + 3193975642099712 x - 2385018853548032$$ Coefficient ring: $$\Z[a_1, \ldots, a_{7}]$$ Coefficient ring index: $$2^{9}\cdot 3^{5}$$ Twist minimal: no (minimal twist has level 177) Fricke sign: $$-1$$ Sato-Tate group: $\mathrm{SU}(2)$
$q$-expansion
Coefficients of the $$q$$-expansion are expressed in terms of a basis $$1,\beta_1,\ldots,\beta_{15}$$ for the coefficient ring described below. We also show the integral $$q$$-expansion of the trace form.
$$f(q)$$ $$=$$ $$q + \beta_{1} q^{2} + ( 61 + \beta_{2} ) q^{4} + ( 5 - \beta_{1} - \beta_{4} ) q^{5} + ( -148 + 5 \beta_{1} + \beta_{2} - \beta_{9} ) q^{7} + ( -67 + 42 \beta_{1} + \beta_{3} ) q^{8} +O(q^{10})$$ $$q + \beta_{1} q^{2} + ( 61 + \beta_{2} ) q^{4} + ( 5 - \beta_{1} - \beta_{4} ) q^{5} + ( -148 + 5 \beta_{1} + \beta_{2} - \beta_{9} ) q^{7} + ( -67 + 42 \beta_{1} + \beta_{3} ) q^{8} + ( -204 - 41 \beta_{1} - 3 \beta_{2} + \beta_{3} - \beta_{7} + 3 \beta_{9} - \beta_{10} - \beta_{13} + \beta_{14} ) q^{10} + ( -73 + 37 \beta_{1} - 3 \beta_{2} + 3 \beta_{4} + \beta_{6} - \beta_{7} - \beta_{8} - \beta_{9} - 2 \beta_{12} + 2 \beta_{14} ) q^{11} + ( -527 + 42 \beta_{1} - 15 \beta_{2} + 3 \beta_{3} - 2 \beta_{4} + 2 \beta_{5} - 2 \beta_{8} + 2 \beta_{10} - \beta_{11} - 3 \beta_{12} + \beta_{13} - \beta_{15} ) q^{13} + ( 852 - 67 \beta_{1} + 10 \beta_{2} - 7 \beta_{3} + 30 \beta_{4} + 3 \beta_{5} - 5 \beta_{6} - 4 \beta_{7} + 2 \beta_{8} - \beta_{9} - 4 \beta_{10} - 3 \beta_{11} + 6 \beta_{12} - 6 \beta_{13} - 3 \beta_{14} - 2 \beta_{15} ) q^{14} + ( 218 - 19 \beta_{1} + 3 \beta_{2} - 2 \beta_{3} - 19 \beta_{4} - \beta_{5} - \beta_{6} - 2 \beta_{7} + 3 \beta_{8} + 3 \beta_{9} + 2 \beta_{10} - 3 \beta_{11} + 3 \beta_{12} + 4 \beta_{13} - 4 \beta_{14} - \beta_{15} ) q^{16} + ( 2857 - 110 \beta_{1} + 44 \beta_{2} - \beta_{3} + 9 \beta_{4} + \beta_{5} - 2 \beta_{6} + 3 \beta_{7} + 2 \beta_{8} + 2 \beta_{9} + 4 \beta_{11} - 3 \beta_{12} + 7 \beta_{13} + \beta_{15} ) q^{17} + ( -2481 - 118 \beta_{1} - 109 \beta_{2} + 2 \beta_{3} - 14 \beta_{4} - 6 \beta_{5} + 4 \beta_{6} + 5 \beta_{7} - 2 \beta_{8} + \beta_{9} - 4 \beta_{10} + 7 \beta_{11} + 2 \beta_{12} + 6 \beta_{13} + 3 \beta_{14} + 8 \beta_{15} ) q^{19} + ( -8074 - 175 \beta_{1} + 89 \beta_{2} + 7 \beta_{3} - 64 \beta_{4} - 16 \beta_{5} + 25 \beta_{6} + 9 \beta_{7} - 8 \beta_{8} - 18 \beta_{9} + 10 \beta_{10} - 2 \beta_{11} - 6 \beta_{12} + 17 \beta_{13} + 3 \beta_{14} + 6 \beta_{15} ) q^{20} + ( 6881 - 147 \beta_{1} - 48 \beta_{2} - 22 \beta_{3} - 15 \beta_{4} + 3 \beta_{6} + 16 \beta_{7} + 4 \beta_{8} - 7 \beta_{9} - 9 \beta_{10} + \beta_{11} + 12 \beta_{12} - 22 \beta_{13} - 5 \beta_{14} - 7 \beta_{15} ) q^{22} + ( 90 + 277 \beta_{1} + 70 \beta_{2} + 8 \beta_{3} - 6 \beta_{4} - 9 \beta_{5} - 8 \beta_{6} + 24 \beta_{7} - 5 \beta_{8} + 4 \beta_{9} + 23 \beta_{10} + 4 \beta_{11} + 12 \beta_{12} - 15 \beta_{14} + 6 \beta_{15} ) q^{23} + ( 17915 - 124 \beta_{1} - 41 \beta_{2} - 51 \beta_{3} - 6 \beta_{4} + \beta_{5} - 32 \beta_{6} + 21 \beta_{7} + 19 \beta_{8} + 23 \beta_{9} + 15 \beta_{10} + 21 \beta_{11} - \beta_{12} - \beta_{13} - 3 \beta_{14} + 5 \beta_{15} ) q^{25} + ( 8835 - 2022 \beta_{1} + 87 \beta_{2} + 6 \beta_{3} + 48 \beta_{4} + 11 \beta_{5} - 16 \beta_{6} + 29 \beta_{7} + 51 \beta_{8} + 71 \beta_{9} + 14 \beta_{10} + 44 \beta_{11} - 9 \beta_{12} - 21 \beta_{13} - 12 \beta_{14} - 10 \beta_{15} ) q^{26} + ( 6175 + 2451 \beta_{1} - 155 \beta_{2} - 4 \beta_{3} - 96 \beta_{4} - 21 \beta_{5} + 32 \beta_{6} + 6 \beta_{7} + 9 \beta_{8} - 108 \beta_{9} + 37 \beta_{10} + 28 \beta_{11} + 13 \beta_{12} - 10 \beta_{13} - 39 \beta_{14} + 28 \beta_{15} ) q^{28} + ( -8188 - 2323 \beta_{1} - 91 \beta_{2} - 44 \beta_{3} + 17 \beta_{4} + 21 \beta_{5} - 7 \beta_{6} + 18 \beta_{7} - 29 \beta_{8} - 19 \beta_{9} - 38 \beta_{10} - 6 \beta_{11} + 10 \beta_{12} - 14 \beta_{13} - 19 \beta_{14} + 20 \beta_{15} ) q^{29} + ( -10334 + 3825 \beta_{1} - 214 \beta_{2} - 4 \beta_{3} - 28 \beta_{4} - 53 \beta_{5} + 42 \beta_{6} + 2 \beta_{7} - 6 \beta_{8} - 6 \beta_{9} - 14 \beta_{10} - 29 \beta_{11} + 22 \beta_{12} + 14 \beta_{13} + 10 \beta_{14} - 10 \beta_{15} ) q^{31} + ( 4541 - 6197 \beta_{1} - 106 \beta_{2} + 6 \beta_{3} + 35 \beta_{4} - 58 \beta_{5} + 10 \beta_{6} - 19 \beta_{7} - 16 \beta_{8} + 40 \beta_{9} - 6 \beta_{10} + 20 \beta_{11} + 16 \beta_{12} + 20 \beta_{13} + 2 \beta_{14} + 8 \beta_{15} ) q^{32} + ( -24213 + 7668 \beta_{1} - 227 \beta_{2} + 40 \beta_{3} + 117 \beta_{4} + 58 \beta_{5} - 41 \beta_{6} + 26 \beta_{7} - 53 \beta_{8} + 49 \beta_{9} + 25 \beta_{10} - 4 \beta_{11} - 45 \beta_{12} + 142 \beta_{13} - 5 \beta_{14} - 9 \beta_{15} ) q^{34} + ( 9846 - 12971 \beta_{1} + 367 \beta_{2} - 41 \beta_{3} + 286 \beta_{4} + 14 \beta_{5} + 8 \beta_{6} - 35 \beta_{7} + 76 \beta_{8} + 41 \beta_{9} + 30 \beta_{10} - 73 \beta_{11} + 71 \beta_{12} + 31 \beta_{13} - 26 \beta_{14} - 47 \beta_{15} ) q^{35} + ( -20829 + 5539 \beta_{1} - 21 \beta_{2} - 14 \beta_{3} + 397 \beta_{4} + 68 \beta_{5} + 9 \beta_{6} - 9 \beta_{7} + 15 \beta_{8} + 146 \beta_{9} - 2 \beta_{10} - 65 \beta_{11} - 96 \beta_{12} + 72 \beta_{13} - 7 \beta_{14} - 30 \beta_{15} ) q^{37} + ( -14758 - 14974 \beta_{1} + 218 \beta_{2} - 221 \beta_{3} - 200 \beta_{4} + 63 \beta_{5} - 7 \beta_{6} - 77 \beta_{7} - 84 \beta_{8} + 99 \beta_{9} - 24 \beta_{10} - 134 \beta_{11} + 12 \beta_{12} + 184 \beta_{13} + 62 \beta_{14} + 29 \beta_{15} ) q^{38} + ( -14374 + 3317 \beta_{1} - 700 \beta_{2} - 42 \beta_{3} + 970 \beta_{4} + 32 \beta_{5} - 59 \beta_{6} - 25 \beta_{7} - 20 \beta_{8} + 138 \beta_{9} - 74 \beta_{10} - 154 \beta_{11} + 78 \beta_{12} - 3 \beta_{13} + 55 \beta_{14} - 42 \beta_{15} ) q^{40} + ( -38117 - 8031 \beta_{1} + 186 \beta_{2} - 118 \beta_{3} - 166 \beta_{4} - 123 \beta_{5} + 9 \beta_{6} - 84 \beta_{7} - 38 \beta_{8} - 379 \beta_{9} - 123 \beta_{10} - 54 \beta_{11} - 22 \beta_{12} - 96 \beta_{13} - 29 \beta_{14} - 52 \beta_{15} ) q^{41} + ( -93992 + 11917 \beta_{1} - 807 \beta_{2} - 6 \beta_{3} - 194 \beta_{4} - 13 \beta_{5} + 67 \beta_{6} - 173 \beta_{7} - 70 \beta_{8} + 30 \beta_{9} - 73 \beta_{10} + 47 \beta_{11} + 180 \beta_{12} - 142 \beta_{13} - 72 \beta_{14} + 10 \beta_{15} ) q^{43} + ( -14557 - 4839 \beta_{1} - 1604 \beta_{2} - 120 \beta_{3} + 329 \beta_{4} + 156 \beta_{5} - 38 \beta_{6} - 28 \beta_{7} - 20 \beta_{8} + 44 \beta_{9} - 60 \beta_{10} - 41 \beta_{11} - 92 \beta_{12} - 174 \beta_{13} + 85 \beta_{14} + 53 \beta_{15} ) q^{44} + ( 51875 + 6443 \beta_{1} + 469 \beta_{2} + 139 \beta_{3} + 1062 \beta_{4} - 65 \beta_{5} - 212 \beta_{6} - 3 \beta_{7} + 218 \beta_{8} + 290 \beta_{9} + 77 \beta_{10} + 98 \beta_{11} - 46 \beta_{12} - 90 \beta_{13} - 88 \beta_{14} - 3 \beta_{15} ) q^{46} + ( 105509 - 20309 \beta_{1} - 2207 \beta_{2} + 149 \beta_{3} + 1235 \beta_{4} + 199 \beta_{5} - 42 \beta_{6} - 71 \beta_{7} + 215 \beta_{8} + 254 \beta_{9} + 223 \beta_{10} + 222 \beta_{11} - \beta_{12} + 43 \beta_{13} - 36 \beta_{14} - 133 \beta_{15} ) q^{47} + ( 118775 - 980 \beta_{1} + 731 \beta_{2} + 11 \beta_{3} - 73 \beta_{4} + 156 \beta_{5} + 81 \beta_{6} - 187 \beta_{7} + 94 \beta_{8} + 630 \beta_{9} + 145 \beta_{10} + 20 \beta_{11} + 5 \beta_{12} - 161 \beta_{13} + 47 \beta_{14} + 85 \beta_{15} ) q^{49} + ( -23630 + 9196 \beta_{1} - 4419 \beta_{2} + 107 \beta_{3} + 1342 \beta_{4} - 45 \beta_{5} - 191 \beta_{6} + 255 \beta_{7} - 299 \beta_{8} - 205 \beta_{9} - 24 \beta_{10} + 209 \beta_{11} - 251 \beta_{12} - 88 \beta_{13} - 72 \beta_{14} - 57 \beta_{15} ) q^{50} + ( -317278 + 15682 \beta_{1} - 1827 \beta_{2} - 88 \beta_{3} + 303 \beta_{4} - 115 \beta_{5} - 56 \beta_{6} + 168 \beta_{7} - 445 \beta_{8} - 343 \beta_{9} - 82 \beta_{10} + 40 \beta_{11} - 387 \beta_{12} + 123 \beta_{13} + 84 \beta_{14} - 32 \beta_{15} ) q^{52} + ( -30712 - 18819 \beta_{1} - 2750 \beta_{2} + 440 \beta_{3} + 1836 \beta_{4} + 50 \beta_{5} + 139 \beta_{6} + 65 \beta_{7} + 252 \beta_{8} + 207 \beta_{9} + 145 \beta_{10} + 182 \beta_{11} - 2 \beta_{12} - 30 \beta_{13} - 132 \beta_{14} + 118 \beta_{15} ) q^{53} + ( -294432 + 14476 \beta_{1} + 257 \beta_{2} + 315 \beta_{3} - 574 \beta_{4} - 53 \beta_{5} + 212 \beta_{6} - 51 \beta_{7} + 83 \beta_{8} + 187 \beta_{9} - 93 \beta_{10} + 73 \beta_{11} - 11 \beta_{12} - 351 \beta_{13} - 19 \beta_{14} - 315 \beta_{15} ) q^{55} + ( 364649 - 9102 \beta_{1} - 2139 \beta_{2} - 202 \beta_{3} + 1762 \beta_{4} + 62 \beta_{5} - 292 \beta_{6} - 277 \beta_{7} - 16 \beta_{8} + 232 \beta_{9} - 242 \beta_{10} - 201 \beta_{11} + 232 \beta_{12} - 782 \beta_{13} + 115 \beta_{14} - 11 \beta_{15} ) q^{56} + ( -430877 - 17438 \beta_{1} - 3686 \beta_{2} - 378 \beta_{3} + 284 \beta_{4} + 589 \beta_{5} - 6 \beta_{6} - 60 \beta_{7} + 280 \beta_{8} + 171 \beta_{9} + 216 \beta_{10} + 264 \beta_{11} - 288 \beta_{12} + 133 \beta_{13} + 373 \beta_{14} + 295 \beta_{15} ) q^{58} -205379 q^{59} + ( -386219 + 9867 \beta_{1} + 56 \beta_{2} - 500 \beta_{3} - 667 \beta_{4} - 512 \beta_{5} - 202 \beta_{6} + 100 \beta_{7} - 67 \beta_{8} - 221 \beta_{9} - 291 \beta_{10} - 372 \beta_{11} + 440 \beta_{12} - 848 \beta_{13} + 180 \beta_{14} - 198 \beta_{15} ) q^{61} + ( 737550 - 37632 \beta_{1} + 3802 \beta_{2} + 220 \beta_{3} - 901 \beta_{4} - 485 \beta_{5} + 509 \beta_{6} - 237 \beta_{7} - 266 \beta_{8} + 206 \beta_{9} - 85 \beta_{10} - 348 \beta_{11} - 90 \beta_{12} + 269 \beta_{13} + 547 \beta_{14} + 139 \beta_{15} ) q^{62} + ( -1191377 - 3508 \beta_{1} - 5760 \beta_{2} + 373 \beta_{3} - 138 \beta_{4} - 266 \beta_{5} + 242 \beta_{6} + 432 \beta_{7} - 222 \beta_{8} - 266 \beta_{9} + 108 \beta_{10} + 202 \beta_{11} - 182 \beta_{12} + 192 \beta_{13} + 504 \beta_{14} + 318 \beta_{15} ) q^{64} + ( 346608 - 39465 \beta_{1} - 1883 \beta_{2} - 551 \beta_{3} + 2002 \beta_{4} - 303 \beta_{5} + 195 \beta_{6} - 84 \beta_{7} - 62 \beta_{8} + 432 \beta_{9} - 729 \beta_{10} - 842 \beta_{11} + 733 \beta_{12} - 479 \beta_{13} + 750 \beta_{14} - 131 \beta_{15} ) q^{65} + ( -1018619 - 34597 \beta_{1} + 118 \beta_{2} - 655 \beta_{3} - 766 \beta_{4} + 721 \beta_{5} - 163 \beta_{6} - 47 \beta_{7} + 207 \beta_{8} + 318 \beta_{9} - 298 \beta_{10} - 371 \beta_{11} - 43 \beta_{12} + 577 \beta_{13} - 47 \beta_{14} + 137 \beta_{15} ) q^{67} + ( 1093752 - 30501 \beta_{1} + 5203 \beta_{2} + 587 \beta_{3} - 934 \beta_{4} + 710 \beta_{5} - 149 \beta_{6} + 433 \beta_{7} + 466 \beta_{8} + 1883 \beta_{9} + 991 \beta_{10} + 577 \beta_{11} - 482 \beta_{12} + 1796 \beta_{13} - 145 \beta_{14} + 51 \beta_{15} ) q^{68} + ( -2472995 + 56644 \beta_{1} - 13976 \beta_{2} + 1606 \beta_{3} + 690 \beta_{4} - 970 \beta_{5} + 885 \beta_{6} - 230 \beta_{7} - 1189 \beta_{8} - 2179 \beta_{9} - 167 \beta_{10} - 125 \beta_{11} - 177 \beta_{12} + 650 \beta_{13} - 48 \beta_{14} + 92 \beta_{15} ) q^{70} + ( 680947 - 12116 \beta_{1} - 5457 \beta_{2} + 1339 \beta_{3} + 4414 \beta_{4} - 1343 \beta_{5} + 1399 \beta_{6} - 281 \beta_{7} - 753 \beta_{8} - 1766 \beta_{9} - 226 \beta_{10} - 226 \beta_{11} - 753 \beta_{12} - 585 \beta_{13} - 124 \beta_{14} + 167 \beta_{15} ) q^{71} + ( -1328867 + 25474 \beta_{1} - 6451 \beta_{2} + 557 \beta_{3} + 1803 \beta_{4} + 158 \beta_{5} - 712 \beta_{6} + 181 \beta_{7} + 429 \beta_{8} + 257 \beta_{9} - 135 \beta_{10} + 358 \beta_{11} + 271 \beta_{12} + 119 \beta_{13} - 739 \beta_{14} - 565 \beta_{15} ) q^{73} + ( 1046161 - 2540 \beta_{1} + 1917 \beta_{2} + 2188 \beta_{3} - 2667 \beta_{4} - 235 \beta_{5} + 832 \beta_{6} + 1748 \beta_{7} - 440 \beta_{8} + 31 \beta_{9} + 1144 \beta_{10} + 1455 \beta_{11} - 1464 \beta_{12} + 1389 \beta_{13} + 198 \beta_{14} + 24 \beta_{15} ) q^{74} + ( -2558134 + 7170 \beta_{1} - 12403 \beta_{2} + 2258 \beta_{3} - 1677 \beta_{4} + 167 \beta_{5} + 1226 \beta_{6} + 160 \beta_{7} - 331 \beta_{8} + 540 \beta_{9} + 257 \beta_{10} + 683 \beta_{11} - 555 \beta_{12} + 1520 \beta_{13} + 686 \beta_{14} + 29 \beta_{15} ) q^{76} + ( 216064 - 9652 \beta_{1} - 6385 \beta_{2} + 1350 \beta_{3} + 1142 \beta_{4} + 92 \beta_{5} + 71 \beta_{6} - 633 \beta_{7} - 511 \beta_{8} - 856 \beta_{9} + 386 \beta_{10} + 995 \beta_{11} - 364 \beta_{12} + 1644 \beta_{13} - 379 \beta_{14} + 670 \beta_{15} ) q^{77} + ( -209482 - 66750 \beta_{1} + 3869 \beta_{2} - 1154 \beta_{3} - 2484 \beta_{4} - 1050 \beta_{5} - 303 \beta_{6} - 119 \beta_{7} + 952 \beta_{8} - 163 \beta_{9} - 487 \beta_{10} - 491 \beta_{11} + 1176 \beta_{12} + 188 \beta_{13} - 763 \beta_{14} + 904 \beta_{15} ) q^{79} + ( 1727817 - 23662 \beta_{1} + 2617 \beta_{2} - 383 \beta_{3} - 1623 \beta_{4} + 213 \beta_{5} - 802 \beta_{6} + 309 \beta_{7} + 557 \beta_{8} - 1649 \beta_{9} + 368 \beta_{10} + 1185 \beta_{11} - 249 \beta_{12} + 841 \beta_{13} - 737 \beta_{14} + 79 \beta_{15} ) q^{80} + ( -1550026 - 41754 \beta_{1} - 13695 \beta_{2} - 887 \beta_{3} + 5713 \beta_{4} - 209 \beta_{5} - 1139 \beta_{6} - 459 \beta_{7} + 2042 \beta_{8} - 19 \beta_{9} - 454 \beta_{10} - 123 \beta_{11} + 2270 \beta_{12} - 3872 \beta_{13} - 359 \beta_{14} - 388 \beta_{15} ) q^{82} + ( 108681 + 30161 \beta_{1} - 2422 \beta_{2} - 3368 \beta_{3} + 3210 \beta_{4} + 41 \beta_{5} - 1807 \beta_{6} + 234 \beta_{7} - 854 \beta_{8} - 613 \beta_{9} - 2327 \beta_{10} - 2878 \beta_{11} + 2292 \beta_{12} - 2366 \beta_{13} + 341 \beta_{14} - 502 \beta_{15} ) q^{83} + ( -1426791 - 57033 \beta_{1} + 6025 \beta_{2} + 704 \beta_{3} - 8550 \beta_{4} - 1054 \beta_{5} + 1779 \beta_{6} - 484 \beta_{7} - 269 \beta_{8} - 1232 \beta_{9} + 440 \beta_{10} - 214 \beta_{11} + 88 \beta_{12} + 1452 \beta_{13} - 438 \beta_{14} + 582 \beta_{15} ) q^{85} + ( 2315364 - 174324 \beta_{1} + 14369 \beta_{2} - 2184 \beta_{3} - 7287 \beta_{4} + 764 \beta_{5} + 828 \beta_{6} - 1842 \beta_{7} + 1302 \beta_{8} - 1728 \beta_{9} + 12 \beta_{10} - 927 \beta_{11} + 1102 \beta_{12} - 522 \beta_{13} + 855 \beta_{14} + 1269 \beta_{15} ) q^{86} + ( -1688029 - 140269 \beta_{1} - 5813 \beta_{2} + 39 \beta_{3} - 1629 \beta_{4} + 106 \beta_{5} + 598 \beta_{6} - 632 \beta_{7} - 870 \beta_{8} - 2556 \beta_{9} + 826 \beta_{10} + 1029 \beta_{11} - 1650 \beta_{12} + 26 \beta_{13} + 241 \beta_{14} + 855 \beta_{15} ) q^{88} + ( -642950 - 31348 \beta_{1} + 1116 \beta_{2} - 1367 \beta_{3} + 1029 \beta_{4} + 1090 \beta_{5} - 830 \beta_{6} + 424 \beta_{7} + 3038 \beta_{8} - 239 \beta_{9} - 924 \beta_{10} - 501 \beta_{11} + 3135 \beta_{12} - 2365 \beta_{13} - 1418 \beta_{14} - 785 \beta_{15} ) q^{89} + ( 106518 - 172430 \beta_{1} - 882 \beta_{2} - 818 \beta_{3} + 7029 \beta_{4} + 967 \beta_{5} - 3731 \beta_{6} + 988 \beta_{7} + 1551 \beta_{8} + 3065 \beta_{9} - 360 \beta_{10} + 769 \beta_{11} + 308 \beta_{12} + 54 \beta_{13} + 714 \beta_{14} - 32 \beta_{15} ) q^{91} + ( 1216284 + 115470 \beta_{1} + 12313 \beta_{2} + 1304 \beta_{3} - 6549 \beta_{4} - 2107 \beta_{5} - 84 \beta_{6} + 36 \beta_{7} + 283 \beta_{8} - 5428 \beta_{9} - 209 \beta_{10} + 97 \beta_{11} - 733 \beta_{12} + 410 \beta_{13} - 2500 \beta_{14} - 1893 \beta_{15} ) q^{92} + ( -3686652 - 65779 \beta_{1} - 23447 \beta_{2} - 3608 \beta_{3} + 4694 \beta_{4} + 2020 \beta_{5} - 896 \beta_{6} + 536 \beta_{7} - 2393 \beta_{8} - 5140 \beta_{9} + 516 \beta_{10} - 683 \beta_{11} - 1857 \beta_{12} + 2872 \beta_{13} - 1866 \beta_{14} - 938 \beta_{15} ) q^{94} + ( 1789684 + 105868 \beta_{1} + 422 \beta_{2} - 2008 \beta_{3} + 3584 \beta_{4} + 4053 \beta_{5} - 6239 \beta_{6} - 501 \beta_{7} + 2186 \beta_{8} + 5845 \beta_{9} + 459 \beta_{10} + 2035 \beta_{11} + 60 \beta_{12} - 1960 \beta_{13} - 2648 \beta_{14} + 320 \beta_{15} ) q^{95} + ( -1504208 - 198778 \beta_{1} - 18212 \beta_{2} + 1005 \beta_{3} + 11283 \beta_{4} + 438 \beta_{5} + 264 \beta_{6} - 1150 \beta_{7} - 1885 \beta_{8} - 438 \beta_{9} + 427 \beta_{10} - 1835 \beta_{11} + 2793 \beta_{12} - 2651 \beta_{13} - 206 \beta_{14} - 1015 \beta_{15} ) q^{97} + ( -221055 + 237718 \beta_{1} - 11120 \beta_{2} + 3418 \beta_{3} - 16786 \beta_{4} - 2408 \beta_{5} + 3387 \beta_{6} + 1335 \beta_{7} - 2639 \beta_{8} - 4935 \beta_{9} - 725 \beta_{10} + 614 \beta_{11} - 343 \beta_{12} - 2032 \beta_{13} + 31 \beta_{14} + 487 \beta_{15} ) q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$16q + 6q^{2} + 974q^{4} + 68q^{5} - 2343q^{7} - 819q^{8} + O(q^{10})$$ $$16q + 6q^{2} + 974q^{4} + 68q^{5} - 2343q^{7} - 819q^{8} - 3479q^{10} - 898q^{11} - 8172q^{13} + 13315q^{14} + 3138q^{16} + 44985q^{17} - 40137q^{19} - 130657q^{20} + 109394q^{22} + 2833q^{23} + 285746q^{25} + 129420q^{26} + 112890q^{28} - 144375q^{29} - 141759q^{31} + 36224q^{32} - 341332q^{34} + 78859q^{35} - 297971q^{37} - 329075q^{38} - 203048q^{40} - 659077q^{41} - 1431608q^{43} - 254916q^{44} + 873113q^{46} + 1574073q^{47} + 1893545q^{49} - 302533q^{50} - 4972548q^{52} - 587736q^{53} - 4624036q^{55} + 5798506q^{56} - 6991380q^{58} - 3286064q^{59} - 6117131q^{61} + 11570258q^{62} - 19063011q^{64} + 5335514q^{65} - 16518710q^{67} + 17284669q^{68} - 39189486q^{70} + 10882582q^{71} - 21097441q^{73} + 16717030q^{74} - 40864952q^{76} + 3404601q^{77} - 3784458q^{79} + 27466195q^{80} - 24990117q^{82} + 1951425q^{83} - 23238675q^{85} + 35910572q^{86} - 27843055q^{88} - 10499443q^{89} + 699217q^{91} + 20062766q^{92} - 59358988q^{94} + 29236333q^{95} - 25158976q^{97} - 2120460q^{98} + O(q^{100})$$
Basis of coefficient ring in terms of a root $$\nu$$ of $$x^{16} - 6 x^{15} - 1493 x^{14} + 8791 x^{13} + 890490 x^{12} - 5107725 x^{11} - 269092298 x^{10} + 1488374176 x^{9} + 42885295136 x^{8} - 226132003872 x^{7} - 3353576629440 x^{6} + 16796366777600 x^{5} + 99470801612800 x^{4} - 494039551757568 x^{3} - 493048066650624 x^{2} + 3193975642099712 x - 2385018853548032$$:
$$\beta_{0}$$ $$=$$ $$1$$ $$\beta_{1}$$ $$=$$ $$\nu$$ $$\beta_{2}$$ $$=$$ $$\nu^{2} - 189$$ $$\beta_{3}$$ $$=$$ $$\nu^{3} - 298 \nu + 67$$ $$\beta_{4}$$ $$=$$ $$($$$$-$$$$72\!\cdots\!81$$$$\nu^{15} -$$$$79\!\cdots\!72$$$$\nu^{14} +$$$$49\!\cdots\!17$$$$\nu^{13} +$$$$10\!\cdots\!15$$$$\nu^{12} +$$$$14\!\cdots\!20$$$$\nu^{11} -$$$$57\!\cdots\!15$$$$\nu^{10} -$$$$20\!\cdots\!52$$$$\nu^{9} +$$$$15\!\cdots\!68$$$$\nu^{8} +$$$$67\!\cdots\!68$$$$\nu^{7} -$$$$19\!\cdots\!64$$$$\nu^{6} -$$$$86\!\cdots\!32$$$$\nu^{5} +$$$$11\!\cdots\!64$$$$\nu^{4} +$$$$39\!\cdots\!32$$$$\nu^{3} -$$$$27\!\cdots\!36$$$$\nu^{2} -$$$$45\!\cdots\!44$$$$\nu +$$$$98\!\cdots\!76$$$$)/$$$$16\!\cdots\!20$$ $$\beta_{5}$$ $$=$$ $$($$$$-$$$$14\!\cdots\!49$$$$\nu^{15} -$$$$34\!\cdots\!24$$$$\nu^{14} +$$$$17\!\cdots\!69$$$$\nu^{13} +$$$$45\!\cdots\!99$$$$\nu^{12} -$$$$76\!\cdots\!24$$$$\nu^{11} -$$$$23\!\cdots\!23$$$$\nu^{10} +$$$$13\!\cdots\!60$$$$\nu^{9} +$$$$55\!\cdots\!00$$$$\nu^{8} -$$$$52\!\cdots\!20$$$$\nu^{7} -$$$$63\!\cdots\!16$$$$\nu^{6} -$$$$90\!\cdots\!80$$$$\nu^{5} +$$$$30\!\cdots\!12$$$$\nu^{4} +$$$$53\!\cdots\!96$$$$\nu^{3} -$$$$52\!\cdots\!12$$$$\nu^{2} -$$$$77\!\cdots\!96$$$$\nu +$$$$18\!\cdots\!64$$$$)/$$$$80\!\cdots\!16$$ $$\beta_{6}$$ $$=$$ $$($$$$36\!\cdots\!57$$$$\nu^{15} -$$$$43\!\cdots\!56$$$$\nu^{14} -$$$$55\!\cdots\!09$$$$\nu^{13} +$$$$60\!\cdots\!45$$$$\nu^{12} +$$$$34\!\cdots\!00$$$$\nu^{11} -$$$$33\!\cdots\!65$$$$\nu^{10} -$$$$10\!\cdots\!56$$$$\nu^{9} +$$$$91\!\cdots\!84$$$$\nu^{8} +$$$$17\!\cdots\!04$$$$\nu^{7} -$$$$12\!\cdots\!92$$$$\nu^{6} -$$$$15\!\cdots\!16$$$$\nu^{5} +$$$$87\!\cdots\!92$$$$\nu^{4} +$$$$51\!\cdots\!56$$$$\nu^{3} -$$$$23\!\cdots\!08$$$$\nu^{2} -$$$$47\!\cdots\!12$$$$\nu +$$$$12\!\cdots\!48$$$$)/$$$$16\!\cdots\!20$$ $$\beta_{7}$$ $$=$$ $$($$$$50\!\cdots\!83$$$$\nu^{15} +$$$$18\!\cdots\!96$$$$\nu^{14} -$$$$69\!\cdots\!11$$$$\nu^{13} -$$$$21\!\cdots\!25$$$$\nu^{12} +$$$$38\!\cdots\!20$$$$\nu^{11} +$$$$95\!\cdots\!05$$$$\nu^{10} -$$$$10\!\cdots\!04$$$$\nu^{9} -$$$$17\!\cdots\!84$$$$\nu^{8} +$$$$14\!\cdots\!36$$$$\nu^{7} +$$$$10\!\cdots\!72$$$$\nu^{6} -$$$$98\!\cdots\!84$$$$\nu^{5} +$$$$48\!\cdots\!88$$$$\nu^{4} +$$$$29\!\cdots\!84$$$$\nu^{3} -$$$$29\!\cdots\!32$$$$\nu^{2} -$$$$31\!\cdots\!68$$$$\nu +$$$$10\!\cdots\!52$$$$)/$$$$16\!\cdots\!20$$ $$\beta_{8}$$ $$=$$ $$($$$$-$$$$50\!\cdots\!91$$$$\nu^{15} +$$$$13\!\cdots\!68$$$$\nu^{14} +$$$$77\!\cdots\!47$$$$\nu^{13} -$$$$21\!\cdots\!15$$$$\nu^{12} -$$$$46\!\cdots\!20$$$$\nu^{11} +$$$$13\!\cdots\!35$$$$\nu^{10} +$$$$14\!\cdots\!88$$$$\nu^{9} -$$$$40\!\cdots\!92$$$$\nu^{8} -$$$$22\!\cdots\!52$$$$\nu^{7} +$$$$63\!\cdots\!76$$$$\nu^{6} +$$$$17\!\cdots\!88$$$$\nu^{5} -$$$$46\!\cdots\!56$$$$\nu^{4} -$$$$53\!\cdots\!28$$$$\nu^{3} +$$$$12\!\cdots\!04$$$$\nu^{2} +$$$$30\!\cdots\!16$$$$\nu -$$$$48\!\cdots\!64$$$$)/$$$$16\!\cdots\!20$$ $$\beta_{9}$$ $$=$$ $$($$$$11\!\cdots\!16$$$$\nu^{15} +$$$$14\!\cdots\!67$$$$\nu^{14} -$$$$15\!\cdots\!77$$$$\nu^{13} -$$$$14\!\cdots\!45$$$$\nu^{12} +$$$$90\!\cdots\!00$$$$\nu^{11} +$$$$43\!\cdots\!85$$$$\nu^{10} -$$$$25\!\cdots\!53$$$$\nu^{9} +$$$$16\!\cdots\!57$$$$\nu^{8} +$$$$38\!\cdots\!42$$$$\nu^{7} -$$$$27\!\cdots\!16$$$$\nu^{6} -$$$$28\!\cdots\!08$$$$\nu^{5} +$$$$41\!\cdots\!36$$$$\nu^{4} +$$$$85\!\cdots\!08$$$$\nu^{3} -$$$$16\!\cdots\!04$$$$\nu^{2} -$$$$61\!\cdots\!56$$$$\nu +$$$$10\!\cdots\!64$$$$)/$$$$25\!\cdots\!80$$ $$\beta_{10}$$ $$=$$ $$($$$$72\!\cdots\!59$$$$\nu^{15} +$$$$61\!\cdots\!88$$$$\nu^{14} -$$$$10\!\cdots\!23$$$$\nu^{13} -$$$$31\!\cdots\!25$$$$\nu^{12} +$$$$59\!\cdots\!80$$$$\nu^{11} -$$$$20\!\cdots\!95$$$$\nu^{10} -$$$$17\!\cdots\!12$$$$\nu^{9} +$$$$19\!\cdots\!88$$$$\nu^{8} +$$$$25\!\cdots\!28$$$$\nu^{7} -$$$$51\!\cdots\!64$$$$\nu^{6} -$$$$18\!\cdots\!32$$$$\nu^{5} +$$$$53\!\cdots\!84$$$$\nu^{4} +$$$$52\!\cdots\!52$$$$\nu^{3} -$$$$17\!\cdots\!16$$$$\nu^{2} -$$$$27\!\cdots\!84$$$$\nu +$$$$79\!\cdots\!16$$$$)/$$$$16\!\cdots\!20$$ $$\beta_{11}$$ $$=$$ $$($$$$-$$$$77\!\cdots\!87$$$$\nu^{15} -$$$$25\!\cdots\!84$$$$\nu^{14} +$$$$11\!\cdots\!39$$$$\nu^{13} +$$$$29\!\cdots\!65$$$$\nu^{12} -$$$$62\!\cdots\!60$$$$\nu^{11} -$$$$12\!\cdots\!65$$$$\nu^{10} +$$$$17\!\cdots\!76$$$$\nu^{9} +$$$$19\!\cdots\!96$$$$\nu^{8} -$$$$26\!\cdots\!24$$$$\nu^{7} -$$$$70\!\cdots\!68$$$$\nu^{6} +$$$$19\!\cdots\!76$$$$\nu^{5} -$$$$22\!\cdots\!92$$$$\nu^{4} -$$$$62\!\cdots\!16$$$$\nu^{3} +$$$$11\!\cdots\!88$$$$\nu^{2} +$$$$63\!\cdots\!52$$$$\nu -$$$$87\!\cdots\!08$$$$)/$$$$16\!\cdots\!20$$ $$\beta_{12}$$ $$=$$ $$($$$$-$$$$42\!\cdots\!39$$$$\nu^{15} -$$$$40\!\cdots\!68$$$$\nu^{14} +$$$$58\!\cdots\!43$$$$\nu^{13} +$$$$52\!\cdots\!05$$$$\nu^{12} -$$$$31\!\cdots\!40$$$$\nu^{11} -$$$$25\!\cdots\!45$$$$\nu^{10} +$$$$84\!\cdots\!52$$$$\nu^{9} +$$$$58\!\cdots\!92$$$$\nu^{8} -$$$$11\!\cdots\!68$$$$\nu^{7} -$$$$61\!\cdots\!56$$$$\nu^{6} +$$$$77\!\cdots\!12$$$$\nu^{5} +$$$$21\!\cdots\!76$$$$\nu^{4} -$$$$22\!\cdots\!12$$$$\nu^{3} -$$$$87\!\cdots\!84$$$$\nu^{2} +$$$$20\!\cdots\!64$$$$\nu -$$$$20\!\cdots\!96$$$$)/$$$$80\!\cdots\!60$$ $$\beta_{13}$$ $$=$$ $$($$$$-$$$$63\!\cdots\!26$$$$\nu^{15} -$$$$21\!\cdots\!27$$$$\nu^{14} +$$$$90\!\cdots\!92$$$$\nu^{13} +$$$$25\!\cdots\!85$$$$\nu^{12} -$$$$50\!\cdots\!85$$$$\nu^{11} -$$$$11\!\cdots\!80$$$$\nu^{10} +$$$$14\!\cdots\!83$$$$\nu^{9} +$$$$21\!\cdots\!18$$$$\nu^{8} -$$$$20\!\cdots\!32$$$$\nu^{7} -$$$$10\!\cdots\!84$$$$\nu^{6} +$$$$14\!\cdots\!88$$$$\nu^{5} -$$$$95\!\cdots\!36$$$$\nu^{4} -$$$$43\!\cdots\!48$$$$\nu^{3} +$$$$63\!\cdots\!84$$$$\nu^{2} +$$$$31\!\cdots\!16$$$$\nu -$$$$41\!\cdots\!04$$$$)/$$$$10\!\cdots\!20$$ $$\beta_{14}$$ $$=$$ $$($$$$-$$$$13\!\cdots\!11$$$$\nu^{15} +$$$$26\!\cdots\!38$$$$\nu^{14} +$$$$20\!\cdots\!67$$$$\nu^{13} -$$$$42\!\cdots\!45$$$$\nu^{12} -$$$$11\!\cdots\!90$$$$\nu^{11} +$$$$26\!\cdots\!75$$$$\nu^{10} +$$$$35\!\cdots\!58$$$$\nu^{9} -$$$$82\!\cdots\!92$$$$\nu^{8} -$$$$57\!\cdots\!52$$$$\nu^{7} +$$$$13\!\cdots\!76$$$$\nu^{6} +$$$$46\!\cdots\!08$$$$\nu^{5} -$$$$10\!\cdots\!56$$$$\nu^{4} -$$$$15\!\cdots\!68$$$$\nu^{3} +$$$$32\!\cdots\!24$$$$\nu^{2} +$$$$12\!\cdots\!36$$$$\nu -$$$$22\!\cdots\!24$$$$)/$$$$20\!\cdots\!40$$ $$\beta_{15}$$ $$=$$ $$($$$$69\!\cdots\!33$$$$\nu^{15} -$$$$51\!\cdots\!59$$$$\nu^{14} -$$$$10\!\cdots\!11$$$$\nu^{13} +$$$$70\!\cdots\!20$$$$\nu^{12} +$$$$67\!\cdots\!15$$$$\nu^{11} -$$$$37\!\cdots\!35$$$$\nu^{10} -$$$$21\!\cdots\!09$$$$\nu^{9} +$$$$99\!\cdots\!06$$$$\nu^{8} +$$$$36\!\cdots\!36$$$$\nu^{7} -$$$$13\!\cdots\!08$$$$\nu^{6} -$$$$31\!\cdots\!64$$$$\nu^{5} +$$$$80\!\cdots\!68$$$$\nu^{4} +$$$$10\!\cdots\!84$$$$\nu^{3} -$$$$20\!\cdots\!32$$$$\nu^{2} -$$$$89\!\cdots\!08$$$$\nu +$$$$11\!\cdots\!92$$$$)/$$$$10\!\cdots\!20$$
$$1$$ $$=$$ $$\beta_0$$ $$\nu$$ $$=$$ $$\beta_{1}$$ $$\nu^{2}$$ $$=$$ $$\beta_{2} + 189$$ $$\nu^{3}$$ $$=$$ $$\beta_{3} + 298 \beta_{1} - 67$$ $$\nu^{4}$$ $$=$$ $$-\beta_{15} - 4 \beta_{14} + 4 \beta_{13} + 3 \beta_{12} - 3 \beta_{11} + 2 \beta_{10} + 3 \beta_{9} + 3 \beta_{8} - 2 \beta_{7} - \beta_{6} - \beta_{5} - 19 \beta_{4} - 2 \beta_{3} + 387 \beta_{2} - 19 \beta_{1} + 56410$$ $$\nu^{5}$$ $$=$$ $$8 \beta_{15} + 2 \beta_{14} + 20 \beta_{13} + 16 \beta_{12} + 20 \beta_{11} - 6 \beta_{10} + 40 \beta_{9} - 16 \beta_{8} - 19 \beta_{7} + 10 \beta_{6} - 58 \beta_{5} + 35 \beta_{4} + 518 \beta_{3} - 106 \beta_{2} + 97227 \beta_{1} - 29763$$ $$\nu^{6}$$ $$=$$ $$-322 \beta_{15} - 2056 \beta_{14} + 2752 \beta_{13} + 1738 \beta_{12} - 1718 \beta_{11} + 1388 \beta_{10} + 1654 \beta_{9} + 1698 \beta_{8} - 848 \beta_{7} - 398 \beta_{6} - 906 \beta_{5} - 12298 \beta_{4} - 907 \beta_{3} + 143616 \beta_{2} - 15668 \beta_{1} + 18428719$$ $$\nu^{7}$$ $$=$$ $$3715 \beta_{15} + 1540 \beta_{14} + 14628 \beta_{13} + 11923 \beta_{12} + 7041 \beta_{11} - 7546 \beta_{10} + 30515 \beta_{9} - 12781 \beta_{8} - 13624 \beta_{7} + 5243 \beta_{6} - 36341 \beta_{5} + 25687 \beta_{4} + 218800 \beta_{3} - 49769 \beta_{2} + 33214587 \beta_{1} - 12727306$$ $$\nu^{8}$$ $$=$$ $$-54326 \beta_{15} - 837682 \beta_{14} + 1420036 \beta_{13} + 734014 \beta_{12} - 710438 \beta_{11} + 722166 \beta_{10} + 738550 \beta_{9} + 771358 \beta_{8} - 286527 \beta_{7} - 66320 \beta_{6} - 512220 \beta_{5} - 6123319 \beta_{4} - 241240 \beta_{3} + 53275788 \beta_{2} - 6922547 \beta_{1} + 6300524291$$ $$\nu^{9}$$ $$=$$ $$1081644 \beta_{15} + 1020800 \beta_{14} + 7884360 \beta_{13} + 6213940 \beta_{12} + 1058156 \beta_{11} - 5009772 \beta_{10} + 17333224 \beta_{9} - 7295620 \beta_{8} - 7331266 \beta_{7} + 1834072 \beta_{6} - 16583580 \beta_{5} + 13533134 \beta_{4} + 86669521 \beta_{3} - 16175238 \beta_{2} + 11689751028 \beta_{1} - 4947659831$$ $$\nu^{10}$$ $$=$$ $$9178535 \beta_{15} - 317171524 \beta_{14} + 657958388 \beta_{13} + 275901219 \beta_{12} - 259385355 \beta_{11} + 336047130 \beta_{10} + 308264147 \beta_{9} + 325066915 \beta_{8} - 83949594 \beta_{7} + 19910823 \beta_{6} - 243727129 \beta_{5} - 2768075571 \beta_{4} - 29133994 \beta_{3} + 19841524915 \beta_{2} - 2072757707 \beta_{1} + 2218326673922$$ $$\nu^{11}$$ $$=$$ $$192171720 \beta_{15} + 611574026 \beta_{14} + 3800835556 \beta_{13} + 2776451832 \beta_{12} - 369416716 \beta_{11} - 2662505174 \beta_{10} + 8697745536 \beta_{9} - 3626096648 \beta_{8} - 3496352747 \beta_{7} + 487732514 \beta_{6} - 6729436450 \beta_{5} + 6493743835 \beta_{4} + 33456096830 \beta_{3} - 4025081962 \beta_{2} + 4198394323443 \beta_{1} - 1752912931667$$ $$\nu^{12}$$ $$=$$ $$14484661278 \beta_{15} - 116815310624 \beta_{14} + 289230246224 \beta_{13} + 97765146802 \beta_{12} - 88736673590 \beta_{11} + 147941094428 \beta_{10} + 124943198350 \beta_{9} + 132108919402 \beta_{8} - 20221237448 \beta_{7} + 25572353802 \beta_{6} - 106658166258 \beta_{5} - 1191879523154 \beta_{4} + 14768573773 \beta_{3} + 7420591546960 \beta_{2} - 311700004700 \beta_{1} + 796832833506959$$ $$\nu^{13}$$ $$=$$ $$-21120806365 \beta_{15} + 332609278476 \beta_{14} + 1734027120372 \beta_{13} + 1141712395035 \beta_{12} - 429566174527 \beta_{11} - 1267333743370 \beta_{10} + 4078194850923 \beta_{9} - 1669184390405 \beta_{8} - 1559118630512 \beta_{7} + 75884758643 \beta_{6} - 2580600494013 \beta_{5} + 3001940238351 \beta_{4} + 12776997190808 \beta_{3} - 574272081961 \beta_{2} + 1529257432641459 \beta_{1} - 570094464406250$$ $$\nu^{14}$$ $$=$$ $$9321682989434 \beta_{15} - 42615689960586 \beta_{14} + 123413715766356 \beta_{13} + 33342192214390 \beta_{12} - 29070197630774 \beta_{11} + 63088856352646 \beta_{10} + 49897316740638 \beta_{9} + 52566842529846 \beta_{8} - 2844933629239 \beta_{7} + 16261067736600 \beta_{6} - 44553716705652 \beta_{5} - 498779313344495 \beta_{4} + 15193934723680 \beta_{3} + 2785776883737756 \beta_{2} + 124691688780213 \beta_{1} + 290243769849439443$$ $$\nu^{15}$$ $$=$$ $$-43827714804276 \beta_{15} + 167484351779752 \beta_{14} + 765851434829912 \beta_{13} + 446629910493564 \beta_{12} - 262328813562644 \beta_{11} - 565726399182620 \beta_{10} + 1833434032720608 \beta_{9} - 731877362581724 \beta_{8} - 666505217257930 \beta_{7} - 18705578790416 \beta_{6} - 959151595388804 \beta_{5} + 1355259616083414 \beta_{4} + 4860395355063145 \beta_{3} + 152225579361114 \beta_{2} + 562659361261144860 \beta_{1} - 169125649025696791$$
Embeddings
For each embedding $$\iota_m$$ of the coefficient field, the values $$\iota_m(a_n)$$ are shown below.
