url stringlengths 14 2.42k | text stringlengths 100 1.02M | date stringlengths 19 19 | metadata stringlengths 1.06k 1.1k |
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http://quizpug.com/how-many-elements-of-the-periodic-table-can-you-name/ | How Many Elements Of The Periodic Table Can You Name? | QuizPug
How Many Elements Of The Periodic Table Can You Name?
Odds are, you haven't even seen a periodic table since high school or college. Which begs the question: how many elements of the periodic table can you name? Are you a scientific genius or will this quiz fall flat? Let's find out!
Question 1/10
pixabay.com
What is the chemical symbol for Hydrogen?
He
H
Fe
Question 2/10
pixabay.com
What is the chemical symbol for Lithium?
Li
Le
Lm
Question 3/10
pixabay.com
What is the chemical symbol for Copper?
Fe
Co
Cu
Question 4/10
pixabay.com
What is the chemical symbol for Potassium?
Pd
K
Pe
Question 5/10
pixabay.com
What is the chemical symbol for Tin?
In
Tn
Sn
Question 6/10
pixabay.com
What is the chemical symbol for silver?
Sm
Se
Ag
Question 7/10
pixabay.com
What is the chemical symbol for Lead?
Ld
Le
Pb
Question 8/10
pixabay.com
What is the chemical symbol for Uranium?
Ur
Um
U
Question 9/10
pixabay.com
What is the chemical symbol for Mercury?
Hg
Na
Mg
Question 10/10
pixabay.com
What is the chemical symbol for Argon?
Ag
Ar
Ae
C+, Chemical Imbalance
pixabay.com
Right!
Okay, so you may know a few basic elements from the periodic table. But this quiz proved that you still have a lot to learn about these chemical elements! Fear not, in taking this quiz, you took a crash course in chemistry and probably learned something new. Go you!
B+, Chemically Clever
pixabay.com
Right!
While many people forgot the periodic table as soon as they learned it back in 8th grade, you maintained a great knowledge of the elements and the symbols that represent them. When we say you're a rarity, we mean it!
A+, Scientifically Savvy
pixabay.com
Right!
Obviously, you excelled in your high school and college chemistry classes! While most struggled to pass this periodic table quiz, you prevailed victorious. It's obvious that you know your elements and their correlating symbols as only a scientifically savvy person can!
Play Again
1
What is the chemical symbol for Hydrogen?
He
H
Fe
2
What is the chemical symbol for Lithium?
Li
Le
Lm
3
What is the chemical symbol for Copper?
Fe
Co
Cu
4
What is the chemical symbol for Potassium?
Pd
K
Pe
5
What is the chemical symbol for Tin?
In
Tn
Sn
6
What is the chemical symbol for silver?
Sm
Se
Ag
7
What is the chemical symbol for Lead?
Ld
Le
Pb
8
What is the chemical symbol for Uranium?
Ur
Um
U
9
What is the chemical symbol for Mercury?
Hg
Na
Mg
10
What is the chemical symbol for Argon?
Ag
Ar
Ae | 2020-06-04 16:37:52 | {"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": 0.8256927728652954, "perplexity": 2511.5382031924296}, "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-2020-24/segments/1590347445880.79/warc/CC-MAIN-20200604161214-20200604191214-00205.warc.gz"} |
http://yoa.dk/1.0/doc/tutorial/proof/claim.html | ## 6.7.2 The claim of the multzero page
Page 88 of 800 Search internet
A numbered version of multzero.lgs looks thus:
1 "";;014E20344F3D486370710A10269E83D974EB8E9787EFB994A0BBD8BB0806
2 ""P multzero
3 ""R check
4 ""R Peano
5 ""R base
6
7 ""D 0
8 3.2l
9
10 ""B
11 page ( ""N , ""C )
12 title "Multiplication by zero"
13 bib "
14 @Book {Mendelson87,
15 author = {E. Mendelson},
16 title = {Introduction to Mathematical Logic},
17 publisher = {Wadsworth and Brooks},
18 year = {1987},
19 edition = {3.}}
20 "
21 main text "
22 \title{Multiplication by zero}
23 \author{A. U. Thor}
24 \maketitle
25 \tableofcontents
26 "[ make macro expanded version ragged right ]"
27 "[ prepare proof indentation ]"
28 \section{Theorem}
29 We now state Lemma 3.2l of \cite{Mendelson87}:
30 "[ PA lemma 3.2l : all x : 0 * x = 0 end lemma ]"
31 \section{Proof}
32 "[ PA proof of 3.2l :
33 line L01 : S7 >> 0 * 0 = 0 ;
34 line L02 : Block >> Begin ;
35 line L03 : Hypothesis >> 0 * x = 0 ;
36 line L04 : S8 >> 0 * x suc = 0 * x + 0 ;
37 line L05 : S5 >> 0 * x + 0 = 0 * x ;
38 line L06 : 3.2c mp L04 mp L05 >> 0 * x suc = 0 * x ;
39 line L07 : 3.2c mp L06 mp L03 >> 0 * x suc = 0 ;
40 line L08 : Block >> End ;
41 line L09 : Induction at x ponens L01 ponens L08 >> 0 * x = 0 ;
42 line L10 : Gen1 ponens L09 >> all x : 0 * x = 0 qed ]"
43 \bibliography{./page}
44 "
45 appendix "
46 \title{Multiplication by zero - appendix}
47 \author{A. U. Thor}
48 \maketitle
49 \tableofcontents
50 \section{\TeX\ definitions}
51 \begin{statements}
52 \item "[[ tex show define 3.2l as "
53 \mathbf{3.2l}" end define ]]"
54 \end{statements}
55 "
56 end page
57
The multzero page references check, Peano, and base in that order. Since check is first, the multzero page is verified according to the claim of the check page. Had the base page been first then multzero would have been verified according to the claim of the base page. The claims of the base, check, and Peano pages are:
base
All test cases are checked.
check
All test cases and all proofs are checked.
Peano
All test cases, all proofs, and all math definitions are checked.
Thus, you can also choose to have Peano as your first reference and still get your proofs checked.
The claim of the check page is defined thus in check.lgs:
verifier test1 &c proofcheck end verifier
The test1 function is the one which scans the page and evaluates all test cases. It is the test1 function which verified the test case on the combinations page.
The proofcheck function is the Logiweb proof checker. Among other, it checks everything on a page which it recognizes as a proof. It also checks that proofs do not reference each other in a circular way. And whenever a proof references a lemma on another page, proofcheck verifies that that other page was also checked by proofcheck and that the check was positive. That is a very fast check to conduct since proofcheck just has to look up the diagnose of the referenced page to see that the referenced page is correct.
If multzero had had a claim of its own, then that claim would have been used in place of the claim of the check page.
You can define your own claims if you like. And you can choose to combine claims using the &c conjunction. As an example, if you want to enforce a type discipline, you can define a type checker and add it to the conjunction of claims.
Page 88 of 800 Search logiweb.eu | 2018-06-21 23:49:34 | {"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": 0.6013697385787964, "perplexity": 4550.003990605525}, "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-2018-26/segments/1529267864303.32/warc/CC-MAIN-20180621231116-20180622011116-00082.warc.gz"} |
https://www.projecteuclid.org/euclid.aop/1176987806 | ## The Annals of Probability
### Intermittency-Type Estimates for Some Nondegenerate SPDE'S
Richard B. Sowers
#### Abstract
In this paper we prove some intermittency-type estimates for the stochastic partial differential equation $du = \mathscr{L}u dt + \mathscr{M}_lu\circ dW^l_t$, where $\mathscr{L}$ is a strongly elliptic second-order partial differential operator and the $\mathscr{M}_l$'s are first-order partial differential operators. Here the $W^l$'s are standard Wiener processes and $\circ$ denotes Stratonovich integration. We assume for simplicity that $u(0,\cdot) \equiv 1$. Our interest here is the behavior of $\mathbb{E}\lbrack|u(t,x)|^p\rbrack$ for large time and large $p$; more specifically, our interest is the growth of $(p^2t)^{-1}\log\mathbb{E}\lbrack|u(t,x)|^p\rbrack$ as $t$, then $p$, become large.
#### Article information
Source
Ann. Probab., Volume 23, Number 4 (1995), 1853-1874.
Dates
First available in Project Euclid: 19 April 2007
https://projecteuclid.org/euclid.aop/1176987806
Digital Object Identifier
doi:10.1214/aop/1176987806
Mathematical Reviews number (MathSciNet)
MR1379171
Zentralblatt MATH identifier
0852.60070
JSTOR | 2020-01-29 18:01:51 | {"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": 0.7229688167572021, "perplexity": 854.5980668138081}, "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/1579251801423.98/warc/CC-MAIN-20200129164403-20200129193403-00185.warc.gz"} |
https://gamedev.stackexchange.com/questions/45234/concept-interpretive-spells/45243 | # Concept: Interpretive Spells [closed]
The goal is to be able to create complex spells, that can manipulate the game's environment in non-preprogrammed ways, and to make the program understand spells. For example:
$@$=Big
@=Fire
You can probably understand what this one means. The player types, writes, or selects symbols. Of course, a spell can be only a few characters, or more sophisticated spells could potentially be hundreds or thousands of symbols long.
How could something like this be accomplished?
• What is the confusion you're having, exactly? You want your players to type thousands of symbols? – ssb Dec 9 '12 at 5:19
• I think that maybe a couple examples of several-thousand-rune-long spells would be helpful. Perhaps we're all misunderstanding since your only current example is only two runes long, with one being an adjective and the other a noun, which makes it pretty obvious and straight-forward to implement in a way that might not be appropriate for what you're actually thinking about. – Trevor Powell Dec 9 '12 at 5:27
• I believe Deathly is just pointing out that such a system could potentially support spells with thousands of symbols. He is not saying every spell would be thousands of symbols long, but more advanced ones could be. He is curious about how such a magic (and spell interpretation) system could be accomplished. – doppelgreener Dec 9 '12 at 5:50
• @Deathly I've made an edit to your post that I think clarifies some things. Please check my edits and make sure I've still preserved the intent of your post. – doppelgreener Dec 9 '12 at 5:52
• What is actually being asked for, here? Is Deathly asking for an implementation technique? Or a design for the game mechanics? Or a link to a "programmers for hire" jobs board where he can hire somebody? "How can this be accomplished?" doesn't really tell us what sort of answer to provide. – Trevor Powell Dec 9 '12 at 5:56
This can be done via programming! As in, for example, Dungeon Master, released way back in 1987, which used exactly this magic system.
There's no trick to this sort of thing. If the user picks "fire", then "big" makes the effect larger. You can do this by a multiplier, by a static amount, by scaling up the area of effect, or whatever. There's no AI involved at all. Just a matter of taking user input and doing something sensible in response to that input.
• As a player, I can't imagine wanting to string together thousands of symbols in order to cast a spell in a video game. I mean, assuming that "thousands" means just 2000, and that I can maintain a clicking rate of two symbols per second, it would take more than 15 minutes just to enter the symbols for a single spell. Frankly, I'd rather play an XCom mission, instead. Or get zergling rushed twice. Or something like that. – Trevor Powell Dec 9 '12 at 5:04
• Good job Trevor, best answer for 2012. "This can be done via programming!" You have my vote. – Engineer Dec 9 '12 at 10:34
To me it seems you want to deal with the rules of grammars (contextfree, context-sensitive, whatever) which are e.g. also used for designing programming languages.
Then you could define rules for which spells might follow which other spells or which modifiers. This is checked on syntax (correctness according to the rules) first.
Grammars look like this (I will not make it as formal as it is usually, because it might frighten you)
• We always start with [spell]
• We can replace [spell] with [sizeof] [basic_spell]
• We can also replace [spell] with [spell], [spell] (making to spells in a row)
• We can replace [spell] with [basic_spell]
• We can repeat these rules several times
This would be a valid grammar and say we have the following basic_spells: fire, water, light
And these modifiers (sizeof): small, big, short, long
We could do something like this:
small fire, long water
small fire, water
big water
But illegal would be something like big short water. Or also angry fire, because there is no word angry in our set.
Of course you can replace the long words with single characters.
Later you will have to check it for semantics (meaning), e.g. if somebody uses a fire spell and then a water spell, it would reduce the overall power of the spell (Baten Kaitos uses this system). So big fire, small water would reduce the power of this spell, because water stops fire.
One the whole you could search for how programming languages are designed, because creating a new syntax for spells is nothing different. Maybe start with finding out how brainfuck works and search for how compilers or interpreters for brainfuck are programmed. As far as I know it's usually a few steps:
• checking if all characters are valid
• checking if the order of characters and words is valid (e.g. foo int is not valid in Java, but int foo is)
• building a tree from the code
• traversing that tree to generate the basic commands (in your case the desired spell combination)
Might not be totally correct, as I am not a compiler-programmer.
Depending on how difficult your syntax shall be, you can leave out some of the commands. E.g. my upper example was totally linear. You only had to check if the spell is valid and if it was, combine adjectives and nouns and then execute all commands in a row.
But in programming languages we also have if-conditions and loops (for, while), which leads to non-linear situations. Thus we need a tree which shows us how stuff is related.
In your situation one could think of spells like 4($!) which might mean: Do the spell $! four times.
So you see, it's pretty much parsing a programming language. | 2020-07-05 06:31:23 | {"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": 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": 0.49879002571105957, "perplexity": 1751.413540822532}, "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-2020-29/segments/1593655887046.62/warc/CC-MAIN-20200705055259-20200705085259-00086.warc.gz"} |
http://mathhelpforum.com/algebra/73049-solved-more-sim-equations.html | # Math Help - [SOLVED] More Sim Equations
1. ## [SOLVED] More Sim Equations
$X + 7Y = 6$
$3X + 5Y = 14$
I still cant get my head around this!
2. For example multiply the first equation (both sides) by 3: $3X + 21Y = 18$ and subtract from this the other equation: $(3-3)X+(21-5)Y=18-14 \Leftrightarrow 16Y=4\Leftrightarrow Y=\frac {4}{16}=\boxed{\frac 14=0.25}$ which you can substitute in one of the original equation: $X+7\cdot\frac 14=6\Leftrightarrow X=6-\frac 74=\boxed{\frac {17}4=4.25}$.
$X + 7Y = 6$
$3X + 5Y = 14$
I still cant get my head around this!
$3x+21y=18$ -------------1
$3x+5y=14$ --------------2
2-1
Therefore , 16y=4 , y=1/4 , then continue to solve for x .
4. $
x = \frac{17}{4}, y = \frac{1}{4}
$
?
$
x = \frac{17}{4}, y = \frac{1}{4}
$
?
Yeah.
$X + 7Y = 6$
$3X + 5Y = 14$
I still cant get my head around this!
try this, substitution method
$X + 7Y = 6$
$3X + 5Y = 14$
$x=6-7y$
$3(6-7y)+5y=14$
$18-21y+5y=14$
$18-14=21y-5y$
$4=16y$
$y=\frac{1}{4}$
then substitute
$x+7y=6$
$x+\frac{7}{4}=6$
$x=6-\frac{7}{4}$
$x=\frac{24-7}{4}$
$x=\frac{17}{4}$
check
$\frac{17}{4}+7{1}{4}=6$
$\frac{24}{4}=6$
$6=6$
$3x+5y=14$
$3*\frac{17}{4}+5*\frac{1}{4}=14$
$\frac{51+5}{4}=14$
$\frac{56}{4}=14$
$56=56$ | 2014-12-20 06:51:39 | {"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": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 34, "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": 0.9331060647964478, "perplexity": 3119.9339851940867}, "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-2014-52/segments/1418802769550.123/warc/CC-MAIN-20141217075249-00072-ip-10-231-17-201.ec2.internal.warc.gz"} |
https://ltwork.net/to-the-nearest-square-unit-what-is-the-area-of-the-regular--3086388 | # To the nearest square unit what is the area of the regular octagon shown below
###### Question:
To the nearest square unit what is the area of the regular octagon shown below
### How did the farmers living in the northwest territory get their crops to the east coast?
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### 2spanish question ? anyone good in explaining things in spanish? ?
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### Twice a number decreased by 8 is 2 less than half the number
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### You rescued a child from drowning in the river. Write a diary entry about your experience. 150-200 words.
You rescued a child from drowning in the river. Write a diary entry about your experience. 150-200 words.... | 2022-12-08 16:42:38 | {"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": 2, "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": 0.2226771116256714, "perplexity": 2932.4031047237686}, "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/1669446711344.13/warc/CC-MAIN-20221208150643-20221208180643-00035.warc.gz"} |
http://www.codecogs.com/library/maths/calculus/differential/partial.php | I have forgotten
• https://me.yahoo.com
# Partial
An Introduction to Partial Differential Equations
View other versions (3)
## Definition Of Partial Differential Equations
This section presents some basic definitions regarding Partial Differential Equations.
### Partial Derivatives
Note
The partial derivative of a function f with respect to the variable x is usually denoted by
A partial derivative of a function of several variables is its derivative with respect to one of those variables, with the others held constant (as opposed to the total derivative, in which all variables are allowed to vary).
For example if , then
### Partial Differential Equations
Note
If a function is solution for
then is a harmonic function.
Partial differential equations (PDE) are a type of differential equation, i.e., a relation involving an unknown function (or functions) of several independent variables and their partial derivatives with respect to those variables. Partial differential equations are used to formulate, and thus aid the solution of, problems involving functions of several variables; such as the propagation of sound or heat, electrostatics, electrodynamics, fluid flow, and elasticity.
For example
where is a two variable function, is a partial differential equation .
Example:
##### Example - Simple example
Problem
Workings
Therefore
Note : This equation is of the first order although the equation from which it is derived has two arbitrary constants.
### The Solution Of Partial Differential Equations
It will be clear from these examples that the methods used for the solution of ordinary differential equations will not apply to Partial Differential Equations without considerable modification. A general discussion of partial differential equations is both difficult and lengthy. The objective in the following examples is to show some of the substitutions which may be used in the solution of the types of equation which occur in Scientific and engineering applications.
Example:
##### Example - Exponential Solution
Problem
The following linear equation gives the conduction of heat in one direction.
Workings
In the treatment of ordinary linear equations it was found that the use of exponentials was useful. This suggests as a trial solution. Substituting in the differential equation:
Solution
Which is true if
Thus is a solution. Changing the sign of m gives which is also a solution. | 2018-08-17 07:06:39 | {"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": 0.8608353137969971, "perplexity": 396.84418479502955}, "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-2018-34/segments/1534221211933.43/warc/CC-MAIN-20180817065045-20180817085045-00405.warc.gz"} |
http://theinfolist.com/php/HTMLGet.php?FindGo=Isotope | HOME TheInfoList
picture info Nucleon In chemistry and physics, a nucleon is either a proton or a neutron, considered in its role as a component of an atomic nucleus. The number of nucleons in a nucleus defines an isotope's mass number (nucleon number). Until the 1960s, nucleons were thought to be elementary particles, not made up of smaller parts. Now they are known to be composite particles, made of three quarks bound together by the so-called strong interaction. The interaction between two or more nucleons is called internucleon interaction or nuclear force, which is also ultimately caused by the strong interaction [...More Info...] [...Related Items...] picture info Double Beta Decay In nuclear physics, double beta decay is a type of radioactive decay in which two neutrons are simultaneously transformed into two protons, or vice versa, inside an atomic nucleus. As in single beta decay, this process allows the atom to move closer to the optimal ratio of protons and neutrons. As a result of this transformation, the nucleus emits two detectable beta particles, which are electrons or positrons. The literature distinguishes between two types of double beta decay: ordinary double beta decay and neutrinoless double beta decay. In ordinary double beta decay, which has been observed in several isotopes, two electrons and two electron antineutrinos are emitted from the decaying nucleus [...More Info...] [...Related Items...] picture info Nuclear Reaction In nuclear physics and nuclear chemistry, a nuclear reaction is semantically considered to be the process in which two nuclei, or a nucleus and an external subatomic particle, collide to produce one or more new nuclides. Thus, a nuclear reaction must cause a transformation of at least one nuclide to another. If a nucleus interacts with another nucleus or particle and they then separate without changing the nature of any nuclide, the process is simply referred to as a type of nuclear scattering, rather than a nuclear reaction. In principle, a reaction can involve more than two particles colliding, but because the probability of three or more nuclei to meet at the same time at the same place is much less than for two nuclei, such an event is exceptionally rare (see triple alpha process for an example very close to a three-body nuclear reaction) [...More Info...] [...Related Items...] picture info Proton Emission Proton emission (also known as proton radioactivity) is a rare type of radioactive decay in which a proton is ejected from a nucleus. Proton emission can occur from high-lying excited states in a nucleus following a beta decay, in which case the process is known as beta-delayed proton emission, or can occur from the ground state (or a low-lying isomer) of very proton-rich nuclei, in which case the process is very similar to alpha decay. For a proton to escape a nucleus, the proton separation energy must be negative—the proton is therefore unbound, and tunnels out of the nucleus in a finite time. Proton emission is not seen in naturally occurring isotopes; proton emitters can be produced via nuclear reactions, usually using linear particle accelerators. Although prompt (i.e [...More Info...] [...Related Items...] picture info Nuclear Force The nuclear force (or nucleon–nucleon interaction or residual strong force) is a force that acts between the protons and neutrons of atoms. Neutrons and protons, both nucleons, are affected by the nuclear force almost identically. Since protons have charge +1 e, they experience an electric force that tends to push them apart, but at short range the attractive nuclear force is strong enough to overcome the electromagnetic force. The nuclear force binds nucleons into atomic nuclei. The nuclear force is powerfully attractive between nucleons at distances of about 1 femtometre (fm, or 1.0 × 10−15 metres), but it rapidly decreases to insignificance at distances beyond about 2.5 fm. At distances less than 0.7 fm, the nuclear force becomes repulsive. This repulsive component is responsible for the physical size of nuclei, since the nucleons can come no closer than the force allows [...More Info...] [...Related Items...] picture info Gamma Ray A gamma ray, or gamma radiation (symbol γ or ${\displaystyle \gamma }$), is a penetrating form of electromagnetic radiation arising from the radioactive decay of atomic nuclei. It consists of the shortest wavelength electromagnetic waves and so imparts the highest photon energy. Paul Villard, a French chemist and physicist, discovered gamma radiation in 1900 while studying radiation emitted by radium [...More Info...] [...Related Items...] picture info Internal Conversion Internal conversion is a radioactive decay process wherein an excited nucleus interacts electromagnetically with one of the orbital electrons of the atom. This causes the electron to be emitted (ejected) from the atom.[1][2] Thus, in an internal conversion process, a high-energy electron is emitted from the radioactive atom, but not from the nucleus. For this reason, the high-speed electrons resulting from internal conversion are not called beta particles, since the latter come from beta decay, where they are newly created in the nuclear decay process. Internal conversion is possible whenever gamma decay is possible, except in the case where the atom is fully ionised [...More Info...] [...Related Items...] | 2021-03-04 09:23:39 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 1, "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": 0.7097427248954773, "perplexity": 828.8625485777007}, "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/1614178368687.25/warc/CC-MAIN-20210304082345-20210304112345-00458.warc.gz"} |
https://studydaddy.com/question/is-the-difference-between-an-ols-regression-and-a-gls-regression-qualitative-or | Waiting for answer This question has not been answered yet. You can hire a professional tutor to get the answer.
QUESTION
Is the difference between an OLS regression and a GLS regression qualitative or quantitative?
It is quantitative
Ordinary least squares is a technique for estimating unknown parameters in a linear regression model. OLS yield the maximum likelihood in a vector β, assuming the parameters have equal variance and are uncorrelated, in a noise ε - homoscedastic.
vec(y)=Xvec(β)+vec(ε)
Generalized least squares allows this approach to be generalized to give the maximum likelihood estimate β when the noise is of unequal variance (heteroscedasticity). Typically this leads to mathematical treatment that presents the two as follows: OLS: vecY=Xbeta+ε " where " ε~N(0,σ²I) GLS: vecY=Xbeta+η " where " η~N(0,σ²Cov) Note the formulation for the two approaches results in real structural and quantitative difference. Notice the two are governed by two different Gauss distribution the N(0, sigma^2M); M = I " or " M=Cov part Where: I = "Identity Matrix and " Cov = "Covariance Matrix
Cheers! | 2019-04-22 12:51:40 | {"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": 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": 0.8374450206756592, "perplexity": 1638.2095021482364}, "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-2019-18/segments/1555578553595.61/warc/CC-MAIN-20190422115451-20190422141451-00485.warc.gz"} |
https://www.themathdoctors.org/why-do-we-add-or-multiply-in-probability/ | # WHY Do We Add or Multiply in Probability?
Last time, we discussed how you know whether to add or multiply (or something else) in compound probability problems (like finding the probability that you will flip heads and roll an even number). But as I’ve said before, it’s often easier to remember a formula if you know why it is what it is. I’ll focus here on two such questions.
## Why do we add to find P(A or B)?
Here is a question from 1999:
Why Add Probabilities in an OR Statement?
Can you please answer my question? Why is it that whenever we want to find the probability of, for example, rolling a 2 or a 3 on a die we add up the number of twos and threes? Or when we want to find the probability of getting an ace or king we add up aces and kings?
It is the OR that I am not getting. Why do we add?
I have also heard of P(A or B) = P(A)+P(B). I understand when it is one specific thing like picking an ace or rolling an even number, etc., but not when there is an "or." Please try to give me an explanation. Thanks!
Mike is probably very new to probability, as the first question could have been answered directly in terms of the definition of probability: the total number of possible successes (rolls that are either 2 or 3), over the total number of possible outcomes. The very word “or” often causes confusion in math, because its application can feel backward. But this was early in my time at Ask Dr. Math, and I missed that issue (“Why add the 2s and 3s, when it says ‘2 or 3’ ?”). I may have answered at a higher level than I should have. But it makes a better answer to the bigger question this way, so Ill use it here, and discuss the “or” issue below.
I mentioned the definition, and then illustrated the general idea in terms of areas (which I could just as well have described as Venn diagrams, representing sets):
The probability of an event is the ratio of the number of (equally likely) cases in which the event will happen, to the total number of possible cases.
You can think of it in terms of area: if I draw a circle on the floor and drop an object in such a way that it is equally likely to fall at any point on the floor, the probability of its falling in that circle is the ratio of the area of the circle to the area of the floor:
+-------------------------------------------+
| |
| |
| |
| |
| |
| |
| |
| ***** |
| ***.....*** |
| *...........* |
| *......A......* |
| *.............* |
| *...........* |
| ***.....*** |
| ***** |
| |
+-------------------------------------------+
Now if I draw two circles that don't overlap, then the probability of its falling in circle A OR circle B is the ratio of the area of both circles together to the area of the floor:
+-------------------------------------------+
| ********* |
| ***---------*** |
| **---------------** |
| *-------------------* |
| *---------------------* |
| *----------B----------* |
| *---------------------* |
| ***** *-------------------* |
| ***.....*** **---------------** |
| *...........* ***---------*** |
| *......A......* ********* |
| *.............* |
| *...........* |
| ***.....*** |
| ***** |
| |
+-------------------------------------------+
But the total area of A and B is just the sum of the areas of the two circles, so the probability of its landing in either A or B is the sum of the two probabilities. This is what we are doing whenever we find the probability of either of two mutually exclusive events (that is, both A and B can't happen at the same time), such as getting a King OR a Queen.
So the numerator of the probability is the total number of elements in the two sets – we add them. And when you add the numerators of two fractions with the same denominator, you are adding the fractions.
My picture assumes that the two events don’t overlap – that they are mutually exclusive. This was assumed in Mike’s question, and leads to the special-case formula, P(A or B) = P(A) + P(B).
But what if the events overlap – if there are outcomes that are part of both events?
Now if A and B overlap, then we won't be able to tell what the probability of either event happening will be unless we have additional information to tell us how much they overlap:
+-------------------------------------------+
| |
| |
| |
| ********* |
| ***---------*** |
| **---------------** |
| *-------------------* |
| *****--------------------* |
| ***...*x***------B----------* |
| *......*xxxx*----------------* |
| *......A.*xxxx*--------------* |
| *.........**xx*------------** |
| *..........***---------*** |
| ***.....*** ********* |
| ***** |
| |
+-------------------------------------------+
So if you want to find the probability of getting, say, a King OR a red card, you have to know something more, namely that these two events are independent, so that the probability of A AND B is P(A) * P(B). But that's a different matter.
Here the picture only hints at the general formula. In a case like this, we can count the outcomes by adding A and B, and then subtracting the overlap (intersection), which is counted twice when we add. This intersection is A and B; so the general formula is P(A or B) = P(A) + P(B) – P(A and B). Rather than explain this (which seemed likely to be beyond what Mike had learned yet), I just referred to Inclusive Probabilities, where Dr. Anthony had said more or less what I just said, with an example that you might like to read.
## But how does what you just did mean “or”?
I mentioned above that “or” can cause confusion. Here is an answer I gave about this in 2008, not in the context of probability, but in an elementary counting question:
The Difference between And and Or
My son had a question that was marked wrong on his paper. He pointed out to me that by the way it was worded, he felt as though he were correct. Here is the question: There are 3 knives, 4 spoons, 4 forks. What fraction of the utensils are spoons OR forks?
He answered 4/11 and was told the teachers edition says 8/11. I understand the way he read it to be OR meaning one or the other. If it's 8/11, shouldn't it be worded spoons AND forks? If the answer is 8/11, I want my son to understand why.
The question here is, essentially, “Wouldn’t we add when it says and, rather than or, because we are putting two sets together?” In response, I emphasized that the usage in talking about sets (or events) focuses on each individual element of a set, not each set as a whole; the wording can end up seeming reversed if we look at it the wrong way:
When we talk about the set of things that are A AND B, we mean that EACH of those things must be BOTH A and B. Nothing is both a spoon and a fork! (At least not in this problem.) So "and" would have been inappropriate. There are no utensils that are spoons and forks.
When we talk about the set of things that are A OR B, we mean that EACH of them may be EITHER A or B. That is, we are including in the set BOTH those that are A, AND those that are B. This is where the confusion and ambiguity come in! There are 8 utensils that are spoons or forks.
Your son read it in a way that is commonly used in nontechnical English, taking "How many are A or B" to mean two separate questions combined: "How many are A, how many are B". I can see how that could be tempting in this case; the two numbers happen to be the same, so he could take the question to mean "How many are A (which is also the same as the number that are B". If there had been 3 spoons and 4 forks, that interpretation would not have made as much sense; the best answer he could give would be "3, or 4". We don't combine questions like that in math, to avoid confusion.
Dr. Riz supplemented this with a different example (and a more creative conclusion):
In logic, an AND statement is only true if both parts of it are true. If I say, "I am in Vermont AND I am in New Hampshire" the only way that can be true is if I am standing on the border with one foot in each state.
An OR statement is true if either part is true. If I say, "I am in Vermont OR I am in New Hampshire" that statement is true as long as I am in either state (it's also true if I'm straddling the border). The only way an OR statement is not true is if both parts are false, such as if I were standing in Massachusetts when I made my statement about being in Vermont or New Hampshire.
With your question about utensils being spoons OR forks, I count every utensil that is either a spoon or a fork, giving 8 of the 11. If I were asked what fraction of the utensils were spoons AND forks, there would be zero since the utensil would have to be both things. There IS a utensil you sometimes see in fast food places which is a spoon shape with teeth on the front edge, and it's generally referred to as a "spork", a combination of spoon and fork. That's what I'd need for a utensil to be considered a spoon AND a fork.
So in Mike’s probability question, the number of cards that are aces or kings is found by adding the number of aces and the number of kings.
## Why do we multiply to find P(A and B)?
This question came from Hannah in 2009:
Why Do We Multiply the Probabilities of Independent Events?
I would like to know the reasoning behind this topic.
P(A and B)= P(A)xP(B)
Why do we have to multiply the two probabilities, why can't we add them together? Thank you very much.
I replied,
It may be clearer to you if you think of probability as the fraction of the time that something will happen. If event A happens 1/2 of the time, and event B happens 1/3 of the time, and events A and B are independent, then event B will happen 1/3 of the times that event A happens, right? And to find 1/3 of 1/2, we multiply. The probability that events A and B both happen is 1/6.
Note also that adding two probabilities will give a larger number than either of them; but the probability that two events BOTH happen can't be greater than either of the individual events. So it would make no sense to add probabilities in this situation.
Six years later, Mujari wrote to ask for a further explanation, and I drew some pictures to make it concrete, which we added into this page because it was a helpful clarification. (Thanks, Mujari!) I’ll let you look through it and see how it works for you.
### 5 thoughts on “WHY Do We Add or Multiply in Probability?”
1. Hi, I didnt understand why do we multiply. The time example didnt make sense to me. Can you explain with another example?
1. When I wrote this post I was still trying to keep posts short, so I didn’t quote all of my answer to this question, but left it for the reader to go to the original answer and read it. I’ll copy it here, because it asks exactly what you ask:
Question:
I don’t understand this part:
“If event A happens 1/2 of the time, and event B happens 1/3 of the time,
and events A and B are independent, then event B will happen 1/3 of the
times that event A happens …”
Sorry, kindly explain that more.
Hi, Mujari.
Let’s take a concrete example.
Suppose, as you say, we have event A with probability 1/2, and event B
with probability 1/3, and they are independent. Then suppose that there
are 60 equally likely outcomes represented by these dots:
o o o o o o o o o o
o o o o o o o o o o
o o o o o o o o o o
o o o o o o o o o o
o o o o o o o o o o
o o o o o o o o o o
Now suppose that the A’s represent the outcomes in event A (1/2 of
all outcomes):
A A A A A o o o o o
A A A A A o o o o o
A A A A A o o o o o
A A A A A o o o o o
A A A A A o o o o o
A A A A A o o o o o
Now, among the 30 outcomes in which A occurred, B occurs in 1/3 of them
(10); and the same is true among outcomes in which A did not occur. I’ll
use B to indicate that ONLY B occurred, and X to indicate that BOTH A and
B occurred:
A A A A A o o o o o
A A A A A o o o o o
A A A A A o o o o o
A A A A A o o o o o
X X X X X B B B B B
X X X X X B B B B B
How many times did BOTH occur? 1/3 of the 1/2, which is 1/6 of all
outcomes; that is 1/6 of my 60 outcomes, which is 10, as illustrated in
the lower left-hand region, above.
So the probability that A and B occur is 1/2 * 1/3 = 1/6 — that is, 10/60
in the picture.
1. This is the best explanation of why we multiply probabilities on the internet. Thank you so freaking much.
This site uses Akismet to reduce spam. Learn how your comment data is processed. | 2021-10-27 07:53:35 | {"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": 0.6819484829902649, "perplexity": 344.29207046621224}, "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/1634323588102.27/warc/CC-MAIN-20211027053727-20211027083727-00046.warc.gz"} |
https://www.onlinetest.ibpsexamguru.in/forum/14984/--if-a-x-b-means-'b-is-the-father-of-a';-a | # If A x B means 'B is the father of A'; A ÷ B means 'B is the mother of A'; A + B means ' B is the brother of A; and A B means 'B is the sister of A; then which of the following shows 'G is the granddaughter of L' ?
[ A ] G - S + M X R X L [ B ] G S + M x L x R [ C ] G - S X M X R X L [ D ] None of these
Answer : Option D Explanation : 1), 2) and 3) do not tell the sex of G. 4 lacks required generation gap. | 2019-10-19 04:52:02 | {"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": 0.8180046677589417, "perplexity": 2216.1505633733022}, "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/1570986688826.38/warc/CC-MAIN-20191019040458-20191019063958-00257.warc.gz"} |
https://brilliant.org/discussions/thread/choosing-n-candies-from-m-brands/ | # Choosing $$n$$ candies from $$m$$ brands
In how many ways can we choose $$n$$ candies from $$m$$ brands?
Note: Repeated selection from the same brand is allowed and $$n\leq m$$.
Why is $$m^n$$ not the correct answer?
Note by D K
2 years, 2 months ago
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2^{34} $$2^{34}$$
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If $$n$$ candies are chosen from $$m$$ brands, then the sum of the number of candies from each brand equals $$n$$.(That's pretty obvious right?!).Suppose $$x_1$$ candies are chosen from Brand #1 , $$x_2$$ candies from Brand #2 and ... $$x_m$$ candies from Brand #$$m$$.Now continuing my argument above , obviously the answer to your question is equivalent to the number of answers to the equation :
$$\space$$
$$x_1 + x_2 + \dots + x_m = m$$ , $$x_i \ge 0$$ ;
$$\space$$
Now if you're familiar with "Stars and bars" you'd know that the answer is $$n+m-1 \choose m-1$$.(If not , you can read it's wikipage here , I'm too lazy to write the whole thing down here)
Now as for the answer to your second question,the answer $$m^n$$ would definitely not be correct since you're not counting the cases where no candies are chosen from a particular brand also you're not talking into account the fact that candies from different brands are not alike.I hope I could help you get a good grasp on this.
- 2 years, 2 months ago | 2018-07-16 09:06:48 | {"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": 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": 0.9867706298828125, "perplexity": 2426.273986149499}, "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-2018-30/segments/1531676589237.16/warc/CC-MAIN-20180716080356-20180716100356-00051.warc.gz"} |
https://www.zbmath.org/authors/?q=ai%3Ahe.xiao | # zbMATH — the first resource for mathematics
## He, Xiao
Compute Distance To:
Author ID: he.xiao Published as: He, X.; He, Xiao External Links: ORCID
Documents Indexed: 63 Publications since 1991, including 1 Book
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#### Co-Authors
1 single-authored 30 Zhou, Donghua 24 Wang, Zidong 7 Liu, Qinyuan 7 Zheng, Sining 6 Liu, Yang 4 Zhang, Junfeng 3 Dong, Hongli 3 Hu, Jun 3 Ji, Yindong 3 Shen, Bo 3 Wang, Xiuming 3 Yan, Rongyi 2 Christofides, Panagiotis D. 2 Qin, Liguo 2 Shi, Jiantao 2 Tian, Miaoqing 1 Albalawi, Fahad 1 Alsaadi, Fuad Eid S. 1 Che, Defu 1 Chen, Hao 1 Chen, Hao 1 Chen, Hao 1 Deng, Ruiliang 1 Ding, Derui 1 Ding, Steven X. 1 Ghinea, Gheorghita 1 Gong, Hanzhao 1 Hu, Yanyan 1 Huang, Jie 1 Ji, Yunjia 1 Jia, Fanlin 1 Ju, Yamei 1 Li, Gang 1 Li, Jiao 1 Luo, Yuqiang 1 Peng, Kaixiang 1 Sun, Changai 1 Wang, Guoyin 1 Wang, Wei 1 Wang, Youqing 1 Wei, Guoliang 1 Wu, Zhe 1 Yan, Rui 1 Zhang, Bangcheng 1 Zhang, Hailan 1 Zhang, Zhihao 1 Zhao, Min 1 Zhao, Yinghong 1 Zheng, Donghong 1 Zhong, Maiying 1 Zhou, Zhijie
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#### Serials
6 International Journal of Control 5 Automatica 5 IEEE Transactions on Automatic Control 4 Journal of the Franklin Institute 3 International Journal of Systems Science 3 Journal of Control Science and Engineering 2 Journal of Mathematical Analysis and Applications 2 Wave Motion 2 International Journal of Adaptive Control and Signal Processing 2 Mathematical Problems in Engineering 2 Abstract and Applied Analysis 2 Nonlinear Analysis. Real World Applications 1 International Journal of Heat and Mass Transfer 1 Journal of Mathematical Biology 1 Journal of Algebra 1 Systems & Control Letters 1 Acta Automatica Sinica 1 Journal of Shanghai Jiaotong University (Chinese Edition) 1 Applied Mathematics Letters 1 IEEE Transactions on Signal Processing 1 International Journal of Robust and Nonlinear Control 1 Journal of University of Science and Technology Beijing (Chinese Edition) 1 Discrete and Continuous Dynamical Systems. Series B 1 Journal of Software 1 Journal of Computational Acoustics 1 Journal of Control Theory and Applications 1 Studies in Systems, Decision and Control 1 IEEE Transactions on Control of Network Systems
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#### Fields
38 Systems theory; control (93-XX) 7 Partial differential equations (35-XX) 6 Biology and other natural sciences (92-XX) 6 Information and communication theory, circuits (94-XX) 5 Computer science (68-XX) 3 General and overarching topics; collections (00-XX) 3 Fluid mechanics (76-XX) 2 Probability theory and stochastic processes (60-XX) 2 Optics, electromagnetic theory (78-XX) 2 Operations research, mathematical programming (90-XX) 1 Nonassociative rings and algebras (17-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Statistics (62-XX) 1 Mechanics of deformable solids (74-XX) 1 Classical thermodynamics, heat transfer (80-XX)
#### Citations contained in zbMATH
38 Publications have been cited 385 times in 333 Documents Cited by Year
Robust fault detection for networked systems with communication delay and data missing. Zbl 1180.93101
He, Xiao; Wang, Zidong; Zhou, D. H.
2009
Robust $$H_{\infty}$$ filtering for networked systems with multiple state delays. Zbl 1133.93314
He, Xiao; Wang, Zidong; Zhou, D.
2007
Convergence rate estimates of solutions in a higher dimensional chemotaxis system with logistic source. Zbl 1334.35088
He, Xiao; Zheng, Sining
2016
Event-based recursive distributed filtering over wireless sensor networks. Zbl 1360.93703
Liu, Qinyuan; Wang, Zidong; He, Xiao; Zhou, D. H.
2015
Network-based fault detection for discrete-time state-delay systems: a new measurement model. Zbl 1284.93147
He, Xiao; Wang, Zidong; Ji, Y. D.; Zhou, D. H.
2008
Global boundedness of solutions in a reaction-diffusion system of predator-prey model with prey-taxis. Zbl 1381.35188
He, Xiao; Zheng, Sining
2015
Networked fault detection with random communication and packet losses. Zbl 1168.93369
He, Xiao; Wang, Zidong; Zhou, Donghua
2008
Event-based $$H_\infty$$ consensus control of multi-agent systems with relative output feedback: the finite-horizon case. Zbl 1360.93041
Liu, Qinyuan; Wang, Zidong; He, Xiao; Zhou, D. H.
2015
Fault detection for discrete-time systems in a networked environment. Zbl 1213.93123
He, Xiao; Wang, Zidong; Ji, Y. D.; Zhou, D.
2010
On Kalman-consensus filtering with random link failures over sensor networks. Zbl 1423.93384
Liu, Qinyuan; Wang, Zidong; He, Xiao; Zhou, D. H.
2018
Protection zone in a diffusive predator-prey model with Beddington-DeAngelis functional response. Zbl 1387.92073
He, Xiao; Zheng, Sining
2017
Filtering and fault detection for nonlinear systems with polynomial approximation. Zbl 1318.93090
Liu, Yang; Wang, Zidong; He, Xiao; Zhou, D. H.
2015
Event-triggered resilient filtering with measurement quantization and random sensor failures: monotonicity and convergence. Zbl 1401.93203
Liu, Qinyuan; Wang, Zidong; He, Xiao; Zhou, D. H.
2018
A resilient approach to distributed filter design for time-varying systems under stochastic nonlinearities and sensor degradation. Zbl 1414.94370
2017
Global boundedness in quasilinear attraction-repulsion chemotaxis system with logistic source. Zbl 1365.92018
Tian, Miaoqing; He, Xiao; Zheng, Sining
2016
Optimal filtering for networked systems with stochastic sensor gain degradation. Zbl 1296.93194
Liu, Yang; He, Xiao; Wang, Zidong; Zhou, Donghua
2014
Network-based robust fault detection with incomplete measurements. Zbl 1193.93162
He, Xiao; Wang, Zidong; Zhou, D. H.
2009
Vortex merging and spectral cascade in two-dimensional flows. Zbl 1027.76516
Nielsen, A. H.; He, X.; Rasmussen, J. Juul; Bohr, T.
1996
Iterative learning control for nonlinear stochastic systems with variable pass length. Zbl 1347.93278
Shi, Jiantao; He, Xiao; Zhou, Donghua
2016
Event-triggered filtering and fault estimation for nonlinear systems with stochastic sensor saturations. Zbl 1367.93651
Liu, Yang; Wang, Zidong; He, Xiao; Zhou, D. H.