For more information on an embedded modular form you can click on its label.
Label $$\iota_m(\nu)$$ $$a_{2}$$ $$a_{3}$$ $$a_{4}$$ $$a_{5}$$ $$a_{6}$$ $$a_{7}$$ $$a_{8}$$ $$a_{9}$$ $$a_{10}$$
1.1
−19.6562 −18.7189 −17.9442 −14.0604 −13.0039 −7.02227 −3.09726 1.05882 1.97136 4.55626 7.00808 14.7989 15.0467 16.2952 19.0314 19.7363
−19.6562 0 258.365 436.761 0 956.841 −2562.48 0 −8585.06
1.2 −18.7189 0 222.398 −443.832 0 −1695.79 −1767.03 0 8308.06
1.3 −17.9442 0 193.993 −1.22320 0 −719.259 −1184.20 0 21.9494
1.4 −14.0604 0 69.6949 −153.219 0 −215.221 819.793 0 2154.32
1.5 −13.0039 0 41.1009 −167.303 0 887.373 1130.03 0 2175.59
1.6 −7.02227 0 −78.6878 266.773 0 665.758 1451.42 0 −1873.35
1.7 −3.09726 0 −118.407 156.435 0 11.3597 763.187 0 −484.520
1.8 1.05882 0 −126.879 −151.597 0 −1574.54 −269.870 0 −160.513
1.9 1.97136 0 −124.114 339.775 0 364.700 −497.007 0 669.820
1.10 4.55626 0 −107.241 540.445 0 −1238.10 −1071.82 0 2462.40
1.11 7.00808 0 −78.8868 −449.079 0 −271.717 −1449.88 0 −3147.18
1.12 14.7989 0 91.0084 296.536 0 −1410.76 −547.437 0 4388.42
1.13 15.0467 0 98.4026 −159.890 0 980.332 −445.343 0 −2405.81
1.14 16.2952 0 137.534 −495.569 0 565.301 155.363 0 −8075.41
1.15 19.0314 0 234.195 −37.6075 0 1158.54 2021.05 0 −715.724
1.16 19.7363 0 261.522 90.5952 0 −807.818 2635.23 0 1788.01
$$n$$: e.g. 2-40 or 990-1000 Embeddings: e.g. 1-3 or 1.16 Significant digits: Format: Complex embeddings Normalized embeddings Satake parameters Satake angles
Atkin-Lehner signs
$$p$$ Sign
$$3$$ $$-1$$
$$59$$ $$1$$
Inner twists
This newform does not admit any (nontrivial) inner twists.
Twists
By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 531.8.a.b 16
3.b odd 2 1 177.8.a.a 16
By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
177.8.a.a 16 3.b odd 2 1
531.8.a.b 16 1.a even 1 1 trivial
Hecke kernels
This newform subspace can be constructed as the kernel of the linear operator $$33\!\cdots\!40$$$$T_{2}^{6} +$$$$16\!\cdots\!00$$$$T_{2}^{5} +$$$$99\!\cdots\!00$$$$T_{2}^{4} -$$$$49\!\cdots\!68$$$$T_{2}^{3} -$$$$49\!\cdots\!24$$$$T_{2}^{2} +$$$$31\!\cdots\!12$$$$T_{2} -$$$$23\!\cdots\!32$$">$$T_{2}^{16} - \cdots$$ acting on $$S_{8}^{\mathrm{new}}(\Gamma_0(531))$$.
Hecke characteristic polynomials
$p$ $F_p(T)$
$2$ $$-2385018853548032 + 3193975642099712 T - 493048066650624 T^{2} - 494039551757568 T^{3} + 99470801612800 T^{4} + 16796366777600 T^{5} - 3353576629440 T^{6} - 226132003872 T^{7} + 42885295136 T^{8} + 1488374176 T^{9} - 269092298 T^{10} - 5107725 T^{11} + 890490 T^{12} + 8791 T^{13} - 1493 T^{14} - 6 T^{15} + T^{16}$$
$3$ $$T^{16}$$
$5$ $$-$$$$25\!\cdots\!00$$$$-$$$$21\!\cdots\!00$$$$T -$$$$55\!\cdots\!00$$$$T^{2} +$$$$39\!\cdots\!00$$$$T^{3} +$$$$11\!\cdots\!50$$$$T^{4} -$$$$11\!\cdots\!50$$$$T^{5} -$$$$71\!\cdots\!25$$$$T^{6} -$$$$30\!\cdots\!20$$$$T^{7} +$$$$20\!\cdots\!29$$$$T^{8} + 1276883506994508700 T^{9} - 30163601555694730 T^{10} - 12282106911840 T^{11} + 220666998180 T^{12} + 47355522 T^{13} - 765561 T^{14} - 68 T^{15} + T^{16}$$
$7$ $$23\!\cdots\!80$$$$-$$$$20\!\cdots\!76$$$$T -$$$$81\!\cdots\!16$$$$T^{2} +$$$$45\!\cdots\!48$$$$T^{3} +$$$$12\!\cdots\!53$$$$T^{4} -$$$$40\!\cdots\!35$$$$T^{5} -$$$$52\!\cdots\!76$$$$T^{6} +$$$$15\!\cdots\!17$$$$T^{7} +$$$$10\!\cdots\!28$$$$T^{8} -$$$$27\!\cdots\!71$$$$T^{9} - 13028951743237034522 T^{10} + 25724670378028207 T^{11} + 10148751808072 T^{12} - 12238111473 T^{13} - 4790292 T^{14} + 2343 T^{15} + T^{16}$$
$11$ $$-$$$$51\!\cdots\!72$$$$-$$$$57\!\cdots\!12$$$$T +$$$$72\!\cdots\!08$$$$T^{2} +$$$$11\!\cdots\!00$$$$T^{3} +$$$$63\!\cdots\!83$$$$T^{4} -$$$$40\!\cdots\!30$$$$T^{5} -$$$$99\!\cdots\!68$$$$T^{6} +$$$$62\!\cdots\!82$$$$T^{7} +$$$$20\!\cdots\!35$$$$T^{8} -$$$$46\!\cdots\!60$$$$T^{9} -$$$$18\!\cdots\!28$$$$T^{10} + 16194688134834128320 T^{11} + 7779298719542601 T^{12} - 220257477422 T^{13} - 148053196 T^{14} + 898 T^{15} + T^{16}$$
$13$ $$25\!\cdots\!00$$$$-$$$$31\!\cdots\!80$$$$T -$$$$70\!\cdots\!90$$$$T^{2} +$$$$97\!\cdots\!14$$$$T^{3} +$$$$15\!\cdots\!63$$$$T^{4} -$$$$83\!\cdots\!66$$$$T^{5} -$$$$13\!\cdots\!18$$$$T^{6} +$$$$31\!\cdots\!20$$$$T^{7} +$$$$49\!\cdots\!63$$$$T^{8} -$$$$63\!\cdots\!28$$$$T^{9} -$$$$93\!\cdots\!98$$$$T^{10} +$$$$67\!\cdots\!06$$$$T^{11} + 95656696630982041 T^{12} - 3704745067846 T^{13} - 492040454 T^{14} + 8172 T^{15} + T^{16}$$
$17$ $$-$$$$41\!\cdots\!40$$$$-$$$$11\!\cdots\!12$$$$T +$$$$74\!\cdots\!92$$$$T^{2} +$$$$10\!\cdots\!88$$$$T^{3} -$$$$52\!\cdots\!27$$$$T^{4} -$$$$97\!\cdots\!33$$$$T^{5} +$$$$14\!\cdots\!94$$$$T^{6} -$$$$74\!\cdots\!67$$$$T^{7} -$$$$11\!\cdots\!92$$$$T^{8} +$$$$92\!\cdots\!87$$$$T^{9} +$$$$28\!\cdots\!08$$$$T^{10} -$$$$39\!\cdots\!49$$$$T^{11} + 45590257642588608 T^{12} + 71095321312497 T^{13} - 1070737138 T^{14} - 44985 T^{15} + T^{16}$$
$19$ $$-$$$$23\!\cdots\!20$$$$-$$$$64\!\cdots\!60$$$$T +$$$$36\!\cdots\!76$$$$T^{2} +$$$$16\!\cdots\!20$$$$T^{3} +$$$$79\!\cdots\!00$$$$T^{4} -$$$$15\!\cdots\!20$$$$T^{5} -$$$$18\!\cdots\!13$$$$T^{6} +$$$$57\!\cdots\!89$$$$T^{7} +$$$$10\!\cdots\!35$$$$T^{8} -$$$$10\!\cdots\!70$$$$T^{9} -$$$$21\!\cdots\!09$$$$T^{10} +$$$$86\!\cdots\!59$$$$T^{11} + 19674435440125746613 T^{12} - 312748284754822 T^{13} - 7492545475 T^{14} + 40137 T^{15} + T^{16}$$
$23$ $$16\!\cdots\!80$$$$-$$$$29\!\cdots\!00$$$$T +$$$$17\!\cdots\!36$$$$T^{2} -$$$$10\!\cdots\!36$$$$T^{3} -$$$$25\!\cdots\!32$$$$T^{4} +$$$$82\!\cdots\!52$$$$T^{5} +$$$$56\!\cdots\!03$$$$T^{6} -$$$$61\!\cdots\!17$$$$T^{7} +$$$$50\!\cdots\!91$$$$T^{8} +$$$$16\!\cdots\!70$$$$T^{9} -$$$$24\!\cdots\!69$$$$T^{10} -$$$$18\!\cdots\!95$$$$T^{11} +$$$$43\!\cdots\!05$$$$T^{12} + 792812076231546 T^{13} - 33662419967 T^{14} - 2833 T^{15} + T^{16}$$
$29$ $$-$$$$67\!\cdots\!20$$$$-$$$$15\!\cdots\!92$$$$T -$$$$14\!\cdots\!08$$$$T^{2} -$$$$62\!\cdots\!16$$$$T^{3} -$$$$13\!\cdots\!94$$$$T^{4} -$$$$83\!\cdots\!96$$$$T^{5} +$$$$18\!\cdots\!41$$$$T^{6} +$$$$31\!\cdots\!31$$$$T^{7} +$$$$39\!\cdots\!69$$$$T^{8} -$$$$27\!\cdots\!30$$$$T^{9} -$$$$10\!\cdots\!63$$$$T^{10} +$$$$11\!\cdots\!85$$$$T^{11} +$$$$60\!\cdots\!51$$$$T^{12} - 20469385938299166 T^{13} - 131675926081 T^{14} + 144375 T^{15} + T^{16}$$
$31$ $$10\!\cdots\!60$$$$-$$$$10\!\cdots\!72$$$$T -$$$$21\!\cdots\!48$$$$T^{2} +$$$$14\!\cdots\!76$$$$T^{3} +$$$$15\!\cdots\!06$$$$T^{4} -$$$$65\!\cdots\!48$$$$T^{5} -$$$$54\!\cdots\!95$$$$T^{6} +$$$$13\!\cdots\!51$$$$T^{7} +$$$$97\!\cdots\!65$$$$T^{8} -$$$$14\!\cdots\!02$$$$T^{9} -$$$$95\!\cdots\!55$$$$T^{10} +$$$$81\!\cdots\!57$$$$T^{11} +$$$$51\!\cdots\!43$$$$T^{12} - 20197683250020434 T^{13} - 128454996345 T^{14} + 141759 T^{15} + T^{16}$$
$37$ $$-$$$$50\!\cdots\!84$$$$-$$$$10\!\cdots\!20$$$$T +$$$$65\!\cdots\!34$$$$T^{2} +$$$$16\!\cdots\!16$$$$T^{3} +$$$$31\!\cdots\!59$$$$T^{4} -$$$$77\!\cdots\!87$$$$T^{5} -$$$$24\!\cdots\!54$$$$T^{6} +$$$$15\!\cdots\!89$$$$T^{7} +$$$$53\!\cdots\!86$$$$T^{8} -$$$$15\!\cdots\!95$$$$T^{9} -$$$$56\!\cdots\!12$$$$T^{10} +$$$$85\!\cdots\!39$$$$T^{11} +$$$$31\!\cdots\!66$$$$T^{12} - 250272440202312489 T^{13} - 878197839972 T^{14} + 297971 T^{15} + T^{16}$$
$41$ $$-$$$$45\!\cdots\!00$$$$+$$$$15\!\cdots\!20$$$$T +$$$$37\!\cdots\!44$$$$T^{2} +$$$$13\!\cdots\!04$$$$T^{3} -$$$$13\!\cdots\!15$$$$T^{4} -$$$$86\!\cdots\!71$$$$T^{5} +$$$$89\!\cdots\!62$$$$T^{6} +$$$$14\!\cdots\!87$$$$T^{7} +$$$$80\!\cdots\!24$$$$T^{8} -$$$$11\!\cdots\!83$$$$T^{9} -$$$$12\!\cdots\!92$$$$T^{10} +$$$$44\!\cdots\!25$$$$T^{11} +$$$$61\!\cdots\!32$$$$T^{12} - 858512390358027885 T^{13} - 1278569786638 T^{14} + 659077 T^{15} + T^{16}$$
$43$ $$-$$$$10\!\cdots\!08$$$$-$$$$85\!\cdots\!12$$$$T +$$$$37\!\cdots\!48$$$$T^{2} +$$$$33\!\cdots\!68$$$$T^{3} -$$$$48\!\cdots\!83$$$$T^{4} -$$$$47\!\cdots\!16$$$$T^{5} +$$$$25\!\cdots\!86$$$$T^{6} +$$$$33\!\cdots\!04$$$$T^{7} -$$$$20\!\cdots\!01$$$$T^{8} -$$$$13\!\cdots\!76$$$$T^{9} -$$$$30\!\cdots\!32$$$$T^{10} +$$$$28\!\cdots\!16$$$$T^{11} +$$$$12\!\cdots\!87$$$$T^{12} - 3138661091232654520 T^{13} - 1825919654306 T^{14} + 1431608 T^{15} + T^{16}$$
$47$ $$-$$$$82\!\cdots\!24$$$$+$$$$18\!\cdots\!28$$$$T +$$$$48\!\cdots\!56$$$$T^{2} -$$$$26\!\cdots\!20$$$$T^{3} -$$$$18\!\cdots\!68$$$$T^{4} +$$$$22\!\cdots\!24$$$$T^{5} -$$$$35\!\cdots\!39$$$$T^{6} -$$$$77\!\cdots\!97$$$$T^{7} +$$$$31\!\cdots\!67$$$$T^{8} +$$$$14\!\cdots\!06$$$$T^{9} -$$$$73\!\cdots\!79$$$$T^{10} -$$$$14\!\cdots\!27$$$$T^{11} +$$$$82\!\cdots\!37$$$$T^{12} + 7529304337576894050 T^{13} - 4570866681065 T^{14} - 1574073 T^{15} + T^{16}$$
$53$ $$21\!\cdots\!48$$$$+$$$$10\!\cdots\!16$$$$T +$$$$12\!\cdots\!16$$$$T^{2} +$$$$33\!\cdots\!28$$$$T^{3} -$$$$13\!\cdots\!62$$$$T^{4} -$$$$61\!\cdots\!10$$$$T^{5} -$$$$51\!\cdots\!17$$$$T^{6} +$$$$22\!\cdots\!32$$$$T^{7} +$$$$14\!\cdots\!53$$$$T^{8} -$$$$32\!\cdots\!20$$$$T^{9} -$$$$29\!\cdots\!22$$$$T^{10} +$$$$21\!\cdots\!44$$$$T^{11} +$$$$23\!\cdots\!36$$$$T^{12} - 6276448053670807446 T^{13} - 8103424856601 T^{14} + 587736 T^{15} + T^{16}$$
$59$ $$( 205379 + T )^{16}$$
$61$ $$-$$$$45\!\cdots\!36$$$$+$$$$15\!\cdots\!72$$$$T +$$$$11\!\cdots\!72$$$$T^{2} -$$$$11\!\cdots\!24$$$$T^{3} -$$$$65\!\cdots\!86$$$$T^{4} +$$$$39\!\cdots\!92$$$$T^{5} +$$$$16\!\cdots\!41$$$$T^{6} -$$$$32\!\cdots\!85$$$$T^{7} -$$$$16\!\cdots\!11$$$$T^{8} -$$$$49\!\cdots\!50$$$$T^{9} +$$$$69\!\cdots\!45$$$$T^{10} +$$$$35\!\cdots\!65$$$$T^{11} -$$$$98\!\cdots\!93$$$$T^{12} - 82817544807912341990 T^{13} - 2914515679197 T^{14} + 6117131 T^{15} + T^{16}$$
$67$ $$35\!\cdots\!68$$$$+$$$$71\!\cdots\!84$$$$T +$$$$20\!\cdots\!68$$$$T^{2} +$$$$63\!\cdots\!12$$$$T^{3} -$$$$49\!\cdots\!56$$$$T^{4} -$$$$75\!\cdots\!68$$$$T^{5} -$$$$24\!\cdots\!95$$$$T^{6} +$$$$32\!\cdots\!94$$$$T^{7} +$$$$33\!\cdots\!05$$$$T^{8} +$$$$72\!\cdots\!28$$$$T^{9} -$$$$56\!\cdots\!86$$$$T^{10} -$$$$38\!\cdots\!12$$$$T^{11} -$$$$64\!\cdots\!50$$$$T^{12} +$$$$18\!\cdots\!84$$$$T^{13} + 99098156876413 T^{14} + 16518710 T^{15} + T^{16}$$
$71$ $$-$$$$74\!\cdots\!48$$$$+$$$$11\!\cdots\!72$$$$T +$$$$61\!\cdots\!22$$$$T^{2} -$$$$10\!\cdots\!74$$$$T^{3} -$$$$20\!\cdots\!63$$$$T^{4} +$$$$35\!\cdots\!88$$$$T^{5} +$$$$33\!\cdots\!28$$$$T^{6} -$$$$60\!\cdots\!70$$$$T^{7} -$$$$24\!\cdots\!45$$$$T^{8} +$$$$57\!\cdots\!56$$$$T^{9} +$$$$26\!\cdots\!26$$$$T^{10} -$$$$30\!\cdots\!98$$$$T^{11} +$$$$10\!\cdots\!07$$$$T^{12} +$$$$89\!\cdots\!20$$$$T^{13} - 58727757650844 T^{14} - 10882582 T^{15} + T^{16}$$
$73$ $$-$$$$69\!\cdots\!00$$$$-$$$$88\!\cdots\!60$$$$T +$$$$29\!\cdots\!56$$$$T^{2} +$$$$58\!\cdots\!88$$$$T^{3} +$$$$25\!\cdots\!92$$$$T^{4} -$$$$62\!\cdots\!12$$$$T^{5} -$$$$43\!\cdots\!11$$$$T^{6} +$$$$45\!\cdots\!17$$$$T^{7} +$$$$16\!\cdots\!27$$$$T^{8} +$$$$49\!\cdots\!54$$$$T^{9} -$$$$12\!\cdots\!99$$$$T^{10} -$$$$10\!\cdots\!77$$$$T^{11} -$$$$14\!\cdots\!75$$$$T^{12} +$$$$38\!\cdots\!74$$$$T^{13} + 160731807982939 T^{14} + 21097441 T^{15} + T^{16}$$
$79$ $$-$$$$49\!\cdots\!16$$$$-$$$$85\!\cdots\!68$$$$T -$$$$25\!\cdots\!88$$$$T^{2} +$$$$58\!\cdots\!84$$$$T^{3} +$$$$16\!\cdots\!67$$$$T^{4} -$$$$13\!\cdots\!58$$$$T^{5} -$$$$48\!\cdots\!88$$$$T^{6} +$$$$15\!\cdots\!02$$$$T^{7} +$$$$57\!\cdots\!55$$$$T^{8} -$$$$89\!\cdots\!04$$$$T^{9} -$$$$34\!\cdots\!12$$$$T^{10} +$$$$29\!\cdots\!08$$$$T^{11} +$$$$10\!\cdots\!81$$$$T^{12} -$$$$52\!\cdots\!18$$$$T^{13} - 164311559623024 T^{14} + 3784458 T^{15} + T^{16}$$
$83$ $$-$$$$91\!\cdots\!72$$$$+$$$$17\!\cdots\!56$$$$T -$$$$66\!\cdots\!44$$$$T^{2} -$$$$81\!\cdots\!48$$$$T^{3} +$$$$14\!\cdots\!07$$$$T^{4} +$$$$13\!\cdots\!51$$$$T^{5} -$$$$30\!\cdots\!24$$$$T^{6} -$$$$11\!\cdots\!87$$$$T^{7} +$$$$27\!\cdots\!30$$$$T^{8} +$$$$43\!\cdots\!03$$$$T^{9} -$$$$11\!\cdots\!98$$$$T^{10} -$$$$80\!\cdots\!81$$$$T^{11} +$$$$25\!\cdots\!82$$$$T^{12} +$$$$67\!\cdots\!61$$$$T^{13} - 256440516265952 T^{14} - 1951425 T^{15} + T^{16}$$
$89$ $$38\!\cdots\!60$$$$-$$$$54\!\cdots\!28$$$$T -$$$$45\!\cdots\!48$$$$T^{2} +$$$$25\!\cdots\!56$$$$T^{3} +$$$$10\!\cdots\!24$$$$T^{4} -$$$$39\!\cdots\!16$$$$T^{5} -$$$$11\!\cdots\!05$$$$T^{6} +$$$$29\!\cdots\!39$$$$T^{7} +$$$$61\!\cdots\!75$$$$T^{8} -$$$$11\!\cdots\!66$$$$T^{9} -$$$$18\!\cdots\!89$$$$T^{10} +$$$$25\!\cdots\!29$$$$T^{11} +$$$$31\!\cdots\!09$$$$T^{12} -$$$$26\!\cdots\!90$$$$T^{13} - 281604197712695 T^{14} + 10499443 T^{15} + T^{16}$$
$97$ $$16\!\cdots\!80$$$$+$$$$71\!\cdots\!20$$$$T -$$$$40\!\cdots\!24$$$$T^{2} -$$$$65\!\cdots\!60$$$$T^{3} -$$$$24\!\cdots\!92$$$$T^{4} +$$$$39\!\cdots\!36$$$$T^{5} +$$$$34\!\cdots\!31$$$$T^{6} +$$$$23\!\cdots\!80$$$$T^{7} -$$$$11\!\cdots\!91$$$$T^{8} -$$$$16\!\cdots\!40$$$$T^{9} +$$$$10\!\cdots\!38$$$$T^{10} +$$$$24\!\cdots\!16$$$$T^{11} +$$$$67\!\cdots\!02$$$$T^{12} -$$$$13\!\cdots\!12$$$$T^{13} - 372261609039309 T^{14} + 25158976 T^{15} + T^{16}$$
show more
show less | 2021-04-20 06:46:17 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9781821966171265, "perplexity": 8810.80637656281}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-17/segments/1618039379601.74/warc/CC-MAIN-20210420060507-20210420090507-00163.warc.gz"} |
https://qotd.hideoushumpbackfreak.com/2021/01/31/qotd.html | # 01/31/2021
…the most dazzling human achievements are, in fact, the aggregate of countless individual elements, each of which is, in a sense, ordinary.
— Angela Duckworth, Grit | 2021-05-15 21:44:56 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8002167344093323, "perplexity": 7728.7050677681145}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-21/segments/1620243991378.52/warc/CC-MAIN-20210515192444-20210515222444-00321.warc.gz"} |
https://proxies123.com/tag/processes/ | ## inequality – Convergence in probability and almost surely convergence for maximal empirical processes
For any $$n$$, let $$X_1, …, X_n$$ be i.i.d. random variables on the probability space $$(Omega, mathcal{F}, Pr)$$. Define
$$mu_n(A) = frac{1}{n} sum_{i=1}^n 1_{{X_i in A}}, \ mu(A) = Pr(X_1 in A).$$
Consider any $$mathcal{A} subset mathcal{F}$$, and define
$$g(X_1, …, X_n) := sup_{A in mathcal{A}} |mu_n(A) – mu(A)|$$
Prove that $$g(X_1, …, X_n)$$ converges in probability to $$0$$ if and only if $$g(X_1, …, X_n)$$ converges almost surely to $$0$$.
p/s: This problem is posed as an exercise in the book “Combinatorial methods in density estimation” by Luc Devroye and Gabor Lugosi (exercise 3.2 with a hint to use the bounded difference inequality). I have tried but could not solve it. Hopefully, someone could help. Thank you.
## bitcoincore development – What is the motivation behind Russell Yanofsky’s work to separate Bitcoin Core into independent node, wallet and GUI processes?
There are benefits to both users and developers to having Bitcoin Core split into separate node, wallet and GUI processes.
As Alyssa Hertig outlines here the benefit to users will be being able to run the Bitcoin Core node on a different machine to the Bitcoin Core wallet rather than being forced to run them on the same machine. A user could leave a node running continuously in the background but start and stop the wallets and the GUI as needed. It also opens up the prospect of using a different (i.e. not the Bitcoin Core) GUI or wallet with the Bitcoin Core node.
For Bitcoin Core developers, Yanofsky highlights maintainability and security as the key advantages.
Process separation will make Bitcoin Core more easily maintainable as it defines interfaces at process boundaries. Different parts of the code can interact by calling each other instead of sharing state. This helps code review by making it easier to identify dependencies between parts of the code. Defining boundaries in the codebase will also code review more scalable as reviewers will just need to understand part of the codebase well rather than needing to understand interdependencies across the whole codebase.
From a security perspective, the wallet and node code could run with different privileges and vulnerabilities should be harder to exploit given they will be limited to a single process. Inter-process communication (IPC) makes new debugging tools available such as the IPC_DEBUG environment variable to log all IPC calls.
There are some potential disadvantages that Yanofsky highlights. Inter-process communication is generally slower. IPC code can be tricky to write and may have bugs. Bad interfaces and unnecessary layers of abstraction can make it harder to implement new features. Features such as SPV (Simplified Payment Verification) that cross process boundaries will likely be more difficult to build.
Overall it seems clear the advantages outweigh the disadvantages. At the time of writing (August 2020) there are four remaining PRs to be reviewed and merged into Bitcoin Core and then Bitcoin Core should be multiprocess!
For more details on the process separation project see here.
## stochastic processes – On a degenerate SDE in the unit ball
This is a question about a diffusion process on the unit ball.
In this article J.S, the author considered the following SDE in the closed unit ball $$E subset mathbb{R}^n$$:
begin{align*} (1)quad dX_t=sqrt{2(1-|X_t|^2)},dB_t-cX_t,dt, end{align*}
where $${B_t}_{t ge 0}$$ is an $$n$$-dimensional Brownian motion, $$|cdot|$$ denotes the Euclidean norm on $$mathbb{R}^n$$ and $$c$$ is a nonnegative constant. We define an elliptic operator $$(mathcal{A},text{Dom}(mathcal{A}))$$ by $$mathcal{A}=C^2(mathbb{R}^n)|_E$$ and
begin{align*} mathcal{A}f=sqrt{2(1-|x|^2)}Delta f-c xcdot nabla f,quad f in text{Dom}(mathcal{A}). end{align*}
Then, standard results from martingale problems show that there exists a diffusion process $${X_t}_{t ge 0}$$ on $$E$$ such that
$$f(X_t)-f(x)-int_{0}^{t}mathcal{A}f(X_s),ds quad(t ge 0,, x in E)$$
is a martingale. Thus, the SDE $$(1)$$ possesses a solution. Furthermore, we can show that the solution is unique in the sense of distribution (by the way, the pathwise uniqueness for (1) is a very profound problem).
My question is as follows.
If $$c=0$$, then $$mathcal{A}$$ is a weighted Laplacian on $$E$$. However, we do not impose the Neumann boundary condition on $$mathcal{A}$$. Thus, the operator $$mathcal{A}$$ is not associated with a time-changed reflected Brownian motion on $$E$$, right? Indeed, there is no local time in the display of (1).
Even if $$c=0$$, is it difficult to describe the quadratic (Dirichlet) form of $$X$$? I am also interested in the fundamental solution of $$X$$. I’m not really sure that it exists…
I’m asking these questions to see what kind of diffusion process $$X$$ is.
## terminal – bash fork retry no child processes cpanel
sorry for my English language
i working on a node.js app test project on cpanel
i used cpanel terminal and i used `nodemon index.js` command then i got this message error:
``````jailshell: fork: retry: No child processes
jailshell: fork: retry: No child processes
jailshell: fork: retry: No child processes
jailshell: fork: retry: No child processes
jailshell: fork: retry: No child processes
``````
how can stop this error?
## network – Running some processes and not others over VPN
I’m looking to secure some apps using an OpenVPN connection.
I want the apps not to work when the VPN isn’t active.
I can’t necessarily track which servers the apps are trying to access, so manually specifying routes either from the server or client end is prohibitive. I also don’t want all traffic going over the VPN.
So here’s what I have so far:
1. Something needs to work at the application layer to ‘capture’ all traffic from an application.
2. Something else needs to work at the network layer to take all of that traffic and push it over the VPN.
And then I need a way to specify which apps and which interface, and be sure that if that interface is down or disconnected, no traffic flows.
So far I think this might be doable with `pf` (I found Murus, a GUI front-end), except that it doesn’t seem to deal with applications per-se, but rather networks and ports, which as stated above is problematic.
Then there’s `Little Snitch`, which deals with applications but is a binary go/no-go decision maker, rather than directing some traffic here and some traffic there.
That said, I did find a not-well-documented feature where it seems like you can create a rule for a process in `Little Snitch`, and give it access to `pf`. So perhaps there’s a way to write a `pf` rule that then directs that traffic over the VPN.
Open to suggestions.
## stochastic processes – Optimal rule for multiple stopping times for defect finding
Suppose a quality inspector is inspecting $$b$$ black and $$w$$ white gadgets. It is known in advance that there are in total $$d_b$$ defective black and $$d_w$$ white gadgets. The device comes down along an assembly line one by one. As each gadget passes, the inspector observes its color, and he chooses to let the gadget pass or use a device to detect whether the gadget is defective. But he can only use the device a total of $$n$$ times. What is the optimal stopping rule to use the inspecting device to maximize the expected number of defective gadgets found.
=====
Suppose at each pass the number of black gadgets already device inspected is $$i_b$$, amongst them $$f_b$$ are detected to be defective. Then the probability of this current black gadget detected to be defective is $$p_b=frac{d_b-f_b}{b-i_b}$$. Symmetrical probability holds for the white gadgets.
I have a conjecture for the explicit solution, which is a greedy algorithm, as follows and am seeking a proof.
At each pass of the gadget, the inspector waits for the gadget with the color to show up with the defect probability equal to $$p:=max(p_b, p_w)$$ to inspect with the device unless the number of device usages left is greater than the number of gadgets the defective probability of which equals to $$p$$.
I have set up the dynamic programming formulation but fail to see immediately either the proof or a counterexample to my conjecture.
## hardware – When Intel / AMD choose their Nanometer Processes, why were the specific numbers, 5, 7, 10, 14, 22, 32, 45, etc chosen?
When looking at the roadmaps for the CPU manufacturing process
Intel Expects to Launch 10nm Chips in 2017
1. 10 µm – 1971
2. 6 µm – 1974
3. 3 µm – 1977
4. 1.5 µm – 1981
5. 1 µm – 1984
6. 800 nm – 1987
7. 600 nm – 1990
8. 350 nm – 1993
9. 250 nm – 1996
10. 180 nm – 1999
11. 130 nm – 2001
12. 90 nm – 2003
13. 65 nm – 2005
14. 45 nm – 2007
15. 32 nm – 2009
16. 22 nm – 2012
17. 14 nm – 2014
18. 10 nm – 2016
19. 7 nm – 2018
20. 5 nm – 2020
21. 3 nm – ~2022
Why are these numbers chosen specifically? I have looked around, and there are deviations, such as:
Samsung Electronics began mass production of 64 Gb NAND flash memory chips using a 20 nm process in 2010.[114]
TSMC first began 16 nm FinFET chip production in 2013.[115]
And many others.
and so on. Yet as far as Intel and AMD are concerned, they are both in lockstep. Is there something to these numbers that lends themselves to the manufacturing process? Or is the selection completely arbitrary?
## stochastic processes – An integral involving Levy process with no positive jumps
Let $$L_t$$ be a Levy process with no positive jumps, but $$L_t$$ is not strictly decreasing, i.e
$$L_t = gamma t + sigma B_t + J_t,$$
where $$B_t$$ is a Brownian motion, $$J_t$$ is a pure jump process with only negative jumps, $$gamma geq 0$$, $$sigma geq 0$$, and at least one of $$gamma$$ and $$sigma$$ is non-zero. In this case, it is known that the 1-dim distribution of $$L_t$$ is absolutely continuous.
Let $$p(t,x)$$ be the probability density function of $$L_t$$:
$$P(L_t in B) = int_B p(t,s) ds.$$
Fix $$a > 0$$.
Now for $$t > 0$$ and $$x < a$$, let
$$q(t,x) = int_0^t frac{a}{s} p(s,a)p(t-s,x-a)ds.$$
I have reason to believe that $$q(t,x) to p(t,a)$$ as $$xnearrow a$$, but haven’t been able to prove it.
## Should Online Processes Assume that the User has Access to a Printer?
As printing on paper is a rapidly vanishing action, should online processes assume that the user has access to a printer ?
As in ‘Print QR code and take to collection point’ – which I saw recently.
## reference request – Rate of convergence for point processes in Skorokhod J1 topology
Skorohod J1 Topology space $$D(0,1)$$ is a metric space, see its definition in https://encyclopediaofmath.org/wiki/Skorokhod_topology
Assume we have a sequence of point processes $$(X^n_t: (Omega, P) to mathbb{Z}^+)_{t in (0,1)}$$ for any $$n ge 0$$ (i.e., stochastic processes with positive integer values), e.g., Poisson processes. So each sample path of $$X^n$$ is in $$D(0,1)$$.
Do we have reference materials which estimate the convergence rate $$rho_n$$ of point processes in Prokhorov metric, i.e.,
$$inf{{epsilon>0: P(X^n in A) le P(X^0 in A^{epsilon})+epsilon}, forall A subset D(0,1)}=O(rho_n) to 0,$$
where $$A^{epsilon}$$ means $$epsilon$$-neighborhood of $$A$$.
Edit: I know Kubilius obtained a rate of convergence in Prokhorov metric for weak invariance principle (i.e., $$X^n$$ are processes with values in $$mathbb{R}$$ instead without jumps, and converge to Brownian motion):
Kubilius, K. Rate of convergence in the invariance principle for martingale difference arrays, Lith Math J. 34 (1994) pp 383–392, doi:10.1007/BF02336885 | 2020-08-14 14:48:06 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 75, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.52260422706604, "perplexity": 944.9168676612932}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-34/segments/1596439739328.66/warc/CC-MAIN-20200814130401-20200814160401-00125.warc.gz"} |
https://security.stackexchange.com/questions/104576/my-college-is-forcing-me-to-install-their-ssl-certificate-how-to-protect-my-pri/104581 | # My college is forcing me to install their SSL certificate. How to protect my privacy?
My college administration is forcing us to install Cyberoam Firewall SSL certificate so that they can view all the encrypted traffic to "improve our security". If I don't install the certificate than I won't be able to use their network.
What are the ways I can protect my privacy in such a situation? Will using a VPN be enough to hide all my traffic or there are other ways?
• Comments are not for extended discussion; this conversation has been moved to chat. – schroeder Nov 5 '15 at 5:11
• Again, comments aren't for chat. I have removed all comments posted since the original migration to chat. Please go to the chat and comment there for discussion. – Jeff Ferland Nov 5 '15 at 19:41
• An easy way to not compromise your computer, use the compromised network and not a lot of effort (like installing a VM): Install an individual Browser which uses its own certificate store (not the system store) and install the certificate only in that browser. User that browser only for work in the compromised network, not anything private or any software downloads. – Falco Nov 9 '15 at 11:43
• If you do install their cert (e.g., in a VM), and if you use Firefox, I recommend you set security.cert_pinning.enforcement_level in about:config to 2 (strict). This will prevent them from bypassing public key pinning (i.e., prevent them from MITMing sites that have established a public-key pin). See Mozilla bug 1168603 for explanation why. – D.W. Nov 13 '15 at 0:19
• which college do you attend? – ŹV - Nov 14 '15 at 22:58
Don't install their certificate on any device/OS installation which you ever want to use for private activity. Once you do, your traffic is subject to MITM attacks even if you are not using your college's network. Such an attack requires having the private key for the certificate you installed, but in practice this is quite easy because these "security products" are so badly designed, and often use either very weak key generation or use a fixed private key that's the same for all deployments and available to any of their customers. In a comment that's since been moved to chat, TOOGAM wrote:
Specific problem known about this specific vendor's certificate "It is therefore possible to intercept traffic from any victim of a Cyberoam device with any other Cyberoam device - or to extract the key from the device and import it into other DPI devices"
If you don't need resources on their network, just use wifi tethering on your phone or get a dedicated 3G USB dongle or similar for use when you're on campus. Alternatively, if non-HTTP traffic is not subject to the MITM, you may be able to use a VPN without installing the certificate. In this case, just get a cheap VPN provider or VPN to your home network if you have one.
If you do need access to resources that are only available from the campus network, install another OS in a virtual machine with the MITM CA installed only in the VM, and use the browser in the VM for accessing these resources.
• Comments are not for extended discussion; this conversation has been moved to chat. – Rory Alsop Nov 12 '15 at 20:17
• Is the ability for the college to monitor the communications (on devices with the certificate installed) something specific to this SSL certificate, or something that all certificate providers can do? E.g. Eduroam that is provided by many colleges? – Winterflags Nov 14 '15 at 18:40
• @Winterflags: Any time you install a custom CA certificate, you're telling your browser/system to accept certificates signed by that CA as if they were signed by one of the "real" CAs that are trusted by default. Anyone with the private key for the custom CA can issue forged certificates for any site and your browser will accept them just like it would the real certificates. – R.. Nov 14 '15 at 23:37
• As far as I can tell, Eduroam has nothing to do with custom CA certs but rather (as one option) uses client certificates as an authentication method. However if you're concerned it would be a good idea to open a new question about what Eduroam does rather than discussing it in the comments on this question. – R.. Nov 14 '15 at 23:38
A VPN is certainly a good solution, provided they don't block that, too.
The best solution for protecting your privacy, though, is probably to try your hardest to get this policy overturned. This is an absolutely abhorrent 'security' policy. It's literally a built-in man-in-the-middle attack against everyone on campus. If their firewall becomes compromised, the attacker can then intercept anything anyone on campus has sent over the Internet, including passwords, credit card numbers, etc.
It turns out that these devices are even worse than they first sounded. As TOOGAM pointed out in a comment, the people at the Tor Project found that, at least as of 2012, all of these devices used the same CA certificate! This means that anyone with access to one of these deep packet inspection devices from Cyberoam or a CA certificate exported from one of them can intercept traffic from anyone who has that root CA certificate installed. Even if this has been remedied in the past 3 years, this casts extreme doubt on the competence of the makers of this device to secure it. This is all the more reason that you should definitely not install this certificate and you should raise as much support for the removal of this device from your campus as you possibly can.
Furthermore, as has been pointed out in comments that have since been cleaned up, use of this device violates the Terms of Service of almost every website on the planet because it discloses your login credentials to a third party (the college.) This means you cannot legally abide by both this policy and the ToS of almost any website.
If this were a public college in the U.S. and they didn't remove this device immediately, for a security hole of this magnitude I would strongly consider contacting my local FBI Cyber Task Force, who should be willing to give the college a very stern talking to. They take this sort of thing very seriously and for good reason.
• +1 for "if their firewall becomes compromised, the attacker can then intercept anything anyone on campus has sent over the Internet"! This college really needs to change what they are doing! – Numeri Nov 5 '15 at 14:16
• @whatsisname True, but the FBI special agents I've talked to in the CTF here actually take large security holes at large institutions (both public and private) rather seriously, as they (rightly, IMO) consider them to be a serious threat to national security. A lot of APTs use compromised domestic systems to stage their more sophisticated attacks, as these will usually be given less scrutiny by intrusion detection systems, especially if the compromised system belongs to a large, reputable organization. – reirab Nov 6 '15 at 5:52
• @JonBentley: They do not "have every reason to presume is secure"; in fact, quite the opposite. They are explicitly installing a backdoor that somebody else has instructed them to install. – R.. Nov 8 '15 at 1:35
• @JonBentley I'd assume that the college at least made it clear that they were spying on the encrypted traffic. If they didn't make that clear, then a reasonable expectation of privacy would likely exist, which opens up a whole new can of worms for the college in terms of legal liability (at least civil and perhaps criminal.) I'll try to edit in some TOS excerpts tomorrow. For a quick example, though, StackExchange's own TOS states that the user shall indemnify StackExchange for any liability arising from the user or anyone else using their account. – reirab Nov 8 '15 at 8:11
• @JonBentley I think that all reirab is trying to say is that many sites require you to keep your credentials safe in their TOS, and the college's requirements explicitly violate this. Whether you or the college is held responsible isn't the point; the point is that you can't follow both policies and that it will be a huge mess if your accounts get compromised because of it. – jpmc26 Nov 10 '15 at 2:18
Your college is providing the "network connection" service under some conditions, one of them being the ability for the college system administrators to inspect all the traffic. While it is tempting to defeat the nosiness of such sysadmins with some technical gimmick (e.g. a VPN, as was suggested in another answer), this would be an explicit attempt at defeating the "security systems" of the college network and this can land you in a huge heap of trouble. The wisest course of action would then not to do that, and instead use your own Internet (e.g. through your personal phone).
• Comments are not for extended discussion; this conversation has been moved to chat. – Rory Alsop Nov 4 '15 at 19:01
• @PaulDraper "workaround" would be a synonym here. – djechlin Nov 6 '15 at 6:49
• Unless the conditions prohibit the use of a VPN then you probably aren't breaking them. The security systems are probably there so that if law enforcement want to know who is visiting a specific page or site then they can be located. If you were going over a VPN then law enforcement wouldn't end up at the University connection, but instead wherever your VPN terminates, meaning the University wouldn't have to do anything. – Matthew Steeples Nov 9 '15 at 11:44
• @immibis The VPN provider wouldn't need to though. If law enforcement goes to a VPN provider and asks who was using this IP address, then they already have the user's details because they'll have used a username and a password. They won't deflect the responsibility of identifying the person to someone else. Chances are if law enforcement are chasing you for something, being in breach of the university regulations is low down your list of worries! – Matthew Steeples Nov 11 '15 at 10:05
• @immibis True, but I'm working on the assumption that the VPN provider is not free, so therefore knows more about you than just your username. Granted you could have used stolen card details, prepay credit card or whatever else, but I'm not approaching this from the point of view of how to get away with something, merely illustrating that the university may just be doing this to cover their own backsides – Matthew Steeples Nov 12 '15 at 22:30
Don't use their network for anything personal. That's the best way to protect your privacy from them.
If you don't have any choice, then use a Virtual Machine, and install the certificate on the virtual machine instead of your main machine. It may allow you to protect your privacy.
Personally, I always used a separate computer for these kind of issues. No way would I allow a company/educational institution install anything on my own equipment, unless I planned on nuking it from orbit later.
• +1, though "Don't use their network at all to the maximum extent you can avoid it" might be even better advice. – reirab Nov 4 '15 at 16:44
• This is bad advice. Once you've installed the certificate, you're vulnerable even when not using their network. Most of these MITM products use the same private key everywhere, or weak key generation, meaning an attacker on any third-party network you connect to could equally be MITM'ing you using the fact that your browser trusts the malicious CA cert from your college. – R.. Nov 4 '15 at 17:11
• This isn't really feasible for students who live on campus. – Michelle Nov 4 '15 at 17:13
• Use an ssh-based VPN and connect the first time from some other network and establish a key auth. They can't breach that. – Joshua Nov 4 '15 at 20:00
• +1 million for the Virtual Machine idea. Install the cert there, use it only for schoolwork, and never! do anything sensitive inside it. You might also (not instead) do the same trick for sensitive activity (like banking) - have a VM just for secure things, and only boot it up off-campus and with a VPN. – willoller Nov 4 '15 at 22:30
If ssh is not filtered out, then you can use ssh to produce a SOCKS proxy running over an ssh tunnel. You need not install any software to make this work. You do not need VPN software. The following will will work on a Linux machine or a Mac (and can probably be able to be made to work on Windows):
• Get a shell account (or a VM, but that's over the top) somewhere
• Check you can log into it with ssh from outside your institution and accept the host key (outside the institution to ensure they aren't MTiM'ing ssh - unlikely)
• In a terminal ssh -D 8080 -N username@host.name.here (note this will appear to hang)
• Now use 127.0.0.1:8080 as your SOCKS proxy
Once this works, you can (optionally) use autossh in place of ssh and it will keep the tunnel up - you will probably need to install that.
The reason why this works is that your HTTPS traffic no longer flows over port 443. It flows (re-encrypted) over port 22. By assumption, they aren't intercepting the ssh protocol. And if they are, you can tell. Your traffic looks like ssh traffic (because it is ssh traffic) - though detailed traffic analysis might suggest it is ssh traffic carrying proxied web requests. It thus is not immediately identifiable as VPN traffic. Moreover, your college is likely not to block ssh traffic as it will be used by CS students.
An alternate route would be to tether to your cell phone and use a data plan.
• I would change the command to be ssh -f -D 8080 -N username@host.example.com. The -f will put it in the background such that the command will not appear to hang. – kasperd Nov 5 '15 at 22:38
• "By assumption, they aren't intercepting the ssh protocol. And if they are, you can tell." - could you explain how you can tell if they are doing a MiTM on the ssh traffic? – Floris Nov 9 '15 at 21:36
• @Floris it is entirely possible to know if they are intercepting SSH, but you have to know the fingerprint of the server's key before trying to connect through the compromised network. This is called "trust on first use," and SSH saves the fingerprint of the key it sees the first time it connects to a server (this can be disabled, of course). On subsequent connections, if the fingerprint changes, it prints a very nasty notice. – thirtythreeforty Nov 9 '15 at 22:26
• @thirtythreeforty ah yes - I have seen that notice... Definitely makes you sit up and pay attention. So the trick is to make this connection first when there is no possibility of a MiTM attack, and then not blindly dismiss warnings. Thanks for the clarification! – Floris Nov 9 '15 at 23:04
See if you are allowed to use a VPN (some protocols may be forbidden, VPNs may be too).
If you are, then use a VPN, and never connect to any site directly through their network. (Unless you are using certificate pinning, but then the connection is likely to fail because the certificate won't match). Precise routing tables can help you with that. You may not even have to install the certificate (you may need it to install the certificate to log into something when connecting to the network, though).
If you are not allowed to, well...
• Don't install the certificate on any computer you use for personal stuff. Use a different machine or a VM. Never do anything personnal on that computer/VM.
• Take the matter to whichever authority has competence. May be ask on http://law.stackexchange.com for advice on whether you can protest against this.
Don't do anything against the T&Cs, that's the best way to be simply banned from the network, or worse.
Don't use the network.
That's pretty much your only option. Any attempt at circumventing their "security" measures would most likely be considered "unauthorized access" under the CFAA (assuming US jurisdiction) and could result in many many years of prison time.
You could try taking them to court, but your chances are pretty slim. Public and private institutions have been doing this sort of network monitoring and interception for many years without running afoul of the law.
• I don't really think you will go to jail for using VPN or SSH tunnel in the US. In some other jurisdictions (e.g. UAE), maybe. – ximaera May 28 at 10:15
is forcing us to install Cyberoam Firewall SSL certificate so that they can view all the encrypted traffic to "improve our security".
Malware is sent over HTTPS too, so it probably is really their intention to improve the security by analyzing encrypted traffic for malware. If they just want to block access to some sites they could probably do it without SSL interception.
SSL interception is very common in companies for exact the same reason, i.e. to protect the company against malware.
Will using a VPN be enough to hide all my traffic or there are other ways?
That depends on their network configuration. If they are smart enough the will block the usage of VPN etc. And I would imagine that they explicitly forbid bypassing the firewall using such technologies, because this means bypassing the protection and making the network less secure. Thus expect to loose the network connection if you use a VPN.
If I don't install the certificate than I won't be able to use their network.
If you own the network there are enough ways to attack the computer or invade the privacy of the users, even without the use of SSL interception. If you don't trust them don't use their network, no matter if they use SSL interception or not.
• Not only is malware sent over HTTPS, some of it will use SSL to phone home. – Iszi Nov 4 '15 at 17:48
• Unless the university is also providing the computers, comparing this to what a company does to their own equipment is an apples to oranges comparison - unless you have examples of a company installing a cert on a personal computer? – user2813274 Nov 4 '15 at 23:05
• I think it's more likely that they are using content filters to stop "forbidden" content like pirated movies, music and software than stopping malware. If they wanted to stop malware, they could just offer free anti-virus that will help protect users even when they are not on the college network. – Johnny Nov 5 '15 at 0:34
• @user2813274 Chances are the university does provide computers, but also allows students to use their personal devices (as a "bonus feature" that it's not necessary for them to provide). In this case, if the asker does not want the university network's policies to apply to his/her personal device, he/she should simply not connect his/her personal device to the university network, and use the provided computers instead. – immibis Nov 5 '15 at 4:02
• @Johnny: filtering which hosts can be accessed can often already be done without SSL interception. And the is a huge difference between offering a free anti-virus and making sure that everybody is using it. Apart from that lots of today's anti-virus come with their own SSL interception. – Steffen Ullrich Nov 5 '15 at 5:24
How would they be able to verify whether or not you had/had not installed their SSL certificate? Are they also running software on your local machine? Otherwise I would think the adverse effects would just be you having to deal with a lot of certificate errors on your end.
What I'd do if I were you is either dual-boot or virtualize. Have your unsafe OS where you install all their "security tools" and certificates and (and don't use anything you don't want someone to see), and then when you want privacy, move back over to your secure OS. If you live on campus and will pretty much always be using their network, then just have your secure OS use a VPN by default, which should skirt their requirements. There are ways they can notice that, but you can always tell them you have a job or something and need it for work, and they might believe you and leave you alone.
Alternatively I'd say get an cellular hotspot. But I know that when I was in college I couldn't afford the kind of data plan that would need.
• If it works the same way as the bluecoat monitoring system my employer uses; without their cert installed you won't be able to access any HTTPS sites that aren't white listed. It's been long enough since the last time I had to load a new cert that I don't remember if the failure mode was BC blocking the outbound request, or intercepting the handshake MITMing it and returning a result protected by the BC cert instead of the sites normal cert and triggering the invalid cert error in the browser. – Dan Neely Nov 4 '15 at 16:57
• " the adverse effects would just be you having to deal with a lot of certificate errors on your end." - well yeah, you'd run into a certificate error for every single website, and bypassing the certificate errors has the same effect as installing the certificate. – immibis Nov 5 '15 at 0:47
• Cert errors are the minimum hassle. If they configure the equipment to block all non-compliant SSL, then no SSL sites will work. If they go even further and require all web traffic to proxy via SSL, then potentially all web traffic could be blocked. Basically, if you want to use their gateway, you're going to have to follow their rules. – GuitarPicker Nov 5 '15 at 19:40
Proposed solution: Use a virtual machine with the Certificate installed when you want to use their network. This way it will be very clear to you when you are using their network and when you are not. You can also discard the VM when you no longer need to use their network.
• This doesn't protect him/her from having his e-mail password sniffed, or his bank details, or his private conversations, or, or, or... – J.J Nov 4 '15 at 20:23
• @J.J - That is true, however it prevents him from accidentally accessing his email/bank/privateInfo while connected to their network. It is a very clear UX trigger that will remind the user not to access private data. – sixtyfootersdude Nov 5 '15 at 19:45
You can use their certificate, and use a VPN on top of that.
You can create a custom routing table, routing everything but the internal network traffic through the VPN. This way they can only decrypt the connections between you and the systems on the college network. Everything else will be routed via your VPN connection, and will be safe.
But using a VPN will make all your traffic be directed for a single server (your VPN provider), and will surely look very suspicious on the logs. If your college does not allow VPN connections, it's best not use one, or use it only for specific tasks (like email checking, for example). Using FoxyProxy on Firefox can help you with that.
• I dealt with a similarly restrictive school and resorted to a VPN, they didn't like it, but one of the network staff pointed out that VPN traffic is no longer their problem. – Logarr Nov 4 '15 at 16:02
• Any solution that involves installing their certificate makes you vulnerable even when not using their network. This is bad advice. – R.. Nov 4 '15 at 17:12
• You don't have to install the certificate system-wide. Install it only on your alternative browser. – ThoriumBR Nov 4 '15 at 17:43
• @ThoriumBR: That's a reasonable idea too. – R.. Nov 5 '15 at 0:36
• That's a good idea for limiting the scope of what they can inspect, but don't expect your other browsers and applications to have any connectivity. – GuitarPicker Nov 5 '15 at 19:42
I believe you can safely use a Chrome OS device, with a dedicated "school" Google account that you use solely for access to the school network. Switching to a different account (e.g. your personal account) will no longer use the school's certificate or any of that user's settings, and Chrome OS is designed to securely isolate accounts.
This help article (written for domain admins, not users) mentions that this is possible, and also notes that it only applies while the domain user is logged in.
Do not bypass the firewall. Some other answers have already covered the technical options, but this is inadvisable - all of the filtering products I have seen will either block bypass, or allow it but notify an administrator, which will get you in to trouble. It may seem like a smart hack to do something that you aren't allowed to do, but the authorities will stomp on you - either by banning you from the network, which will make your studies difficult, or expelling you from the college. Either way, the potential impact on your long term life isn't worth the short term gain of having an unfiltered internet connection at college.
The only real technical option is to use your own internet connection via a 3G mobile or similar technology. You could install a local proxy, and route your HTTPS connections over the 3G link, and everything else over the college network.
SSL interception by internet filters in education institutions is becoming a widespread practice. If you want to take a stand against this, investigate your legal options. In many jurisdictions, interception of private communications without the consent of both parties is a violation of wiretap law. Even if the argument holds that you wilfully consented to the interception by installing the SSL certificate, it is certainly the case that the remote web site did not. As far as I know, no student has ever challenged SSL interception on this basis, but someone has to be the first. I was once told by senior staff at a filtering company that if SSL interception is illegal, it's not their problem - it's their customer who is breaking the law - and they have to offer it as an option or else they will lose sales.
The security on these internet filters/firewalls is often appallingly bad:
• Some use the same SSL certificate for all of their customers. Trivial to extract with admin or physical access. If one firewall is compromised, every firewall is.
• Use of old software with known security vulnerabilities. I know of one commercial provider with a current product line based on software released in 2004. If you can get user access, root access is trivial.
• Insecure remote access. Support teams typically use the same installation and remote maintenance password for all customers. An attacker who knows that password can remotely access any customer system.
• There is a "white list" of sites that SSL interception is not supposed to be done on (such as major banks). However, if you have access to the system it is trivial to modify the software to ignore or drop the white list.
• I know of at least one case where an external attacker managed to gain access to the development server holding the source code for a major firewall product. The lead developer told me, "we have no idea how far they got in the internal network, or what they did once they were in."
The take home message is that these devices are quite vulnerable to a determined hacker, and once access is gained, they could trivially intercept every password of every SSL connection of hundreds of thousands of users. I'm surprised that we haven't heard anything yet about this kind of attack being carried out, but perhaps it already has and the hackers are too busy emptying bank accounts to brag about it. Public knowledge of such an attack would be hugely damaging for any firewall/filter supplier, and they would do everything they could to cover it up.
Update Dec 2015: Backdoors found in Juniper firewall, present since 2012.
• "The lead developer told me, "we have no idea how far they got in the internal network, or what they did once they were in."" <- well yeah, presumably network security is not their job. – immibis Nov 10 '15 at 23:32
• @immibis "We" as in "the company", not "I personally" – bain Nov 11 '15 at 12:29
I looked for a way to use Tor over HTTP (without the proxy CONNECT command) when I first read your question but older answers all said it was currently impossible (I only found one proposal from 2013 that never got anywhere). Now I just stumbled across this, not sure it's what you need but it totally looks like it:
https://trac.torproject.org/projects/tor/wiki/doc/meek
meek is a pluggable transport that uses HTTP for carrying bytes and TLS for obfuscation
## protected by AviD♦Nov 5 '15 at 9:03
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https://dsp.stackexchange.com/tags/signal-energy/hot | # Tag Info
8
If you multiply a continuous-time finite energy signal $f(t)$ with an impulse train you get $$\tilde{f}(t)=\sum_{n=-\infty}^{\infty}f(nT)\delta(t-nT)\tag{1}$$ where $T$ is the sampling interval and $\delta(t)$ is the Dirac delta impulse. Note that the "signal" $\tilde{f}(t)$ is a mathematical fiction, it cannot exist in practice, and it cannot even ...
8
Parseval's theorem will hold, but take into account that your signal in the time domain will no longer be $x[n]$. Namely, if you have that $$\sum_{n=0}^{N-1} \Big| x[n] \Big|^2 = \frac{1}{N} \sum_{k=0}^{N-1} \Big| X[k] \Big|^2$$ then, if you window the signal $x[n]$ with a window $w[n]$, your signal will now be $\hat{x}[n]=x[n]w[n]$, and the theorem will ...
7
[Added a reference on Schwartz's impossibility theorem for products of distribution] The continuous Dirac delta $\delta$ is not considered a true function or signal, but a distribution. From its wikipedia page: The delta function can also be defined in the sense of distributions exactly as above in the one-dimensional case.[25] However, despite ...
6
No it is not. Total Variation is like the amount of changes in the signal. Though changes require energy it doesn't mean they are proportional. For instance, imagine that during a Window we see a constant signal of high value. Clearly this high energy signal (Unless energy for you is the Variance, usually it is the 2nd moment) yet its Total Variation is zero....
5
Note that the condition $$\int_{-\infty}^{\infty}|f(t)|^2dt<\infty\tag{1}$$ (i.e., that the signal $f(t)$ has finite energy) is very restrictive when we try to model signals, even though obviously any actually occurring signal must have finite energy. Modeling signals as random processes means that we ignore condition $(1)$. Models are always ...
5
You simply have to apply the definition of energy. Assuming all signals involved are real, the energy of $g_3(t)$ is given by \begin{align} E &= \int_{-\infty}^\infty g_3^2(t) \, dt \\ &= \int_{-\infty}^\infty \big(g_1(t) + g_2(t)\big)^2 \, dt \\ &= \int_{-\infty}^\infty g_1^2(t) \, dt + 2\int_{-\infty}^\infty g_1(t)g_2(t) \, dt + \int_{-\infty}^...
5
While the Fourier transform, discrete or continuous, can be regarded as unitary transform i.e a naturally norm preserving change between orthonormal bases in a normed complex vector space, the windowed FT does not in general possess this quality. And non-unitary operators cannot be turned into unitary ones by re-scaling. Here is why: Unitary operators can ...
5
Yes indeed! In theory as long as the wavelet is orthogonal, the sum of the squares of all the coefficients should be equal to the energy of the signal. In practice, one should be careful that: the decomposition is not "expansive", i.e. the number of samples and of coefficients is the same. wavelet filter coefficients are not re-scaled, as happens in some ...
5
I think you are correct. People are being fast and loose with the expression in your Eq. (2), but it captures the behaviour of the energy of the signal up to a constant $T_s$ factor (the sampling period), which is maybe why they do it. As you say, the signal energy is given by $$E_s = \int_{-\infty}^{+\infty} |x(t)|^2\;dt \tag{1}$$ If you want to ...
4
[EDIT: 20180307, expanded some details] Globaly no, windowing does NOT affect Parseval's theorem (because theorems are only affected, more precisely not applicable, when their hypotheses are not met), in the sense that the equality in energy relates a signal (windowed $x_w$ or not, $x$, resp.) and its Fourier transform (from a windowed signal, $X_w$ or ...
4
The typical inverse tangent function maps the input range of $t \in (-\infty,\infty)$ into an output range of $(-\pi/2, \pi/2)$ as in the figure below: Based on this, its values are bounded for all $t$. Yet, since the intergal of its square is unbounded, then it cannot be an energy signal;i.e., $$\int_{-\infty}^{\infty} |\tan^{-1}(t)|^2 dt ~~~~~\to \... 4 The procedure is always the same. You need to compute the expectation E\{|A_k|^2\}, where A_k are the complex symbols of the constellation:$$E\{|A_k|^2\}=\sum_kP_k|A_k|^2\tag{1}$$P_k is the probability that the k^{th} symbol is chosen. Usually you can assume that all symbols are equally likely, i.e., P_k=1/M, where M is the number of symbols. 4 By the Convolution Theorem multiplication in Time / Spatial domain is equivalent of Convolution in the Frequency Domain. The sampling rate (In its classic interpretation) is proportional to the support of a function in the frequency domain. So if a function has a certain support in frequency, what would be its support after convolution with itself? Indeed ... 3 Your result is correct but note that for complex signals, the even and odd parts are defined by$$x_e(t)=\frac12\left[x(t)+x^*(-t)\right]\tag{1}$$and$$x_o(t)=\frac12\left[x(t)-x^*(-t)\right]\tag{2}$$where ^* denotes complex conjugation. From (1) and (2) it follows that the real part of x_e(t) is even and its imaginary part is odd, whereas x_o(... 3 windowing your data, x[n], with window w[n] is equivalent to windowing the square of your data (or square-magnitude), \Big|x[n]\Big|^2, with the square of the window w^2[n]. so think of this square of the window w^2[n] as just another window. now stochastically your typical squared sample x^2[n] will have some expected mean-square. the ... 3 \delta(x) doesn't really exist at all for any particular x. Like Laurent Duval said, Dirac is not an \mathbb{R}\to\mathbb{R} function, rather the whole mapping$$\backslash f \mapsto f(a) \equiv \int_\mathbb{R}\!\!\mathrm{d}t\: f(t) \cdot \delta(t-a)"$$is a functional, mapping functions to values of the function evaluated at some particular point. ... 3 You're right that the square of a Dirac delta impulse is undefined, so energy and power cannot be defined in the usual way for signals containing Dirac impulses. However, in analogy with discrete-time signals, it is common to define energy and power of a signal consisting of Dirac impulses in the following way. If a signal x(t) is given by$$x(t)=\sum_{n=...
3
one thing about a non-minimum phase system (with a rational transfer function), is that it can be thought of as the series concatenation (or cascade) of a minimum-phase system, having identical magnitude response as the given non-min-phase filter, with an all-pass filter. the APF will have a poles that cancels specific zeros of the min-phase system that are ...
3
I think simple. We want to model a random physical phenomenon for analysis purpose. One way is to model it by a stochastic process $X(t)$, i.e. a time series of random variables $\left\lbrace X(t_k) = X(t=t_k), t_k \in \mathbb{R} \right\rbrace$. The random variable $X(t_k)$ is associated with a probability distribution function (PDF) with some finite ...
3
Hi: In statistics we call that the probability of type I error ( rejecting when true ) and type II error ( accepting when false ). The way it's done there is that, once you make an assumption about the distribution of the data ( i.e: normal, t, whatever ), you decide on the null and the alternative, along with what you want the P(type I error ) to be ( say 0....
3
The signal, whose total energy you want to calculate, is periodic therefore it will have infinite energy... To see that note, the following Fourier transform pair: $$x(t) = \cos(2\pi f_0 t) \longleftrightarrow X(f) = 0.5 \delta(f + f_0) + 0.5 \delta(f - f_0)$$ And based on Parseval's relation, $$E_x = \int_{-\infty}^{\infty} |x(t)|^2 dt = \int_{-\... 3 Without information on Φ, you can obtain almost anything, since \lambda Φ could be a valid CS matrix as well. Generally, one imposes structure contraints, such as unit energy for their rows or columns. This being said, compressive sensing does not compress data in a strict sense, and energy is a poor measure of compressibility. Entropy and norm ratios ... 3 The OP is correct in their dimensional analysis |X(f)|^2 is NOT the power spectral density, despite what other authors might claim. Other authors probably call this the power spectral density because it is close to right and it captures most of the important features without having to delve into technicalities. Power has dimensions of [\text{signal}^2]. ... 3 Constellation diagrams exist in what is called signal space which is an abstraction used to describe finite-energy signals. The coordinate axes, even if they are marked x and y as in Marcus Muller's answer, really represent unit-energy signals such as$$s_I(t) = \sqrt{\frac 2T}\cos(2\pi f_c t)\mathbf 1_{t \in [0,T)}(t),s_Q(t) = -\sqrt{\frac 2T}\sin(...
3
I guess this probably just a mistake in your analysis code. Quantization noise is white and for a noise signal it's uncorrelated to the original signal, so spectrum of the original noise doesn't matter. I did repeat your steps and saw exactly what I expected: The quantization noise is white and the spectrum of the quantized signal follows the original signal ...
3
Potentially, no. I will attempt to find that $L_2$ is not closed under convolution. In other words, a convolution of two $L_2$ functions (or energy functions) is not necessarily in $L_2$. Convolution is a complicated operation, so working in the Fourier domain with products of functions is tempting. However, if Fourier provides an isometry between the primal ...
2
In addition to Marcus Müller comment, If a signal has finite energy then the signal value must reach zero after long enough time, but for random signals your signals generally don't have such restriction.
2
If $x(t)$ and $X(f)$ are Fourier transform pairs then the value $$\int_{-\infty}^{\infty}|X(f)|df$$ can serve as an upper bound on the magnitude of $x(t)$: $$|x(t)|=\left|\int_{-\infty}^{\infty}X(f)e^{j2\pi f t}df\right|\le \int_{-\infty}^{\infty}|X(f)|df$$
2
Matt L.'s answer is great because it uses an insight from signal processing. Here's a purely "turn the crank" method that uses no signal processing: \begin{align} \int_{-\infty}^\infty \frac{\sin^2(\pi x)}{(\pi x)^2} dx &= \frac{1}{\pi}\int_{-\infty}^\infty \frac{\sin^2 x}{x^2} dx \tag{1} \\ &= \frac{1}{\pi}\left[ \sin^2x \int \frac{1}{x^2} dx\...
Only top voted, non community-wiki answers of a minimum length are eligible | 2022-01-26 00:04:47 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9874929189682007, "perplexity": 590.9252510011017}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-05/segments/1642320304876.16/warc/CC-MAIN-20220125220353-20220126010353-00611.warc.gz"} |
http://www.ltas-cm3.ulg.ac.be/FractureMechanics/?p=Lecture6_P4 | # Computational & Multiscale Mechanics of Materials
## Fracture Mechanics Online Class
Other online classes : Aircraft structures
# Numerical Methods > Multiscale methods
During the last decades, multiscale methods have been developed to capture the physics at different scales. Multiscale models are based on the idea of resolving smaller scales, with correct physical models to extract responses that can be used at the macroscopic scale. As an example the Gurson's model is a multiscale homogenization method as it is solving a microscopic problem (plastic flow around the microvoids) to derive a macroscopic homogenized constitutive behavior (the apparent plastic yield surface).
The general idea of a multi-scale method is illustrated in Picture VI.32 in which two boundary value problems (BVP) are solved concurrently:
• The macroscale problem, which is typically the studied structure;
• The mesoscale problem (on a meso-scale Volume Element), which represents the material with its heterogeneities.
The link between the two boundary value problems involves two steps:
• The downscaling: the deformation gradient field is sent from the macroscale to the mesoscale, for example, to define the boundary conditions of the mesoscale BVP;
• The upscaling:the resolution of the mesoscale BVP leads to a homogenized material behavior that can be used at the macroscale.
Multiscale methods assume lengths scale separation, $L_{\text{macro}}>>L_{\text{Volume Element}}>>L_{\text{micro}}$, which is not trivially satisfied in case of failure (but this is beyond the scope of this introduction).
## Example: Failure of composite laminates
Multiscale models can be used for heterogeneous materials, for which failure involves complex mechanisms, such as composite laminates, see Picture VI.33. An example of application is displayed in Picture VI.34 for the model of the failure of a [$90^o$ / $45^o$ / $-45^o$ / $90^o$ / $0^o$ ] - open hole laminate. In this numerical model:
• Each ply is modeled using a multiscale model embedding a non-local damage model. The different material behaviors of the fibers and of the matrix, the orientation of the fibers ... can thus be accounted for without meshing explicitly the fibers;
• DG-based cohesive elements are used to model the delamination between the plies.
The crack evolution in the different plies is represented by the damage in Picture VI.34, where it can be seen that the numerical model is in good agreement with the experiments.
## Example: failure of polycrystalline materials
The failure of polycrystalline materials is another example of the multi-scale heterogeneous material study, see Picture VI.35. In this model
• At the macro-scale, the grains are modeled with the finite element method using a crystal plasticity model;
• At the macro-scale, the grain boundaries are modeled using cohesive elements;
• Both the crystal plasticity model and the cohesive law of the cohesive elements are defined using atomistic simulations on meso-scale volume elements, as shown in Picture VI.36.
Such a multiscale model is able to account for the effects of
• The misorientation between the grains, and of the
• Grain size,
on the failure of the polycrystalline structure.
Last update: September 02, 2015 | 2019-06-17 07:12:19 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6433549523353577, "perplexity": 1461.8682575183645}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-26/segments/1560627998440.47/warc/CC-MAIN-20190617063049-20190617085049-00063.warc.gz"} |
http://openstudy.com/updates/559a1b04e4b0105c3c348beb | ## superhelp101 one year ago Question:
1. superhelp101
In the following reaction, what coefficient will be written before the water molecule (H2O) to balance the chemical equation? (1 point) _____ H3PO4 + _____ Mg(OH)2 _____H2O + _____ Mg3 (PO4)2 2 3 5 6 I just want to make sure, I got 6 @Koikkara
2. Koikkara
$$H3PO4+MG(OH)2=Mg3(PO4)2+H2O~?$$ Again, try this too in the similar way..
3. Koikkara
$$H3PO4)>~Balance~H3, look ~out~you~have~h2`on~the~right~hand~side~$$
4. Koikkara
after arranging the either way, you will get, $$2 H3PO4 + 3 Mg(OH)2 --> Mg3(PO4)2 + 6 H20$$ $$\Large\rm\color{blue}{Answer~only~for~reference~!!}$$
5. superhelp101
Thanks XD | 2017-01-20 14:48:31 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8120895028114319, "perplexity": 7347.9643800153}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-04/segments/1484560280835.22/warc/CC-MAIN-20170116095120-00428-ip-10-171-10-70.ec2.internal.warc.gz"} |
https://www.doubtnut.com/ncert-solutions/class-12-maths-chapter-4-determinants-exercise-05-1 | # NCERT Class 12 Determinants Exercise 05 Maths Solutions
## Class 12 Determinants Exercise 05 Maths NCERT Solutions
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### NCERT Class 12 | DETERMINANTS | Exercise 05 | Question No. 15
For the matrix A=[1 1 1 1 2-3 2 1 3] . Show that A^3-6A^2+5A+11 I=0 . Hence, find A^(-1) .
### NCERT Class 12 | DETERMINANTS | Exercise 05 | Question No. 14
For the matrix A=[[3,2],[1,1]], find the numbers a and b such that A^2+aA+bI=O.
### NCERT Class 12 | DETERMINANTS | Exercise 05 | Question No. 18
If A is an invertible matrix of order 2, then det (A^(-1)) is equal to (a) det (A) (B) 1/(det""""(A) (C) 1 (D) 0
### NCERT Class 12 | DETERMINANTS | Exercise 05 | Question No. 11
Find the inverse the matrix (if it exists)given in [0 0 0 0cosalphasinalpha0sinalpha-cosalpha]
### NCERT Class 12 | DETERMINANTS | Exercise 05 | Question No. 12
Let A=[3 7 2 5] and B=[6 8 7 9] . Verify that (A B)^(-1)=B^(-1)A^(-1) . | 2021-04-20 13:52:23 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6291659474372864, "perplexity": 3376.492131180584}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-17/segments/1618039398307.76/warc/CC-MAIN-20210420122023-20210420152023-00429.warc.gz"} |
https://electronics.stackexchange.com/questions/291602/whats-an-air-gap-layer-in-a-pcb | # What's an Air Gap Layer in a PCB?
At work I've inherited a multilayer PCB design that I need to send out for quote and eventual fabrication. It contains two inner layers that are labeled "AIRGAP". What is the purpose of these air gap layers?
The board stackup is as follows:
1. Top Silkscreen
3. Top Copper
4. Ground Layer
5. Ground Layer Airgap
6. VCC Layer
7. VCC Layer Airgap
8. Bottom Copper
The highest voltage on the board is about 40 volts, so I wouldn't think it's a high-voltage design.
Would this be considered a four-layer board, or more? Some of the board houses we've sent it to are confused as well.
• I have not come across this air gap before .Study your circuit diagram and see where this airgap is .The air gap could be in some low leakage stuff like picoamps .or it could besomething that needs low capacitance . remember the dielectric constant of FR4 .lAlso it could be some low loss high Q thing .Remember the dissipation factor of FR4 .Maybe it could be some drift thing .The capacitance of FR4 does have a tempco that could be significant in your circuit .If you posted the circuit then the reason for the airgap could be ascertained – Autistic Mar 10 '17 at 23:33
• Allen, what PCB design artifacts have you inherited? (The artifacts may include but are not limited to: Gerber files, design files in the native EDA software formats, physical samples of the PCB, original designers alive.) – Nick Alexeev Mar 10 '17 at 23:37
• @NickAlexeev Artifacts include schematic, BOM, and Gerbers--but not the native design files. The two "air gap" layers are each separate Gerber files. – Allen Moore Mar 10 '17 at 23:40
• Do the airgap gerber layers have copper? What does it connect to? Are their vias? I have not come across this term either. – mkeith Mar 11 '17 at 0:12
• I would expect the airgap layers to show areas that will be milled out of the board. Can you look at these layers, and known copper and silkscreen layers, to see if there are any tracks or components in areas marked by tracks on the airgap layers? Can you get a board that these Gerbers represent? – Peter Bennett Mar 11 '17 at 0:16
As Peter Bennett said, the air gap layer is probably a Gerber containing areas to be milled out of the layers, possibly the top and bottom prepreg, leaving the core intact. Since there are only 4 copper layers, this would likely leave open cavities on the top and bottom with copper potentially exposed on the power/ground layers.
This could be used to recess components into the PCB.
In some cases, components are completely embedded into the PCB.
I believe this process typically would have the (in this case) core run through a pick and place machine, soldered, cleaned and then laminated and the holes plated through with the top and bottom prepreg.
Here is an example of a stackup with completely embedded components from Altium:
An air gap is a physical less than conductive distance between two sections of a electronic circuit. It is intended to enforce a non conductive section between two points using non conductive (in normal circumstances) material. This air gap is chosen based on the typical working voltage of the circuit. A mains voltage air gap will be smaller than an air gap for 1k volt or higher circuits, for example. The spacing between two multi killivolt paths will be much larger than the spacing between two bare mains voltage paths.
The typical air gap is calculated based on the conductivity of atmosphere (a mix of various gases). Of atmosphere would conduct at that voltage at a given distance, the air gap is not enough.
An air gap is for creepage an clearance for high voltages to meet regulatory. I'll bet the designers have a different depth on the PCB for the milling trace and they use that distance in the stack up to achieve a custom depth. This is probably so the depth will show up in the 3D design or for manufacturing, and a milling track could be created with a custom depth in the PCB.
So if the design is for a power supply or something with creep-age and clearance then that's what it is. If it actually is an air gap layer I'd be shocked.
Edit: One other place I have seen air gaps (which this probably is) is in rigid flat flex PCB's which have kapton inner layers and FR4 outer layers. The air gap is to promote flexibility if you have more than 2 kapton inner layers as shown in the 8 layer stackup.
• The design is for an industrial control board with a microcontroller that switches various DC loads. – Allen Moore Mar 10 '17 at 23:51
• What is the highest voltage on the board? – Voltage Spike Mar 11 '17 at 5:29
As the question asked I looked into WikiPedia and found this statement on AIR GAP:
By insulating copper wires within a chip with vacuum holes, capacitance can be minimized enabling chips to work faster or draw less power. A vacuum is believed to be the ultimate insulator for what is known as wiring capacitance, which occurs when two adjacent wires on a chip draw electrical energy from one another, generating undesirable heat and slowing the speed at which data can move through a chip. IBM estimates that this technology alone can lead to 35% higher speeds in current flow or 15% lower power consumption.
Here also is the manufacturing tech from IBM on air gaps from WikiPedia:
IBM researchers have figured out a way to manufacture these "airgaps" on a massive scale, using the self-assembly properties of certain polymers, and then combine this with regular CMOS manufacturing techniques, saving enormous resources since they don't have to retool the entire process. When making the chips the entire wafer is prepared with a polymer material that when removed at a later stage leaves trillions of holes, just 20 nanometers in diameter, evenly spaced. Even though the name suggests that the holes are filled with air, they are in fact filled with nothing, vacuum. IBM has already proven this technique in their labs, and is already deployed in their manufacturing plant in East Fishkill, New York where they have made prototype POWER6 processors using this technology. Full scale deployment is scheduled for IBM's 45 nm node in 2009 after which this technology will also be available to IBM's customers.
As an after thought air gap could refer to spark gap for when circuit reverses current when hit buy a surge of energy like a lighting or over charging your device.
• And none of this has any relation to a PCB, which is what is asked. – pipe Jun 8 '17 at 2:57
• Airgap was developed in a collaborative effort between IBM's Almaden Research Center and T.J. Watson Research Center, and the University of Albany, New York. – William Laurence Clarkson Jun 8 '17 at 3:10
• yes it does know your manufacturing History – William Laurence Clarkson Jun 8 '17 at 3:20
• Last time I checked we don't use CMOS processes to manufacture PCB's, this is a regulatory thing. Yes there are multiple definitions. Please read the qeustion – Voltage Spike Jun 8 '17 at 5:33 | 2019-11-19 12:27:53 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3846471905708313, "perplexity": 2273.387531448051}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-47/segments/1573496670151.97/warc/CC-MAIN-20191119121339-20191119145339-00476.warc.gz"} |
https://hal.archives-ouvertes.fr/hal-00346040 | # Fluctuation theory and exit systems for positive self-similar Markov processes
Abstract : For a positive self-similar Markov process, $X$, we construct a local time for the random set, $\Theta,$ of times where the process reaches its past supremum. Using this local time we describe an exit system for the excursions of $X$ out of its past supremum. Next, we define and study the \textit{ladder process} $(R,H)$ associated to a positive self-similar Markov process $X$, viz. a bivariate Markov process with a scaling property whose coordinates are the right inverse of the local time of the random set $\Theta$ and the process $X$ sampled on the local time scale. The process $(R,H)$ is described in terms of ladder process associated to the Lévy process associated to $X$ via Lamperti's transformation. In the case where $X$ never hits $0$ and the upward ladder height process is not arithmetic and has finite mean we prove the finite dimensional convergence of $(R,H)$ as the starting point of $X$ tends to $0.$ Finally, we use these results to provide an alternative proof to the weak convergence of $X$ as the starting point tends to $0.$ Our approach allows us to address two issues that remained open in \cite{CCh}, namely to remove a redundant hypothesis and to provide a formula for the entrance law of $X$ in the case where the underlying Lévy process oscillates.
Keywords :
Domain :
Cited literature [29 references]
https://hal.archives-ouvertes.fr/hal-00346040
Contributor : Loïc Chaumont <>
Submitted on : Wednesday, December 10, 2008 - 10:25:59 PM
Last modification on : Monday, March 9, 2020 - 6:15:52 PM
Document(s) archivé(s) le : Tuesday, June 8, 2010 - 4:11:15 PM
### File
ckpr.pdf
Files produced by the author(s)
### Identifiers
• HAL Id : hal-00346040, version 1
### Citation
Loïc Chaumont, Andreas Kyprianou, Juan Carlos Pardo, Victor Rivero. Fluctuation theory and exit systems for positive self-similar Markov processes. 2008. ⟨hal-00346040⟩
Record views | 2020-06-06 08:51:50 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.38210928440093994, "perplexity": 807.6947230793259}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-24/segments/1590348511950.89/warc/CC-MAIN-20200606062649-20200606092649-00092.warc.gz"} |
https://unmethours.com/questions/44436/revisions/ | Question-and-Answer Resource for the Building Energy Modeling Community
Get started with the Help page
# Revision history [back]
### EMS actuator for Slat angle
Hi everyone, I am trying to control the Slat angle based on the actuator available as per the application guide.
I am able to control shading type to blinds on or off, but I am not able to control the slat angle via actuator.
EnergyManagementSystem:Actuator,
Sub Surface 1, !- Actuated Component Unique Name
Window Shading Control, !- Actuated Component Type
Control Status; !- Actuated Component Control Type
EnergyManagementSystem:Actuator,
Window1_slat_angle, !- Name
Sub Surface 1, !- Actuated Component Unique Name
Slat Angle Control, !- Actuated Component Type
Slat Angle; !- Actuated Component Control Type
Sub Surface 1 is a window, I am unable to find the actuated component type for slat angle, as per the application guide slat angle can be controlled.
Any help appreciated.
2 retagged __AmirRoth__ 4388 ●5 ●16 http://bleedinggreenna...
### EMS actuator for Slat angle
Hi everyone, I am trying to control the Slat angle based on the actuator available as per the application guide.
I am able to control shading type to blinds on or off, but I am not able to control the slat angle via actuator.
EnergyManagementSystem:Actuator,
Sub Surface 1, !- Actuated Component Unique Name
Window Shading Control, !- Actuated Component Type
Control Status; !- Actuated Component Control Type
EnergyManagementSystem:Actuator,
Window1_slat_angle, !- Name
Sub Surface 1, !- Actuated Component Unique Name
Slat Angle Control, !- Actuated Component Type
Slat Angle; !- Actuated Component Control Type
Sub Surface 1 is a window, I am unable to find the actuated component type for slat angle, as per the application guide slat angle can be controlled.
Any help appreciated.
### EMS actuator for Slat angle
Hi everyone, I am trying to control the Slat angle based on the actuator available as per the application guide.
I am able to control shading type to blinds on or off, but I am not able to control the slat angle via actuator.
EnergyManagementSystem:Actuator,
Sub Surface 1, !- Actuated Component Unique Name
Window Shading Control, !- Actuated Component Type
Control Status; !- Actuated Component Control Type
EnergyManagementSystem:Actuator,
Window1_slat_angle, !- Name
Sub Surface 1, !- Actuated Component Unique Name
Slat Angle Control, !- Actuated Component Type
Slat Angle; !- Actuated Component Control Type
Sub Surface 1 is a window, I am unable to find the actuated component type for slat angle, as per the application guide slat angle can be controlled.
### EMS actuator for Slat angle
Hi everyone, I am trying to control the Slat angle based on the actuator available as per the application guide.
I am able to control shading type to blinds on or off, but I am not able to control the slat angle via actuator.
EnergyManagementSystem:Actuator, | 2022-01-21 07:56:27 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.22890911996364594, "perplexity": 14977.866599303063}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-05/segments/1642320302740.94/warc/CC-MAIN-20220121071203-20220121101203-00561.warc.gz"} |
https://socratic.org/questions/58cc10e3b72cff6c99b2ae8a | # Given that the saturated vapour pressure of water is 3.7831*kPa at 301*K, what is the molar quantity of a 32.11*mL volume of oxygen gas collected OVER water at atmospheric pressure?
Mar 17, 2017
We can use $n = \frac{P V}{R T}$, the Ideal Gas Equation, but of course, there is a catch......
#### Explanation:
Water exerts an equilibrium vapour pressure, as a function of temperature. So the total pressure is the sum of this vapour pressure, and the pressure of dioxygen gas.
${P}_{\text{Gas collected"=P_"Dioxygen"+P_"SVP}}$, where ${P}_{\text{SVP"="the saturated vapour pressure}}$, which you have kindly quoted for us.
So no, we make the calculation: $1.011 \cdot a t m \equiv 1.011 \cdot \cancel{a t m} \times 101.325 \cdot k P a \cdot \cancel{a t {m}^{-} 1} = 102.4396 \cdot k P a$
And thus ${P}_{\text{Dioxygen}} = \left(102.4396 - 3.7831\right) \cdot k P a = 98.6565 \cdot k P a$
And now we plug in the numbers for the mole measurement:
${n}_{\text{dioxygen}} = \frac{98.6565 \cdot \cancel{k P a} \times 32.11 \times {10}^{-} 3 \cancel{L}}{8.314 \cancel{L \cdot k P a \cdot {K}^{-} 1} \cdot m o {l}^{-} 1 \times 301 \cdot \cancel{K}}$
$= 1.267 \times {10}^{-} 3 \cdot \frac{1}{\frac{1}{m o l}} = 1.267 \times {10}^{-} 3 \cdot m o l$
And finally, for the mass of oxygen gas, we take the product: $= 32.00 \cdot g \cdot m o {l}^{-} 1 \times 1.267 \times {10}^{-} 3 \cdot m o l \cong 40 \cdot m g$
Note that you must simply KNOW that oxygen, hydrogen, nitrogen, fluorine, and chlorine ARE diatomic molecules under standard conditions. In fact, all of the elemental gases, SAVE the Noble Gases, are binuclear. | 2021-07-25 12:41:43 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 8, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8426253199577332, "perplexity": 1035.1364479255017}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-31/segments/1627046151672.96/warc/CC-MAIN-20210725111913-20210725141913-00339.warc.gz"} |
https://www.museobarracco.it/en/percorsi/percorsi_per_sale/piano_secondo/sala_v_arte_greca | # Room 5 - Greek Art
Room 5, devoted to Greek art
It displays a notable series of sculptures created between the late 6th century B.C. and the end of the 5th, plus fine Roman copies of Greek works from that period.
Sculpture
Roman copy of a Greek original by Phidias (mid-5th century B.C.)
Sculpture
2nd century A.D. copy of the Greek original by Myron (mid-5th century B.C.)
Funerary monument and ornaments
Attic original, 525-510 B.C.
Sculpture
Original from Magna Graecia, late 6th - early 5th century B.C.
Sculpture
Roman copy of the Greek original by Myron (mid-5th century B.C.)
Sculpture
Roman work inspired by a Greek original from the mid-5th century B.C.
Sculpture
Roman copy of a Greek original from the mid-5th century B.C.
Sculpture
Late Hellenistic copy of a Greek original by Polyclitus (second half of the 5th century B.C.)
Sculpture
Late Hellenistic copy of a Greek original by Polyclitus (second half of the 5th century B.C.)
Sculpture
1st-century A.D. Roman copy of a Greek original by Polyclitus (second half of the 5th century B.C.) | 2023-01-30 14:24:28 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8394741415977478, "perplexity": 13671.910660739117}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764499819.32/warc/CC-MAIN-20230130133622-20230130163622-00133.warc.gz"} |
http://www.ncatlab.org/nlab/show/Eckmann-Hilton+argument | # nLab Eckmann-Hilton argument
### Context
#### Higher category theory
higher category theory
# The Eckmann–Hilton argument
## Statements
In its usual form, the Eckmann–Hilton argument shows that a monoid or group object in the category of monoids or groups is commutative. In other terms, if a set is equipped with two monoid structures, such that one is a homomorphism for the other, then the two structures coincide and the resulting monoid is commutative.
From the nPOV, we may want to think of the statement in this way:
###### Proposition
Let $C$ be a 2-category and $x\in C$ an object. Write ${\mathrm{Id}}_{x}$ for the identity morphism of $X$ and $\mathrm{End}\left({\mathrm{Id}}_{x}\right)$ for the set of endo-2-morphisms on $X$. Then:
On the face of it, this is a special case of the general situation, although in fact every case is an example for appropriate $C$.
A more general version is this: If a set is equipped with two binary operations with identity elements, as long as they commute with each other in the sense that one is (with respect to the other) a homomorphism of sets with binary operations, then everything else follows:
1. the other is also a homomorphism with respect to the first;
2. each also preserves the other's identity;
3. the identities are the same;
4. the operations are the same;
5. the operation is commutative;
6. the operation is associative.
This can also be internalised in any monoidal category.
## Proofs
A pasting diagram-proof of 1 is depicted in Cheng below. Here we prove the $6$-element general form in $\mathrm{Set}$.
###### Proof
The basic equation that we have (that one operation $*$ is a homomorphism with respect to another operation $\circ$) is
$\left(a\circ b\right)*\left(c\circ d\right)=\left(a*c\right)\circ \left(b*d\right).$(a \circ b) * (c \circ d) = (a * c) \circ (b * d) .
In $\mathrm{End}\left({\mathrm{Id}}_{x}\right)$, this is the exchange law.
We prove the list of results from above in order:
1. Simply read the basic equation backwards to see that $\circ$ is a homomorphism with respect to $*$.
2. Now if ${1}_{*}$ is the identity of $*$ and ${1}_{\circ }$ is the identity of $\circ$, we have
${1}_{\star }\circ {1}_{\star }=\left({1}_{\star }\circ {1}_{\star }\right)*{1}_{\star }=\left({1}_{\star }\circ {1}_{\star }\right)*\left({1}_{\star }\circ {1}_{\circ }\right)=\left({1}_{\star }*{1}_{\star }\right)\circ \left({1}_{\star }*{1}_{\circ }\right)={1}_{\star }\circ {1}_{\circ }={1}_{\star }.$1_\star \circ 1_\star = (1_\star \circ 1_\star) * 1_\star = (1_\star \circ 1_\star) * (1_\star \circ 1_\circ) = (1_\star * 1_\star) \circ (1_\star * 1_\circ) = 1_\star \circ 1_\circ = 1_\star .
A similar argument proves the other half.
3. Then
${1}_{\star }={1}_{\star }*{1}_{\star }=\left({1}_{\star }\circ {1}_{\circ }\right)*\left({1}_{\circ }\circ {1}_{\star }\right)=\left({1}_{\star }*{1}_{\circ }\right)\circ \left({1}_{\circ }*{1}_{\star }\right)={1}_{\circ }\circ {1}_{\circ }={1}_{\circ },$1_\star = 1_\star * 1_\star = (1_\star \circ 1_\circ) * (1_\circ \circ 1_\star) = (1_\star * 1_\circ) \circ (1_\circ * 1_\star) = 1_\circ \circ 1_\circ = 1_\circ ,
so the identities are the same; we will now write this identity simply as $1$.
4. Now
$a*b=\left(a\circ 1\right)*\left(1\circ b\right)=\left(a*1\right)\circ \left(1*b\right)=a\circ b,$a * b = (a \circ 1) * (1 \circ b) = (a * 1) \circ (1 * b) = a \circ b ,
so the operations are the same; we will write them both with concatenation.
5. Then
$ab=\left(1a\right)\left(b1\right)=\left(1b\right)\left(a1\right)=ba,$a b = (1 a) (b 1) = (1 b) (a 1) = b a ,
so this operation is commutative.
6. Finally,
$\left(ab\right)c=\left(ab\right)\left(1c\right)=\left(a1\right)\left(bc\right)=a\left(bc\right),$(a b) c = (a b) (1 c) = (a 1) (b c) = a (b c) ,
so the operation is associative.
If you start with a monoid object in $\mathrm{Mon}$, then only (4&5) need to be shown; the others are part of the hypothesis. This classic form of the Eckmann–Hilton argument may be combined into a single calculation:
$a*b=\left(a\circ 1\right)*\left(1\circ b\right)=\left(a*1\right)\circ \left(1*b\right)=a\circ b=\left(1*a\right)\circ \left(b*1\right)=\left(1*b\right)\circ \left(a*1\right)=b*a,$a * b = (a \circ 1) * (1 \circ b) = (a * 1) \circ (1 * b) = a \circ b = (1 * a) \circ (b * 1) = (1 * b) \circ (a * 1) = b * a ,
where the desired results involve the first, middle, and last expressions.
## Corollaries
A $2$-tuply monoidal $0$-category, if defined as a pointed simply connected bicategory, is also the same as an abelian monoid.
A $2$-tuply monoidal $1$-category, if defined as a pointed simply connected tricategory, is the same as a braided monoidal category.
Every homotopy group ${\pi }_{n}$ for $n\ge 2$ is abelian.
## History
The beautiful and powerful Eckmann-Hilton argument is due to Beno Eckmann and Peter Hilton.
## References
An expositions of the argument is given here:
The diagram proof is displayed here
and an animation of it is here
For higher analogues see within the discussion of commutative algebraic monads at:
Revised on November 11, 2010 02:55:17 by Toby Bartels (76.85.201.22) | 2013-06-18 07:19:45 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 34, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9832382202148438, "perplexity": 901.6054811462741}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2013-20/segments/1368707184996/warc/CC-MAIN-20130516122624-00098-ip-10-60-113-184.ec2.internal.warc.gz"} |
https://www.math.ntnu.no/conservation/2001/011.html | A Gas-kinetic BGK Scheme for the Navier-Stokes Equations and Its Connection with Artificial Dissipation and Godunov Method
Kun Xu
Abstract: This paper presents an improved gas-kinetic scheme based on the Bhatnagar-Gross-Krook (BGK) model for the compressible Navier-Stokes equations. The current method extends the previous gas-kinetic Navier-Stokes solver developed by Xu and Prendergast (J. Comput. Phys., {\bf 114}, 9) by (a). implementing a general nonequilibrium state based on the Chapman-Enskog expansion of the BGK model as the initial gas distribution function at each time step, (b). using a different way in the construction of the equilibrium state at a cell interface, and (c). keeping two slopes of the macroscopic variables in the evaluation of spatial variations of the equilibrium state. As a result, the previous requirement of particle collision time $\tau$ being less than the time step $\Delta t$ for the validity of the BGK Navier-Stokes solver is removed, and the scheme becomes more robust than the previous one. The current BGK method approximates the Navier-Stokes solutions accurately regardless of the ratio between the particle collision time and the numerical time step. The Kinetic Flux Vector Splitting Navier-Stokes (KFVS NS) solver developed by Chou and Baganoff comes to be the limiting case of the current method when the particle collision time is much larger than the time step. The Equilibrium Flux Method (EFM) of Pullin for the Euler equations is also a limiting case of the current method when the nonequilibrium part in the initial gas distribution function disappears and the collision time is much larger than the time step. The dissipative mechanism in the KFVS and many other FVS schemes is qualitatively analyzed from their relation with the BGK scheme. Also, in this paper, the appropriate implementation of boundary condition for the kinetic scheme, different limiting solutions, and the Prandtl number fix are presented. The connection among von Neumann $\&$ Richtmyer's artificial dissipation, Godunov method, and the gas-kinetic BGK scheme is discussed, from which two concepts of {\sl dynamical} and {\sl kinematical dissipation} are introduced. The principles for constructing accurate and robust numerical schemes for the compressible flow simulation are proposed. Many numerical tests, which include highly non-equilibrium case, i.e., Mach $10$ shock structure, are included to validate the BGK scheme for the viscous solutions and support the physical and numerical analysis for different schemes.