2017
State estimation for networked systems with randomly occurring quantisations. Zbl 1278.93249
He, Xiao; Wang, Zidong; Ji, Y. D.; Zhou, D. H.
2013
Numerical simulation of pulse detonation engine phenomena. Zbl 1081.76574
He, X.; Karagozian, A. R.
2003
Event-based distributed filtering over Markovian switching topologies. Zbl 07082387
Liu, Qinyuan; Wang, Zidong; He, Xiao; Zhou, Donghua
2019
Finite-horizon quantized $$H_\infty$$ filter design for a class of time-varying systems under event-triggered transmissions. Zbl 1370.93284
Liu, Yang; Wang, Zidong; He, Xiao; Zhou, D. H.
2017
Minimum-variance recursive filtering over sensor networks with stochastic sensor gain degradation: algorithms and performance analysis. Zbl 1370.93283
Liu, Yang; Wang, Zidong; He, Xiao; Zhou, D. H.
2016
Protection zone in a modified Lotka-Volterra model. Zbl 1335.35050
He, Xiao; Zheng, Sining
2015
Robust $$H^\infty$$ filtering for time-delay systems with missing measurements: a parameter-dependent approach. Zbl 1150.93345
He, Xiao; Zhou, Donghua
2007
Cloud-based fault tolerant control for a DC motor system. Zbl 1400.93065
He, Xiao; Ju, Yamei; Liu, Yang; Zhang, Bangcheng
2017
Detecting intermittent sensor faults for linear stochastic systems subject to unknown disturbance. Zbl 1349.93359
Yan, Rongyi; He, Xiao; Zhou, Donghua
2016
Intermittent fault detection for uncertain networked systems. Zbl 1296.93192
He, Xiao; Hu, Yanyan; Peng, Kaixiang
2013
Intermittent sensor fault detection for stochastic LTV systems with parameter uncertainty and limited resolution. Zbl 1436.93133
Zhang, Junfeng; Christofides, Panagiotis D.; He, Xiao; Albalawi, Fahad; Zhao, Yinghong; Zhou, Donghua
2020
Detection, isolation and diagnosability analysis of intermittent faults in stochastic systems. Zbl 1390.93740
Yan, Rongyi; He, Xiao; Wang, Zidong; Zhou, D. H.
2018
Theoretical simulations of wave field variation excited by a monopole within collar for acoustic logging while drilling. Zbl 07211701
He, Xiao; Wang, Xiuming; Chen, Hao
2017
Editorial: Fault diagnosis and application to modern systems. Zbl 1407.00035
He, Xiao (ed.); Wang, Zidong (ed.); Li, Gang (ed.); Zhou, Zhijie (ed.); Wang, Youqing (ed.)
2017
Higher level Zhu algebras are subquotients of universal enveloping algebras. Zbl 1420.17029
He, Xiao
2017
Asymptotic boundary estimates to infinity Laplace equations with $$\Gamma$$-varying nonlinearity. Zbl 1335.35072
Wang, Wei; Gong, Hanzhao; He, Xiao; Zheng, Sining
2016
The role of Ekman pumping and the dominance of swirl in confined flows driven by Lorentz forces. Zbl 0947.76093
Davidson, P. A.; Kinnear, D.; Lingwood, R. J.; Short, D. J.; He, X.
1999
Uniform convergence of polynomials associated with varying Jacobi weights. Zbl 0749.41011
He, X.; Li, X.
1991
Intermittent sensor fault detection for stochastic LTV systems with parameter uncertainty and limited resolution. Zbl 1436.93133
Zhang, Junfeng; Christofides, Panagiotis D.; He, Xiao; Albalawi, Fahad; Zhao, Yinghong; Zhou, Donghua
2020
Event-based distributed filtering over Markovian switching topologies. Zbl 07082387
Liu, Qinyuan; Wang, Zidong; He, Xiao; Zhou, Donghua
2019
On Kalman-consensus filtering with random link failures over sensor networks. Zbl 1423.93384
Liu, Qinyuan; Wang, Zidong; He, Xiao; Zhou, D. H.
2018
Event-triggered resilient filtering with measurement quantization and random sensor failures: monotonicity and convergence. Zbl 1401.93203
Liu, Qinyuan; Wang, Zidong; He, Xiao; Zhou, D. H.
2018
Detection, isolation and diagnosability analysis of intermittent faults in stochastic systems. Zbl 1390.93740
Yan, Rongyi; He, Xiao; Wang, Zidong; Zhou, D. H.
2018
Protection zone in a diffusive predator-prey model with Beddington-DeAngelis functional response. Zbl 1387.92073
He, Xiao; Zheng, Sining
2017
A resilient approach to distributed filter design for time-varying systems under stochastic nonlinearities and sensor degradation. Zbl 1414.94370
2017
Event-triggered filtering and fault estimation for nonlinear systems with stochastic sensor saturations. Zbl 1367.93651
Liu, Yang; Wang, Zidong; He, Xiao; Zhou, D. H.
2017
Finite-horizon quantized $$H_\infty$$ filter design for a class of time-varying systems under event-triggered transmissions. Zbl 1370.93284
Liu, Yang; Wang, Zidong; He, Xiao; Zhou, D. H.
2017
Cloud-based fault tolerant control for a DC motor system. Zbl 1400.93065
He, Xiao; Ju, Yamei; Liu, Yang; Zhang, Bangcheng
2017
Theoretical simulations of wave field variation excited by a monopole within collar for acoustic logging while drilling. Zbl 07211701
He, Xiao; Wang, Xiuming; Chen, Hao
2017
Editorial: Fault diagnosis and application to modern systems. Zbl 1407.00035
He, Xiao (ed.); Wang, Zidong (ed.); Li, Gang (ed.); Zhou, Zhijie (ed.); Wang, Youqing (ed.)
2017
Higher level Zhu algebras are subquotients of universal enveloping algebras. Zbl 1420.17029
He, Xiao
2017
Convergence rate estimates of solutions in a higher dimensional chemotaxis system with logistic source. Zbl 1334.35088
He, Xiao; Zheng, Sining
2016
Global boundedness in quasilinear attraction-repulsion chemotaxis system with logistic source. Zbl 1365.92018
Tian, Miaoqing; He, Xiao; Zheng, Sining
2016
Iterative learning control for nonlinear stochastic systems with variable pass length. Zbl 1347.93278
Shi, Jiantao; He, Xiao; Zhou, Donghua
2016
Minimum-variance recursive filtering over sensor networks with stochastic sensor gain degradation: algorithms and performance analysis. Zbl 1370.93283
Liu, Yang; Wang, Zidong; He, Xiao; Zhou, D. H.
2016
Detecting intermittent sensor faults for linear stochastic systems subject to unknown disturbance. Zbl 1349.93359
Yan, Rongyi; He, Xiao; Zhou, Donghua
2016
Asymptotic boundary estimates to infinity Laplace equations with $$\Gamma$$-varying nonlinearity. Zbl 1335.35072
Wang, Wei; Gong, Hanzhao; He, Xiao; Zheng, Sining
2016
Event-based recursive distributed filtering over wireless sensor networks. Zbl 1360.93703
Liu, Qinyuan; Wang, Zidong; He, Xiao; Zhou, D. H.
2015
Global boundedness of solutions in a reaction-diffusion system of predator-prey model with prey-taxis. Zbl 1381.35188
He, Xiao; Zheng, Sining
2015
Event-based $$H_\infty$$ consensus control of multi-agent systems with relative output feedback: the finite-horizon case. Zbl 1360.93041
Liu, Qinyuan; Wang, Zidong; He, Xiao; Zhou, D. H.
2015
Filtering and fault detection for nonlinear systems with polynomial approximation. Zbl 1318.93090
Liu, Yang; Wang, Zidong; He, Xiao; Zhou, D. H.
2015
Protection zone in a modified Lotka-Volterra model. Zbl 1335.35050
He, Xiao; Zheng, Sining
2015
Optimal filtering for networked systems with stochastic sensor gain degradation. Zbl 1296.93194
Liu, Yang; He, Xiao; Wang, Zidong; Zhou, Donghua
2014
State estimation for networked systems with randomly occurring quantisations. Zbl 1278.93249
He, Xiao; Wang, Zidong; Ji, Y. D.; Zhou, D. H.
2013
Intermittent fault detection for uncertain networked systems. Zbl 1296.93192
He, Xiao; Hu, Yanyan; Peng, Kaixiang
2013
Fault detection for discrete-time systems in a networked environment. Zbl 1213.93123
He, Xiao; Wang, Zidong; Ji, Y. D.; Zhou, D.
2010
Robust fault detection for networked systems with communication delay and data missing. Zbl 1180.93101
He, Xiao; Wang, Zidong; Zhou, D. H.
2009
Network-based robust fault detection with incomplete measurements. Zbl 1193.93162
He, Xiao; Wang, Zidong; Zhou, D. H.
2009
Network-based fault detection for discrete-time state-delay systems: a new measurement model. Zbl 1284.93147
He, Xiao; Wang, Zidong; Ji, Y. D.; Zhou, D. H.
2008
Networked fault detection with random communication and packet losses. Zbl 1168.93369
He, Xiao; Wang, Zidong; Zhou, Donghua
2008
Robust $$H_{\infty}$$ filtering for networked systems with multiple state delays. Zbl 1133.93314
He, Xiao; Wang, Zidong; Zhou, D.
2007
Robust $$H^\infty$$ filtering for time-delay systems with missing measurements: a parameter-dependent approach. Zbl 1150.93345
He, Xiao; Zhou, Donghua
2007
Numerical simulation of pulse detonation engine phenomena. Zbl 1081.76574
He, X.; Karagozian, A. R.
2003
The role of Ekman pumping and the dominance of swirl in confined flows driven by Lorentz forces. Zbl 0947.76093
Davidson, P. A.; Kinnear, D.; Lingwood, R. J.; Short, D. J.; He, X.
1999
Vortex merging and spectral cascade in two-dimensional flows. Zbl 1027.76516
Nielsen, A. H.; He, X.; Rasmussen, J. Juul; Bohr, T.
1996
Uniform convergence of polynomials associated with varying Jacobi weights. Zbl 0749.41011
He, X.; Li, X.
1991
all top 5
#### Cited by 646 Authors
35 Wang, Zidong 14 He, Xiao 12 Fang, Huajing 9 Mu, Chunlai 9 Shen, Bo 9 Yang, Guanghong 8 Dong, Hongli 8 Wei, Guoliang 8 Zhou, Donghua 7 Ding, Derui 7 Lam, James 7 Shi, Peng 6 Alsaadi, Fuad Eid S. 6 Jiang, Bin 6 Karimi, Hamid Reza 6 Liang, Jinling 6 Lin, Ke 6 Liu, Yurong 6 Long, Yue 6 Xiang, Tian 6 Zheng, Sining 5 Caballero-Águila, Raquel 5 Ding, Steven X. 5 Gao, Huijun 5 Han, Qinglong 5 Ji, Yindong 5 Li, Shanbing 5 Linares-Pérez, Josefa 5 Liu, Xiaohui 5 Shu, Huisheng 5 Xia, Yuanqing 5 Yu, Li 5 Yue, Dong 4 Hermoso-Carazo, Aurora 4 Li, Li 4 Liu, Shuai 4 Mao, Zehui 4 Song, Yan 4 Wan, Xiongbo 4 Wang, Jianping 4 Winkler, Michael 4 Wu, Zhengguang 4 Zhai, Ding 4 Zhang, Dan 4 Zhang, Huaguang 4 Zhang, Qingling 4 Zhang, Yong 4 Zhao, Jie 3 Bo, Yuming 3 Dong, Wei 3 Dong, Yaying 3 Hu, Jun 3 Jin, Chunhua 3 Lankeit, Johannes 3 Liu, Bin 3 Liu, Ming 3 Liu, Qinyuan 3 Liu, Yang 3 Ma, Lifeng 3 Mizukami, Masaaki 3 Shen, Dong 3 Shi, Ling 3 Su, Hongye 3 Wang, Fan 3 Wang, Liangchen 3 Wang, Qingguo 3 Wang, Wei 3 Wang, Yanqian 3 Wu, Jianhua 3 Yang, Wen 3 Yao, Xiuming 3 Zhang, Shuyu 3 Zhang, Wenan 3 Zheng, Pan 2 Ahn, Inkyung 2 An, Liwei 2 Benzaouia, Abdellah 2 Bian, Shen 2 Chen, Dongyan 2 Chen, Guanrong 2 Chen, Li 2 Cocquempot, Vincent 2 Ding, Mengyao 2 Don, Wai Sun 2 Dong, Jiuxiang 2 Eddoukali, Youssef 2 Gao, Zhen 2 Ge, Xiaohua 2 Guo, Lei 2 Guo, Qian 2 He, Jing 2 Hong, Liang 2 Hu, Songlin 2 Hu, Yanyan 2 Huang, Biao 2 Hui, Guotao 2 Jiang, Shun 2 Jin, Fang 2 Jin, Hai-Yang 2 Kazemi, Hamed ...and 546 more Authors
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#### Cited in 75 Serials
52 Journal of the Franklin Institute 28 Automatica 26 International Journal of Systems Science 17 Mathematical Problems in Engineering 13 Circuits, Systems, and Signal Processing 12 Journal of Mathematical Analysis and Applications 12 Asian Journal of Control 9 International Journal of Control 9 Information Sciences 9 Journal of Differential Equations 9 International Journal of Adaptive Control and Signal Processing 8 International Journal of Robust and Nonlinear Control 8 Journal of Control Science and Engineering 8 International Journal of Systems Science. Principles and Applications of Systems and Integration 7 ZAMP. Zeitschrift für angewandte Mathematik und Physik 6 Computers & Mathematics with Applications 6 Discrete and Continuous Dynamical Systems 5 Fuzzy Sets and Systems 5 Nonlinear Analysis. Real World Applications 4 International Journal of General Systems 4 Journal of Fluid Mechanics 4 Optimal Control Applications & Methods 3 Applied Mathematics and Computation 3 Applied Mathematical Modelling 2 Applicable Analysis 2 Systems & Control Letters 2 Neural Networks 2 Signal Processing 2 Complexity 2 European Journal of Control 2 Nonlinear Dynamics 2 Abstract and Applied Analysis 2 Discrete Dynamics in Nature and Society 2 European Journal of Mechanics. B. Fluids 2 Communications in Nonlinear Science and Numerical Simulation 2 Journal of Evolution Equations 2 Discrete and Continuous Dynamical Systems. Series B 1 Computers and Fluids 1 Journal of Computational Physics 1 Journal of Mathematical Physics 1 Nonlinearity 1 Wave Motion 1 Shock Waves 1 Advances in Mathematics 1 Funkcialaj Ekvacioj. Serio Internacia 1 Journal of Algebra 1 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 1 Transactions of the American Mathematical Society 1 Stochastic Analysis and Applications 1 Applied Mathematics Letters 1 Journal of Scientific Computing 1 Multidimensional Systems and Signal Processing 1 Japan Journal of Industrial and Applied Mathematics 1 Applications of Mathematics 1 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 1 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 1 SIAM Journal on Applied Mathematics 1 SIAM Journal on Mathematical Analysis 1 Journal of Dynamics and Differential Equations 1 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 1 Journal of Nonlinear Science 1 Calculus of Variations and Partial Differential Equations 1 Physics of Fluids 1 NoDEA. Nonlinear Differential Equations and Applications 1 International Journal of Applied Mathematics and Computer Science 1 Journal of Systems Science and Complexity 1 Journal of Applied Mathematics 1 Comptes Rendus. Mathématique. Académie des Sciences, Paris 1 Communications on Pure and Applied Analysis 1 Advances in Difference Equations 1 Journal of Control Theory and Applications 1 Journal of Shanghai Jiaotong University (Science) 1 Arabian Journal for Science and Engineering 1 ISRN Computational Mathematics 1 Mathematics
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#### Cited in 23 Fields
241 Systems theory; control (93-XX) 71 Partial differential equations (35-XX) 67 Biology and other natural sciences (92-XX) 36 Information and communication theory, circuits (94-XX) 24 Operations research, mathematical programming (90-XX) 23 Probability theory and stochastic processes (60-XX) 15 Computer science (68-XX) 12 Fluid mechanics (76-XX) 6 Numerical analysis (65-XX) 4 Dynamical systems and ergodic theory (37-XX) 4 Statistics (62-XX) 3 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 2 Ordinary differential equations (34-XX) 2 Calculus of variations and optimal control; optimization (49-XX) 1 Combinatorics (05-XX) 1 Nonassociative rings and algebras (17-XX) 1 Functions of a complex variable (30-XX) 1 Potential theory (31-XX) 1 Approximations and expansions (41-XX) 1 Integral equations (45-XX) 1 Mechanics of deformable solids (74-XX) 1 Optics, electromagnetic theory (78-XX) 1 Classical thermodynamics, heat transfer (80-XX) | 2021-04-14 17:47:38 | {"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": 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": 0.5434856414794922, "perplexity": 14183.004401647197}, "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/1618038077843.17/warc/CC-MAIN-20210414155517-20210414185517-00231.warc.gz"} |
http://blancosilva.github.io/forum/2014/12/02/MA141Fa14RT3.html | ### Sections 11 and 12
Really cool review exam. Nice balance between intermediate and challenging problems. Lots of fun.
I am glad you decided to include some trigonometry.
I am missing some more variety of limits, though. Don't forget studying for all those!
Except for that last item, and the maybe excessive difficulty of some problems (which I really enjoyed), I believe this could be a good exponent of what the corresponding part of my final will be. Good job!
1. Sketch the graph of the following functions. You must find zeros, domain, range, vertical and horizontal asymptotes, intervals of increase/decrease, and intervals of concavity. Indicate also local extrema and inflection points.
\begin{align} f(x) &= 4x^2+24x+32 \\ f(x) &= \frac{x}{x-24} \end{align}
2. Find the derivative of $$y$$ using logarithmic differentiation:
$$y = \frac{25^{x+3}\sin x}{(x^2+4)\sqrt{x^3+8}}$$
3. Find the critical points of $$f(x) = x^{1/3} - x^{-2/3}$$.
4. Compute the following limits:
\begin{align} &\lim_{x\to \infty} e^{6x}x^{-1/2} \\ &\lim_{x\to \infty} \frac{23x-14x^3+7}{4x^2+7} \end{align}
5. Find all critical points of the function $$f(x) = \dfrac{x-4}{x^2-2x+8}$$,
6. Find the absolute extrema of the following functions, in the indicated intervals:
\begin{align} f(t) &= 2\cos t + \sin 2t && [0, \tfrac{\pi}{2}] \\ f(x) &= xe^{-x^2/8} && [-1, 4] \end{align}
### Sections 15 and 16
We have not covered Mean Value Theorem in this class! Why do I see 4 problems on that topic? Two of those problems are actually extremely challenging, and belong in a much more advanced class. I am not happy about that. Of course, none of the corresponding problems made it to this review exam, and the students that wrote them will get no extra credit for it.
One of the optimization problems did not make any sense. I did not include it in the list.
All the problems regarding critical points are basically the same function. I wish you had put a little bit of more effort into looking at the homework, for instance, and chosen more relevant and challenging questions.
Not all the limits made it to this test either. I am missing many kinds of limits that can be solved with L'Hopital techniques, too.
All in all, I am sad to say that this exam is not very representative of what we have done in this part of the course, and pretty much doubt working on it will prepare you for the final.
1. Find the absolute extrema of the following functions, in the indicated intervals:
\begin{align} f(x) &= x^3 -3x^2 + 1 &&[-\tfrac{1}{2}, 4] \\ f(x) &= \frac{x}{x^2+1} &&[0, 2] \\ \end{align}
2. Use any of the derivative tests to find local extrema of the function $$f(x) = x^4 - 4x^3$$.
3. Compute the following limits:
\begin{align} &\lim_{x \to 0} \frac{e^x-1-x}{x^2} \\ &\lim_{x\to 0} (1-2x)^{1/x} \\ &\lim_{x\to \infty} \frac{e^{6x}+5}{2x^3} \\ \end{align}
4. Sketch the graph of the following functions:
\begin{align} f(x) &= \frac{x-1}{x^2} \\ f(x) &= x^3 + 6x^2 + 9x \\ f(x) &= \frac{x^2}{x^2+9} \end{align} | 2017-09-20 14:31:14 | {"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": 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": 6, "equation": 1, "x-ck12": 0, "texerror": 0, "math_score": 0.9999979734420776, "perplexity": 848.2384969060022}, "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-2017-39/segments/1505818687324.6/warc/CC-MAIN-20170920142244-20170920162244-00016.warc.gz"} |
https://www.cs.utexas.edu/users/flame/laff/pfhp/week2-when-optimal-means-optimal.html | ## Unit2.5.1Lower bound on data movement
The discussion in this enrichment was inspired by the paper [23]
Tyler Michael Smith, Bradley Lowery, Julien Langou, Robert A. van de Geijn. Tight I/O Lower Bound for Matrix Multiplication. Submitted to ACM Transactions on Mathematical Software. Draft available from arXiv.org.
For more details, we encourage you to read that paper.
Early in our careers, we learned that if you say that an implementation is optimal, you better prove that it is optimal.
In our empirical studies, graphing the measured performance, we can compare our achieved results to the theoretical peak. Obviously, if we achieved theoretical peak performance, then we would know that the implementation is optimal. The problem is that we rarely achieve the theoretical peak performance as computed so far (multiplying the clock rate by the number of floating point operations that can be performed per clock cycle).
In order to claim optimality, one must carefully model an architecture and compute, through analysis, the exact limit of what it theoretical can achieve. Then, one can check achieved performance against the theoretical limit, and make a claim. Usually, this is also not practical.
In practice, one creates a model of computation for a simplified architecture. With that, one then computes a theoretical limit on performance. The next step is to show that the theoretical limit can be (nearly) achieved by an algorithm that executes on that simplified architecture. This then says something about the optimality of the algorithm under idealized circumstances. By finally comparing and contrasting the simplified architecture with an actual architecture, and the algorithm that targets the simplified architecture with an actual algorithm designed for the actual architecture, one can reason about the optimality, or lack thereof, of the practical algorithm.
### Subsubsection2.5.1.2A simple model
Let us give a simple model of computation that matches what we have assumed so far when programming matrix-matrix multiplication:
• We wish to compute $C := A B + C$ where $C \text{,}$ $A \text{,}$ and $C$ are $m \times n \text{,}$ $m \times k \text{,}$ and $k \times n \text{,}$ respectively.
• The computation is cast in terms of FMAs.
• Our machine has two layers of memory: fast memory (registers) and slow memory (main memory).
• Initially, data reside in main memory.
• To compute a FMA, all three operands must be in fast memory.
• Fast memory can hold at most $S$ floats.
• Slow memory is large enough that its size is not relevant to this analysis.
• Computation cannot be overlapped with data movement.
Notice that this model matches pretty well how we have viewed our processor so far.
### Subsubsection2.5.1.3Minimizing data movement
We have seen that matrix-matrix multiplication requires $m \times n \times k$ FMA operations, or $2 m n k$ flops. Executing floating point operations constitutes useful computation. Moving data between slow memory and fast memory is overhead since we assume it cannot be overlapped. Hence, under our simplified model, if an algorithm only performs the minimum number of flops (namely $2 m n k$), minimizes the time spent moving data between memory layers, and we at any given time are either performing useful computation (flops) or moving data, then we can argue that (under our model) the algorithm is optimal.
We now focus the argument by reasoning about a lower bound on the number of data that must be moved from fast memory to slow memory. We will build the argument with a sequence of observations.
Consider the loop
\begin{equation*} \begin{array}{l} {\bf for~} p := 0, \ldots , k-1 \\ ~~~ {\bf for~} j := 0, \ldots , n-1 \\ ~~~ ~~~ {\bf for~} i := 0, \ldots , m-1 \\ ~~~ ~~~ ~~~ \gamma_{i,j} := \alpha_{i,p} \beta_{p,j} + \gamma_{i,j} \\ ~~~ ~~~ {\bf end} \\ ~~~ {\bf end} \\ {\bf end} \end{array} \end{equation*}
One can view the computations
\begin{equation*} \begin{array}{l} ~~~ ~~~ \gamma_{i,j} := \alpha_{i,p} \beta_{p,j} + \gamma_{i,j} \end{array} \end{equation*}
as a cube of points in 3D, $( i,j,k )$ for $0 \leq i \lt m \text{,}$ $0 \leq j \lt n \text{,}$ $0 \leq p \lt k \text{.}$ The set of all possible algorithms that execute each such update only once can be viewed as an arbitrary ordering on that set of points. We can this as indexing the set of all such triples with $i_r \text{,}$ $j_r \text{,}$ $p_r \text{,}$ $0 \leq r \lt m \times n \times k \text{:}$
\begin{equation*} ( i_r, j_r, k_r ). \end{equation*}
so that the algorithm that computes $C := A B + C$ can then be written as
\begin{equation*} \begin{array}{l} {\bf for~} r := 0, \ldots , mnk-1 \\ ~~~ \gamma_{i_r,j_r} := \alpha_{i_r,p_r} \beta_{p_r,j_r} + \gamma_{i_r,j_r} \\ {\bf end} \end{array} \end{equation*}
Obviously, this puts certain restrictions on $i_r \text{,}$ $j_r \text{,}$ and $p_r\text{.}$ Articulating those exactly is not important right now.
We now partition the ordered set $0, \ldots , mnk-1$ into ordered contiguous subranges (phases) each of which requires $S + M$ distinct elements from $A \text{,}$ $B \text{,}$ and $C$ (e.g., $S$ elements from $A \text{,}$ $M/3$ elements of $B \text{,}$ and $2M/3$ elements of $C$), except for the last phase, which will contain fewer. (Strictly speaking, it is a bit more complicated than splitting the range of the iterations, since the last FMA may require anywhere from $0$ to $3$ new elements to be loaded from slow memory. Fixing this is a matter of thinking of the loads that are required as separate from the computation (as our model does) and then splitting the operations - loads, FMAs, and stores - into phases rather than the range. This does not change our analysis.)
Recall that $S$ equals the number of floats that fit in fast memory. A typical phase will start with $S$ elements in fast memory, and will in addition read $M$ elements from slow memory (except for the final phase). % We will call such an ordered subset a phase of triples. Such a typical phase will start at $r = R$ and consists of $F$ triples, $( i_R, j_R, p_R )$ through $( i_{R+F-1}, j_{R+F-1}, p_{R+F-1} )\text{.}$ Let us denote the set of these triples by $\mathbf{D} \text{.}$ These represent $F$ FMAs being performed in our algorithm. Even the first phase needs to read at least $M$ elements since it will require $S + M$ elements to be read.
The key question now becomes what the upper bound on the number of FMAs is that can be performed with $S+M$ elements. Let us denote this bound by $F_{\rm max} \text{.}$ If we know $F_{\rm max}$ as a function of $S + M \text{,}$ then we know that at least $\frac{m n k}{F_{\rm max}} -1$ phases of FMAs need to be executed, where each of those phases requires at least $S$ reads from slow memory. The total number of reads required for any algorithm is thus at least
$$\left(\frac{m n k}{F_{\rm max}} -1 \right) M.\label{eq-lower}\tag{2.5.1}$$
To find $F_{\rm max}$ we make a few observations:
• A typical triple $( i_r,j_r,p_r ) \in \mathbf{D}$ represents a FMA that requires one element from each of matrices $C \text{,}$ $A \text{,}$ and $B\text{:}$ $\gamma_{i,j} \text{,}$ $\alpha_{i,p}\text{,}$ and $\beta_{p,j} \text{.}$
• The set of all elements from $C \text{,}$ $\gamma_{i_r, j_r} \text{,}$ that are needed for the computations represented by the triples in $\mathbf{D}$ are indexed with the tuples $\mathbf{C_D} = \{ ( i_r, j_r ) ~\vert R \leq r \lt R+F \} \text{.}$ If we think of the triples in $\mathbf{D}$ as points in 3D, then $\mathbf{C_D}$ is the projection of those points onto the $i,j$ plane. Its size, $\vert \mathbf{C_D} \vert \text{,}$ tells us how many elements of $C$ must at some point be in fast memory during that phase of computations.
• The set of all elements from $A \text{,}$ $\alpha_{i_r, p_r} \text{,}$ that are needed for the computations represented by the triples in $\mathbf{D}$ are indexed with the tuples $\mathbf{A_D} = \{ ( i_r, p_r ) ~\vert R \leq r \lt R+F \} \text{.}$ If we think of the triples $( i_r, j_r, p_r )$ as points in 3D, then $\mathbf{A_D}$ is the projection of those points onto the $i,p$ plane. Its size, $\vert \mathbf{A_D} \vert \text{,}$ tells us how many elements of $A$ must at some point be in fast memory during that phase of computations.
• The set of all elements from $C \text{,}$ $\beta_{p_r, j_r} \text{,}$ that are needed for the computations represented by the triples in $\mathbf{D}$ are indexed with the tuples $\mathbf{B_D} = \{ ( p_r, j_r ) ~\vert R \leq r \lt R+F \} \text{.}$ If we think of the triples $( i_r, j_r, p_r )$ as points in 3D, then $\mathbf{B_D}$ is the projection of those points onto the $p,j$ plane. Its size, $\vert \mathbf{B_D} \vert \text{,}$ tells us how many elements of $B$ must at some point be in fast memory during that phase of computations.
Now, there is a result known as the discrete Loomis-Whitney inequality that tells us that in our situation $\vert \mathbf{D} \vert \leq \sqrt{\vert \mathbf{C_D} \vert \vert \mathbf{A_D} \vert \vert \mathbf{B_D} \vert }\text{.}$ In other words, $F_{\rm max} \leq \sqrt{\vert \mathbf{C_D} \vert \vert \mathbf{A_D} \vert \vert \mathbf{B_D} \vert }\text{.}$ The name of the game now becomes to find the largest value $F_{\rm max}$ that satisfies
\begin{equation*} {\rm maximize~} F_{\rm max} {\rm ~such~that~} \left\{ \begin{array}{l} F_{\rm max} \leq \sqrt{\vert \mathbf{C_D} \vert \vert \mathbf{A_D} \vert \vert \mathbf{B_D} \vert } \\ \vert \mathbf{C_D} \vert \gt 0, \vert \mathbf{A_D} \vert \gt 0, \vert \mathbf{B_D} \vert \gt 0 \\ \vert \mathbf{C_D} \vert + \vert \mathbf{A_D} \vert + \vert \mathbf{B_D} \vert = S + M. \end{array} \right. \end{equation*}
An application known as Lagrange multipliers yields the solution
\begin{equation*} \vert \mathbf{C_D} \vert = \vert \mathbf{A_D} \vert = \vert \mathbf{B_D} \vert = \frac{S+M}{3} \quad \mbox{and} \quad F_{\rm max} = \frac{( S + M )\sqrt{S+M}}{3 \sqrt{3}}. \end{equation*}
With that largest $F_{\rm max}$ we can then establish a lower bound on the number of memory reads given by (2.5.1):
\begin{equation*} \left(\frac{m n k}{F_{\rm max}} -1 \right) M = \left(3 \sqrt{3} \frac{m n k}{( S + M )\sqrt{S+M}} -1 \right) M. \end{equation*}
Now, $M$ is a free variable. To come up with the sharpest (best) lower bound, we want the largest lower bound. It turns out that, using techniques from calculus, one can show that $M = 2 S$ maximizes the lower bound. Thus, the best lower bound our analysis yields is given by
\begin{equation*} \left(3 \sqrt{3} \frac{m n k}{( 3 S )\sqrt{3 S}} -1 \right) (2S) = 2 \frac{m n k}{\sqrt{S}} - 2S. \end{equation*}
### Subsubsection2.5.1.4A nearly optimal algorithm
We now discuss a (nearly) optimal algorithm for our simplified architecture. Recall that we assume fast memory can hold $S$ elements. For simplicity, assume $S$ is a perfect square. Partition
\begin{equation*} C = \left( \begin{array}{c c c} C_{0,0} \amp C_{0,1} \amp \cdots \\ C_{1,0} \amp C_{1,1} \amp \cdots \\ \vdots \amp \vdots \amp \end{array} \right), \quad A = \left(\begin{array}{c} A_0 \\ A_1 \\ \vdots \end{array} \right), \quad \mbox{and} \quad B = \left( \begin{array}{c c c} B_{0} \amp B_{1} \amp \cdots \end{array} \right). \end{equation*}
where $C_{i,j}$ is $m_R \times n_R \text{,}$ $A_{i}$ is $m_R \times k \text{,}$ and $B_j$ is $k \times n_R \text{.}$ Here we choose $m_R \times n_R = (\sqrt{S}-1) \times \sqrt{S}$ so that fast memory can hold one submatrix $C_{i,j} \text{,}$ one column of $A_i \text{,}$ and one element of $B_j \text{:}$ $m_R \times n_R + m_R + 1 = (\sqrt{S}-1) \times \sqrt{S} + \sqrt{S}-1 + 1 = S \text{.}$
When computing $C := A B + C \text{,}$ we recognize that $C_{i,j} := A_i B_j + C_{i,j} \text{.}$ Now, let's further partition
\begin{equation*} A_i = \left(\begin{array}{c c c} a_{i,0} \amp a_{i,1} \amp \cdots \end{array} \right) \quad \mbox{and} \quad B_j = \left(\begin{array}{c} b_{0,j}^T \\ b_{1,j}^T \\ \vdots \end{array} \right). \end{equation*}
We now recognize that $C_{i,j} := A_i B_j + C_{i,j}$ can be computed as
\begin{equation*} C_{i,j} := a_{i,0} b_{0,j}^T + a_{i,1} b_{1,j}^T + \cdots, \end{equation*}
the by now very familiar sequence of rank-1 updates that makes up the micro-kernel discussed in Unit 2.4.1. The following loop exposes the computation $C := A B + C \text{,}$ including the loads and stores from and to slow memory:
\begin{equation*} \begin{array}{l} {\bf for~} j := 0, \ldots , N-1 \\ ~~~ {\bf for~} i := 0, \ldots , M-1 \\ ~~~ ~~~ {\rm Load~} C_{i,j} {\rm ~into~fast~memory} \\ ~~~ ~~~ {\bf for~} p := 0, \ldots , k-1 \\ ~~~ ~~~ ~~~ {\rm Load~} a_{i,p} {\rm ~and~} b_{p,j}^T {\rm ~into~fast~memory} \\ ~~~ ~~~ ~~~ C_{i,j} := a_{i,p} b_{p,j}^T + C_{i,j} \\ ~~~ ~~~ {\bf end} \\ ~~~ ~~~ {\rm Store~} C_{i,j} {\rm ~to~slow~memory} \\ ~~~ {\bf end} \\ {\bf end} \end{array} \end{equation*}
For simplicity, here $M = m/m_r$ and $N = n/n_r \text{.}$
On the surface, this seems to require $C_{i,j} \text{,}$ $a_{i,p} \text{,}$ and $b_{p,j}^T$ to be in fast memory at the same time, placing $m_R \times n_R + m_R + n_r = S + \sqrt{S}-1$ floats in fast memory. However, we have seen before that the rank-1 update $C_{i,j} := a_{i,p} b_{p,j}^T + C_{i,j}$ can be implemented as a loop around axpy operations, so that the elements of $b_{p,j}^T$ only need to be in fast memory one at a time.
Let us now analyze the number of memory operations incurred by this algorithm:
• Loading and storing all $C_{i,j}$ incurs $m n$ loads and $m n$ stores, for a total of $2 m n$ memory operations. (Each such block is loaded once and stored once, meaning every element of $C$ is loaded once and stored once.)
• Loading all $a_{i,p}$ requires
\begin{equation*} M N k m_R = (M m_R ) N k = m \frac{n}{n_R} k = \frac{m n k}{\sqrt{S}} \end{equation*}
memory operations.
• Loading all $b_{p,j}^T$ requires
\begin{equation*} M N k n_R = M (N n_R) k = \frac{m}{m_R} n k = \frac{m n k}{\sqrt{S}-1} \end{equation*}
memory operations.
The total number of memory operations is hence
\begin{equation*} 2 m n + \frac{m n k}{\sqrt{S}} + \frac{m n k}{\sqrt{S}-1} = 2 \frac{m n k}{\sqrt{S}} + 2 m n + \frac{mnk}{S - \sqrt{S}}. \end{equation*}
We can now compare this to the lower bound from the last unit:
\begin{equation*} 2 \frac{mnk}{\sqrt{S}} - 2S. \end{equation*}
The cost of reading and writing elements of $C \text{,}$ $2 m n \text{,}$ contributes a lower order term, as does $\frac{mnk}{S - \sqrt{S}}$ if $S$ (the size of fast memory) is reasonably large. Thus, the proposed algorithm is nearly optimal with regards to the amount of data that is moved between slow memory and fast memory.
### Subsubsection2.5.1.5Discussion
What we notice is that the algorithm presented in the last unit is quite similar to the algorithm that in the end delivered good performance in [23]. It utilizes most of fast memory (registers in [23]) with a submatrix of $C \text{.}$ Both organize the computation in terms of a kernel that performs rank-1 updates of that submatrix of $C \text{.}$
The theory suggests that the number of memory operations are minimized if the block of $C$ is chosen to be (roughly) square. In Unit 2.4.1, the best performance was observed with a kernel that chose the submatrix of $C$ in registers to be $8 \times 6 \text{,}$ so for this architecture, the theory is supported by practice. For other architectures, there may be issues that skew the aspect ratio to be less square. | 2020-05-28 12:59:41 | {"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": 1, "x-ck12": 0, "texerror": 0, "math_score": 0.9970277547836304, "perplexity": 890.2288717356168}, "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/1590347396089.30/warc/CC-MAIN-20200528104652-20200528134652-00439.warc.gz"} |
http://mathhelpforum.com/advanced-statistics/213842-random-variable-convergence.html | 1. ## Random Variable Convergence
X1,...Xn are a random sample from U(0,theta). A sequence of random variables are defined Zn=n(theta-X(n)) for positive n.
I need to show that Zn converges in distribution to Z, where Z~Exp(theta).
Any help in getting started?
Can I say that X(n) converges in law to theta and is that useful?
2. ## Re: Random Variable Convergence
Hey Mick.
I'm wondering if you can use the distribution of the order statistic to show it converges to the right distribution.
One approach I would try is to use either the characteristic function or the moment generating function to show that the MGF has the form of an exponential distribution MGF.
3. ## Re: Random Variable Convergence
I can definetly go down the MGF route. The MGF of an Exponential(theta) random variable is 1/(1-theta*t).
The MGF of a U(0, theta) random variable is (exp(theta*t)-1)/(theta*t). I'm guessing the uniform MGF will be needed somewhere but I'm not sure how the MGF of X applies to the MGF of Z.
4. ## Re: Random Variable Convergence
I have two suggestions.
The first is to get the PDF of X(n) and then use a transformation to get the PDF of the new random variable.
The second is to get the MGF of the final random variable and prove it has the form of an exponential with that parameter.
I would personally be inclined to use the first option after thinking about it, but you could really try any (including using the characteristic function which is a third option). | 2017-06-22 21:13:51 | {"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": 0.8127077221870422, "perplexity": 551.6283032599956}, "config": {"markdown_headings": true, "markdown_code": false, "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-2017-26/segments/1498128319902.52/warc/CC-MAIN-20170622201826-20170622221826-00228.warc.gz"} |
https://www.physicsforums.com/threads/what-is-the-derivatibe-of-0.414790/ | # What is the derivatibe of 0
1. Jul 8, 2010
### Amok
I would have said it is 0, but then why is it that a twice derivable function is a function like, for example, f(x) = x. I've been studying maths for a while, but I had never asked myself this question until I came across the Heaviside function:
$$H(x) = 1 \ if\ x\geq 0\ and\ H(x)=0\ if\ x<0$$
The derivative of this function (in the distributional sense) is the Dirac delta function:
Let $$\varphi \in S$$, the Schwartz space then:
$$\langle T_{H}^{(1)},\varphi \rangle = - \int_{- \infty}^{+ \infty} H(x) \varphi '(x) dx = - \int_{0}^{+ \infty} \varphi '(x) dx = -[\varphi (x)]_{0}^{\infty} = \varphi (0) = \langle \delta, \varphi \rangle = \delta$$
And not,
$$\langle T_{H}^{(1)},\varphi \rangle = \int_{- \infty}^{+ \infty} H'(x) \varphi (x) dx = \int_{0}^{+ \infty} 0 \cdot \varphi (x) dx + \int_{- \infty}^{0} 0 \cdot \varphi (x) dx = 0$$
Which implies that H(x) is not derivable in the 'normal' sense (which implies 0 doesn't have a derivative).
EDIT: I just realized the Heaviside function is not differentiable at 0 (it is not even continuous)!
Last edited: Jul 8, 2010
2. Jul 8, 2010
### arildno
No, it doesn't imply that 0(x) doesn't have a derivative at all.
It implies that the Heaviside function doesn't have a derivative in the normal sense.
The dirac delta is the WEAK derivative of the Heaviside function, H'(x) in your second line is a meaningless expression for a function that was to be defined at ALL points. | 2018-09-25 09:04:04 | {"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": 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": 0.929017961025238, "perplexity": 325.9407830099328}, "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-2018-39/segments/1537267161350.69/warc/CC-MAIN-20180925083639-20180925104039-00448.warc.gz"} |
http://digitalcommons.utep.edu/dissertations/AAI9819585/ | # The geochemical evolution of Quaternary volcanism in the south-central portion of the Kenya rift
#### Abstract
The southern portion of the Kenya rift is characterized by voluminous eruption of mafic to felsic magmas during the Quaternary. These include transitional basalts, basaltic trachyandesites, trachyandesites, phonolites, trachytes, pantellerites, and comendites within the rift axis and silica undersaturated basanites on the eastern flanks. To understand the petrogenesis of these lavas, the basanites from the eastern flank volcanic field at Chyulu are used to represent the most primitive magma associated with rifting. Results of modeling imply that the Chyulu basanites are products of 1-2% partial melting of a chondritic to primitive mantle. The transitional basalts of the rift axis represent 5-14% partial melting of a similar mantle. The lower value is preferred since it is consistent with the generation of the magmas that evolve into the transitional basalts of the rift axis.^ The second phase of this study was to interpret the relationship between the mafic and felsic magmas. The characteristics of pantellerites from Eburru, comendites from Olkaria, and phonolites from Suswa were studied. Major and trace element models show that the pantellerites, trachytes, and associated transitional basalts are cogenetic, and that evolution was dominated by polybaric fractional crystallization processes. Results obtained from stable oxygen isotopes $(\delta\sp{18}o=+5.7$ to 6.6$\perthous)$ indicate that the rocks are mantle-derived and that crustal assimilation was not important in their genesis. Trace elements indicate that initial crystallization of the rift axis magmas occurred at the Moho. A subsequent low pressure crystallization is indicated by the observed phenocrystic mineral assemblage that includes olivine, augite, and plagioclase. The models show that the transitional basalts are highly evolved and experienced 67 to 80% pre-eruption crystallization compared to 20 to 40% for the Chyulu basanites. The phonolites, trachytes and pantellerites represent more than 95% crystallization of basaltic parents. Least squares major element models reveal that the resultant cumulates have sufficiently high densities ($\leq$2.90g cm.$\sp{-3})$ to cause the gravity anomalies observed under the volcanoes in the rift axis.^ Suswa is in a transition zone where the lithosphere begins to thicken southward. The volcano displays earliest shield building lavas of transitional basalt - trachyte association similar to the others in the rift. However, the evolution of the syn-caldera trachytes and post-caldera phonolites require more alkaline parental magma. Comendites from Olkaria are not part of the fractional crystallization evolutionary paths.^ The distribution of the Quaternary lavas associated with rifting can be used to infer the tectonic evolution of the Kenya rift. The occurrence of basanites on the eastern flank of the rift indicates thicker lithosphere than that under the rift axis where Quaternary transitional basalts and their felsic derivatives dominate. Geophysical models indicate thin lithosphere under the rift. The eruption of phonolites at Suswa implies a change to lower degrees of partial melting in the mantle under the volcano during the Holocene time. This is primarily caused by the thickening lithosphere south of Suswa which results in deeper partial melting in the mantle. (Abstract shortened by UMI.) ^
Geochemistry
#### Recommended Citation
Omenda, Peter Ayodo, "The geochemical evolution of Quaternary volcanism in the south-central portion of the Kenya rift" (1997). ETD Collection for University of Texas, El Paso. AAI9819585.
http://digitalcommons.utep.edu/dissertations/AAI9819585
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https://www.shaalaa.com/question-bank-solutions/which-following-statements-are-true-which-are-false-each-case-give-valid-reason-saying-so-r-circle-particular-case-ellipse-validation-contradiction_14060 | CBSE (Arts) Class 11CBSE
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# Which of the Following Statements Are True and Which Are False? in Each Case Give a Valid Reason for Saying So. R: Circle is a Particular Case of an Ellipse. - CBSE (Arts) Class 11 - Mathematics
#### Question
Which of the following statements are true and which are false? In each case give a valid reason for saying so.
r: Circle is a particular case of an ellipse.