Paper:
Available as PostScript (2.2 Mbytes) or gzipped PostScript (402 Kbytes; uncompress using gunzip).
Author(s):
Kun Xu, <makxu@ust.hk>
Publishing information:
submitted to J. Comput. Phys., August 2000 | 2017-12-16 03:04:17 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5068824887275696, "perplexity": 786.065511427234}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-51/segments/1512948581053.56/warc/CC-MAIN-20171216030243-20171216052243-00211.warc.gz"} |
https://space.stackexchange.com/questions/22847/roughly-what-is-the-rate-of-energy-loss-of-survivable-capsule-re-entries | # Roughly what is the rate of energy loss of survivable capsule re-entries?
In this answer I've estimated the peak rate of energy loss of a particularly unwise re-entry as 3 to 4 gigawatts. Never mind that it's 15-20 gees of acceleration, that's a lot of power injected into the gas and plasma directly in front of the heat-shield.
My guess is that for survivable capsule re-entries with existing heat shields, the power generation is way lower than that, even on a log scale.
Are there any ballpark, order of magnitude-type numbers out there for the rate of energy loss to the atmosphere in manned capsule reentries?
Here is the descent profile for Soyuz.
At 08:53:30 the speed is 7.62km/s and touchdown is at 09:14:39.
Over 1269 seconds the object sheds 7.62 km/s. Kinetic energy is $.5mv^2$. So that's 29,032,200 joules per kilogram.
29,032,200 joules/1269 seconds = 22878 watts. Over that 21 minute interval I get about 23 kilowatts per kilogram.
According to the descent profile, Soyuz descent maximum g load is around 4 g's.
I am trying to find the descent profiles of the Apollo capsules. They would enter the earth's atmosphere at almost 11 km/s. But so far I haven't been able to find descent profiles that give altitudes and speeds at different times.
In the scenario you link to I get max speed of 4.52 km/s at about 71 km altitude. Impact is 117 seconds later. For this I get 87 kilowatts per kilogram. More than triple of the Soyuz capsule. This is with a 1.85 meter radius, 6500 kilograms and a drag coefficient of .5
Increasing the radius to 2.9 meters, max speed of 4.5 km/s is reached at about 79 km altitude. Impact is 185 seconds later. Over that 185 seconds the capsule endures 54 kilowatts per kilogram. More than double the Soyuz.
• I think $dE/dt$ can be calculated directly from the spacecraft mass and deceleration in g's, right? All you need is the spacecraft's velocity at the moment of maximum g-force. Isn't the power just $P=Fv=mav$ where $a=4g$?
– uhoh
Sep 2 '17 at 15:09
• The majority of the kinetic energy loss happens in a narrow time window, somewhere between tens of seconds and a few minutes depending on the vehicle, anywhere between 20 and 200 seconds. This time is so short that heat is not distributed uniformly, so kW/kg is not a relevant concept. Capsules that have survivably re-entered from orbit with several humans on board are all about the same size, (around the 2 to 2.5 meters diameter ballpark) so let's just talk about the peak power heating them; maximum of mass x deceleration x velocity.
– uhoh
Sep 2 '17 at 18:11
• Definitely don't count the parachute descent towards the duration. Since 08:53:30 +03:01:00 -0:21:09 Entry Guidance enabled (80.4km, 7.62km/s) ) until parachute opening (09:00:18 +03:07:48 -0:14:31 Parachute Opening (10.8km, 217m/s)) you have 462 seconds, and average power output of 0.18 gigawatt. If you narrow it down to neighborhood of peak g-load, you'll likely exceed a gigawatt for a short time.
– SF.
Sep 5 '17 at 11:57
• Also, for the Space Shuttle profile, during the blackout you're getting about 1.7 GW.
– SF.
Sep 5 '17 at 12:00 | 2021-10-19 17:58:19 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.666649580001831, "perplexity": 1663.85304291699}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-43/segments/1634323585280.84/warc/CC-MAIN-20211019171139-20211019201139-00138.warc.gz"} |
http://chicagocmwc.com/western-australia/how-to-find-inverse-trig-functions.php | ## How To Find Inverse Trig Functions
#### Inverse Trig Functions Texas A&M University
WHAT IS AN INVERSE TRIG FUNCTION? • Used to solve for the angle when you know two sides of a right triangle. For example if a ramp is resting against a trailer, then you could find the angle of …
#### Inverse Trigonometric Functions Worksheet and Solutions
Change the sliders to restrict the domain to enable the definition of an inverse function. In the applet above you can see that there are several ways of restricting the domain of $$\sin(x)$$ in order to enable the definition of an inverse.
#### trigonometry Sums of inverse trigonometric functions
Home›Math›Trigonometry› Arctan Arctangent function. Arctan(x), tan-1 (x), inverse tangent function. Definition of arctan; Graph of arctan; Arctan rules; Arctan table; Arctan calculator; Arctan definition. The arctangent of x is defined as the inverse tangent function of x when x is real (x ??). When the tangent of y is equal to x: tan y = x. Then the arctangent of x is equal to the
#### Inverse Trig Functions Texas A&M University
Four Facts About Functions and Their Inverse Functions: 1. A function must be one-to-one (any horizontal line intersects it at most once) in order to have an inverse function. 2. The graph of an inverse function is the reflection of the original function about the line y x. 3. If (x,y) is a point on the graph of the original function, then (y,x) is a point on the graph of the inverse function
How to find inverse trig functions
#### trigonometry Sums of inverse trigonometric functions
Inverse Trig Functions and Their Domains. In this section, we provide a basic overview of inverse trig functions and their domains. If you need to review basic functions before completing the exercises on this page, please see our posts entitled Function Notation and Inverse Functions.
#### Inverse Hyperbolic Trig Functions S.O.S. Mathematics
Given an angle ?, we now know how to calculate the trig functions sin ?, cos ? and tan ? using a scientific calculator. Often, however, we need to be able to find the angle ? given the values of one of the trig functions sin ?, cos ? or tan ?.
#### Evaluate inverse trig functions YouTube
Trigonometry. Identities Proving Identities Trig Equations Evaluate Functions Simplify. Pre Calculus. Equations Inequalities System of Equations System of Inequalities Polynomials Rationales Coordinate Geometry Complex Numbers Polar/Cartesian Functions Arithmetic & Comp. Conic Sections Trigonometry. Calculus. Derivatives Derivative Applications Limits Integrals Integral Applications …
#### Inverse Trigonometric Functions Maths First Institute of
Change the sliders to restrict the domain to enable the definition of an inverse function. In the applet above you can see that there are several ways of restricting the domain of $$\sin(x)$$ in order to enable the definition of an inverse.
#### Inverse Hyperbolic Trig Functions S.O.S. Mathematics
3/12/2012 · The inverse trigonometric functions are used to obtain theta, the angle which yielded the trigonometric function value. It is usually helpful to use the calculator to calculate the inverse
#### trigonometry Sums of inverse trigonometric functions
Four Facts About Functions and Their Inverse Functions: 1. A function must be one-to-one (any horizontal line intersects it at most once) in order to have an inverse function. 2. The graph of an inverse function is the reflection of the original function about the line y x. 3. If (x,y) is a point on the graph of the original function, then (y,x) is a point on the graph of the inverse function
#### Beautiful Math Introducing Inverse Trig Functions
Finding an Angle Given Two Sides This is a video describing the use of the inverse trig function to find the length of a side.
#### Trigonometry MATLAB & Simulink
Finding an Angle Given Two Sides This is a video describing the use of the inverse trig function to find the length of a side.
#### Inverse Trigonometry (with videos worksheets games
Trigonometry. Identities Proving Identities Trig Equations Evaluate Functions Simplify. Pre Calculus. Equations Inequalities System of Equations System of Inequalities Polynomials Rationales Coordinate Geometry Complex Numbers Polar/Cartesian Functions Arithmetic & Comp. Conic Sections Trigonometry. Calculus. Derivatives Derivative Applications Limits Integrals Integral Applications …
### How to find inverse trig functions - Trigonometry MATLAB & Simulink
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Torsional stress is much more difficult to calculate when the cross-section is not circular. Below I show how to calculate the torsional stress and angle of twist for an equilateral triangle, rectangle…
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Wales: Newport WAL, Swansea WAL, Wrexham WAL, Newport WAL, Barry WAL, WAL United Kingdom CF24 8D2 | 2019-06-19 06:40:40 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.44388800859451294, "perplexity": 11668.729695786136}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-26/segments/1560627998923.96/warc/CC-MAIN-20190619063711-20190619085711-00375.warc.gz"} |
http://www.codebymath.com/index.php/welcome/lesson/solve-equations | # Lesson goal: Solve Equations
Previous: Factor a polynomial | Home | Next: Take a derivative
Solving equations always comes up in many areas of math, so we've developed a function called solve that knows how to solve linear equations. Linear equations are equations where the exponents of the variables you want to solve for are always one ($1$).
The solve function works like this:
answer=solve("your-equations","variables-to-solve-for")
Move the mouse over a dotted box for more information.
# Now you try. Try solving a linear equation. After that, try solving two equations with two unknowns (that is a "system of equations").
Type your code here:
See your results here:
This example will solve $4x-3y=-3$ for $x$. You might also try:
• Solving $5x+3y=6$ and $2x-4y=5$ for $x$ and $y$.
• Solving $2a+5b=3$ and $2a+b=9$ for $a$ and $b$.
• $u+4u=56$ for $u$.
Dismiss.
Show a friend, family member, or teacher what you've done!
Here is a share link to your code:
Does your code work? Want to run it on your iPhone?
Here's your code:
1. Use [Control]-[C] (Windows) or [⌘]-[C] (MacOS) to copy your code.
2. Paste it using [Control]-[V] (Windows) or [⌘]-[V] (MacOS) into this page
3. Then click the "Use on iPhone" button that you'll see. | 2018-03-24 02:29:47 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5957186222076416, "perplexity": 2429.8013533255134}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-13/segments/1521257649627.3/warc/CC-MAIN-20180324015136-20180324035136-00106.warc.gz"} |
https://electronics.stackexchange.com/questions/174694/how-to-choose-components-for-a-circuit/174703 | # How to choose components for a circuit
I designed a simple circuit:
that I would like to put components on - the point of the circuit is to light the LED when the voltage source is above 4 volts (it won't be more than 5), so I am looking for a transistor which would have a sharp on/off state at a fixed voltage (say .7 volts, so I can put in some numbers)
at 5 volts, I will put a 330 ohm resistor for R3 to limit the current to 5v (max) /330 = 15ma across the LED (rated for 20mA)
at 4 volts, I want the voltage for the transistor to be .7V, so I will choose R1/R2 = (4-.7)/.7 = 47:10, or 47k for R1 and 10k for R2, which at 4v would give me roughly 70uA for the transistor (if this is not enough, I can increase it by lowering the resistance values)
all of the above can be tweaked, but now I am not sure how to choose a transistor such that this would work - I can go with either pnp or npn transistors by re-organizing the components, but I don't know what else to look for or how to go from here
P.S. if anyone wants to edit the schematic, it's available here
• That circuit will not work. There is no way for the LED to become forward biased. Jun 9, 2015 at 18:42
• @IgnacioVazquez-Abrams not sure I understand, or did I just put the LED in reverse? Jun 9, 2015 at 18:44
• Even if the LED was the correct way around, that transistor will never turn on. And there's no such thing as "a transistor which would have a sharp on/off state at a fixed voltage" Jun 9, 2015 at 18:44
• Oops you shorted your battery ;-) Yes, flipping the battery would work. If all questions were that simple ;-) Now your circuit is up-side-down. All the electrons will fall out ! Jun 9, 2015 at 19:05
Solution without the zener (as suggested above): 2 Common emitters in series give more than enough gain so the transition voltage from LED off-on will be extremely small.
Oldfashioned fun with transistors, look, no microcontroller needed :-)
• So you are adding a second transistor to make the on-off voltage window smaller? I don't quite understand what function of R7 is Jun 9, 2015 at 19:35
• Yes, the collector of the PNP would be pulled up (higher voltage) as soon as Q1 starts to conduct, this in turn pulls up the base of Q2 (via R7). R7 limits the current into the base of Q2. If Q1 is conducting, without R7 the Base of Q2 would be pulled to supply. Remember that the BE junction of a transistor is basically a diode. The current through Q1 and B to E of Q2 would get too high and destroy Q1 and Q2 (assuming the supply would deliver enough current for this to happen). Jun 9, 2015 at 20:44
NOTE: It is long. But when you're done, you'll know a lot more to design more, even cooler schematics than you imagined possible. I have included some Breaks where you could stop, go to bed or have a drink and decide later whether you feel you need to learn more.
First, I'm going to go with an NPN transistor, because:
1. You say you're happy to flip some things around for NPN.
2. NPN has a somewhat nicer response at the same cost, or a lower cost at the same response.
3. If other people starting out with transistors stumble by, they best start with NPN, since most Tutorials and examples hang most towards NPN because of reason 2.
The first thing to know about an NPN transistor is that, as you are hinting at, it has a "turn-on knee" at Vb-e of 0.7V on average. There are exceptions and some deviance from that number, as with any awesome rules, but let's say for the first steps into the domain: For now, it's just going to be 0.7V.
For the real early starters: Vb-e means "Voltage on base measured against emitter", or "How much higher the voltage is on the base compared to the emitter".
Time for a little picture, I think:
simulate this circuit – Schematic created using CircuitLab
As you can see, I'm using your initial use-case to illustrate some steps.
The first thing you did was spot on! How do I know for sure what R3 can be? You take the maximum voltage that can be across it and calculate the resistance by the maximum current you want through it. You did that last bit a bit the other way around and took 5V for the resistor, but you verified that you weren't killing your LED in case your 4V became 5V. Good job!
So, say I want 10mA through my LED and I know the LED has 2V across it at that point (you need a datasheet or some experience to know that voltage. A Red LED will almost always be happy enough about 10mA and 2V if it can handle that current.
The maximum voltage is 5V, the LED needs 2V, so the resistor needs to "waste" 3V at the 10mA, so the resistor becomes: R = 3V / 10mA = 300Ohm. Since 300Ohm is harder to find than 330Ohm, I'm going to choose 330 as well, which gives: I = 3V / 330 Ohm = 9.1mA - That's perfectly fine for an indicator!
So now we know another important thing: The current through the LED is 9.1mA.
Why is this important? Because the transistor is a tiny little cheater. It's not really a switch, it just pretends to be in your first experiments, until you start doing some maths and it turns out it isn't at all. Some transistors are called MOST and some are called Bipolar, they all cheat, but in different ways. Since you are starting with the Bipolar transistor (PNP or NPN) and this is common to do, I will limit myself to those in this particular answer. Just remember that my explanations only count for Bipolars, not for MOSFETS.
A bipolar transistor is a current-controlled-current-source (or more semantically correct in our set-up would be current-drain, but commonly we call them all "CCCC").
What?
It means: Your NPN transistor can only conduct current through its Collector (the one without the arrow) into the Emitter (the one with the arrow), when there is also current flowing into the base (the one sticking out at the left side). This base current also flows to the emitter. For a PNP transistor, the current can only flow out of the Collector, from the Emitter, if there's also current flowing out of the base.
In the rest of my little tale of currents and transistors, I will assume simply we are talking about an NPN transistor, so I don't have to keep specifying into and out of in every sentence, but the main difference holds for all parts.
The 0.7V for the base-emitter voltage is merely an indication. It means that any current flowing into the base will see approximately one diode drop inside the transistor.
This is a good point to go and have a coffee/tea/soda break and let your neurons relax a minute
So, what next?
Next in adding values to your schematic is knowing the current amplification of your transistor. It can often be identified as "h(FE)" where the 'FE' bit is often subscript and the h is a bit stretched and italic, but not always. But sometimes it's also only identified in a graph called "DC current transfer function", "DC current ratio" or such terms. The best place to find it is in a graph anyway, because a single number is always an average and that might be at a collector current of 1mA, 100mA or 1A, but in 99 out of a 100 designs it's never at your point. In a graph you can just look up your situation.
EDIT: It has been pointed out to me I was remiss in not pointing out here that DC gain is not a very reliable number. And I agree. We will also see that later, but it cannot be said expressly enough. There are much better ways to do this, but they include different thought tangents that will make this all even harder. So this is our first step, deeper techniques will come later in your 'education'.
To further help you with that process, I fear we need to know which transistor we are using. Bummer! Or, I can just use an age-old favourite of educational projects and tutorials, which gives me three choices for an NPN: BC550, 2N2222 or more recently 2N3904. I am going to choose the 2N2222, because of three reasons:
1. It has its own Wiki Page! (How awesome is that!?)
2. I haven't actually used one in over ten years.
3. I like alliteration and repetition, especially in learning, so there you are.
But remember, everything I do here is repeatable for any other transistor. Some datasheets give much more information, some much less, but most of the steps can be done for most of it.
Because the Wikipedia page refers to the ST datasheet, so will I:
Check one: Can it do 10mA? -> Page 1: First paragraph: "Up to 500mA": YES! Awesomesauce, as I believe Ms Day would call it.
Check two: Does it do 5V? -> Absolute Maximum on Page 1 says yes! Yay! Wait, absolute? maximum? Hm.
Absolute Maximum in datasheets isn't really what you want to look at. What you want to look at in a datasheet is the normal parameters, because your design will be a little bit wrong. No component is off by 0%, everything is a little bit 'wrong'. If you then design from the absolute maximum and your "off by" is in the wrong direction: Oops! smoke
Absolute maximum is just there for in case of "Ah damn, it broke, why!?" or the very rare occasion you want to push the absolute limit and you know exactly what that means in the design.
So we look one page further. "Electrical Characteristics", that sounds fun and unassuming, let's use that one! In fact, in nearly all datasheets of anything silicon (The most common Transistors, Chips, Diodes, etc) that will very likely be exactly the name of the table you're looking for to find voltages, currents and all that jazz.
Luckily: Yes it can do 5V!
V(br)-cbo, or "collector-base break down voltage" is the voltage at which the transistor says "poof" or shorts out when it is across the collector and base.
V(br)-ceo, or "collector-emitter break down voltage" is the voltage at which the transistor says "poof" or shorts out when it is across collector and emitter.
Both are much more than 5V (not much of a surprise), and for now those are the most relevant. The emitter-base breakdown voltage, V(br)-ebo, is also important in some designs, but I'll explain later why here it isn't.
Always check to see if the absolute maximum voltage you will ever have in your system when the transistor is turned off is lower than both those voltages. Not the same, lower. The same is too risky.
For this relatively simple application, that's all the safety checks we need. If you do a lot of tricks with resistor dividers and/or zeners with Collector currents at 50mA to 75mA or even higher, you have to do a bit more checking and a bit more maths to see if it can handle the power it has to dissipate, but with 10mA and a LED on 5V, it'll be fine. Even without a LED and 10mA and no resistor the power in the transistor will be: P = 5V * 10mA = 50mW is already WAAAAYYY below the 0.5W it can handle at 25 degrees Celsius ambient.
Small note: Such assumptions about power dissipation should be done carefully. If you have 50mW versus 500mW: You'll be safe. If you have 400mW versus 500mW, you should do more thinking/designing to find what it is exactly and if the way you mount/hold the transistor actually still allows 500mW. And always look at the ambient temperature. In this datasheet they also say "case temperature" as well, but that's because it's metal and they mean: "If YOU actively keep the case at that temperature at all times"
Hey, dude, what were we actually looking for?
Amplification! So: What is the amplification? Here we hit the wall I warned about before. This datasheet has no graphs! -sadface!- But it does have a table with all manners of numbers. Funny joke though: They differentiate the absolute minimum and the maximum is always the same.
Luckily, the datasheet confuses matter more by adding another parameter to their differentiation. We know about the collector current, but what the hell is V(ce) doing there? We'e'eelll, thing is, that sort of matters too. This is another reason nothing will be 100% exactly like you design it.
Because at this point the data we have is so limited and our LED current is sooooo far below the 150mA they use at 1V (we want low, because we don't even have 10V!) we are going to ball-park it anyway, so we might as well ignore that 1V there. (It would give us a LED current, just for reference of: I = (5V - 2V - 1V) / 330 Ohm = 6mA I think that's still plenty, but we'll keep working with 10mA.) If you design with worst-case numbers, you can always change them if it turns out better. If you design with best case numbers and it turns out worse, you might need new components.
So, at 1V, our lowest gain given is 50. This number can be vastly different across types, so if you're doing an accurate design, always look it up!
(EDIT: My secret isn't really right: The h(FE) may turn out to be about 60 or 70 with the 2N2222, or might be 25-ish, but can easily be 50-ish. With a 2N3904 the h(FE) is much better at 10mA and 1V, but I made my choicey-bed and I will lay in it too).
This seems like a good point to go and get that cookie that you wanted at the last break, but forgot, because you were jumping to learn more!
We now know how the transistor works and with what numbers and we know how to properly calculate the resistors. We even know to find a few numbers that help us adjust those resistors later, if we find our design is off. (For example: Your LED only gets 6mA at 5V. Why? We just saw that in the datasheet: The transistor keeps a tiny bit of the voltage for itself to have some fun with, but we aren't 100% sure how much yet, because the numbers aren't there for our situation.)
Now, summarised, what do we know?:
• The LED current is assumed 10mA at 5V.
• We want the LED to start turning on at 4V and keep being on at 5V (though possibly brighter)
• We know the current through the collector of Q1 is the same as the LED.
• We know that we can expect Q1 to amplify at least 50 times.
• We know Q1's base will conduct current.
• We know Q1's base wants to be 0.7V when it "turns on".
What don't we know, that we should know?
You don't know that you don't know, yet, but actually, that last point: The transistor always wants to try and have that 0.7V that we figured out at its base. Not just when it is on, or super-on or even mega-on. So if we would connect it right to the voltage source +, it would try to be 0.7V and just pull out whatever the voltage source will give it until, again, it says "poof". So you need a limiting resistor there. But it also explains a little why there isn't a hard on/off (more on that later).
It also explains why the V(br)-beo we saw isn't important: Since there is a limiting resistor (as a part of your divider) that is going to be large enough to keep the base at its desired 0.7V (because we will design it that way), we can assume in all the operating conditions of this design that the base will stay neatly at 0.7V or below.
Time to re-post that picture, because we are going back to that, and don't you just HATE all that scrolling up and down? Me too! Know what? I'll fill in that LED resistor, it looks much too confused right now!
simulate this circuit
At first sight, R1 and R2 are just a cute little voltage divider. But, we just learnt something: The base "steals" current from you! Crap-sticks!
So, how much then? That's where the amplification comes in, that we assume 50, since we don't know better. This amplification is the number of times the transistor will try to amplify the base current through its collector. In our case, the collector current is limited, so we calculate the other way to find our points of interest. We calculate the base current from the collector current with the amplification.
We also need to decide our set-point. Let's say we define that the LED needs to have 2mA to be considered "on". This depends a bit on the LED in question, but a reasonably modern LED from eBay will be quite bright enough at that current. This is where the "not on/off" starts to show: For this kind of design, you need to assume one set current that is first on, and it cannot be 0, because your maths will not work out.
So, at "turning on" we now have the data we need: -> V(in) = 4V. -> V(base) = 0.7V -> I(collector) = I(LED) = 2mA -> I(base) = I(collector) / 50 = 40uA. (see how that will significantly change your maths with a divider current of 70uA?)
So, we can calculate: -> V(R1) = V(base) = 0.7V -> V(R2) = 4V - V(base) = 3.3V And we assume that R1 will be 10k, because we get to choose one.
Now the currents will be: -> I(R1) = V(R1) / R1 = 0.7V / 10kOhm = 70uA -> I(R2) = I(R1) + I(base) = 70uA + 40uA = 110uA Because the current will be flowing into the base from the voltage source's + terminal, so for R2, the current is that of R1 and that of the transistor base. So now R2 becomes: -> R2 = V(R2) / I(R2) = 3.3V / 110uA = 30kOhm Here, you can also use 33kOhm, it will just mean your LED will get a little less current at 4V. As an exercise to see if you get it all, you can calculate that current yourself.
Cool! Done! Building! Now! YAAAAAY!
Hold on, young grasshopper. ... A couple of things remain.
To see that your LED will not be off at 3.5V, we re-calculate with: -> V(R1) = V(base) = STILL 0.7V (remember?). -> I(R1) = still 70uA, becuase it's still 10kOhm and it still has 0.7V across it. -> R2 is unchanged = 30kOhm. -> V(in) = 3.5V. -> V(R2) = V(in) - V(base) = 2.8V. -> I(R2) = V(R2) / R2 = 2.8V / 30kOhm =~ 93uA. -> I(base) =~ 93uA - 70uA = 23uA. Now, if the amplification is neatly 50, the LED current would still be 50 times the base current, is: I(LED) = I(collector) = 50*I(base) =~ 1.2mA. For most modern LEDs that's still plenty to show very visible light!
But when WILL it be entirely off? (Assuming all our on-paper assumptions and numbers are exactly 100% the same as the real-world ones we will see when we build it -- hint: they aren't - but the numbers we calculate are a good start for a first try!)
For the LED to be off, what do we know? It has no current through it! If it has no current through it, we know the transistor's base current needs to be 0 as well. As a little safety margin you could assume the base voltage will already have dropped a little, because when the base current gets really small, it will go down a bit. Let's say, it's about 0.6V with a teensy tiny current. Again an assumption, but I want to show you that even that number isn't perfectly fixed, so some small differences in behaviour in the real world can also be explained with that.
Because this is the exact moment the current turns off, we can assume the base voltage to still be the same as the eensy-teensy-tiny-current voltage: -> I(base) = 0 -> V(base) = 0.6V -> I(R1) = 0.6V / 10kOhm = 60uA -> I(R2) = I(R1) + I(base) = I(R1) + 0 = I(R1) = 60uA -> V(R1) = I(R1) * R1 = 60uA * 30kOhm = 1.8V. -> V(in)-turn-off = V(base) + V(R1) = 0.6V + 1.8V = 2.4V
Ahw! The poops! That's almost half of what I wanted!
Yup. Of course, the LED will be visibly off a tiny bit before that, so it might, all numbers given, be 2.5V, but it's a game of give or take. You can't hurry ... eh... designs? (I'm assuming that at some point someone who knows 'can't hurry love' will pass by, so I'm leaving that in!)
But! In your face! You are calculating with 0mA! So can I! Hah! You lied!
Yes I did. And no I didn't. Let's verify the mathses, shall we?
Yadda, yadda, setpoint, 0mA, V(in) = 4V. So, here goes (and, yes it'll be closer to your values): -> V(in) = 4V -> I(base) = 0mA -> V(base) = 0.6V -> R1 = 10kOhm -> V(R1) = V(base) = 0.6V -> I(R1) = 60uA (see above) -> I(R2) = 60uA -> V(R2) = V(in) - V(base) = 3.4V. -> R2 = V(R2) / I(R2) =~ 57kOhm (56k also happens to exist in cheap forms! hurray!) Perfect. It's off at 4V. But... What happens at 4.5V with those resistors? For the benefit of the doubt, I'll keep V(base) at 0.6V, but the calculated 'effect' will be more depressing if it actually goes up (some datasheets give nice graphs for that V(base) for a given I(base) too!): -> V(in) = 4.5V -> V(base) = 0.6V -> I(R1) = 60uA -> V(R2) = 4.5V - 0.6V = 3.9V -> I(R2) =~ 3.9V / 57kOhm =~ 69uA -> I(base) = I(R2) - I(R1) =~ 69uA - 60uA = 9uA -> I(LED) = I(c) = 50*I(base) =~ 440uA. That's not going to be very bright at all, is it? Maybe it will be enough for you, but I'm guessing it's a bit tight. And that's already very close at your "V-max".
You can do some middling of effect by calculating for 0mA at 3.5V and seeing where that gets you for about 4.1V and such, but I will leave that as an exercise. You should be able to use all the maths and typeys I did above to do that all on your lonesome.
And, remember: This all depends on that current gain we looked up. If you can find a normal NPN transistor with an amplification of 200 (2N3904-ish) or even 500 (also affordably findable) at 10mA collector current the turn on/off point will get much sharper. Then again, it will also get much sharper when you decrease the resistors, so if you start with R1 to be 1kOhm, for example. (Verify yourself).
Just be very careful: Darlington Transistors cheat even on the cheating we already discussed. They have very high V(ce)-on values, up to 4V in some cases, which leaves nothing for your LED, so for now just avoid them, you'll get to ask and learn about them later, when you have even weirder tricks to do.
(Darlingtons can go beyond a factor 5000 amplification, so they are tempting, but elas, not for you, not today. You can find the name "Darlington" in the description all the way at the top of the datasheet and/or the symbol will be drawn with two transistors connected to each other instead of one.)
The End?
Not yet.
After taking a one-day break to regroup, I am now going to continue with the design as promised, to show how and why two transistors in series are much more awesome and sharp switching than just one.
In fact, the theory can be extended to three, four or even a hundred transistors, each one driven by another one. But in practise you will see some annoying behaviour spring up quite quickly. (More about that all the way at the end).
Firstly, we need a new schematic! We know that the NPN transistor we just used is good for the LED, so we're keeping that. We're also keeping the LED and the LED's resistor, because if we leave them out it'll be way too easy to keep the LED turned off at 3.5V. Unless you have magical LEDs that are turned on when they lay unused in your drawer. Can I have some?
For the rest, some things are going to change now. We know the transistor doesn't like being tied to a power rail by its base in our specific set-up, so let's put in a safety resistor, in case our voltages get a peak, making weird stuff happen. So up to now, we have this:
simulate this circuit That looks perfectly fine.
Well, except for the dangly bit (unconnected wire) on the left side of R3 and those question-marks. In general dangly bits and question-marks are super awesome, of course, but in the case of schematics they aren't.
So, we know that we will connect the resistor to another transistor, but which one and how? Well, there are actually many ways to do that, with both NPN and PNP transistors. I would be a liar if I told you my choices were the only ones. But, I want to keep it simple and in line with what we have already learnt. So, we take a PNP transistor.
Let me also add in some more very confused resistors, while I am at it:
simulate this circuit
As you can see the other transistor I chose is the 2N3906 (yes, I did, and it is also the default). This isn't the brother of the 2N2222. (PNP's are brothers to their NPN sisters, clearly, because often the NPN's are easier to work with, but as we have seen, are SOOOO much more complicated than you had wanted. Actually, that second point isn't good for the comparison of transistors, PNP's are equally complicated to NPN's.)
In fact, the 2N3906 is the brother of 2N3904. 2N3904 is in turn the younger cousin of the 2N2222. So why I didn't choose her in the first place is anybody's guess ;-).
Let's look at the 2N3906 datasheet. It works with the 50 to 100uA range that we can expect our 2N2222 to want. It even has 0.1mA (=100uA) collector current, with only 1 volt V(ec) right there on page 2. Brilliant! But it gets better guys and gals, this one has graphs on page 4, 5 and 6. It's a bit more likely for newer devices, but it isn't a per-device thing, more a per-manufacturer thing.
So, let's do our checks: Current? Yes! Voltage? Yes!
Let's find out the gain. We know from before that the 2N2222 will need anything between 0uA and 100uA for the LED to go between off and 5mA or 10mA. In this set-up, all the collector current for Q2 (the 2N3906) is the base current for Q1 (the 2N2222). So let's look at the graphs:
On page 5, you can see a nice graphs with a pretty smooth line for the DC current gain. But you must not be fooled! It says, just above it, that's the curve for 10V V(ec).
So, is there another graph for gain? There's one for the temperature, with 1V across C and E. Fun, but we are going to assume 25 degrees Celcius.
There's a V(ce) voltage versus base current graph for given collector currents and that's it. Such a shame. But, we can use the first and the last graph to make an acceptable guess.
You are also welcome to just use the minimum from the table again, but because graphs kick ass, I will show you how to make this estimation. It will not be perfect, because the data we have isn't, but it'll be better. Even if it ends up the same: Now you're more sure.
Be aware that the first graph (figure 9) is a logarithmic one in both directions, just like the one under it. The extra line between 100 and 200 is 150, but halfway between 100 and 150 isn't 125.
If you look at that first graph you see at 10mA the gain is about 155. At 0.1mA, our area of interest, the line intersects at a gain of about 125 I would estimate. I promise that point about the 125 before was a complete accident, but you can see the line is above where halfway is.
This means the fall-off in gain from 10mA to 0.1mA can be expressed as a factor 125/155 =~ 0.806.
Then go to the 10mA graph in figure 14: Again logarithmic in the --> direction. At 1V we see it's near 0.08mA. So at 1V and 10mA it is at 0.08mA I(base). Let's calculate the gain from this: -> h(FE)-10mA = 10mA / 0.08mA = 125 -> h(FE)-expected-0.1mA =~ 125 * 0.806 = 100.8 So we could have just used the table, but in some cases this little bit of extra attention gives you 80, or 120, or 150, where you would have assumed 100. It would still not have been super accurate, but a better guess.
Now, here comes the maths again, this time with a 5mA LED current at the turn-on point and the assumed 10k resistor. This time the 10k Resistor is the top one (R1), because the base of the PNP transistor is the known quantity, which is 0.6V below the 4V: -> I(LED) = 5mA -> V(in) = 4V -> I(collector-Q2) = I(base-Q1) = I(LED) / 50 = 0.1mA -> I(base-Q2) = I(collector-Q2) / 100 = 0.001mA = 1uA -> V(R1) = V(eb-Q2) = 0.6V (See figure 15: we're at 0.1mA I(c), so one decade below 1mA is about (extend the line) 0.6V). -> I(R1) = 0.6V / 10kOhm = 60uA -> I(R2) = I(R1) + I(base-Q2) = 61uA -> R2 = V(R2) / I(R2) = (4V - 0.7V) / 61uA =~ 54kOhm, make that 56kOhm for quicker turn off. So, as you can see: Now we almost have your resistor values.
Only R3 remains. What's that one going to be?
R3 is only there for protection, so let's say it might have a 10V peak and we want to limit I(base-Q1) to never more than 5mA: R3 = 10V / 5mA = 2kOhm. At our working point with 0.1mA into Q1's base, it'll only use up 0.2V. That is fine, because it leaves V(ec-Q2) = 4V - 0.2V - 0.6V = 3.8V for the emitter-collector of Q2, so that's much more than we counted on, which is only good: It makes the transistor work better and will give you room to experiment with larger R2.
Recap: R1 = 10k; R2 = 56k; R3 = 2k
Let's calculate what happens with 10k and 56k at 3.5V: -> V(in) = 3.5V -> V(R1+R2) = 3.5V -> Assume V(eb-Q2) to be 0.55V: -> I(R2) = V(R2) / R2 = (3.5V - 0.55V) / 56kOhm =~ 53uA At 0.55V, R1 will "want" to conduct 55uA, but R2 will then only conduct 53uA. This means the voltage divider will operate normally and the transistor will truly be turned off.
Note: It's possible (fig 15) that at 0.55V for V(eb-Q2) it will still give off 0.1uA to 0.5uA on the base, but the gain will be so horrible, you shouldn't expect the collector current to get above 5uA. At 5uA, the NPN will turn that into at most 250uA. PROFIT!
(At 5uA I(base-Q1) the NPN will also amplify less than the 50 times at 100uA, so it'll be even less, which again, rounds down to off, compared to 5mA only half a volt higher).
Your total gain is so high and unpredictable in the real world that you don't have to re-calculate again and again, you can build this and test. With what you know about the inner workings you can adjust R1 or R2 if it doesn't work well enough the first try.
The End. I hope many people will take a lot of new knowledge from it, anything beyond this is for other questions at other times
I did promise you an answer to a question you may have asked earlier:
Why not use many transistors to make it switch off at 3.9999999V?
Well, cascading a load of transistors can be a fun experiment and you should to do that if you want to find out more by playing around. But more than two transistors will not help very much any more.
The third transistor's gain will already be reduced, its collector current will not be more than a couple of micro-ampere at most. As we saw in the datasheet the gain is dependent on the collector current and if your transistor is designed for 50mA, 5uA is peanuts. So from the fourth transistor and on we will almost certainly not improve any more and we are very likely to make it much worse, in fact.
Not to mention that over-engineering has its limits. With one transistor you may be able to find a good working point, spending more money on another one makes sense to make it easier to get that point to work well and sharply. If you build your circuit with a third transistor you are already getting so "accurate" that for it to make sense you will need 0.01% accurate resistors and exact current transfer functions for the transistors and all kinds of stuff you don't want to spend time or money on.
Done learning for now? No? David L Jones can tell you much more about Semiconductors and why they work like this.
Obviously, this all holds for this schematic and many like it, but not for all.
A good audio amp can have many more than three stages and it'll be a good design, because they use different types at each stage with a lot of even more fancy maths going on.
They start with one that only has a very low gain, even worse than the 2N2222 at 5mA, but can do many Amperes at its collector. Then one that can go up to an ampere with a 20 to 40 gain. Then one made specifically for low-noise up to 100mA - like the 2N3904 and 3906, sometimes helped by one of the same or similar type to keep it in its best working region (that's where even more of the complex maths come in).
Below that there's often at least another one that reduces it to very low current, possibly followed by another. And then before that there's a set of two that are coupled in a special way that make it work, along with another 2 to 80, like a sort of op-amp.
• Nice piece of work Asmyldof ! This is a clear example of how much fun electronics is, especially when you know what you're talking about (that took me some years though :-) ). And this is only 3 Resistors, a LED and an NPN. Go figure ;-) Jun 9, 2015 at 20:54
• @Rimpelbekkie And, done! Did you know you were only allowed 30000 characters in an answer? I do! Now! Spent another 1.5hour editorial-ing :-D Jun 10, 2015 at 22:29
• hfe is not a great design parameter, because it can vary quite a bit. Better to design to Vce at saturation, and then make sure you're saturated. Jun 11, 2015 at 19:38
• I agree -- but you might add that the diode won't necessarily just click on like a switch. It will creep on a bit, starting at maybe 3.6V, and get brighter all the way to 5. Any complete answer should probably say "not necessarily the best approach" Jun 11, 2015 at 20:03
• @ScottSeidman I gave in and re-re-editted it to include the notice :-) And a movie of David Jones explaining Silicon transistors at the end, for the extra hungry learner. Jun 11, 2015 at 22:19
If you want a sharp cutoff, then you'll need a different circuit. All transistors have a linear region, which means that you'll get the dimmer effect no matter what you do or how many transistors you use. All you can do is reduce the dimmer effect, but not eliminate it. To get a hard cutoff instead, you want as close to infinite gain as you can get, so try one of these instead:
simulate this circuit – Schematic created using CircuitLab
This is a "long-tailed-pair" that is used as a comparator. The node between Q1, Q2, and R5 will be about 0.7V above the lowest base voltage, so only the transistor with the lowest input will be on. R5 limits the base current. R3 limits the current for zener diode D1. Build this and experiment with values:
• If you need higher gain (more step, less dimmer), R5 should be bigger, and you might want to use a darlington for Q3.
• Choose D1's voltage to be roughly half of the supply voltage that you want to detect. It doesn't have to be anywhere near perfect because the voltage divider R1/R2 can be adjusted to match.
• I'd use a potentiometer for R1/R2 at first. Once the circuit works, take it out, measure it, and put fixed resistors in, or just leave it there and make sure that it won't move.
If you insist on calculating values and having it work the first try, then read Asmyldof's answer and be prepared to find that the first try still doesn't work because you forgot to account for something.
simulate this circuit
This is an off-the-shelf comparator chip. Its use in this application is identical to the discrete version above, except that there are a few more transistors built-in to give it a really high gain.
simulate this circuit
This variation creates a bit of hysteresis, that is, it takes a slightly higher voltage to turn it on and a slightly lower voltage to turn it off. As a side-effect, once it starts to move, it'll reinforce itself in that direction and go all the way. So if you're okay with slightly different thresholds to turn on vs. off, then this is probably what you want.
• I'd use a potentiometer for R6/R7 at first. Once the circuit works, take it out, measure it, and put fixed resistors in, or just leave it there and make sure that it won't move. Basically the same procedure as R1/R2.
As before, if you insist on calculating values and having it work the first try, then read Asmyldof's answer and be prepared to find that the first try still doesn't work because you forgot to account for something.
• This question sure got some people motivated :-) Jun 12, 2015 at 9:24 | 2022-08-16 12:54:53 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.611977219581604, "perplexity": 1494.9959284461268}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-33/segments/1659882572304.13/warc/CC-MAIN-20220816120802-20220816150802-00262.warc.gz"} |
https://forum.wilmott.com/viewtopic.php?f=34&t=102266&p=856356 | SERVING THE QUANTITATIVE FINANCE COMMUNITY
EdisonCruise
Topic Author
Posts: 117
Joined: September 15th, 2012, 4:22 am
### How to solve this ODE?
The following ODE is obtained from the Ornstein-Uhlenbeck process. I read it from the paper Optimal Mean Reversion Trading with Transaction Costs and Stop-Loss Exit.
$$\frac{\sigma^2}{2} \frac{d^2u(x)}{dx^2}+\mu(\theta-x) \frac{du(x)}{dx}=ru(x)$$
The paper does not provide the boundary conditions and I cannot find a clear explaination in its references. However, the paper just provides its solution
$$F(x)=\int_{0}^{\infty} u^{\frac{r}{\mu}-1}e^{\sqrt{\frac{2 \mu}{\sigma^2}}(x-\theta)u-\frac{u^2}{2}}du$$
$$G(x)=\int_{0}^{\infty} u^{\frac{r}{\mu}-1}e^{\sqrt{\frac{2 \mu}{\sigma^2}}(\theta-x)u-\frac{u^2}{2}}du$$
For this ODE, I have two questions:
(1) What are the boundary conditions to get the above two integration equations?
(2) the above two integrations are improper integraions. I have tryied to used the Matlab integral function to calculate them numerically, but for some parameters matlab raises the max interval warning. Is there routine/code can calculate these integration accurately?
Thank you.
Alan
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### Re: How to solve this ODE?
(1) Looking at the paper, esp. (3.5), pretty sure F and G should be ODE solutions that (along with their derivatives) vanish at $-\infty$ and $+\infty$ respectively. (See Borodin & Salminen Handbook, pg 19). For $\mu > 0$ they clearly vanish appropriately. Below I check that they are ODE solutions. General theory says any solns with these properties, up to multiplicative constants, are unique.
(2) Not a Matlab user -- but, as long as $r/\mu > 0$, shouldn't be a problem. Suggest you practice with $\int_0^1 u^{a-1} \, du$ until you can do that one correctly numerically, for arbitrary small $a > 0$. Then, perhaps break up the ones you want into (0,1) and (1,infty).
Checking that (F,G) are ODE solutions. Write the ODE as $\mathcal{A} \, u(x) = 0$. Then, some algebra will show something like:
$\mathcal{A} \, F(x) = -\mu \int_0^{\infty} \frac{\partial}{\partial u} \left\{ u^{r/\mu} \, e^{\sqrt{\mu} \, x \, u - u^2/2} \right\} \, du = 0$, since $r/\mu > 0$, and
where I take $\theta=0$, $\sigma^2=2$ for simplicity. I may have some typo's -- left to you to correct. Same idea works for G.
Cuchulainn
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### Re: How to solve this ODE?
I see what you are doing but I do not see what the rationale is or what the compelling reason is for (3.3) and (3.4) is. These are elegant 'closed' solutions to (3.1) but at the end of they must be solved numerically. No free lunch.
My first reactions
(1) Differential equations on $\mathbb{R}$ don't have boundary conditions but rather asymptotic values at $(-\infty, \infty)$. But in a computer some kind of domain truncation/transformation is needed and then some kind of 'approximate' boundary conditions. One example is $y = 1/(1 + e^{-x})$ that transforms (3.1) into
$\frac{1}{2}\sigma^2 y(1-y)\frac{\partial }{\partial y}(y(1-y)\frac{\partial u}{\partial y}) + ...$ on $(0,1)$ (A)
So you know have a degenerate DE and it reduces on ${0,1}$ to $ru = 0$. It can be made rigorous using Fichera theory.
(2) Those integrals look horrendous, numerically. My first reaction would be (instead) to solve (A) using some kind of solver.
But maybe it is a hard requirement that the forms (3.3) and (3.4) are necessary for he rest of the paper..?
I would be interested in knowing the relative value of this alternative solution.
BTW The approach I sketched works very well for time-dependent problems, so it should work in the elliptic case as well.
//
Then we are back to the timeless question
https://forum.wilmott.com/viewtopic.php?f=19&t=23637
Step over the gap, not into it. Watch the space between platform and train.
http://www.datasimfinancial.com
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Alan
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### Re: How to solve this ODE?
Not sure who 'you' is, but, as I said, the integrals should not be a problem. If you can integrate x^{a-1}, you can integrate these.
EdisonCruise
Topic Author
Posts: 117
Joined: September 15th, 2012, 4:22 am
### Re: How to solve this ODE?
Thank you all for your suggestions. Following Alan’s suggestions to split the integration limits, I can do the integration by a change of variable method to go around the singularity point. However, I am still not sure on the below two questions:
(1) Boundary conditions
It seems that as $x\rightarrow -\infty$, $F(x)\rightarrow 0$ (when x=-1e8), but as $x \rightarrow +\infty$, $F(x)\rightarrow+\infty$.
I have attached the figure for F(x) and G(x), with parameters $\sigma=0.5,\theta=0,\kappa=0.5,r=0.1$.
(2) Variational inequalities
Actually I want to solve the variational inequalities by finite difference method below. It is equation (3.17) in the paper Optimal Mean Reversion Trading with Transaction Costs and Stop-Loss Exit.
$$min[rV(x)-\frac{\sigma^2}{2} \frac{d^2V(x)}{dx^2}-\mu(\theta-x) \frac{dV(x)}{dx}, V(x)-(x-c)]=0$$
Again, I am not sure what boundary conditions should be used.
I have tried to use the Projected SOR method to solve this equation, as in the examples given in the book Finite Difference Methods in Financial Engineering by Daniel J. Duffy. The boundary conditions I have tried:
(a) Right boundary: $x-c$. Left boundary: vanishing the second derivative of V(x)
(b) Vanishing the second derivative of V(x) on the left and right boundary.
But both do not work. The solution is sensitive to the initial guess and tend to converge to $x-c$.
Maybe my implementation of PSOR is not correct, but I hope to make sure my boundary conditions appropriate.
Cuchulainn
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### Re: How to solve this ODE?
Not sure who 'you' is, but, as I said, the integrals should not be a problem. If you can integrate x^{a-1}, you can integrate these.
'You' is Leung and Li.
My point is not so much the actual mechanical integration but the amount of effort it take to work out (3.3), (3.4) compared to my approach. Why do we take this approach? Maybe a Plan B does no harm.
It's an aside I suppose, but my question remains unanswered.