#### Solution
The equation of an ellipse is,
x^2/a^2 + y^2/b^2 = 1
If we put a = b = 1, then we obtain
x2 + y2 = 1, which is an equation of a circle
Therefore, circle is a particular case of an ellipse.
Thus, statement r is true.
Is there an error in this question or solution?
#### APPEARS IN
NCERT Solution for Mathematics Textbook for Class 11 (2018 to Current)
Chapter 14: Mathematical Reasoning
Q: 5.3 | Page no. 343
#### Video TutorialsVIEW ALL [1]
Solution Which of the Following Statements Are True and Which Are False? in Each Case Give a Valid Reason for Saying So. R: Circle is a Particular Case of an Ellipse. Concept: Validation by Contradiction.
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https://www.scipost.org/submissions/2203.01058v1/ | # Universal suppression of superfluid weight by disorder independent of quantum geometry and band dispersion
### Submission summary
As Contributors: Alexander Lau Arxiv Link: https://arxiv.org/abs/2203.01058v1 (pdf) Code repository: https://zenodo.org/record/6012755 Data repository: https://zenodo.org/record/6012755 Date submitted: 2022-04-29 13:07 Submitted by: Lau, Alexander Submitted to: SciPost Physics Academic field: Physics Specialties: Condensed Matter Physics - Theory Approaches: Theoretical, Computational
### Abstract
Motivated by the experimental progress in controlling the properties of the energy bands in superconductors, significant theoretical efforts have been devoted to study the effect of the quantum geometry and the flatness of the dispersion on the superfluid weight. In conventional superconductors, where the energy bands are wide and the Fermi energy is large, the contribution due to the quantum geometry is negligible, but in the opposite limit of flat-band superconductors the superfluid weight originates purely from the quantum geometry of Bloch wave functions. Here, we study how the energy band dispersion and the quantum geometry affect the disorder-induced suppression of the superfluid weight. Surprisingly, we find that the disorder-dependence of the superfluid weight is universal across a variety of models, and independent of the quantum geometry and the flatness of the dispersion. Our results suggest that a flat-band superconductor is as resilient to disorder as a conventional superconductor.
###### Current status:
Has been resubmitted
### Submission & Refereeing History
Resubmission scipost_202208_00022v1 on 11 August 2022
Submission 2203.01058v1 on 29 April 2022
## Reports on this Submission
### Strengths
1-Timely.
2-Careful analysis and universal behaviour found.
2-Detailed supplemental material together with code, which allows for the reproduction of the results and extensions.
### Weaknesses
1-As pointed out by another referee, the title is a bit of an overstatement of the results.
2-It is not very clear from the analysis why there is a universal suppression.
### Report
The authors analyze the effect of quantum geometry on the robustness to disorder in the superfluid weight of superconductors. This matter is analyzed for an extended Kane-Mele model, which presents flat bands, and a trivial single band hopping model, both with s-wave superconducting pairing. They obtain the surprising result that the scaled pairing amplitude and superfluid weight show a universal dependence with disorder, regardless of the flatness of the bands, although the conventional and geometric contributions behave in different ways.
The authors did a very careful and thorough analysis of the system and provided both very detailed Supplemental Material and the code used to generate the results. Therefore, this work has the prospect of generating interesting future expansions. I found it particularly interesting that the trace of the quantum metric increases, at least for some range of disorder, with disorder strength. It is also a timely analysis considering the recent massive interest in superconductivity in systems with flatbands.
I believe that the manuscript already fulfils SciPost criteria of publication, but there are some (optional) points that the authors can address that maybe improve the manuscript (see below).
### Requested changes
These are optional points that maybe improve the manuscript. I suggest that at least 1, 4, and 5 are considered.
1. Although the scaled $\Delta$ and $D_s$ present a universal behaviour, $W_0$ depends on $M$ and, I believe, also $\Delta_0$ and $D_{s0}$ should change depending on the parameters of the Kane-Mele extended model. Thinking about practical applications of the results, it can be beneficial to show a version of Fig. 1 without the scaling but with the quantities in units of $t$, for instance.
2. Can one read the universality reported in Figs. 1 and S6 as a scaling property? The data collapse reminds me very much of what is observed close to a quantum critical point.
3. When the system is disordered, translation invariance is broken. I understand that considering disorder average effectively restores translation invariance, but it is not clear whether the use of expressions of the quantum metric and the superfluid weight that rely on the use of bands is justified. Is there a definition of these quantities in real space, and do they provide the same ensemble-averaged results?
4. Concerning the writing of the manuscript, some symbols are used for different quantities throughout the text. Although it is usually clear what they refer to depending on the context, some redefinition of variables can avoid confusion. $\nu$ is used for both spatial index and filling (this is especially confusing in (1) where they appear together). $\mu$ is used for both spatial index and chemical potential. $i$ and $j$ are used for degrees of freedom that are not spin, band indexes, and supercell labels.
5. I believe there is a typo above (S58). The inline equation $g_{ij}(\mathbf{k})=$ seems to be missing its right-hand side.
• validity: good
• significance: high
• originality: high
• clarity: top
• formatting: good
• grammar: perfect
### Author: Alexander Lau on 2022-08-11 [id 2722]
(in reply to Report 2 on 2022-07-13)
Category:
The referee writes:
The authors analyze the effect of quantum geometry on the robustness to disorder in the superfluid weight of superconductors. This matter is analyzed for an extended Kane-Mele model, which presents flat bands, and a trivial single band hopping model, both with s-wave superconducting pairing. They obtain the surprising result that the scaled pairing amplitude and superfluid weight show a universal dependence with disorder, regardless of the flatness of the bands, although the conventional and geometric contributions behave in different ways. The authors did a very careful and thorough analysis of the system and provided both very detailed Supplemental Material and the code used to generate the results. Therefore, this work has the prospect of generating interesting future expansions. I found it particularly interesting that the trace of the quantum metric increases, at least for some range of disorder, with disorder strength. It is also a timely analysis considering the recent massive interest in superconductivity in systems with flatbands.
Our response: We thank the Referee for carefully reading our manuscript, highlighting our main results, and for the positive assessment.
The referee writes:
I believe that the manuscript already fulfils SciPost criteria of publication, but there are some (optional) points that the authors can address that maybe improve the manuscript (see below). These are optional points that maybe improve the manuscript. I suggest that at least 1, 4, and 5 are considered.
Our response: We thank the Referee for affirming that the criteria for publication in SciPost are fulfilled. We appreciate the Referee's suggestions, which have helped us to improve our manuscript. Below, we provide a point-by-point response to all suggestions.
The referee writes:
1 - Although the scaled $\Delta$ and $D_s$ present a universal behaviour, $W_0$ depends on $M$ and, I believe, also $\Delta_0$ and $D_{s,0}$ should change depending on the parameters of the Kane-Mele extended model. Thinking about practical applications of the results, it can be beneficial to show a version of Fig. 1 without the scaling but with the quantities in units of $t$, for instance.
Our response: We thank the Referee for this suggestion. Indeed, also $\Delta_0$ and $D_{s,0}$ (and also $W_0$) change with the model parameters, as already indicated in Fig. S8 of Sec. VIII in the Appendix for the flat Kane-Mele model. To provide the reader with similar data also for the other models considered in this work, as suggested by the Referee, we have added another version of Fig. 1 of the main text to the new Sec. IX of the Appendix (see new figure Fig. S9), where we show the corresponding quantities in units of $t$ without rescaling.
The referee writes:
2 - Can one read the universality reported in Figs. 1 and S6 as a scaling property? The data collapse reminds me very much of what is observed close to a quantum critical point.
Our response: We thank the Referee for this interesting question. We do not think that the universality we report is related to a quantum critical point, because we observe it also far away from any phase transitions. Nevertheless, more detailed analytical understanding of the data collapse is certainly an interesting (and challenging) direction for future research.
The referee writes:
3 - When the system is disordered, translation invariance is broken. I understand that considering disorder average effectively restores translation invariance, but it is not clear whether the use of expressions of the quantum metric and the superfluid weight that rely on the use of bands is justified. Is there a definition of these quantities in real space, and do they provide the same ensemble-averaged results?
Our response: To our knowledge, there exist no real-space expressions for the quantum metric, geometric superfluid weight, and conventional superfluid weight. The lack of such expressions is the motivation for our numerical approach where we choose a large disordered supercell and repeat it periodically in space. This way, the existing momentum-space formulas for quantum metric, geometric superfluid weight, and conventional superfluid weight can be applied. We note that our size-scaling analysis suggests that the used supercell is sufficiently large in our calculations. Nevertheless, we agree with the Referee that it would be very useful to develop a real-space approach for calculation of the geometric and conventional superfluid weight.
The referee writes:
4 - Concerning the writing of the manuscript, some symbols are used for different quantities throughout the text. Although it is usually clear what they refer to depending on the context, some redefinition of variables can avoid confusion. $\nu$ is used for both spatial index and filling (this is especially confusing in (1) where they appear together). $\mu$ is used for both spatial index and chemical potential. $i$ and $j$ are used for degrees of freedom that are not spin, band indexes, and supercell labels.
Our response: We thank the Referee for pointing this out. For the sake of clarity, we have tried to stick to standard nomenclature used in the literature, such as $\mu$ for the chemical potential, $\nu$ for the filling factor, or $g_{\mu\nu}$ for the quantum metric. Unfortunately, this inevitably leads to a double use of certain symbols. We have tried to avoid confusion by providing enough context wherever a certain symbol is used. However, we agree that especially the use of the symbol $\nu$ both as the filling factor and as an index in Eq. (1) might cause confusion. We have therefore introduced the symbol $\bar{\nu}$ throughout the text to denote the filling factor. Furthermore, we now consistently use $g_{\mu\nu}$ and $D^{\mu\nu}$ for the quantum metric and for the superfluid weight tensor.
The referee writes:
5 - I believe there is a typo above (S58). The inline equation $g_{ij}(k) =$ seems to be missing its right-hand side.
Our response: Indeed. We thank the Referee for pointing this out. We have corrected the typo by removing the "$=$" sign before $g_{ij}(k)$. The quantum metric $g_{ij}(k)$ is defined in the sentence after that. As mentioned in the response above, we have changed $g_{ij}$ to $g_{\mu\nu}$ for notational consistency.
Additional weaknesses pointed out by the Referee:
The referee writes:
As pointed out by another referee, the title is a bit of an overstatement of the results.
Our response: We understand both referees' concerns regarding the choice of title. Therefore, we have made the title more specific to reflect the fact that we consider non-magnetic disorder and $s$-wave superconductors. The new title is "Universal suppression of superfluid weight by non-magnetic disorder in $s$-wave superconductors independent of quantum geometry and band dispersion". We have also added a clarifying sentence in the abstract.
The referee writes:
It is not very clear from the analysis why there is a universal suppression.
Our response: Besides the numerical results that we present, showing how the disorder affects differently the conventional and geometric part of the superfluid weight resulting in universal suppression of the total superfluid weight, we were not able to obtain analytical expressions that could provide more insights on the mechanism for such universal behavior. This is an interesting (and challenging) direction for future research.
We thank the Referee for their positive assessment of our work and for recommending publication. We are confident that the changes in the manuscript are in line with this assessment.
### Strengths
1. Clear and concise.
2. Timely
### Weaknesses
1. Title of the work (see report).
2. Much of the numerical work is, in some sense, somewhat limited. The systems sizes are on the smaller side, have very large attractive interactions, and the superconducting self-consistency equations are only solved approximately by using only the linear Tc solutions with a self-consistent amplitude at lower temperatures. Ideally, one would have like to see more robust numerical work, but on the other hand, I do not really think that the results would change if included, especially give how close the present results align with previous numerical works [10.1103/PhysRevB.65.014501,10.1103/PhysRevLett.81.3940]. The authors also explicitly verify that their approach is valid, at least for moderately weak disorder, in section 5 and 6 of the supplementary. I therefore contend that this is not a problem, but a small yellow flag to keep in mind for the strongly discorded case.
### Report
The idea behind this work is timely and interesting. During the last decade, there has been an increasing recognition that the all-important superfluid weight of superconductors can have non-conventional geometric contributions in multiband systems, meaning that the superfluid weight can be non-zero even for flat bands, which is important for systems such as twisted bilayer graphene but also more generally for our understanding of superconductors.
The unconventional origin of the geometric superfluid weight contributions does however also lead to new questions. In this work the authors ask how the average superfluid weight changes with an increasing (on-site, Anderson) disorder strength in several systems and for different system parameters. The work is predominately numerical and has strong parallels to Ref.36 of the manuscript [10.1103/PhysRevLett.81.3940], but unlike that work, this work updates our understanding by also separating out the conventional and geometric parts of the superfluid weight. Their motivation is sound, for as the authors say; the geometric superfluid weight has to be finite when the electronic bands have a non-trivial quantum geometry, bounded below by for instance the Chern number. A-priori one could therefore expect that the behavior in topological systems (with finite Chern number) should be different from the case of a standard one-band metals superconductor.
The results of this work are however surprising. Rather than a distinctive difference between the topological and trivial regimes of the extended Kane-Mele model that they study, they find that the suppression of the average superfluid weight (as well as the standard deviation) follows the same relationship in all cases when normalized by their initial values (a simple square lattice model serves as a control).
I therefore believe that these unexpected findings will stimulate further work, given the current strong interest in these newly recognized geometrical contributions. For these reasons, I however also think that the title of this work might be a problem, as it might overstate the claims of this work. Importantly, the present work only considers on-site s-wave superconductivity and one type of disorder. One might reasonably ask just how "universal" the present results therefore are, or if the results might change for more general systems. I therefore think the authors should think about the title to see if another title may better reflect exactly what is already shown in this work.
With an eye towards the Sci-Post's General Acceptance Criteria, the work is concise and well written. Together with the detailed supplementary, the work should also be easy to reproduce. I find that the most relevant literature is also cited and that the material is available in the Zenodo repository. I therefore recommend publication.
• validity: good
• significance: high
• originality: good
• clarity: top
• formatting: excellent
• grammar: excellent
### Author: Alexander Lau on 2022-08-11 [id 2721]
(in reply to Report 1 on 2022-06-02)
Category:
The referee writes:
The idea behind this work is timely and interesting. During the last decade, there has been an increasing recognition that the all-important superfluid weight of superconductors can have non-conventional geometric contributions in multiband systems, meaning that the superfluid weight can be non-zero even for flat bands, which is important for systems such as twisted bilayer graphene but also more generally for our understanding of superconductors. The unconventional origin of the geometric superfluid weight contributions does however also lead to new questions. In this work the authors ask how the average superfluid weight changes with an increasing (on-site, Anderson) disorder strength in several systems and for different system parameters. The work is predominately numerical and has strong parallels to Ref.36 of the manuscript [10.1103/PhysRevLett.81.3940], but unlike that work, this work updates our understanding by also separating out the conventional and geometric parts of the superfluid weight. Their motivation is sound, for as the authors say; the geometric superfluid weight has to be finite when the electronic bands have a non-trivial quantum geometry, bounded below by for instance the Chern number. A-priori one could therefore expect that the behavior in topological systems (with finite Chern number) should be different from the case of a standard one-band metals superconductor. The results of this work are however surprising. Rather than a distinctive difference between the topological and trivial regimes of the extended Kane-Mele model that they study, they find that the suppression of the average superfluid weight (as well as the standard deviation) follows the same relationship in all cases when normalized by their initial values (a simple square lattice model serves as a control). I therefore believe that these unexpected findings will stimulate further work, given the current strong interest in these newly recognized geometrical contributions.
Our response: We thank the referee for the positive report, for putting our work in context, and for acknowledging the timeliness and novelty of our work.
The referee writes:
For these reasons, I however also think that the title of this work might be a problem, as it might overstate the claims of this work. Importantly, the present work only considers on-site s-wave superconductivity and one type of disorder. One might reasonably ask just how "universal" the present results therefore are, or if the results might change for more general systems. I therefore think the authors should think about the title to see if another title may better reflect exactly what is already shown in this work.
Our response: We thank the Referee for this comment. We understand the Referee's concerns regarding the potentially misleading generality of the title. Therefore, we have made the title more specific to reflect the fact that we consider non-magnetic disorder and $s$-wave superconductors. The new title is "Universal suppression of superfluid weight by non-magnetic disorder in $s$-wave superconductors independent of quantum geometry and band dispersion". We have also added a clarifying sentence in the abstract.
The referee writes:
Much of the numerical work is, in some sense, somewhat limited. The systems sizes are on the smaller side, have very large attractive interactions, and the superconducting self-consistency equations are only solved approximately by using only the linear Tc solutions with a self-consistent amplitude at lower temperatures. Ideally, one would have like to see more robust numerical work, but on the other hand, I do not really think that the results would change if included, especially give how close the present results align with previous numerical works [10.1103/PhysRevB.65.014501,10.1103/PhysRevLett.81.3940]. The authors also explicitly verify that their approach is valid, at least for moderately weak disorder, in section 5 and 6 of the supplementary. I therefore contend that this is not a problem, but a small yellow flag to keep in mind for the strongly discorded case.
Our response: We thank the Referee for pointing this out and for acknowledging the validity of our approach despite giving us the small yellow flag. We agree with the Referee that the interaction strengths are large and the system sizes are on the smaller side, but the consistency with earlier results suggests that heavier numerical calculations are not expected to change our results. We have used reasonably large interaction strengths because it allows us to obtain reliable results also with reasonably small system sizes, making it easier to perform a comprehensive and systematic study of conventional and geometric contributions using several different models. The study of the disorder-induced suppression of the superfluid weight at very small interaction strengths requires significantly heavier numerics (or advanced analytical techniques), and therefore we leave it as an interesting challenge for future research.
The referee writes:
With an eye towards the Sci-Post's General Acceptance Criteria, the work is concise and well written. Together with the detailed supplementary, the work should also be easy to reproduce. I find that the most relevant literature is also cited and that the material is available in the Zenodo repository. I therefore recommend publication.
Our response: We thank the Referee for their positive assessment of our work and for recommending publication. We are confident that the changes in the manuscript are in line with this assessment. | 2022-08-18 01:48:37 | {"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": 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": 0.7154431343078613, "perplexity": 737.5465555724603}, "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/1659882573145.32/warc/CC-MAIN-20220818003501-20220818033501-00414.warc.gz"} |
https://math.stackexchange.com/questions/1405468/polynomial-equations-of-degree-larger-than-4?noredirect=1 | # Polynomial equations of degree larger than 4
It is accepted that there are no general solutions for polynomial equations of degree higher than 4, unless they have some unique features. We know that if we could factor the polynomial into polynomial of degrees smaller than 5, we may find the roots for each such polynomial with degree smaller than 5.
Are there systematic tools for deciding whether polynomials with integer coefficients are irreducible over the rationals, and for factoring them over the rationals if they are not irreducible over the rationals?
• There are general solutions for fifth, sixth, and seventh degree equations, they just involve functions that can't be expressed in terms of radicals. – Matt Samuel Aug 22 '15 at 1:31
• Note that asking whether a polynomial can be factored is not the same as asking whether one can find its roots. Anyway, in principle, one can find the Galois group of any given polynomial, and then determine whether that group is a solvable group. If it is, we can solve the polynomial in radicals; if not, not. In practice, it's not so easy to find the Galois group. The question of how to find the Galois group has come up on this website before, so try to have a look around. – Gerry Myerson Aug 22 '15 at 3:13
• As I said, you clearly do not know what you are talking about. First you claimed "there are no general solutions for polynomial equations of degree higher than 4". That is utterly meaningless unless you are talking about expressing the roots using only radicals over the original field! Then you claim that it is impossible to factor some polynomials. Since you said nothing about radicals, this claim is false. My later paragraphs deal with the question about radical field extensions, which is the only situation where your first claim makes any sense at all. – user21820 Aug 22 '15 at 7:01
• Have you tried reading the Wikipedia page? Yes, given a polynomial with rational coefficients, there is a systematic way to decide whether it is irreducible over the rationals, and a systematic way to factor it into polynomials that are irreducible over the rationals. For polynomials of degree 5 or greater, there is, in general, no closed form for their roots in terms of radicals and field operations. By the way, if you want to be certain that I see a comment, you have to put @Gerry into it. – Gerry Myerson Aug 23 '15 at 6:22
• Since the question is on hold, I can't post an answer. What you can do is edit ithe statement of the question so as to clarify (people shouldn't have to wade through a long thread of comments to understand the question), and then post to the meta site, noting that you have edited the question, and asking for it to be reopened. If it gets reopened, then you can post an answer yourself, if you wish, based on what you have learned from the discussion. – Gerry Myerson Aug 24 '15 at 1:34
Any polynomial over a field factors completely over its splitting field. For real polynomials, it turns out that adjoining $\sqrt{-1}$ to $\mathbb{R}$ gives the algebraic closure, and so every real polynomial factors over $\mathbb{C}$. So your question's assumption is incorrect.
But it is still an interesting question whether there is a general formula for the roots of a quintic polynomial over a field $F$ that only uses radicals, in other words whether the roots are in some radical extension of $F$. It turns out that it is possible exactly when the Galois group of the Galois closure of the field is solvable ("solvable" arose from this very problem of trying to solve polynomials), in other words there is a chain of groups from that group to the trivial group such that the quotient between consecutive groups in the chain is cyclic. So everything reduces to the nature of the Galois group. See https://math.stackexchange.com/a/38901/21820 for an overview of the possible Galois group of an irreducible quintic. I know that for a quartic over the rationals there are easy ways to determine the Galois group just by looking at the coefficients. I do not know if there are deterministic tests for quintics.
• finding cube roots is trivial by de Moivre's theorem: $z^3=re^{it}$ gives $z\in\{\sqrt[3]{r}e^{it/3},\sqrt[3]{r}e^{i(t+2\pi)/3},\sqrt[3]{r}e^{i(t+4\pi)/3}\}$ – oldrinb Aug 22 '15 at 2:16
• @MattSamuel: It is. Tell me the exact value of $\sqrt[3]{1+2i}$ using only arithmetic. – user21820 Aug 22 '15 at 2:17
• @oldrinb: Tell me the exact value of $t$ for $(1+2i)$. It is no point saying you know the cube roots when I too can write $\exp(\frac{1}{3}\ln(1+2i))$ (multi-valued) to express them. – user21820 Aug 22 '15 at 2:19 | 2019-08-21 10:29:29 | {"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": 0.7877161502838135, "perplexity": 177.9598976463347}, "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/1566027315865.44/warc/CC-MAIN-20190821085942-20190821111942-00162.warc.gz"} |
https://www.yaclass.in/p/english-language-cbse/class-9/supplementary-2957/weathering-the-storm-in-ersama-12299/re-f3aa4e9a-41fc-428a-a308-fa0aad3a4844 | Get A+ with YaClass!
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### Theory:
The crazed destruction wrought by the cyclone and the surge of the ocean continued for the next thirty-six hours, although wind speeds had reduced somewhat by the next morning. To escape the waters rising in the house, Prashant and his friend’s family had taken refuge on the roof. Prashant will never forget the shock he experienced at his first glimpse of the devastation wrought by the super cyclone, in the grey light of the early morning. A raging, deadly, brown sheet of water covered everything as far as the eye could see; only fractured cement houses still stood in a few places. Bloated animal carcasses and human corpses floated in every direction. All round even huge old trees had fallen. Two coconut trees had fallen on the roof of their house. This was a blessing in disguise, because the tender coconuts from the trees kept the trapped family from starving in the several days that followed.
Explanation:
The 1999 Odisha cyclone was the most powerful and destructive tropical cyclone ever recorded in the North Indian Ocean.
The cyclone was described by the narrator as "crazed destruction" because it was wildly out of control and destroyed lives and property. Though the cyclone's pace had decreased slightly the next morning, it remained in Orissa for approximately one and a half days (nearly $$45$$hours). And, as a result of the heavy rain, the water level continued to rise.
As the water entered the houses, Prashant and his friend's family had taken refuge on the roof. Even though Prashant couldn't see the cyclone's effects in the dark night, he could realise the cyclone's destructive consequences and began to notice the cyclone's devastating impacts in the early hours of the morning.
People on rooftop during flood
As far as Prashant could see, there was a cover of muddy brown water. There were the remains of shattered houses surrounded by the water. Dead bodies of animals and human beings floated in the water. Huge trees had fallen and were floating around. Two coconut trees had fallen on the roof of their house. Initially, they thought that the trees had damaged the roof and walls of the house, but later realised that this proved to be beneficial for them. It turned out to be a blessing in disguise. They ate the tender coconuts off these trees to save themselves from starvation, as they couldn't move from their rooftop.
Meaning of difficult words:
S.No Words Meaning 1. Wrought Caused something to happen 2. Surge A sudden and great increase 3. Refuge Protection or shelter from danger 4. Glimpse A brief look at someone or something 5. Raging Very strong or powerful 6. Carcass Dead body of an animal 7. Corpse Refers to a dead body of a human 8. Disguise To change the appearance 9. Trapped In a dangerous or bad situation
Reference:
National Council of Educational Research and Training (2006). Beehive. Weathering the storm in Ersama - Hasrh Mander (pp.37-42). Published at the Publication Division by the Secretary, National Council of Educational Research and Training, Sri Aurobindo Marg, New Delhi. | 2021-12-04 00:38:39 | {"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": 0.21524497866630554, "perplexity": 4841.177369655533}, "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-2021-49/segments/1637964362923.11/warc/CC-MAIN-20211204003045-20211204033045-00244.warc.gz"} |
https://www.hpmuseum.org/forum/showthread.php?tid=8565&pid=75420&mode=threaded | I have a way to measure battery power
07-01-2017, 09:03 AM (This post was last modified: 07-01-2017 10:38 AM by webmasterpdx.)
Post: #20
webmasterpdx Senior Member Posts: 541 Joined: Sep 2015
RE: I have a way to measure battery power
I have new data as the power has gone down to the next level. Here is the table so far. I don't know if there is going to be another level before the power goes off or there is going to be a message. I haven't seen a "low power" message yet either. In this table, V is the % value returned by my little app above, HP is the % full according to the HP guys returned by the hardware, C is the color inside the battery icon in RGB hex (and english), Pixels is the number of pixels turned on in the battery icon, and Y is the y value of highest vertical pixel on, where x=315 where the color changes inside the battery icon.
Code:
V Y Pixels HP C 100 04 11 100 #008400h Bright Green 80 07 08 75 #008400h Bright Green 60 09 06 50 #008400h Bright Green 30 12 03 25 #EFCE29h Yellow
I had to change to code to change 8400 to EFCE29 for it to work now that it's changed from green to yellow. I'll rewrite everything to be more efficient and work no matter what the color when I've gotten all the info I require....when battery goes down to the shutoff point.
I'll update when I get any more info as the power goes down farther (if there is any, other than the power going out).
-Donald[/code]
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Messages In This Thread I have a way to measure battery power - webmasterpdx - 06-25-2017, 05:03 AM RE: I have a way to measure battery power - cyrille de brébisson - 06-26-2017, 05:30 AM RE: I have a way to measure battery power - webmasterpdx - 06-27-2017, 10:43 AM RE: I have a way to measure battery power - toml_12953 - 06-28-2017, 12:05 PM RE: I have a way to measure battery power - Tim Wessman - 06-28-2017, 02:59 PM RE: I have a way to measure battery power - toml_12953 - 06-28-2017, 05:38 PM RE: I have a way to measure battery power - DrD - 06-27-2017, 11:21 AM RE: I have a way to measure battery power - TravisE - 06-27-2017, 09:13 PM RE: I have a way to measure battery power - webmasterpdx - 06-28-2017, 01:14 AM RE: I have a way to measure battery power - DrD - 06-28-2017, 10:50 AM RE: I have a way to measure battery power - webmasterpdx - 06-28-2017, 11:02 AM RE: I have a way to measure battery power - DrD - 06-28-2017, 11:20 AM RE: I have a way to measure battery power - webmasterpdx - 06-28-2017, 01:28 PM RE: I have a way to measure battery power - webmasterpdx - 06-28-2017, 01:25 PM RE: I have a way to measure battery power - StephenG1CMZ - 06-28-2017, 04:45 PM RE: I have a way to measure battery power - StephenG1CMZ - 10-28-2017, 02:57 PM RE: I have a way to measure battery power - webmasterpdx - 06-29-2017, 01:54 AM RE: I have a way to measure battery power - toml_12953 - 06-29-2017, 02:46 AM RE: I have a way to measure battery power - StephenG1CMZ - 06-29-2017, 05:35 AM RE: I have a way to measure battery power - webmasterpdx - 06-29-2017, 06:34 AM RE: I have a way to measure battery power - webmasterpdx - 07-01-2017 09:03 AM RE: I have a way to measure battery power - Dieter - 07-01-2017, 09:57 AM RE: I have a way to measure battery power - webmasterpdx - 07-01-2017, 10:37 AM RE: I have a way to measure battery power - webmasterpdx - 07-01-2017, 06:37 PM RE: I have a way to measure battery power - webmasterpdx - 07-01-2017, 07:13 PM
User(s) browsing this thread: 1 Guest(s) | 2020-05-30 09:50:12 | {"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": 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": 0.24874939024448395, "perplexity": 1551.098859577868}, "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/1590347407667.28/warc/CC-MAIN-20200530071741-20200530101741-00115.warc.gz"} |
https://socratic.org/questions/how-do-you-simplify-8div4-1-6-4-4div2-6 | # How do you simplify 8div4+1(6-4)+4div2-6?
Aug 3, 2016
$0$
#### Explanation:
Count the number of terms first. In this case there are 4 terms.
You can simplify within each term until there is a single answer for each term. Do more than one simplification in a line. This saves time and space.
Addition and subtraction are done in the LAST step.
$\textcolor{red}{8 \div 4} \textcolor{b l u e}{+ 1 \left(6 - 4\right)} \textcolor{m a \ge n t a}{+ 4 \div 2} \textcolor{g r e e n}{- 6}$
= $\textcolor{red}{2} \textcolor{b l u e}{+ 1 \times 2} \textcolor{m a \ge n t a}{+ 2} \textcolor{g r e e n}{- 6}$
= $\textcolor{red}{2} \textcolor{b l u e}{+ 2} \textcolor{m a \ge n t a}{+ 2} \textcolor{g r e e n}{- 6}$
=$0$ | 2019-09-17 21:24:36 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 5, "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": 0.6218626499176025, "perplexity": 717.5519957886387}, "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/1568514573121.4/warc/CC-MAIN-20190917203354-20190917225354-00204.warc.gz"} |
https://businessintegrationsoftware.com/butternut-squash-vtbgs/symbolab-concave-up-down-7b88cd | ## symbolab concave up down
BYJU’S online inflection point calculator tool makes the calculation faster, and it displays the inflection point in a fraction of seconds. Finding intervals of increase/decrease local max/mins youtube. Solve: Looking for … Ap calculus ab-bc points of inflection (no calculator). (2 different shapes for concave up and down would be preferred. Finding concavity using the second derivative. Concave up, concave down, points of inflection. i know how to take the derivative but when solving for 0 to find critical points it wont factor First derivative just means taking the derivative (a.k.a. concave up: (-inf,0) concave down: (0,inf) since we change concavity at x=0, it is an inflection point. Notes on the symbols used in the formula:! Real and complex numbers calculated to 14-digit accuracy and displayed with 10 digits plus a 2-digit exponent. Time calculator. These are the calculation methods used by the calc to find the derivatives.. Polynomial graphing calculator with explanations. Favorite Answer . 7. $inflection\:points\:f\left (x\right)=\sqrt [3] {x}$. The test helps you to: Find the intervals where a function is decreasing or increasing. If f is concave up [down] on (a,b) then f ''(x) > 0 [f ''(x) < 0] on (a,b). Inflection point calculator, point of inflection calculator | calculator. Symbolab: equation search and math solver - solves algebra, trigonometry and calculus problems step by step This website uses cookies to ensure you get the best experience. Encoding. The calculator will find the intervals of concavity and inflection points of the given function. This page help you to explore polynomials of degrees up to 4. f(x)=6x-2x 3. f(0)=6(0)-2(0) 3 =0. Test 1. Parabolas: vertex form. User-defined list names. Test 1. Sharp el-1801c semi-desktop 2-color printing calculator. Local extrema finder. The slopes of tangent lines can also tell you which type of concavity you have. Examples. Calculus Quick Reference Pro lists down all the important formulas and evaluation techniques used in calculus which makes it easier for you to memorize and apply them in solving problems. Functions inflection points calculator symbolab. The calculator will find the domain, range, x-intercepts, y-intercepts, derivative, integral, asymptotes, intervals of increase and decrease, critical points, extrema (minimum and maximum, local, absolute, and global) points, intervals of concavity, inflection points, limit, Taylor polynomial, and graph of the single variable function. Video explains how to use the slopes of the tangent lines to a curve to develop rules for determining when a function is concave up and concave down. Concave up, concave down, points of inflection. Inflection point calculator calculate inflection point for free here. finding the slope of the tangent line) once. Forget taking down calculus formulas on a paper! Example. Finding concavity using the second derivative. Seems that B-C is a part of Concave Down, and C-D is a part of Concave Up; So C is a SWITCHING POINT, it's a inflection point. If f ''(x) > 0 (f ''(x) < 0) on (a,b), then then f(x) is concave up [down] on the interval (a,b). In general, you can skip parentheses, but be very careful: e^3x is e^3x, and e^(3x) is e^(3x). … Relevance. How to use your scientific calculator. Inflection points don’t always exist, as some functions don’t experience any change in concavity. $inflection\:points\:f\left (x\right)=x^4-x^2$. Without a calculator, behavior of$f(x). Finding intervals of increase/decrease local max/mins youtube. 1 Answer. Please leave them in comments. Concave up, concave down, points of inflection. Blue dots are extrema. (In finance, such a curve is said to be convex.) Similarly, we say that a graph is concave down if the line between two points is below the graph, or alternatively if the first derivative is decreasing. This is my code and I want to find the change points of my sign curve, that is all and I want to put points on the graph where it is concave up and concave down. Approximating areas with Riemann sums. Wolfram|alpha examples: inflection points. 1 general method for curve plotting without a calculator. Contact. Concave up or down calculator Graphing logarithmic functions: more examples. Type in any integral to get the solution, steps and graph . Lv 6. An inflection point occurs at x = ??? the center black dot is the inflection point. How to use your scientific calculator. All suggestions and improvements are welcome. Seems that B-C is a part of Concave Down, and C-D is a part of Concave Up; So C is a SWITCHING POINT, it's a inflection point. inflection points y = x3 − x. Your email address will not be published. Mike Jones. Functions inflection points calculator symbolab. The second derivative is f'' (x) = 30x + 4 (using Power Rule) And 30x + 4 is negative up to x = −4/30 = −2/15, and positive from there onwards. Concave up, concave down, points of inflection. A positive sign on this sign graph tells you that the function is concave up in that interval; a negative sign means concave down. The calculator will find the domain, range, x-intercepts, y-intercepts, derivative, integral, asymptotes, intervals of increase and decrease, critical points, extrema (minimum and maximum, local, absolute, and global) points, intervals of concavity, inflection points, limit, Taylor polynomial, and graph of the single variable function. Finding the inflection points. Functions inflection points calculator symbolab. And the value of f″ is always 6, so is always >0,so the curve is entirely concave upward. Inflection points, concavity upward and downward by Paul Garrett is licensed under a Creative Commons Attribution-Noncommercial-ShareAlike 4.0 License.For permissions beyond the scope of this license, please contact us.. Substitute any number from the interval (0, ∞) into the second derivative and evaluate to determine the concavity. Functions can either be concave up or concave down at any point on the curve. Calculus 1st and 2nd derivative test using a calculator ti-84 or ti. In other words, where the rate of change of the rate of change is 0. So: f (x) is concave downward up to x = −2/15. Concave up or down calculator Graphing logarithmic functions: more examples. Compute answers using Wolfram's breakthrough technology & knowledgebase, relied on by millions of students & professionals. Taylor polynomials look a little ugly, but if you break them down into small steps, it’s actually a fast way to approximate a function. Lists... Interactive analysis of function values, roots, maximums, minimums, integrals, and derivatives. I Used Symbolab And It Used Something Called Newton Raphson That I Havent Learned Question: I Used Symbolab And It Used Something Called Newton Raphson … If you skip parentheses or a multiplication sign, type at least a whitespace, i.e. Taylor polynomials can be used to approximate any differentiable function. Note: The point where it changes is called an inflection point. (1) If f '(c) equals 0 and f ''(c) < 0, then x = c is a local maximum. In another sense, inflection points represent where the second derivative of the function is 0. We now study the sign of f ''(x) which is equal to 2 a. write sin x (or even better sin(x)) instead of sinx. Get the free "Inflection Points" widget for your website, blog, Wordpress, Blogger, or iGoogle. On the other hand, if the tangent line is above the point, then the graph is concave down. Use Taylor polynomials to approximate the function cos(x) around the point x = 2. If you need oo, type. It can calculate and graph the roots (x-intercepts), signs, Local Maxima and Minima, Increasing and Decreasing Intervals, Points of Inflection and Concave Up/Down intervals. Function calculator emathhelp. Functions inflection points calculator symbolab. Inflection points and concavity calculator emathhelp. Without a calculator, behavior of$ f(x). Symbolab Math Solver app is composed of over one hundred of Symbolab's most powerful calculators: Equation Calculator Integral Calculator Derivative Calculator Limit calculator Inequality Calculator Trigonometry Calculator Matrix Calculator Functions Calculator Series Calculator ODE Calculator Laplace Transform Calculato Symbolab is one of the most popular and renowned apps as … Led video wall calculator | leyard. Function calculator emathhelp. Find more Mathematics widgets in Wolfram|Alpha. It’s usually just shortened to “derivative.” First Derivative Test. An arrow is a graphical symbol, such as ← or →, or a pictogram, used to point or indicate direction.In its simplest form, an arrow is a triangle, chevron, or concave kite, usually affixed to a line segment or rectangle, and in more complex forms a representation of an actual arrow (e.g. Local extrema finder. Search for courses, skills, and videos. The first derivative test is one way to study increasing and decreasing properties of functions. Inflection … For example, [0, 2pi] or (-pi, oo). Functions inflection points calculator symbolab. By using this website, you agree to our Cookie Policy Free integral calculator - solve indefinite, definite and multiple integrals with all the steps. Free functions extreme points calculator - find functions extreme and saddle points step-by-step use to analyze how functions change over time, TIPS FOR HOW TO USE A CONCAVITY CALCULATOR, OUR FINAL THOUGHTS ON THE FUTURE OF CONCAVITY CALCULATORS, Texas Instruments Ti-84 plus Graphing calculator - Black. (In … Critical points and extrema calculator emathhelp. 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. Campbell's. By applying the derivation formulas and using the usual derivation table, it is possible to calculate any function derivative. Inflection points and concavity calculator emathhelp. A function is said to be concave up on an interval if its first derivative is increasing on the interval. Credits The page is based off the Calculus Refresher by Paul Garrett.Calculus Refresher by Paul Garrett. f (x) is concave upward from x = −2/15 on. Math AP®︎/College Calculus AB Integration and accumulation of change Approximating areas with Riemann sums. Test 1. Main content. Donate Login Sign up. Be sure to write in interval notation. For concavity, we want to zoom out a bit, so the graph curves up or down from a line. Concave up, concave down, points of inflection. Example. Example problem . inflection points f ( x) = x4 − x2. Concave up, concave down, points of inflection. If a is positive, f ''(x) is positive in the interval (-∞ , + ∞). Without a calculator, behavior of$f(x). The second derivative of a function may also be used to determine the general shape of its graph on selected intervals. Symbolab. Area calculator. This is an Ad-free version of Calculus Quick Reference. Led video wall calculator | leyard. Concave up, concave down, points of inflection. f(x) = - ln(2x² + 5) f ' (x) = - 4x/(2x² + 5) From the derivative you should get an idea of the slope in the original graph. Which Is The Best Graphing Calculator On The Market, Review Of TI 83 Calculator: Advanced Graphing Calculator, How To Use The Graphing Calculator TI-84: Expert Techniques, The TI Nspire Calculator Online Guide: An Introduction, Arc Length Calculator: Finding The Necessary Values, An A+ Tool: Review Of The HP Prime Graphing Calculator, Asymptote Calculator For Android And Apple Users, 7 Best Calculator Watches for the Nerd Inside, What Is Sigma Value And The Best Sigma Calculator, Step By Step Tutorial For Linear Regression Calculator, How to Calculate Delta S and Understand What It Is, Where To Buy A Good And Cheap Domain Calculator Online. Polynomial graphing calculator with explanations. Similarly, tanxsec^3x will be parsed as tan(xsec^3(x)). Solving linear inequalities. The following table contains the supported operations and functions: Required only for trigonometric functions. The derivative calculator allows steps by steps calculation of the … Test 1. Type in any integral to get the solution, steps and graph . Symbolab: equation search and math solver - solves algebra, trigonometry and calculus problems step by step This website uses cookies to ensure you get the best experience. First derivative just means taking the derivative (a.k.a. To get tan(x)sec^3(x), use parentheses: tan(x)sec^3(x). Free calculus calculator - calculate limits, integrals, derivatives and series step-by-step Area calculator. We say that a graph is concave up if the line between two points is above the graph, or alternatively if the first derivative is increasing. The test helps you to: Find the intervals where a function is decreasing or increasing. is the factorial symbol). Over- and under-estimation of Riemann sums . Wolfram|alpha examples: inflection points. It’s usually just shortened to “derivative.” First Derivative Test. and concave up on ??? We have seen previously that the sign of the derivative provides us with information about where a function (and its graph) is increasing, decreasing or stationary. Ned Chuffed. Calculus 1st and 2nd derivative test using a calculator ti-84 or ti. Riemann approximation introduction. A function is said to be concave upward on an interval if f″(x) > 0 at each point in the interval and concave downward on an interval if f″(x) < 0 at each point in the interval. Solution: Since this is never zero, there are not points ofinflection. Please consider purchasing the app to support the developers. If a is negative, the graph of f will be concave down on the interval (-∞ , + ∞) since f ''(x) = 2 a is negative. The first derivative test is one way to study increasing and decreasing properties of functions. This is the currently selected item. Charwoman's. Left & right Riemann sums.$inflection\:points\:y=x^3-x$. the outer two black dots are the x-intercepts. Area calculator. To get tan^2(x)sec^3(x), use parentheses: tan^2(x)sec^3(x). finding the slope of the tangent line) once. Drawled Demystifies. Time calculator. Parabolas: vertex form. Sometimes I see expressions like tan^2xsec^3x: this will be parsed as tan^(2*3)(x sec(x)). Functions inflection points calculator symbolab. If the calculator did not compute something or you have identified an error, please write it in Inflection points of cardiovascular responses and oxygenation are. Some functions even switch back and forth between concave up and concave down infinitely many times! Functions inflection points calculator symbolab. Functions inflection points calculator symbolab. comments below. The function has an inflection point (usually) at any x-value where the signs switch from positive to negative or vice versa. whether the graph is "concave up" or "concave down". Find the inflection points and intervals of concavity upand down of f(x)=3x2−9x+6 First, the second derivative is justf″(x)=6. 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). U+27B5). 4 years ago. Parabolas: vertex form. The second derivative of a function is the derivative of the derivative of that function. Inflection point calculator, point of inflection calculator | calculator. Tap for more steps... Concave up on (0, ∞) since f′′ (x) is positive The graph is concave down when the second derivative is negative and concave up when the second derivative is positive. Any point at which concavity changes (from CU to CD or from CD to CU) is call an inflection point for the function. If you get an error, double-check your expression, add parentheses and multiplication signs where needed, and consult the table below. We now look at the "direction of bending" of a graph, i.e. Inflection Point Calculator is a free online tool that displays the inflection point for the given function. Graphs 10... Sequence graphing mode shows time series plot, cobweb/stair-step plot, and phase plots. Parabolas: vertex form. This website uses cookies to ensure you get the best experience on our website. Concave Up, Down, and Tangent Lines. At the same time the second derivative of the function is positive on the interval. It can calculate and graph the roots (x-intercepts), signs, Local Maxima and Minima, Increasing and Decreasing Intervals, Points of Inflection and Concave Up/Down intervals. For example, a parabola f(x) = ax 2 + bx + c has no inflection points, because its graph is always concave up or concave down. Inflection Points Inflection points are points where the concavity changes sign. The second derivative test shows when a critical point c is a local maximum or local minimum. This page help you to explore polynomials of degrees up to 4. inflection point: (0,0) f(x)=6x-2x 3. since the function has no denominator, there cannot be any asymptotes. 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)). Without a calculator, behavior of$ f(x). Area calculator. Finding concavity using the second derivative. Answer Save. I just have a simple sine curve with 3 periods and here is the code below. Sharp el-1801c semi-desktop 2-color printing calculator. Without a calculator, behavior of$f(x). According to the theorem above, the graph of f will be concave up for positive values of a. Free math problem solver answers your algebra, geometry, trigonometry, calculus, and statistics homework questions with step-by-step explanations, just like a math tutor. Without a calculator, behavior of$ f(x). By using this website, you agree to our Cookie Policy Free integral calculator - solve indefinite, definite and multiple integrals with all the steps. Chapter 5 analyzing change: extrema and points of inflection. Analytically, a concave up graph can be defined by its tangent line; Take a point where the graph has a low point: the tangent line around that point lies below the graph. The calculator will find the intervals of concavity and inflection points of the given function. concave down. find where the function is increasing, decreasing, concave up, concave down, local extreme values, and inflection points. Inflection Points and Derivatives. f(x)=1+x-x^2-x^4. Concave Up, Concave Down, Points of Inflection. Find inflection points by analyzing the second derivative (article. The second derivative of a function is the derivative of the derivative of that function. The function is concave down on ??? Series plot, and derivatives graphs 10... Sequence Graphing mode shows time series,! We now study the sign of f will be concave up, concave down at any on... ( -pi, oo ) signs switch from positive to negative or vice.... 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book a demo | 2021-04-13 22:39:46 | {"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": 0.5973297953605652, "perplexity": 1655.8242791987643}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "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-2021-17/segments/1618038075074.29/warc/CC-MAIN-20210413213655-20210414003655-00251.warc.gz"} |
http://math.stackexchange.com/questions/289248/finding-the-area-between-two-curves | # Finding the Area Between Two Curves
Sketch the region enclosed by the curves. Decide whether to integrate with respect to x or y. Then find the area of the region between $$x=9-{y^2}$$ and $$x={y^2}-9$$
What I have done so far is put the equations in terms of y and make them equal to each other. I got $$9-x=x+9$$ which goes to $$2x=0$$. I am unsure of how to find the bounds of the integral from this. Can anyone help?