Step over the gap, not into it. Watch the space between platform and train.
http://www.datasimfinancial.com
http://www.datasim.nl
Cuchulainn
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Joined: July 16th, 2004, 7:38 am
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### Re: How to solve this ODE?
EdisonCruise,
I can't say much about $F(x)$ but if the problem is well-posed one would expect the solution to be zero at edges? Is the formula correct?
Some remarks on the other things:
1. PSOR should work (it could be slow) but a (necessary?) condition is that the fd matrix $A$ be positive definite. This property could be compromised due to causes.
2. Is $A$ positive definite? Is there convection-dominance?
3. I guess you do some kind of domain truncation and then BC are $\frac {\partial^2 u}{\partial x^2} = 0$?
4. Do the BCs in 3 compromise positive-definiteness?
5. As a sanity clause, you could try this optimisation using an algorithm other than PSOR (in Matlab, Python)? This is a standard example in Quadratic Programming.
6. Images not displayed correctly?
7. PSOR works for non-symmetric matrices but ideally diagonally dominant, the later being realised on page 129 of my FDM book.
I can offer some possible solutions, but let's first pinpoint the problem.
Step over the gap, not into it. Watch the space between platform and train.
http://www.datasimfinancial.com
http://www.datasim.nl
Alan
Posts: 10323
Joined: December 19th, 2001, 4:01 am
Location: California
Contact:
### Re: How to solve this ODE?
Thank you all for your suggestions. Following Alan’s suggestions to split the integration limits, I can do the integration by a change of variable method to go around the singularity point. However, I am still not sure on the below two questions:
(1) Boundary conditions
It seems that as $x\rightarrow -\infty$, $F(x)\rightarrow 0$ (when x=-1e8), but as $x \rightarrow +\infty$, $F(x)\rightarrow+\infty$.
(2) Variational inequalities
Actually I want to solve the variational inequalities by finite difference method below. It is equation (3.17) in the paper Optimal Mean Reversion Trading with Transaction Costs and Stop-Loss Exit.
$$min[rV(x)-\frac{\sigma^2}{2} \frac{d^2V(x)}{dx^2}-\mu(\theta-x) \frac{dV(x)}{dx}, V(x)-(x-c)]=0$$
Again, I am not sure what boundary conditions should be used.
(1) F(x) is behaving just like it's supposed to.
(2) The authors give you an explicit solution in their Th 4.2. Suggest you code it up. (4.2) shows the solution is proportional to F(x) for $x \le b^*$ and is continuous at $x = b^*$. You might want to investigate if it 'smooth pastes'. Maybe you don't need to know that for numerics -- I don't know. Personally, would just use the given solution. Anyway, can you solve for the perpetual American put value numerically? This problem is analogous. What bc do you need for that?
EdisonCruise
Topic Author
Posts: 117
Joined: September 15th, 2012, 4:22 am
### Re: How to solve this ODE?
Thank you so much for your suggestions. I think I can solve this ODE numerically with
(1) A psuedo time term is added to the equation as below:
$$min[rV(x)-\frac{\sigma^2}{2} \frac{d^2V(x)}{dx^2}-\mu(\theta-x) \frac{dV(x)}{dx}+\frac{dV(x)}{dt}, V(x)-(x-c)]=0$$
(2) boundary conditions: $\frac {\partial^2 u}{\partial x^2} = 0$ on both sides
(3) numerical schemes: 2nd order central difference for $x$ derivatives and a runge-kutta type explicit scheme for temporal integration. In each time step after integration, $x-c$ is compared with the value to get the minimum.
This method seems to converge with arbitrary initial conditions and it takes about 2e4 time steps.
I have to get this numerical solution, because it will be used for more complicated problems. However, I am still curious on two issues:
(1) Does the paper obtain the closed-form solution with $\frac {\partial^2 u}{\partial x^2} = 0$ as the boudary conditions?
(2) It seems that adding a psuedo time can work for this problem and the same numerical scheme seems applicable to price American type option. This method seems to be simpler than the PSOR method, which needs a sub-iteration in each time step, or other free boundary method. Is there any disvatange of this method compared with PSOR? Maybe it is too slow to converge in this case I think.
Cuchulainn
Posts: 62913
Joined: July 16th, 2004, 7:38 am
Location: Amsterdam
Contact:
### Re: How to solve this ODE?
I was investigating this issue of fictitious time here
https://forum.wilmott.com/viewtopic.php?f=8&t=101205&start=90
Tue Mar 17, 2020 9:45 am
At the least, we need to prove asymptotic convergence. Friedman 1992 pde book discusses it in chapter 6.
RK4 is probably OK but maybe adaptive schemes for stiff ODEs might be more efficient ($dt = 10^{-4}$ is kind of big.)
Step over the gap, not into it. Watch the space between platform and train.
http://www.datasimfinancial.com
http://www.datasim.nl | 2020-09-25 08:25:17 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 2, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7748783230781555, "perplexity": 959.2532222088319}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-40/segments/1600400222515.48/warc/CC-MAIN-20200925053037-20200925083037-00352.warc.gz"} |
https://0xrick.github.io/hack-the-box/bitlab/ | # Hack The Box - Bitlab
## Quick Summary
Hey guys, today Bitlab retired and here’s my write-up about it. It was a nice CTF-style machine that mainly had a direct file upload and a simple reverse engineering challenge. It’s a Linux box and its ip is 10.10.10.114, I added it to /etc/hosts as bitlab.htb. Let’s jump right in !
## Nmap
As always we will start with nmap to scan for open ports and services:
We got http on port 80 and ssh on port 22, robots.txt existed on the web server and it had a lot of entries.
## Web Enumeration
Gitlab was running on the web server and we need credentials:
I checked /robots.txt to see if there was anything interesting:
Most of the disallowed entries were paths related to the Gitlab application. I checked /help and found a page called bookmarks.html:
There was an interesting link called Gitlab Login:
Clicking on that link didn’t result in anything, so I checked the source of the page, the href attribute had some javascript code:
I took that code, edited it a little bit and used the js console to execute it:
Then I printed the variable _0x4b18 which had the credentials for Gitlab:
## File Upload –> RCE –> Shell as www-data
After logging in with the credentials (clave : 11des0081x) I found two repositories, Profile and Deployer:
I also checked the snippets and I found an interesting code snippet that had the database credentials which will be useful later:
Back to the repositories, I checked Profile and it was pretty empty:
The path /profile was one of the disallowed entries in /robots.txt, I wanted to check if that path was related to the repository, so I checked if the same image (developer.jpg) existed, and it did:
Now we can simply upload a php shell and access it through /profile, I uploaded the php-simple-backdoor:
Then I merged it to the master branch:
I used the netcat openbsd reverse shell payload from PayloadsAllTheThings to get a shell, had to urlencode it first:
## Database Access –> Clave’s Password –> SSH as Clave –> User Flag
After getting a shell as www-data I wanted to use the credentials I got earlier from the code snippet and see what was in the database, however psql wasn’t installed:
So I had to do it with php:
I executed the same query from the code snippet which queried everything from the table profiles, and I got clave’s password which I could use to get ssh access:
We owned user.
## Reversing RemoteConnection.exe –> Root’s Password –> SSH as Root –> Root Flag
In the home directory of clave there was a Windows executable called RemoteConnection.exe:
Then I started looking at the code decompilation with Ghidra. One function that caught my attention was FUN_00401520():
It looked like it was checking if the name of the user running the program was clave, then It executed PuTTY with some parameters that I couldn’t see:
This is how the same part looked like in IDA:
I copied the executable to a Windows machine and I tried to run it, however it just kept crashing.
I opened it in immunity debugger to find out what was happening, and I found an access violation:
It happened before reaching the function I’m interested in so I had to fix it. What I did was simply replacing the instructions that caused that access violation with NOPs.
I had to set a breakpoint before the cmp instruction, so I searched for the word “clave” in the referenced text strings and I followed it in the disassembler:
Then I executed the program and whenever I hit an access violation I replaced the instructions with NOPs, it happened twice then I reached my breakpoint:
After reaching the breakpoint I could see the parameters that the program gives to putty.exe in both eax and ebx, It was starting an ssh session as root and I could see the password:
And we owned root !
That’s it , Feedback is appreciated ! | 2020-05-27 06:32:16 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.24963967502117157, "perplexity": 3540.290677358192}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-24/segments/1590347392141.7/warc/CC-MAIN-20200527044512-20200527074512-00256.warc.gz"} |
https://hilbertthm90.wordpress.com/2010/09/22/infinitesimal-lifting-property/ | # Infinitesimal Lifting Property
I’ve basically recuperated from my test and I’m trying to get back into the AG frame of mind. I have about 5 posts half written, so I’m going to actually try to finish this one and start up a nice little series. I’m taking a class on deformation theory this quarter (which hasn’t actually started yet), so this series will review some of the very, very small amount of deformation theory scattered throughout the exercises of Hartshorne.
Let’s start with some basics on the infinitesimal lifting property. First assume ${k}$ an algebraically closed field and ${A}$ a finitely generated ${k}$-algebra with Spec ${A}$ a nonsingular variety (over ${k}$). Suppose ${0\rightarrow I\rightarrow B'\rightarrow B\rightarrow 0}$ is exact with ${B'}$ a ${k}$-algebra and ${I}$ an ideal with ${I^2=0}$. Then ${A}$ satisfies the infinitesimal lifting property: whenever there is a ${k}$-algebra hom ${f:A\rightarrow B}$, there is a lift ${g: A\rightarrow B'}$ making the obvious diagram commute.
First note that if ${g, g':A\rightarrow B'}$ are two such lifts then, ${\theta=g-g'}$ is a ${k}$-derivation of ${A}$ into ${I}$. A quick subtlety is that a “${k}$-derivation” is an ${A}$-module map that is a derivation and evaluates to zero on ${k}$. So we need to understand how ${I}$ is an ${A}$-module. But ${I^2=0}$, so it is a ${B}$-module, which in turn is an ${A}$-module (via ${g}$ and ${g'}$ which will be used). The reason ${im \theta\subset I}$ is that ${\theta}$ is a lift of the zero map since ${g}$ and ${g'}$ both lift ${f}$. Since the sequence is exact and ${\theta}$ lands in the kernel, it is in the image of the one before it, i.e. ${I}$.
Derivation:
$\displaystyle \begin{array}{rcl} \theta(ab) & = & g(a)g(b)-g'(a)g'(b) \\ & = & g(a)g(b)-g(a)g'(b)+g(a)g'(b)-g'(a)g'(b)\\ & = & g(a)(g(b)-g'(b))+(g(a)-g'(a))g'(b)\\ & = & g(a)\theta(b) + \theta(a)g'(b)\\ & = & a\cdot\theta(b)+b\cdot\theta(a) \end{array}$
Evaluates to 0 on ${k}$: Since ${g(1)=g'(1)=1}$, ${\theta(1)=0}$. Thus ${\theta(k)=k\cdot 0 = 0}$.
Since ${\Omega_{A/k}}$ is a universal object, we can consider ${\theta\in Hom_A(\Omega_{A/k}, I)}$. Conversely, given any ${\theta\in Hom_A(\Omega_{A/k}, I)}$, we can compose with the universal map ${d}$ to get ${\theta'=\theta\circ d: A\rightarrow I}$ is a ${k}$-derivation. Compose this with the inclusion ${I\rightarrow B'}$, call this ${\psi: A\rightarrow B'}$. Since composing again with ${B'\rightarrow B}$ gives ${0}$, ${\psi}$ is a lift of ${0}$ and hence ${g'=\psi + g}$ is a lift of ${f}$ (note we’ve only guaranteed ${k}$-linear so far, not algebra hom). Finally let’s check it preserves multiplication:
$\displaystyle \begin{array}{rcl} \psi(ab)+g(ab) & = & \theta'(ab)+g(ab) \\ & = & \theta'(a)g(b)+g(a)\theta'(b)+g(ab)\\ & = & \theta'(a)\theta'(b) + \theta'(a)g(b)+g(a)\theta'(b)+g(a)g(b)\\ & = & (\theta'(a)+g(a))(\theta'(b)+g(b))\\ & = & g'(a)g'(b) \end{array}$
Now let ${P=k[x_1, \ldots , x_n]}$ for which ${A=P/J}$ for some ${J}$. So we get another exact sequence ${0\rightarrow J\rightarrow P\rightarrow A\rightarrow 0}$. We now check that there is a map ${h:P\rightarrow B'}$ such that the square ${\begin{matrix} P & \stackrel{h}{\longrightarrow} & B' \\ \downarrow & & \downarrow \\ A & \stackrel{f}{\longrightarrow} & B \end{matrix}}$ commutes and this induces an ${A}$-linear map ${\overline{h}: J/J^2\rightarrow I}$.
Note a map out of ${P}$ is completely determined by where the ${x_i}$ go. Since ${B'\rightarrow B}$ surjective, choose any ${b_i\in B'}$ such that ${b_i\mapsto f(\overline{x_i})}$. Extend this to get ${h}$. By definition ${h}$ makes the square commute. Chasing around exactness, we get that if ${a\in J}$, then considering ${a\in P}$ gives ${h(a)\in I}$. Thus restricting gives ${\overline{h}: J\rightarrow I}$. Since ${I^2=0}$ we have ${h(a^2)=h(a)^2=0}$, so this descends to a map ${\overline{h}: J/J^2\rightarrow I}$. It is clearly ${A}$-linear.
Let ${X=}$ Spec ${P}$ and ${Y=}$ Spec ${A}$. The sheaf of ideals ${\mathcal{J}=\tilde{J}}$ defines ${Y}$ as a subscheme. Then by nonsingularity (Theorem 8.17 of Hartshorne) we have an exact sequence ${0\rightarrow \mathcal{J}/\mathcal{J}^2\rightarrow \Omega_{X/k}\otimes \mathcal{O}_Y\rightarrow \Omega_{Y/k}\rightarrow 0}$. Take global sections of this sequence to get the exact sequence ${0\rightarrow J/J^2\rightarrow \Omega_{P/k}\otimes A\rightarrow \Omega_{A/k}\rightarrow 0}$ (${H^1}$ vanishes by Serre).
Now apply the functor ${Hom_A(\cdot, I)}$ to get the exact sequence ${0\rightarrow Hom_A(\Omega_{A/k}, I)\rightarrow Hom_P(\Omega_{P/k}, I)\rightarrow Hom_A(J/J^2, I)\rightarrow 0}$. Exactness on the right is due to ${\Omega_{A/k}}$ being locally free and hence projective, so ${Ext^1}$ vanishes.
That surjectivity is exactly what we needed to say a lift exists. Take ${\overline{h}\in Hom_A(J/J^2, I)}$ as constructed before. Then choose ${\theta\in Hom_P(\Omega_{P/k}, I)}$ that maps to it. Compose with the universal map and inclusion to get a derivation ${P\rightarrow B'}$ (we’ll just relabel this ${\theta}$). Set ${h'=h-\theta}$. Since if ${j\in J}$ we have ${h'(j)=h(j)-\theta(j)=\overline{h}(j)-\overline{h}(j)=0}$ it descends to a map ${g:A\rightarrow B'}$ which is the desired lift.
Next time we’ll move on to infinitesimal extensions and rephrase what we just did in those terms. | 2016-10-26 22:59:05 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 101, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9751227498054504, "perplexity": 131.24087551436216}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-44/segments/1476988721008.78/warc/CC-MAIN-20161020183841-00207-ip-10-171-6-4.ec2.internal.warc.gz"} |
https://tex.stackexchange.com/questions/441945/apply-math-operations-on-loaded-data-inside-pgf-tikz-plot-for-each-column/442061 | # Apply Math operations on loaded data inside PGF/Tikz plot for each column
I am new to LaTeX plotting system and I have got lost in a problem, I have a csv file which has 11 columns, and I want to plot columns 2 to 11 vs column 1. So I do it as given in the following code (Taken from stackexchange, Thanks). My question is as follows, I want to divide x column by the maximum value in the x column and divide each y column by the maximum value in all y columns,
\documentclass{article}
\usepackage{pgfplots}
\usepackage{filecontents}
\begin{document}
\begin{tikzpicture}
\begin{axis}[
width=1.0\textwidth,
scale only axis,
xlabel={$x$},
ylabel={Column Data}]
% Graph column 0 versus column 1
\addplot table[x index=0 ,y index=1,col sep=comma] {Axial.csv};
\addlegendentry{200}% y index+1 since humans count from 1
% Graph column 0 versus column 2
\addplot table[x index=0,y index=2,col sep=comma] {Axial.csv};
\addlegendentry{500}
% Graph column 0 versus column 3
\addplot table[x index=0,y index=3,col sep=comma] {Axial.csv};
\addlegendentry{1000}
% Graph column 0 versus column 4
\addplot table[x index=0,y index=4,col sep=comma] {Axial.csv};
\addlegendentry{2000}
% Graph column 0 versus column 5
\addplot table[x index=0,y index=5,col sep=comma] {Axial.csv};
\addlegendentry{3000}
% Graph column 0 versus column 6
\addplot table[x index=0,y index=6,col sep=comma] {Axial.csv};
\addlegendentry{4000}
% Graph column 0 versus column 7
\addplot table[x index=0,y index=7,col sep=comma] {Axial.csv};
\addlegendentry{5000}
% Graph column 0 versus column 8
\addplot table[x index=0,y index=8,col sep=comma] {Axial.csv};
\addlegendentry{6000}
% Graph column 0 versus column 9
\addplot table[x index=0,y index=9,col sep=comma] {Axial.csv};
\addlegendentry{7000}
% Graph column 0 versus column 10
\addplot table[x index=0,y index=10,col sep=comma] {Axial.csv};
\addlegendentry{8000}
\end{axis}
\end{tikzpicture}
\end{document}
I would really appreciate if you help me with this issue. Best
• Welcome to TeX.SE! Here is an example for the computation of the maximum. If you want someone to write an answer, you'd need to specify the content of Axial.csv. – user121799 Jul 17 '18 at 5:49
• Thank you for your response. The csv file is as follows, ufile.io/dkqeh – Alireza Jul 17 '18 at 12:39
## 1 Answer
OK, here we go then. I created a macro that find the minimal and maximal values of a column. The starting point was this answer but I modified it somewhat. And I would not at all be surprised if this function was already built in somewhere, at least internally it must be because of the way point meta works. Then I created new columns that emerge by the original ones by dividing by the maximal value, as requested. To this end I used copy & paste since this was quicker than fighting with expansion issues that happen in my naive attempts to do that in a loop. And I changed the code such that the csv file is only read once. Here's the code.
\documentclass{article}
\usepackage{pgfplots}
\usepackage{pgfplotstable}
\usepackage{filecontents}
\newcommand{\findminmax}[1]{% https://tex.stackexchange.com/a/107364/121799
% Count rows
\pgfplotstablegetrowsof{\mytable}
\pgfmathtruncatemacro{\numrows}{\pgfplotsretval-1}
\typeout{\numrows\space rows}
% Initiate max value
\pgfplotstablegetelem{0}{#1}\of{\mytable}
\pgfmathtruncatemacro{\mymax}{\pgfplotsretval}
\pgfmathtruncatemacro{\mymin}{\pgfplotsretval}
\typeout{initially:\space\mymin}
\pgfplotsinvokeforeach {1,...,\numrows}{
\pgfplotstablegetelem{##1}{#1}\of{\mytable}
\pgfmathsetmacro{\mymax}{max(\pgfplotsretval,\mymax)}
\pgfmathsetmacro{\mymin}{min(\pgfplotsretval,\mymin)}
}
\let\ymax=\mymax%
\let\ymin=\mymin%
}
\begin{document}
\pgfplotstableread[col sep=comma,header=true]{%
Axial.csv}\mytable
\findminmax{0}
\let\xmax=\ymax
\pgfplotstablecreatecol[expr={(\thisrow{0})/\xmax}]{newx}{\mytable}
% \pgfplotsinvokeforeach{1,2,...,10}{\findminmax{#1}
% \typeout{#1:\ymin-\ymax}
% \pgfplotstablecreatecol[expr={(\thisrow{#1})/\ymax}]{new#1}{\mytable}
% }
%
% yes, the following is very ugly, but faster than fumbling with the expansion
% magic that comes with pgfplots(table), at least for non-wizards like me ;-)
\findminmax{1}
\pgfplotstablecreatecol[expr={(\thisrow{1})/\ymax}]{new1}{\mytable}
\findminmax{2}
\pgfplotstablecreatecol[expr={(\thisrow{1})/\ymax}]{new2}{\mytable}
\findminmax{3}
\pgfplotstablecreatecol[expr={(\thisrow{1})/\ymax}]{new3}{\mytable}
\findminmax{4}
\pgfplotstablecreatecol[expr={(\thisrow{1})/\ymax}]{new4}{\mytable}
\findminmax{5}
\pgfplotstablecreatecol[expr={(\thisrow{1})/\ymax}]{new5}{\mytable}
\findminmax{6}
\pgfplotstablecreatecol[expr={(\thisrow{1})/\ymax}]{new6}{\mytable}
\findminmax{7}
\pgfplotstablecreatecol[expr={(\thisrow{1})/\ymax}]{new7}{\mytable}
\findminmax{8}
\pgfplotstablecreatecol[expr={(\thisrow{1})/\ymax}]{new8}{\mytable}
\findminmax{9}
\pgfplotstablecreatecol[expr={(\thisrow{1})/\ymax}]{new9}{\mytable}
\findminmax{10}
\pgfplotstablecreatecol[expr={(\thisrow{1})/\ymax}]{new10}{\mytable}
\begin{tikzpicture}
\begin{axis}[
width=1.0\textwidth,
scale only axis,
xlabel={$x$},
ylabel={Column Data}]
% Graph column 0 versus column 1
\addplot table[x=newx ,y=new1,col sep=comma] \mytable;
\addlegendentry{200}% y index+1 since humans count from 1
% Graph column 0 versus column 2
\addplot table[x=newx,y=new2,col sep=comma] \mytable;
\addlegendentry{500}
% Graph column 0 versus column 3
\addplot table[x=newx,y=new3,col sep=comma] \mytable;
\addlegendentry{1000}
% Graph column 0 versus column 4
\addplot table[x=newx,y=new4,col sep=comma] \mytable;
\addlegendentry{2000}
% Graph column 0 versus column 5
\addplot table[x=newx,y=new5,col sep=comma] \mytable;
\addlegendentry{3000}
% Graph column 0 versus column 6
\addplot table[x=newx,y=new6,col sep=comma] \mytable;
\addlegendentry{4000}
% Graph column 0 versus column 7
\addplot table[x=newx,y=new7,col sep=comma] \mytable;
\addlegendentry{5000}
% Graph column 0 versus column 8
\addplot table[x=newx,y=new8,col sep=comma] \mytable;
\addlegendentry{6000}
% Graph column 0 versus column 9
\addplot table[x=newx,y=new9,col sep=comma] \mytable;
\addlegendentry{7000}
% Graph column 0 versus column 10
\addplot table[x=newx,y=new10,col sep=comma] \mytable;
\addlegendentry{8000}
\end{axis}
\end{tikzpicture}
\end{document}
• @Mike I erased my comments. And please see here in order to understand some delays. ;-) – user121799 Jul 29 '18 at 18:05
• I deleted mine too. And I wasn't aware of these kind of delays, thanks for the hint. – Mike Jul 29 '18 at 18:57 | 2019-08-19 20:45:41 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.38686656951904297, "perplexity": 3583.982069423073}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-35/segments/1566027314959.58/warc/CC-MAIN-20190819201207-20190819223207-00010.warc.gz"} |
https://mmclassification.readthedocs.io/zh_CN/dev-1.x/papers/beitv2.html | # BEiT V2¶
## 摘要¶
Masked image modeling (MIM) has demonstrated impressive results in self-supervised representation learning by recovering corrupted image patches. However, most existing studies operate on low-level image pixels, which hinders the exploitation of high-level semantics for representation models. In this work, we propose to use a semantic-rich visual tokenizer as the reconstruction target for masked prediction, providing a systematic way to promote MIM from pixel-level to semantic-level. Specifically, we propose vector-quantized knowledge distillation to train the tokenizer, which discretizes a continuous semantic space to compact codes. We then pretrain vision Transformers by predicting the original visual tokens for the masked image patches. Furthermore, we introduce a patch aggregation strategy which associates discrete image patches to enhance global semantic representation. Experiments on image classification and semantic segmentation show that BEiT v2 outperforms all compared MIM methods. On ImageNet-1K (224 size), the base-size BEiT v2 achieves 85.5% top-1 accuracy for fine-tuning and 80.1% top-1 accuracy for linear probing. The large-size BEiT v2 obtains 87.3% top-1 accuracy for ImageNet-1K (224 size) fine-tuning, and 56.7% mIoU on ADE20K for semantic segmentation.
## 结果和模型¶
### ImageNet-1k¶
Flops(G)
Top-1 (%)
Top-5 (%)
BEiTv2-base*
ImageNet-1k & ImageNet-21k
86.53
17.58
86.47
97.99
config
model
Models with * are converted from the official repo. The config files of these models are only for inference.
For BEiTv2 self-supervised learning algorithm, welcome to MMSelfSup page to get more information.
## 引用¶
@article{beitv2,
title={{BEiT v2}: Masked Image Modeling with Vector-Quantized Visual Tokenizers},
author={Zhiliang Peng and Li Dong and Hangbo Bao and Qixiang Ye and Furu Wei},
year={2022},
eprint={2208.06366},
archivePrefix={arXiv},
primaryClass={cs.CV}
} | 2023-03-20 22:38:18 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.2907390594482422, "perplexity": 13658.12165501097}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296943562.70/warc/CC-MAIN-20230320211022-20230321001022-00095.warc.gz"} |
http://heareresearch.blogspot.com/2015/07/7-8-2015-craf-rep-comparison.html | ## Wednesday, July 8, 2015
### 7 8 2015 CRAF rep comparison
Today I compared the replicates of CRAF which I posted about here and here. The main difference in this comparison to the Actin comparison is that both CRAF plates were made at the same time with the same mastermix while the Actin plates were prepared separately. I've run the raw fluorescence data through a script I wrote to produce a graph of showing the differences between replicate 1 and 2.
repcomparison.R
#Load in required packages for functions below
require(qpcR)
## Loading required package: qpcR
## Loading required package: Matrix
require(plyr)
## Loading required package: plyr
require(ggplot2)
## Loading required package: ggplot2
require(splitstackshape)
## Loading required package: splitstackshape
## Loading required package: data.table
#Read in raw fluorescence data from 1st Actin replicate
#Remove blank first column entitled "X"
act3$X<-NULL #Rename columns so that qpcR package and appropriately handle the data act3<-rename(act3, c("Cycle" = "Cycles", "A1" = "H_C_1", "A2" = "N_C_1", "A3"= "S_C_1", "A4"="H_T_1", "A5"="N_T_1","A6"="S_T_1", "A7"="NT_C_1","B1" = "H_C_2", "B2" = "N_C_2","B3"= "S_C_2", "B4"="H_T_2", "B5"="N_T_2", "B6"="S_T_2","B7"="NT_C_2", "C1" = "H_C_3", "C2" = "N_C_3","C3"= "S_C_3","C4"="H_T_3", "C5"="N_T_3", "C6"="S_T_3", "C7"="NT_C_3","D1" = "H_C_4", "D2" = "N_C_4","D3"= "S_C_4", "D4"="H_T_4", "D5"="N_T_4", "D6"="S_T_4", "D7"="NT_C_4","E1" = "H_C_5", "E2" = "N_C_5", "E3"= "S_C_5", "E4"="H_T_5", "E5"="N_T_5", "E6"="S_T_5", "F1" = "H_C_6", "F2" = "N_C_6","F3"= "S_C_6", "F4"="H_T_6", "F5"="N_T_6", "F6"="S_T_6","G1" = "H_C_7", "G2" = "N_C_7", "G3"= "S_C_7", "G4"="H_T_7", "G5"="N_T_7", "G6"="S_T_7", "H1" = "H_C_8", "H2" = "N_C_8","H3"= "S_C_8", "H4"="H_T_8", "H5"="N_T_8", "H6"="S_T_8")) #Run data through pcrbatch in qpcR package which analyzes fluorescence and produces efficiency and cycle threshold values act3ct<-pcrbatch(act3, fluo=NULL) ## Making model for H_C_1 (l4) ## => Fitting passed... ## ## Making model for N_C_1 (l4) ## => Fitting passed... ## ## Making model for S_C_1 (l4) ## => Fitting passed... ## ## Making model for H_T_1 (l4) ## => Fitting passed... ## ## Making model for N_T_1 (l4) ## => Fitting passed... ## ## Making model for S_T_1 (l4) ## => Fitting passed... ## ## Making model for NT_C_1 (l4) ## => Fitting passed... ## ## Making model for H_C_2 (l4) ## => Fitting passed... ## ## Making model for N_C_2 (l4) ## => Fitting passed... ## ## Making model for S_C_2 (l4) ## => Fitting passed... ## ## Making model for H_T_2 (l4) ## => Fitting passed... ## ## Making model for N_T_2 (l4) ## => Fitting passed... ## ## Making model for S_T_2 (l4) ## => Fitting passed... ## ## Making model for NT_C_2 (l4) ## => Fitting passed... ## ## Making model for H_C_3 (l4) ## => Fitting passed... ## ## Making model for N_C_3 (l4) ## => Fitting passed... ## ## Making model for S_C_3 (l4) ## => Fitting passed... ## ## Making model for H_T_3 (l4) ## => Fitting passed... ## ## Making model for N_T_3 (l4) ## => Fitting passed... ## ## Making model for S_T_3 (l4) ## => Fitting passed... ## ## Making model for NT_C_3 (l4) ## => Fitting passed... ## ## Making model for H_C_4 (l4) ## => Fitting passed... ## ## Making model for N_C_4 (l4) ## => Fitting passed... ## ## Making model for S_C_4 (l4) ## => Fitting passed... ## ## Making model for H_T_4 (l4) ## => Fitting passed... ## ## Making model for N_T_4 (l4) ## => Fitting passed... ## ## Making model for S_T_4 (l4) ## => Fitting passed... ## ## Making model for NT_C_4 (l4) ## => Fitting passed... ## ## Making model for H_C_5 (l4) ## => Fitting passed... ## ## Making model for N_C_5 (l4) ## => Fitting passed... ## ## Making model for S_C_5 (l4) ## => Fitting passed... ## ## Making model for H_T_5 (l4) ## => Fitting passed... ## ## Making model for N_T_5 (l4) ## => Fitting passed... ## ## Making model for S_T_5 (l4) ## => Fitting passed... ## ## Making model for H_C_6 (l4) ## => Fitting passed... ## ## Making model for N_C_6 (l4) ## => Fitting passed... ## ## Making model for S_C_6 (l4) ## => Fitting passed... ## ## Making model for H_T_6 (l4) ## => Fitting passed... ## ## Making model for N_T_6 (l4) ## => Fitting passed... ## ## Making model for S_T_6 (l4) ## => Fitting passed... ## ## Making model for H_C_7 (l4) ## => Fitting passed... ## ## Making model for N_C_7 (l4) ## => Fitting passed... ## ## Making model for S_C_7 (l4) ## => Fitting passed... ## ## Making model for H_T_7 (l4) ## => Fitting passed... ## ## Making model for N_T_7 (l4) ## => Fitting passed... ## ## Making model for S_T_7 (l4) ## => Fitting passed... ## ## Making model for H_C_8 (l4) ## => Fitting passed... ## ## Making model for N_C_8 (l4) ## => Fitting passed... ## ## Making model for S_C_8 (l4) ## => Fitting passed... ## ## Making model for H_T_8 (l4) ## => Fitting passed... ## ## Making model for N_T_8 (l4) ## => Fitting passed... ## ## Making model for S_T_8 (l4) ## => Fitting passed... ## ## Calculating delta of first/second derivative maxima... ## .........10.........20.........30.........40.........50 ## .. ## Found univariate outlier for NT_C_3 NT_C_4 ## Tagging name of NT_C_3 NT_C_4 ... ## Analyzing H_C_1 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing N_C_1 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing S_C_1 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing H_T_1 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing N_T_1 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing S_T_1 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing NT_C_1 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing H_C_2 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing N_C_2 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing S_C_2 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing H_T_2 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing N_T_2 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing S_T_2 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing NT_C_2 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing H_C_3 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing N_C_3 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing S_C_3 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing H_T_3 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing N_T_3 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing S_T_3 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing **NT_C_3** ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing H_C_4 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing N_C_4 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing S_C_4 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing H_T_4 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing N_T_4 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing S_T_4 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing **NT_C_4** ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing H_C_5 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing N_C_5 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing S_C_5 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing H_T_5 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing N_T_5 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing S_T_5 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing H_C_6 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing N_C_6 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing S_C_6 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing H_T_6 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing N_T_6 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing S_T_6 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing H_C_7 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing N_C_7 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing S_C_7 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing H_T_7 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing N_T_7 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing S_T_7 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing H_C_8 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing N_C_8 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing S_C_8 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing H_T_8 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing N_T_8 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing S_T_8 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... #pcrbatch creates a file with each sample as an individual column in the dataframe. The problem with this is #that I want to compare all the Ct (labelled sig.cpD2) and generate expression data for them but these values have to be #in individual columns. To do this I must transpose the data and set the first row as the column names. act3res<-setNames(data.frame(t(act3ct)),act3ct[,1]) #Now I must remove the first row as it is a duplicate and will cause errors with future analysis act3res<-act3res[-1,] #since the sample names are now in the first column the column title is row.names. This makes analys hard based on the ability to call the first column. #to eliminate this issue, I copied the first column into a new column called "Names" act3res$Names<-rownames(act3res)
#Since each sample name contains information such as Population, Treatment, and Sample Number I want to separate out these factors
#into new columns so that I can run future analysis based on population, treatment, or both. Also note the "drop = F" this is so the original names column remains.
act3res2<-cSplit_f(act3res, splitCols=c("Names"), sep="_", drop = F)
#After splitting the names column into three new columns I need to rename them appropriately.
act3res2<-rename(act3res2, c("Names_1"="Pop", "Names_2"="Treat", "Names_3"="Sample"))
#I also create a column with the target gene name. This isn't used in this analysis but will be helpful for future work.
act3res2$Gene<-rep("CRAF", length(act3res2)) #In transposing the data frame, the column entries became factors which cannot be used for equations. #to fix this, I set the entries for sig.eff (efficiency) and sig.cpD2 (Ct value) to numeric. Be aware, without the as.character function the factors will be transformed inappropriately. act3res2$sig.eff<-as.numeric(as.character(act3res2$sig.eff)) act3res2$sig.cpD2<-as.numeric(as.character(act3res2sig.cpD2)) #Now I plot the Ct values to see how they align without converting them to expression. ggplot(act3res2, aes(x=Names,y=sig.cpD2, fill=Pop))+geom_bar(stat="identity") #Now I want to get expression information from my data set. qpcR has a way of doing this but its complicated and I'm not comfortable using it. #Luckily there is an equation I can use to do it. The equation is expression = 1/(1+efficiency)^Ctvalue. I tried multiple ways to get this to work in R #but it doesn't handle the complicated equation easily. #To work around this, I created a function in R to run the equation and produce an outcome. x = efficiency argument, y=Ctvalue argument expr<-function(x,y){ newVar<-(1+x)^y 1/newVar } #Now I run the data through the function and produce a useful expression value act3res2expression<-expr(act3res2$sig.eff, act3res2$sig.cpD2)
#Graphing the expression values is a good way to examine the data quickly for errors that might have occurred.
ggplot(act3res2, aes(x=Names,y=expression, fill=Pop))+geom_bar(stat="identity")
#Before I'm able to compare the replicates I need to process the raw fluorescence from the second Actin run.
#To do this I perform all the same steps as the previous replicate.
act4$X<-NULL act4<-rename(act4, c("Cycle" = "Cycles", "A1" = "H_C_1", "A2" = "N_C_1", "A3"= "S_C_1", "A4"="H_T_1", "A5"="N_T_1","A6"="S_T_1", "A7"="NT_C_1","B1" = "H_C_2", "B2" = "N_C_2","B3"= "S_C_2", "B4"="H_T_2", "B5"="N_T_2", "B6"="S_T_2","B7"="NT_C_2", "C1" = "H_C_3", "C2" = "N_C_3","C3"= "S_C_3","C4"="H_T_3", "C5"="N_T_3", "C6"="S_T_3", "C7"="NT_C_3","D1" = "H_C_4", "D2" = "N_C_4","D3"= "S_C_4", "D4"="H_T_4", "D5"="N_T_4", "D6"="S_T_4", "D7"="NT_C_4","E1" = "H_C_5", "E2" = "N_C_5", "E3"= "S_C_5", "E4"="H_T_5", "E5"="N_T_5", "E6"="S_T_5", "F1" = "H_C_6", "F2" = "N_C_6","F3"= "S_C_6", "F4"="H_T_6", "F5"="N_T_6", "F6"="S_T_6","G1" = "H_C_7", "G2" = "N_C_7", "G3"= "S_C_7", "G4"="H_T_7", "G5"="N_T_7", "G6"="S_T_7", "H1" = "H_C_8", "H2" = "N_C_8","H3"= "S_C_8", "H4"="H_T_8", "H5"="N_T_8", "H6"="S_T_8")) act4ct<-pcrbatch(act4, fluo=NULL) ## Making model for H_C_1 (l4) ## => Fitting passed... ## ## Making model for N_C_1 (l4) ## => Fitting passed... ## ## Making model for S_C_1 (l4) ## => Fitting passed... ## ## Making model for H_T_1 (l4) ## => Fitting passed... ## ## Making model for N_T_1 (l4) ## => Fitting passed... ## ## Making model for S_T_1 (l4) ## => Fitting passed... ## ## Making model for NT_C_1 (l4) ## => Fitting passed... ## ## Making model for H_C_2 (l4) ## => Fitting passed... ## ## Making model for N_C_2 (l4) ## => Fitting passed... ## ## Making model for S_C_2 (l4) ## => Fitting passed... ## ## Making model for H_T_2 (l4) ## => Fitting passed... ## ## Making model for N_T_2 (l4) ## => Fitting passed... ## ## Making model for S_T_2 (l4) ## => Fitting passed... ## ## Making model for NT_C_2 (l4) ## => Fitting passed... ## ## Making model for H_C_3 (l4) ## => Fitting passed... ## ## Making model for N_C_3 (l4) ## => Fitting passed... ## ## Making model for S_C_3 (l4) ## => Fitting passed... ## ## Making model for H_T_3 (l4) ## => Fitting passed... ## ## Making model for N_T_3 (l4) ## => Fitting passed... ## ## Making model for S_T_3 (l4) ## => Fitting passed... ## ## Making model for NT_C_3 (l4) ## => Fitting passed... ## ## Making model for H_C_4 (l4) ## => Fitting passed... ## ## Making model for N_C_4 (l4) ## => Fitting passed... ## ## Making model for S_C_4 (l4) ## => Fitting passed... ## ## Making model for H_T_4 (l4) ## => Fitting passed... ## ## Making model for N_T_4 (l4) ## => Fitting passed... ## ## Making model for S_T_4 (l4) ## => Fitting passed... ## ## Making model for NT_C_4 (l4) ## => Fitting passed... ## ## Making model for H_C_5 (l4) ## => Fitting passed... ## ## Making model for N_C_5 (l4) ## => Fitting passed... ## ## Making model for S_C_5 (l4) ## => Fitting passed... ## ## Making model for H_T_5 (l4) ## => Fitting passed... ## ## Making model for N_T_5 (l4) ## => Fitting passed... ## ## Making model for S_T_5 (l4) ## => Fitting passed... ## ## Making model for H_C_6 (l4) ## => Fitting passed... ## ## Making model for N_C_6 (l4) ## => Fitting passed... ## ## Making model for S_C_6 (l4) ## => Fitting passed... ## ## Making model for H_T_6 (l4) ## => Fitting passed... ## ## Making model for N_T_6 (l4) ## => Fitting passed... ## ## Making model for S_T_6 (l4) ## => Fitting passed... ## ## Making model for H_C_7 (l4) ## => Fitting passed... ## ## Making model for N_C_7 (l4) ## => Fitting passed... ## ## Making model for S_C_7 (l4) ## => Fitting passed... ## ## Making model for H_T_7 (l4) ## => Fitting passed... ## ## Making model for N_T_7 (l4) ## => Fitting passed... ## ## Making model for S_T_7 (l4) ## => Fitting passed... ## ## Making model for H_C_8 (l4) ## => Fitting passed... ## ## Making model for N_C_8 (l4) ## => Fitting passed... ## ## Making model for S_C_8 (l4) ## => Fitting passed... ## ## Making model for H_T_8 (l4) ## => Fitting passed... ## ## Making model for N_T_8 (l4) ## => Fitting passed... ## ## Making model for S_T_8 (l4) ## => Fitting passed... ## ## Calculating delta of first/second derivative maxima... ## .........10.........20.........30.........40.........50 ## .. ## Found univariate outlier for NT_C_1 NT_C_3 ## Tagging name of NT_C_1 NT_C_3 ... ## Analyzing H_C_1 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing N_C_1 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing S_C_1 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing H_T_1 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing N_T_1 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing S_T_1 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing **NT_C_1** ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing H_C_2 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing N_C_2 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing S_C_2 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing H_T_2 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing N_T_2 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing S_T_2 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing NT_C_2 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing H_C_3 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing N_C_3 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing S_C_3 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing H_T_3 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing N_T_3 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing S_T_3 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing **NT_C_3** ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing H_C_4 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing N_C_4 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing S_C_4 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing H_T_4 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing N_T_4 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing S_T_4 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing NT_C_4 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing H_C_5 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing N_C_5 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing S_C_5 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing H_T_5 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing N_T_5 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing S_T_5 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing H_C_6 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing N_C_6 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing S_C_6 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing H_T_6 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing N_T_6 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing S_T_6 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing H_C_7 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing N_C_7 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing S_C_7 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing H_T_7 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing N_T_7 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing S_T_7 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing H_C_8 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing N_C_8 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing S_C_8 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing H_T_8 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing N_T_8 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing S_T_8 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... act4res<-setNames(data.frame(t(act4ct)),act4ct[,1]) act4res<-act4res[-1,] act4res$Names<-rownames(act4res)
act4res2<-cSplit_f(act4res, splitCols=c("Names"), sep="_", drop = F)
act4res2<-rename(act4res2, c("Names_1"="Pop", "Names_2"="Treat", "Names_3"="Sample"))
act4res2$Gene<-rep("CRAF", length(act4res2)) act4res2$sig.eff<-as.numeric(as.character(act4res2$sig.eff)) act4res2$sig.cpD2<-as.numeric(as.character(act4res2$sig.cpD2)) ggplot(act4res2, aes(x=Names,y=sig.cpD2, fill=Pop))+geom_bar(stat="identity") expr<-function(x,y){ newVar<-(1+x)^y 1/newVar } act4res2$expression<-expr(act4res2$sig.eff, act4res2$sig.cpD2)
ggplot(act4res2, aes(x=Names,y=expression, fill=Pop))+geom_bar(stat="identity")
#Now that I have Ct values, efficiencies and expression values for both replicates I can create a table of the differences between reps.
#To do this I create a data frame with a single formula that creates a column of values generated by subtracting the first run from the second.
repcomp<-as.data.frame(act3res2$sig.cpD2-act4res2$sig.cpD2)
#Now I need to add some Names for the samples to use with ggplot.Since the names column contains all the relevant information
#I copy only that column and run the split function on it again as well as the rename function.
repcomp$Names<-act3res2$Names
repcomp<-cSplit_f(repcomp, splitCols=c("Names"), sep="_", drop = F)
#To better address the difference column in ggplot I need to rename it something simple and short.
repcomp<-rename(repcomp, c("act3res2$sig.cpD2 - act4res2$sig.cpD2"="rep.diff", "Names_1"="Pop", "Names_2"="Treat", "Names_3"="Sample"))
repcomp<-repcomp[which(repcomp\$Pop!=c("NT","**NT")),]
#Now I just run the data through ggplot to generate a bar graph exploring the differences between the two replicate in terms of Ct values.
ggplot(repcomp, aes(x=Names, y=rep.diff, fill=Pop))+geom_bar(stat="identity")
The results look good. The maximum difference between samples is less than 2 Ct which is more in line with what I want from replicates. This means producing both plates at the same time reduces human error on my part and creates much cleaner replicates. I'm going to rerun the CARM target today using this same method to verify that producing both plates at once is preferable. | 2018-02-24 01:54:20 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.29603147506713867, "perplexity": 2326.7907480329372}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-09/segments/1518891815034.13/warc/CC-MAIN-20180224013638-20180224033638-00417.warc.gz"} |
https://blog.spp2026.de/category/whats-new-on-the-arxiv/ | ### Spaces of positively curved Riemannian metrics
It is by now a classical topic in index theory to study on a (closed) Riemannian (spin) manifold the space of all Riemannian metrics of positive scalar curvature. We have several results showing that this space is usually highly complicated from a homotopy theoretic point of view (provided it is non-empty). Instead of studying positivity … Continue reading "Spaces of positively curved Riemannian metrics"
### Computer assistance and pure mathematics
Today I want to tell you a story of a preprint in pure mathematics that came into existence only by crucial help of precise computer computations. To explain the results, let us first define for a set $$A \subset \mathbb{N}_{>1}$$ of natural numbers $f(A) := \sum_{n \in A} \frac{1}{n \log(n)}\,.$ For $$k \ge 1$$ let … Continue reading "Computer assistance and pure mathematics"
### Conjugation Curvature
Recently I saw some papers on the arXiv on conjugation curvature of finitely generated groups (also called medium-scale curvature, transportation curvature, metric Ricci curvature or comparison curvature for Cayley graphs). I got a bit interested in it and so decided to write up a short post about it. Let $$G$$ be a finitely generated group … Continue reading "Conjugation Curvature"
### Collatz conjecture
Given a natural number n, the Collatz sequence it generates is the following: if n is even, then divide it by 2, if n is odd, then multiply it by 3 and add 1; and now iterate this procedure. The Collatz conjecture states that you will always end up with the number 1 after finitely … Continue reading "Collatz conjecture"
### Large scale properties of 3-manifold groups
A week ago there was a preprint posted on the arXiv by Peter Haïssinsky and Cyril Lecuire about Quasi-isometric rigidity of three manifold groups (arXiv:2005.06813). Building on work by many other people, they complete the proof that the class of 3-manifold groups is quasi-isometrically rigid, meaning the following: if a finitely generated group G is quasi-isometric … Continue reading "Large scale properties of 3-manifold groups"
### Banach conjecture
There was a paper today in the arXiv mailing list (arXiv:2006.00336) proving yet another case of the Banach conjecture. I never heard of this conjecture before, but it is easy to state and seems to me to be a foundational recognition principle for those Banach spaces that are actually Hilbert spaces. The conjecture was stated … Continue reading "Banach conjecture"
### Instability of Anti-de Sitter Space-Time
A recent article in the QuantaMagazine (link) discusses a paper of Georgios Moschidis (arXiv:1812.04268) who proved instability of Anti-de Sitter space-time for a certain Einstein-matter system. Recall that the Anti-de Sitter space-time is the maximally symmetric solution of the vacuum Einstein equations in the presence of a negative cosmological constant. One can attach a boundary-at-infinity to Anti-de Sitter … Continue reading "Instability of Anti-de Sitter Space-Time"
### Local-to-global principles for the topology of boundaries of hyperbolic groups
Two weeks ago a paper was posted (by Benjamin Barrett) on the arXiv (arXiv:2004.11650) proving the following theorem about Gromov boundaries of word hyperbolic groups: Let $$G$$ be a one-ended hyperbolic group. Then $$\partial G$$ is locally simply-connected if and only if for every point $$\xi\in \partial G$$ the space $$\partial G \setminus \xi$$ is … Continue reading "Local-to-global principles for the topology of boundaries of hyperbolic groups"
### Aspherical manifolds and positive scalar curvature
Recall the following conjecture about aspherical manifolds (i.e., manifolds whose universal cover is contractible): If M is a closed, aspherical manifold, then M does not admit any Riemannian metric of positive scalar curvature. In January I saw a preprint being posted on the arXiv (2001.02644) claiming to have resolved this conjecture. If it turns out … Continue reading "Aspherical manifolds and positive scalar curvature"
### A Prime Breakthrough
It seems that at the beginning of this year a major breakthrough on prime numbers was achieved. I learned about it from this blog: link. Let me summarize the result quickly for you if you don’t want to read the other blog post. Almost a hundred years ago Jensen and Pólya proved that the Riemannian … Continue reading "A Prime Breakthrough" | 2020-08-07 13:06:37 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5265858173370361, "perplexity": 552.4104698779579}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-34/segments/1596439737178.6/warc/CC-MAIN-20200807113613-20200807143613-00154.warc.gz"} |
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As we've started discussing, Stack Exchange is planning to redo the editor for all questions and answers across all their sites. As articulated by Emilio Pisanty, these changes will have significant ...