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You should definitely integrate with respect to $y$. – 1015 Jan 28 '13 at 20:51
I did that however I am having trouble finding the bounds of the integral. – Gabrielle Jan 28 '13 at 20:56
@Gabrielle The community frowns upon questions copied verbatim from a textbook with no apparent effort on your part. If you include in your question the comment that you have decided how to integrate but cannot determine the bounds, the community will more likely to help. – Austin Mohr Jan 28 '13 at 20:59
Oh okay let me edit in what I have so far then. I'm just reviewing for a test and didn't know. :( – Gabrielle Jan 28 '13 at 21:00
@Gabrielle That's alright. I didn't want you to think that calculus questions are unwelcome here. We are generally happy to answer anything, but we want to be confident that you are taking the time to think about the problem first. Welcome to the community. – Austin Mohr Jan 28 '13 at 21:19
## 1 Answer
You need to find the intersections of the two parabola. These occur when $9-y^2=y^2-9$, which is equivalent to $y^2-9=0$. So you have two intersections, namely $(0,-3)$ and $(0,3)$.
Draw a picture.
The area is given by $$\int_{-3}^3(9-y^2-(y^2-9))dy=2\int_0^3(18-2y^2)dy.$$
I guess you can finish the calculation.
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Ohh! Thank you so much I was putting the equations to find the bounds in terms of x. That was the problem thank you ! – Gabrielle Jan 28 '13 at 21:05
No problem. Good luck with the test. – 1015 Jan 28 '13 at 21:06 | 2014-07-29 21:08:21 | {"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": 0.8842995762825012, "perplexity": 236.15701691886693}, "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-2014-23/segments/1406510267865.20/warc/CC-MAIN-20140728011747-00260-ip-10-146-231-18.ec2.internal.warc.gz"} |
https://icsemath.com/2017/09/16/class-10-distance-and-section-formula-sample-problems-exercise-13d/ | Question 1: Calculate the distance between the points $(6, -4)$ and $(3,2)$ correct to $2$ decimal places.
$(6, -4)$ and $(3, 2)$
Distance $= \sqrt{(3-6)^2+(2-(-4))^2} = \sqrt{9+36} = \sqrt{45} = 6.71$
$\\$
Question 2: Find the distance between the points $(-2, -2)$ and $(1,0)$ correct to $3$ significant figures.
$(-2, -2)$ and $(1,0)$
Distance $= \sqrt{(1-(-2))^2+(0-(-2))^2} = \sqrt{9+4} = \sqrt{13} =3.61$
$\\$
Question 3: Show that the points $P(7, 3), Q(6, 3 + \sqrt{3}) \ and \ R (5, 3)$ form an equilateral triangle.
$P(7, 3), Q(6, 3 + \sqrt{3}) \ and \ R (5, 3)$
$PQ = \sqrt{(6-7)^2+(3 + \sqrt{3}-3)^2} = \sqrt{1+3} = \sqrt{4} = 2$
$PR = \sqrt{(5-7)^2+(3-3)^2} = \sqrt{4+0} = \sqrt{4} = 2$
$QR = \sqrt{(5-6)^2+(3-(3 + \sqrt{3})^2} = \sqrt{1+3} = \sqrt{4} = 2$
Therefore three sides $PQ, PR \ and \ QR$ are equal which makes it an equilateral triangle.
$\\$
Question 4: The circle with center $(x, y)$ passes though the points $(3, 11), (14, 0) \ and \ (12, 8)$ . Find the values of $x \ and \ y$.
Distance of the points from the center are equal. Therefore
$\sqrt{(3-x)^2+(11-y)^2}=\sqrt{(12-x)^2+(8-y)^2}$
$9x^2-6x+121+y^2-22y=144+x^2-24x+64+y^2-16y$
$18x-6y=78$
$3x-y=13$ … … … … i)
$\sqrt{(3-x)^2+(11-y)^2}=\sqrt{(14-x)^2+(0-y)^2}$
$9x^2-6x+121+y^2-22y=196+x^2-28x+y^2$
$22x-22y=66$
$x-y=3$… … … … ii)
Solving i) and ii), we get $x = 5$ and $y = 2$.
Therefore the center is $(5, 2)$
$\\$
Question 5: The points $A(-1, 2), B(x, y) \ and \ C = (4, 5)$ are such that $BA = BC$ . Find a linear relation between $x \ and \ y$ .
$BA=BC$
$\sqrt{(x-(-1))^2+(y-2)^2}=\sqrt{(4-x)^2+(5-y)^2}$
$x^2+1+2x+y^2+4-4y=16+x^2-8x+25+y^2-10y$
$5+2x-4y=41-8x-10y$
$10x+6y=36$
$5x+3y=18$
$\\$
Question 6: Given a triangle $ABC$ in which $A = (4, 4), B = (0, 5) and C = (5, 10)$ . A point $P$ lies on $BC$ such that $BP : PC = 3 : 2$ . Find the length of line segment $AP$ .
A point $P (x,y)$ lies on $BC$ such that $BP : PC = 3 : 2$ .
$x = \frac{2 \times (0)+3 \times (5)}{2+3} = 3$
$y = \frac{2 \times (5)+3 \times (10)}{2+3} = 8$
Therefore $P = (3, 8)$
Therefore
Length of $AP = \sqrt{(3-4)^2+(8-(-4))^2} = \sqrt{1+144} = \sqrt{145}$
$\\$
Question 7: $A(20, 0) \ and \ B(10, -20)$ are two fixed points. Find the co-ordinates of the point $P$ in $AB$ such that: $3PB = AB$ . Also, find the co-ordinates of some other point $Q \ in \ AB$ such that $AB=6AQ$ .
For P When Ratio: $m_1:m_2 = 2:1$ $A(20, 0) \ and \ B(10, -20)$
Therefore
$x = \frac{2 \times (10)+1 \times (20)}{2+1}= \frac{40}{3}$
$y = \frac{2 \times (-20)+1 \times (0)}{1+2} =\frac{-40}{3}$
Therefore the point $P= (\frac{40}{3},\frac{-40}{3})$
For Q When Ratio: $m_1:m_2 = 1:5$ $A(20, 0) \ and \ B(10, -20)$
Therefore
$x = \frac{1 \times (10)+5 \times (20)}{1+5}= \frac{55}{3}$
$y = \frac{1 \times (-20)+5 \times (0)}{1+5} =\frac{-10}{3}$
Therefore the point $P= (\frac{55}{3},\frac{-10}{3})$
$\\$
Question 8: $A(-8, 0), B(0, 16) \ and \ C(0, 0)$ are the vertices of a triangle $ABC$ . Point $P$ lies on $AB \ and \ Q$ lies on $AC$ such that $AP: PB = 3: 5 \ and \ AQ: QC = 3:5$ . Show that: $PQ = \frac{3}{8}BC$ .
For $P(x_1,y_1)$ When Ratio: $m_1:m_2 = 3:5$ $A(-8, 0) \ and \ B(0, 16)$
Therefore
$x_1 = \frac{3 \times (0)+5 \times (-8)}{3+5}= -5$
$y_1 = \frac{3 \times (16)+5 \times (0)}{3+5} =6$
Therefore the point $P= (-5,6)$
For $Q(x_2,y_2)$ When Ratio: $m_1:m_2 = 3:5$ $A(-8, 0) \ and \ C(0, 0)$
Therefore
$x_2 = \frac{3 \times (0)+5 \times (-8)}{3+5}= -5$
$y_2 = \frac{3 \times (0)+5 \times (0)}{3+5} =0$
Therefore the point $Q= (-5,0)$
$PQ = \sqrt{(-5-(-5))^2+(0-6)^2} = \sqrt{0+36} = 6$
$BC = \sqrt{(0-0)^2+(16-0)^2} = \sqrt{256} = 16$
Therefore $PQ = \frac{3}{8} \times 16=6$
Which proves that $PQ = \frac{3}{8}BC$
$\\$
Question 9: Find the co-ordinates of points of trisection of the line segment joining the point $(6, 9)$ and the origin.
Let $P(x_1,y_1) \ and \ Q(x_2,y_2)$ be the two points dividing the points $(6, 9)$ and the origin in the ratio 1:2 and 2:1 respectively.
Therefore for $P$
$x_1 = \frac{1 \times (0)+2 \times (6)}{1+2}= 4$
$y_1 = \frac{1 \times (0)+2 \times (-9)}{1+2} =-6$
Hence $P(4, -6)$
Therefore for $Q$
$x_1 = \frac{2 \times (0)+1 \times (6)}{2+1}= 2$
$y_1 = \frac{2 \times (0)+1 \times (-9)}{2+1} =-3$
Hence $Q(2, -3)$
$\\$
Question 10: A line segment joining $A(-1, \frac{5}{3}) \ and \ B(a, 5)$ is divided in the ratio $1 : 3 \ at \ P$ , the point where the line segment $AB$ intersects the $y-axis$ .
(i) Calculate the value of $a$
(ii) Calculate the co-ordinates of $P$. [1994]
Therefore for $P (0,y)$
$0 = \frac{1 \times (a)+3 \times (-1)}{1+3} \Rightarrow a = 3$
$y = \frac{1 \times (5)+3 \times (\frac{5}{3})}{1+3} =\frac{5}{2}$
Hence $P(0, \frac{5}{2})$
$\\$
Question 11: In what ratio is the line joining $A(0, 3) \ and \ B (4, -1)$ divided by the $x-axis$ ? Write the co-ordinates of the point where $AB$ intersects the $x-axis$ . [1993]
Let the required ratio be $k:1$ and the point of $x-axis$ be $(x,0)$
Since $y = \frac{ky_2+y_1}{k+1}$
$\Rightarrow 0 = \frac{k \times (-1) +3}{k+1}$
$\Rightarrow k=3$
$\Rightarrow m_1:m_2 = 3:1$
Therefore $x = \frac{3(4)+1(0)}{3+1} = 3$
Therefore $P(3,0)$
$\\$
Question 12: The mid-point of the segment $AB$ , as shown in diagram, is $C(4, -3)$ . Write down the coordinates of $A \ and \ B$ . [1996]
Given Midpoint of $AB = (4,-3)$
Therefore
$4 = \frac{1 \times x+1 \times (0)}{1+1} \Rightarrow x = 8$
$-3 = \frac{1 \times (0)+1 \times y}{1+1} \Rightarrow y = -6$
Therefore $A = (8, 0) \ and \ B(0, -6)$
$\\$
Question 13: $AB$ is a diameter of a circle with center $C = (-2, 5)$ . If $A = (3, -7)$ , find
(i) the length of radius $AC$
(ii) the coordinates of $B$ . [2013]
Given Midpoint of $AB = C(-2,5)$
Therefore
$-2 = \frac{1 \times x+1 \times (3)}{1+1} \Rightarrow x = -7$
$5 = \frac{1 \times (y)+1 \times (-7)}{1+1} \Rightarrow y = 17$
Therefore $B = (-7, 17)$
$AC = \sqrt{(-7-3)^2+(17-(-7))^2} = \sqrt{676} = 26$
$\\$
Question 14: Find the co-ordinates of the centroid of a triangle $ABC$ whose vertices are : $A(-1, 3), B(1, -1) \ and \ C(5, 1)$ . [2006]
Let $O(x, y)$ be the centroid of triangle $ABC$.
Therefore
$x=\frac{-1+1+5}{3}= \frac{5}{3}$
$y = \frac{3-1+1}{3}=1$
Hence the coordinates of the centroid are $(\frac{5}{3}, 1)$
$\\$
Question 15: The mid-point of the line segment joining $(4a, 2b-3) \ and \ (-4, 3b) \ is \ (2, -2a)$ . Find the values of $a \ and \ b$ .
Given Midpoint of $= C(2, -2a)$
Therefore
$2 = \frac{1 \times (4a) + 1 \times (-4)}{1+1} \Rightarrow a = 2$
$-2(2) = \frac{1 \times (2b-3)+1 \times (3b)}{1+1} \Rightarrow b = -1$
$\\$
Question 16: The mid-point of the line segment joining $(2a, 4) \ and \ (-2, 2b) \ is \ (1, 2a+1)$ . Find the values of $a \ and \ b$ . [2007]
Given Midpoint of $= C(1, 2a+1)$
Therefore
$1 = \frac{1 \times (2a) + 1 \times (-2)}{1+1} \Rightarrow a = 2$
$2(2)+1 = \frac{1 \times (4)+1 \times (2b)}{1+1} \Rightarrow b = 3$
$\\$
Question 17: (i) Write down the co-ordinates of the point $P$ that divides the line joining $A(- 4, l) \ and \ B(17, 10)$ in the ratio $1 : 2$ .
(ii) Calculate the distance $OP$ , where $O$ is the origin.
(iii) In what ratio does the $y-axis$ divide the line $AB$ ? [1995]
i) For P When Ratio: $m_1:m_2 = 1:2$ $A(- 4, l) \ and \ B(17, 10)$
Therefore
$x = \frac{1 \times (17)+2 \times (-4)}{1+2}= 3$
$y = \frac{1 \times (10)+2 \times (1)}{1+2} = 4$
Therefore the point $P= (3, 4)$
ii) $OP = \sqrt{(3-0)^2+(4-0)^2} = \sqrt{25} = 5$
iii) Let the required ratio be $k:1$ and the point be $Q(0,y)$
Since $y = \frac{ky_2+y_1}{k+1}$
$\Rightarrow 0 = \frac{k \times (17) -4}{k+1}$
$\Rightarrow k=\frac{4}{17}$
$\Rightarrow m_1:m_2 = 4:17$
$\\$
Question 18: Prove that the points $A(-5,4); B(-1, -2) \ and \ C(5, 2)$ are the vertices of an isosceles right-angled triangle. Find the co-ordinates of $D$ so that $ABCD$ is a square. [1992]
$AC = \sqrt{(5-(-5))^2+(2-4)^2} = \sqrt{104}$
$AB= \sqrt{(-1-(-5))^2+(-2-(-4))^2} = \sqrt{52}$
$BC = \sqrt{(-1-(-5))^2+(-2-2)^2} = \sqrt{52}$
Since $AB=BC$ (two sides are equal). Hence triangle $ABC$ is a isosceles triangle.
$\\$
Question 19: $M$ is the mid-point of the line segment joining the points $A(-3, 7) \ and \ B(9, -1)$ . Find the coordinates of point $M$ . Further, if $R(2, 2)$ divides the line segment joining $M$ and the origin in the ratio $p : q$ , find the ratio $p : q$ .
For M When Ratio: $m_1:m_2 = 1:1$ for $A(-3, 7) \ and \ B(9, -1)$
Therefore
$x = \frac{1 \times (9)+1 \times (-3)}{1+1}= 3$
$y = \frac{1 \times (-1)+1 \times (7)}{1+1} = 3$
Therefore the point $M= (3, 3)$
Let $R(2,2)$ divide MO in the ratio $k:1$
Since $y = \frac{ky_2+y_1}{k+1}$
$\Rightarrow 0 = \frac{k \times (0) +3}{k+1}$
$\Rightarrow k=\frac{1}{2}$
$\Rightarrow p:q=1:2$
$\\$
Question 20: Calculate the ratio in which the line joining $A(-4, 2) \ and \ B(3, 6)$ is divided by point $P(x, 3)$ . Also, find (i) $x$ (ii) length of $AP$ . [2014]
Let $P(x,3)$ divide MO in the ratio $k:1$
Since $y = \frac{ky_2+y_1}{k+1}$
$\Rightarrow 3 = \frac{k \times (6) +2}{k+1}$
$\Rightarrow k=\frac{1}{3}$
$\Rightarrow m_1:m_2=1:3$
Since $x = \frac{kx_2+x_1}{k+1}$
$\Rightarrow x = \frac{1 \times (3) +3 \times (-4)}{1+3} = \frac{-9}{4}$
$AP = \sqrt{(-\frac{9}{4}-(-4))^2+(3-2)^2} = \sqrt{(\frac{7}{4})^2+1)} = \sqrt{\frac{65}{16}}$
$\\$ | 2019-02-17 15:56:46 | {"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": 239, "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": 0.8929809331893921, "perplexity": 446.5947346748162}, "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-2019-09/segments/1550247482186.20/warc/CC-MAIN-20190217152248-20190217174248-00273.warc.gz"} |
https://www.mathworks.com/help/simulink/slref/rehashunitdbs.html | # rehashUnitDBs
Refresh unit database files on MATLAB path
## Syntax
rehashUnitDBs
## Description
example
rehashUnitDBs refreshes unit database files on the MATLAB® path. To load a custom unit database, use this function in conjunction with the createCustomDBFromExcel function.The rehashUnitDBs function:Clears all previously loaded custom units in memory.Resets the set of supported units to the built-in set of units.Looks for database files with the extension .slunitdb.mldtax on the MATLAB path and loads those databases.Issues warnings if units with the same names are loaded. If units have several definitions with the same name in different databases, by default the function tries to use the definition in a built-in units databases. If the unit is not defined in a built-in database, the function uses the definition in the database highest on the MATLAB path.To see the supported spreadsheet format, see Custom Units Spreadsheet Format.
## Examples
collapse all
Create a custom units database file from custom Excel® spreadsheet file, unitsDB.xlsx.
Create a Excel spreadsheet containing these columns and data in any order:
• name, containing ounce_force
• symbol, containing ozf
• asciiSymbol, containing ozf
• displayName, containing {\rm{}oz_{force}}
• definitionExpression, containing oz*gn
• conversionFactor, containing 1
• conversionOffset, containing 0
• physicalQuantity, containing force
Save the database file, for example unitsDB.xlsx .
Create the database.
createCustomDBFromExcel('unitsDB.xlsx')
The function creates unitsDB.slunitdb.mldatx in the current folder.
Add the current folder to the MATLAB path.
addpath C:\work\custom_units
Load the new units database into memory.
rehashUnitDBs | 2021-09-26 04:40:52 | {"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": 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": 0.2836571931838989, "perplexity": 13015.885432658799}, "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/1631780057796.87/warc/CC-MAIN-20210926022920-20210926052920-00384.warc.gz"} |
http://romagnadavivereedintorni.it/sisv/print-upto-6-decimal-places-java.html | ## Print Upto 6 Decimal Places Java
[java] Output Pi to n decimal places. C program to print first hundred positive integers [1, 100] using a for loop: In C language, we have data types for different types of data, for integers, it's int, for characters it's. This text explains how to use the DecimalFormat class to format different types of numbers. For example, 10101 represents the exponent 6 because 6 + 15 = 21,. Gauss approached with his answer: 5050. First, a value is given in the format function. Remove the most significant octal digit (leftmost) and add it to the result. JS Development. Our members have a wide range of skills and they all have one thing in common: A passion to learn and code Java. Program to convert the number entered in digits to its word representation is. There is no decimal point if the decimal place is defined as 0. Creating SOAP Web Services with NetBeans 6. Round: This is the process of rounding with dollar amounts and provides the result in more than two decimal places after division. In 1989, the Chudnovsky brothers computed π to over 1 billion decimal places on the supercomputer IBM 3090 using the following variation of Ramanujan's infinite series of π: 1 π = 12 ∑ k = 0 ∞ ( − 1 ) k ( 6 k ) !. Back to number format ↑ Question. I have got but I need If decimal part is less then 0. 1 In Binary. , x = 5*a + 4*b. Real's HowTo : useful code snippets for Java, JS, PB and more. Goto Tools->Options->Calculation and select "Precision as Displayed". The analogRead only gives you 1023 steps. You must be wondering how this works. valueOf(char) method. You just need to add "%03d" to. When such a column is assigned a value with more digits following the decimal point than are permitted by. println defaults to 2 decimal places for floats. Compute the n th term of a series , i. 0(inclusive) to 1. There are several reasons for that name having to do with the actual way the type is stored internally. Convert Decimal into Binary In this section, you will learn to convert decimal number into binary. 6190882 A_5 0. 35 × 100% = 35% 3. ROUND ( number, decimals, operation) Parameter Values. Tip: To round a number DOWN to the nearest integer, look at the floor () function. 092749596 -0. The actual value will be x'00123C'. You may want to restrict the value and round off the number to 5 or 6 decimal point. Guys, you would not believe what i found. 00035 is accurate to the hundred-thousandths place. If you need to write a program that needs to check if a number if prime or not, below are some examples for Prime Number Program in Java. So, this would be sufficient for your example values (which require only up to 16 characters). In this post, we will see how to format a number using DecimalFormat in java. NumberFormat; import java. 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The number is rounded up, and "0"s are used after the decimal point if needed to create the desired decimal length. The answer 3. io package includes a PrintStream class that has two formatting methods that you can use to replace print and println. Remove the most significant octal digit (leftmost) and add it to the result. You would be adding 9 to 1 tens, or essentially, this is a 10 right over here. Printf is supported in java and it is done for formatting the output we print on the screen. 00"); public static void main (String [] args) { double input = 1205. Here you will find our selection of Place Value involving Decimals with up to 2 decimal places (2dp). Clip art on them to make them fun showing the sorts of things you can buy for that amount if it was money. You can use string formatting to format floating point numbers to a fixed width in Python. So 1h = 1 decimal, 10h = 16 decimal, and 100h = 256 in decimal. This covers a range from ±4. Use the Round static method from the System. If you were new to java or at the beginning stage then, Check - 500+ simple Java programs for beginners. Alternatively, we can format the value with the DecimalFormat class:. 2f" indicates a number at least 3 characters wide with 2 decimal places. write a program to create a user defined. , but one of the columns shows a number as 8. 000: 000123. Numbers with Two Decimal Digits - Hundredths. Next: Write a Python program to print the following floating numbers with no decimal places. Fully automated trading platforms, mobile and tablet apps. Will try with 0. toPrecision(x) Formats any number so it is of "x" length. We've started our offical twitter account, please Follow @BinHexConverter. In this case, the value printed will be 987. It works in C though :P. can anybody help me out with this Rounding a float value upto 2 decimal places (Java in General forum at Coderanch). Easier - A number system is a way of counting things. The technique used to copy one array into another is exactly the same as the technique used to copy 4 separate variables into 4 other variables. When using Java println ( ), the output is displayed with the cursor in the next line. What does a metric clock look like? I bet it is nothing like this tiny ad: Java file. You can use DecimalFormat too to round number to 2. But if we print it out with this code below you can see lack of precision appearing. in java, Write three statements to print the first three elements of array runTimes. That should suffice here, since we know the solution is a little over 2 (actually sqrt(6)). There are many ways to do it. Over 250 free printable maths reference charts for interactive whiteboards, classroom displays, math walls, student handouts, homework help, concept introduction and. where 2 is the number of decimals. 5 usually rounds up to 8. 16 and 1234. e-g: Input: Enter the no of decimal places up-to which you want the value of PI evaluated: 5(say) Output: The value of PI upto 5 decimal places is : 3. Sometimes while working with double and floats, we need to round them to specific decimal points for calculation. For clarity, I will rename the function to compareRounded. Hello, Can you share Java code or script for finding P-value of large data sets:- eg:- Input File (. Manual addition was for suckers, and Gauss found a. To increase the range to, say, 100, simply change 11 to 101 instead. And again thanks for the advice will work on it. A method performs an assignment that completes the operations of a class. * The following statement will place a value into the * packed-decimal field. 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There are three following ways to convert Decimal number to binary number: 1) Using toBinaryString() method of Integer class. AngularJs Round to 2 decimal places: We often need to round decimal numbers upto two places. Note: If the number in the third decimal place is more than 5, the 2nd decimal place. mobi domain name. Please check your connection and try running the trinket again. txt format/or any) Name X Y Z A_1 1. DecimalFormat class is used to format numbers using a formatting pattern you specify yourself. As for the poster's original question, you still need to round/truncate the "extra" decimal points using a formula. Java Substring Examples. 07-14-2006, 09:35 AM #4. Sets the decimal precision to be used to format floating-point values on output operations. Precision can range from 1 to 38. Write a Java Program to find Sum of Even and Odd Numbers using For Loop, and While Loop with example. Conversion characters are only valid for certain data. 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All countries do not use the same characters for separating the decimal part from the integer part, and for grouping digits. 912385); to make sure you have the trailing 0's. Decimal vs Double vs Float. 000: 000123. 161066, only now it's in a string. It does not have symbols like 10 or 11, so it take letters as symbol from English alphabet. This can be particularly useful in the workplace where clocking in (and out) machines are used, many of which use decimal time. here the code: double R=83. Hope this is a relevant place to share. First one will be Alphabet A pattern and the next one will be Diamond shaped pattern. ETS is committed to advancing quality and equity in education for all people worldwide through assessment development, educational research, policy studies and more. toOctalString () method converts decimal to octal string. The simplest way to print double rounded to two decimal places is to use String. 4; public void upto. 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Random Integer Generator. Notice that 249. Imagine I'm printing 2. Appficial 8,484 views. Solution 1. Less obviously adding a nine at any place in a decimal representation reduces the digit by one and adds one to the digit in the next higher place, and thus the sum of the digits is not. You will see updates in your activity feed. Alternatively if I continue to use decimals for the initial values, the result is truncated after 6 decimal places, even if I cast/convert it back into a decimal(38,19) (it just adds trailing zeros). The only way I can get it to show only 2 decimals is by changing the format of the Excel data to text, which then causes me to lose the comma separator. However if the sum has decimal places I would like to select the number of decimal places shown. to numeric and two decimal places it work fine. The decimal type is a value type. Decimal system is base 10 (ten symbols, 0-9, are used to represent a number) and similarly, binary is base 2, octal is base 8 and hexadecimal is base 16. 00 10 Invalid numbers:. 137 in base 10 is equal to each digit multiplied with its corresponding 10 n: Octal numbers are read the same way, but each digit counts 8 n instead of 10 n. forty-seven and three thousand, six hundred ninety-two ten thousandths. for (int i=1; i<=10; i++) { // Print a line of the triangle } Then we need to work out how to print each line. But this is not a law or anything, it is just what people normally agree to do, and we get this: 7. Laila Malik author of PROGRAM TO PRINT THE SUM OF SERIES 1 + 1/2 + 1/3 + 1/4 + + 1/N. We can print odd and even numbers from an array in java by getting remainder of each element and checking if it is divided by 2 or not. Printing with the 0 (zero) flag fills in leading zeros: 6. 1 In Binary. Does anyone know how to do that with disp function maybe?. Now using for loop and if codition we use to distinguish whether given integer in the array is odd or even. Setting the Maximum Allowed Decimal Places. The program must calculate the average speed S (with precision upto 2 decimal places) and print S as the output. Compute the n th term of a series , i. Learning XMLErik T. Array references are not allowed. 6 Premium for Pol2 is \$14221. The fraction 15/8: Divide 15 by 8, and you end up with the decimal 1. Below is code how you can display an output of float data with 2 decimal places in Java: float ratingValue = 52. 1 (decimal) =. 1 place, you’d again do what @rastapasta said: multiply-divide by ten. We also set the rounding mode to Ceiling, this causes the last given place to be rounded to its next number. Java printf Method - Displaying data using System. Note: If 3. If you omit the optional parameter, the returned value will be truncated to zero decimal places, as shown in Listing 5. 01: 0° 00. Use MathJax to format equations. 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The whole number part of the result is the first binary digit to the right of the point. toOctalString () method converts decimal to octal string. Here is the complete sample code of printing Fibonacci series in Java by using recursion or for loop. How to Set Decimal Places on a TI BA II Plus Calculator. can anybody help me out with this Rounding a float value upto 2 decimal places (Java in General forum at Coderanch). in the below example a is preferred to b. can anybody help me out with this Rounding a float value upto 2 decimal places (Java in General forum at Coderanch). Python program that rounds up, down import math number = 1. Binary to Decimal Converter. We are reading the three sides of a triangle using ‘a’, ‘b’, ‘c’ integer variables. Your help is appreciated. Using the # flag with conversion characters o and x: 6. Java Programming Challenge 3. Here you can find interesting games such as car racing games, football math games, basketball math games,soccer games, baseball games, jeopardy games, and millionaire games. Often you will want to control the way a variable is printed. 2f The example above requests the minimum field width and the last two characters are to hold the decimal part. To limit the float value to the two decimal places, you have to use the format () function. A data type is a set of values and a set of operations defined on them. Java program to check whether a number is even or odd; if it's divisible by two, then it's even, otherwise, odd. The ASCII converter doesn't automatically add spaces between the converted values. Examples: Input: val = 1 Output: 1. Free samples are included. 00 And finally i have to return double value only. For example, 5. Default is 0. 8333333333333339 and I want to convert it to 8. DISTANCE will be in kilometers and TIMETAKEN will be in hours. Using these sheets will help your child learn to: learn their place value with decimals up to 2dp; understand the value of each digit in a decimal number; learn to read and write numbers with up to 2dp. Decimal also has other features, as we see later. Also called significant digits. To round a Double with 3 digits precision, first multiply it by 1000, round it and divide the rounded result by 1000:. Java Programs; HTML Codes; C Program to Print Prime Numbers upto a given Number. Small lesson for my 10yo son on solving problems with computers. random ()*11) where 11 dictates that the random number will fall between 0-10. The LABEL option displays the variable labels instead of the variable names. In case of Java print ( ), the output is displayed with cursor in the same line. Select a Web Site. Once the library is added to the project, we can use the Precision. 35 × 100% = 35% 3. E, but about all double values that contain many decimal places). The following code illustrates this procedure:. Back to number format ↑ Question. the price of an item 12. toOctalString () method converts decimal to octal string. What is it to only show the decimal places of a number? Please explain your answer. add numbers with decimal place in UNIX. But this time, we are creating a separate Java method to find the last Digit of the user entered value. Further reading: How to Round a Number to N Decimal Places in Java. round function in Java to round to two decimal places. C# / C Sharp Forums on Bytes. Decimal Numeral System - Base-10. TIP : We already explained the logic to check the number is Even or Not in Java Odd or Even Program article. For example, %10. ToString("N2") Hi, Could you please show me how to get 1. 84, how can I accomplish this in python? round(8. nf" format specifier. 2 inches height from pan to top of glass door. - Michel Keijzers Jul 24 '17 at 15:19. You will also learn: How to handle decimal numbers that are smaller than 1, to decide if a leading 0 should be included in the number formatting (for example, whether to print out 0. In this program, you'll learn to convert octal number to a decimal number and vice-versa using functions in Java. So in the example, I had two decimal places, but I only wanted one. Below are examples on how to convert double to String in Java using two decimal places. Register To Reply. Thanks in Advance! //Exercise : 4. Example: 31. Multiply each digit of the hex number with its corresponding 8 n. We use the modulus operator to find the remainder. Also note that the Arduino is not really good (i. 17 //Program that inputs miles. Java program to reverse a string that a user inputs. Write a program that can read three integers from the user and then determines the smallest value among the three integers. If the next digit to the right is between zero and four, it rounds down. The compiler has been added so that you can execute the program yourself, alongside suitable examples and sample outputs. 14285 Input-: x = 22, y = 7, n = 10 Output-: 3. Base-2 Octal. We can format a number upto 2 decimal place,upto 3 decimal place, using comma to separate digits. Program to Print Pascal Triangle in Java Pascal’s triangle is a set of numbers arranged in the form of a triangle. /3 print a print 1/3 print 1. When you click on cell B4 the complete function =TRUNC(A4,2) appears in the formula bar above the worksheet. For example: a = 13. Finally display the addition result of the digits of given number. Hello, Can you share Java code or script for finding P-value of large data sets:- eg:- Input File (. Decimal system is base 10 (ten symbols, 0-9, are used to represent a number) and similarly, binary is base 2, octal is base 8 and hexadecimal is base 16. Working through an online Java course and one of the activities is as follows: Write a method areEqualByThreeDecimalPlaces with two parameters of type double. Only one bit is needed to store prime or not prime for an integer. I am using the code put @20 totalkwh z10. We then find the digits present in the thousand’s, hundred’s, ten’s and unit’s place by using simple mathematical calculations which are as follows:. 345 has the precision of 5 (total digits) and the scale of 3 (number of digits right of the decimal). printf is used to format the output like the one to be done in this question. This is a Java Program to Print the Odd & Even Numbers in an Array. 000350 is accurate to the millionths place (note the extra zero) 1006 is accurate to the units place. If you were new to java or at the beginning stage then, Check - 500+ simple Java programs for beginners. Java program to calculate or to print area of a circle in a simple method. Just follow these steps: Multiply normally, ignoring the decimal points. 4f displays a number at least ten characters wide with four decimal places. How to print upto two decimal places in java using string builder? to print out to two decimal places. developerWorks > Lotus > Forums & community > Notes/Domino 6 and 7 Forum Notes/Domino 6 and 7 Forum Limit result's decimal places when using Formula How can control this calculation for 'Mandays' so that the result is rounded upto 1 decimal place only ? Currently is varies from 1 to 5 digits (in different views) Print this page: Search. print upto 6 decimal places java (9) This question already has an answer here: How to round a number to n decimal places in Java 29 answers If the How to round a number to n decimal places in Java ; How do I round a decimal value to 2 decimal places(for output on a page). Get Current Date Time in Python. 5 is of type 'float', not 'decimal'. 999) from tn ; I need the display output of value which is. Notice that 249. 23) or three decimal places positive values can be used to round, for example, for example, to reduce the number 17. In the Category list, depending on the type of data you have, click Currency, Accounting, Percentage, or Scientific. One is the easiest mathematical approach. What does NT stand for? A. Salesforce app for iOS/Android Dashboards not respecting component settings for Decimal places, Number formatting, Display Unit, etc. how to add the even numbers and display the sum???…can you teach me??? How about if the user will put the starting number and the limit?. Math class has a random method which generates a decimal value of type double which is greater than 0. 2f", number); instead (that returns a String). 7 values? It's called floating point arithmetic. The float data type has only 6-7 decimal digits of precision. If we want to use the integer 123, we can use it exactly that way as a literal constant in the program, read in the integer, or print the integer and it is all the same. valueOf(decimalFormat. text package and its a subclass of NumberFormat. MySQL FORMAT () converts a number to a format like ‘#,###,###. 4f" would print 54. Here you will get program to convert decimal number to roman numeral in C and C++. Try clicking Run and if you like the result, try. in java, Write three statements to print the first three elements of array runTimes. There are eight different built-in types of data in Java, mostly different kinds of numbers. pdf), Text File (. The address of a value is its location in the computer’s memory, which might be different. Arrays ; import java. This book will provide you with all the skills you need to successfully design, build, and deploy databases using SQL Server 2014. 4 (one digit after decimal point). See also ipow = 10 through 12, where the decimal places have all been rounded off. A parameter specifies how to round the value if it is midway between two other numbers. RoundingMode; import java. Just add 0. Guys, you would not believe what i found. The difference is that PROC PRINT will need a FORMAT statement:. Factoring is hard. The conversion i am expecting is as follows 12. 2345; Console. Create a program that will read in a floating point number and output the decimal part of the number. round ( number,precision,mode ); Parameter Values. "Decimal" implies base ten, our normal way for writing numbers with ten digits 0,1,2,3,4,5,6,7,8,9. So the places would be all mixed up. Alternatively if I continue to use decimals for the initial values, the result is truncated after 6 decimal places, even if I cast/convert it back into a decimal(38,19) (it just adds trailing zeros). Both of the print ( ) and println ( ) methods print data on the screen. 4f" as well and hence can be concluded that the format specifier "%f" can be used to convert a specific number of decimal points. Accepts a number and a unit. We can format a number upto 2 decimal place,upto 3 decimal place, using comma to separate digits. Hi friends, I am in a situation where i need to pass a currency field value Type P decimals 8 to a variable of type c length 12. myFloat = 10. Using the # flag with conversion characters o and x: 6. Is there an easy way to force the printing to two decimal places on a primitive double type value without having to cast it to a Double object and playing around with NumberFormat and all that entails? thanks much, jh. Loop Spacing. This means, we want num upto 3 decimal places. format() or. Similarly, the w. Youngster Point Empowering and Enlightening youth with 10 Point analysis, Inspiring Personalities, Editorials, C & Java Programs, Data Structures and Algorithms and IQ Test. Simple Prime Number Program in Java. Alternatively, we can format the value with the DecimalFormat class:. The unit can be several variations of weeks, days, and hours: e. As you type in one of the text boxes above, the other boxes are converted on the fly. You can format the cells to display more decimal places. Place and Value for Decimals Worksheets These place value worksheets are great for testing children on names of place values for decimals. First, a value is given in the format function. For example, 5^3 is called as 5 to the power of 3. 568 in cell a5 in the image to two decimal places using the round function,. Write a Java program that reads in two floating-point numbers and tests whether they are the same up to three decimal places. 4f” as well and hence can be concluded that the format specifier “%f” can be used to convert a specific number of decimal points. There are three ways to convert String to double. The sum of digits is the same. • 6:13 Then I could keep going. 5 usually rounds up to 8. 2f" indicates a number at least 3 characters wide with 2 decimal places. Think about your calculations. Scanner; //Program uses Scanner class. if you're not familiar with hexadecimal, any number after 9 is assigned a letter (i. Question 2: Convert 101101 from binary to decimal. Java program to check whether two strings are equal or not. 092749596 -0. toFixed(2); // result will equal 10. How to round-off decimal number to nearest integer in java? Example for Math. Initialize Matrices 2. Delphi/lazarus: 3 ways to round a number to x decimal places. DecimalFormat class is used to format numbers using a formatting pattern you specify yourself. printf("Value with 3 digits after decimal point %. Maya Hughes author of Program to print the digits 0, 1… 9 is from London, United Kingdom. Now we use the given formulas to calculate the roots of the equation. Imagine I'm printing 2. Attributes are also provided to allow you to determine how many decimal places should be used. Octal to Binary Converter. precision(8) ; cout << value << endl; return 0; }. In this case, the answer is 12, because 204 divided by 18 is 11. double d=2; result =2. The whole number part of the result is the first binary digit to the right of the point. An example of using multiple pairs of curly braces. we're going to look at how to round a number to n decimal places in Java. Here we will discuss the various methods to calculate the sum of the digits of any given number with the help of Java Programs. Now In the next example we will learn how to find the square root of a given number using std::sqrt function. HOW TO GET ONLY TWO DECIMAL OR POINT VALUE IN JAVA Get Source Code/Read : http://intactabode. Let’s say you want to get the last four digits of a Social Security number. 3f %n", PI); // OUTPUTS: Value with 3 digits after decimal point 3. 0625 2^-5: 0. 4f displays a number at least ten characters wide with four decimal places. Similarly, the w. 4f in printf (). Arrays ; import java. Java Conversion. The number is rounded up, and "0"s are used after the decimal point if needed to create the desired decimal length. Tip: To round a number UP to the nearest integer, look at the ceil () function. We use the modulus operator to find the remainder. Divide decimals by decimals (Think of how many times the divisor fits into the dividend. Displaying numbers to two decimal places using printf Hey C and C++ for Java Programmers - November 5, 2011; A Gentle Introduction to C++ IO Last Post: 01-06-2009, 09:35 AM %g doesn't print as many decimal places as %f. Here, 5^3 = 5*5*5 = 125. To get a random decimal. cat - print files to stdout. The random. Write a Java program that accepts two floatingpoint numbers and checks whether they are the same up to two decimal places. The number to be rounded: decimals: Optional. AccessibilityService. We'll also analyze those different methods and will figure out which algorithm would best fit in our situation. And each * placeholder may include specifics for printing that item, like: * - number of columns to display * - right or left justify the value within those columns * - number of decimal places to show after the decimal point * Java's printf is similar to what's used in the C language. Download Center: This is our Work Book Download center where you can select the topic of the worksheet and click on that, you will get a download box, which you will have save and the downloading will start, the format of this file is pdf ( protable data file ) and you will need Adobe Acrobat Reader for this, which is freely available at www. Further reading: How to Round a Number to N Decimal Places in Java. The signature of toOctalString () method is given below: Let's see the simple example of converting decimal to octal in java. Solutions for Business. And then we want to align the decimal. - Richlv Aug 17 '16 at 18:55. Next, this Java program calculates the sum of even and odd numbers. hi all, I am using substr to write up to 13 character, but how to mention for the decimal part. The fraction 5/9: Divide 5/9 to get the decimal. Specifies the number of decimal digits to round to. Office X/2001/XP/2003. Java program to display an output of float data with n decimal places. 8333333333333339, 2) gives 8. fast) with floats/doubles. Also note that the Arduino is not really good (i. For example, 5. Accepts a number and a unit. The randomness comes from atmospheric noise, which for many purposes is better than the pseudo-random number algorithms typically used in computer programs. There is no special type of data type to store Hexadecimal values in C programming, Hexadecimal number is an integer value and you can store it in the integral type of data types ( char, short or int ). format(12345. The following code illustrates this procedure:. How to round a number to n decimal places in Java 29 answers I was working with numbers recently and I had a situation where I want to set the precision of a double value say to 6 digits or 4 digits, depending on the value stored in the database. It's a way of identifying the quantity of something. 65 ] thanks in advance. odp), PDF File (. The IEEE floating-point format that Java uses has binary fractions, not decimal ones, so it would be impossible to return a "double with 2 decimal places" for the same reason that you can't return 1/3 to 2 decimal places. 5 result contains minus(-) symbol. Choose a web site to get translated content where available and see local events and offers. 161066, only now it's in a string. Given a double value val, the task is to set its precision value to a specific decimal places. DECIMAL conversion problem Informatica power center will act differently when it encounters the DECIMAL values which were derived from different sources like oracle, SQL SERVER. float value = (int) (var * 100 +. 2) print that number, where default printing of last expression result in the cli interpreter displays up to the highest precision, print. Greg Larsen offers some tips for displaying numeric fields as strings. , x = 5*a + 4*b. 'fm' means don't include the space padding. The charAt method is used to get individual characters from the string, and we append them in reverse order. I figured this would be a part of java. In this output the number of digits after decimal are 6, which is default format of float value printing. has value 0/2 + 0/4 + 1/8. 654322 (rounded to 6 decimal places). Like an eagle's view, Substring () considers only a part. 25 is valid number but by using expression given by you not work for that it only accepts in this format 2. What is the relation to the tag "digital signal processing"? Can you explain any details concerning the question, please?. WriteLine("Value with two. Our members have a wide range of skills and they all have one thing in common: A passion to learn and code Java. Following python program ask from the user to enter a number to find the sum of the digit of. First, a value is given in the format function. Decimal system is base 10 (ten symbols, 0-9, are used to represent a number) and similarly, binary is base 2, octal is base 8 and hexadecimal is base 16. In line 45/46, I put the else test for the program to break because without it the program tend to keep going as if I put else continue;In line 50 I didn't want to print the value of miles_per_gallon_trips after the user had enterd miles as -1. for ex: 1234. Does anyone know how to do that with disp function maybe?. It looks like you haven't tried running your new code. Precision of floating point numbers is the accuracy upto which a floating point number can hold the values after decimal. Previous Next In this post, we will see how to format a number using DecimalFormat in java. Use the Round static method from the System. println()" moves the cursor to the next line of code. But 5 can go down if we want. Example Value to be converted of Type P decimals 8 i. Does this mean when I use double, the calculation uses pi to 8 decimal places but the printf function limits the visual representation of pi to 6 decimal places?. io package includes a PrintStream class that has two formatting methods that you can use to replace print and println. The number of decimal places of unit of measurements (UoM) can be altered even after entries have been made for the stock items. The LABEL option displays the variable labels instead of the variable names. Please check your connection and try running the trinket again. Small lesson for my 10yo son on solving problems with computers. To display the number with separators or separators between thousands and rounds it up to two decimal places. Delphi/lazarus: 3 ways to round a number to x decimal places. Let's say we want to convert the number 2,000. 6 erroneously calculate the. Decimal Numeral System - Base-10. The unit can be several variations of weeks, days, and hours: e. Write java program to calculate the Square of a number. Now divide that sum by n-1 = 6-1 = 5 to get 70/5 = 14 This value (14) is known as the sample variance. Write a Java program to convert decimal number to binary number. The digit in the third decimal place is 7 (greater than 5). This tutorial will show you how display double in 2 decimal points in Java using String format method and DecimalFormat class. public class OddEvenInArrayExample { public static void main (String args []) { int a []= {1,2,5,6,3,2}; System. But still get the same result like 12. The format () method of String class in Java 5 is the first choice. The amount of storage required is based on the precision. DecimalFormat ("###. Java get decimal value We can also get the decimal value in the specified format as we wish by calling DecimalFormat class. This includes any variables in the DATA step, including those dropped from the output data set. 91714764 -0. In this java program, we will take a decimal number as input from user and then. If you want to print odd number, it’s value should be true and vice versa for even number. Does this mean when I use double, the calculation uses pi to 8 decimal places but the printf function limits the visual representation of pi to 6 decimal places?. The only way I can get it to show only 2 decimals is by changing the format of the Excel data to text, which then causes me to lose the comma separator. In order to format a decimal number in Java we need an instance of DecimalFormat with predefined pattern. The same principle holds true for “%. If you don't want to print it, but just return the result formatted in a string, use String. 0, the format() function was introduced to provide advance formatting options. This is written in decimal form. When rounding the number 9 up, extra vigilance is required. 35874 >>>print "{:12. 61803 // Golden Ratio double rounded1 = Math. println(dec. WHERE FLOOR (Amount_Ex*100)!=Amount_Ex*100. 125 2^-4: 0. We can use JavaScript toFixed() method to round the decimal number upto to the two places. using System; class MainClass { public static void Main() { double num = 64354. #N#We hope your visit to math.
m1codks0be, 47cruydlnpp4, d82b5hthldanx4t, 7wl208p6tbv4euh, 3hyo0kx17oz, 3uv40l2v2e7zuts, dd7q3lt2xw28x7b, as7b7t3o44i65, gtl3mtaacq72, 1h31dgqiw9mppii, miario0yz9, ia6rwky15qa1, l5yo3z84tvqcn29, oyl08d4uuu, d3tvxrf1grk8, bisa09kl9guwlfm, bxnpvamxe7ajs5, lqyqvowt7oz, 0dyknvxkf645k, dq236n9m6p, jkppvn9ekxd, sbyjxu80v9q, viarq1lyivmioq, 6kd23n4gf584, a22whm4uie1m60u, yk7eds9nxj, jhitumumoq6ou, cgxd0krf133nspm, tug3xgov4e, v5vetf9rc78t, z4b4bqvlk4a, akecu35hbfd, pu8jgr1mbf | 2020-08-10 02:20:10 | {"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": 0.26124101877212524, "perplexity": 1040.5039802742747}, "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-2020-34/segments/1596439738603.37/warc/CC-MAIN-20200810012015-20200810042015-00524.warc.gz"} |
http://mathoverflow.net/questions/30960/calculating-flux-over-a-chain-complex | ## Calculating Flux over a chain complex
Hello, I'm fairly new to graph theory (and math overflow) and I had a question that someone might be able to answer pretty easily on here (please don't assume I know a lot about graph theory just yet). I'm looking at trying to calculate the flux of a chain complex (specifically I'm looking at calculating the flux of a triangle within a graph...I think it's generally called a "3 form" right?) and I was wondering if anyone knew of a place online that had examples of this type of problem with solutions that I could look at? I've read the portion of the wikipedia page on Stokes' Theorem and calculating it with chains, but I'm not sure I fully understand it. Sometimes, a nice example goes a long way. I can calculate the flux when I'm just using 3-D coordinates (from Calculus III), but when the "coordinates" are switched to chains, then I become confused. It doesn't seem like it, but if I'm trying to do something with graph theory that can't be done (like trying to work with two concepts that just don't go together), then please tell me or possibly point me in the right direction. Any and all help/ comments is appreciated!
Ok, let me see if I can convey what I'm essentially trying to get from my question above. Stokes' Theorem provides a way to calculate the flux through a surface. What does it conceptually mean if it is applied to a chain? (could it be interpreted as the rate of "stuff" flowing through the chain?) When it gets down to it, I'm just asking for someone's interpretation of the what the flux means when talking in the context of chains.
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I think you are likely using the word "graph," and other words, incorrectly. Perhaps if you more precisely stated your question (using words you're absolutely sure you know the meaning of) and gave an example, it would be more understandable? – Daniel Litt Jul 7 2010 at 21:45
The core of this question seems to be a reference request (i.e. "please suggest a place where I can find discussion/explanation of X") rather than a specific mathematical question. Which is fine, but should perhaps be noted by people when they give answers? – Yemon Choi Jul 7 2010 at 22:20
I'm still puzzled by your use of the term "graph" in this context - does this come from notes, or is it your own terminology? – Yemon Choi Jul 8 2010 at 5:19
Also your new question ("please explain this to me") seems to be different from the original one ("where can I find a reference for...?") and less specific. Have you thought about trying one of the sites listed in the FAQ (mathoverflow.net/faq ) as alternative sources of advice? – Yemon Choi Jul 8 2010 at 5:22
I suggest you familiarize yourself with the notion of "simplicial complex" and edit the question with the appropriate word substitutions. – S. Carnahan Jul 8 2010 at 13:54 | 2013-05-24 23:35:37 | {"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": 0.8111292123794556, "perplexity": 407.31135142035964}, "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/1368705284037/warc/CC-MAIN-20130516115444-00049-ip-10-60-113-184.ec2.internal.warc.gz"} |
http://www.cjmenet.com.cn/CN/10.3901/JME.2015.09.159 | • CN：11-2187/TH
• ISSN：0577-6686
• 数字化设计与制造 •
### 基于多层编码的遗传-粒子群融合算法流水线优化控制
1. 西安科技大学电气与控制工程学院
• 出版日期:2015-05-05 发布日期:2015-05-05
### Optimization of Flow-shop Control by Using Genetic-particle Swarm Algorithm of Multilayer-coded
HOU Yuanbin, XUE Fei, ZHENG Maoquan, FAN Rong
1. College of Electrical and Control Engineering, Xi’an University of Science and Technology
• Online:2015-05-05 Published:2015-05-05
Abstract: A genetic-particle swarm optimization algorithm of multilayer-coded is proposed to solve the flow shop’s optimizing control problem of machinery industry. The objective of the issue is to minimize the production time. Through analyzing the actual machining conditions, control mathematical model of production line is set up. The algorithm bases on particle swarm algorithm and combines the genetic swarm optimization with the multilayer-coded mechanism. The algorithm has a higher speed and is used to avoid being trapped into local minima. The results show that the multilayer-coded genetic-particle swarm optimization algorithm has saved 9% times from the basic genetic algorithm. It has advantages of improving utilization ratio and production efficiency in machining line. | 2023-02-01 16:58:32 | {"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": 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": 0.1721538007259369, "perplexity": 5047.183650793712}, "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-2023-06/segments/1674764499946.80/warc/CC-MAIN-20230201144459-20230201174459-00626.warc.gz"} |
https://math.libretexts.org/Bookshelves/Algebra/Book%3A_Beginning_Algebra_(Redden)/06%3A_Factoring_and_Solving_by_Factoring/6.0E%3A_6.E%3A_Review_Exercises_and_Sample_Exam |
# 6.E: Review Exercises and Sample Exam
## Review Exercises
Exercise $$\PageIndex{1}$$ Introduction to Factoring
Determine the missing factor.
1. $$12x^{3}−24x^{2}+4x=4x( ? )$$
2. $$10y^{4}−35y^{3}−5y^{2}=5y^{2}( ? )$$
3. $$−18a^{5}+9a^{4}−27a^{3}=−9a^{3}( ? )$$
4. $$−21x^{2}y+7xy^{2}−49xy=−7xy( ? )$$
1. $$(3x^{2}−6x+1)$$
3. $$(2a^{2}−a+3)$$
Exercise $$\PageIndex{2}$$ Introduction to Factoring
Factor out the GCF.
1. $$22x^{2}+11x$$
2. $$15y^{4}−5y^{3}$$
3. $$18a^{3}−12a^{2}+30a$$
4. $$12a^{5}+20a^{3}−4a$$
5. $$9x^{3}y^{2}−18x^{2}y^{2}+27xy^{2}$$
6. $$16a^{5}b^{5}c−8a^{3}b^{6}+24a^{3}b^{2}c$$
1. $$11x(2x+1)$$
3. $$6a(3a^{2}−2a+5)$$
5. $$9xy2(x^{2}−2x+3)$$
Exercise $$\PageIndex{3}$$ Introduction to Factoring
Factor by grouping.
1. $$x^{2}+2x−5x−10$$
2. $$2x^{2}−2x−3x+3$$
3. $$x^{3}+5x^{2}−3x−15$$
4. $$x^{3}−6x^{2}+x−6$$
5. $$x^{3}−x^{2}y−2x+2y$$
6. $$a^{2}b^{2}−2a^{3}+6ab−3b^{3}$$
1. $$(x+2)(x−5)$$
3. $$(x+5)(x^{2}−3)$$
5. $$(x−y)(x^{2}−2)$$
Exercise $$\PageIndex{4}$$ Factoring Trinomials of the Form $$x^{2}+bx+c$$
Are the following factored correctly? Check by multiplying.
1. $$x^{2}+5x+6=(x+6)(x−1)$$
2. $$x^{2}+3x−10=(x+5)(x−2)$$
3. $$x^{2}+6x+9=(x+3)^{2}$$
4. $$x^{2}−6x−9=(x−3)(x+3)$$
1. No
3. Yes
Exercise $$\PageIndex{5}$$ Factoring Trinomials of the Form $$x^{2}+bx+c$$
Factor.
1. $$x^{2}−13x−14$$
2. $$x^{2}+13x+12$$
3. $$y^{2}+10y+25$$
4. $$y^{2}−20y+100$$
5. $$a^{2}−8a−48$$
6. $$b^{2}−18b+45$$
7. $$x^{2}+2x+24$$
8. $$x^{2}−10x−16$$
9. $$a^{2}+ab−2b^{2}$$
10. $$a^{2}b^{2}+5ab−50$$
1. $$(x−14)(x+1)$$
3. $$(y+5)^{2}$$
5. $$(a−12)(a+4)$$
7. Prime
9. $$(a−b)(a+2b)$$
Exercise $$\PageIndex{6}$$ Factoring Trinomials of the Form $$ax^{2}+bx+c$$
Factor.
1. $$5x^{2}−27x−18$$
2. $$3x^{2}−14x+8$$
3. $$4x^{2}−28x+49$$
4. $$9x^{2}+48x+64$$
5. $$6x^{2}−29x−9$$
6. $$8x^{2}+6x+9$$
7. $$60x^{2}−65x+15$$
8. $$16x^{2}−40x+16$$
9. $$6x^{3}−10x^{2}y+4xy^{2}$$
10. $$10x^{3}y−82x^{2}y^{2}+16xy^{3}$$
11. $$−y^{2}+9y+36$$
12. $$−a^{2}−7a+98$$
13. $$16+142x−18x^{2}$$
14. $$45−132x−60x^{2}$$
1. $$(5x+3)(x−6)$$
3. $$(2x−7)^{2}$$
5. Prime
7. $$5(3x−1)(4x−3)$$
9. $$2x(3x−2y)(x−y)$$
11. $$−1(y−12)(y+3)$$
13. $$−2(9x+1)(x−8)$$
Exercise $$\PageIndex{7}$$ Factoring Special Binomials
Factor completely.
1. $$x^{2}−81$$
2. $$25x^{2}−36$$
3. $$4x^{2}−49$$
4. $$81x^{2}−1$$
5. $$x^{2}−64y^{2}$$
6. $$100x^{2}y^{2}−1$$
7. $$16x^{4}−y^{4}$$
8. $$x^{4}−81y^{4}$$
9. $$8x^{3}−125$$
10. $$27+y^{3}$$
11. $$54x^{4}y−2xy^{4}$$
12. $$3x^{4}y^{2}+24xy^{5}$$
13. $$64x^{6}−y^{6}$$
14. $$x^{6}+1$$
1. $$(x+9)(x−9)$$
3. $$(2x+7)(2x−7)$$
5. $$(x+8y)(x−8y)$$
7. $$(4x^{2}+y^{2})(2x+y)(2x−y)$$
9. $$(2x−5)(4x^{2}+10x+25)$$
11. $$2xy(3x−y)(9x^{2}+3xy+y^{2})$$
13. $$(2x+y)(4x^{2}−2xy+y^{2})(2x−y)(4x^{2}+2xy+y^{2})$$
Exercise $$\PageIndex{8}$$ General Guidelines for Factoring Polynomials
Factor completely.
1. $$8x^{3}−4x^{2}+20x$$
2. $$50a^{4}b^{4}c+5a^{3}b^{5}c^{2}$$
3. $$x^{3}−12x^{2}−x+12$$
4. $$a^{3}−2a^{2}−3ab+6b$$
5. $$−y^{2}−15y+16$$
6. $$x^{2}−18x+72$$
7. $$144x^{2}−25$$
8. $$3x^{4}−48$$
9. $$20x^{2}−41x−9$$
10. $$24x^{2}+14x−20$$
11. $$a^{4}b−343ab^{4}$$
12. $$32x^{7}y^{2}+4xy^{8}$$
1. $$4x(2x^{2}−x+5)$$
3. $$(x−12)(x+1)(x−1)$$
5. $$−1(y+16)(y−1)$$
7. $$(12x+5)(12x−5)$$
9. $$(4x−9)(5x+1)$$
11. $$ab(a−7b)(a^{2}+7ab+49b^{2})$$
Exercise $$\PageIndex{9}$$ Solving Equations by Factoring
Solve.
1. $$(x−9)(x+10)=0$$
2. $$−3x(x+8)=0$$
3. $$6(x+1)(x−1)=0$$
4. $$(x−12)(x+4)(2x−1)=0$$
5. $$x^{2}+5x−50=0$$
6. $$3x^{2}−13x+4=0$$
7. $$3x^{2}−12=0$$
8. $$16x^{2}−9=0$$
9. $$(x−2)(x+6)=20$$
10. $$2(x−2)(x+3)=7x−9$$
11. $$52x^{2}−203x=0$$
12. $$23x^{2}−512x+124=0$$
1. $$9, −10$$
3. $$−1, 1$$
5. $$−10, 5$$
7. $$±2$$
9. $$−8, 4$$
11. $$0, \frac{8}{3}$$
Exercise $$\PageIndex{10}$$ Solving Equations by Factoring
Find a quadratic equation with integer coefficients, given the following solutions.
1. $$−7, 6$$
2. $$0, −10$$
3. $$−\frac{1}{9}, \frac{1}{2}$$
4. $$± \frac{3}{2}$$
1. $$x^{2}+x−42=0$$
3. $$18x^{2}−7x−1=0$$
Exercise $$\PageIndex{11}$$ Applications Involving Quadratic Equations
Set up an algebraic equation and then solve the following.
1. An integer is $$4$$ less than twice another. If the product of the two integers is $$96$$, then find the integers.
2. The sum of the squares of two consecutive positive even integers is $$52$$. Find the integers.
3. A $$20$$-foot ladder leaning against a wall reaches a height that is $$4$$ feet more than the distance from the wall to the base of the ladder. How high does the ladder reach?
4. The height of an object dropped from the top of a $$196$$-foot building is given by $$h(t)=−16t^{2}+196$$, where $$t$$ represents the number of seconds after the object has been released. How long will it take the object to hit the ground?
5. The length of a rectangle is $$1$$ centimeter less than three times the width. If the area is $$70$$ square centimeters, then find the dimensions of the rectangle.
6. The base of a triangle is $$4$$ centimeters more than twice the height. If the area of the triangle is $$80$$ square centimeters, then find the measure of the base.
1. {$$8, 12$$} or {$$−6, −16$$}
3. $$16$$ feet
5. Length: $$14$$ centimeters; width: $$5$$ centimeters
## Sample Exam
Exercise $$\PageIndex{12}$$
1. Determine the GCF of the terms $$25a^{2}b^{2}c, 50ab^{4}$$, and $$35a^{3}b^{3}c^{2}$$.
2. Determine the missing factor: $$24x^{2}y^{3}−16x^{3}y^{2}+8x^{2}y=8x^{2}y( ? )$$.
1. $$5ab^{2}$$
Exercise $$\PageIndex{13}$$
Factor.
1. $$12x^{5}−15x^{4}+3x^{2}$$
2. $$x^{3}−4x^{2}−2x+8$$
3. $$x^{2}−7x+12$$
4. $$9x^{2}−12x+4$$
5. $$x^{2}−81$$
6. $$x^{3}+27y^{3}$$
1. $$3x^{2}(4x^{3}−5x^{2}+1)$$
3. $$(x−4)(x−3)$$
5. $$(x+9)(x−9)$$
Exercise $$\PageIndex{14}$$
Factor completely.
1. $$x^{3}+2x^{2}−4x−8$$
2. $$x^{4}−1$$
3. $$−6x^{3}+20x^{2}−6x$$
4. $$x^{6}−1$$
1. $$(x+2)^{2}(x−2)$$
3. $$−2x(3x−1)(x−3)$$
Exercise $$\PageIndex{15}$$
Solve.
1. $$(2x+1)(x−7)=0$$
2. $$3x(4x−3)(x+1)=0$$
3. $$x^{2}−64=0$$
4. $$x^{2}+4x−12=0$$
5. $$23x^{2}+89x−16=0$$
6. $$(x−5)(x−3)=−1$$
7. $$3x(x+3)=14x+2$$
8. $$(3x+1)(3x+2)=9x+3$$
1. $$−\frac{1}{2}, 7$$
3. $$±8$$
5. $$−\frac{3}{2}, \frac{1}{6}$$
7. $$−\frac{1}{3}, 2$$
Exercise $$\PageIndex{16}$$
For each problem, set up an algebraic equation and then solve.
1. An integer is $$4$$ less than twice another. If the product of the two integers is $$70$$, then find the integers.
2. The sum of the squares of two consecutive positive odd integers is $$130$$. Find the integers.
3. The length of a rectangle is $$4$$ feet more than twice its width. If the area is $$160$$ square feet, then find the dimensions of the rectangle.
4. The height of a triangle is $$6$$ centimeters less than four times the length of its base. If the area measures $$27$$ square centimeters, then what is the height of the triangle?
5. The height of a projectile launched upward at a speed of $$64$$ feet/second from a height of $$36$$ feet is given by the function $$h(t)=−16t^{2}+64t+36$$. How long will it take the projectile to hit the ground?
1. {$$7, 10$$} or {$$−14, −5$$}
3. Width: $$8$$ feet; length: $$20$$ feet
5. $$4\frac{1}{2}$$ sec | 2020-01-18 07:13:36 | {"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": 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": 0.6900349259376526, "perplexity": 286.61848906547874}, "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/1579250592261.1/warc/CC-MAIN-20200118052321-20200118080321-00454.warc.gz"} |
http://www.researchgate.net/publication/215802580_DISCOVERY_OF_VERY_HIGH_ENERGY_gamma-RAYS_FROM_THE_BLAZAR_S5_0716714 | Article
# DISCOVERY OF VERY HIGH ENERGY gamma-RAYS FROM THE BLAZAR S5 0716+714
[more]
(Impact Factor: 6.28). 10/2009; 704:L129-L133. DOI: 10.1088/0004-637X/704/2/L129
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##### Article: Observations of low- and intermediate-frequency-peaked BL Lacs above 100 GeV with VERITAS
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ABSTRACT: Most of the ~50 blazars detected to date at TeV energies (E>0.1 TeV) are high-frequency-peaked BL Lacs (HBLs). Only a handful episodic TeV detections of low- and intermediate-frequency-peaked BL Lacs (LBL/IBLs, with synchrotron peak frequencies in the infrared and optical regime) have been reported, typically during high-flux states. The VERITAS array, a ground-based TeV observatory located in southern Arizona has observed five known TeV LBL/IBLs since 2009: 3C 66A, W Comae, PKS 1424+240, S5 0716+714 and BL Lacertae, with at least 5-10 hours/year, which so far resulted in the detection of a bright, sub-hour timescale gamma-ray flare of BL Lacertae in June 2011. We also report the detection and characterization of two new IBLs: VER J0521+211 and B2 1215+30.
The European Physical Journal Conferences 10/2013; 61. DOI:10.1051/epjconf/20136104012
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##### Article: The high-energy $\gamma$-ray emission of AP Librae
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ABSTRACT: The $\gamma$-ray spectrum of the low-frequency-peaked BL Lac (LBL) object AP Librae is studied, following the discovery of very-high-energy (VHE; $E>100\,{\rm GeV}$) $\gamma$-ray emission up to the TeV range by the H.E.S.S. experiment. This makes AP Librae one of the few VHE emitters of the LBL type. The measured spectrum yields a flux of $(8.8 \pm 1.5_{\rm stat} \pm 1.8_{\rm sys}) \times 10^{-12}\ {\rm cm}^{-2} {\rm s}^{-1}$ above 130 GeV and a spectral index of $\Gamma = 2.65\pm0.19_{\rm stat}\pm0.20_{\rm sys}$. This study also makes use of \textit{Fermi}-LAT, observations in the high energy (HE, E$>$100 MeV) range, providing the longest continuous light curve (5 years) ever published on this source. The source underwent a flaring event between MJD 56306-56376 in the HE range, with a flux increase of a factor 3.5 in the 14-day bin light curve and no significant variation in spectral shape with respect to the low-flux state. While the H.E.S.S., and (low state) \textit{Fermi}-LAT fluxes are in good agreement where they overlap, a spectral curvature between the steep VHE spectrum and the \textit{Fermi}-LAT, spectrum is observed. The maximum of the $\gamma$-ray emission in the spectral energy distribution is located below the GeV energy range.
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##### Article: Multi-Wavelength Variability Properties of Fermi Blazar S5 0716+714
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ABSTRACT: S5 0716+714 is a typical BL Lacertae object. In this paper we present the analysis and results of long term simultaneous observations in the radio, near-infrared, optical, X-ray and $\gamma$-ray bands, together with our own photometric observations for this source. The light curves show that the variability amplitudes in $\gamma$-ray and optical bands are larger than those in the hard X-ray and radio bands and that the spectral energy distribution (SED) peaks move to shorter wavelengths when the source becomes brighter, which are similar to other blazars, i.e., more variable at wavelengths shorter than the SED peak frequencies. Analysis shows that the characteristic variability timescales in the 14.5 GHz, the optical, the X-ray, and the $\gamma$-ray bands are comparable to each other. The variations of the hard X-ray and 14.5 GHz emissions are correlated with zero-lag, so are the V band and $\gamma$-ray variations, which are consistent with the leptonic models. Coincidences of $\gamma$-ray and optical flares with a dramatic change of the optical polarization are detected. Hadronic models do not have the same nature explanation for these observations as the leptonic models. A strong optical flare correlating a $\gamma$-ray flare whose peak flux is lower than the average flux is detected. Leptonic model can explain this variability phenomenon through simultaneous SED modeling. Different leptonic models are distinguished by average SED modeling. The synchrotron plus synchrotron self-Compton (SSC) model is ruled out due to the extreme input parameters. Scattering of external seed photons, such as the hot dust or broad line region emission, and the SSC process are probably both needed to explain the $\gamma$-ray emission of S5 0716+714.
The Astrophysical Journal 01/2014; 783(2). DOI:10.1088/0004-637X/783/2/83 · 6.28 Impact Factor | 2015-04-27 10:46:09 | {"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": 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": 0.7617785930633545, "perplexity": 6134.947484194948}, "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-2015-18/segments/1429246658061.59/warc/CC-MAIN-20150417045738-00024-ip-10-235-10-82.ec2.internal.warc.gz"} |
https://support.bioconductor.org/p/109379/ | Question: Affy's exprs not working.. intensity works..
0
12 months ago by
elmira.amiri0 wrote:
Hi,
I have a recent problem running the exprs() function on an AffyBatch object. Previously, I was able to run it, but all of a sudden, when I run, the following code snippet, I get a list instead of an object. And therefore, when I want to display it in Jupyter notebook, it gives me the following error:
> affy_obj
AffyBatch object
size of arrays=1164x1164 features (106 kb)
cdf=HG-U133_Plus_2 (54675 affyids)
> expr = exprs(affy_obj)
ERROR while rich displaying an object: Error in FUN(X[[i]], ...): attempt to use zero-length variable name
However, if I use intensity() function, it works. Anyone knows what am I missing?
affy intensity exprs • 216 views
modified 12 months ago by James W. MacDonald50k • written 12 months ago by elmira.amiri0
Answer: Affy's exprs not working.. intensity works..
2
12 months ago by
United States
James W. MacDonald50k wrote:
You have probably loaded a package that masks exprs. There is some package from the tidyverse that will do that, and probably other packages as well. The fix is to specify the package and function directly, using the double colon operator.
affy::exprs(affy_obj)
should work just fine.
Yes, it works.
Thanks James. | 2019-05-21 17:33:44 | {"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": 0.295617938041687, "perplexity": 7133.915721273335}, "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/1558232256494.24/warc/CC-MAIN-20190521162634-20190521184634-00506.warc.gz"} |
https://exploringnumbertheory.wordpress.com/2013/07/page/2/ | # Fermat’s Little Theorem and Mental Poker
In this post we demonstrate another use of the Fermat’s Little Theorem.
How can two people play poker when they are not sitting face to face from each other? If the game of poker is played over long distance (e.g. via a telephone line or some electronic communication channel), there will be a need to ensure a fair game. For example, the two players must use the same deck of cards (ensuring that there will be no duplicates). The deck of cards will need to be well shuffled. Each player cannot see the cards of the other player. One solution is to use a trusted third party to do the shuffling and selecting of cards. If a third party cannot be found or it is felt that the third party cannot be trusted to be fair, then one should consider the cryptographic solution described in this post. This soultion was proposed by Rivest, Shamir and Adlemen in 1982 (the creators of the RSA algorithm).
The term mental poker refers to the game of poker played over long distance that has a mechanism for ensuring a fair game without the need for a trusted third party. Mental poker can also refer to other cryptographic games played over long distance without the need for a trusted third party (e.g. tossing a coin over long distance).
___________________________________________________________________________________________________________________
Setting Up the Deck of Cards
Let’s say that the players are Andy and Becky. Since they are not using a physical deck of cards, they need to represent the cards by numbers. Let’s say that they agree to number the cards as follows:
$\displaystyle \heartsuit 2=1020 \ \ \ \ \ \ \ \ \ \ \ \diamondsuit 2=2020 \ \ \ \ \ \ \ \ \ \ \ \spadesuit 2=3020 \ \ \ \ \ \ \ \ \ \ \ \clubsuit 2=4020$
$\displaystyle \heartsuit 3=1030 \ \ \ \ \ \ \ \ \ \ \ \diamondsuit 3=2030 \ \ \ \ \ \ \ \ \ \ \ \spadesuit 3=3030 \ \ \ \ \ \ \ \ \ \ \ \clubsuit 3=4030$
$\displaystyle \heartsuit 4=1040 \ \ \ \ \ \ \ \ \ \ \ \diamondsuit 4=2040 \ \ \ \ \ \ \ \ \ \ \ \spadesuit 4=3040 \ \ \ \ \ \ \ \ \ \ \ \clubsuit 4=4040$
$\cdots \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \cdots \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \cdots \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \cdots$
$\cdots \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \cdots \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \cdots \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \cdots$
$\cdots \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \cdots \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \cdots \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \cdots$
$\displaystyle \heartsuit Q=1120 \ \ \ \ \ \ \ \ \ \ \ \diamondsuit Q=2120 \ \ \ \ \ \ \ \ \ \ \spadesuit Q=3120 \ \ \ \ \ \ \ \ \clubsuit Q=4120$
$\displaystyle \heartsuit K=1130 \ \ \ \ \ \ \ \ \ \ \ \diamondsuit K=2130 \ \ \ \ \ \ \ \ \ \spadesuit K=3130 \ \ \ \ \ \ \ \ \clubsuit K=4130$
$\displaystyle \heartsuit A=1140 \ \ \ \ \ \ \ \ \ \ \ \diamondsuit A=2140 \ \ \ \ \ \ \ \ \ \ \spadesuit A=3140 \ \ \ \ \ \ \ \ \ \clubsuit A=4140$
___________________________________________________________________________________________________________________
The card numbers need to be encrypted before they can be passed between the two players. Here’s how it works.
Both players agree to choose a large prime number $p$. This number $p$ needs to be larger than all the card numbers and the encrypted card numbers. The larger $p$ is, the harder it will be for any one of the players to cheat.
Now each of the players needs to choose an encryption-decryption key (a padlock) that the player keeps secret. Let’s start with Andy. He chooses a pair of positive numbers $a_0$ and $a_1$ such that the following holds:
$a_0 \cdot a_1 \equiv 1 \ (\text{mod} \ p-1)$
Equivalently the pair $a_0$ and $a_1$ satisfies the equation $a_0 \cdot a_1=1+(p-1) \cdot k$ for some integer $k$. The number $a_0$ will be used for locking (encryption) and the number $a_1$ will be used for unlocking (decryption). Andy will also keep this pair of numbers away from Becky.
How will Andy use this padlock? Suppose that $m$ is a number to be encrypted. To encrypt the number, Andy raises $m$ to the power of $a_0$ and then finds the remainder upon division by $p$. He will call the remainder $f_a(m)$. Using congruence notation, the following is the encryption function:
$f_a(m) \equiv m^{a_0} \ (\text{mod} \ p)$
If Andy needs to recover $m$ from the encrypted card number $c=f_a(m)$, all he has to do is to raise $c$ to the power of $a_1$ and then find the remainder upon division by $p$. Call the remainder $g_a(c)$, which will be the original card number $m$. Using congruence notation, the following is the decryption function:
$g_a(c) \equiv c^{a_1} \ (\text{mod} \ p)$
The decrypted number is the original number. Thus we have $g_a(c)=m$. A proof of this relies on the Fermat’s Little Theorem (see proof).
Because the numbers involved are usually large, no one will try to raise $m$ to the power of $a_0$ and then divides by $p$ to find the remainder. Instead, Andy should use special software. If software is not available, Andy can rely on congruence modulo arithmetic, which should also be done by a computer. See below for a demonstration of the congruence modulo arithmetic.
The other player Becky also needs a padlock. Specifically, she chooses a pair of numbers $b_0$ and $b_1$ that satisfy the following:
$b_0 \cdot b_1 \equiv 1 \ (\text{mod} \ p-1)$
This pair of number serves the same purpose as the pair that belongs to Andy. Of course, $b_0$ and $b_1$ need to be kept secret from Andy. The following shows the encryption and decryption functions for Becky’s padlock.
$f_b(m) \equiv m^{b_0} \ (\text{mod} \ p)$
$g_b(c) \equiv c^{b_1} \ (\text{mod} \ p)$
___________________________________________________________________________________________________________________
How to Play the Game
Suppose the card numbers are $m_1, m_2, m_3, \cdots, m_{52}$ (the above is one example of card number assigment). Andy then encrypts the card number using his encryption function $f_a(m)$. The following lists the encrypted card numbers.
$\displaystyle f_a(m_1),\ f_a(m_2), \ f_a(m_3),\cdots,f_a(m_{52})$
Andy then passes these encrypted card numbers to Becky. She shuffles the encrypted deck thorughly. She then chooses a 5-card hand for Andy. Becky then chooses another 5-card hand for herself. Becky uses her key to encrypt her 5-card hand. Becky passes both 5-card hands to Andy. The following shows what Becky passes to Andy.
Andy’s 5-card hand: $f_a(m_i) \equiv m_i^{a_0} \ (\text{mod} \ p)$ for 5 distinct values of $i$.
Becky’s 5-card hand: $f_b(f_a(m_j)) \equiv f_a(m_j)^{b_0} \ (\text{mod} \ p)$ for 5 distinct values of $j$.
Once Andy gets the two 5-card hands, he decrypts his own 5-card hand and gets back the original card numbers. He also decrypts Becky’s 5-card hand and passes that back to Becky.
Andy’s 5-card hand: $g_a(f_a(m_i)) \equiv (m_i^{a_0})^{a_1} \equiv m_i \ (\text{mod} \ p)$
Becky’s 5-card hand: $g_a(f_b(f_a(m_j))) \equiv (f_a(m_j)^{b_0})^{a_1}=(f_a(m_j)^{a_1})^{b_0} \equiv m_j^{b_0} \ (\text{mod} \ p)$, which Andy passes back to Becky.
Once Becky’s recieves her 5-card hand back from Andy, she decrypts the cards immediately and gets back the original card numbers.
Becky’s 5-card hand: $g_b(m_j^{b_0}) \equiv (m_j^{b_0})^{b_1} \equiv m_j \ (\text{mod} \ p)$
Now each of the players has a 5-card hand that is only known to himself or herself. If they need to select new cards from the deck, they can follow the same back-and-forth procedures of encrypting and decrypting.
How fair is the poker game played in this manner? How secure is the game? It is very fair and secure if the players follow the rules and do not cheat. It is obviously possible to cheat. When Andy passes the 52 encrypted card numbers to Becky, Becky certainly can try to break Andy’s lock by figuring out Andy’s $a_0$. When Becky passes her encrypted cards to Andy, he can try to figure out Becky’s $b_0$. For that to happen, the player who wants to cheat will need to have enormous amount of computational resources at the ready. Thus the prime number $p$ should be large enough to make cheating an intractable problem. On the other hand, even when the prime number is of a moderate size, there has to be a fair amount of computational resources in order to play the game efficiently, with all the encrypting and decrypting that have to be done.
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Fermat’s Little Theorem
We now use Fermat’s Little Theorem to show that the encryption-decryption key works correctly and accurately. We show the following:
$(m^{a_0})^{a_1} \equiv m \ (\text{mod} \ p) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (1)$
For the descriptions of the numbers $m$, $p$, $a_0$ and $a_1$, see the above section Setting Up the Padlocks. First we state the Fermat’s Little Theorem.
Fermat’s Little Theorem
Let $q$ be a prime number. Then for any integer $a$, $a^q-a$ is an integer multiple of $q$ (or $q$ divides $a^q-a$). Using congruence notation, the theorem can be expressed as:
$a^q \equiv a \ (\text{mod} \ q)$
If the integer $a$ is not divisible by $q$, then we can divide out $a$ and the theorem can be expressed as:
$a^{q-1} \equiv 1 \ (\text{mod} \ q)$
For a proof and a fuller discussion of Fermat’s little theorem, see this post.
We now prove the property $(1)$. Recall that the pair of positive integers $a_0$ and $a_1$ are keys to lock and unlock a number $m$. They are chosen such that $a_0 \cdot a_1 \equiv 1 \ (\text{mod} \ p-1)$, or equivalently $a_0 \cdot a_1=1+(p-1) \cdot k$ for some integer $k$. This integer $k$ must be positive since $a_0$ and $a_1$ are both positive.
In the derivation below, we repeated use the fact that $m^p \equiv m \ (\text{mod} \ p)$ (applying the Fermat’s Little Theorem).
\displaystyle \begin{aligned} m&\equiv m^p \ (\text{mod} \ p)=m \cdot m^{p-1} \\&\equiv m^p \cdot m^{p-1} \ (\text{mod} \ p)=m \cdot m^{2(p-1)} \\&\equiv m^p \cdot m^{2(p-1)} \ (\text{mod} \ p)=m \cdot m^{3(p-1)} \\&\cdots \\&\cdots \\&\cdots \\&\equiv m^p \cdot m^{(k-1)(p-1)} \ (\text{mod} \ p)=m \cdot m^{k(p-1)} \\&=m \cdot m^{k(p-1)} \equiv m^{a_0 \cdot a_1} \ (\text{mod} \ p) \end{aligned}
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Example of Congruence Calculation
For a numerical example, we use a small prime number $p=55,049$. Though a small prime number, it is large enough to make the illustration meaningful. Andy chooses $a_0 \cdot a_1$ such that $a_0 \cdot a_1=1+(p-1) \cdot k$ for some integer $k$. Andy decides to use $k=3817$, leading to $a_0=2,657$ and $a_1=79,081$.
As illustration of how the calculation is done, let $m=1020$ (the number for $\heartsuit 2$ as indicated above).
To decrypt this card, Andy needs to raise $1020$ to the 2657th power and then find the remainder upon division by $p=50,049$. This is the definition for $1010200^{269}$ modulo $p$. But the calculation is not easy to do directly without special software. We present here a “divide and conquer” approach that use the division algorithm in each step to reduce the exponent by half.
To start, note that $1020^2 \equiv 49518 \ (\text{mod} \ 55049)$, meaning that the remainder is $49518$ when $1020^2$ is divided by $55049$. In the following series of steps, a congruence calculation is performed in each step (using the division algorithm) to reduce the exponent by half.
\displaystyle \begin{aligned} 1020^{2657}&\equiv (1020^2)^{1328} \cdot 1020 \ (\text{mod} \ 55049) \\&\text{ } \\&\equiv 49518^{1328} \cdot 1020 \equiv (49518^2)^{664} \cdot 1020 \\&\text{ } \\& \equiv 39766^{664} \cdot 1020 \equiv (39766^2)^{332} \cdot 1020 \\&\text{ } \\& \equiv 52231^{332} \cdot 1020 \equiv (52231^2)^{166} \cdot 1020 \\&\text{ } \\&\equiv 14068^{166} \cdot 1020 \equiv (14068^2)^{83} \cdot 1020 \\&\text{ } \\& \equiv 7469^{83} \cdot 1020 \equiv (7469^2)^{41} \cdot 7469 \cdot 1020 \\&\text{ } \\& \equiv 21324^{41} \cdot 7469 \cdot 1020 \\&\text{ } \\&\equiv 21324^{41} \cdot 21618 \equiv (21324^2)^{20} \cdot 21324 \cdot 21618 \\&\text{ } \\& \equiv 8236^{20} \cdot 21324 \cdot 21618 \\&\text{ } \\& \equiv 8236^{20} \cdot 1906 \equiv (8236^2)^{10} \cdot 1906 \\&\text{ } \\& \equiv 11328^{10} \cdot 1906 \equiv (11328^2)^{5} \cdot 1906 \\&\text{ } \\& \equiv 4365^5 \cdot 1906 \equiv (4365^2)^2 \cdot 4365 \cdot 1906 \\&\text{ } \\& \equiv 6271^2 \cdot 4365 \cdot 1906 \\&\text{ } \\&\equiv 6271^2 \cdot 7291 \\&\text{ } \\&\equiv 20455 \cdot 7291 \\&\text{ } \\&\equiv 9664 \ (\text{mod} \ 55049) \end{aligned}
Thus the card number $1020$ is encrypted as $9664$. To recover the original card number from this encrypted number, Andy needs to raise $9664$ to the power of $a_1=79081$. Here, we get an assist from Fermat’s Little Theorem in addition to the ‘divide and conquer” congruence arithmetic that is used above.
According to Fermat’s Little Theorem, $9664^{55048} \equiv 1 \ (\text{mod} \ 55049)$. Thus we have
$9664^{79081} \equiv 9664^{55048} \cdot 9664^{24033} \equiv 9664^{24033} \ (\text{mod} \ 55049)$
With the help of Fermat’s Little Theorem, the exponent $79081$ has come down to $24033$. In the rest of the way, the “divide and conquer” approach is used.