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### What do we mean by welcoming when we're a site aimed at researchers?
I was just browsing the main page this morning, and I decided to look at some of the posts by new people. One of the questions had garnered three votes to close and a comment from a regular user to ...
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### Nudge: the new Stacks editor has significant implications for this site
You have probably seen already a link, on the Featured on Meta sidebar, to an announcement of an upcoming upgrade to the text editor on Stack Exchange, Opt-in alpha test for a new Stacks editor. As a ...
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### Do we use the downvote button more than other sites?
Is there data available (besides crawling thousands of questions) on how often we use the downvote button, and how quickly? The motivation for this question is Carlo Beenakker's recent answer on MOM. ...
1answer
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### Is this an appropriate MathOverflow question: can I ask for some intuition and “excitement” behind the Dynamical Mordell-Lang conjecture?
I am a math undergraduate at my local university, and I have decided to make it a habit to attend the weekly seminars that are given by the faculty. Today, the talk was on the Dynamic Mordell-Lang ...
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### Requests for reopen and undelete votes for on-hold, closed, and deleted questions
Since I expect this may prove rather useful, I'm blatantly purloining Asaf's question from meta.math.se. Please post general requests for reopen votes as answers below. Beware that "short" ...
2answers
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### Is it appropriate to ask why a textbook on nonlinear algebra not well known?
I am wondering if it would be worthwhile to ask why a certain textbook and/or its authors (Dolotin and Morozov) are not well known. From the description of the book: This unique text presents the ...
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### Why is my question is closed and do I get views?
I have a question about my MathOverflow post: the minimum amount of x, x(x(125x + 300) + 240) + 64 is zero, what is 5 times of x? Why is my question is closed and do I get views?
0answers
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### 2020: a year in moderation
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1answer
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### Tea archive (mathoverflow.tqft.net) seems to be down
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1answer
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### Why isn't the link processed in this comment?
At The concept of duality, it looks like the link in the comment is perfectly well formed. Why isn't it parsed as a link?
1answer
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### Should MathOverflow request suggested tags feature?
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### Is anybody else not seeing comments on their iPhone?
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### Scope and mission of MathOverflow
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### MathOverflow policymaking and transparency
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### A radical proposal on votes and reputation
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3answers
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### What are our procedures if a user complains about harassment or abuse?
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### Once a thread is deleted, is it really too late to bring it back?
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### “Scope” of being blocked from asking
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### Appropriateness and cross-posting
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242 views
### Should we have a tag for second-order logic?
There are a number of questions on this site about second-order logic (admittedly I may have asked a few more of them than is reasonable). For example, searching "second-order logic" (in ...
5answers
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### Is it possible to temporarily comment out part of a post?
Scenario (true story): after posting something I became doubtful about certain claim there, so I want to hide it until I clarify my doubts. Of course I could just move that part to a temporary file, ...
1answer
74 views
### \DeclareMathOperator at the beginning of a comment disables some link parsing
In a comment of the form $\DeclareMathOperator\a{a}$Here's a [link](http://mathoverflow.net) and [another link](http://mathoverflow.net) $\a$, neither link is ...
0answers
77 views
1answer
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### Questions seemingly/apparently/ostensibly too elementary for overlfow
Well I don't really get notifications of flag responses sooo... Nov 6 at 14:01 helpful - I suggest you take this up in meta; there is not enough space to answer here. But there are a number of ...
0answers
90 views
### Please help me improve my Q&A and possibly reopen certain questions
Prepare to downvote me. But don't think of not downvoting me just because I pre-emptively self-deprecated myself to put a show of humility. Just pretend I'm as arrogant as I may be perceived to be in ...
0answers
59 views
### Why is the ‘mathematical logic’ tag spelt [lo.logic]? [duplicate]
On MathOverflow, questions about mathematical logic bear the tag lo.logic, which has a synonym of logic. Where did this lo.logic spelling come from? Why is it not ...
15 30 50 per page | 2021-03-08 06:19:04 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5736700892448425, "perplexity": 1702.0462707209335}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178381989.92/warc/CC-MAIN-20210308052217-20210308082217-00573.warc.gz"} |
https://napsterinblue.github.io/notes/stats/basics/conf_ints/ | # Confidence Intervals
### Confidence Interval vs Level
If you’ve got a bunch of data and you’re trying to approximate the average value, you’re going to have to bake in some wiggle room for your prediction.
Assuming that you’ve already cleared our usual sampling conditions, we want essentially want to come up with an expression of
$ourEstimate \pm marginOfError$
How we calculate this “marginOfError” depends on whether we’re looking at a sample mean or proportion (more below), but is basically the product of two parts:
• The standard error, an approximation of the Standard Deviation
• Our test statistic, which is a function of what distribution we’re using (mean vs proportion) and our confidence level
#### Confidence Level
The confidence level is expressed as a percentage and essentially says
In an infinite number of trials, X% of these error bands would contain our population mean
#### Confidence Interval
By extension of that, these “error bands” are your confidence interval.
### Proportion
Calculating the confidence interval for a sample proportion follows the equation
$\hat{p} \pm Z^* \sqrt\frac{\hat{p}(1-\hat{p})}{n}$
Arriving at a Z_star value for a given confidence level has traditionally involved using a lookup table much more robust than below
CL Z*
==========
80% 1.28
90% 1.645
95% 1.96
98% 2.33
99% 2.58
### Mean
Similarly, calculating the confidence interval for a sample mean looks like the following
$\bar{X} \pm t^* \frac{s_x}{\sqrt{n}}$
The lookup table for t_star is a bit more complicated than it’s Z counterpart and also involves another dimension for degrees of freedom.
### In Python
So how do we calculate these in Python?
import numpy as np
from scipy import stats
#### Proportion
1000 values of either 0 or 1
X = np.random.randint(0, 2, (1000))
p_hat = X.mean()
std_err = np.sqrt((p_hat * (1 - p_hat)) / len(X))
print(p_hat - 1.96 * std_err,
p_hat + 1.96 * std_err)
0.477013645945 0.538986354055
scipy has a ROBUST stats api with a ton of functionality, including calculating confidence intervals
stats.norm.interval(0.95, loc=np.mean(X), scale=stats.sem(X))
(0.47699871080518186, 0.53900128919481816)
But I found that for my purposes, I was seldom reaching for the customization they provide. So instead, I threw together stats101 as a thin wrapper with more of the arguments handled automagically.
Now we just apply the confidence level and our data
from stats101 import confidence_interval
confidence_interval.proportion(0.90, X)
(0.48198289796420185, 0.53401710203579811)
confidence_interval.proportion(0.95, X)
(0.47699871080518186, 0.53900128919481816)
confidence_interval.proportion(0.99, X)
(0.46725739973505387, 0.54874260026494615)
#### Mean
Works just as easy for a sample mean
X = np.random.randint(0, 100, (1000))
confidence_interval.mean(0.8, X)
(47.149856666859471, 49.460143333140529)
confidence_interval.mean(0.95, X)
(46.537387386009932, 50.072612613990067)
confidence_interval.mean(0.99, X)
(45.980336643055075, 50.629663356944924) | 2021-01-16 06:37:14 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.567098081111908, "perplexity": 3246.2922633629764}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-04/segments/1610703500028.5/warc/CC-MAIN-20210116044418-20210116074418-00522.warc.gz"} |
https://kasinodqav.web.app/stallard52304ju/roulette-record-of-successive-red-spins-xas.html | # Roulette record of successive red spins
By Editor
Roulette- Probability that Red Comes Up 10 Times in a Row.
Distribution of red/black sequences in number of roulette ... In 1500 spins, there are 1498 possible triplets of spins. For any triplet of spins, the chances of all three coming up red is (18/38) * (18/38) * (18/38) or 0.10628371482 assuming double zero wheel. So you can expect to see 3 consecutive reds 1498 * 0.10628371482 times or 159 times. Of course a sequence of 5 reds is treated as three sequences of 3. Record Roulette The record was registered inwhen red color came spin 32 times in a row! The probability of the 32fold repetition of the same color in American Roulette is much more lower: Thus this roulette even less average than occurrence of a single number six times in a row. Longest Roulette Color Streak — What is the longest ...
## The events "given that the roulette hits $5$ reds, the next hit is red" and "the roulette hits $6$ reds" are different. The first has probability $\frac{1}{2}$ because different spins of the roulette are independent and the second has probability $\frac{1}{64}$ by the multiplication principle.
Roulette - Wikipedia Roulette is a casino game named after the French word meaning little wheel.In the game, players may choose to place bets on either a single number, various groupings of numbers, the colors red or black, whether the number is odd or even, or if the numbers are high (19–36) or low (1–18). probability of 18 reds(roulette) in a row explained by a ...
### Odds of Ten Reds in a Row | Roulette Stakes
Today's Gambling Myth: The Monte Carlo Fallacy It all boils down to one basic, misguided belief: In games of chance, like roulette or craps, if a certain outcome hasn’t happened in awhile, it’s more likely to occur in the future. Seriously, black has hit, like, six times in a row. Has to be red next. Definitely. How often does 6 consecutive red or black spins happen on ... If you're betting red on an American roulette wheel, you should expect to lose 6 or more times, once every 89.387 spins of the wheel. I tested these against a few runs with a random number generator, creating batches of zeros and ones with 0 = black and 1 = red. Roulette Probability Analysis - Kanzen's Roulette Advice Roulette Probability Analysis. At roulette each spin is a new spin and the outcome is never determined by prior spins. After eight successive blacks, a black is as likely to come up as a red. You may argue that the reds and blacks will eventually even out over a long run, and you would be right. probability of 18 reds(roulette) in a row explained by a ...
## Roulette- Probability that Red Comes Up 10 Times in a Row.
What Are The Odds of Red or Black Spinning In a Row ... If you want to get technical, the odds of red then black spinning are 1 in (0.4865 x 0.4865). But it’s the same as red then red spinning, or black then black. The odds of dozens spinning in a row. There are three dozens on the table, and 37 numbers. So the odds of a dozen spinning once is 12/37. Betting on consecutive colors in roulette - DiceTalk This line of thinking is incorrect because past events do not change the probability that certain events will occur in the future when this events are independent. Since roulette spins are independent, the chances of red/black ocurring after a series of red, or series of black outcomes is ~50%. Longest Roulette Streak - carolynhester.com Straight up bets betting on a single number payout is 35 to 1 odds of winning are 1 in 37 European Table Single 0 and 1 in 38 Roulette Table Double 0 Most spins roulette a showing: Most repeated Straight Longest Assume the spin roulette porte coulissante castorama hour at a casino is around 40 - This data covers 25, hours streak wheel spins. | 2021-09-22 12:22:14 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5498477816581726, "perplexity": 1315.515406219426}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-39/segments/1631780057347.80/warc/CC-MAIN-20210922102402-20210922132402-00240.warc.gz"} |
https://www.groundai.com/project/spherical-codes-maximal-local-packing-density-and-the-golden-ratio/ | I INTRODUCTION
Spherical codes, maximal local packing density, and the golden ratio
Adam B. Hopkins, Frank H. Stillinger and Salvatore Torquato
Department of Chemistry, Princeton University, Princeton, New Jersey 08544
Program in Applied and Computational Mathematics, Princeton University, Princeton, New Jersey 08544
Princeton Center for Theoretical Science, Princeton University, Princeton, New Jersey 08544
Princeton Institute for the Science and Technology of Materials, Princeton University, Princeton, New Jersey 08544
School of Natural Sciences, Institute for Advanced Study, Princeton University, Princeton, New Jersey 08544 The densest local packing (DLP) problem in -dimensional Euclidean space involves the placement of nonoverlapping spheres of unit diameter near an additional fixed unit-diameter sphere such that the greatest distance from the center of the fixed sphere to the centers of any of the surrounding spheres is minimized. Solutions to the DLP problem are relevant to the realizability of pair correlation functions for sphere packings and might prove useful in improving upon the best known upper bounds on the maximum packing fraction of sphere packings in dimensions greater than three. The optimal spherical code problem in involves the placement of the centers of nonoverlapping spheres of unit diameter onto the surface of a sphere of radius such that is minimized. It is proved that in any dimension, all solutions between unity and the golden ratio to the optimal spherical code problem for spheres are also solutions to the corresponding DLP problem. It follows that for any packing of nonoverlapping spheres of unit diameter, a spherical region of radius less than or equal to centered on an arbitrary sphere center cannot enclose a number of sphere centers greater than one more than the number that can be placed on the region’s surface.
## I Introduction
The densest local packing (DLP) problem in seeks an arrangement of spheres of unit diameter near (local to) an additional fixed central sphere such that the greatest radius between the centers of the surrounding spheres and the center of the central sphere is minimized. For an optimal configuration of spheres, i.e., a configuration for which is minimized, we call the minimized greatest radius . The ’’ in the notation serves to distinguish from , where in the optimal spherical code (OSC) problem is the radius of the minimal radius sphere onto the surface of which can be placed the centers of nonoverlapping spheres of unit diameter. For , , Fig. 1 depicts a conjectured optimal configuration for the DLP problem with minimal radius alongside an optimal spherical code configuration with minimal distance .
The kissing number problem in seeks the maximum number of nonoverlapping spheres that may simultaneously be in contact with a (additional) sphere;CSSPLG1999 () it is a special case of the DLP problem in that is equal to the greatest for which . The DLP problem can also be said to encompass the sphere packing problem in that in the limit as , optimal sphere packings and optimal DLP packings are equivalent.
The maximum possible with for an optimal DLP configuration of spheres in is the maximum of the function . The function is defined for packings of nonoverlapping spheres of unit diameter as the number of sphere centers that are within distance from a sphere center at position , with an index over all centers and where the value of does not count the sphere center at . For a statistically homogeneous packing, the maximum at fixed of is an upper bound on the maximum of the function , where is the expected number of sphere centers within distance from any given sphere center, or equivalently the average of over all . For a packing that is also statistically isotropic, can be related to the pair correlation function , a function proportional to the probability density of finding a separation between any two points and normalized such that it takes the value of unity when no spatial correlations are present, by
Z(R)=ρs1(1)∫R0xd−1g2(x)dx, (1)
where is the constant number density of points and is the surface area of a sphere of radius in dimensions,
s1(r)=2πd/2rd−1Γ(d/2). (2)
The optimal spherical code (OSC) and DLP problems are similar. A spherical code is defined for parameters as a set of vectors from the origin to points on such that the inner product between any two distinct vectors is less than or equal to . The OSC problem is to minimize given , or to maximize given . There have been a number of investigations into the optimality and uniqueness of specific spherical codes (for example, see Ericson and ZinovievEZCES2001 () and Cohn and KumarCK2007a ()), and into providing bounds on given and .CSSPLG1999 ()
A spherical code may be represented by a packing of nonoverlapping spheres of unit diameter with centers distributed on the surface of a sphere of radius . In this representation, the OSC problem for a given requires finding the minimum , , such that no two spheres overlap, i.e., such that the distance between the centers of any two spheres is greater than or equal to unity.
The OSC problem formulated in terms of nonoverlapping spheres and the DLP problem differ for all where only in that the former restricts the placement of sphere centers to a subset of the space allowed in the latter. From this observation, it is clear that when there exists a configuration of spheres that is a solution to the DLP problem with minimal radius that is also a spherical code, it is additionally a solution to the corresponding OSC problem, with .
## Ii The Densest Local Packing Problem and Realizability
Only functions obeying certain necessary conditions known as realizability conditions can be correlation functions of point processes in .Lenard1975a (); TS2002a (); KLS2007a () Two realizability conditions on the pair correlation function are the nonnegativity of and its corresponding structure factor at all points and .TS2002a () These two conditions appear to be strong conditions for the realizability of sphere packings (point processes in which the minimum pair separation distance is unity), especially as the space dimension increases.TS2006a () They have been employed, among other uses, to provide conjectures for a lower bound on the maximum packing fraction of an infinite sphere packing in any dimension,TS2006a () and to demonstrate the feasibility in three dimensions of a sequence of disordered packings whose disorder vanishes as density approaches the maximum possible.HST2009a ()
Cohn and ElkiesCE2003a () employ analogs of these two conditions, in conjunction with a linear programming technique, to find the best known bounds on the packing fraction of infinite sphere packings in (at least) dimensions four through 36. In the conclusions of a previous work,HST2009a () we discuss how a third realizability condition, found by solving the DLP problem for a packing of 13 spheres in three dimensions, can improve upon the three-dimensional bound found in Ref. 9.
The technique employed in Ref. 7 to find conjectured lower bounds has been shown to be the dual of the primal infinite-dimensional linear program employed in Ref. 9, and Cohn and KumarCK2009a () have since shown that there is no duality gap between the two programs. This means that when the best test functions are employed, the upper and conjectured lower bounds will coincide. Cohn and Elkies in Ref. 9 were able to find a test function that yields the best upper bound on the maximal packing fraction in three dimensions, a packing fraction of , which is well above the true maximum. This means that there is a test function for the lower bound formulation that will deliver the same packing fraction of , which is clearly not realizable.
A putative improvement on the upper bound in was obtained by employing an estimate for in the DLP problem in .CKT2009a () Requiring that up to some small positive beyond contact, with the estimate for , reduces the bound in Ref. 9. For example, estimating footnote1 () reduces the bound from to . This result strongly suggests that DLP solutions introduce more information than is contained in the pair correlation function alone, in that there is at least one test that obeys the two nonnegativity conditions but violates the bound .
Further solutions to the DLP problem provide additional realizability conditions that might be employed to improve upon the upper bounds on infinite sphere packings in dimensions greater than three. For a statistically homogeneous and isotropic packing of spheres, these additional conditions may be written as
Z(R)≤Zmax(R), (3)
where the function is defined in as the maximum number of sphere centers that fit within distance from a central sphere center.footnote2 () It is clear that in is completely defined by the solutions to the densest local packing problem at all .
In the following section, we show that any configuration of -dimensional spheres near a (additional) sphere fixed at the origin, with the greatest of the distances from the origin to the sphere centers equal to the golden ratio, may be transformed to a spherical code in the sense of nonoverlapping spheres, also of radius . As this statement is applicable to any configuration of spheres that is a solution to the DLP problem with , it follows that any optimal spherical code with radius is also an optimal configuration for the corresponding DLP problem, with .
## Iii Translating Unit-Diameter Spheres to the Surface at Radius R≤τ
The key idea behind the proof of the above statement involves translating sphere centers radially outward to a spherical surface of radius . The idea of radially translating points to a spherical surface has been employed by MelissenMelissen1994a () to aid a proof of the optimality of certain packings of 11 congruent nonoverlapping circles in a circle and more recently by Cohn and KumarCK2009b () to rescale vectors in to terminate on . However, prior to this work, the maximum radius from the center of a fixed nonoverlapping sphere to which the centers of surrounding spheres can be translated without resulting overlap was not known.
Specifically, for any number of nonoverlapping spheres of unit diameter initially situated such that their centers are contained in a spherical shell of radial span with , all sphere centers at a distance less than from the center of the shell may be translated radially outward to distance without any resulting overlap between spheres. This statement more generally applies (via a simple scaling argument) to congruent nonoverlapping spheres of arbitrary diameter that are contained within a spherical shell of radial span , .
Define in as the set of all packings of any number of nonoverlapping spheres of unit diameter with centers situated in a spherical shell of radial span , with the greatest of the distances from the center of the shell (the origin) to the sphere centers. An element of the set represents any arrangement of spheres with greatest distance situated near an additional nonoverlapping sphere fixed at the origin.
###### Theorem 1.
Consider any single element of in . For , all spheres may be translated radially outward such that their centers are at distance from the origin and still remain an element of . For , , there exist elements of such that an outward radial translation of a given sphere center to distance will yield overlap between at least two of the spheres.
###### Proof.
The proof proceeds from the law of cosines in the method of the proof of Lemma 4.1 in Ref. 15. For any two of the spheres with centers situated at distances , from the origin and separated by distance , the cosine of the angle formed between the two centers at the origin, taken such that , is
cosθ=b2+c2−a22bc. (4)
For nonoverlapping spheres of unit diameter, , and
cosθ≤b2+c2−12bc, (5)
where the equality holds when the two spheres are in contact.
Over the range , , the function in Eq. (5) is convex individually in both and . This implies that must be at a maximum at one of the corners of the square , . If , the point (or equivalently ) yields the maximum, whereas for , the point yields the maximum, with and both yielding the maximum at .
It follows directly that for , the minimum possible angle at the origin between any two of the centers of spheres that are an element of is the angle present when two of the centers are placed at distance from the origin and distance unity from one another. An outward radial translation of one or both of any pair of centers to distance will therefore yield no overlap between the two spheres, as the angle between the centers must be greater than or equal to the angle present when two spheres are in contact with one another with centers at distance from the origin. As this holds for any pair of the sphere centers, all centers at a distance less than , , may be translated radially outward to distance without any resulting overlap.
For , , overlap between two spheres is possible after an outward radial translation. For example, when two spheres are initially in contact with centers at distance unity from each other and at distances and from the origin, the angle formed at the origin between centers is smaller than the angle present when the spheres are in contact with centers both at distance . A radial translation outward of the sphere center at distance to distance would thus yield overlap. This concludes the proof of Theorem 1. ∎
## Iv Results and Discussion
Theorem 1 applies to any configuration of nonoverlapping spheres that are an element of . In particular, in an optimal DLP configuration for spheres in with , which is by definition an element of , any of the spheres with centers not at distance from the origin may be translated radially outward to distance without any overlap between spheres. The resulting configuration is both a solution to the DLP problem and, in the sense of nonoverlapping spheres, to the corresponding OSC problem, with . Theorem 1 therefore implies that while for there may be solutions to the densest local packing problem that are not spherical codes, for there are no solutions to the optimal spherical code problem that are not also solutions to the corresponding densest local packing problem.
The kissing numbers in are only known rigorously for , and ;Musin2008a (); CSSPLG1999 () for , , and , they are , , and ,Musin2008a () respectively. For , the solution to the DLP problem is simply by necessity as the nonoverlapping sphere of unit diameter at the origin is fixed. For such that , where we define in as the greatest integer such that , the optimal spherical codes are solutions to the corresponding DLP problems with . The questions concerning the values of in each dimension and how grows with naturally emerge.
In one dimension, the answer to the first question is trivial, with . In two dimensions, optimal spherical codes can be found analytically via simple trigonometry, with for , or . Strong conjectured solutions for that serve (at least) as upper bounds to the OSC problem are well-known in low dimensions greater than two for small .SloaneSCweb () For , these yield the conjecture with . For , a unique optimal spherical code is known such that , giving the result that .footnote3 ()
The question of precisely how grows with is still open, and is more complicated; however, bounds may be established via known bounds on (given and ) for optimal spherical codes, such as with those given in chapter two of Ref. 1. The lower bound (due to WynerWyner1965a ()) on for a spherical code of minimum angle in dimension is
N(d,ϕ)≥1sind(ϕ), (6)
giving for , and . This may be compared to the lower bound on the kissing number obtained from (6), . The upper bound due to RankinRankin1955a () is
N(d,ϕ)≤(12πd3cos(ϕ))1/2(√2sin(ϕ/2))−d, (7)
giving, for , . This may be compared to the Kabatiansky-LevenshteinKL1978a () upper bound on the kissing number, . Comparing the upper bound on the kissing number and the lower bound on , it is clear that grows exponentially faster than .
ACKNOWLEDGEMENTS:
The authors thank Henry Cohn for valuable comments and suggestions concerning the manuscript. S.T. thanks the Institute for Advanced Study for its hospitality during his stay there. This work was supported by the Division of Mathematical Sciences at the National Science Foundation under Award Number DMS-0804431 and by the MRSEC Program of the National Science Foundation under Award Number DMR-0820341.
### References
1. Conway, J. H. and Sloane, N. J. A. Sphere Packings, Lattices and Groups. Springer, (1999).
2. Ericson, T. and Zinoviev, V. Codes on Euclidean Spheres. North-Holland, (2001).
3. Cohn, H. and Kumar, A. New York J. Math. 13, 147–157 (2007).
4. Lenard, A. Arch. Ration. Mech. Anal. 59, 219–239, 241–256 (1975).
5. Torquato, S. and Stillinger, F. J. Phys. Chem. B 106, 8354–8359 (2002).
6. Kuna, T., Lebowitz, J. L., and Speer, E. R. J. Stat. Phys. 129, 417–439 (2007).
7. Torquato, S. and Stillinger, F. H. Exp. Math. 15, 307–331 (2006).
8. Hopkins, A. B., Stillinger, F. H., and Torquato, S. Phys. Rev. E 79, 031123 (2009).
9. Cohn, H. and Elkies, N. Ann. Math. 157, 689–714 (2003).
10. Cohn, H. and Kumar, A. Unpublished.
11. Cohn, H., Kumar, A., and Torquato, S. Unpublished.
12. The actual number is strongly conjectured to be , equal to the current best lower bound for in .
13. In the sense of defined in Eq. (1) for a statistically homogeneous packing, is generally not a sharp upper bound for , i.e., there is not always a configuration of spheres for which equality in (3) holds. This is because is defined locally, in terms of one central sphere, whereas in Eq. (1) is defined globally in terms of a probability density, or in the case of a finite packing, in terms of an average over all spheres.
14. Melissen, H. Geom. Dedicata 50, 15–25 (1994).
15. Cohn, H. and Kumar, A. To appear in Ann. Math.
16. Musin, O. R. Ann. Math. 168, 1–32 (2008).
17. Sloane, N. J. A., Hardin, R. H., and Smith, W. D.
18. It has been shown that the vertices of the -cell are the unique spherical code,Boroczky1978a (); BD2001a () which corresponds in to .
19. Wyner, A. D. Bell Sys. Tech. J. 44, 1061–1122 (1965).
20. Rankin, R. A. Proc. Glasgow Math. Assoc. 2, 139–144 (1955).
21. Kabatiansky, G. A. and Levenshtein, V. I. Probs. of Info. Trans. 14, 1–17 (1978).
22. Böröczky, K. Acta Math. Acad. Sci. Hung. 32, 243–261 (1978).
23. Boyvalenkov, P. and Danev, D. Arch. Math. 77, 360–368 (2001).
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The feedback must be of minimum 40 characters and the title a minimum of 5 characters | 2020-11-26 08:56:37 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.886265754699707, "perplexity": 500.6397938175313}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-50/segments/1606141187753.32/warc/CC-MAIN-20201126084625-20201126114625-00286.warc.gz"} |
https://www.physicsforums.com/threads/school-names-matter.719770/ | # School names matter?
Tags:
## What kind of engineering degree did you get?
2 vote(s)
50.0%
0 vote(s)
0.0%
1 vote(s)
25.0%
4. ### Dropout (steve jobs type, programmer...)
1 vote(s)
25.0%
1. Oct 30, 2013
### publicboolean
School names matter!?
I need help bad. I'm stuck in the college mentality and I'm hoping someone can snap me out of it. I'm so stressed about which school i should get into that it's eating my time up studying physics. Here's my situation. I'm ready to transfer to San Francisco State University this Spring 2014. Although, I really want to put my app in at UC Berkeley or Stanford but they require all the way up to Linear Algebra to even be considered for admission. The timing of my life led me to finish everything except Linear Algebra, including all my Gen Ed at a weird time of year (70+ credits already with 3.78 gpa). That means if I want a "prestigious name" school, I need to wait until next fall, to be eligible to apply for the NEXT fall 2015!. That puts me graduating about 2017!. All because I wanted to wait for a hotshot school that may or may not even let me in.
OR....I am already accepted to SFSU and begin this spring, roll right into my upper level classes right along with my oddly timed semester of Linear Algebra and graduate sometime by the end of 2015.
My main point... Does it really matter in the real world where I get my electrical engineering degree? I already have 15 years experience as an electronics tech, and prior military with a good record and security clearances. I just want someone to tell me that it doesn't matter, and that i should quit fussing about and go to an average state school like thousands of other people do every year. But, if you are positive that the delay for a chance at UCBerkeley or Stanford is worth it, let me know with some numbers. Real world examples and stuff! (i.e. , girls, respect..) Thanks in advance.
Sincerely,
Joe Student
2. Oct 30, 2013
### Student100
You don't even know if you'd be . accepted at those schools, waitlisted... ect. The other UC schools may be an option too. UC san Diego has a well represented engineering department and don't require linear be done first, though it's recommended. You should apply for next fall.
3. Nov 4, 2013
### BOAS
It is true that a degree from UC Berkeley sounds impressive but I can guarantee you that a first class degree from San Francisco is better than a second class degree from anywhere.
4. Nov 4, 2013
Staff Emeritus
San Francisco is in the United States, where there are not "first class" and "second class" degrees. That's a UK thing.
5. Nov 4, 2013
### BOAS
I'm aware of where San Francisco is, my presumption being that you don't just "graduate", there's a form of grading system.
6. Nov 4, 2013 | 2018-01-20 05:45:12 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.20240183174610138, "perplexity": 1946.7061784691143}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-05/segments/1516084889325.32/warc/CC-MAIN-20180120043530-20180120063530-00063.warc.gz"} |
https://math.stackexchange.com/questions/1854123/prove-if-a1-then-lim-n-rightarrow-inftyan-infty | Prove if $a>1$ then $\lim_{n\rightarrow\infty}a^{n}=\infty$
Good morning i was thinking about this problem and I make this. I need someone review my exercise and say me if that good or bad. Thank!
Problem: Prove if $a>1$ then $\lim_{n\rightarrow\infty}a^{n}=\infty$
Proof:
Suppose $\left\{ a^{n}\right\}$ is monotonically increasing. In other words $a^{n}<a^{n+1}< a^{n+2}...$ and Suppose $\left\{ a^{n}\right\}$ is Bounded set then $\left\{ a^{n}\right\}$ converge. By definition $\lim_{n\rightarrow\infty}a^{n}=L$.
We know this
$\left(a^{n+1}-a^{n}\right)=a^{n}(a-1)$ , $(a-1)>0$. Because $a>1$
Then
$a^{n}(a-1)>(a-1)\Rightarrow a^{n}>1$
Exist $N ∈ \mathbb{N}$ such that $a^{N}$ > $L$ and $\left\{ a^{n}\right\}$ is non bounded set Then $\left\{ a^{n}\right\}$ diverge and
$\lim_{n\rightarrow\infty}a^{n}=\infty$
• en.wikipedia.org/wiki/Bernoulli%27s_inequality – Gabriel Romon Jul 9 '16 at 15:20
• Your proof is not good. How can you conclude that $a^n(a-1)>(a-1)$?Maybe you already assume that $a^n>1$?And the following statement is also not completely correct. I think you may take the following answers to complete your proof. – Deepleeqe Jul 9 '16 at 15:47
• a>1 so $a^{n+1} = a(a^n) > a^n$ solves Deepleeqe's objection. My concern is there exist N so that $a^N > L$. Why? that seems like you are assuming what you wish to prove. – fleablood Jul 9 '16 at 22:12
An other way
Let $a>1$. $$a^n=e^{n\ln(a)}\underset{\ln(a)>0}{>}n\ln(a)\underset{n\to \infty }{\longrightarrow }\infty .$$
An other way (using Bernoulli)
Since $a>1$, there is $\varepsilon>0$ s.t. $$a=1+\varepsilon.$$ Using Bernoulli, $$a^n=(1+\varepsilon)^n\geq n\varepsilon+1.$$
Simply use this version of Bernoulli's inequality:
For any $a>0$, one has $\quad a^n-1\ge n(a-1)$
to show than $a^n$ can be made larger than any prescribed number.
You can achieve your proof using contradiction: If the limit $L$ of $(a^n)$ is finite then
$$\lim_{n\to\infty} a^{n+1}-a^n=0=\lim_{n\to\infty} a^n(a-1)=L(a-1)\implies L=0$$ which is a contradiction.
An alternative proof is: let $h>0$ such that $a=1+h$ so
$$a^n=(1+h)^n\ge 1+nh\xrightarrow{n\to\infty}+\infty$$
• My proof are bad? Sure? – Bvss12 Jul 9 '16 at 15:34
• @Battani Probably by the fact that $L(a-1)=0=\lim(a^{n+1}-a^n)$ and that $a-1\ne 0$. – BigbearZzz Jul 9 '16 at 16:32
What you need to show is that for any $x > 0$, there is an $N > 0$ such that $a^N > x$.
Given that you have shown the difference between elements is greater than $a - 1$, this means that you can choose $N$ to be any integer larger than $\frac{x}{a-1}$.
• But my proof is bad, sure? Thanks. – Bvss12 Jul 9 '16 at 15:24
A problem I see with your proof is that $$(a-1)>0$$ does NOT implies that $$a^n(a-1)>(a-1).$$
This means that you cannot just cancel $(a-1)$ on both sides to get $a^n>1$. Anyway, the fact can be easily proved by induction so this is not the real problem here.
The main problem with your proof is that you seemed to claim that if $a^n>1$ for all $n\in\Bbb N$, then there exists an $N\in\Bbb N$ such that $$a^N>L\ .$$ This does not follow logically from your previous points.
If you somehow think that I misunderstood you, you'll have to be more explicit in each of your steps.
• Yes it does imply that. A positive times something greater than 1 (which a^n clearly is) is more than the same positive times 1. – Jacob Wakem Jul 9 '16 at 21:13
• " (which a^n clearly is)" if it was that "clear" we could have simply said "a^n is clearly monotonically increasing". To claim (a - 1) > 1 implies a^n(a - 1) > a-1 we have to show a^n > 1. Which is easy. But easy in such a way that the entire discussion should have been avoided. – fleablood Jul 9 '16 at 22:17
• @JacobWakem If you read my post carefully, you'll see that I never denied the truthfulness of the statement $a^n>1$. The OP tried to deduce $a^n(a-1)>(a-1)$ from $(a-1)>0$, without assuming that $a^n>1$ in the beginning, that's what I denied. – BigbearZzz Jul 10 '16 at 1:54
• @BigbearZzz Ah I see. Maybe its just an intuitive leap, I don't know. – Jacob Wakem Jul 10 '16 at 2:08
Your phrasing is very bad — for instance, you say 'suppose $\{a^n\}$ is monotonically increasing', but in fact that's not something you should suppose; it's something that's true, and you should prove it.
You've got a good idea in the next step: once you know that $\{a_n\}$ is monotonic increasing, you can use the Monotone Convergence theorem to derive a contradiction. Unfortunately, as others have noted your attempted proof from there is mathematical gibberish.