\displaystyle \begin{aligned} 9664^{24033}&\equiv (9664^2)^{12016} \cdot 9664 \ (\text{mod} \ 55049) \\&\text{ } \\&\equiv 29782^{12016} \cdot 9664 \equiv (29782^2)^{6008} \cdot 9664 \\&\text{ } \\&\equiv 8237^{6008} \cdot 9664 \equiv (8237^2)^{3004} \cdot 9664 \\&\text{ } \\&\equiv 27801^{3004} \cdot 9664 \equiv (27801^2)^{1502} \cdot 9664 \\&\text{ } \\&\equiv 7641^{1502} \cdot 9664 \equiv (7641^2)^{751} \cdot 9664 \\&\text{ } \\&\equiv 32941^{751} \cdot 9664 \equiv (32941^2)^{375} \cdot 32941 \cdot 9664 \\&\text{ } \\&\equiv 38642^{375} \cdot 32941 \cdot 9664 \\&\text{ } \\&\equiv 38642^{375} \cdot 48506 \equiv (38642^2)^{187} \cdot 38642 \cdot 48506 \\&\text{ } \\&\equiv 39^{187} \cdot 38642 \cdot 48506 \\&\text{ } \\&\equiv 39^{187} \cdot 5451 \equiv (39^2)^{93} \cdot 39 \cdot 5451 \\&\text{ } \\&\equiv 1521^{93} \cdot 39 \cdot 5451 \\&\text{ } \\&\equiv 1521^{93} \cdot 47442 \equiv (1521^2)^{46} \cdot 1521 \cdot 47442 \\&\text{ } \\&\equiv 1383^{46} \cdot 1521 \cdot 47442 \\&\text{ } \\&\equiv 1383^{46} \cdot 45092 \equiv (1383^2)^{23} \cdot 45092 \\&\text{ } \\&\equiv 41023^{23} \cdot 45092 \equiv (41023^2)^{11} \cdot 41023 \cdot 45092 \\&\text{ } \\&\equiv 38599^{11} \cdot 41023 \cdot 45092 \\&\text{ } \\&\equiv 38599^{11} \cdot 52618 \equiv (38599^2)^{5} \cdot 38599 \cdot 52618 \\&\text{ } \\&\equiv 36665^5 \cdot 38599 \cdot 52618 \\&\text{ } \\&\equiv 36665^5 \cdot 24376 \equiv (36665^2)^{2} \cdot 36665 \cdot 24376 \\&\text{ } \\&\equiv 25645^2 \cdot 36665 \cdot 24376 \\&\text{ } \\&\equiv 25645^2 \cdot 25525 \\&\text{ } \\&\equiv 50671 \cdot 25525 \\&\text{ } \\&\equiv 1020 \ (\text{mod} \ 55049) \end{aligned}
In each step of the above calculation, the division algorithm is applied to reduce the exponent by half. For example, to go from the first line to the second line, $9664^2$ is divided by $55049$ to obtain the remainder $29782$, i.e. $9664^2 \equiv 29782 \ (\text{mod} \ 55049)$. The number $1020$ in the last line is the remainder when $50671 \cdot 25525$ is divided by $55049$.
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$\copyright \ 2013 \text{ by Dan Ma}$
# Fermat’s Little Theorem and RSA Algorithm
RSA is a cryptographic algorithm that is used to send and receive messages. We use the Fermat’s Little Theorem to prove that RSA works correctly and accurately. In other words, the decrypted message is indeed the original message from the sender. Mathematically we show that applying the encryption function and the decryption function successively produces the identity function.
To see how RSA works, see the previous post An Illustration of the RSA Algorithm.
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RSA Algorithm
We first briefly describe the algorithm and then present the mathematical statement to validate.
Let $N=p \cdot q$ where $p$ and $q$ are two prime numbers. Let $\phi=(p-1) \cdot (q-1)$. Choose an integer $e$ with $1 such that $e$ and $\phi$ are relatively prime.
The public key consists of $N$ and $e$ where $e$ is the encryption key. Once it is published, anyone can use it to encrypt messages to send to the creator of the public key. The following is the encryption function:
$f(M) \equiv M^e \ (\text{mod} \ N)$
where $M$ is a positive integer and is the original message.
The private key is a positive integer $d$ that satisfies:
$d \cdot e \equiv 1 \ (\text{mod} \ \phi=(p-1) \cdot (q-1))$
In other words, $d$ is the multiplicative inverse of $e$ in the modular arithmetic of modulo $\phi$. The above condition is equivalent to: $de-1=(p-1) \cdot (q-1) \cdot k$ for some integer $k$.
The number $d$ is the decryption key that will be used to decode messages. So it should remain private.
Once the creator of the public key receives an encrypted message $C=f(M)$, he or she uses the following decryption function to obtain the original message $M$.
$g(C) \equiv C^d \ (\text{mod} \ N)$
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The Mathematical Statement to Validate
What we prove is that the decryption function is to undo the encryption function. Specifically, we prove the following:
$g(C)=g(f(M))=(M^e)^d=M^{ed} \equiv M \ (\text{Mod} \ N) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (1)$
In other words, applying the decryption function $g$ to the encryption function $f$ produces the original message.
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Fermat’s Little Theorem
In this section, we list out the tools we need to prove the correctness of RSA.
Theorem 1 (Fermat’s Little Theorem)
If $p$ is a prime number and $a$ is an integer such that $a$ and $p$ are relatively prime, then
$a^{p-1}-1$ is an integer multiple of $p$
or equivalently $a^{p-1} \equiv 1 \ (\text{mod} \ p)$.
For a proof of Fermat’s little theorem, see this post.
Lemma 2 (Euclid’s Lemma)
Let $a$, $b$ and $d$ be integers where $d \ne 0$. Then if $d$ divides $a \cdot b$ (symbolically $d \lvert a \cdot b$), then either $d \lvert a$ or $d \lvert b$.
Euclid’s Lemma is needed to prove the following Lemma.
Lemma 3
Let $M$ be an integer. Let $p$ and $q$ be prime numbers with $p \ne q$.
Then if $a \equiv M \ (\text{mod} \ p)$ and $a \equiv M \ (\text{mod} \ q)$, then $a \equiv M \ (\text{mod} \ p \cdot q)$.
Proof of Lemma 3
Suppose we have $a \equiv M \ (\text{mod} \ p)$ and $a \equiv M \ (\text{mod} \ q)$. Then for some integers $i$ and $j$, we have:
$a=M+p \cdot i$ and $a=M+q \cdot j$.
Then $p \cdot i=q \cdot j$. This implies that $p$ divides $q \cdot j$ ($p \lvert q \cdot j$). By Euclid’s lemma, we have either $p \lvert q$ or $p \lvert j$. Since $p$ and $q$ are distinct prime numbers, we cannot have $p \lvert q$. So we have $p \lvert j$ and that $j=p \cdot w$ for some integer $w$.
Now, $a=M+q \cdot j=M+q \cdot p \cdot w$, implying that $a \equiv M \ (\text{mod} \ p \cdot q)$. $\blacksquare$
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The Proof of (1)
We now prove the property $(1)$ described above. We show that
$(M^e)^d=M^{ed} \equiv M \ (\text{Mod} \ N=p \cdot q)$
We first show that $M^{ed} \equiv M \ (\text{Mod} \ p)$ and $M^{ed} \equiv M \ (\text{Mod} \ q)$. Then the desired result follows from Lemma 3.
To show $M^{ed} \equiv M \ (\text{Mod} \ p)$, we consider two cases: $M \equiv 0 \ (\text{Mod} \ p)$ or $M \not \equiv 0 \ (\text{Mod} \ p)$.
Case 1. $M \equiv 0 \ (\text{Mod} \ p)$. Then $M$ is an integer multiple of $p$, say $M=p \cdot w$ where $w$ is an integer. Then $M^{ed}=(p \cdot w)^{ed}=p \cdot p^{ed-1} \cdot w^{ed}$. So both $M$ and $M^{ed}$ are integer multiples of $p$. Thus $M^{ed} \equiv M \ (\text{Mod} \ p)$.
Case 2. $M \not \equiv 0 \ (\text{Mod} \ p)$. This means that $p$ and $M$ are relatively prime (having no common divisor other than 1). Thus we can use Fermat’s Little Theorem. We have $M^{p-1} \equiv 1 \ (\text{mod} \ p)$.
From the way the decryption key $d$ is defined above, we have $ed-1=(p-1) \cdot (q-1) \cdot k$ for some integer $k$. We then have:
\displaystyle \begin{aligned} M^{ed}&=M^{ed-1} \cdot M \\&=M^{(p-1) \cdot (q-1) \cdot k} \cdot M \\&=(M^{p-1})^{(q-1) \cdot k} \cdot M \\&\equiv (1)^{(q-1) \cdot k} \cdot M \ (\text{Mod} \ p) \ * \\&\equiv M \ (\text{Mod} \ p) \end{aligned}
At the step with *, we apply Fermat’s Little Theorem. So we have $M^{ed} \equiv M \ (\text{Mod} \ p)$.
The same reason reasoning can show that $M^{ed} \equiv M \ (\text{Mod} \ q)$.
By Lemma 3, it follows that $M^{ed} \equiv M \ (\text{Mod} \ N=p \cdot q)$. $\blacksquare$
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$\copyright \ 2013 \text{ by Dan Ma}$
Revised August 9, 2014.
# An Illustration of the RSA Algorithm
The following 617-digit number (all 617 digits starting with $251$ and ending in $357$) is a product of two prime numbers $p$ and $q$. How long will it take to find these two prime factors?
25195908475657893494027183240048398571429282126204
03202777713783604366202070759555626401852588078440
69182906412495150821892985591491761845028084891200
72844992687392807287776735971418347270261896375014
97182469116507761337985909570009733045974880842840
17974291006424586918171951187461215151726546322822
16869987549182422433637259085141865462043576798423
38718477444792073993423658482382428119816381501067
48104516603773060562016196762561338441436038339044
14952634432190114657544454178424020924616515723350
77870774981712577246796292638635637328991215483143
81678998850404453640235273819513786365643912120103
97122822120720357
The above number is a challenge to the public to come up with the two prime factors (see RSA challenge number and RSA factoring challenge). No one has been able to successfully meet the challenge. In fact, even with the current state of the art in supercomputing technology, it could take millions of years to factor a number as big as the one shown above. According to the organization that posed the challenge (RSA Laboratories), barring fundamental algorithmic or computing advances, the above number or other similarly sized number is expected to stay unfactored in the decades to come.
RSA is a cryptographic algorithm that is used to send and receive sensitive data. The name RSA stands for the last names of the creators of the algorithm – Ron Rivest, Adi Shamir and Leonard Adleman.
The algorithm uses a pair of large prime numbers in setting up a public key to encrypt and a private key to decrypt data. The public key is known to the public and includes a large integer $N$ (such as the one indicated at the beginning of the post) that is a product of two prime numbers $p$ and $q$. The private key is computed using two prime factors $p$ and $q$ and is needed to decrypt the messages encrypted by the public key. The RSA scheme is built on the monumental difficulty in factoring large numbers. Barring some system vulnerability that hackers can exploit, it is all but certain that messages sent via RSA scheme can only be read by the intended party – the legitimate party that possesses the private key.
This post gives an illustration of how the RSA algorithm work using much smaller prime numbers. The RSA algorithm is also an application of the Fermat’s Little Theorem (see the post Fermat’s Little Theorem and RSA Algorithm).
The example given below makes use of congruence arithmetic. If $a$, $b$ and $m$ are integers, the symbol $a \equiv b \ (\text{mod } m)$ means that the difference $a-b$ is divisible by $m$ (we say that $a$ is congruent to $b$ modulo $m$). For example, $15 \equiv 3 \ (\text{mod } 12)$ (in terms of clock arithmetic, 6 hours after 9 o’clock is not 15th o’clock but is 3 o’clock). For more information about congruence relation and congruence arithmetic, see this blog post or this Wikipedia entry.
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Example of RSA
The example uses small prime numbers to make the illustration easy to follow. The example has the following steps:
1. Andy creates a public key and a private key. He gives the public key to Becky and keeps the private key to himself.
2. Becky then uses the public key to encrypt a message and sends it to Andy.
3. Andy then uses the private key to decrypt the message received from Becky.
4. $\text{ }$
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Step 1 – Generating the Public Key and Private Key
Choose two prime numbers $p$ and $q$. In this example, let $p=29$ and $q=47$. Then calculate the following numbers:
$N=p \times q=1363$
$(p-1) \times (q-1)=1288$
Choose an integer $e$ with $1 such that $e$ and $(p-1) \times (q-1)$ are relatively prime (meaning the only common divisor is 1). For this example, Andy chooses $e=11$.
The public key consists of $N=1363$ and $e=11$, which Andy passes to Becky. Becky will use the public key to encrypt any message that she wishes to send to Andy (see Step 2 below). The number $e$ is the encryption key.
Andy can also make the public key known to any one from whom Andy wishes to receive message.
The private key is the number $d$ such that:
$e \cdot d \equiv 1 \ (\text{mod } (p-1) \cdot (q-1))$
In this example, find the number $d$ such that
$11 \cdot d \equiv 1 \ (\text{mod } 1288)$
Specifically, we need to find the number $d$ that satisfies $11d=1+1288 k$ for some integer $k$. When $k=10$, we have a solution $d=1171$.
The number $d=1171$ will be used to decrypt any message that will come from Becky. So Andy needs to keep $d$ private and secure.
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Step 2 – Encrypting a Message using the Public Key
Becky wishes to send a message $T$ (in text) to Andy. Becky first translates $T$ into an integer $M$ (e.g. using a mapping to translate strings of letters and other symbols into blocks of numbers). This same mapping will be used by Andy to translate the decrypted message $M$ back to the text message $T$. Note that the mapping for translating letters into numbers and back is not part of the RSA algorithm, which only encrypts and decrypts numeric messages.
Suppose the message is $M=289$. The following is the encryption function – the function that generates the encrypted message $C$
$f(M) \equiv M^e \ (\text{mod } N)$
In this example, the encryption function is:
$f(M) \equiv 289^{11} \ (\text{mod } 1363)$
The encrypted message is the number $C=f(M)$ is the remainder that is obtained when $289^{11}$ is divided by $N=1363$. This can be done in a process using congruence arithemtic that can be described as “divide and conquer”. The process is to reduce the exponent by half in each step of the step by step approach.
First, note that $289^2 \equiv 378 \ (\text{mod} \ 1363)$ since $378$ is the remainder when $289^2$ is divided by $1363$ (i.e. division algorithm). Then use the division algorithm successively as shown in the following:
\displaystyle \begin{aligned} 289^{11}&\equiv (289^2)^5 \cdot 289 \ (\text{mod} \ 1363) \\&\text{ } \\&\equiv 378^5 \cdot 289 \equiv (378^2)^2 \cdot 378 \cdot 289 \\&\text{ } \\& \equiv 1132^2 \cdot 378 \cdot 289 \\&\text{ } \\&\equiv 1132^2 \cdot 202 \\&\text{ } \\&\equiv 204 \cdot 202 \\&\text{ } \\&\equiv 318 \ (\text{mod} \ 1363) \end{aligned}
In the “divide and conquer” approach, a congruence calculation in done in each step to reduce the exponent (applying the division algorithm). For example, to go from the first line to the second line, the remainder $378$ is obtained when $289^2$ is divided by $1363$. The number $318$ is the remainder when $204 \cdot 202$ is divided by $1363$.
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Step 3 – Decrypting the Message Receiving from Becky
Andy receives the encrypted message $C=318$. To decrypt $C$, the private key $d$ that is calculated in Step 1 above is used. The following is the decryption function – the function that generates the decrypted message $M$.
$g(C) \equiv C^d \ (\text{mod } N)$
In particular, Any needs to find the number $M=g(C)$ that satisfies the following:
$g(C) \equiv 318^{1171} \ (\text{mod } 1363)$
The decrypted message $M=g(C)$ is the remainder when $318^{1171}$ is divided by $1363$. A “divide and conquer” approach can be used.
\displaystyle \begin{aligned} 318^{1171}&\equiv (318^2)^{585} \cdot 318 \ (\text{mod} \ 1363) \\&\text{ } \\&\equiv 262^{585} \cdot 318 \equiv (262^2)^{292} \cdot 262 \cdot 318 \\&\text{ } \\& \equiv 494^{292} \cdot 262 \cdot 318 \\&\text{ } \\&\equiv 494^{292} \cdot 173 \equiv (494^2)^{146} \cdot 173 \\&\text{ } \\& \equiv 59^{146} \cdot 173 \equiv (59^2)^{73} \cdot 173 \\&\text{ } \\& \equiv 755^{73} \cdot 173 \equiv (755^2)^{36} \cdot 755 \cdot 173 \\&\text{ } \\& \equiv 291^{36} \cdot 755 \cdot 173 \\&\text{ } \\&\equiv 291^{36} \cdot 1130 \equiv (291^2)^{18} \cdot 1130 \\&\text{ } \\& \equiv 175^{18} \cdot 1130 \equiv (175^2)^{9} \cdot 1130 \\&\text{ } \\& \equiv 639^{9} \cdot 1130 \equiv (639^2)^{4} \cdot 639 \cdot 1130 \\&\text{ } \\& \equiv 784^{4} \cdot 639 \cdot 1130 \\&\text{ } \\&\equiv 784^{4} \cdot 1043 \equiv (784^2)^{2} \cdot 1043 \\&\text{ } \\& \equiv 1306^{2} \cdot 1043 \\&\text{ } \\&\equiv 523 \cdot 1043 \\&\text{ } \\&\equiv 289 \ (\text{mod} \ 1363) \end{aligned}
We just illustrates how Andy decrypts Becky’s message of $C=318$ to find the original message of $M=289$. The calculation is tedious if done manually but is simple for a computer.
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Summary
We summarize the main steps in the above example.
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Step 1 – Generating the Public Key and Private Key
Choose two prime numbers $p$ and $q$. Then calculate the following numbers:
$N=p \times q$
$(p-1) \times (q-1)$
Choose an integer $e$ with $1 such that $e$ and $(p-1) \times (q-1)$ are relatively prime (meaning the only common divisor is 1).
The public key consists of $N$ and $e$, which Andy passes to Becky. Becky will use the public key to encrypt any message that she wishes to send to Andy. The number $e$ is the encryption key.
Andy can also make the public key known to any one from whom Andy wishes to receive message.
The private key is the number $d$ such that:
$e \cdot d \equiv 1 \ (\text{mod } (p-1) \cdot (q-1))$
The number $d$ is the decryption key and will be used to decrypt any message that will come from Becky. So Andy needs to keep $d$ private and secure.
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Step 2 – Encrypting a Message using the Public Key
Becky wishes to send a message $T$ (in text) to Andy. Becky first translates $T$ into an integer $M$ (e.g. using a mapping to translate strings of letters and other symbols into blocks of numbers). This same mapping will be used by Andy to translate the decrypted message $M$ back to the text message $T$.
The following is the encryption function – the function that generates the encrypted message $C$.
$f(M) \equiv M^e \ (\text{mod } N)$
The encrypted message that Becky will send to Andy is $C=f(M)$.
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Step 3 – Decrypting the Message Receiving from Becky
Andy receives the encrypted message $C$. To decrypt $C$, the private key $d$ that is calculated in Step 1 above is used. The following is the decryption function – the function that generates the decrypted message $M$.
$g(C) \equiv C^d \ (\text{mod } N)$
The original message sent from Becky is $M=g(C)$.
Note that $M=g(f(M))$. Thus the function $f$ is the inverse function of $g$ (and vice versa). This fact can be established by using Fermat’s Little Theorem (see the post Fermat’s Little Theorem and RSA Algorithm).
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RSA Exercise
Suppose you are Andy. You set $p=53$ and $q=67$. You also choose $e=7$.
You give the public key $N=3551$ and $e=7$.
Becky sends you an encrypted message $C=2691$.
What is the original message?
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A lot of information about RSA can be found online. Here’s a few useful links for introductory information.
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$\copyright \ 2013 \text{ by Dan Ma}$
Revised August 9, 2014.
# Sieve of Eratosthenes
The sieve of Eratosthenes is an easy to use algorithm for finding all prime numbers up to a certain limit. It is named after Eratosthenes of Cyrene, a Greek mathematician who lived in third century BC. In this post we illustrate the sieve of Eratosthenes in a series of diagrams.
The sieve identifies the prime numbers below a limit $n$ by eliminating all composite numbers below $n$. The following describes the steps:
• Start with a listing of all positive integers $\le n$.
• $\text{ }$
• Select the number 2 and mark all multiples of 2 that are greater than 2 (in the diagrams below we use shading), essentially marking all even integers in the listing (except for 2).
• $\text{ }$
• In each subsequent step, find the first number $p$ greater than the previously selected number. Then mark all multiples of $p$ that are greater than $p$, i.e., marking $2p, 3p, 4p, \cdots$.
• $\text{ }$
• The process is stopped when multiples of $x$ have been marked for all integers $x \le \sqrt{n}$.
The justification for $\sqrt{n}$ in the above description is that any composite integer in the listing would have a prime divisor below $\sqrt{n}$. See the corollary at the end of the post.
The sieve of Eratosthenes is of course best done using using computer. We illustrate the process by finding all prime number below $n=169$.
___________________________________________________________________________________________________________________
We start with Figure 1 which is a listing of all integers below 169.
Figure 1 – Positive Integers Below 169
Next, in Figure 2, we shade all multiples of 2 that are above 2. In other words we shade all even integers below 169 (excluding 2).
Figure 2 – Multiples of 2 are Shaded
The first number greater than 2 that has not been shaded is 3. In Figure 3 below, we shade all multiples of 3 that are greater than 3 and that have not been previously shaded (e.g. 9, 15, etc).
Figure 3 – Multiples of 3 are Shaded
The first number greater than 3 that has not been shaded is 5. In Figure 4 below, we shade all multiples of 5 that are greater than 5 and that have not been previously shaded.
Figure 4 – Multiples of 5 are Shaded
The first number greater than 5 that has not been shaded is 7. In Figure 5 below, we shade all multiples of 7 that are greater than 7 and that have not been previously shaded (e.g. 49, 77, 91, etc).
Figure 5 – Multiples of 7 are Shaded
The first number greater than 7 that has not been shaded is 11. In Figure 6 below, we shade all multiples of 11 that are greater than 11 and that have not been previously shaded. In this step, we only need to shade 121 and 143.
Figure 6 – Multiples of 11 are Shaded
The first number greater than 11 that has not been shaded is 13. In Figure 7 below, we shade all multiples of 13 that are greater than 13 and that have not been previously shaded. In this step, we only need to shade 169.
Figure 7 – Multiples of 13 are Shaded
By the time we finish with Figure 7, all multiples of $x$ have been shaded for all $x \le 13=\sqrt{169}$. So the remaining unshaded numbers are prime numbers. Note that for any integer in the above diagrams, if it is composite, it would have a prime divisor at or below 13 (see the corollary below).
Thus there are 39 prime numbers below 169 and they are:
2, 3, 5, 7,
11, 13, 17, 19,
23, 29,
31, 37,
41, 43, 47,
53, 59,
61, 67,
71, 73, 79,
83, 89,
97,
101, 103, 107, 109,
113,
127,
131, 137, 139,
149,
151, 157,
163, 167
___________________________________________________________________________________________________________________
Why the Sieve Works
The marking or shading of multiples of numbers can stop at $\sqrt{n}$ is justified by the following two lemmas.
Lemma 1
Let $n$ be a composite integer greater than 1. Then $n$ has a divisor $d$ such that $1.
Proof.
Since $n$ is composite, there are integers $d$ and $h$ such that $n=d \cdot h$ with $1 and $1. If one of $d$ and $h$ is $\le \sqrt{n}$, then we are done.
Suppose that both $d>\sqrt{n}$ and $h>\sqrt{n}$. Then we have:
$n=d \cdot h>\sqrt{n} \cdot \sqrt{n}=n$
Thus one of $d$ and $h$ is $\le \sqrt{n}$. $\blacksquare$
Lemma 2
Let $n$ be a composite integer greater than 1. Then $n$ has a prime divisor $d$ such that $1.
Proof.
By Lemma 1, $n$ has a divisor $d$ such that $1. Since there can be only finitely many such divisors and since any finite set of real numbers has a least element, let $d$ be the smallest divisor of $n$ such that $1. Then $d$ must be a prime number. If not, by Lemma 1 $d$ would have a divisor $w$ with $1. This would mean $w$ is a divisor of $n$ contradicting the fact that $d$ is the smallest divisor of $n$. $\blacksquare$
Because of these two lemmas, in checking whether a positive integer is a prime number, we only need to check for divisors $\le \sqrt{n}$. We have the following corollary, which is the basis of the sieve of Eratosthenes.
Corollary
Let $n$ be any integer greater than 2. Any composite number $k$ in the following listing
$\left\{2,3,4,5,6, \cdots, n-1,n \right\}$
has a prime factor $p \le \sqrt{n}$.
Thus in the process for the sieve of Eratosthenes for identifying the prime numbers $\le n$, we only need to eliminate the multiples of $p$ for all $p \le \sqrt{n}$.
___________________________________________________________________________________________________________________
$\copyright \ 2013 \text{ by Dan Ma}$ | 2019-07-17 01:29:38 | {"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": 0, "img_math": 409, "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": 0.9999608993530273, "perplexity": 950.0758105860067}, "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-2019-30/segments/1563195525004.24/warc/CC-MAIN-20190717001433-20190717023433-00129.warc.gz"} |
https://homework.cpm.org/category/CC/textbook/cca/chapter/2/lesson/2.1.4/problem/2-45 | ### Home > CCA > Chapter 2 > Lesson 2.1.4 > Problem2-45
2-45.
Evaluate the expressions below for the given values. Homework Help ✎
1. x2 + 3x for x = −3
2. 5 − (x − 2)2 for x = −1
3. $\frac { - 5 } { k + 1 }$ for k = −1
4. $| \frac { x } { x + y } |$x2 + y for x = 2, y = −3
• Substitute the given value for the variable and evaluate.
• (c): undefined (d): −5 | 2019-08-25 18:35:32 | {"extraction_info": {"found_math": true, "script_math_tex": 2, "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": 0.48034006357192993, "perplexity": 4534.090771221351}, "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-2019-35/segments/1566027330786.8/warc/CC-MAIN-20190825173827-20190825195827-00326.warc.gz"} |
http://www.dpreview.com/forums/post/36860727 | # Canon 24mm f/1.4L II or 35mm f/1.4L?
Started Nov 8, 2010 | Discussions thread
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Canon 24mm f/1.4L II or 35mm f/1.4L? Nov 8, 2010
inbetween then and now, I've read somewhere about people 'investing' in L glass for this focal range. Many get the 35mm f/1.4L, while a minority use the 24mm alternative. I've read the reviews at 'the digital picture' and they both seem quite similar to me and it comes down to the focal length needed. Is this understanding correct?
I have the 15-85mm lense now so i tried zooming at 24mm and 35mm to get a feel of them and thought 24mm being wider was a lot more useful (probably too pampered by the 15mm since i came from compact cameras before where i found 15mm to be very wide even on a 1.6x crop). is the 35mm better in some way over the 24mm?
as I mentioned in another thread ( http://forums.dpreview.com/forums/readflat.asp?forum=1029&message=36860421 ), I'll be heading to Osaka and will consider getting second hand L glass if it's a worthy investment over the sigma 30mm f/1.4... that'll depend on whether i find the right lense at the right price while i'm there... but are the Canon L lenses so much better than the Sigma? | 2015-05-27 09:03:46 | {"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": 0.851228654384613, "perplexity": 3977.833734292986}, "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-2015-22/segments/1432207928923.21/warc/CC-MAIN-20150521113208-00203-ip-10-180-206-219.ec2.internal.warc.gz"} |
https://ai.stackexchange.com/questions/27107/in-a-convolutional-neural-network-how-is-the-error-delta-propagated-between-con | # In a convolutional neural network, how is the error delta propagated between convolutional layers?
I'm coding some stuff for CNNs, just relying on numpy (and scipy just for the convolution operation for pure performance reasons).
I've coded a small network consisting of a convolutional layer with several feature maps, the max pooling layer and a dense layer for the output, so far so good, extrapolating the backpropagation from fully connected neural networks was quite intuitive.
But now I'm stuck when several convolutional layers are chained. Imagine the following architecture:
• Output neurons: 10
• Input matrix (I): 28x28
• First convolutional layer (CN1): 3x5x5, stride 1 (output shape is 3x24x24)
• First pooling layer (MP1): 2x2 (output shape is 3x12x12)
• Second convolutional layer (CN2): 3x5x5, stride 1(output shape is 3x8x8)
• Second pooling layer (MP2): 2x2 (output shape is 3x4x4)
• Dense layer (D): 10x48 (fully connected to flattened MP2)
Propagating the error back:
• Error delta in output layer: 10x1 (cost delta)
• Error delta in MP2: 3x4x4 (48x1 unflattened, calculating the error delta for the dense layer as usual)
• Error delta in CN2: 3x8x8 (error delta of MP2 but just upsampled)
How do I keep from here? I don't know how to keep propagating the error to the previous layer, if the error delta in the current one is 3x8x8, and the kernel 3x5x5, performing the convolution between the error delta and the filter for calculating the delta for the previous layer, that gives a 3x4x4 delta. | 2021-06-23 01:18:40 | {"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": 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": 0.8307928442955017, "perplexity": 5467.3775103905555}, "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-2021-25/segments/1623488528979.69/warc/CC-MAIN-20210623011557-20210623041557-00051.warc.gz"} |
https://ergodicity.net/2009/11/ | Lazy random walks on the torus via Dirichlet forms
One of the simple example graphs I’ve used in some of my research on gossip algorithms has been the 2-dimensional torus with $n$ vertices, which looks like a $\sqrt{n} \times \sqrt{n}$ grid with the top and left edges wrapped around to connect with the bottom and right edges. Every vertex has 4 neighbors. Now imagine a very lazy random walk on this graph in which a random walker moves from vertex $u$ to one of its neighbors with probability $1/n$. It’s “well known” that this random walk takes around $n^2$ steps to mix. That is, if $P$ is the matrix of transition probabilities then
$T_{r} = \frac{1}{1 - \lambda_2(P)} \approx n^2$
Here $\lambda_2(P)$ is the second largest eigenvalue of $P$ and the relaxation time $T_{r}$ is the inverse of the spectral gap of the matrix. One way of characterizing $T_{r}$ for reversible Markov chains is via the Dirichlet form. For a function $f : V \to \mathbb{R}$ on the states of the chain define the Dirichlet form $D(f,f)$ by
$D(f,f) = \frac{1}{2} \sum_{u,v \in V} \pi_u P_{uv} (f(u) - f(v))^2$
In our example the stationary distribution $pi_u = 1/n$ and $P_{uv} = 1/n$ for all edges in the graph. We write $f \perp \pi$ if
$\sum_{v \in V} \pi_v f(v) = 0$
Define a norm associated with $\pi$ via
$\|f\|^2 = \sum_{v \in V} \pi_i f(v)^2$
Then the characterization is
$T_{r} = \sup_{f \perp \pi, f \ne 0} \frac{ \|f\|^2 }{ D(f,f) }$
One question I asked myself today was whether it was “easy” to see what $f$ you should choose in the grid example to get the scaling of $n^2$. Here’s one choice that gives the correct scaling. We’ll set $f$ to be constant on each column. Assume without loss of generality that $\sqrt{n}$ is divisible by 4 and set $m = \sqrt{n}/4$. The values for $f$ on the columns will be like two triangles:
$\{\frac{1}{n}, \frac{2}{n}, \ldots, \frac{m}{n}, \frac{m}{n}, \frac{m-1}{n}, \ldots, \frac{1}{n}, \frac{-1}{n}, \frac{-2}{n}, \ldots, \frac{-m}{n}, \frac{-m}{n}, \frac{-m+1}{n}, \ldots, \frac{-1}{n} \}$
Now we can evaluate the norm, noting that there are $\sqrt{n}$ vertices per column:
$\|f\|^2 = 4 \sum_{i =1}^{m} \frac{1}{n} \sqrt{n} \frac{i^2}{n^2} = c \frac{1}{n}$
This is because the sum of the first $m$ squares scales like $m^3$ and $m = \sqrt{n}/4$. Now turning to the Dirichlet form, note that each difference between columns is at most $2/n$ and there are fewer than $n$ edges for which $f(u) \ne f(v)$. Thus:
$D(f,f) \le \frac{1}{2} n \frac{1}{n} \frac{1}{n} \frac{4}{n^2} = c' \frac{1}{n^3}$
Taking the ratio gives the lower bound of $T_r \ge c''/n^2$ as desired.
The first $f$ I tried was just equal to +1 on the first half of the columns and -1 on the second half of the columns. This ends up giving a suboptimal bound, because the norm $\|f\|^2 = 1$ but in the denominator we get $2 \sqrt{n}$ positive terms. The key is to make all the differences $(f(u) - f(v))^2$ in the denominator small while keeping the average of $\|f\|^2$ large enough. Even though you sum over $n$ small differences in the denominator, it stays small enough to pay for the $\|f\|^2 = c/n$ in the numerator.
While doing this calculation, I noticed that the book Markov Chains and Mixing Times is also online — it makes a handy reference and is a little easier to use than my old go-to, the Aldous-Fill book.
paper a (long time period) : Assouad, Fano, and Le Cam
Kamalika pointed me to this paper by Bin Yu in a Festschrift for Lucien Le Cam. People who read this blog who took information theory are undoubtedly familiar with Fano’s inequality, and those who are more on the CS theory side may have heard of Assouad (but not for this lemma). This paper describes the relationship between several lower bounds on hypothesis testing and parameter estimation.
Suppose we have a parametric family of distributions $\mathcal{P} = \{P_{\theta} : \theta \in \mathcal{D}\}$, where $\mathcal{D}$ is a metric space with metric $d(\cdot,\cdot)$. For two distributions $P_1$ and $P_2$ define the affinity $\|P_1 \wedge P_2 \|$ by:
$\|P_1 \wedge P_2 \| = 1 - \frac{1}{2} \| P_1 - P_2 \|_1$
Let $\mathop{\rm co}(\cdot)$ denote the convex hull. Then Le Cam’s lemmas is the following.
Le Cam’s Lemma. Let $\hat{\theta}$ be an estimator of $\theta(P)$ on $\mathcal{P}$. Suppose $D_1$ and $D_2$ be two sets such that $d(s_1,s_2) \ge 2 \delta$ for all $(s_1,s_2) \in D_1 \times D_2$, and $\mathcal{P}_1$ and $\mathcal{P}_2$ be two subsets of $\mathcal{P}$ such that $\theta(P) \in D_i$ when $P \in \mathcal{P}_i$. Then
$\sup_{P \in \mathcal{P}} \mathbb{E}_P[ d(\hat{\theta}, \theta(P)) ] \ge \delta \cdot \sup_{P_i \in \mathop{\rm co}(\mathcal{P}_i)} \| P_1 \wedge P_2 \|$
This lemma gives a lower bound on the error of parameter estimates in terms of the total variational distance between the distributions associated to different parameter sets. It’s a bit different than the bounds we usually think of like Stein’s Lemma, and also a bit different than bounds like the Cramer-Rao bound.
Le Cam’s lemma can be used to prove Assouad’s lemma, which is a statement about a more structured set of distributions indexed by the $H = \{-1, 1\}^m$, the vertices of the hypercube. We’ll write $t \sim_j t'$ for $t,t' \in H$ if they differ in the j-th coordinate.
Assouad’s Lemma. Let $\mathcal{F}_m = \{P_{t} : t \in H\}$ be a set of $2^m$ probability measures indexed by $H$, and suppose there are $m$ pseudo-distances $d_m$ on $\mathcal{D}$ such that for any pair $(x,y)$
$d(x,y) = \sum_{j}^m d_j(x,y)$
and that if $t \sim_j t'$
$d_j( \theta(P_t), \theta(P_{t'}) ) \ge \alpha_m$
Then
$\max_{P_t \in \mathcal{F}_m} \mathbb{E}_{t}[ d(\hat{\theta},\theta(P_t))] \ge m \cdot \frac{\alpha_m}{2} \min\{ \|P_t \wedge P_{t'} \| : t \sim_j t', j \le m\}$
The min comes about because it is the weakest over all neighbors (that is, over all j) of $P_t$ in the hypercube. Assouad’s Lemma has been used in various different places, from covariance estimation, learning, and other minimax problems.
Yu then shows how to prove Fano’s inequality from Assouad’s inequality. In information theory we see Fano’s Lemma as a statement about random variables and then it gets used in converse arguments for coding theorems to bound the entropy of the message set. Note that a decoder is really trying to do a multi-way hypothesis test, so we can think about the result in terms of hypothesis testing instead. This version can also be found in the Wikipedia article on Fano’s inequality.
Fano’s Lemma. Let $\mathcal{M}_r \subset \mathcal{P}$ contain $r$ probability measures such that for all $j \ne j'$ with $j,j' \le r$
$d(\theta(P_j), \theta(P_{j'})) \ge \alpha_r$
and
$D(P_j~\|~P_{j'}) \le \beta_r$
Then
$\max_j \mathbb{E}_j[ d(\hat{\theta},\theta(P_j)) ] \ge \frac{\alpha_r}{2}\left( 1 - \frac{\beta_r + \log 2}{\log r} \right)$
Here $D(\cdot\|\cdot)$ is the KL-divergence. The proof follows from the regular Fano’s inequality by choosing a message $W$ uniformly in $\{1, 2, \ldots, r\}$ and then setting the output $Y$ to have the distribution $P_j$ conditioned on $W = j$.
The rest of the paper is definitely worth reading, but to me it was nice to see that Fano’s inequality is interesting beyond coding theory, and is in fact just one of several kinds of lower bound for estimation error. | 2021-10-27 07:01:26 | {"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": 0, "mathjax_asciimath": 0, "img_math": 94, "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": 0.8948411345481873, "perplexity": 154.23894489850602}, "config": {"markdown_headings": false, "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-2021-43/segments/1634323588102.27/warc/CC-MAIN-20211027053727-20211027083727-00082.warc.gz"} |
https://chemistry.stackexchange.com/questions/142084/mechanism-of-acid-catalyzed-robinson-annulation | # Mechanism of acid-catalyzed Robinson annulation?
My professor posed my organic chemistry class a challenge problem for bonus points and I've been racking my brain over the last three days trying to work it out and I want to know if my solution is plausible. The problem asks us to draw the best curved arrow mechanism for the reaction in the bottom left corner of the photo included in this post (a substituted cyclobutane molecule to a substituted cycloalkene). At first, this seemed like a simple intramolecular Robinson annulation, however it appears to be catalyzed using the hydronium ion, rather than the hydroxide ion. No other reactants are stated, including light, heat, nor a double equivalence of the starting compound. Working through every mechanism that I could think of, I eventually ended up with the solution in the picture below. I assumed that reaction rates and percent yields were unimportant, as long as the mechanism is plausible. Does this solution break any rules of organic chemistry? Is there a better solution?
• Overall, a good solution. You don't need the enol in the first line. The allylic anion in the fourth structure is too basic. Protonate as you did in the first step but push electrons to fragment the ring. Enols do not sit around for several steps. They tautomerize to carbonyls. Formation of the cyclohexenone is fine except I would have opted for the enol of the ketone in the 3rd structure of the penultimate line to assist in the loss of water. This would lead directly to 3-methylcyclohexenone. Oct 28 '20 at 15:11
Addendum: The process is not a Robinson annulation, which involves an initial Michael addition followed by an aldol condensation. The latter reaction includes the transformation 3 $$\rightarrow$$ 8. The transformation 1 $$\rightarrow$$ 3 may described as a retro-aldol reaction. | 2021-12-02 20:03:15 | {"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": 2, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5391323566436768, "perplexity": 943.39842891175}, "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/1637964362287.26/warc/CC-MAIN-20211202175510-20211202205510-00451.warc.gz"} |
https://aptitude.gateoverflow.in/8805/Cat-2001-question-50 | # CAT 2001 | Question: 50
25 views
Answer the following questions based on the information given below.
The petrol consumption rate of a new model car 'Palto' depends on its speed and may be described by the graph below.
Manasa would like to minimize the fuel consumption for the trip by driving at the appropriate speed. How should she change the speed?
1. Increase the speed
2. Decrease the speed
3. Maintain the speed at $60$ km/hour
4. Cannot be determined
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1
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Answer the following questions based on the information given below. The petrol consumption rate of a new model car 'Palto' depends on its speed and may be described by the graph below. Manasa makes the $200$ km trip from Mumbai to Pune at a steady speed of $60$ km/hour. What is the amount of petrol consumed for the journey? $12.5$ litres $13.33$ litres $16$ litres $19.75$ litres
2
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The batting average $\text{(BA)}$ of a test batsman is computed from runs scored and innings played-completed innings and incomplete innings (not out) in the following manner: $r_1$ = number of runs scored in completed innings; $n_1$ = number of completed innings $r_2$ = ... $\text{MBA}_1$ and $\text{MBA}_2$ None of these
Let $n$ be the number of different $5$ digit numbers, divisible by $4$ with the digits $1, 2, 3, 4, 5$ and $6,$ no digit being repeated in the numbers. What is the value of $n?$ $144$ $168$ $192$ None of these
The figure below shows the network connecting cities A, B, C, D, E and F. The arrows indicate permissible direction of travel. What is the number of distinct paths from A to F? $9$ $10$ $11$ None of these
A change making machine contains $1$ rupee, $2$ rupee and $5$ rupee coins. The total number of coins is $300.$ The amount is Rs. $960.$ If the number of $1$ rupee coins and the number of $2$ rupee coins are interchanged, the value comes down by Rs. $40.$ The total number of $5$ rupee coins is $100$ $140$ $60$ $150$ | 2022-05-20 05:04:55 | {"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": 0.6921129822731018, "perplexity": 625.7452254652679}, "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/1652662531352.50/warc/CC-MAIN-20220520030533-20220520060533-00276.warc.gz"} |
https://stat.ethz.ch/R-manual/R-patched/library/stats/html/Exponential.html | Exponential {stats} R Documentation
## The Exponential Distribution
### Description
Density, distribution function, quantile function and random generation for the exponential distribution with rate rate (i.e., mean 1/rate).
### Usage
dexp(x, rate = 1, log = FALSE)
pexp(q, rate = 1, lower.tail = TRUE, log.p = FALSE)
qexp(p, rate = 1, lower.tail = TRUE, log.p = FALSE)
rexp(n, rate = 1)
### Arguments
x, q vector of quantiles. p vector of probabilities. n number of observations. If length(n) > 1, the length is taken to be the number required. rate vector of rates. log, log.p logical; if TRUE, probabilities p are given as log(p). lower.tail logical; if TRUE (default), probabilities are P[X \le x], otherwise, P[X > x].
### Details
If rate is not specified, it assumes the default value of 1.
The exponential distribution with rate \lambda has density
f(x) = \lambda {e}^{- \lambda x}
for x \ge 0.
### Value
dexp gives the density, pexp gives the distribution function, qexp gives the quantile function, and rexp generates random deviates.
The length of the result is determined by n for rexp, and is the maximum of the lengths of the numerical arguments for the other functions.
The numerical arguments other than n are recycled to the length of the result. Only the first elements of the logical arguments are used.
### Note
The cumulative hazard H(t) = - \log(1 - F(t)) is -pexp(t, r, lower = FALSE, log = TRUE).
### Source
dexp, pexp and qexp are all calculated from numerically stable versions of the definitions.
rexp uses
Ahrens, J. H. and Dieter, U. (1972). Computer methods for sampling from the exponential and normal distributions. Communications of the ACM, 15, 873–882.
### References
Becker, R. A., Chambers, J. M. and Wilks, A. R. (1988) The New S Language. Wadsworth & Brooks/Cole.
Johnson, N. L., Kotz, S. and Balakrishnan, N. (1995) Continuous Univariate Distributions, volume 1, chapter 19. Wiley, New York.
exp for the exponential function.
Distributions for other standard distributions, including dgamma for the gamma distribution and dweibull for the Weibull distribution, both of which generalize the exponential.
### Examples
dexp(1) - exp(-1) #-> 0
## a fast way to generate *sorted* U[0,1] random numbers:
rsunif <- function(n) { n1 <- n+1
cE <- cumsum(rexp(n1)); cE[seq_len(n)]/cE[n1] }
plot(rsunif(1000), ylim=0:1, pch=".") | 2022-08-09 13:03:20 | {"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": 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": 0.7299718260765076, "perplexity": 5334.995323632208}, "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/1659882570977.50/warc/CC-MAIN-20220809124724-20220809154724-00362.warc.gz"} |
http://cms.math.ca/cmb/msc/52A15?fromjnl=cmb&jnl=CMB | Search: MSC category 52A15 ( Convex sets in $3$ dimensions (including convex surfaces) [See also 53A05, 53C45] )
Shaken Rogers's Theorem for Homothetic Sections We shall prove the following shaken Rogers's theorem for homothetic sections: Let $K$ and $L$ be strictly convex bodies and suppose that for every plane $H$ through the origin we can choose continuously sections of $K$ and $L$, parallel to $H$, which are directly homothetic. Then $K$ and $L$ are directly homothetic. Keywords:convex bodies, homothetic bodies, sections and projections, Rogers's TheoremCategory:52A15 | 2015-05-25 05:38:01 | {"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": 0.9165161848068237, "perplexity": 1877.5686811035116}, "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-2015-22/segments/1432207928414.45/warc/CC-MAIN-20150521113208-00118-ip-10-180-206-219.ec2.internal.warc.gz"} |
http://math.stackexchange.com/questions/222596/finding-the-conditional-mean-and-conditional-variance | # Finding the conditional mean and conditional variance
$$f_{X,Y}(x,y) = \begin{cases} \frac12 & \text{if |x|+|y| < 1} \\ 0 & \text{otherwise} \\ \end{cases}$$
Find the conditional mean and the conditional variance of Y given X=x.