Instead, you can use an argument like this: Suppose that $\{a^n\}$ were bounded. Then by the Monotone Convergence theorem it has a limit $L$. By the definition of limit, for every $\epsilon$ we can choose an $n_0$ such that $|L-a^n|\lt\epsilon$ for all $n\gt n_0$. Now, the plan is to find a particular $\epsilon$ for which this breaks down. If we pick some specific $m\gt n_0$ and the 'right' epsilon, then the idea is that $a^m$ is 'close enough' to $L$ that $a^{m+1}=a\cdot a^m$ is guaranteed to be larger than $L$ (what size does $\epsilon$ have to be for you to guarantee this?); then $a^{m+2}=a\cdot a^{m+1}\gt aL$. But this implies that $|a^{m+2}-L|\gt (aL-L)=(a-1)L$, and if $\epsilon$ is chosen correctly, then this supplies the contradiction and proves that the assumption of boundedness must be wrong. | 2019-10-22 08:47:43 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9204898476600647, "perplexity": 224.56811125328687}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-43/segments/1570987813307.73/warc/CC-MAIN-20191022081307-20191022104807-00126.warc.gz"} |
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https://setiapoker.org/justin-timberlake-fmcyqg/2c8b32-reaction-of-metals-with-bases | # reaction of metals with bases
5. Common examples of strong bases include hydroxides of alkali metals and alkaline earth metals… Can calcium hydroxide + sulphuric acid be a way of preparing insoluble calcium sulphate? Acids react with metals, bases and carbonates to produce salts. Metal hydroxides like this are described as basic hydroxides. For example, sodium hydroxide reacts with zinc and water to form sodium zincate and hydrogen gas. (Ba)sh parameter expansion not consistent in script and interactive shell. Sn(II) is oxidized by Hg 2 2+. Show More. Base + Non-metal oxide Salt + Water Example: 2 N a O H + C O 2 N a 2 C O 3 + H 2 O Recall that an activity series is a list of metals in descending order of reactivity. 4. General equation for the reaction of an acid with a metal. Alkaline earth metals (Be,Mg,Ca,Sr,Ba,Ra) have similar and different characteristics to alkali metals. Neutralisation is the reaction between an acid and a base. To subscribe to this RSS feed, copy and paste this URL into your RSS reader. Let us consider the reaction of sodium carbonate with dilute HCl. 2:37 describe the reactions of hydrochloric acid, sulfuric acid and nitric acid with metals, bases and metal carbonates (excluding the reactions between nitric acid and metals) to form salts 2:38 know that metal oxides, metal hydroxides and ammonia can act as bases, and that alkalis are bases … Reaction with Acids → Metal + Dilute acid → Metal salt + H 2 → H 2 doesn’t evolve in the case of HNO 3 as it is a strong oxidising agent. This video explains the reaction of metals with cold water and acids. Use MathJax to format equations. Depends on the metal. As discussed previously, metals that are more active than acids can undergo a single displacement reaction.For example, zinc metal reacts with hydrochloric acid producing zinc chloride and hydrogen gas. When aluminium metal is heated with sodium hydroxide solution,the sodium aluminate and hydrogen gas is formed. This is the general equation for the reaction between an acid and a metal hydroxide. The type of salt that forms will depend on the specific metal and acid which are used in the reaction. Metal Hydrogencarbonates are formed by reaction of metal salt with HCO 3 or with a hydrogencarbonates of a more reactive metal. e.g. Acids react with most metals and, when they do, a salt is produced. Neutralisation is the reaction between an acid and a base. The reaction between non-metals and bases is a very complex one. C) with bases. Proper technique to adding a wire to existing pigtail. For example, acids have some general rules. This reaction is called a neutralization reaction. aluminium and sodium hydroxide react giving gelatinous precipitate of aluminium oxide. Metal carbonates and Metal Hydrogencarbonates reacts with acids and produces corresponding metal salt, carbon dioxide and water. Most of the metals react with acids to form salt and hydrogen gas. Question: Discuss Reaction Of Group 2 Alkaline Earth Metal With Acids And Bases. CBSE Class 8 Science Reaction of Metals With Water, Acids & Bases. However, the latter reaction occurs faster because of the increased acidity of water (K a value of 1 × 10 −15). Give example for each reaction Some they are even solid at room temperatures like Carbon, sulfurand phosphorus. Calcium hydroxide, which is a base, reacts Base + Non-metal oxide Salt + Water Example: 2 N a O H + C O 2 N a 2 C O 3 + H 2 O Observing Acid-Metal Reactions. On the same level of generalization, the rule is "no reaction", but this rule has quite a few exceptions (probably more than the rules you quoted above). General equation for the reaction of an acid with a metal. Reactivity of bases with non-metallic oxide - definition Non-metal oxides are acidic in nature. Reaction of acids with metal carbonates and bicarbonates. Reactions of non-metals with bases are complex. Reaction of metal carbonates and metal hydrogen carbonates w, Reaction of non-metallic oxides with base. Most metals do not react with bases but zinc metal does because it is amphoteric. Metal oxides and metal hydroxides can act as bases; When they react with acid, a neutralisation reaction occurs; In all acid-base neutralisation reactions, salt and water are produced; Acid + Base → Salt + Water. The full equation for the reaction between sodium hydroxide solution and dilute sulfuric acid is. Acids and Bases React with Metals. Such base may be metal oxides, metal hydroxides, metal carbonates and ammonia. The metals combine with remaining part of acids to form a salt. About This Quiz & Worksheet. NaOH) by their reaction with Litmus solution (blue/red) Zinc metal Solid sodium carbonate Materials Required Test tubes, test tube stand, test tube holder, cork, droppers, boiling tube, match-box, burner, […] The type of salt that forms will depend on the specific acid and metal hydroxide which were used in the reaction. Common examples of strong bases include hydroxides of alkali metals and alkaline earth metals, like NaOH and Ca(OH) 2, respectively. Here we discuss about occurrence, reactions, physical properties of alkaline earth metals. For example reaction of zinc with sodium hydroxide. Non-metals are themselves acceptors of electrons so there is no way they can donate electrons to the hydrogen ion of the acid. It only takes a minute to sign up. By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy. Only the less reactive metals like copper,silver and gold do not react with dilute acids. 4. Non-metals are those which lack all the metallic attributes. Do all metals react with acids in the same way? The general word equation for the reaction between an acid and a metal is: acid + metal → salt + hydrogen gas. What's chemistry without combining a bunch of stuff together, right? Examples of Reaction Between Acids and Bases: Acids react with most metals to form a salt and hydrogen gas. Chemical Properties of Metals and Non-metals - 2. ; Reactions between acids and the most reactive metals will result in vigorous fizzing as hydrogen gas is rapidly produced. But unlike the reaction between acids and bases, we do not get water. Metals always forms basic oxide and hydroxides on reaction with acid. If a US president is convicted for insurrection, does that also prevent his children from running for president? Metals that are above hydrogen in the activity series will replace the hydrogen from an acid in a single-replacement reaction, as shown below: Acids react with bases to produce a salt compound and water. Reaction of metals with acids. Example : Aluminium will form a salt with acids, like: Al+3HCl->AlCl_3+1.5H_2 (aluminium chloride) Or Al+3H^+ ->Al^(3+) +1.5H_2 But also with a base, like: Al+3NaOH->Na_3AlO_3+1.5H_2 (sodium aluminate) Or Al+3OH^(-) ->AlO_3^(3-)+1.5H_2 (I know I should have … On the same level of generalization, the rule is "no reaction", but this rule has quite a few exceptions (probably more than the rules you quoted above). For example reaction of sulphuric acid with zinc. This app allows you to study about Base reaction with metal in an easy and int… Indicators are used to determine whether a solution is acidic or alkaline. The reaction of ethanol with sodium metal (a base) produces sodium ethoxide and hydrogen gas. Only the less reactive metals like copper,silver and gold do not react with dilute acids. A soluble base like sodium hydroxide is called an alkali. We see how metal carbonates and bicarbonates react with acid to form salt, water, and release carbon dioxide. Metals react with acids and displaces hydrogen from the acids to produce hydrogen gas and metal salt. Acids react with metallic oxides to give salt and water similar to the reaction acid and base So, metallic oxides are called basic oxide Reaction of a Non – metallic oxide with base When base reacts with non-metallic oxide then it forms salt and water Non – metallic oxide + base – salt + water Non-metals:The reactions of non-metals with bases are complex. You will learn about them in higher classes. Observing Acid-Metal Reactions. Likewise, similar reactions occur with potassium metal. This reaction is identical to the reaction of sodium metal with water. E) with water. Why does the U.S. have much higher litigation cost than other countries? 2Zn + O 2 → 2ZnO ; Iron does not burn in air but iron filings when sprinkled in the flame burns vigorously. 3Fe + O 2 → Fe 3 O 4; Reaction of Metals with Oxygen: Least reactive metals . If a matchstick is brought near the mouth of the tube containing the product of the reaction then we hear a pop sound. Acids react with most metals and, when they do, a salt is produced. Indicators are used to determine whether a solution is acidic or alkaline. Acids and bases will react to produce a salt and water: Acid + Base → Salt + Water. When a base reacts with non-metal oxide, both neutralize each other resulting respective salt and water are produced. However, the latter reaction occurs faster because of the increased acidity of water (K a value of 1 × 10 −15). Acids react with active metals to yield hydrogen gas. For instance, Magnesium reacts with dilute hydrochloric acid to form magnesium chloride and hydrogen. Practice: Identifying the gas released. The type of salt that forms will depend on the specific metal and acid which are used in the reaction. zinc and sulphuric acid react giving zinc sulphate, a salt and hydrogen gas. It is this hydrogen gas that burns with a pop sound. Reactivity of bases with non-metallic oxide - definition Non-metal oxides are acidic in nature. Important Questions Ask Doubt. The reaction of chlorine with bases like sodium hydroxide gives products like sodium hypochlorite, sodium chloride as well as water. Not all non-metals do not react with bases, but some do, particularly, the halogens. Metals in chemical reactions forms positive ions, for example dissociation of HCl in water forms H + ion. But all metals do not react with bases to produce hydrogen gas Some non metals react with bases but no hydrogen gas is produced Reaction of acids and bases Reaction of acids with metal carbonates and bicarbonates Google Classroom Facebook Twitter You could perform the above activity using small pieces of zinc and sodium hydroxide solution (instead of magnesium ribbon and dilute sulphuric acid) to test that hydrogen is evolved in the reaction. If a matchstick is brought near the mouth of the tube containing the product of the reaction … Acid + Base – Salt + Water suppose we add NaOH to hydrochloric acid, the sodium salt gets formed along with water, which is the best example of neutralization reaction. Reaction of metals with bases - definition Base+metals → base/metals/salt + H 2 “Bases react with metal” is an amazing educational lab experiment tool. They are mostly gases and sometimes liquid. Can an electron and a proton be artificially or naturally merged to form a neutron? $\begingroup$ To put things into perspective: you might have heard that many metals react with acids. ... Non-metals will normally not react with water, however, non-metal oxides will react with water to form acids. Not all metals react this way, but many do. Reaction of Metal with Acid Metal + Acid Metal Salt + Hydrogen Example Magnesium + Hydrochloric Acid Magnesium Chloride + Hydrogen Gas (Mg) (HCI) (MgCl 2) (H2) This is a Metal Salt Aluminum + Hydrochloric Acid Aluminum Chloride + Hydrogen Gas (AI) (HCI) (AlCl3) (H2) This is a Metal Salt Reaction of Non-Metal with Acid Non Metal + Acid No Reaction Example … Zinc burns in air, only when strongly heated, forming zinc oxide. CBSE Class 10 Science Lab Manual – Properties of Acids and Bases EXPERIMENT 2(a) Aim To study the properties of acids (dil. “Bases react with metal” is an educative application in support to high school students. Some metals react with bases to produce hydrogen gas. Non-metals: The reactions of non-metals with bases are complex. You will learn about them in higher classes. But unlike the reaction between acids and bases, we do not get water. An acid in a water solution tastes sour, changes the colour of blue litmus paper to red, reacts with some metals (e.g., iron) to liberate hydrogen, reacts with bases to form salts, and promotes certain chemical reactions (acid catalysis). Displacement Reactions. Or calling a metal amphoteric is something done in informal talk and should be avoided in the exams? Javascript function to return an array that needs to be in a specific order, depending on the order of a different array, How to mount Macintosh Performa's HFS (not HFS+) Filesystem, Concatenate files placing an empty line between them, Intersection of two Jordan curves lying in the rectangle. MathJax reference. This is the currently selected item. Reaction of metals and with a base Some metals react with a base to form salts and hydrogen gas. Very few metals react with bases. Metals react with acids and displaces hydrogen from the acids to produce hydrogen gas and metal salt. Only a few, like aluminium, zinc, and lead, react with solutions of strong bases like sodium hydroxide to produce a compound of that metal and hydrogen gas. Electrochemical series is the development of a series of metals that are arranged as per their reactivity in a sequence from highest to lowest. Making statements based on opinion; back them up with references or personal experience. When metals react with acid bubbles of gas are produced. Alkalis (soluble bases) include soluble metal hydroxides, soluble metal carbonates and ammonia. How can Arrhenius bases also be Brønsted-Lowry bases? Water-soluble bases would react with amphoteric metals to produce hydrogen and the corresponding salt: … site design / logo © 2021 Stack Exchange Inc; user contributions licensed under cc by-sa. A strong base is a basic chemical compound that can remove a proton (H +) from (or deprotonate) a molecule of even a very weak acid (such as water) in an acid-base reaction. Reaction of acids and bases with metals (video) | Khan Academy All your questions are applicable to that reaction as well. HCl) and bases (dil. Metal + Acid ——–> Salt + Hydrogen. Reactions of acids with metals. When metals react with acid produce hydrogen gas along with salt of the metal. Reaction of Metal with Base Metal + Base Salt + Hydrogen Gas Example Aluminum + Sodium Hydroxide (AI) (NaOH) Sodium Aluminate + Hydrogen (NaAlO2) (H2) It is a Base It is a Salt. Zn (s) + 2 NaOH (aq) + 2 H 2 O (l) → Na 2 Zn (OH) 4 (aq) + H 2 (g). Water-soluble bases would react with amphoteric metals to produce hydrogen and the corresponding salt: But others, called amphoteric metals, may form salts with them. Example : Aluminium will form a salt with acids, like: Al+3HCl->AlCl_3+1.5H_2 (aluminium chloride) Or Al+3H^+ ->Al^(3+) +1.5H_2 But also with a base, like: Al+3NaOH->Na_3AlO_3+1.5H_2 (sodium aluminate) Or Al+3OH^(-) ->AlO_3^(3-)+1.5H_2 (I know I should have … Book, possibly titled: "Of Tea Cups and Wizards, Dragons"....can’t remember. Most metals will not react with bases. The full equation for the reaction between sodium hydroxide solution and dilute sulfuric acid is. When a base reacts with non-metal oxide, both neutralize each other resulting respective salt and water are produced. When Acid Gets Mixed Up With A Base:- When the acids get mixed up with a base, the reaction is … Is it possible for planetary rings to be perpendicular (or near perpendicular) to the planet's orbit around the host star? Some metals react with water or steam forming metal hydroxides. Discuss reaction of group 2 alkaline earth metal with acids and bases. Are there general rules for Base + Metal Compound reactions like there are for Acids? e.g. Metals react with acids and displaces hydrogen from the acids to produce hydrogen gas and metal salt. Some metals react with Bases to produce Salt and Hydrogen Gas Note : Metals like Zinc (Zn) and Aluminium (Al) react with bases to produce hydrogen. Which satellite provided the data? Thanks for contributing an answer to Chemistry Stack Exchange! Metals undergo redox reaction instead of acid-base reactions, don't they? fly wheels)? All metal hydroxides, solid or in solution, are bases because they contain hydroxide ions. All metal hydroxides, solid or in solution, are bases because they contain hydroxide ions. So if I write in an examination that certain metal is amphoteric, will it be accepted by a general examiner? Metal hydroxides like this are described as basic hydroxides. But others, called amphoteric metals, may form salts with them. Reaction of tin with metals/metal ions. Are there any alternatives to the handshake worldwide? Progress through the quiz and worksheet to see how much you know about reactions of acids with metals. $$2\ce{Al + 2KOH + 6H2O \to 2KAl(OH)4 + 3H2}$$. Alkali is considered as strong base. The reaction of ethanol with sodium metal (a base) produces sodium ethoxide and hydrogen gas. (In most inorganic curriculums, this is a pretty heavily used example, and even the defining feature of acids, at least until you get to Brønsted–Lowry). In a displacement reaction, a metal reacts with a salt solution and ‘displaces’ (or replaces) the metal present in it. For each type of reaction, ... Acids react with bases to form a neutralization reaction which results in a salt and water. Likewise, similar reactions occur with potassium metal. Water-soluble bases would react with amphoteric metals to produce hydrogen and the corresponding salt: 2\ce{Al + … Alkalis (soluble bases) include soluble metal hydroxides, soluble metal carbonates and ammonia. Give Example For Each Reaction Give Example For Each Reaction This problem has been solved! This reaction is used for qualitative analysis for Sn(II): Hg 2 2+ (aq) + Sn 2+ (aq) 2 Hg (l) + Sn 4+ (aq) Under acidic conditions and in the presence of chloride ions, Hg(II) is reduced to Hg(I) by Sn(II), forming Hg 2 Cl 2: Why did it take so long to notice that the ozone layer had holes in it? When sodium hydroxide solution is heated with zinc, then sodium zincate and hydrogen gas are formed. All metal oxides, metal hydroxides can act as bases. Hence, non-metals in general do not react with dilute acids. This reaction is identical to the reaction of sodium metal with water. Do carboxyl groups behave like bases and amino groups behave like acids when peptide bonds are created? Some metal reacts with a base to form salts and hydrogen gas. Amazing app will teach the user, bases reactions with metal. Reaction of metals with acids. Displacement reactions are explained on the basis of the activity series of metals. Reaction with Oxygen. How do I write out the chemical reaction of ammonia with strong acid? On the same level of generalization, the rule is "no reaction", but this rule has quite a few exceptions (probably more than the rules you quoted above). Asking for help, clarification, or responding to other answers. Burning paper is shown in to the mouth of the test tube and it put down with ‘pop 'sound which indicate presence of hydrogen. A soluble base like sodium hydroxide is called an alkali. Acids react with metals, bases and carbonates to produce salts. Alkalis (bases that are soluble in water) react with the metal to produce salt and hydrogen gas. Reaction of Base with Metals: Transcript. 3.11 Explain the general reactions of aqueous solutions of acids with: metals, metal oxides, metal hydroxides, metal carbonates to produce salts 3.15 Explain why, if soluble salts are prepared from an acid and an insoluble reactant: excess of the reactant is added; the excess reactant is removed; the solution remaining is only salt and water Since a chemical reaction between an acid and a metal will produce hydrogen gas, this can be used to determine whether a particular metal has reacted with an acid or not. The ionic salt of alkali and alkaline earth metals are soluble in water. Reaction of Metals with oxygen: Moderately reactive metals . Most of the metals react with acids to form salt and hydrogen gas. Reaction with acids: Bases react with acids to form salt and water. ; Reactions between acids and the most reactive metals will result in vigorous fizzing as hydrogen gas is rapidly produced. Bases are substances that taste bitter and change the colour of red litmus paper to blue. Stack Exchange network consists of 176 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. The base in our reaction was a metal hydroxide, so the general equation becomes: acid + metal hydroxide → salt + water. Acid + Metal Carbonate => Salt + Water + Carbon Dioxide. 3.11 Explain the general reactions of aqueous solutions of acids with: metals, metal oxides, metal hydroxides, metal carbonates to produce salts 3.15 Explain why, if soluble salts are prepared from an acid and an insoluble reactant: excess of the reactant is added; the excess reactant is removed; the solution remaining is only salt and water rev 2021.1.11.38289, The best answers are voted up and rise to the top, Chemistry Stack Exchange works best with JavaScript enabled, Start here for a quick overview of the site, Detailed answers to any questions you might have, Discuss the workings and policies of this site, Learn more about Stack Overflow the company, Learn more about hiring developers or posting ads with us. Chemical Properties of Bases: Reaction with metals: Certain metals such as zinc, aluminium and tin react with alkali solutions on heating and hydrogen gas is evolved. Can 1 kilogram of radioactive material with half life of 5 years just decay in the next minute? Chemistry Stack Exchange is a question and answer site for scientists, academics, teachers, and students in the field of chemistry. Why is there no Vice Presidential line of succession? If a matchstick is brought near the mouth of the tube containing the product of the reaction … Examples of reaction between acids and bases: Acids with metal carbonates . Oxides of non-metals are formed when it reacts with oxygen. What are the earliest inventions to store and release energy (e.g. Bases also react with certain metals, like zinc or aluminum, to produce hydrogen gas. Since a chemical reaction between an acid and a metal will produce hydrogen gas, this can be used to determine whether a particular metal has reacted with an acid or not. Eg : Zn+2HCl ZnCl2 + H2 6. When a Base Is Mixed Up With a Metal:-When a base, get mixed up with a metal, the … That is, it reacts with acids as well as bases. Alkaline earth metals are reactive but less than alkali metals. Bases, both soluble and insoluble, react with acids to form salts. Copper does not react with hydrochloric acid because it is below hydrogen in the electrochemical series due to which it does not react liberate hydrogen but reacts with sulphuric acid. Concepts. Class 10 Chemistry Acids Bases Salts: Reaction of metals with acids: Reaction of metals with acids. To learn more, see our tips on writing great answers. Reactions of acids with metals. metallic oxides react with acids to give salts and water, similar to the reaction of a base with an acid, metallic oxides are said to be basic oxides. Metals form salts with acids. How do I run more than 2 circuits in conduit? Depends on the metal. These are also known as alkali. Class 10 Chemistry Acids Bases Salts: Reaction of metals with acids: Reaction of metals with acids. D) with acids. For example – sodium hydroxide, magnesium hydroxide, calcium hydroxide, etc. NaOH + Al ——-> NaAlO2 + H2 3. How do I express the notion of "drama" in Chinese? Such base may be metal oxides, metal hydroxides, metal carbonates and ammonia. Bases, both soluble and insoluble, react with acids to form salts. Mismatch between my puzzle rating and game rating on chess.com. When they react with acid, a neutralisation reaction occurs. Reaction of acids and bases with metals. It oxidises H 2. Acids react with metal oxides to give salt and water. They are good insulators of heat and electricity. Metals: Most metals do not react with bases. A strong base is a basic chemical compound that can remove a proton (H +) from (or deprotonate) a molecule of even a very weak acid (such as water) in an acid-base reaction. 2.1.6 Reaction of a Non-metallic Oxide with Base You saw the reaction between carbon dioxide and calcium hydroxide (lime water) in Activity 2.5. Metal + Acid ——–> Salt + Hydrogen. The present knowledge of reactions between the alkali metals, lithium, sodium, potassium and rubidium with the platinum group metals, platinum, palladium, rhodium, iridium, osmium and ruthenium, their reaction products, and the relevant binary phase diagrams, is surveyed. The general word equation for the reaction between an acid and a metal is: acid + metal → salt + hydrogen gas. How can a metal be 'amphoteric'? Most metals will not react with bases. | 2021-10-27 23:49:07 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.49920642375946045, "perplexity": 4208.797116845883}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-43/segments/1634323588244.55/warc/CC-MAIN-20211027212831-20211028002831-00622.warc.gz"} |
https://www.zbmath.org/?q=an%3A1083.35058 | ## Some special solutions of the multidimensional Euler equations in $$\mathbb R^N$$.(English)Zbl 1083.35058
The multidimensional Euler equations for compressible gas are considered. The gas is polytropic, so the pressure $$p$$ depends on the density $$\rho$$: $$p(\rho)=\frac{\rho^\gamma}{\gamma}$$. For the case of spherical symmetry the equations become simpler. The special solution for constant with respect to $$x$$ density are obtained. Then the author finds out that the critical mass is infinite and thus no blow-up is possible for finite mass. For infinite mass the solution blows up everywhere in finite time for suitable initial velocity. Finally, using the total potential energy argument, the author proves that for $$\gamma>1$$ finite total energy implies there is no $$\delta$$-function of bigger blow-up.
### MSC:
35L60 First-order nonlinear hyperbolic equations 35L65 Hyperbolic conservation laws 35B40 Asymptotic behavior of solutions to PDEs 76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics
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https://www.controlbooth.com/threads/new-spots.400/ | # New spots?
#### soundman
##### Well-Known Member
My TD wants to toss our altaman satilites of the spot bay because they our so darn loud. The good news is he wants to get new ones but right now he talking about getting 2 more midgets which would barly make it to the stage in the dark much less when the lights were at a decent level. What spots would you guys suggest we need something quite and bright enough to go the distance 100~150 feet I think.
#### wolf825
##### Senior Team Emeritus
soundman said:
My TD wants to toss our altaman satilites of the spot bay because they our so darn loud. The good news is he wants to get new ones but right now he talking about getting 2 more midgets which would barly make it to the stage in the dark much less when the lights were at a decent level. What spots would you guys suggest we need something quite and bright enough to go the distance 100~150 feet I think.
Well the noise issue isn't going to go away really--there's a reason those fans are there. But having a couple of Satalites, if you are using them in the 150 foot range, they aren't really doing a good job lighting what you hit either, so I can sympathize. Whats noisy--are the fans clanging against the covers? thats a common problem with satalites...a little prying and the screen comes away from rubbing the fan.
FWIW, the Midget isn't going to be much better in terms of light output..in fact may be worse. For that distance I would look at a Super Arc 400 at the very least, or maybe a StarkLight--tho the Superarc (model 1267) will be a lot brighter for you. IMO when calculating distance, you wanna take your actual distance and add 25' to it so you get that punch you want. Check out the specs to see which amount of lumens at a distance. Most manufacturers (Lycian, Strong, Altman) have their specs on their website.
Otherwise--if you want totally silent, you can tell your TD to get a Source 4 5-degree on a yoke....
wolf
#### ship
##### Senior Team Emeritus
While Stark and Lycian make good dependable fixtures, I have more experience with the Lycian brand and know either are worth the extra money above something made in Italy or China. Such foreign fixtures will work fine for a number of years, but once things start to go wrong it’s hit or miss if you can find parts for them. Much less a service center that will not only work on it but send you an emergency loaner while yours is in for service. Lycian at one point offered to send me out a huge 1290 fixture as free temporary loaner while one of ours that was dropped off a truss was in for repair. Rush shipping alone will have been a pretty penny for them to pick up granted it cost like 2,000.00 to get the thing realigned and400.00 to ship it.
I don’t know much about Robert Juliat spots so I won’t comment about them. Altman and L&E make follow spots also of interest. The L&E version would be a bit short on power for your purposes - kind of like a Altman 1000 but with a HX-600.
Altman makes the Satellite Voyager and Explorer spots in your range and like with Lycian, Strong and L&E would probably bend over backwards to keep a follow spot customer in their premium lines. In other words, they might offer up free loaners from their rental stock where needed. While I have not used Altman's HMI sources, their fixtures seem fairly rugged for the money. If nothing else, the parts are easy to get and replace.
First, no matter what brand you buy, you might look into an article about followspot photometrics and intensity.
http://www.lycian.com/to_order/photometrics.html
Than at least for Lycian, you can go to the following part of the website to range their various fixtures for your distance:
http://www.lycian.com/products.specs/products.specs.htm
Strong is at http://www.strongint.com/
Lycian seems to recommend the following fixtures by the Photometrics chart:
Midget, 1209HP Lots of schools around me use various versions of this budget fixture. Good and dependable and easy to use. The hot restrike 575w lamp for it is fairly dependable and forgiving for an arc lamp. A normal lamp is the Philips MSR 575HR with 750hr/49,000Lumen/6,000̊K in stats.
Starklite II, 1271 is one of the fixtures the place I work for uses along with the M2, 1290 and 1272. The 1271 has a separate ballast which like with any 1200w fixture can be troublesome but given it's not mounted on the fixture it's easy to swap it out for a loaner while yours is in the shop. It also has interchangeable lenses so you can put it into different locations. The lamps for it are a bit more tricky to install and temperamental than the above however. It's lamp ranges from 750hr to 1,000hr depending on brand and it's 110,000Lumens/6,000̊K for an Osram HMI 1200w/GS. If you have a large program and use the spots a lot this might be a good investment otherwise the Midget would be a more cost effective fixture.
The M2 follow spot with medium or long lens would be the expensive high tech solution that still might be of interest. I say this because if the football team does not have a followspot, your departments might be able to pool resources and use the same fixtures. I hear school distracts like the concept of sharing between departments. The theater could get some sweet revenge in making the foot ball team pay in part for your new fixture that you only let them use twice a year. You can swap out lenses between short medium and long throw and use either a 2,500w or a 1,200w lamp. I believe the above 1271 lamp is the 1200w lamp used, otherwise it’s a Mac 2K lamp. I don’t think we used it in 1,200w mode yet so I don’t know which lamp it uses yet. The 25,000w lamp used is 500hr/240,000Lumens/6,000°K which is brighter than a pro grade 2Kw Xenon follow spot lamp. Problem is that you would have to buy differing lamp housings and lens assemblies and either different ballasts or no doubt even more expensive dual purpose electronic ballasts. In other words, it’s kind of like buying two follow spots for the price of only getting one. It also requires 208v power as opposed to the above that’s 120v power supplies.
With any Strong or Lycian follow spot, you might be able to find some on the used fixture market or even factory reconditioned. Because these lights are investments and good companies such used fixtures would could be made dependable as if new for less cost. Upon used buying them however, it would be wise to send either brand, even an Altman used fixture back to the factory for a once over. It does not take much to get the optics off alignment or there could be unforseen problems with them that you want taken care of before you start to use them. That would be my recommendation - go used if you can find some of the above. Oh’ one more thing, rent what ever follow spot you want to buy for a show before you purchase it. Get to know physically if it’s going to work due to the investment. That and buy what other similar schools are using so not only can you swap should there be an immediate problem, you might loan between schools for large shows. Otherwise comments from like schools on the value of their light might be of use for you.
#### cruiser
##### Active Member
Good Info ship..... we dont have either of those fixture's here so i cant really make a comment back.
we have two robert juliat spots at work, they are 656 feet from the stage i converted meters so i might be a bit out. It is 200meters....
we have the "margot" which is a 2000/2500watt model which has a zoom of 8 - 16degrees.
I have found it to be a great spot with great user control features. They have pretty quiet fans, about the same as your average pc fan, so not too bad considering. but at our theatre the audience cannot hear em, sound proof glass =)
they are french made, ive been sick and away from work too long to remember the correct termenology, but they run of the GPO but have a transformer box that has circuit breakers in it for the fan and lamp.
http://www.robertjuliat.fr
#### wolf825
##### Senior Team Emeritus
cruiser said:
Ahh...don't see many or any of those in the states...but I have heard they are like a Super Trouper in brightness, reliability and throw. I've been very interested in the followspots with the CMY color mixing abilities and so forth using glass filters. I don't see why other company's do not explore this for followspots... It makes a LOT of sense IMO... I think Clay Paky makes some of these--I got to play with a few at LDI a few years back. While the light output could have been better IMO (seemed better for a short throw)--overall it wasn't that bad, I don't see why other company's don't offer this feature or explore this function. It was DMX linkable--so the console could change the color and open the iris & shutter...so all the followspot operator has to do is point. The one I saw also had programmable buttons so you could set your color choices on a pad..do fades and so forth on the handles....seemed like a very nice streamlined idea. But so far no one at Lycian, Strong or any other company's have picked up on this idea of using dichro glass & CMY mixing to get all colors in a followspot.. No more stocking gel or cutting and loading gel--just ready to go. Again--don't know why others have not explored this..especially since most followspots cost as much as a moving head.
Any ideas on this one Ship?
-wolf
#### Inaki2
##### Active Member
I believe he main reason would be that brands such as Lycian and Straong offer stuff for intensive touring. A rigged fixture to protect CMY and controller and optics would be very expensive. Even though the idea is good, CMY takes away a lot of output also, and big wattage versions would be complicated and expensive to make due to heat problems.
#### wolf825
##### Senior Team Emeritus
Inaki2 said:
I believe he main reason would be that brands such as Lycian and Straong offer stuff for intensive touring. A rigged fixture to protect CMY and controller and optics would be very expensive. Even though the idea is good, CMY takes away a lot of output also, and big wattage versions would be complicated and expensive to make due to heat problems.
one of the cooler truss spots I've seen was on the last Korn tour I worked on when they were in town...they were retro-fitted Cyberlights for truss spots--had the hood and mirror removed, a fixed lense, and handles on the sides & rear to point and shoot.. A DMX loop and they were done and controlled from the console--all the op had to do was sit there and follow their target...brilliant idea. I can see where a long thro unit may not be so favorable in output--but some of those fixtures and movers do a great job as a followspot...
-wolf
#### Inaki2
##### Active Member
Wow...cool idea indeed!
#### soundman
##### Well-Known Member
Thanks for all the info, I am not sure what the distance from the spot bay to the back wall is but 150 sounds right.
#### ship
##### Senior Team Emeritus
Wait a minute, I think we did that tour! Seem to remember something about doing that though it was done outside my world - they don't let my Sawzall come anywhere near such fixtures unless as a last opion.
As for adding CMY color mixing... I'm kind of a 1979 technology person. In spite of doing my darndest to shove follow spot repair off onto the moving lights people, it still for the most part falls on my shoulders. CMY color mixing would either confound and curse me or be another good reason they need to service the big heavy things. In other words, I would be hesitent to want such a thing because it's kind of complex to repair. A follow spot is already too complex for most spot op's to work on, adding more would be even more difficult to keep in good working condition. All it takes is the lens to get slightly out of focus on it's rail and that color mixer might just become toast.
As long as I don't have to work on them, I don't care what technology is in them - as if I were asked for my opinion of the M2 anyway. They showed up, parts broke on them instantly and I was in charged of getting the replacements. Not to mention they forgot to buy lamps for them before the week they left for the tour. "Hello, anyone have in stock any of the new 2.5Kw HMI lamps out there? No, Okay I'll keep calling around" - and pay premium price for who ever has it. That and the road boxes were perfectly designed for the instrument, remove a foam block and it fits the opposing lens assembly. Of course there is no room for the light's feeder cable, spare lamps or anything else such as the spare lenses... after thoughts all.
Clay Packey is a brand I forgot about, good stuff from what I hear of them. Also, I was not slacking Robert Juliard, I'm not familior with the brand other than knowing their name. Other companies might be Ariel Davis #3100, Colortran - we used to have them in high school to replace the Altman Dyna Beam that I now own, Capital Stage Lighting if they still exist, CCT lighting though it seems kind of short in range, Ludwig Pani, Times Square which would be another domestic brand that should be looked into for the low end line of follow spots, Clay Paky as mentioned, and Phoebus.
Only other thing I can see holding back the technology is the fact that a good follow spot already costs an arm and a leg. Given the CMY follow spots would only be sold with the top of the line equipment, how much above the top would that cost for something that's more of an after thought production wise due to the human element of it? A Lycian 1290 costs what $10,000.00, a M2 something like$15,000.00, add another \$5K onto that for the color mixing and it's a question of cost over usefulness I think.
#### wolf825
##### Senior Team Emeritus
Hi Ship,
But what if things got simpler for the followspots--I mean instead of DMX control, you have a slider on the followspot in place of the filter and it was gdichroic glass...say graidiated fan style to slide in the color density. I dunno...I just am probably tired of cutting gel at the last minute cause some LD didn't remember to say they wanted R44 pink in the followspots. I just think it would be a nice feature to have in a followspot--whether its manual or DMX contraolled. At the price of most followspots anyway--they cost the same as a mover in most cases and they don't have near all the same moving parts or features.
Ahh--I had wondered if the Korn gig came from your shop...seem to recall seeing the name a few times but wasn't sure. I was mostly on kabuki drop and video since I was the only person on the local crew who had a clue how to do that stuff and run those cables and set up solenoids etc... Nice that I can be able to flex into any position on a crew, but I kinda wish I was on my favorite sound or lights stuff for the big stuff. If it was your rig--what the heck was the light console...cause I had never ever seen one like it and had no idea what it was (nor could I get close enough).. Looked like an obsession all tricked out and thensome...very wierd. The sound & desks were from Clair tho...I know that gear well.
-wolf
#### ship
##### Senior Team Emeritus
Hey, comes to mind that this what spot used should be something almost everyone can chime in on.
What spot do you use? How do ya like it? How about offering up some opinions on the spots you have experience with to help Soundman choose? Cruiser, Wolf and I have offered up opinions on what we would look into given the range, what do all of you use? Come on those lurkers, you ask for help at times, how about helping others? Sould have at least 300 posts about what you are using instead of becoming board by another Wolf/Ship taken over discussion.
Wolf, on the controller if you wish I can enter the Hire Track rogram that tracked all the gear used on the show but my guess is that the controller was the new Martin light board. We like that controller. I don't have access to it at home and hope unlike my boss I never do. Something about it like having to search for what my boss names the stuff verses what I would call it is just a major pain in my rear.
So you worked with my selonoids/kibuka system? How do you like how we do them? I spend a lot of time with such things between doubling our inventory and re-doing the older system that has wiring that's scary and dry rotting. Granted the clamp mounting bolt is from heck, on the whole I think it's a good system - one of the few old designs that I like. Or were they using the rolling pipe/peg system to drop the drape? We have two Kabuki systems.
CMY on follow spots, I don't care as long as I don't have to figure out how to fix them. As for the price, we just invested in the Catalyst system big time, yea they have all kinds of bells and whistles, but the major selling point for the designers is that you can pre-program what they do. On design, I believe more of their effort and funding is spent in what they pre-program than what the spots are doing.
At least I believe the spot cues are designed into the show during rehearsal. Investing more money into something that's manual but it's color is light board or even selective but manual is getting complex for something that's still going to for the most part get designed during rehearsal. Plus there are thousands of dollars in follow spots already for such shows. Until the designers want that new thing, they are not going to be bought and it would seem none of the designers have your idea at least yet while they have new moving light toys to create with. Your idea is interesting, I can just remember running Gizel and doing the bouncing faery thing. The spot fading to another color while in the air might be of interest given it was not light board controlled due to timing and the operator being the only person with the feel for it as the top of the leap is reached. Besides, Job security. Do you have a Rosco Gel cutter in your wallet also? | 2022-10-04 09:49:16 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.17824196815490723, "perplexity": 2094.906826295326}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-40/segments/1664030337490.6/warc/CC-MAIN-20221004085909-20221004115909-00135.warc.gz"} |
https://proofwiki.org/wiki/Completion_of_Valued_Field | # Completion of Valued Field
## Theorem
Let $\struct {k, \norm {\,\cdot\,} }$ be a valued field.
Then there exists a completion $\struct {k', \norm {\,\cdot\,}'}$ of $\struct {k, \norm {\,\cdot\,} }$ such that $\struct {k', \norm {\,\cdot\,}'}$ is a valued field.
Furthermore, every completion of $\struct{k, \norm {\,\cdot\,} }$ is isometrically isomorphic to $\struct {k', \norm {\,\cdot\,}'}$.
## Proof
By Completion of Normed Division Ring then $\struct {k, \norm {\, \cdot \,} }$ has a normed division ring completion $\struct {k', \norm {\, \cdot \,}'}$
By Normed Division Ring is Field iff Completion is Field then $\struct {k', \norm {\, \cdot \,}'}$ is a field.
By Normed Division Ring Completions are Isometric and Isomorphic then every completion of $\struct {k, \norm {\,\cdot\,} }$ is isometrically isomorphic to $\struct {k', \norm {\,\cdot\,}'}$.
$\blacksquare$ | 2020-09-23 19:34:20 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9827441573143005, "perplexity": 247.51589925052482}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-40/segments/1600400212039.16/warc/CC-MAIN-20200923175652-20200923205652-00061.warc.gz"} |
https://chemistry.stackexchange.com/questions/47754/how-to-determine-the-hydroxide-ion-concentration-in-an-acidic-aqueous-solution | # How to determine the hydroxide ion concentration in an acidic aqueous solution?
When doing a titration with $\ce{HCl}$ and $\ce{NaOH}$, both being strong and dissociating completely, if you add a volume of $\ce{NaOH}$ that is less than needed to reach the equivalence point, you say all the $\ce{OH-}$ reacted with an equal amount of $\ce{H+}$ from $\ce{HCl}$.
It would be amount of substance $\ce{HCl}$ - amount of substance of $\ce{OH-}$ = $[\ce{H3O+}]$, and all of the $\ce{OH-}$ is gone, so $[\ce{OH-}] = 0$. But if you take the pH found using the $[\ce{H3O+}]$ value, use that to find pOH and then use that to find $[\ce{OH-}]$ you get a very small value, but not zero. So if I need to report a $[\ce{OH-}]$ value, do I just put 0 or the one gotten from pOH?
The problem that you are facing comes from the fact that technically, not all of the $\ce {OH-}$ reacts with the $\ce {H+}$. It is only because the amount of OH- that doesn't react is so negligible compared to the amount that does, that the $\ce {[H_3O+]}$ can be taken to be $\ce{[HCl]-[$\ce{OH-}$]}$.
So, yes, to find the remaining (negligible) amount of $\ce{OH-}$, you must use the "very small value" given by either subtracting $\ce {pH}$ from $14 =\ce{pOH}$ or doing $\ce K_w/[\ce{H+}]=[\ce{OH-}]$ (which amounts to the same thing). | 2019-04-24 07:51:55 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7790828943252563, "perplexity": 275.869826934848}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-18/segments/1555578636101.74/warc/CC-MAIN-20190424074540-20190424100540-00453.warc.gz"} |
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# how to make a system of equations
Click here for more information on our affordable subscription options. It is considered a linear system because all the equations in the set are lines. The solution for the above system of equations is shown here: A = np.array([[20, 10], [17, 22]]) B = np.array([350, 500]) X = np.linalg.solve(A,B) print(X) And here is the output: [10. 9,000 equations in 567 variables, 4. etc. And frequently, you will find systems of equations that are linear, with two equations and two unknowns. A system of equations is a group of equations with the same variables. By using this website, you agree to our Cookie Policy. Systems of equations word problem (coins) Example: A man has 14 coins in his pocket, all of which are dimes and quarters. Under Equation Tools, on the Design tab, in the Structures group, click the Bracket button: If she bought a total of 7 shoes, then how many of each kind of shoe did she buy? sarah and keith purchased 40 stamps, a mixture off 44 cent and 20 cent stamps. A group of 36 people attend a ball game. To insert a system of linear equations, do the following:. Our system of equations is: x+y = 375 x = y+37 Now to solve: I would use the substitution method since one of the equations is solved for x. Many possible correct responses. A System of Equations is exactly what it says it is. To find the amount of 20% acid solution needed, substitute 12 for the y in either equation; we'll use the simpler equation: x + y = 20 x + 12 = 20 x = 8. Tyler charges $2 up front, and then$3 per day to pet sit. B. It may seem like a lot, but once you figure out what's going on, you can solve in a matter seconds. If the total value of his change is $2.75, how many dimes and how many quarters does he have? We'll make a linear system (a system of linear equations) whose only solution in (4, -3). In a system of linear equations, each equation corresponds with a straight line corresponds and one seeks out the point where the two lines intersect. I don't get this-- Isaac bought a total of 32 pieces of candy. Any equation that cannot be written in this form in nonlinear. A System of Equations With No Solution. First go to the Algebra Calculator main page. This tutorial will introduce you to these systems. Value problems are ones where each variable has a value attached to it. Or click the example. Just follow these steps: Section 5-4 : Systems of Differential Equations. In general, you can skip the multiplication sign, so 5x is equivalent to 5*x. A system of equations refers to a number of equations with an equal number of variables. This kind of system is called system of linear equations with 2 variables. Get access to hundreds of video examples and practice problems with your subscription! Conclusion . Solve by writing system of equations. Create a System of Equations, Given 1 Equation and the Solution Directions: Write at least two linear equations so that the solution of the system of equations of that line and 4x + y = 8 is (3, -4) We could name them Moonshadow and Talulabelle, but that's just cruel. This page is only going to make sense when you know a little about Systems of Linear Equations and Matrices, so please go and learn about those if you don't know them already! How to Solve a System Using The Substitution Method Step 1 : First, solve one linear equation for y in terms of x . Students need to learn and practice three main techniques for solving systems of linear equations: graphing, addition and substitution. Multiply the second equation by -2, then add the two equations together: 2x + 7y = 100-2x - 2y = -40 5y = 60 y = 12. Your email address will not be published. Now you can easily solve any system of equations by following these steps. Now I can solve the system for the number of adults and the number of children. Linear equation theory is the basic and fundamental part of the linear algebra. 15.] How? Write a system to help determine the amount each paid. Wikipedia defines a system of linear equationsas: The ultimate goal of solving a system of linear equations is to find the values of the unknown variables. In a system of linear equations, where each equation is in the form Ax + By + Cz + . Solving Systems of Equations Using Mathcad Charles Nippert This set of notes is written to help you learn how to solve simultaneous equations using Mathcad. You can add the same value to each side of an equation. Convert the equations into y= form In order to graph an equation on your calculator, the left side of the equation must only contain y. (The two equations represent the same line.) Of COURSE zero does not equal negative two! Using your calculator to find A –1 * B is a piece of cake. In the figure above, there are two variables to solve and they are x and y. What is Joe's rate? For example, the marketing team for … Built into the Wolfram Language is the world's largest collection of both numerical and symbolic equation solving capabilities\[LongDash]with many original algorithms, all automatically accessed through a small number of exceptionally powerful functions. Dealing with more than one equation is what intimidates some … Click here for more information on our Algebra Class e-courses. She also remember that yhe value was worth$2.60 . How many of each question are on the test? Thus the pair (x, y) is the one andonly solution to the system of equations. Suppose you're going to run a lemonade and cookie stand. This is similar to an indeterminate system, except that, instead of having an obviously TRUE equation, we have an obviously FALSE equation. y = x – 7 2x + 3 y = -6 Source: Nanette Johnson. Next, we need to use the information we're given about those quantities to write two equations. Enter your queries using plain English. Save my name, email, and website in this browser for the next time I comment. 2 equations in 3 variables, 2. The output shows that the price of one mango is $10 and the price of one orange is$15. Join in and write your own page! You can use any method to solve the system of equations. Write the coefficients of the y -terms as the numbers down the second column. Our mission is to provide a free, world-class education to anyone, anywhere. I have added it to the answer , Pingback: Open Middle | Mathematics, Learning and Technology, Your email address will not be published. Put it all together. For more solutions see https://www.desmos.com/calculator/clsixz0vom (courtesy of Colleen Young), Tags 8.EE.8a 8.EE.8b A.REI.6 Daniel Luevanos DOK 2: Skill / Concept, Directions: Using the digits 1 to 9 at most twice each, make the sum of …, What a wonderful problem – thank you. One of the last examples on Systems of Linear Equations was this one:We then went on to solve it using \"elimination\" ... but we can solve it using Matrices! First note that there are several (or many) ways to do this. The substitution method we used for linear systems is the same method we will use for nonlinear systems. Figure 1. Simply click here to return to. How do I write this problem as an equation so I can solve it? Choose a, b and c the make the equation true. To describe a word problem using a system of equations, we need to figure out what the two unknown quantities are and give them names, usually x and y. Solve System of Equations. Liz paid $36 more than Ashley. In the introduction to this section we briefly discussed how a system of differential equations can arise from a population problem in which we keep track of the population of both the prey and the predator. In general, you can skip the multiplication sign, so 5x is equivalent to 5*x. Mrs.Hsing paid$18.35 for 1.5 lbs. Use this system of equations calculator to solve linear equations with different variables. Another approach to solve the system of equations is Excel Solver Add-in. An equation with unknowns is a search problem: we are searching for the value of the unknowns that will make the equation be true. In general, you can skip parentheses, but be very careful: e^3x is e^3x, and e^(3x) is e^(3x). If there are z -terms, write the coefficients as the numbers down the third column. For example: © 2016-2020 Open Middle Partnership. Underdetermined linear systems involve more unknowns than equations. If B ≠ O, it is called a non-homogeneous system of equations. Another way to solve a system of equations is by substitution. All rights reserved. Solve System of Linear Equations Using linsolve. By Yang Kuang, Elleyne Kase . Just follow these steps: Enter the coefficient matrix, A. Show Instructions. Show Instructions. Equivalent equations have the property that one equation can be made into the other equation by algebraic manipulation. Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously. To describe a word problem using a system of equations, we need to figure out what the two unknown quantities are and give them names, usually x and y. We'll look at two ways: Standard Form Linear Equations A linear equation can be written in several forms. So a System of Equations could have many equations and many variables. (Columbia). One of the last examples on Systems of Linear Equations was this one: In this unit, we learn how to write systems of equations, solve those systems, and interpret what those solutions mean. How to add an equation in your document, see Working with Microsoft Equation. It’s a system, meaning 2 or more, equations. Recall that a linear equation can take the form $$Ax+By+C=0$$. For most values of the unknowns, the equation will be false: $y + 1 = 3$ is a false statement for infinitely many possible choice… This example shows how the solution to underdetermined systems is not unique. The equations can be split into matrices A, x, and b . To solve a system of equations, you need to figure out the variable values that solve all the equations involved. This is pretty easy to do, especially if you are dealing with linear equations. To solve a system of linear equations with steps, use the system of linear equations calculator. In the second equation, x is already isolated. One application of system of equations are known as value problems. 6 equations in 4 variables, 3. What was the price per pound of each item? In your own equation, enter f (x)=.. 2. . 3x + y = 9 . Example (Click to view) x+y=7; x+2y=11 Try it now. Simply click here to return to Students. Solving Systems of Non-linear Equations. How? The most typical system you will find is a system of linear equations. Writing a System of Equations from an Augmented Matrix. Onesolution In this case the two equations describe linesthat intersect at one particular point. System of equations appear everywhere in Math, in all subjects. Finish by … To solve the system of equations, we can utilize functions and the equation solver tool. We'll substitute y+ 37 for x into the first equation. System of linear equations System of linear equations can arise naturally from many real life examples. First, select the range G6:G8. And you use each equation as a constraint on your variables, and you try to find the intersection of the equations to find a solution to all of them. Being able to systematically solve systems of equations will prove to be a crucial skill to master. Here are some examples illustrating how to ask about solving systems of equations. Any system of equations can be written as the matrix equation, A * X = B. Using your calculator to find A –1 * B is a piece of cake. https://www.desmos.com/calculator/clsixz0vom, Thanks for this Colleen. In general, you can skip parentheses, but be very careful: e^3x is e^3x, and e^(3x) is e^(3x). By pre-multiplying each side of the equation by A –1 and simplifying, you get the equation X = A –1 * B. Need More Help With Your Algebra Studies? Create a System of Two Equations Directions: Using the digits 1 to 30, at most one time each, fill in the boxes to create a system of two linear equations where (3, 2) is the solution to the system. Writing Systems of Linear Equations from Word Problems Some word problems require the use of systems of linear equations . To solve a system of linear equations with steps, use the system of linear equations calculator. a 11 x 1 + a 12 x 2 + … + a 1 n x n = b 1 a 21 x 1 + a 22 x 2 + … + a 2 n x n = b 2 ⋯ a m 1 x 1 + a m 2 x 2 + … + It’s a system, meaning 2 or more, equations. Write the coefficients of the x -terms as the numbers down the first column. Now solve the system of equations 2x + 7y = 100 x + y = 20. You will solve a system of 2 simultaneous linear equations using successive approximations or by using the symbolic processor. With this method, you are essentially simplifying one equation and incorporating it into the other, which allows you to eliminate one of the unknown variables. There are multiple ways to solve such a system, such as Elimination of Variables, Cramer's Rule, Row Reduction Technique, and the Matrix Solution. We will make our system of linear equations more general by working with a 3-dimensional data instead. The lines intersect at infinitely many points. In this non-linear system, users are free to take whatever path through the material best serves their needs. Jenny charges $4 per day to pet sit. Find the equations to: Alice spent$131 on shoes. Generally speaking, those problems come up when there are two unknowns or variables to solve. Students are to create a system of equations that has (0, -5) as the solution. The Example. Another modification could be using Desmos. This section shows you how to solve a system of linear equations using the Symbolic Math Toolbox™. Sample Problem . Create the symbolic array S of the values -2*pi to 2*pi at intervals of pi/2. In mathematical terms, the system of equation is set of two or more equations having the same set of unknown variables like x, y, z where we need to find the values of unknown variables to solve these equations. They don't have to be, but they tend to have more than one unknown. A System of Equations is exactly what it says it is. Virtual Nerd's patent-pending tutorial system provides in-context information, hints, and links to supporting tutorials, synchronized with videos, each 3 to 7 minutes long. There can be any combination: 1. He paid 26.35. A system of linear equations. Mr.Chandra bought 2 lbs. number of adults: a. number of children: c. With these variables, I can create equations for the totals they've given me: total number: a + c = 2200. total income: 4a + 1.5c = 5050. For Excel Solver we need to set up the data of the system of equations as follows; For matrix A we need to enter the formula for each of the equations in column C as shown. We could name them Moonshadow and Talulabelle, but that's just cruel. So if you have a system: x – 6 = −6 and x + y = 8, you can add x + y to the left side of the first equation and add 8 to the right side of the equation. Please tell me how i would start to solve this, Your teacher is giving you a test worth 100 points. e.g., 2x + 5y = 0 3x – 2y = 0 is a homogeneous system of linear equations whereas the system of equations given by e.g., 2x + 3y = 5 x + y = 2 is a non-homogeneous system of linear equations. You can write any system of equations as a matrix. He bought 3 times as many chocolate as he did hard candies. Not ready to subscribe? However, it is important to understand how to move back and forth between formats in order to make finding solutions smoother and more intuitive. Choose two of the and find the third. The elimination method for solving systems of linear equations uses the addition property of equality. Solve System of Linear Equations Using solve. In mathematics, a system of linear equations (or linear system) is a collection of one or more linear equations involving the same set of variables. A system of equations simply means that we have multiple equations, all of which must be satisfied at the same time, and multiple unknowns, which are shared between the equations. A system of linear equations can be represented as the matrix equation, where A is the coefficient matrix, and is the vector containing the right sides of equations, If you do not have the system of linear equations in the form AX = B, use equationsToMatrix to convert the equations into this form. Solve by Addition Write one equation above the other. There is a package systeme for systems of linear equations with automatic alignment of the variables and values - it even detects the variables for you. Example: If we make a=1 and b=1, then because we have 1(4)+1(-3)=c , we can see that we need c=1. 1. Solving a system of equations using a matrix is a great method, especially for larger systems (with more variables and more equations). Jorge paddles his canoe 4 miles in 1 hour . High School Math Solutions – Systems of Equations Calculator, Elimination A system of equations is a collection of two or more equations with the same set of variables. Using a system of equations, however, allows me to use two different variables for the two different unknowns. We will only look at the case of two linear equations in two unknowns. There will be 40 questions on the test some worth 2 points and others 4 points. It's easy to do. Consider the following system of linear equations: 3x + y = 6 x = 18 -3y. Free system of equations calculator - solve system of equations step-by-step This website uses cookies to ensure you get the best experience. of chicken loaf. Type the following: The first equation x+y=7; Then a comma , Then the second equation x+2y=11; Try it now: x+y=7, x+2y=11 Clickable Demo Try entering x+y=7, x+2y=11 into the text box. The methods you will use can be easily adapted to other systems of equations. There were twice as many children as adults in the group. Share. – Kamil Jan 4 '15 at 23:37 Please edit your post to show a complete, compilable document starting with \documentclass... and ending with \end{document} . Using Excel Solver Add-in. Khan Academy is a 501(c)(3) nonprofit organization. The length was 4 less than twice the width l. Find the length. Open Middle is the registered trademark of the Open Middle Partnership. For example, + − = − + = − − + − = is a system of three equations in the three variables x, y, z.A solution to a linear system is an assignment of values to the variables such that all the equations are simultaneously satisfied. Using Matrices makes life easier because we can use a computer program (such as the Matrix Calculator) to do all the \"number crunching\".But first we need to write the question in Matrix form. A system of equations is a set of two or more equations that you deal with at one time. Step 2 : Then substitute that expression for y in the other linear equation. The article explains how to solve a system of linear equations using Python's Numpy library. A system of a linear equation comprises two or more equations and one seeks a common solution to the equations. In this art… Let’s generate an example for the plot above: where the coefficients of x_0, x_1, and x_2 and the corresponding values 8, 4, 5 are the samples of points in the plot. of cheddar cheese and 3 lbs. Solve System of Linear Equations Using linsolve. Okay so now you're taking the regents and you come across a system of equations. Find the number of each type of stamp if they spent16.40, The winning entry at a cake baking contest was an Italian Cream Cake.The perimeter of the rectangular cake was 46 inches. We want a, b and c so that a(4)+b(-3)=c (This will make (i) and (iii) true.) We will need to use 12 ounces of the 70% acid solution. You think to yourself I wish I could solve using my TI-84 calculator. I could not resist a play with Desmos to generate more solutions! Enter your equations in the boxes above, and press Calculate! Any system of equations can be written as the matrix equation, A * X = B. I need to have \systeme because I want that there appears an array on the left to make it clear to the reader that it is a system of equations. The situation gets much more complex as the number of unknowns increases, and larger systems are commonly attacked with the aid of a computer. Here is a link to the problem I graphed using Desmos. To avoid ambiguous queries, make sure to use parentheses where necessary. send us a message to give us more detail! The matrix left division operation in MATLAB finds a basic least-squares solution, which has at most m nonzero components for an m-by-n coefficient matrix. The return trip upstream takes 2 hours. We can use augmented matrices to help us solve systems of equations because they simplify operations when the systems are not encumbered by the variables. Join in and write your own page! x+y = 375 - substitute y+37 for x y+37 +y = 375 2y +37 = 375 Combine like terms 2y + 37-37 = 375 - … The system of equation refers to the collection of two or more linear equation working together involving the same set of variables. Liz and Ashley buy a radio for $128. Solving Systems of Linear Equations Using Matrices Hi there! Underdetermined Systems. Required fields are marked *. You really are not in the mood of actually solving. It's easy to do. Clearly this point is on both lines,and therefore its coordinates (x, y) will satisfy theequation of either line. number of adults: a. number of children: c. With these variables, I can create equations for the totals they've given me: total number: a + c = 2200. total income: 4a + 1.5c = 5050. Arithmetic w/ Polynomials & Rational Expressions, Reasoning with Equations and Inequalities, Linear, Quadratic, and Exponential Models, Similarity, Right Triangles, and Trigonometry, Expressing Geometric Properties with Equations, Interpreting Categorical and Quantitative Data, Making Inferences and Justifying Conclusions, Conditional Probability & the Rules of Probability, https://www.desmos.com/calculator/clsixz0vom, Open Middle | Mathematics, Learning and Technology, Comparing Hundredths and Tenths 2 Open Middle, Comparing Hundredths and Tenths 1 Open Middle, Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License. For instance, consider our earlier example of x + 2 = 6 and 2 x = 8. x + 2 = 6 There are no values of x and y that make both of the equations true. Solve the following system of equations: x+y=7, x+2y=11 How to Solve the System of Equations in Algebra Calculator. "Standard Form" is ax+by=c where a, b and c are constants (numbers). Register for our FREE Pre-Algebra Refresher course. The introduction of the variable z means that the graphed functions now represent planes, rather than lines. What does it mean to be the solution to a system of linear equations? A Simple Example . When solving the system, you must consider all of the equations involved and find a solution that satisfies all of the equations. These unique features make Virtual Nerd a viable alternative to private tutoring. Sneakers cost$15 and Fits cost \$28. To set the x -axis and y -axis values in terms of pi, get the axes handles using axes in a. solve y = 2x, y = x + 10. solve system of equations {y = 2x, y = x + 10, 2x = 5y} y = x^2 - 2, y = 2 - x^2. In the Professional format:. Write and solve by substitution a system of equations to represent this sceniro--- how do you write one. | 2021-01-25 11:11:23 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4889025390148163, "perplexity": 377.55707900964643}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-04/segments/1610703565541.79/warc/CC-MAIN-20210125092143-20210125122143-00768.warc.gz"} |
http://mandysnotes.com/astrocat | # MandysNotes
## Astronomy
### Table of Distances
By
Below is a table of various distances in various units that are important in astronomy and astrophysics.