So far, I did:
\begin{align} f_X(x) & = \int_{|x|-1}^{1-|x|} \frac12 dy \\ & = \frac12(1-|x|-|x|-1) \\ & = 1-|x| \\ \end{align} $$f_{Y|X}(y|x) = \frac1{2(1-|x|)} \\ E(Y|X=x) = \int_{-\infty}^\infty y(\frac1{2(1-|x|)}) dy$$
Are my bounds for calculating the marginal density of X correct? Also, what are the bounds for y when calculating the conditional mean?
-
## 1 Answer
What is stopping you, here as in other questions you asked on the site, is your way of dealing with indicator functions. Let me suggest to systematically include indicator functions in the densities. A first advantage is to reach correct formulas, a second is to make easier the computations you face. In the case at hand, $$f_{X,Y}(x,y)=\frac{\mathbf 1_{|x|+|y|\lt1}}2,\qquad f_X(x)=f_Y(x)=(1-|x|)\,\mathbf 1_{|x|\lt1},$$ hence, for every $|x|\lt1$, $$f_{Y\mid X}(y\mid x)=\frac{\mathbf 1_{|y|\lt1-|x|}}{2(1-|x|)},$$ and, for $|x|\geqslant1$, $f_{Y\mid X}(\cdot\mid x)$ is undefined.
Now, for every $|x|\lt1$, the function $f_{Y\mid X}(\cdot\mid x)$ is even hence $$\mathbb E(Y\mid X=x)=\int_\mathbb Ryf_{Y\mid X}(y\mid x)\,\mathrm dy=0.$$ Likewise, for every $|x|\lt1$, the conditional variance is $$\mathbb E(Y^2\mid X=x)=\int_\mathbb R y^2f_{Y\mid X}(y\mid x)\,\mathrm dy=\int_{-(1-|x|)}^{1-|x|}y^2\frac{\mathrm dy}{2(1-|x|)}=\frac13(1-|x|)^2.$$ Note: A shortcut, which is specific to the present setting, is to note that the random vector $(X,Y)$ is distributed as $(X,(1-|X|)\cdot U)$ where $U$ is independent on $X$ and uniform on $[-1,1]$. Hence, one the event $[|X|\lt1]$, $$\mathbb E(Y\mid X)=(1-|X|)\cdot \mathbb E(U),\qquad\mathbb E(Y\mid X)=(1-|X|)^2\cdot \mathbb E(U^2),$$ and the formulas above reflect the fact that $\mathbb E(U)=0$ and $\mathbb E(U^2)=\frac13$.
- | 2014-07-28 20:31:09 | {"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": 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": 1, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9990826845169067, "perplexity": 236.45615803705945}, "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-2014-23/segments/1406510261958.8/warc/CC-MAIN-20140728011741-00459-ip-10-146-231-18.ec2.internal.warc.gz"} |
https://community.rstudio.com/t/problem-including-complied-rstudio-output-tex-file-in-latex/66053 | # Problem Including complied Rstudio output Tex file in Latex.
Hi, I'm having difficulty including the output.tex file in my Latex file. If i compile just that file i get the desired output which looks like the output file like you would see from the MS word output, but if i try to include the text file as \include{Output.tex} in the middle of my latex document then the formatting of the file is completely different. Any ideas?
Resolved the problem, Convert to a pdf and not a tex file since my main.tex file has different formattings.
This topic was automatically closed 7 days after the last reply. New replies are no longer allowed. | 2020-06-05 16:23:30 | {"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": 0.9809699058532715, "perplexity": 1610.6689296374302}, "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/1590348502097.77/warc/CC-MAIN-20200605143036-20200605173036-00157.warc.gz"} |
https://math.stackexchange.com/questions/3327986/isomorphism-that-is-not-a-bijection-in-underlying-sets/3328012 | # Isomorphism that is not a bijection in underlying sets?
The question is pretty much the same as >here<. This wikipedia article claims that in "Homotopy category of CW complexes" there is an isomorphism which is not bijective in the underlying sets, while this category should admit underlying set (e.g. faithful functor to Set).
I am not really familiar with CW complexes or Homotopy theory really. Can someone elaborate on what is going on? In the linked post, there is a proof that whenever $$f$$ is iso in cat. $$\mathcal{C}$$, then its image $$F(f)$$ under any functor $$F$$ must be iso, because $$F(f^{-1})$$ is its inverse.
• I would say it's very arguable whether objects in the homotopy category "admit underlying sets" or not. If you insist they do, it's in a vastly weaker sense than admitting a faithful functor to sets-there's not even a function on isomorphism classes of objects. I've edited the Wikipedia article to be (hopefully) less confusing. – Kevin Carlson Aug 20 '19 at 20:17
The condition for an arrow $$g:y\to x$$ in a category $$\mathbf C$$ to be the inverse of $$f:x\to y$$ is equational: $$fg=\mathrm{id}_y$$ and $$gf=\mathrm{id}_x$$. Hence it will be preserved by any functor, by which I mean that $$F(g)$$ is a inverse for $$F(f)$$ for any functor $$F$$ with domain $$\mathbf C$$: indeed, $$F(g)F(f) = F(gf) = F(\mathrm{id}_x) = \mathrm{id}_{F(x)}$$ and similarly for the other equation.
Hence, if you have any functor from $$\mathbf C \to \mathsf{Set}$$, it will map isomorphism to bijections. In the Wikipedia article, it is just said "every object admits an underlying set", with no indication that this mapping should be a functor (or even extended to maps): indeed, in the category $$\mathsf{Hot}$$, the objects are CW-complexes and the morphisms are the continuous functions modulo homotopy between them, so you can define a mapping $$\mathsf{Hot}\rightsquigarrow \mathsf{Set}$$ on objects by mapping a CW-complex to its underlying set (just forget the topology), but in no way can you complete that into a functor.
"Underlying set" is simply not a functor on the homotopy category. The closest thing is $$\text{Hom}(\bullet, -)$$ which returns $$\pi_0$$, and which sends homotopy equivalences to bijections as expected. | 2020-01-28 13:31:30 | {"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": 20, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9717534184455872, "perplexity": 208.6914823400942}, "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-20200128122813-20200128152813-00211.warc.gz"} |
https://socratic.org/questions/what-is-the-solution-for-integrate-1-9-12-x-4-x-2#429405 | # What is the solution for : integrate ( 1/(9-12*x+4*x^2)) ?
May 25, 2017
$- \frac{1}{4 x + 6} + C$
#### Explanation:
Let's write the question formatted:
$\int \frac{1}{9 - 12 x + 4 {x}^{2}} \mathrm{dx}$
First off, we can simplify the denominator
$\frac{1}{9 - 12 x + 4 {x}^{2}} = \frac{1}{2 x + 3} ^ 2$
First, we are going to integrate by parts (u-sub)
$\int f \left(u\right) \frac{\mathrm{du}}{\mathrm{dx}} \mathrm{dx} = \int f \left(u\right) \mathrm{du}$
Let $u = 2 x + 3 , \setminus \quad \frac{\mathrm{du}}{\mathrm{dx}} = \frac{d}{\mathrm{dx}} \left[2 x + 3\right] = 2$
We get:
$\frac{1}{2} \int \frac{1}{u} ^ 2 \mathrm{du} = \frac{1}{2} \int {u}^{- 2} \mathrm{du}$
Solve.
$\frac{1}{2} \int {u}^{- 2} \mathrm{du} = - \frac{1}{2 u} + C$
Sub $u$ back.
$- \frac{1}{2 u} + C = - \frac{1}{2 \left(2 x + 3\right)} + C = - \frac{1}{4 x + 6} + C$
$\therefore$ $\int \frac{1}{9 - 12 x + 4 {x}^{2}} \mathrm{dx} = - \frac{1}{4 x + 6} + C$ | 2022-08-16 19:39:45 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 11, "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": 0.9918003082275391, "perplexity": 6801.703283000143}, "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/1659882572515.15/warc/CC-MAIN-20220816181215-20220816211215-00579.warc.gz"} |
http://congresopequenosanimales2016.vetcan.org/fb5ld/p9qpuqa.php?cb1aba=how-big-is-the-crab-nebula | Copyright © 2020 Multiply Media, LLC. Such molecules have only been studied in laboratories before, and finding them in space is a big … The Crab Nebula was a nebula which the First Doctor believed to be outside of Mutter's Spiral. The nebula … How old was queen elizabeth 2 when she became queen? It was the spectacular explosion of a supernova, the violent death of a star that may have been as much as 10 times more massive than our Sun. The Crab Nebula lies about six and a half thousand light years away from Earth and is the remnant of a dramatic explosion, called a supernova, originally seen by Chinese Astronomers in 1054 AD. The Crab Nebula has an apparent magnitude of 8.4 and can be seen with binoculars in … In 1758 it was the first object listed (M1) in Charles Messier’s catalog of nebulous objects. The Crab Nebula This composite image was assembled from 24 individual exposures taken with the NASA Hubble Space TelescopeÕs Wide Field and Planetary Camera 2 in October 1999, January 2000, and December 2000. It had a brighter irregular core, and fainter extensions. The Crab Nebula, the result of a supernova seen in 1054 AD, is filled with mysterious filaments. The Crab Pulsar rotates about 30 times each second. The supernova left behind a magnetized neutron star known as a pulsar. NASA/DOE/Fermi LAT/R. It was somewhat mottled, with hints of filamentary structure, but very subtle. The Crab Nebula was one of the first objects that Chandra examined with its sharp X-ray vision, and it has been a frequent target of the telescope ever since.. Animation depicting the environment around the pulsar. How do you put grass into a personification? A short video about the Pulsar Neutron Star in the Crab Nebula. Definitely. (PROSE: The Sons of the Crab) 1 Features 2 History 2.1 Undated events 3 Behind the scenes The planet Wengrol was located in the Crab Nebula, (PROSE: The Sons of the Crab) as was the planet Tora. The filaments are not only tremendously complex, but appear to have less mass than expelled in the original supernova and a higher speed than expected from a free explosion. For Our editors will review what you’ve submitted and determine whether to revise the article. The Crab is one of the few astronomical objects from which radiation has been detected over the entire measurable spectrum, from radio waves through infrared and visible wavelengths to ultraviolet, X-rays, and gamma rays. How long will the footprints on the moon last? What year did the Spanish arrive in t and t? That's huge! Credit: NASA/ESA.In visible light, the Crab Nebula consists of a broadly oval-shaped mass of filaments, about 6 arcminutes long and 4 arcminutes wide (by comparison, the full moon is 30 arcminutes across) surrounding a diffuse blue central region. Fermi's LAT discovered a gamma-ray 'superflare' from the Crab Nebula on April 12, 2011. The material on this site can not be reproduced, distributed, transmitted, cached or otherwise used, except with prior written permission of Multiply. What are the release dates for The Wonder Pets - 2006 Save the Ladybug? The Crab Nebula got its most familiar name in 1840 when William Parsons, the Third Earl of Rosse, observed the nebula using a 36 inch telescope and created a drawing that he thought looked like a crab. Courtesy of Palomar Observatory/California Institute of Technology When did organ music become associated with baseball? It is one of the largest images taken by Hubble and is the highest resolution image ever made of the entire Crab Nebula. Updates? Credit: Jeff Hester and Paul Scowen (Arizona State University), and NASA This image is also available as hi-res jpeg [575k] Illustration of the Crab Nebula Environment. A History of the Crab Nebula. The Crab nebula is not visible with the naked eye, at least not anymore. Who is the longest reigning WWE Champion of all time? This article was most recently revised and updated by, https://www.britannica.com/place/Crab-Nebula, National Optical Astronomy Observatory - M1, NGC1952, Crab Nebula, M1 - Student Encyclopedia (Ages 11 and up). The supernova was visible in daylight for 23 days and at night for almost 2 years. Its energy fuels the glowing centre of the Crab Nebula. It has a diameter of 11 ly (3.4 pc) and expands at a rate of about 1,500 kilometers per second. It is about the size of Washington DC, but it spins 30 times a second. Watch Horizon - Season 8, Episode 28 - Crab Nebula: This episode of Horizon reports on how the Crab Nebula was discovered, and continuing observation of the space encounter. It is part of the Perseus Arm of our galaxy, the Milky Way.The Crab Nebula was the first object to be entered in Messier’s catalogue and remains one of the most studied objects in the night sky. how to answer a telephone call in a company or in any organisation? The molecule, argon hydride, was seen in the Crab Nebula, the remains of a star that exploded 1000 years ago. Messier 1 (M1), also known as the Crab Nebula, Taurus A, or NGC 1952, is an expanding supernova remnant and pulsar wind nebula. In three dimensions, the nebula is thought to be shaped either like an oblate spheroid (estimated as 1,380 pc/4,500 ly away) or a prolate spheroid (estimated as 2,020 pc/6,600 ly away). The Crab Nebula has a span of 11 light years across and is growing at a rate of around 1 billion kilometers per day. People often ask … The Crab Nebula, also known as Messier 1 and Taurus A, is a supernova remnant located in the direction of Taurus constellation.. The Crab Nebula (M1, NGC 1952) in the constellation Taurus is a gaseous remnant of the galactic supernova of 1054 ce. The Crab Nebula, about 6,500 light-years from Earth, is the scattered fragments of a supernova, or exploding star, observed by earthly skywatchers in the year 1054. It is one of the brightest sources of high-energy radiation in the sky. How big is the crab nebula? What makes a planet a dwarf planet? With an apparent magnitude of 8.4 and located 6,500 light-years from Earth in the constellation Taurus, the Crab Nebula can be spotted with a small telescope and is best observed in January. What year is Maytag washer model cw4544402? By signing up for this email, you are agreeing to news, offers, and information from Encyclopaedia Britannica. Articles from Britannica Encyclopedias for elementary and high school students. how do soil factors contributions to the soil formation? The crab nebula has a diameter of about 11 light years. In fact, all nebulae are bigger than our Sun (and other stars). Buehler . Crab Nebula Superflare - Fermi's Large Area Telescope. At the site of the 1054 supernova is one of the most remarkable objects in the sky, the. When did Elizabeth Berkley get a gap between her front teeth? Multiply that by six and you get how big the crab nebula is. In the nebula's very center lies a pulsar: a neutron star as massive as the Sun but with only the size of a small town. The crab nebula is 6 light-years. Be on the lookout for your Britannica newsletter to get trusted stories delivered right to your inbox. All Rights Reserved. The year 2019 marks the 20th anniversary of the launch of NASA's Chandra X-ray Observatory into space. Roughly 10 light-years in diameter, it is assumed to be the remnant of a supernova (violently exploding star) observed by Chinese and other astronomers first on July 4, 1054. For comparison, the distance from the Sun to Neptune is only 0.000474385765 light years. The filaments are expanding away from the center of the explosion faster than scientists expect. The bright filaments or threads of the nebula are … The discovery of the object as a nebula is attributed to the English physician and amateur astronomer John Bevis in about 1731. This nebula was first observed by the Englishman John Bevis in 1793, who is considered its discoverer, although the nebula had already been seen and recorded by Chinese and Arab astrologers, who had said that it was like a star that could be observed by day, and that it could be seen for a continuous period of 22 months, day and night.William Parsons, third count of Rosse, observed it in 1840 and gave it the name of Crab Nebula, since wh… The nebula was oval shaped. It acquired its name, suggested by its form, in the mid-19th century. The 36 inch telescope however did not allow Parsons to fully resolve the filaments, that coloured web of hot gas that permeates the nebula. The Crab Nebula, or M1 (the first object in Messier’s famous catalog), is a supernova remnant and pulsar wind nebula. The debris cloud has been expanding ever since the original explosion, and now it covers an area of space about 10 light-years across. Next year marks the 20th anniversary of NASA's Chandra X-ray Observatory launch into space. The nebula, I would say, was of medium brightness, but not uniform in texture. It is the expanding remains of an exploded star, a supernova seen in 1054. Omissions? comparison, the distance from the Sun to Neptune is only M1 is about 11 light years in diameter, which translates into 7 arc minutes of apparent diameter. The pulsar is the left member of a pair of stars near the centre of the picture. Launch into other worlds while testing your knowledge about space, celestial bodies, and the solar system. It is an expanding remnant of a star that exploded in a supernova event which was observed by Chinese astronomers in the year 1054 AD. Astronomers using Herschel have made the first discovery in space of a molecule including a noble gas. The pulsar, which flashes in radio, visible, X-ray, and gamma-ray wavelengths at 30 times per second, provides the energy that allows the nebula to glow. How many miles are in a light-year? It is very difficult to spot through binoculars, although possible if you manage to spot the difference between the nebula and the nearby stars. Hundreds of years before Americans began celebrating Independence Day by peppering the sky with fireworks, a more powerful celestial explosion brightened a summer sky. There are no records of its observation at the time by Europeans. It is part of the Perseus Arm of the Milky Way Galaxy. A light-year is about 9,461,000,000,000 km. Let us know if you have suggestions to improve this article (requires login). The crab nebula has a diameter of about 11 light years. The Crab Nebula lies about 6,500 light-years from Earth in the direction of the constellation Taurus. The Crab Nebula is a nebula in the Sanguineous Rim. What exactly is a quasar? In 1921 it was discovered to be still expanding; the present rate is about 1,100 km (700 miles) per second. The crab nebula has a diameter of about 11 light years. * Our Sun's Radius=696,000 km * Crab Nebula's Radius= $5.203 \times 10^{13}$ km approx. The Crab Nebula is … Starting out at 12-15 times more massive than the Sun, all that was left after the dramatic death of the star is a tiny, rapidly rotating neutron star and a complex network of ejected stellar material. A calculator doesn't even have that many digits. (COMIC: The Enlightenment of Ly-Chee the Wise) The planet Yamado was located near the Crab Nebula… In visible light, the Crab Nebula consists of a broadly oval-shaped mass of filaments, about 6 arcminutes long and 4 arcminutes wide (by comparison, the full moon is 30 arcminutes across) surrounding a diffuse blue central region. Messier 1 is easily visible with any telescope, but a 16” or bigger instrument will reveal details within the gases. This observation was made with the Crab Nebula near the meridian, and without the use of any filters. Crab pulsar (NP 0532), as observed by the Hubble Space Telescope. The material ejected from the Crab Nebula is moving at more than 3 million mph (4.8 million kph). The Crab Nebula (M1, NGC 1952) in the constellation Taurus is a gaseous remnant of the galactic supernova of 1054. Corrections? There are many reasons that the Crab Nebula is … The Crab Nebula is located 7,000 light-years away in the constellation Taurus. In three dimensions, the nebula is though… The filaments are the remnants of the progenitor star's atmosphere, and consist largely of ionised helium and 0.000474385765 light years. For comparison, the distance from the Sun to Neptune is only 0.000474385765 light years. The nebula, 6,500 light-years away, is expanding at 1,100 km (700 miles) per second. The Crab Nebula is 10 light-years across, expanding by 1500 kilometers per second, made up of extremely complex filaments that appear to have less mass and a higher speed than expelled from the original supernova. The nebula lies at an approximate distance of 6,500 light years from Earth. The nebula is about 6,500 light-years (2 kpc) from Earth. The Crab Nebula seen in infrared by the Spitzer Space Telescope.Hubble Space Telescope image of a small region of the Crab Nebula, showing Rayleigh–Taylor instabilities in its intricate filamentary structure. The Crab Nebula spans about 10 light-years. Image Credit: NASA, ESA, J. Hester, A. Loll (ASU) Last Updated: Aug. 7, 2017. Why don't libraries smell like bookstores? Crab Nebula, (catalog numbers NGC 1952 and M1), probably the most intensely studied bright nebula, in the constellation Taurus, about 6,500 light-years from Earth. View The Crab Nebula is remnant of a supernova, an exploding star, seen in this picture released on July 7, 2016. pictures and other The Crab Nebula photos at ABC News It is located in the northern constellation Taurus, the Bull. In the late 1960s the Crab pulsar (NP 0532), thought to be the collapsed remnant of the supernova, was discovered near the centre of the nebula. How many candles are on a Hanukkah menorah? For the Wonder Pets - 2006 Save the Ladybug call in a how big is the crab nebula. The English physician and amateur astronomer John Bevis in about 1731 away from the Sun to Neptune only. Area of space about 10 light-years across 6 light-years 30 times each second 2 when she became?. ( 3.4 pc ) and expands at a rate of about 11 light years year marks 20th. Our Sun ( and other stars ) who is the longest reigning WWE Champion of all time 11 light.! To answer a telephone call in a company or in any organisation Last Updated: Aug. 7 2017. ( requires login ) of about 1,500 kilometers per second was discovered be. The constellation Taurus is a gaseous remnant of the constellation Taurus is a Nebula the... The direction of Taurus constellation, as observed by the Hubble space Telescope a! Elizabeth 2 when she became queen pulsar Neutron star known as a Nebula in the Taurus... News, offers, and information from Encyclopaedia Britannica a star that exploded 1000 years ago is visible! Object as a pulsar centre of the Milky Way Galaxy daylight for 23 days at. Elementary and high school students year did the Spanish arrive in t t... Contributions to the English physician and amateur astronomer John Bevis in about 1731 at night for almost years... Are bigger than our Sun ( and other stars ) on the for... Six and you get how big the Crab Nebula lies at an approximate distance of 6,500 light years Taurus,. An approximate distance of 6,500 light years hints of filamentary structure, but very subtle star, a seen. Observation at the site of the galactic supernova of 1054 next year the. Arm of the brightest sources of high-energy radiation in the sky away in the constellation Taurus,.... Star known as Messier 1 and Taurus a, is expanding at 1,100 km ( 700 miles ) per.! 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Are bigger than our Sun ( and other stars ) Sun ( and other stars ) 12 2011... | 2021-04-10 19:36:08 | {"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": 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": 0.3143978714942932, "perplexity": 2268.6833260143067}, "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/1618038057476.6/warc/CC-MAIN-20210410181215-20210410211215-00616.warc.gz"} |
https://physicstravelguide.com/advanced_notions/chemical_potential | # Chemical Potential
## Layman
Explanations in this section should contain no formulas, but instead colloquial things like you would hear them during a coffee break or at a cocktail party.
## Researcher
The motto in this section is: the higher the level of abstraction, the better.
Example1
Example2:
## History
Contributing authors: | 2019-08-19 03:37:38 | {"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": 0.8345796465873718, "perplexity": 4394.2283595250365}, "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-2019-35/segments/1566027314641.41/warc/CC-MAIN-20190819032136-20190819054136-00158.warc.gz"} |
https://physics.stackexchange.com/questions/468897/net-force-acting-on-a-box-in-this-diagram | # Net force acting on a box in this diagram
The 27-kg slider block is moving to the left with a speed of 5 m/s when it is acted upon by the forces $$F_1$$ and $$F_2$$. Neglect friction and the mass of the pulleys and cords.
The net force acting on the object by the ropes should be $$4F_1 - 1F_2$$ according to the solution manual. I guess I never fully understood how different tensions act on objects. I understand intutitvely that there should be only $$1F_2$$ force acting on the box on the left because the string pulls on the box with exactly $$1F_2$$ force.
But for the right portion of the box diagram where $$F_1$$ is acting on the object. Why is it $$4F_1$$ exactly? I am just trying to intuitively make sense out of the equation as opposed to just counting ropes. This may be a real simple question but please help me out.
Edit: I am not asking for a hw solution (I have access to the solution manual), I am simply asking for a deeper explanation on how tensions act as forces in this diagram to solidify my understanding.
• Hi and welcome to the Physics SE! Please note that we don't answer homework or worked example type questions. Please see this page in the site help for more on what topics you can ask about here. – John Rennie Mar 27 '19 at 5:19
• I disagree. The OP has the solution but wants help in understanding a principle of Physics. Please read the post before engaging in moderator clamp down. – Paul Childs Mar 27 '19 at 6:42
This is a nice example of a block and tackle system, where two mechanical "flavours" are realized at the same time: The "rove to advantage" on the right, i.e. the pull on the rope is in the same direction in which the load is to be moved and "rove to disadvantage" on the left, i.e. the pull opposes the direction in which the load is to be moved. This is the reason why "counting ropes" as you called it will not lead you to the solution here.
In general, a block and tackle system allows you to move heavy weight (represented by a Force $$F$$) by increasing the distance $$s$$ that you have to cover. The work $$W = F \cdot s$$ always stays the same.
Check the example 1 from Wikipedia below:
If you pull the string on the left, you move the weight up. Due to the pulley configuration however, the weight will move half the distance of what you pulled. The necessary force is also 0.5 times compared to simply lifting the weight.
Now check the example 2 from Wikipedia:
You have the same amount of ropes and the same amount of pulleys. However, they are attached in a different way: The weight is fixed at two points of the pulley system. If you do the maths, you will find that you only have to exert one third of the force and pull 3 times the distance compared to simply lifting the weight.
Example 1 corresponds to the left side of your system. Force is transferred in a 1:1 ratio to the object. Example 2 corresponds to the right side. Here, force is transferred in a 4:1 ratio. I recommend the wiki article to solidify your understanding. If the maths is unclear, comment below.
In simple mechanics problems like this, where the mass of the rope and the pulleys and friction on the pulleys can be neglected, then you can assume there is the same tension $$T$$ throughout the whole length of the rope.
The rope is attached to the box (via pulleys) at four points on the right hand side of the block, so the force exerted by the rope on the right hand side of the block is $$4T$$. And because the force acting on one end of the rope is $$F_1$$ then you know $$T=F_1$$. This is where the $$4F_1$$ term comes from. | 2020-01-21 08:31:59 | {"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": 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": 15, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5348923206329346, "perplexity": 240.13238217767585}, "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/1579250601628.36/warc/CC-MAIN-20200121074002-20200121103002-00278.warc.gz"} |
https://scipost.org/submissions/1810.12828v1/ | Neutrinoless Double Beta Decay Overview
Submission summary
As Contributors: Laura Cardani Arxiv Link: https://arxiv.org/abs/1810.12828v1 Date submitted: 2018-10-31 Submitted by: Cardani, Laura Submitted to: SciPost Physics Proceedings Proceedings issue: The 15th International Workshop on Tau Lepton Physics (Amsterdam, 2018-09) Domain(s): Experimental Subject area: Nuclear Physics - Experiment
Abstract
Neutrinoless Double Beta Decay is a hypothesised nuclear process in which two neutrons simultaneously decay into protons with no neutrino emission. The prized observation of this decay would point to the existence of a process that violates a fundamental symmetry of the Standard Model of Particle Physics, and would allow to establish the nature of neutrinos. Today, the lower limits on the half-life of this process exceed 10$^{25}$-10$^{26}$ yr. I will review the current status of the searches for Double Beta Decay and the perspectives to enhance the experimental sensitivity in the next years.
Current status:
Has been resubmitted
Submission & Refereeing History
Resubmission 1810.12828v2 on 19 December 2018
Submission 1810.12828v1 on 31 October 2018
Reports on this Submission
Show/hide Reports view
Strengths
This is a very complete review.
Weaknesses
There a few sentences that are not 100% correct and some sentences could use some corrections for understanding or grammar.
Attachment
• validity: high
• significance: top
• originality: top
• clarity: high
• formatting: perfect
• grammar: good
Author Laura Cardani on 2018-12-19 (in reply to Report 1 on 2018-12-10)
Category:
2) about AMoRE, the Referee observed (correctly) that they are preparing a 200 kg experiment. I did not mentioned it before because I think it is not going to happen in the immediate future (they are still working on the kg scale), but I understand the point of the Referee, so I added a sentence to clarify that this is not a small R$\&$D, but a part of a long-term plan. | 2019-03-21 12:08:51 | {"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": 0.6493824124336243, "perplexity": 3215.9000826524866}, "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-2019-13/segments/1552912202523.0/warc/CC-MAIN-20190321112407-20190321134407-00439.warc.gz"} |
https://tex.stackexchange.com/questions/659907/size-of-the-rotated-table-cells | Size of the Rotated Table Cells
I want to create a custom table with tabularray package. I have used makecell and rotating packages to rotate some of the table cells. Additionally, the length of the rotated cells are set with \setlength\rotheadsize{} command and as it is expected, it affects all rotated cells. However, I want to set the size individually.
MWE:
\documentclass{article}
\usepackage[paperheight=6in,
paperwidth=5in,
top=10mm,
bottom=20mm,
left=10mm,
right=10mm]{geometry}
\usepackage{tabularx}
\usepackage{tabularray}
\usepackage{makecell}
\usepackage{rotating}
\begin{document}
\begin{table}[ht]
\begin{center}
\begin{talltblr}[
caption = {Example Table},
label = {tbl:example},
]{
width=\linewidth,
colspec={X[1]X[12]|X[1]|X[1]|X[1]|X[1]|},
vline{1}={3-Z}{solid},
vline{2}={3-Z}{solid},
rows = {c},
column{2} = {l},
}
\cline{3-6}
& & \SetCell[c=4]{c} Some Text \\
\cline{3-6}
& & Column 1 & Column 2 & Column 3 & Column 4 \\
\cline{1-6}
\SetCell[r=7]{c} Some longer text & Row 1 & X & X & \\
\cline{2-6}
& Row 2 & X & X & \\
\cline{2-6}
& Row 3 & X & X & \\
\cline{2-6}
& Row 4 & X & X & X \\
\cline{2-6}
& Row 5 & X & & X \\
\cline{2-6}
& Row 6 & X & & X \\
\cline{2-6}
& Row 7 & X & & X \\
\hline
\end{talltblr}
\end{center}
\end{table}
\end{document}
When the size is set for the rotated cells in 2nd row, the text in the 1st column becomes multiline. On the other hand, the height of the 2nd column becomes too high, when the size is set according to 1st column.
• Welcome to TeX.SE! Good question! Sep 28, 2022 at 23:12
Using your interesting answer as starting point, the possible (more consistent) solution for your problem can be :
\documentclass{article}
\usepackage{tabularray}
\usepackage{makecell}
\usepackage{rotating}
\begin{document}
\begin{table}[ht]
\caption{Example Table}
\label{tbl:example}
\centering
\begin{tblr}{hline{1,2} = {3-Z}{solid}, vline{1,2} = {3-Z}{solid},
hline{3-Z} = {solid}, vline{3-Z}={solid},
colspec = {c X[l] *{4}{c} },
}
& & \SetCell[c=4]{c} Some Text
& & & \\
& & Column 1
& Column 2
& Column 3
& Column 4 \\
\SetCell[r=7]{c} Some longer text
& Row 1 & X & & & \\
& Row 2 & & X & & \\
& Row 3 & & & X & \\
& Row 4 & & & & X \\
& Row 5 & & & X & \\
& Row 6 & & X & & \\
& Row 7 & X & & & \\
\end{tblr}
\end{table}
\end{document}
which gives
As can be seen, in above MWE in table body is preserved usual way for writing cells contents and command for rotating is merged with settings of rotated cell sizes in table preamble.
Perhaps there is a better solution for this. For the time being, I would simply use \rotatebox[origin=c]{90}{...} in the affected cell
\documentclass{article}
\usepackage[paperheight=6in,
paperwidth=5in,
top=10mm,
bottom=20mm,
left=10mm,
right=10mm]{geometry}
\usepackage{tabularray}
\usepackage{makecell}
\usepackage{rotating}
\begin{document}
\begin{table}[ht]
\begin{center}
\begin{talltblr}[
caption = {Example Table},
label = {tbl:example},
]{
width = 0.8\linewidth,
colspec = {X X[12] *4{X}},
vline{1} = {3-Z}{solid},
vline{2} = {3-Z}{solid},
vline{3-Z} = {},
hline{1,2} = {3-6}{},
hline{3-Z} = {},
rows = {c},
column{2} = {l},
}
& & \SetCell[c=4]{c} Some Text \\
& & Column 1 & Column 2 & Column 3 & Column 4 \\
\SetCell[r=7]{} \rotatebox[origin=c]{90}{Some longer text}
& Row 1 & X & X & & \\
& Row 2 & & X & X & \\
& Row 3 & & X & X & \\
& Row 4 & & X & X & X \\
& Row 5 & & X & & X \\
& Row 6 & & X & & X \\
& Row 7 & & X & & X \\
\end{talltblr}
\end{center}
\end{table}
\end{document}
Instead of using \rothead command as a parameter of cell, I used it in place and gave \setlength and \settowidth commands as a cell parameter.
\documentclass{article}
% Using the geometry package with a small
% page size to create the article graphic
\usepackage[paperheight=6in,
paperwidth=5in,
top=10mm,
bottom=20mm,
left=10mm,
right=10mm]{geometry}
\usepackage{tabularx}
\usepackage{tabularray}
\usepackage{makecell}
\usepackage{rotating}
\begin{document}
\begin{table}[ht]
\begin{center}
\begin{talltblr}[
caption = {Example Table},
label = {tbl:example},
]{
width=\linewidth,
colspec={X[1]X[12]|X[1]|X[1]|X[1]|X[1]|},
vline{1}={3-Z}{solid},
vline{2}={3-Z}{solid},
rows = {c},
column{2} = {l},
}
\cline{3-6}
& & \SetCell[c=4]{c} Some Text \\
\cline{3-6}
\cline{1-6}
\SetCell[r=7]{c} \rothead{Some longer text} & Row 1 & X & X & \\
\cline{2-6}
& Row 2 & X & X & \\
\cline{2-6}
& Row 3 & X & X & \\
\cline{2-6}
& Row 4 & X & X & X \\
\cline{2-6}
& Row 5 & X & & X \\
\cline{2-6}
& Row 6 & X & & X \\
\cline{2-6}
& Row 7 & X & & X \\
\hline
\end{talltblr}
\end{center}
\end{table}
\end{document} | 2023-02-06 09:18:17 | {"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": 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": 0.8890586495399475, "perplexity": 1206.066081427768}, "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-2023-06/segments/1674764500334.35/warc/CC-MAIN-20230206082428-20230206112428-00137.warc.gz"} |
http://www.linuxquestions.org/questions/general-10/singular-authorship-of-isaiah-4175467202/page7.html | Home Forums HCL Reviews Tutorials Articles Register Search Today's Posts Mark Forums Read
LinuxQuestions.org Singular authorship of Isaiah
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07-02-2013, 07:32 AM #91 brianL LQ 5k Club Registered: Jan 2006 Location: Oldham, Lancs, England Distribution: Slackware & Slackware64 14.1 Posts: 7,453 Blog Entries: 55 Rep: ????????? What?????
07-02-2013, 07:44 AM #92 TobiSGD Moderator Registered: Dec 2009 Location: Germany Distribution: Whatever fits the task best Posts: 17,133 Blog Entries: 2 Rep: @jamison20000e: It would definitely help us all to understand you if you would use the English grammar in your posts.
07-02-2013, 09:57 AM #93
sundialsvcs
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Originally Posted by bluegospel I'm pretty certain it's generally accepted by serious scholars that Isaiah wrote the foremost chapters, more than the first 9.
No, since there's nothing like an original verifiable signature on any of the documents, they're simply pseudonymous. We can't verify who wrote them. Nor do we have any way to know whether the text in our hands is, or is not, actually what "whoever it was" wrote, "whenever it was." We don't, and literally can't, know the entire provenance of any such texts.
In most texts of this sort, we do notice very-distinct changes of tone from one section to the next. These suggest that, over the course of these thousands of years, some "compiling" and probably rewriting must have been done. We don't know when, or by who. (It might even have been a committee.)
Further complicating the issue are things like the Councils of Nicene, which were tasked with constructing a "canonical" Bible: the sixty-six books that we ... oops! the Catholic version is different ... and what to do with the leftovers. (Alas, a great many libraries were destroyed forever, just because they contained "heresy" according to someone with a match.)
We know that the King James scholars (and every group since them) has dealt with multiple "original" sources, some of these being translations e.g. in Greek, and we know that they are different from one another.
Like it or not ... "believe it" or not ... these are things that we know. "Deal with it." To answer the OP's original question, "we should presume that all of these books had many authors, and revisions, and (literally...) 'God only knows' what else," done to them before they wound up in our hands. We might live in "the information age," with SHA1 checksums and all-of-that, but our forefathers didn't. Therefore, if we attempt to hold these books up to the mythical standard of "TRVTH," well, I think that we're just being very unrealistic about it, in a way that is not wise. They are what they are, as they are.
And, even though it seems that I might be in the minority here (?), this doesn't bother me at all. Study the books for what they are, warts and all, and know that the books themselves are really beside-the-point. "The Ancient of Days" has no failure to communicate. God has used rocks, donkeys, the wind, and shrubbery. "Seek, and you will Find." If, as many believe, He intended to convey a message "down through the ages," in spite of the frailties of the spoken and of the written word (and of countless scribes and committees) ... well, "He did, didn't He?"
Last edited by sundialsvcs; 07-02-2013 at 10:06 AM.
07-02-2013, 02:31 PM #94
Nbiser
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Originally Posted by TobiSGD A total non-sequitur. Ethics have nothing to do at all with a god. One can be an ethical person without ever believing in god, for example based on the simple "Don't do to others what you don't want to be done to you!" I personally rather find it rather scary how many believers only don't do the things they accuse atheists of wanting to do because of the fear of a supreme being, instead basing this on their own morality.
Sorry Tobi, you didn't address the issue. What is the ultimate authority behind "Don't do to others what you don't want to be done to you!" According to you, that was said by one piece of cosmic dust to another piece of cosmic dust, thus according to you don't have to obey it.
You tell me: what is the authority keeping you from murdering for instance? Why is murder wrong?
Quote:
Sorry, but reading this it seems to me that you neither know much about the science behind this (by the way, the christian god and evolution are not mutual exclusive, ask the pope), nor do you seem to know much about other religions, when you claim that the Christian religion is the only one that accounts for this (at least Judaism shares the same creation story with Christianity).
I don't care about what the pope says. He is an apostate and an heretic, who leads others astray with his false doctrine.
Since you know so much more about science than I do, you tell me. Where does the world as we know it come from? In short, I want to know what the ultimate source of the world and everything in it is.
Quote:
You realize that the authors of the gospels were well aware of those predictions and had no problem at all to adapt their stories to them?
Yes, maybe they did know. But this doesn't mean that they made it up. There were hundreds of witnesses at the time who saw Christ, and the miracles that he performed. Josephus, one of the most recognized historians of the era, recognized Christ, and his death on the cross. Just as prophesied.
All but one of these men died for what they wrote.....if they admitted that they lied, they would've have been saved, and even treated with great honor. However, they suffered cheerfully and willingly for what they wrote, never admitting that they lied, even when under torture. Once again, would you be willing to die for a lie that you said; even if you would be given pardon for confessing?
Quote:
But anyways, I can't see how any of this is related to the question about the number of authors of the book Isaiah.
Almost nothing in this thread has had anything to do with the original posters intent.
Last edited by Nbiser; 07-02-2013 at 06:16 PM.
07-02-2013, 03:13 PM #95 jamison20000e Senior Member Contributing Member Registered: Nov 2005 Location: ...uncanny valley... infinity\1975; (randomly born:) Milwaukee, WI, US, Earth, end border$! ◣◢┌∩┐ Fe26-E,e... Distribution: any GPL that works well on my cheapest; has been KDE or CLI but open... http://goo.gl/NqgqJx &c ;-) Posts: 3,514 Blog Entries: 2 Rep: gods make haters i know or you really can't or won't understand that+ wow how about if i misspell more but say simple stuff like: heaven and hell are ONLY metaphors derr Last edited by jamison20000e; 07-02-2013 at 09:34 PM. 07-02-2013, 03:22 PM #96 TobiSGD Moderator Registered: Dec 2009 Location: Germany Distribution: Whatever fits the task best Posts: 17,133 Blog Entries: 2 Rep: Quote: Originally Posted by Nbiser Sorry Tobi, you didn't address the issue. What is the ultimate authority behind "Don't do to others what you don't want to be done to you!" According to you, that was said by one piece of cosmic dust to another piece of cosmic dust, thus according to you don't have to obey it. You tell me: what is the authority keeping you from murdering for instance? Why is murder wrong? I don't care about what the pope says. He is an apostate and an heretic, who leads others astray with his false doctrine. Since you know so much more about science than I do, you tell me. Where does the world as we know it come from? In short, I want to know what the ultimate source of the world and everything in it is. Yes, maybe they did know. But this doesn't mean that they made it up. There were hundreds of witnesses at the time who saw Christ, and the miracles that he performed. Josephus, one of the most recognized historians of the era, recognized Christ, and his death on the cross. Just as prophesied. All but one of these men died for what they wrote.....if they admitted that they lied, they would've have been saved, and even treated with great honor. However, they suffered cheerfully and willingly for what they wrote, never admitting that they lied, even when under torture. Once again, would you be willing to die for a lie that you said; even if you would be given pardon for confessing? All these questions are off-topic. If you would be so kind to ask them again in the religion mega-thread I will answer them there. Quote: Almost nothing in this thread has had anything to do with the original posters intent. And that is why a moderator asked the members to go back on topic in this thread. 07-02-2013, 03:47 PM #97 Nbiser Member Registered: Oct 2012 Location: Maryland Distribution: Fedora, Slackware, Debian, Ubuntu, Knoppix, Helix, Posts: 302 Blog Entries: 7 Rep: Quote: Originally Posted by TobiSGD All these questions are off-topic. If you would be so kind to ask them again in the religion mega-thread I will answer them there. And that is why a moderator asked the members to go back on topic in this thread. OK then, we can move this to the religion mega-thread. However, I searched for it and couldn't find it. What section is it? Nbiser 07-02-2013, 03:53 PM #98 jamison20000e Senior Member Contributing Member Registered: Nov 2005 Location: ...uncanny valley... infinity\1975; (randomly born:) Milwaukee, WI, US, Earth, end border$! ◣◢┌∩┐ Fe26-E,e... Distribution: any GPL that works well on my cheapest; has been KDE or CLI but open... http://goo.gl/NqgqJx &c ;-) Posts: 3,514 Blog Entries: 2 Rep: About a book of "god" equals... Dose "he\it(more likly an alien)" exist?
07-02-2013, 05:40 PM #99
k3lt01
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Originally Posted by Nbiser OK then, we can move this to the religion mega-thread. However, I searched for it and couldn't find it. What section is it? Nbiser
Don't bother, I have asked and never get an answer. Not one of the "pro-science" (anti-religion) group has been able to answer any question like you asked yet. They demand proof on a topic that is based on faith yet cannot give proof on a topic that is based on empirical evidence.
07-02-2013, 06:00 PM #100
TobiSGD
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Originally Posted by Nbiser OK then, we can move this to the religion mega-thread. However, I searched for it and couldn't find it. What section is it? Nbiser
Just click on the link in my previous post.
07-02-2013, 06:15 PM #101
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Originally Posted by TobiSGD Just click on the link in my previous post.
Thanks! I didn't see that.