By
### Stellar Parallax
By
Consider two stars that appear close together in the night sky. Suppose that one star is relatively close to our solar system (what this means exactly we will come to shortly) while the second star is extremely distant.
As the Earth revolves around the sun, the apparent positions of the two stars will shift. The far distant star will not suffer any noticeable change in position, but the nearer star will be seen to move around the distant star in an ellipse.
Let $$\alpha$$ be the maximum angular separation between the two stars expressed in radians.
If $$d_{o}$$ is one A. U., i.e. the distance from the Earth to the Sun, and $$d_{\star},$$ is the distance from the Sun to the star, then $$d_{\star} \alpha \approx d_{0}.$$
Because in practice the distances to stars are so great, and the angles so small, this approximation is an excellent one and we can write:
$d_{\star} = \frac{ d_{0}}{\alpha} = \frac{1 (A.U.)}{\alpha}$
In this way, if we can measure the angle of parallax, $$\alpha$$ we can find the distance to a star.
### Why do Stars Twinkle but Planets Don't?
By
When we view stars from the surface of the Earth, we a looking up through a ''sea'' of air, the atmosphere, about three hundred miles thick.
Stars are suns, like our own sun, and we see them because they emit particles of light called photons.
The closest star to our solar system, Proxima Centauri, is more than a parsec from our Sun
(1 parsec $$\approx 10 \times 10^{13}$$ miles $$\approx 3 \times 10^{18}$$ cm),
and most stars are much farther away (hundreds or thousands of parsecs--the Milky Way Galaxy has a radius of about eight thousand parsecs).
Planets are part of our solar system and so are much closer than the closest star. The Kuiper belt, of which Pluto is a member, is about $$2 \times 10^{-4}$$ parsecs away from the sun (that is, about 2 thousandths of a parsec). | 2017-09-22 08:10:28 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.687767744064331, "perplexity": 659.6912228702118}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-39/segments/1505818688926.38/warc/CC-MAIN-20170922074554-20170922094554-00295.warc.gz"} |
https://forum.math.toronto.edu/index.php?PHPSESSID=78qr26g2qnma5v6quvu57k2jm4&topic=2389.0 | Author Topic: Section 2.2 Question 3 (Read 416 times)
Qing Lyu
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• Posts: 5
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Section 2.2 Question 3
« on: September 24, 2020, 01:36:16 AM »
Hi, I have already got the final answer of this question. However, I don’t understand why the answer on the textbook saying that “also y = 0” after it says y is not equal to 0. And do we need to include any restrictions of y and x when solving this type of question?
Because in addition to solutipons you found, there is another one, namelu $y=0$ | 2022-01-16 20:04:50 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.808933436870575, "perplexity": 1296.1486183657332}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-05/segments/1642320300010.26/warc/CC-MAIN-20220116180715-20220116210715-00572.warc.gz"} |
https://surfboardstore.com.au/products/lsd-the-tex-xf | 0
# LSD The Tex XF
Size
Fins
Color
50 19 7/8 2 3/8 27.9 54 20 1/4 2 1/2 30.8 55 20 1/4 2 1/2 31.3 56 20 1/4 2 5/8 33.9 58 20 3/4 2 5/8 35.4 510 21 2 3/4 38.7 60 21 1/4 2 3/4 40 62 21 1/2 2 7/8 43.7 64 22 3 48
# The Tex is a super stubby little thing for when the waves are super small or you’re just feeling lazy.
### The bloated girth and thickness of Tex will get you trimming and turning on any wave that breaks.
The contemporary single into double concaves gives this craft plenty of spark. A balanced outline combined with a large round squash tail helps with the control of this little animal.
The Tex should be ordered approximately 5 inches shorter or three four liters more than your conventional short board.
Julian at home on The Tex... | 2019-05-25 01:20:04 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.913985550403595, "perplexity": 2430.4517570957655}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-22/segments/1558232257845.26/warc/CC-MAIN-20190525004721-20190525030721-00298.warc.gz"} |
http://www.dcode.fr/matrix-eigenvectors | Search for a tool
Eigenvectors of a Matrix
Tool to calculate eigenvectors of a matrix. Eigenvectors of a matrix are vectors whose direction remains unchanged after multiplying by the matrix. They are associated with an eigenvalue.
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Eigenvectors of a Matrix -
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# Eigenvectors of a Matrix
This script has been updated, please report any problems.
## Eigenvectors Calculator
Tool to calculate eigenvectors of a matrix. Eigenvectors of a matrix are vectors whose direction remains unchanged after multiplying by the matrix. They are associated with an eigenvalue.
### How to calculate eigen vectors of a matrix?
Consider $$M$$ a square matrix of size $$n$$ and $$\lambda_i$$ its eigenvalues. Eigenvectors are the solution of the system $$( M − \lambda I_n ) \vec{X} = \vec{0}$$ with $$I_n$$ the identity matrix.
$$M=\begin{pmatrix} 1 & 2 \\ 4 & 3 \end{pmatrix}$$
Eigenvalues for the matrix M are $$\lambda_1 = 5$$ and $$\lambda_2 = -1$$.
You can seek for example the eigenvector associated to $$\lambda_1 = 5$$. You solve $$( M − 5 I_n ) X = \vec{0}$$ so : $$\begin{pmatrix} 1-5 & 2 \\ 4 & 3-5 \end{pmatrix} . \begin{pmatrix} x_1 \\ x_2 \end{pmatrix} = \begin{pmatrix} 0 \\ 0 \end{pmatrix}$$
and you find
$$\begin{matrix} -4 x_1 + 2 x_2 = 0 \\ 4 x_1 - 2 x_2 = 0 \end{matrix} \iff \begin{matrix} x_1 = 1 \\ x_2 = 2 \end{matrix}$$
The eigenvector associated to $$\lambda_1 = 5$$ is $$\begin{pmatrix} 1 \\ 2 \end{pmatrix}$$. | 2016-12-10 12:42:26 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7101587653160095, "perplexity": 788.9471380326719}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-50/segments/1480698543170.25/warc/CC-MAIN-20161202170903-00210-ip-10-31-129-80.ec2.internal.warc.gz"} |
http://preparetowincombines.com/port-moresby-dazuk/multiple-integral-calculator-9f9df4 | Select Page
Use the integral calculator for free and on any device. ... or by mathematicians' names to facilitate using it across multiple mathematical problems. Part 1 We can compute R fdA on a region R in the following way. We have formulas to find the area of a shape, a polygon (having more than 2 sides). Multiple Integral Calculator. A multiple integral is a generalization of the usual integral in one dimension to functions of multiple variables in higher-dimensional spaces, e.g. Detailed step by step solutions to your Integration by substitution problems online with our math solver and calculator. Show Instructions In general, you can skip the multiplication sign, so 5x is equivalent to 5*x. Chapter 4 : Multiple Integrals. Simpson's rule Calculator Simpson’s rule is a technique to calculate the approximation of definite curve and is used to find area beneath or above the parabola. Proposition 17.1 (Iterated Integrals). Integration by parts formula: ? ∫ ∫ f (x, y) d x d y, \int \int f(x,y) \,dx \, dy, ∫ ∫ f (x, y) d x d y, which is an integral of a function over a two-dimensional region. BYJU’S online triple integral calculator tool makes the calculation faster, and it displays the integrated value in a fraction of seconds. By using this website, you agree to our Cookie Policy. Please leave them in comments. u d v = u v-? Chapter 17 Multiple Integration 256 b) For a general f, the double integral (17.1) is the signed volume bounded by the graph z f x y over the region; that is, the volume of the part of the solid below the xy-planeis taken to be negative. Multiple integrals use a variant of the standard iterator notation. Fill in the blanks and then hit Enter (or click here). In Calculus I we moved on to the subject of integrals once we had finished the discussion of derivatives. Type in any integral to get the solution, steps and graph. 388 Chapter 15 Multiple Integration Of course, for different values of yi this integral has different values; in other words, it is really a function applied to yi: G(y) = Zb a f(x,y)dx. Step 2: Now click the button “Calculate” to get the value All common integration … Limits. In calculus, the double integral of a function f(x, y) over the rectangular region R in the xy plane is defined by Free multiple integrals calculator - solve multiple integrals step-by-step This website uses cookies to ensure you get the best experience. Testing the limited values of inner integral and integrate. Integral Calculator The integral calculator helps you compute antiderivatives and definite integrals. The premium integral involves the limited values of x and the next integral involves the limited values of y. » Integrate can evaluate integrals of rational functions. Constants arise in many areas of mathematics, with constants such as e and π occurring in such diverse contexts as … From the table below, you can notice that sech is not supported, but you can still enter it using the identity sech(x)=1/cosh(x). The following table contains the supported operations and functions: If you like the website, please share it anonymously with your friend or teacher by entering his/her email: In general, you can skip the multiplication sign, so 5x is equivalent to 5*x. The first variable given corresponds to the outermost integral and is done last. 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In general, you can skip parentheses, but be very careful: e^3x is e^3x, and e^(3x) is e^(3x). Integration by substitution Calculator online with solution and steps. Similarly, the average value of a function of two variables over the rectangular region can be determined using the double integral. The resolution of issues with numerous integrals consists, in most instances, of locating a means to lessen the multiple integral to an iterated integral, a string of integrals of one variable, each being directly solvable. In mathematics (specifically multivariable calculus), a multiple integral is a definite integral of a function of several real variables, for instance, f(x, y) or f(x, y, z).Integrals of a function of two variables over a region in (the real-number plane) are called double integrals, and integrals of a function of three variables over a region in (real-number 3D space) are called triple integrals. Please write without any differentials such as dx, dy etc. Besides math integral, covariance is defined in the same way. Trigonometry Calculator. More than just an online triple integral solver. All suggestions and improvements are welcome. The integrals are as follows : indefinite integrals, definite integrals, Antiderivatives, Double Integrals, Triple Integrals and Multiple Integrals. While the line integral depends on a curve defined by one parameter, a two-dimensional surface depends on two parameters. The steps include: Looking at the presented function and limits. After getting the integrated value, begin combining … Required fields are marked *. Triple Integral Calculator is a free online tool that displays the integrated value for the given function. Integral definition assign numbers to define and describe area, volume, displacement & other concepts. Multiple Integrals Double Integrals over Rectangles 26 min 3 Examples Double Integrals over Rectangles as it relates to Riemann Sums from Calc 1 Overview of how to approximate the volume Analytically and Geometrically using Riemann Sums Example of approximating volume over a square region using lower left sample points Example of approximating volume over a… Here are a set of practice problems for the Multiple Integrals chapter of the Calculus III notes. Double integral calculator mostly utilized to count the two-dimensional figures. The calculator will calculate the multiple integral (double, triple). So far, we've used integrals to figure out the area under a curve. Facts, Fiction and Double Integral Calculator Double Integral Calculator Explained . If the calculator did not compute something or you have identified an error, please write it in v d u. To get tan(x)sec^3(x), use parentheses: tan(x)sec^3(x). In calculus, integration is the most important operation along with differentiation.. Solved exercises of Integration by substitution. Step 1: Enter the function and the limits in the input field Compute volumes, integrate densities and calculate three-dimensional integrals in a variety of coordinate systems using Wolfram|Alpha's triple integral calculator. Step 3: Finally, the result of the double integral will be displayed in the new window. Double Integral Calculator is a free online tool that displays the value for the double integral function. Integral definition. Surface integrals are a generalization of line integrals. with bounds) integral, including improper, with steps shown. Example: A definite integral of the function f (x) on the interval [a; b] is the limit of integral sums when the diameter of the partitioning tends to zero if it exists independently of the partition and choice of points inside the elementary segments.. Your email address will not be published. The procedure to use the double integral calculator is as follows: Your email address will not be published. The integral calculator software provides tools to solve the integrals step by step and hence helps the students of mathematics to understand the same. If it's not, you might want to review the definite integration videos. Similarly, tanxsec^3x will be parsed as tan(xsec^3(x)). BYJU’S online double integral calculator tool makes the calculation faster, and it displays the double integral value in a fraction of seconds. The surface element contains information on both the area and the orientation of the surface. Example of How-to Use The Trapezoidal Rule Calculator: Free integral calculator - solve indefinite, definite and multiple integrals with all the steps. ( ) Function: Differentials : For indefinite integrals, you can leave the limits of integration empty. Nonetheless, it isn't obvious from taking a look at … Double Integral Calculator Added Apr 29, 2011 by scottynumbers in Mathematics Computes the value of a double integral; allows for function endpoints and changes to order of integration. Our Derivative Calculator tool supports all the most recent functions, computing and several other variables which are essential in 1 tool. Funcions 3D plotter calculates the analytic and numerical integral and too calculates partial derivatives with respect to x and y for 2 variabled functions. This website uses cookies to ensure you get the best experience. Want to calculate a . Now that we have finished our discussion of derivatives of functions of more than one variable we need to move on to integrals of functions of two or three variables. And let's just review a little bit of the intuition, although this should hopefully be second nature to you at this point. The Integral Calculator lets you calculate integrals and antiderivatives of functions online — for free! multiple-integrals-multivariable-calculator. write sin x (or even better sin(x)) instead of sinx. Example: Proper and improper integrals. This sum has a nice interpretation. Multiple (Double, Triple) Integral Calculator The calculator will calculate the multiple integral (double, triple). Also, be careful when you write fractions: 1/x^2 ln(x) is 1/x^2 ln(x), and 1/(x^2 ln(x)) is 1/(x^2 ln(x)). The Integral Calculator is a simple online tool for calculating any integral problems. A multiple integral is a set of integrals taken over variables, e.g., An th-order integral corresponds, in general, to an -dimensional volume (i.e., a content), with corresponding to an area. You practice by showing you the full working ( step by step solutions your! 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Multiplication signs where needed, and it displays the integrated value in a of. | 2021-07-31 22:30:42 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8563633561134338, "perplexity": 1237.3861831373981}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-31/segments/1627046154126.73/warc/CC-MAIN-20210731203400-20210731233400-00122.warc.gz"} |
https://tex.stackexchange.com/questions/359291/how-to-get-times-new-roman-font-in-beamer | # How to get times new roman font in beamer?
I am using Warsaw theme. I want my beamer slides to have times new roman font.
• This is your 7th question without a MWE. – Dr. Manuel Kuehner Mar 19 '17 at 19:23
• I will improve henceforth – Qwerty Mar 19 '17 at 19:37
Assuming you're using pdfLaTeX to compile your document, you should load the beamer class with the option professionalfonts and issue an instruction such as \usepackage{newtxtext,newtxmath} to load a Times Roman clone.
A full MWE:
\documentclass[professionalfont]{beamer}
\usetheme{Warsaw}
\usepackage{newtxtext,newtxmath}
\begin{document}
\begin{frame}
Hello World. $1+1=2$
\end{frame}
\end{document}
• Didn't know the newtxtext package so far. Good to know. – Dr. Manuel Kuehner Mar 19 '17 at 19:24
• @Dr.ManuelKuehner - The newtxtext and newtxmath packages, which are maintained by Michael Sharpe, represent a significant and systematic development over the txfonts package. – Mico Mar 19 '17 at 19:31
• @Mico- gives an error: File 'newtxtext.sty' not found. I suppose I need to upload this package – Qwerty Mar 19 '17 at 19:49
• @Qwerty - If you don't have newtxtext in your TeX distribution, you could try mathptmx or txfonts -- or, as you mention, simply download and install the newtxtext package. – Mico Mar 19 '17 at 19:52
• @Mico-Great! txfonts helps. I will try newtxtext as well! – Qwerty Mar 19 '17 at 20:00 | 2020-01-28 12:38:22 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7044022083282471, "perplexity": 6071.875823530083}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-05/segments/1579251778272.69/warc/CC-MAIN-20200128122813-20200128152813-00548.warc.gz"} |
https://electronics.stackexchange.com/questions/149454/what-does-current-draw-mean-for-the | # What does current draw mean for the [closed]
Does this mean that the battery only outputs current equal to the amount of current draw? I always thought that batteries outputted a constant output, but apparently after some research I found this to be false. Can someone help explain?
UPDATE What I mean is that if I have a load that requires 100ma and then I get a battery that releases 150mAh, what does that mean? Does the battery always give 150mA or does that mean that the load only draws 100mA from the 150mA battery
## closed as unclear what you're asking by Olin Lathrop, Matt Young, nidhin, Daniel Grillo, PeterJJan 16 '15 at 18:40
Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
• Are you familiar with things like ohms law? – PlasmaHH Jan 16 '15 at 13:42
• Yes. I understand that Current, Resistance, and Voltage are interrelated in electricity and electromagnetism. – Jdude2345 Jan 16 '15 at 13:52
• The milliamp hour rating gives you an idea of how much total power a battery can provide - literally, current * time. Also, that in conjunction with the "C" rating gives you an idea of high-load performance, for example a "20C" 500mAh battery might be useful for briefly powering a 20*.5 = 10 amp load (for 3 minutes), while a "10C" battery of the same capacity may have too much internal impedance to provide more than 5 amps without the voltage severely sagging. – Chris Stratton Jan 17 '15 at 21:05
A battery is considered to be a constant-voltage source and, as such, will output whatever current the load requires in accordance with Ohm's law: ${E = IR}$ , where E is the battery voltage in volts, I is the load current in amperes, and R is the load resistance in ohms.
In order to solve for the load current we can rearrange the formula like this: $I = \frac{E}{R}$ and, assuming a 12 volt battery and a 12 ohm load, we'll have:
$$I = \frac{E}{R} = \frac{12V}{12\Omega} = 1\ ampere$$ | 2019-08-24 04:59:21 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6313045620918274, "perplexity": 764.6615360033948}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-35/segments/1566027319724.97/warc/CC-MAIN-20190824041053-20190824063053-00167.warc.gz"} |
https://ask.sagemath.org/answers/44290/revisions/ | # Revision history [back]
This is not very surprising, since the plot3d returns a sum of Point object primitives, instead of a single primitive, each one will send a one-line string to jmol, see https://git.sagemath.org/sage.git/tree/src/sage/plot/plot3d/shapes2.py
A possible workaround (for 10000 points, not 100000) is to use ployly: install it from a terminal:
sage -pip install plotly
and then do something like (slightly modified from plotly's website to be run on your own worksheet):
import plotly
plotly.offline.init_notebook_mode(connected=True)
from plotly.offline import iplot
import plotly.plotly as py
import plotly.graph_objs as go
# Create random data with numpy
import numpy as np
N = 10000
random_x = np.random.randn(N)
random_y = np.random.randn(N)
random_z = np.random.randn(N)
trace = go.Scatter3d(
x = random_x,
y = random_y,
z = random_z,
mode = 'markers'
)
data = [trace]
iplot(data) | 2020-01-18 22:33:04 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.18322381377220154, "perplexity": 13459.5077212254}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-05/segments/1579250593994.14/warc/CC-MAIN-20200118221909-20200119005909-00167.warc.gz"} |
https://www.bartleby.com/solution-answer/chapter-33-problem-35e-single-variable-calculus-concepts-and-contexts-enhanced-edition-4th-edition/9781337687805/6fd0563d-5563-11e9-8385-02ee952b546e | # The velocity and acceleration at time t.
### Single Variable Calculus: Concepts...
4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805
### Single Variable Calculus: Concepts...
4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805
#### Solutions
Chapter 3.3, Problem 35E
(a)
To determine
## To find: The velocity and acceleration at time t.
Expert Solution
The velocity of smooth level surface is 8cost_.
The acceleration of smooth level surface is 8sint_.
### Explanation of Solution
Given:
The equation of motion is x(t)=8sint, where t is in seconds and x is in centimeters.
Derivative rule:
Constant Multiple Rule:
If c is constant and f(x). is differentiable function, then
ddx[cf(x)]=cddx[f(x)] (1)
Recall:
If x(t)x is a displacement of a particle and the time t is in seconds, then the velocity of the particle is v(t)=dxdt.
If v(t) is a velocity of the particle and the time t is in seconds, then the acceleration of the particle is a(t)=dvdt.
Calculation:
Obtain the velocity at time t.
v(t)=ddt(x(t))=ddt(8sint)
Apply the Constant Multiple Rule as shown in equation (1),
v(t)=8ddx(sint)=8cost
Thus, the velocity of x(t)=8sint is v(t)=8cost.
Obtain the acceleration at time t.
a(t)=ddt(v(t))=ddt(8cost)
Apply the Constant Multiple Rule as shown in equation (1),
a(t)=8ddx(cost)=8(sint)=8sint
Therefore, the acceleration of v(t)=8cost is a(t)=8sint.
(b)
To determine
### To find: The position, velocity and acceleration at t=2π3 and obtain its direction.
Expert Solution
The position, velocity and acceleration at t=2π3 are 43, 4 and 43, respectively.
The direction of the particle is moving to the left (negative direction).
### Explanation of Solution
Given:
The equation of motion is x(t)=8sint, where t is in seconds and x is in centimeters.
Calculation:
The position x(t)=8sint at t=2π3 is computed as follows,
x(2π3)=8sin2π3=8(32) (Q sin2π3=32 )=43
Thus, the position x(t)=8sint at t=2π3 is x(2π3)=43.
From part (a), the velocity of x(t) is v(t)=8cost.
The velocity v(t)=8cost at t=2π3 is computed as follows,
v(2π3)=8cos(2π3)=8(12) (Q cos2π3=12)=4
Thus, the velocity v(t)=8cost at t=2π3 is v(2π2)=4.
From part (a), the acceleration of v(t)=8cost is a(t)=8sint.
The acceleration a(t)=8sint at t=2π3 is computed as follows,
a(2π3)=8sin2π3=8(32) (Q sin2π3=32 )=43
Thus, the acceleration a(t)=8sint at t=2π3 is a(2π3)=43.
Here, the velocity of the particle at t=2π3 is less than zero. That is, v(2π3)<0.
This implies that, the velocity of the particle at t=2π3 is negative.
Therefore,the direction of the particle is moving to the left (negative direction).
### Have a homework question?
Subscribe to bartleby learn! Ask subject matter experts 30 homework questions each month. Plus, you’ll have access to millions of step-by-step textbook answers! | 2021-08-01 19:21:14 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8102211952209473, "perplexity": 2995.4091951814753}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-31/segments/1627046154219.62/warc/CC-MAIN-20210801190212-20210801220212-00184.warc.gz"} |
https://physics.stackexchange.com/questions/313256/is-there-any-physical-significance-to-the-orthonormality-of-states-in-a-wave-fun | # Is there any physical significance to the orthonormality of states in a wave function?
In the infinite square well with bounds $0$ and $a$, the solutions to the time independent Schrodinger equation are: $$\psi_n(x)=\sqrt{\dfrac{2}{a}}\sin{\left(\dfrac{n\pi}{a}x\right)}$$ One of the properties of these wave functions is that they are "mutually orthogonal", meaning that $$\int_0^a \psi_m(x)^* \psi_n(x)dx=\delta_{mn}$$ Where $\delta_{mn}$ is the Kronecker delta. This fact is useful for finding the coefficient $c_n$ in the linear combination $$f(x)=\sum_{n=1}^{\infty}c_n\psi_n(x)$$ However, does orthonormality mean anything in terms of the particle? Do particles with mutually orthogonal stationary states differ from particles without them from a physical point of view?
These orthogonal states are energy eigenstates. Every measurable quantity provides an orthogonal basis of eigenstates. The physical meaning of their orthogonality is that, when energy (in this example) is measured while the system is in one such state, it has no chance of instead being found to be in another. Thus a general state's probability of being observed in state $n$ upon making such a measurement is $c_n^\ast c_n$.
A similar analysis for two consecutive measurements, be they of the sme observable or different observables, can be used to derive the probability distribution for the second measurement's result. This requires understanding the state's time-dependence between measurements. The energy eigenstates' probability distribution doesn't change over time, as the $c_n$ are simply multiplied by the unit complex number $\exp -\frac{iE_n t}{\hbar}$ over a time $t$.
Do particles with mutually orthogonal stationary states differ from particles without them from a physical point of view?
No. I am taking you to mean differ physically in this question. A free particle, of itself, say an electron, is physically identical to a bound electron. It's behaviour is different, but that's it.
• Doesn't answer anything because free electrons also have an energy basis consisting of mutually orthogonal states. – dmckee Feb 20 '17 at 1:46
## protected by Qmechanic♦Feb 20 '17 at 0:21
Thank you for your interest in this question. Because it has attracted low-quality or spam answers that had to be removed, posting an answer now requires 10 reputation on this site (the association bonus does not count). | 2019-10-17 03:01:16 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8545660972595215, "perplexity": 371.50861407260993}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-43/segments/1570986672548.33/warc/CC-MAIN-20191017022259-20191017045759-00160.warc.gz"} |
http://tex.stackexchange.com/questions/62773/ignoring-whitespace-in-a-custom-environment | # Ignoring whitespace in a custom environment
I know there has been questions similar to this previously but none of the proposed solutions seem to work for me.
I have a few custom environments I am using in LaTeX. Below is the code for a "licenses" environment. This environment is basically a table and I use the "license" command to specify each row of the table.
\newenvironment{licenses}
{%
\def\lwidth{0.25\textwidth}%
\def\rwidth{0.69\textwidth}%
%
\ifdef{\separator}{\separator}{}%
##1 & ##3 %
\def\separator{\\}%
}%
%
\begin{longtable}{>{\bfseries}L{\lwidth}!{\VRule}R{\rwidth}}%
}
{\end{longtable}}
I then use the environment as follows... however I have a problem in that the whitespace between each \license command affect the output.
\begin{licenses}
I have tried the \ignorespaces command and also commands similar to \catcode32=9\relax, but none of these seem to work in my case.
Here is a minimum working example:
\documentclass[10pt]{article}
\usepackage{etoolbox} % for ifdef
\usepackage{longtable} % for tables that span more than one page
\usepackage{tabularx} % for newcolumntype
\usepackage{xcolor} % for colours
\definecolor{lightgray}{gray}{0.8}
\newcolumntype{L}[1]{>{\raggedleft}p{#1}}
\newcolumntype{R}[1]{p{#1}}
\newcommand\VRule{\color{lightgray}\vrule width 0.5pt}
{%
\def\lwidth{0.25\textwidth}%
\def\rwidth{0.69\textwidth}%
%
\ifdef{\separator}{\separator}{}%
##1 & ##3 %
\def\separator{\\}%
}%
%
\begin{longtable}{>{\bfseries}L{\lwidth}!{\VRule}R{\rwidth}}
}
{\end{longtable}}
\begin{document}
\end{document}
-
Note that it is not "whitespace" but empty lines, which are converted to \par by tex. You can try redefining locally \par. – JLDiaz Jul 9 '12 at 22:22
While code snippets are useful in explanations, it is always best to compose a fully compilable MWE that illustrates the problem including the \documentclass and the appropriate packages so that those trying to help don't have to recreate it. – Peter Grill Jul 9 '12 at 22:23
Your code fragments don't seem to match: you define \licence to have three arguments (but it doesn't use #2 ? but your use of \license only shows two arguments. Please post a complete document that shows the problem. – David Carlisle Jul 9 '12 at 23:41
@PeterGrill - Sorry about that. Have included a MWE. – Joshua Spence Jul 9 '12 at 23:43
Why are you defining \license in that way? A simple \newcommand{\license}[3]{#1\\} outside the definition of licenses (or even inside it, with double ##) will do, avoiding the blank lines. – egreg Jul 9 '12 at 23:49
Recently, I have been looking for a Command that gobbles all following empty lines. The main idea is to define a command \gobblepars (taken from this blog):
\makeatletter
\newcommand\gobblepars{%
\@ifnextchar\par%
{\expandafter\gobblepars\@gobble}%
{}}
\makeatother
Does it work if you use this command as the very last command of the definition of your \license command?
-
This doesn't seem to work for me. – Joshua Spence Jul 9 '12 at 23:43
@joshua: if only one empty line is enough, look at tex.stackexchange.com/questions/24786/… where I asked a similar question. – Axioplase Jul 10 '12 at 9:22
Assuming that nothing goes in the licenses environment, a refinement of user946850's idea can work:
\documentclass[10pt]{article}
\usepackage{longtable} % for tables that span more than one page
\usepackage{xcolor} % for colours
\definecolor{lightgray}{gray}{0.8}
\newcolumntype{L}[1]{>{\raggedleft}p{#1}}
\newcolumntype{R}[1]{p{#1}}
\newcommand\VRule{\color{lightgray}\vrule width 0.5pt}
#1 & #3 \bingo
}
\makeatletter
\newcommand\bingo{%
\@ifnextchar\par
{\expandafter\bingo\@gobble}
{\@ifnextchar\end{}{\\[2ex]}}}
\makeatother
{%
\def\lwidth{0.25\textwidth}%
\def\rwidth{0.69\textwidth}%
\begin{longtable}{>{\bfseries}L{\lwidth}!{\VRule}R{\rwidth}}
}
{\end{longtable}}
\usepackage{lipsum}
\begin{document} | 2015-11-28 06:10:36 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9397207498550415, "perplexity": 2343.565554803474}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-48/segments/1448398451648.66/warc/CC-MAIN-20151124205411-00023-ip-10-71-132-137.ec2.internal.warc.gz"} |
https://www.aimsciences.org/article/doi/10.3934/cpaa.2013.12.1635 | # American Institute of Mathematical Sciences
July 2013, 12(4): 1635-1656. doi: 10.3934/cpaa.2013.12.1635
## A global attractor for a fluid--plate interaction model
1 Department of Mechanics and Mathematics, Kharkov National University, 4 Svobody sq., 61077, Kharkov, Ukraine 2 Department of Mechanics and Mathematics, Kharkov National University, 4 Svobody Sq., Kharkov, 61022, Ukraine
Received February 2011 Revised June 2012 Published November 2012
We study asymptotic dynamics of a coupled system consisting of linearized 3D Navier--Stokes equations in a bounded domain and a classical (nonlinear) elastic plate equation for transversal displacement on a flexible flat part of the boundary. We show that this problem generates a semiflow on appropriate phase space. Our main result states the existence of a compact finite-dimensional global attractor for this semiflow. We do not assume any kind of mechanical damping in the plate component. Thus our results means that dissipation of the energy in the fluid due to viscosity is sufficient to stabilize the system. To achieve the result we first study the corresponding linearized model and show that this linear model generates strongly continuous exponentially stable semigroup.
Citation: I. D. Chueshov, Iryna Ryzhkova. A global attractor for a fluid--plate interaction model. Communications on Pure & Applied Analysis, 2013, 12 (4) : 1635-1656. doi: 10.3934/cpaa.2013.12.1635
##### References:
[1] G. Avalos, The strong stability and instability of a fluid-structure semigroup,, Appl. Math. Optim., 55 (2007), 163. doi: 10.1007/s00245-006-0884-z. Google Scholar [2] G. Avalos and R. Triggiani, The coupled PDE system arising in fluid-structure interaction I. Explicit semigroup generator and its spectral properties,, in, 440 (2007), 15. doi: 10.1090/conm/440/08475. Google Scholar [3] G. Avalos and R. Triggiani, Semigroup well-posedness in the energy space of a parabolc-hyperbolic coupled Stokes-Lamé PDE system of fluid-structure interaction,, Discr. Contin. Dyn. Sys., 2 (2009), 417. doi: 10.3934/dcdss.2009.2.417. Google Scholar [4] A. V. Babin and M. I. Vishik, "Attractors of Evolution Equations,", North-Holland, (1992). Google Scholar [5] V. Barbu, Z. Grujić, I. Lasiecka and A. Tuffaha, Existence of the energy-level weak solutions for a nonlinear fluid-structure interaction model,, in, 440 (2007), 55. doi: 10.1090/conm/440/08476. Google Scholar [6] V. Barbu, Z. Grujić, I. Lasiecka and A. Tuffaha, Smoothness of weak solutions to a nonlinear fluid-structure interaction model,, Indiana Univ. Math. J., 57 (2008), 1173. doi: 10.1512/iumj.2008.57.3284. Google Scholar [7] H. Beirão da Veiga, On the existence of strong solution to a coupled fluid-structure evolution problem,, J. Math. Fluid Mech., 6 (2004), 21. doi: 10.1007/s00021-003-0082-5. Google Scholar [8] V. V. Bolotin, "Nonconservative Problems of Elastic Stability,", Pergamon Press, (1963). Google Scholar [9] A. Chambolle, B. Desjardins, M. Esteban and C. Grandmont, Existence of weak solutions for the unsteady interaction of a viscous fluid with an elastic plate,, J. Math. Fluid Mech., 7 (2005), 368. doi: 10.1007/s00021-004-0121-y. Google Scholar [10] I. Chueshov, "Introduction to the Theory of Infinite-Dimensional Dissipative Systems,", Acta, (1999). Google Scholar [11] I. Chueshov, A global attractor for a fluid-plate interaction model accounting only for longitudinal deformations of the plate,, Math. Meth. Appl. Sci., 34 (2011), 1801. doi: 10.1002/mma.1496. Google Scholar [12] I. Chueshov and S. Kolbasin, Long-time dynamics in plate models with strong nonlinear damping,, Comm. Pure Appl. Anal., 11 (2012), 659. doi: 10.3934/cpaa.2012.11.659. Google Scholar [13] I. Chueshov and I. Lasiecka, Attractors for second order evolution equations,, J. Dynam. Diff. Eqs., 16 (2004), 469. doi: 10.1007/s10884-004-4289-x. Google Scholar [14] I. Chueshov and I. Lasiecka, "Long-Time Behavior of Second Order Evolution Equations with Nonlinear Damping,", Memoirs of AMS, (2008). Google Scholar [15] I. Chueshov and I. Lasiecka, "Von Karman Evolution Equations,", Sprin\-ger, (2010). doi: 10.1007/978-0-387-87712-9. Google Scholar [16] I. Chueshov and I. Lasiecka, Well-posedness and long time behavior in nonlinear dissipative hyperbolic-like evolutions with critical exponents,, Preprint \arXiv{1204.5864v1}., (). Google Scholar [17] I. Chueshov and I. Ryzhkova, Unsteady interaction of a viscous fluid with an elastic shell modeled by full von Karman equations,, Preprint \arXiv{1112.6094v1}., (). Google Scholar [18] I. Chueshov and I. Ryzhkova, Well-posedness and long time behavior for a class of fluid-plate interaction models,, in, (2011). Google Scholar [19] D. Coutand and S. Shkoller, Motion of an elastic solid inside an incompressible viscous fluid,, Arch. Ration. Mech. Anal., 176 (2005), 25. doi: 10.1007/s00205-004-0340-7. Google Scholar [20] G. Galdi, C. Simader and H. Sohr, A class of solutions to stationary Stokes and Navier-Stokes equations with boundary data in $W^{-1/q,q}$,, Math. Annalen, 331 (2005), 41. doi: 10.1007/s00208-004-0573-7. Google Scholar [21] Q. Du, M. D. Gunzburger, L. S. Hou and J. Lee, Analysis of a linear fluid-structure interaction problem,, Discrete Contin. Dyn. Syst., 9 (2003), 633. doi: 10.3934/dcds.2003.9.633. Google Scholar [22] C. Grandmont, Existence of weak solutions for the unsteady interaction of a viscous fluid with an elastic plate,, SIAM J. Math. Anal., 40 (2008), 716. doi: 10.1137/070699196. Google Scholar [23] M. Grobbelaar-Van Dalsen, On a fluid-structure model in which the dynamics of the structure involves the shear stress due to the fluid,, J. Math. Fluid Mech., 10 (2008), 388. doi: 10.1007/s00021-006-0236-4. Google Scholar [24] M. Grobbelaar-Van Dalsen, A new approach to the stabilization of a fluid-structure interaction model,, Applicable Analysis, 88 (2009), 1053. doi: 10.1080/00036810903114841. Google Scholar [25] M. Grobbelaar-Van Dalsen, Strong stability for a fluid-structure model,, Math. Methods Appl. Sci., 32 (2009), 1452. doi: 10.1002/mma.1104. Google Scholar [26] M. Guidorzi, M. Padula and P. I. Plotnikov, Hopf solutions to a fluid-elastic interaction model,, Math. Models Methods Appl. Sci., 18 (2008), 215. doi: 10.1142/S0218202508002668. Google Scholar [27] N. Kopachevskii and Yu. Pashkova, Small oscillations of a viscous fluid in a vessel bounded by an elastic membrane,, Russian J. Math. Phys., 5 (1998), 459. Google Scholar [28] O. Ladyzhenskaya, "Mathematical Theory of Viscous Incompressible Flow,", GIFML, (1961). Google Scholar [29] J. Lagnese, "Boundary Stabilization of Thin Plates,", SIAM, (1989). doi: 10.1137/1.9781611970821. Google Scholar [30] J. Lagnese, Modeling and stabilization of nonlinear plates,, Int. Ser. Num. Math., 100 (1991), 247. Google Scholar [31] J. Lagnese and J. L. Lions, "Modeling, Analysis and Control of Thin Plates,", Masson, (1988). Google Scholar [32] J. Lequeurre, Existence of strong solutions to a fluid-structure system,, SIAM J. Math. Anal. \textbf{43} (2011), 43 (2011), 389. doi: 10.1137/10078983X. Google Scholar [33] J.-L. Lions and E. Magenes, "Problémes aux Limites non Homogénes et Applications," Vol. 1,, (French), (1968). Google Scholar [34] J. L. Lions, "Quelques Méthodes de Résolution des Problèmes aux Limites Non Linéaires,", (French), (1969). Google Scholar [35] A. Osses and J. Puel, Approximate controllability for a linear model of fluid structure interaction,, ESAIM Control, 4 (1999), 497. doi: 10.1051/cocv:1999119. Google Scholar [36] A. Pazy, "Semigroups of Linear Operators and Applications to Partial Differential Equations,", Springer, (1986). Google Scholar [37] G. Raugel, Global attractors in partial differential equations,, in, 2 (2002), 885. doi: 10.1016/S1874-575X(02)80038-8. Google Scholar [38] J.-P. Raymond, Feedback stabilization of a fluid-structure model,, SIAM Journal on Control and Optimization, 48 (2010), 5398. doi: 10.1137/080744761. Google Scholar [39] J. Simon, Compact sets in the space $L^p(0,T;B)$,, Annali di Matematica Pura ed Applicata, 148 (1987), 65. doi: 10.1007/BF01762360. Google Scholar [40] R. Temam, "Infinite-Dimensional Dynamical Systems in Mechanics and Physics,", Springer, (1988). doi: 10.1007/978-1-4684-0313-8. Google Scholar [41] R. Temam, "Navier-Stokes Equations: Theory and Numerical Analysis,", Reprint of the 1984 edition, (1984). Google Scholar [42] H. Triebel, "Interpolation Theory, Function Spaces, Differential Operators,", North Holland, (1978). Google Scholar
show all references
##### References:
[1] G. Avalos, The strong stability and instability of a fluid-structure semigroup,, Appl. Math. Optim., 55 (2007), 163. doi: 10.1007/s00245-006-0884-z. Google Scholar [2] G. Avalos and R. Triggiani, The coupled PDE system arising in fluid-structure interaction I. Explicit semigroup generator and its spectral properties,, in, 440 (2007), 15. doi: 10.1090/conm/440/08475. Google Scholar [3] G. Avalos and R. Triggiani, Semigroup well-posedness in the energy space of a parabolc-hyperbolic coupled Stokes-Lamé PDE system of fluid-structure interaction,, Discr. Contin. Dyn. Sys., 2 (2009), 417. doi: 10.3934/dcdss.2009.2.417. Google Scholar [4] A. V. Babin and M. I. Vishik, "Attractors of Evolution Equations,", North-Holland, (1992). Google Scholar [5] V. Barbu, Z. Grujić, I. Lasiecka and A. Tuffaha, Existence of the energy-level weak solutions for a nonlinear fluid-structure interaction model,, in, 440 (2007), 55. doi: 10.1090/conm/440/08476. Google Scholar [6] V. Barbu, Z. Grujić, I. Lasiecka and A. Tuffaha, Smoothness of weak solutions to a nonlinear fluid-structure interaction model,, Indiana Univ. Math. J., 57 (2008), 1173. doi: 10.1512/iumj.2008.57.3284. Google Scholar [7] H. Beirão da Veiga, On the existence of strong solution to a coupled fluid-structure evolution problem,, J. Math. Fluid Mech., 6 (2004), 21. doi: 10.1007/s00021-003-0082-5. Google Scholar [8] V. V. Bolotin, "Nonconservative Problems of Elastic Stability,", Pergamon Press, (1963). Google Scholar [9] A. Chambolle, B. Desjardins, M. Esteban and C. Grandmont, Existence of weak solutions for the unsteady interaction of a viscous fluid with an elastic plate,, J. Math. Fluid Mech., 7 (2005), 368. doi: 10.1007/s00021-004-0121-y. Google Scholar [10] I. Chueshov, "Introduction to the Theory of Infinite-Dimensional Dissipative Systems,", Acta, (1999). Google Scholar [11] I. Chueshov, A global attractor for a fluid-plate interaction model accounting only for longitudinal deformations of the plate,, Math. Meth. Appl. Sci., 34 (2011), 1801. doi: 10.1002/mma.1496. Google Scholar [12] I. Chueshov and S. Kolbasin, Long-time dynamics in plate models with strong nonlinear damping,, Comm. Pure Appl. Anal., 11 (2012), 659. doi: 10.3934/cpaa.2012.11.659. Google Scholar [13] I. Chueshov and I. Lasiecka, Attractors for second order evolution equations,, J. Dynam. Diff. Eqs., 16 (2004), 469. doi: 10.1007/s10884-004-4289-x. Google Scholar [14] I. Chueshov and I. Lasiecka, "Long-Time Behavior of Second Order Evolution Equations with Nonlinear Damping,", Memoirs of AMS, (2008). Google Scholar [15] I. Chueshov and I. Lasiecka, "Von Karman Evolution Equations,", Sprin\-ger, (2010). doi: 10.1007/978-0-387-87712-9. Google Scholar [16] I. Chueshov and I. Lasiecka, Well-posedness and long time behavior in nonlinear dissipative hyperbolic-like evolutions with critical exponents,, Preprint \arXiv{1204.5864v1}., (). Google Scholar [17] I. Chueshov and I. Ryzhkova, Unsteady interaction of a viscous fluid with an elastic shell modeled by full von Karman equations,, Preprint \arXiv{1112.6094v1}., (). Google Scholar [18] I. Chueshov and I. Ryzhkova, Well-posedness and long time behavior for a class of fluid-plate interaction models,, in, (2011). Google Scholar [19] D. Coutand and S. Shkoller, Motion of an elastic solid inside an incompressible viscous fluid,, Arch. Ration. Mech. Anal., 176 (2005), 25. doi: 10.1007/s00205-004-0340-7. Google Scholar [20] G. Galdi, C. Simader and H. Sohr, A class of solutions to stationary Stokes and Navier-Stokes equations with boundary data in $W^{-1/q,q}$,, Math. Annalen, 331 (2005), 41. doi: 10.1007/s00208-004-0573-7. Google Scholar [21] Q. Du, M. D. Gunzburger, L. S. Hou and J. Lee, Analysis of a linear fluid-structure interaction problem,, Discrete Contin. Dyn. Syst., 9 (2003), 633. doi: 10.3934/dcds.2003.9.633. Google Scholar [22] C. Grandmont, Existence of weak solutions for the unsteady interaction of a viscous fluid with an elastic plate,, SIAM J. Math. Anal., 40 (2008), 716. doi: 10.1137/070699196. Google Scholar [23] M. Grobbelaar-Van Dalsen, On a fluid-structure model in which the dynamics of the structure involves the shear stress due to the fluid,, J. Math. Fluid Mech., 10 (2008), 388. doi: 10.1007/s00021-006-0236-4. Google Scholar [24] M. Grobbelaar-Van Dalsen, A new approach to the stabilization of a fluid-structure interaction model,, Applicable Analysis, 88 (2009), 1053. doi: 10.1080/00036810903114841. Google Scholar [25] M. Grobbelaar-Van Dalsen, Strong stability for a fluid-structure model,, Math. Methods Appl. Sci., 32 (2009), 1452. doi: 10.1002/mma.1104. Google Scholar [26] M. Guidorzi, M. Padula and P. I. Plotnikov, Hopf solutions to a fluid-elastic interaction model,, Math. Models Methods Appl. Sci., 18 (2008), 215. doi: 10.1142/S0218202508002668. Google Scholar [27] N. Kopachevskii and Yu. Pashkova, Small oscillations of a viscous fluid in a vessel bounded by an elastic membrane,, Russian J. Math. Phys., 5 (1998), 459. Google Scholar [28] O. Ladyzhenskaya, "Mathematical Theory of Viscous Incompressible Flow,", GIFML, (1961). Google Scholar [29] J. Lagnese, "Boundary Stabilization of Thin Plates,", SIAM, (1989). doi: 10.1137/1.9781611970821. Google Scholar [30] J. Lagnese, Modeling and stabilization of nonlinear plates,, Int. Ser. Num. Math., 100 (1991), 247. Google Scholar [31] J. Lagnese and J. L. Lions, "Modeling, Analysis and Control of Thin Plates,", Masson, (1988). Google Scholar [32] J. Lequeurre, Existence of strong solutions to a fluid-structure system,, SIAM J. Math. Anal. \textbf{43} (2011), 43 (2011), 389. doi: 10.1137/10078983X. Google Scholar [33] J.-L. Lions and E. Magenes, "Problémes aux Limites non Homogénes et Applications," Vol. 1,, (French), (1968). Google Scholar [34] J. L. Lions, "Quelques Méthodes de Résolution des Problèmes aux Limites Non Linéaires,", (French), (1969). Google Scholar [35] A. Osses and J. Puel, Approximate controllability for a linear model of fluid structure interaction,, ESAIM Control, 4 (1999), 497. doi: 10.1051/cocv:1999119. Google Scholar [36] A. Pazy, "Semigroups of Linear Operators and Applications to Partial Differential Equations,", Springer, (1986). Google Scholar [37] G. Raugel, Global attractors in partial differential equations,, in, 2 (2002), 885. doi: 10.1016/S1874-575X(02)80038-8. Google Scholar [38] J.-P. Raymond, Feedback stabilization of a fluid-structure model,, SIAM Journal on Control and Optimization, 48 (2010), 5398. doi: 10.1137/080744761. Google Scholar [39] J. Simon, Compact sets in the space $L^p(0,T;B)$,, Annali di Matematica Pura ed Applicata, 148 (1987), 65. doi: 10.1007/BF01762360. Google Scholar [40] R. Temam, "Infinite-Dimensional Dynamical Systems in Mechanics and Physics,", Springer, (1988). doi: 10.1007/978-1-4684-0313-8. Google Scholar [41] R. Temam, "Navier-Stokes Equations: Theory and Numerical Analysis,", Reprint of the 1984 edition, (1984). Google Scholar [42] H. Triebel, "Interpolation Theory, Function Spaces, Differential Operators,", North Holland, (1978). Google Scholar
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