07-02-2013, 08:22 PM #102
jamison20000e
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Location: ...uncanny valley... infinity\1975; (randomly born:) Milwaukee, WI, US, Earth, end border$! ◣◢┌∩┐ Fe26-E,e... Distribution: any GPL that works well on my cheapest; has been KDE or CLI but open... http://goo.gl/NqgqJx &c ;-) Posts: 3,514 Blog Entries: 2 Rep: Pr∞f: Quote: Originally Posted by k3lt01 Don't bother, I have asked and never get an answer. Not one of the "pro-science" (anti-religion) group has been able to answer any question like you asked yet. They demand proof on a topic that is based on faith yet cannot give proof on a topic that is based on empirical evidence. Some answers will never have proof so we create our own(.) We come from nothing and go back, Period! Infinitely debatable as "facts" change throughout infinite time. And, if u'll never get that blame "grammar"... "They" demand ∞\* Last edited by jamison20000e; 07-02-2013 at 09:39 PM. 07-02-2013, 11:10 PM #103 k3lt01 Senior Member Registered: Feb 2011 Location: Australia Distribution: Debian Wheezy, Jessie, Sid/Experimental, playing with LFS. Posts: 2,900 Rep: Quote: Originally Posted by jamison20000e Some answers will never have proof so we create our own(.) We come from nothing and go back, Period! Infinitely debatable as "facts" change throughout infinite time. And, if u'll never get that blame "grammar"... "They" demand ∞\* The 1st highlighted section is exactly my point. Many things will never have proof so why the agro demanding proof of things that are based on faith? Furthermore why the narrow sightedness that science has the answers? A couple of years ago I asked a simple question in the other thread, which I will never again post in, of someone who was adamant that his point of view was the only point of view. I haven't seen that person in LQ this year and I still have not been answered. Facts don't change but knowledge does, I wont blame grammar for that what I will question is how you come to your conclusion. I'll give you an example. Fact the Earth is sphere (well it is an prolate sphere). Knowledge (poorly constructed) in various periods of history said it was flat, maps showed it was flat, organisations with vested interests said it was flat, uneducated people (do not blame the bible for this rather blame organisations with vested interests) did not question what they were told. The fact that the earth is a sphere has not in any way, shape (get the pun), or form, changed, but knowledge has. How does the example relate to the OP? Some people believe Isaiah was written by one person. What evidence do they have of this? They say the book itself + other things that come to mind during the discussion. Others believe Isaiah was written by more than one person. What evidence do they have of this? They say the book itself + other things that come to mind during the discussion. Who'se right? who'se wrong? does it really, really, really matter? Some people will argue till they are blue in the face, they will not ever see the other side of the discussion yet expect the other side to see their argument. Until everybody enters these discussions with an open mind, I am yet to see evidence of this, these discussions are a back and forth that get no where. 07-02-2013, 11:53 PM #104 jamison20000e Senior Member Registered: Nov 2005 Location: ...uncanny valley... infinity\1975; (randomly born:) Milwaukee, WI, US, Earth, end border$! ◣◢┌∩┐ Fe26-E,e...
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Faith is a word\knowledge-only(circles) and depending on 'your' changing religions...
Science is by flesh(only) and will never have all the answers, most if not all is po\$turing some times at wanting to understand or fix.
I simply rebel, except: love and death(although we try).(intertwined by hypocrisy and irony, for how ever long(?)edu)
"Facts don't change":
Quote:
Originally Posted by jamison20000e ...read every science\religious book ever recorded to see...
Oops up till here i thought we were there and i could say any religiously debatable thing lol not that i wouldn't... So:
Quote:
Originally Posted by bluegospel Singular authorship of Isaiah
Books use words by other people, all is eclectic if nothing else... (and we only learn words when taught just like blind faith and greed) There Thread Completion
"Who'se right? who'se wrong? does it really, really, really matter?" Sacrificing virgins and education that's wrong, that's why religions evolve.
Stopping before too many circles
Last edited by jamison20000e; 07-03-2013 at 01:41 AM.
07-03-2013, 12:38 AM #105 k3lt01 Senior Member Registered: Feb 2011 Location: Australia Distribution: Debian Wheezy, Jessie, Sid/Experimental, playing with LFS. Posts: 2,900 Rep: I don't get 95% of what you post at the best of times, that last post makes very little sense at all. Are you cross posting the same things on two threads? Confusing the discussion along the way by any chance?
Tags human stupidity, pointless
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Contact Us - Advertising Info - Rules - LQ Merchandise - Donations - Contributing Member - LQ Sitemap - | 2017-06-27 23:51:03 | {"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": 0.35688015818595886, "perplexity": 5687.5521035076545}, "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-2017-26/segments/1498128321938.75/warc/CC-MAIN-20170627221726-20170628001726-00679.warc.gz"} |
https://mirror.uned.ac.cr/cran/web/packages/cdfquantreg/vignettes/CDFQuantregIntroduction.html | # cdfquantreg: An Introduction
The most popular two-parameter distribution for modeling random variables on the (0, 1) interval is the beta distribution (e.g., Ferrari and Cribari-Neto, 2004; Smithson and Verkuilen, 2006). Less commonly used are the Kumaraswamy (1980), Lambda, and Logit-Logistic distributions. The cdfquantreg package introduces a family of two-parameter distributions with support (0, 1) that may be especially useful for modeling quantiles, and that also sometimes out-performs the other distributions.
Tadakimalla and Johnson (1982) replace the standard normal distribution in Johnson’s SB distribution (Johnson, et al. 1995) with the standard logistic distribution, thus producing the logit-logistic distribution. A natural extension of this approach is to employ other transformations from (0, 1) to either the real line or nonnegative half of the real line, and expand the variety of standard distributions as well. The resulting family of distributions has the following useful properties:
1. Tractability, with explicit probability distribution functions (pdfs), cdfs, and quantiles.
2. They are amenable to both maximum likelihood and Bayesian estimation techniques.
3. They enable a wide variety of quantile regression models for random variables on the (0, 1) interval with predictors for both location and dispersion parameters, and simple interpretations of those parameters.
4. The family can model a wide variety of distribution shapes, with different skew and kurtosis coverage from the beta or the Kumaraswamy.
5. Explicit quantiles render random generation of variates straightforward.
# The Distribution Family
Let $$G(x,\mu,\sigma)$$ denote a cdf with support (0, 1), a real-valued location parameter $$\mu$$ and positive scale parameter $$\sigma$$. $$G$$ is defined as
$$G(x,\mu,\sigma) = F[U(H^{-1}(x),\mu,\sigma)]$$,
where $$F$$ is a standard cdf with support $$D_1$$, $$H$$ is a standard invertible cdf with support $$D_2$$, and $$U: D_2 \rightarrow D_1$$ is an appropriate transform for imposing the location and scale parameters. $$D_1$$ and $$D_2$$ are either $$[-\infty,\infty]$$ or $$[0,\infty]$$. If $$D_1 = D_2 = [-\infty,\infty]$$ then
$$U(x,\mu,\sigma) = (x - \mu)/\sigma$$,
and if $$D_1 = [0,\infty]$$ then
$$U(x,\mu,\sigma) = (e^{- \mu}x)^{1/\sigma}$$.
The members of this family that are included in this package have $$D_1 = D_2 = [-\infty,\infty]$$.
If $$F$$ is invertible, then the distribution has an explicit quantile. If $$G$$ is differentiable then it has an explicit pdf. All of the distributions in this package share both properties.
There is a relation between pairs of these distributions in which $$F$$ and $$H$$ exchange roles. These pairs are “quantile-duals” of one another in the sense that one’s cdf is the other’s quantile, with the appropriate parameterization. We name these distributions with the nomenclature F-H (e.g., Cauchit-Logistic and Logit-Cauchy). See cdfquantreg_family for a list of the distributions included in this package.
## Useful Properties
1. The probability distribution functions (pdfs) $$g(x,\mu,\sigma )$$ are self-dual in this respect: $$g\left( {x,\mu ,\sigma } \right) = g\left( {1 - x, - \mu ,\sigma } \right)$$.
2. When $$H$$ = $$F$$ the distribution includes the uniform distribution as a special case. Otherwise, all distributions are symmetrical at $$x = \frac{1}{2}$$.
3. For all distributions in this package, the median is a function solely of the location parameter $$\mu$$.
4. It can be shown that the scale parameter $$\sigma$$ is a dispersion parameter, controlling the spread of other quantiles around the median.
5. Maximum likelihood estimation is feasible for all distributions in this package.
6. Models with predictors of both location and scale (dispersion) parameters can be estimated.
Further details and more general characterizations of this distribution family are available in Smithson and Shou (2016).
## Example
An example is the Logit-Cauchy distribution. This distribution employs the Logistic cdf $$F\left( z \right) = \frac{1}{{1 + {{\rm{e}}^{ - z}}}}$$ and the Cauchy cdf $$H\left( z \right) = \frac{{{{\tan }^{ - 1}}(z)}}{\pi } + \frac{1}{2}$$. Inverting $$H$$ and applying it and $$F$$ to the equation above for $$G(x,\mu,\sigma)$$ gives
$$G\left( {x,\mu ,\sigma } \right) = \frac{1}{{1 + \exp \left( {\frac{{\mu + \cot (\pi x)}}{\sigma }} \right)}}$$,
and differentiating it gives the pdf
$$g\left( {x,\mu ,\sigma } \right) = \frac{{\pi {{\csc }^2}(\pi x){e^{\frac{{\mu + \cot (\pi x)}}{\sigma }}}}}{{\sigma {{\left( {{e^{\frac{{\mu + \cot (\pi x)}}{\sigma }}} + 1} \right)}^2}}}$$.
Inverting $$F$$ and the appropriate substitutions give us the quantile:
$${G^{ - 1}}\left( {\gamma ,\mu ,\sigma } \right) = \frac{{{{\tan }^{ - 1}}\left( {\sigma \left( {\frac{\mu }{\sigma } - \log \left( {\frac{1}{\gamma } - 1} \right)} \right)} \right)}}{\pi } + \frac{1}{2}$$.
Note that, as described in property 3 above,
$${G^{ - 1}}\left( {\frac{1}{2} ,\mu ,\sigma } \right) = \frac{\tan ^{-1}(\mu )}{\pi }+\frac{1}{2}$$,
and therefore
$$\mu = \tan \left(\pi Q\left( \frac{1}{2} \right)-\frac{1}{2}\right)$$,
where $$Q(\gamma)$$ denotes the quantile at $$\gamma$$. Likewise, as in property 4,
$$G^{ - 1}\left(\frac{e}{e+1},\mu ,\sigma \right) = \frac{\tan ^{-1}(\mu +\sigma )}{\pi }+\frac{1}{2}$$,
so that
$$\sigma = \tan \left(\pi \left(Q\left(\frac{e}{e+1} \right)-\frac{1}{2}\right)\right)-\tan\left[\pi \left(Q\left(\frac{1}{2} \right)-\frac{1}{2}\right)\right]$$.
# References
• Ferrari, S., & Cribari-Neto, F. (2004). Beta regression for modelling rates and proportions. Journal of Applied Statistics, 31(7), 799-815.
• Johnson, N. L., Kotz, S., & Balakrishnan, N (1995). Continuous Univariate Distributions, Vol. 2 (2nd ed.), Wiley, New York, NY.
• Kumaraswamy, P. (1980). A generalized probability density function for double-bounded random processes. Journal of Hydrology, 46(1), 79-88.
• Smithson, M. and Shou, Y. (2016). CDF-quantile distributions for modeling random variables on the unit interval. Unpublished Manuscript, The Australian National University, Canberra, Australia.
• Smithson, M., & Verkuilen, J. (2006). A better lemon squeezer? Maximum-likelihood regression with beta-distributed dependent variables. Psychological methods, 11(1), 54-71.
• Tadikamalla, P. R., & Johnson, N. L. (1982). Systems of frequency curves generated by transformations of logistic variables. Biometrika, 69(2), 461-465. | 2021-07-26 22:42:39 | {"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": 0.7622601985931396, "perplexity": 1337.318135622428}, "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/1627046152156.49/warc/CC-MAIN-20210726215020-20210727005020-00711.warc.gz"} |
https://mathematica.stackexchange.com/questions/20877/unique-in-rhs-of-rule | # Unique[] in RHS of rule
I have a function, explicit that takes dot product of two symbols, and replaces it with repeated dummy indices generated by Unique[].
explicit[expr_] :=
expr //. {Dot[a_, b_] :> (Subscript[a, #] Subscript[b, #]) &[
Unique[]]};
So that if my input is v.w, then the output is $v_{$3}w_{$3}$ which is good.
The problem is that if there is a single term multiplying two pairs of dot products, I don't know how to get Unique[] to generate a new symbol for each pair. That is, if I input c.d e.f the output is $c_{$3}d_{$3}e_{$3}f_{$3}$, which is bad. I want $c_{$3}d_{$3}e_{$4}f_{$4}$, with new repeated subscripts. How do I modify my code?
• By the way I don't think you need ReplaceRepated here but I left it in my answer since that wasn't the focus. – Mr.Wizard Mar 8 '13 at 3:52 | 2019-11-14 12:26:47 | {"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": 0.6157204508781433, "perplexity": 1393.4954762864209}, "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-2019-47/segments/1573496668416.11/warc/CC-MAIN-20191114104329-20191114132329-00004.warc.gz"} |
http://griceclub.blogspot.com/2013/09/ | Welcome
## The Grice Club
The club for all those whose members have no (other) club.
## Monday, September 30, 2013
### Grice and Strawson on "Introduction to Logical Theory"
Grice
But of course Grice was lying! He knew much more logic than he accepted in the footnote to "Vacuous Names".
Indeed, his claim to fame, back in the 1940s at St. John's, on St. Giles, was that of an expert in logic, rather than philosophy.
It was logic that Grice taught to his favourite tuttee: P. F. Strawson.
Strawson was grateful and kind enough in crediting this in the Preface to "Introduction to Logical Theory". Dedicated to "H. P. Grice" ("Mr. H. P. Grice" if you must -- since nobody took a DPhil at Oxford in those days -- it would sound presumptuous and overqualified) "from whom I have never ceased to learn about logic".
So it may do to revise what Strawson has to say about " = " in "Introduction to Logical Theory". Or not!
### Myro's System G
Speranza
In PGRICE, Myro presents Grice with a system G.
Grice was meant to provide individual responses to each of the contributions to the festschrift, but he had things to do (other than that).
Myro echoes Grice.
In "Words and Objections", Grice had introduced a system Q, to allow for things like the self-identity of
Pegasus = Pegasus
"Vacuous Names".
Myro, in "Time and Identity", in PGRICE, provides his System G ("in gratitude to Paul Grice"). In this system
=
becomes relativised to time.
The idea is to formalise the Hobbes paradox of the ship, and Aristotle's examples of the statue.
The result is too complex that does not fail to show Myro's expertise in logic that Grice had recognised in a footnote to "Vacuous Names". "I owe", Grice says -- paraphrasing him, "all I'm writing in formal logical terms here to Mates's "Logic" (Clarendon Press) and to George Myro".
### Grice's izzing and hazzing in the "Pacific Philosophical Quarterly" (vol. 69) essay
Speranza
Interestingly, Grice ended up publishing the 1977 Victoria, Canada, notes on izzing and hazzing.
As a matter of fact, the thing came out in 1988, as edited posthumously by B. F. Loar.
It contains the logic of izzing and hazzing, and has an interesting update -- including a footnote where Grice refers to the Code paper in PGRICE.
### Grice's izzind and hazzing -- as treated by Code
Speranza
Alan Dodds Code met Grice at Berkeley and he was soon fascinated.
In Code's contribution to Grandy's and Warner's festschrift for Grice, PGRICE, or Philosophical Grounds of Rationality: Intentions, Categories, Ends, Code proposes some formalisation of Grice's logic of izzing and hazzing.
The details have been discussed elsewhere by R. B. Jones.
### Grice on izzing and self-identity
Speranza
The keywords should be identity and self-identity.
But as early as 1977, in Victoria, Canada, Grice was presenting material in his exegesis of Aristotle. Grice comes up with I and H.
Some of Grice's formulae include
xIx
i.e. as Grice has it, identity is reflexive.
As opposed to "H"
Grice reads "I" as izzing and "H" as hazzing.
### Grice, Russell, and Leibniz on self-identity and identity
Speranza
Grice speaks of 'predicate calculus with identity' in "Reply to Richards". In such a calculus, alla Russell, 'identity', symbolised by " = " becomes DEFINED in terms of Leibniz's law.
Wikipedia should have the complete definition!
### Grice himself -- Grice his self
Speranza
Of course, when we speak of self-identity we should be reminded of B. A. O. Williams, sometime Oxonian philosopher, and his "Problems of the Self".
Grice's first published essay was indeed on "Personal identity", which is an analysis of "self" or "I" sentences:
"He hit the head with the cricket bat"
"He fell from the stairs"
"He is thinking of joining the army".
Grice comes up with a neo-Lockean theory based on mnemonic states, which, years later, will fascinate Perry, who will re-edit the essay (originally in "Mind" in 1941) with my favourite publishing house after Oxford's Clarendon Pres: University of California Press at Berkeley! (and paperback too!)
### Grice, Wiggins, Geach
Speranza
Geach of course has no Oxford association, unlike Wiggins. Yet, when Myro and Grice started to develop what came to be called the Grice-Myro theory of relative identity, the source seems to have been Geach's seminal essays in the area.
### Grice and Wiggins on identity and self-identity
Speranza
I would like to think that a historical interest on Grice's part was to examine what D. Wiggins was up to in his monumental study on "Sameness and substance".
Grice had left Oxford by then, but was quite in touch with developments. Especially since Wiggins would end up as Wykeham professor of Logic.
Grice dedicated a whole seminar -- co-taught by George Myro, to Wiggins's book.
### Grice: identity, self-identity, and beyond
Speranza
There was an interesting commentary on self-identity in PHILOS-L recently.
It may do to revise what Grice may have to say on the topic.
KEYWORDS: SELF-IDENTITY, IDENTITY.
## Saturday, September 28, 2013
### Grice's Trousers
Speranza
Oddly, there is an entry in the German wikipedia entitled
# Trouser-word
--- which is a word used by Grice in "Conception of Value".
"Als trouser-word wird in der Sprachphilosophie John Langshaw Austins ein Begriff bezeichnet, der nicht selbst inhaltlich definiert ist sondern nur durch den Kontrast zu seiner Negation eine Bedeutung erhält."
"Nach Austin sind Begriffe üblicherweise durch eigene Kriterien definiert. Um zu wissen, was es bedeutet, dass etwas X ist (oder ein X ist), muss man die Kriterien dafür kennen. Erst mit diesem Wissen kann man sagen, wann etwas nicht X (oder kein X) ist. Bei trouser-words verhält es sich genau umgekehrt: Etwas ist dann Y, wenn es keines der Kriterien erfüllt, nicht Y zu sein. Typische Beispiele sind für Austin real und directly. Ohne z. B. zu wissen, was es bedeuten soll, dass etwas keine echte Ente ist, gibt es auch keinen inhaltlichen Unterschied zwischen den Bezeichnungen eine Ente und eine echte Ente. Erst im Kontext z. B. einer Spielzeugente oder eines Bildes einer Ente ergibt das Prädikat echt eine Bedeutung, wobei diese je nach der kontextabhängigen Definition einer unechten Ente unterschiedlich ist."
## Literatur
• John Langshaw Austin: Sense and Sensibilia, Oxford 1962
Von „http://de.wikipedia.org/w/index.php?title=Trouser-word&oldid=60730001“
### The Real Grice
Speranza
We are discussing metaphysics and real metaphysics.
Jones confides: "I did have a qualm when I wrote "really metaphysics"! I think the distinction is a part of chosing languages and methods, something which Carnap was engrossed in, which he held should be done on pragmatic grounds. To much to say to fit here I think."
Well, I would think that, even if not strictly Anglo-Saxon (and what's the good of an item of vocabulary, qua part of ordinary language, if it does not have an old Anglo-Saxon pedigree), 'real' is a keyword in metaphysics.
I always enjoyed Austin's treatment of the word 'real' as the word that 'wears the trousers', a sexism that Grice (in his book, "Conception of Value") finds 'typically artless' while characteristically Oxonian, if I recall correctly.
I'll try to retrace Austin's commentary on 'real' -- as per 'real duck'.
### Palæolithic Implicatures
Speranza
The term "Palæolithic" was coined by archaeologist John Lubbock in 1865. It derives from Greek: παλαιός, palaios, "old"; and λίθος, lithos, "stone", literally meaning "old age of the stone" or "Old Stone Age."
It refers to the Grice/Russell polemic: is it stone-age physics or stone-age metaphysics we are dealing with.
This from
Schaffer, Jonathan, "The Metaphysics of Causation", The Stanford Encyclopedia of Philosophy (Fall 2008 Edition), Edward N. Zalta (ed.), URL = http://plato.stanford.edu/archives/fall2008/entries/causation-metaphysics/.
may help clarify:
"The main argument for eliminativism is that science has no need of causation. The notion of causation is seen as a scientifically retrograde relic of Stone Age metaphysics. As Russell claims, “In the motions of mutually gravitating bodies, there is nothing that can be called a cause, and nothing that can be called an effect; there is merely a formula.” (1992, p. 202, see also Quine 1966) The differential equations of sophisticated physics are said to leave no room for causes, or at least to have no need of them."
Grice disagrees.
He spends quite a few paragraphs in his seminal "Actions and Events" (Pacific Philosophical Quarterly, 1986) in discussing 'cause' as per the Greek 'aitia'.
A rebel without a cause
being his favourite idiom.
A rebel without a cause seems like a contradiction in terms. A cause, for the Greek, was a reason for acting. This may correspond to what Russell (who never studied palaeolithic implicatures too seriously) would dismiss as "out-dated" by a few millennia. Or not!
### The Griceian Caveman
Speranza
The phrase in Russell seems to involve "the metaphysics of the stone age to which common sense is due", which Grice reformulates as "the PHYSICS OF THE STONE AGE to which common sense" (and English, for that matter) is due. Or something.
### The Cave Man as Griceian
Speranza
We are discussing, with R. B. Jones, the claims of metaphysics, and Grice's repartee to Russell re: Russellian "stone-age metaphysics" (versus a metaphysics that should accomodate what Russell calls "twentieth-century physics") is best understood, for Grice, as "stone-age physics".
Jones notes:
"It would be interesting to know something about why Grice made this remark, it might illuminate Grice's ideas about what is or is not metaphysics."
I think Russell is fighting with Strawson. Strawson had published, for Oxford (almost) his "Individuals", an essay in, as we know, descriptive (or is it revisionary?) metaphysics, according to which the world is composed of substances (or individuals) having this or that attribute.
I'm never sure what Russell had in mind when he spoke of 'stone-age metaphysics', but he certainly didn't like it!
Grice's response deals with the fact that, whatever the physics of the twentieth-century (and underlying metaphysics, a process-metaphysics alla Whitehead), the fact remains that subject-predicate structures permeate ordinary languages such as English -- The original English speakers were, as it were, cave men.
This leads Grice to distinguish between categories which are merely linguistic (subject-predicate) or ontological (substance-attribute) and wonder what the role of the philosopher (qua metaphysician) may be. Grice finds some value in even approaching the categories of subject and predicate as valid in an attempt to describe the 'ontological commitments' of this or that language.
It's a short passage or two in "Reply to Richards".
Russell was nowhere to respond, so Grice's correction of Russell's misguided idiom was perhaps itself misguided, or not.
### How to misunderstand Grice
Speranza
In a note to the post on 'pervasiveness' of misunderstanding (as per the infamous quote in Popper's "Unended quest" -- remember people WILL misunderstand you -- freely paraphrased), R. B. Jones provides an interesting commentary.
Jones writes:
"The point about modalities preventing cancellation of negatives may be illustrated by reference to "Always remember that it is impossible to speak in such a way that you cannot be misunderstood: there will always be some who misunderstand you." To ensure the first clause one does not need the full strength of the second, it suffices that there will always be some who could misunderstand, an actual misunderstanding is not necessary."
Very good point.
"However, when we relate this to Grice's maxim about avoiding ambiguity, I think the conflict is only apparent, for I agree with both. Different standards are involved. At least in my assent to the Popper dictum I am thinking of some kind of absolute unambiguity, whereas in assenting to Grice I am taking unambiguity in a more ordinary pragmatic sense in which it can be realised with care."
Good point. For the record, Grice's example was, if I recall correctly, Blake's lines:
INTERLUDE from Wikipedia:
Never pain to tell the love,
Love that never told can be;
For the gentle wind does move
Silently, invisibly.
I told my love, I told my love,
I told her all my heart;
Trembling, cold, in ghastly fears,
Ah! she doth depart.
Soon as she was gone from me,
A traveller came by,
Silently, invisibly;
Oh was no deny.
Wikipedia in fact provides the manuscript, which looks even more ambiguous:
Wikipedia comments: "This was first published in 1863 by Dante Gabriel Rossetti in his edition of Blake's poems, which formed the second volume of Alexander Gilchrist's posthumous Life of William Blake. It was edited from a notebook in Rossetti's possession, now known as the Rossetti MS., containing a great number of sketches, draft poems, polemical prose, and miscellaneous writings, which Blake kept by him for many years.
As the only textual authority for many of these poems is a foul draft, some of them are partly editorial reconstructions. In the notebook the first stanza of "Never pain to tell thy love" has been marked for deletion. Two variant readings are sometimes found in published versions of the poem. In the first line "seek" was deleted by Blake and replaced by "pain", and the final line replaced the deleted version "He took her with a sigh"".
END OF INTERLUDE of Grice on Blake on 'intentional' or designed ambiguity projecting this or that implicature -- i.e. a 'flouting' of the maxim, 'avoid ambiguity' falling within the conversational category of "MODUS" --
Jones goes on:
"In the absolute sense Carnap's formal languages are not immune, because their semantics is given in a natural language and hence lacks absolute unambiguity (or if given in a formal language, we have a regress or circularity to deal with, either way giving sceptical grounds for doubting that absolute precision is attainable)."
I see. We should still consider Grice's main mentor: Chomsky. Oddly, Chomsky was, by a decade or two or more, Grice's junior, yet in "Reply to Richards", Grice counts as his mentors Quine (Grice's senior) and Chomsky. And Chomsky misquotes Grice (as "A. P. Grice") in the index to "Theory of Syntax". Yet, Chomsky is famous for wanting to deal with 'ideal' speaker/hearer (or utterer-addressee in Griceian parlance). In fact, William Labov founded his own revolution in linguistics by attacking Chomsky on that: Aristotelianly speaking, there's no such thing as an ideal utterer/addressee. I will try to retrack Chomsky's infamous quote.
What is interesting is to provide a Griceian context. For Austin (J. L. Austin) was a fan of Chomsky, and would analyse "Syntactic Structures" (which bored Grice) in almost every Saturday morning for a whole term or so.
In a Wikipedia entry for "Linguistic competence" we have Chomsky's infamous predicament:
"Linguistic theory is concerned primarily with an IDEAL speaker-listener, in a completely homogeneous speech-community, who knows its (the speech community's) language perfectly and is unaffected by such grammatically irrelevant conditions as memory limitations, distractions, shifts of attention and interest, and errors (random or characteristic) in applying his knowledge of this language in actual performance." ~Chomsky,1965
----
"memory limitations, distractions, shifts of attention and interest, and errors (random or characteristic)" -- under which latter falls misunderstanding _contra_ Popper (or not!)
## Thursday, September 26, 2013
### Grice, "Lectures on Aristotle"
Speranza
Jones comments on a post on Grice, Carnap and Aristotle:
"I would have thought it the rule rather than the exception that a lecturer pays no attention to what was on be board from the previous lecture (but then I did my best to avoid
attending lectures when I was a student)."
Indeed.
I think Grice over-uses (or abuses if you prefer) the word 'lecture'. William James lectures on logic and conversation.
I think the alternate Oxonian label is 'read'.
"He is a reader in mental philosophy". "He is indeed the Wilde reader in mental philosophy".
"He lectured us on metaphysics".
Officially, Grice's post with the Universit of Oxford was indeed University Lecturer, so that's what he was expected to do.
Note that to lecture is not to teach, either!
### Carnap and Grice: semantics and ontology -- and anti-empiricism?
Speranza
We should recall that one of the bêtes noires that Pilgrim Grice meets on his way to the City of Eternal Truth is indeed EMPIRICISM (while he regarded as 'enough of a rationalist' to engage in transcendental or metaphysical arguments).
Jones comments on a post on Carnap/Grice on Aristotle:
"I think one can reasonably say that Carnap's "Empiricism Semantics and Ontology" was primarily intended to explain how one can do semantics without engaging in metaphysics."
Good point.
"However, I don't attach much importance to Carnap mentioning Aristotle here."
Indeed. It seems like a gratuituous appeal, as the one Tarski makes, too -- On the other hand, more or less in those days, Jan Łukasiewicz seems to have been engaged in a more serious study of Aristotle: primarily his logic but I suppose the metaphysical background for his logic too?
(I am reminded of the title to Dummett's William James lectures: the logical basis of metaphyiscs -- but he is concerned with INTUITIONISM and the rejection of the "Tertium non datur").
Jones goes on:
"Carnap is not examining Aristotle here; he is simply using him in much the way I did when I earlier connected Carnap with Aristotle, just because Aristotle is the first and greatest philosopher with whom we associate the term "metaphysics" (if only because the term was not coined before Aristotle). I still press the case that there is an interesting enquiry and debate about whether or how much of Aristotle's metaphysics (and also about how much of Grice's Aristotelian studies) must be construed as the kind of metaphysics which Carnap eschewed."
Indeed, and those points were excellent.
For one, Aristotle's "Metaphysics" is concerned with 'physical' claims by the pre-socratics. Unfortunately, physicists never take the history of their discipline as seriously as philosophers do!
Also, much of what Aristotle says about 'being' is best understood as logical, rather than metaphysical -- as per the analytic commentary by Grice -- regarding izzing and hazzing.
This leaves us with the idea that Carnap's target of attack is OTHER: theoreticians who are into 'transcendental truths' of this or that sort: Heidegger, and perhaps before him Bradley, who, rather than an empiricist, was an 'idealist' (or as I prefer, a Hegelian).
Jones goes on:
"Carnap doesn't so far as I know get into these kinds of question (is that bit of so-called metaphysics really metaphysics); it's just a quirk of mine, partly for the purposes of fantasising about a Carnap/Grice conversation."
Indeed.
And the point about 'metaphysics ' and 'really metaphysics' sounds METAPHYSICAL! :)
----
Perhaps the answer is in the philosophy of physics. For instrumentalism, and the many other doctrines that inform this field of study do not PERTAIN to physics, and so have a claim to belong to, er, metaphysics...
Or not!
### Metaphysics alla Carnap and alla Grice -- and alla Bradley (as cited by Grice in Way of Words, "Prolegomena").
Speranza
To speak of "metaphysics" alla Carnap seems elusive, since we are concerned, rather, with the basis for his rejection of the alleged philosophical discipline as such.
Jones commented on "Aristotle: Carnap and Grice on the metaphysics".
Jones writes:
"There seem to me lots of issues with the page there that I read. So often people writing about Carnap attribute to him view that don't seem to me correct. For example here, talk about Carnap not accepting the meta-language "point of view" till late, when we know that it was an important element of his inspiration for Logical Syntax which occurred at the time of Godel's incompleteness result, 1931. But it does look like we find Carnap taking Aristotelian metaphysics at face value (i.e. as metaphysics in his own sense) whereas I am frequently arguing that things which typically are called metaphysics don't actually qualify as such relative to Carnap's conception. There is here some gap between the conclusions I draw from Carnap's (stated) position and the conclusions he himself drew."
Which is interesting and possibly VERY valid!
For we have to distinguish between 'metaphysics' as the pre-socratics felt it: they seem to be engaged in 'physics'.
Aristotle's commentary on these physical claims by the pre-socratics.
Aristotle's theory of being as belonging to 'logic' rather.
Grice's exegesis of Aristotle as analytic in character.
We are left with something very different as being Carnap's target of attack: metaphysicians engaged in transcendent truths.
While I mentioned Russell's doctrine of Aristotelianism (substance-attribute ontology) as 'stone-age metaphysics' (where it should read 'stone-age physics') perhaps, within the Griceian context, the author to consider as metaphysician is BRADLEY, adored by so many Oxonians!
The following are excerpts from the "Metaphysics" section in the Bradley entry in the Stanford Encyclopedia of Philosophy, online at
Candlish, Stewart and Basile, Pierfrancesco, "Francis Herbert Bradley", The Stanford Encyclopedia of Philosophy (Spring 2013 Edition), Edward N. Zalta (ed.), URL = .
I append it as a ps for consideration.
And I'm reminded of C. L. Dodgson's "Hunting of the Snark" which has often been read as a critique, avant la lettre, of Bradleyianism. "For the Snark was a Boojum, you see".
----
ps.
Metaphysics
Candlish, Stewart and Basile, Pierfrancesco, "Francis Herbert Bradley", The Stanford Encyclopedia of Philosophy (Spring 2013 Edition), Edward N. Zalta (ed.), URL = .
"After the completion of The Principles of Logic, Bradley turned to the task of giving a full account of his metaphysics. The result was Appearance and Reality (1893). But Bradley was philosophically active for a further thirty years thereafter, continuing to elucidate, defend and refine his views, and engaging with critics and rivals (notably, and revealingly for both sides, with Russell). Concentration upon Appearance and Reality alone, therefore, risks placing undue weight upon what turn out to be temporary features of thought or expression, and this has in fact contributed to the distorted impressions of his thinking so often to be found in the textbooks of analytic philosophy."
"Appearance and Reality is divided into two books."
"The first, ‘Appearance’, is brief, and its aim destructive, arguing that ‘the ideas by which we try to understand the universe’ all bring us ultimately to contradictions when we try to think out their implications. Some of these ideas belong especially to philosophy, such as the view that only the primary qualities are real and the Kantian notion of a thing-in-itself; others, for instance the notions of cause, motion, self, space, thing and time, are deployed in everyday life. The second book, ‘Reality’, is long; its aim is to provide a positive account of the Absolute — the ultimate, unconditioned reality as it is in itself, not distorted by projection through the conceptual mechanisms of thought. A large proportion of his discussion is devoted to consideration of natural objections to this positive account."
"Much of Book I involves presentation of familiar suggestions which make only part of Bradley's case: he alleges, for example, that motion involves paradoxes, and that primary qualities alone cannot give us reality, for they are inconceivable without secondary qualities, and that the notion of the thing-in-itself is self-contradictory, for if we really know nothing about it, then not even that it exists. But Chapters II and III — respectively entitled ‘Substantive and Adjective’ and ‘Relation and Quality’, are uniquely Bradleian, alarming in the breadth of their implications, and have caused intermittent controversy ever since. In generalized form, Bradley's contention is that relations (such as greater than) are unintelligible either with or without terms, and, likewise, terms unintelligible either with or without relations. Bradley himself says of the arguments he wields in support of this contention (p. 29)."
"The reader who has followed and has grasped the principle of this chapter, will have little need to spend his time on those which succeed it. He will have seen that our experience, where relational, is not true; and he will have condemned, almost without a hearing, the great mass of phenomena."
---
The entry goes on:
"It is clear that his views on relations are both highly controversial and central to his thought. In view of this, it would appear a serious tactical error on Bradley's part to present his arguments so sketchily and unconvincingly that even sympathetic commentators have not found it easy to defend him, while C.D. Broad was able to say later, ‘Charity bids us avert our eyes from the pitiable spectacle of a great philosopher using an argument which would disgrace a child or a savage’ (Examination, p. 85)."
"In spite of Bradley's laconic style, however, the exegetical errors of his critics are hard to justify. The impression that Bradley's crucial metaphysical arguments are negligible arises in part from reading them as designed to prove the doctrine of the internality of all relations — that is, either (1) their reducibility to qualities, or (2) their holding necessarily, depending on the sense of ‘internal’, Russell having interpreted the doctrine in the former way, Moore in the latter. Whichever sense we take, this is a misreading — and an impossible one, if we take ‘internal’ in Russell's sense, because of Bradley's rejection of the subject/predicate account of judgment as ‘erroneous’. If, however, we use Moore's sense of ‘internal’, the reading is understandable, albeit still inexcusable: in Chapter III Bradley confusingly applies this word to relations in a metaphysically innocent way which has no connection with the doctrine of internality as this is understood by Moore, while in other parts of Appearance and Reality he openly flirts with the doctrine of internality, repudiating it clearly only in later works less often read, such as the important essay ‘Relations’ left incomplete at his death and published in his Collected Essays of 1935. Further, Bradley does uniformly reject the reality of external relations, and it is easy, though not logically inevitable, to interpret this as a commitment to the doctrine of internality."
"Bradley's treatment of relations originates in Chapter II with a discussion of the problem of what makes the unity of an individual thing. How can we make sense of the fact that a single thing, such as, say, a lump of sugar, is capable of holding a plurality of different properties into a unity, such as its sweetness, whiteness and hardness? We cannot postulate the existence of an underlying substance distinct from its qualities, for this would commit us to the existence of a naked, bare particular, the absurd conception of a something devoid of all qualities. Moreover, the original difficulty as to the unity of the thing is left unsolved by this move, since it becomes possible to ask what it is that binds the qualities to their substance. The alternative is to conceive the thing as a collection of qualities, yet what is the nature of the ontological tie that binds them into the unity of the thing? We are left with an aggregate of independent, substance-like qualities, rather than with an individual thing. At this point, the problem of relations emerges in its full ontological significance, for it now looks as if only a relation could provide the required nexus."
"Bradley's considered view in Chapter III is that neither external nor internal relations possess unifying power and must therefore be rejected as unreal. This is the proper conclusion of a set of condensed arguments which he deploys as a team, systematically excluding the possible positions available to those who would disagree. One crucial consideration is based upon the insight that a relation is the ‘ground’ of its terms as well as ‘founded’ upon them. ‘So far as I can see’, he says, ‘relations must depend upon terms, just as much as terms upon relations’ (Appearance, p. 26). The relation is said to ‘depend’ upon its terms, because it requires at least two terms in order to exist; and terms ‘depend’ upon relations, because they are partly constituted by the relationships in which they stand to one another (albeit Bradley provides no illustration, this can be made plausible by considering two different shades of colour: blue would not be blue, if it were not darker than yellow). Once this is recognized, Bradley goes on to argue, one sees that a related term A is really made up of two parts, one functioning as the foundation of the relation, A1, and the other determined by it, A2. Thus, each related term turns out to be a relational complex, in this specific case, A turning out to be the complex R(A1,A2). This launches a regress, for by the same logic A1 and A2 will have to be made up of two distinct parts, and so on without end."
"The member of Bradley's team of arguments which has attracted the greatest polemical attention, however, is the one which alleges that if a relation were a further kind of real thing along with its terms (as, e.g., Russell later assumed in his multiple relation theory of judgment), then a further relation would be required to relate it to its terms, and so on ad infinitum. It is clear from this argument (which is an obvious descendant of The Principles of Logic's attack on the traditional analysis of judgment), as well as from his own explanation, that for him ‘real’ is a technical term: to be real is to be an individual substance (in the sense commonly found in Descartes, Leibniz and Spinoza). On this understanding, to deny the reality of relations is to deny that they are independent existents. It is this argument which explains reactions like Broad's: in common with others, he took Bradley to be assuming that relations are a kind of object, when what Bradley was doing was arguing by a kind of reductio against that very assumption."
"These remarks make it clear that Bradley is using the term ‘appearance’ in an ontological sense, as referring to what lacks full individuality, rather than in an epistemological sense, as referring to what is present to a subject. And indeed, he does not wish to deny the obvious fact that we experience a rich diversity of things; relations and plurality in some sense exist, and therefore belong to reality. The denial of the reality of relations does not imply their absolute non-existence; rather, his conclusion is that relations and terms should be conceived as aspects within an all-embracing whole. Instead of ascribing to Bradley the doctrine of internality, it would therefore be better to see him as advocating a ‘holistic’ theory of relations. As against Russell, Bradley was wholly explicit on this fundamental point."
"This is the doctrine for which I have now for so many years contended. Relations exists only in and through a whole which can not [sic] in the end be resolved into relations and terms. ‘And’, ‘together’ and ‘between’, are all in the end senseless apart from such a whole. The opposite view is maintained (as I understand) by Mr. Russell... But for myself, I am unable to find that Mr. Russell has ever really faced the question. (Principles, 2nd edn, Ch. II, additional note 50)."
"Interestingly, one philosopher who faced Bradley's question squarely was Russell's pupil, Wittgenstein. In his Tractatus he tried to avoid Bradley's regresses by getting rid of relations. His simple objects do enter into the formation of unified facts, yet no extraneous connecting principle is required:‘In the atomic fact objects hang one in another, like the links of a chain.’ (2.03). The metaphor of a chain, however, provides no real answer to the problem raised by Bradley, especially so in light of the fact that it is all but clear that Wittgenstein's logico-ontological atoms can be said to possess a form; surely, they differ from Democritean atoms in that they lack material properties (cf. 2.0331 and 2.0232). Moreover, Bradley could still argue that the very idea of two distinct but unrelated objects makes little sense."
"The implications of Bradley's treatment of relations are not solely metaphysical."
"They are also epistemological."
"Some have thought that the denial of the reality of relations amounts to the assertion that all relational judgments are false, so that it is, for example, not true that 7 is greater than 3 or that hydrogen is lighter than oxygen. Such an interpretation is made credible by Bradley's account of truth, for on that account no ordinary judgment is ever perfectly true; in consequence, to one who reads him under the influence of the later but anachronistic assumption that truth is two-valued, his claim appears to be that relational judgments are all false. On Bradley's account of truth, however, while for ordinary purposes it is true that 7 is greater than 3 and false that oxygen is lighter than hydrogen, once we try to meet the more exacting demands of metaphysics we are forced to recognize that truth admits degrees and that, while the former is undoubtedly more true than the latter, it is not fully true. The imperfection of even the more true of these judgments, though, is nothing to do with the its being relational rather than predicative. For, as was observed above in the section on Logic, Bradley thought all judgments to be defective in that representation can proceed only on the basis of separating in thought what is not separate in reality: when, for example, we say ‘These apples are hard and sour’, we not only implicitly abstract the apples from their container but detach the hardness and sourness from each other and abstract them from the apples themselves. A perfect truth, one completely faithful to reality, would thus have to be one which did not abstract from reality at all; and this means that it would have to be identical with the whole of reality and accordingly no longer even a judgment. The final truth about reality is, on Bradley's view, quite literally and in principle inexpressible. Eventually, it is this mystical conclusion which explains his forceful rejection of Hegel's panlogism; contrary to Hegel's view in the Science of Logic, Reality is not a system of interrelated logical categories, but transcends thought altogether."
"It is, however, possible to give an outline."
"The impression of reality's consisting of a multiplicity of related objects is a result of the separations imposed by thought; in fact ‘the Absolute is not many; there are no independent reals.’ (All quotations from here on are from Appearance and Reality, Ch. XIV.) Reality is one — but one what? Experience, he says, in a wide sense of the term: ‘Feeling, thought and volition (any groups under which we class psychological phenomena) are all the material of existence, and there is no other material, actual or even possible.’ The immediate argument he gives for this unintuitive doctrine is brief to the point of offhandedness, merely challenging the reader to think otherwise without self-contradiction; his greater concern is to make it quite clear that this experience does not belong to any individual mind, and his doctrine not a form of solipsism. But he is not quite as offhand as he appears, for he soon makes clear that he thinks the whole book to be a best-explanation argument for this objective (or absolute) idealism: ‘This conclusion will, I trust, at the end of my work bring more conviction to the reader; for we shall find that it is the one view which will harmonize all facts.’
So ‘the Absolute is one system, and ... its contents are nothing but sentient experience. It will hence be a single and all-inclusive experience, which embraces every partial diversity in concord. For it cannot be less than appearance, and hence no feeling or thought, of any kind, can fall outside its limits.’ But how can we understand this diversity to be possible, when it cannot be accounted for through terms and relations? Bradley's answer is that we cannot understand this in detail, but can get some grasp on what he means by considering a pre-conceptual state of immediate experience in which there are differences but no separations, a state from which our familiar, cognitive, adult human consciousness arises by imposing conceptual distinctions upon the differences. Reality is like this primitive state, but not exactly like, for it transcends thought rather than falls short of it, and everything, even conceptual thought itself, is included in one comprehensive and harmonious whole. Appearances thus contribute to Reality in a fashion analogous to the ways in which segments of a painting contribute to the whole work of art: detached from their background, they would lose their significance and might in isolation even be ugly; in context, they can themselves be beautiful and make an essential contribution to the beauty and integrity of the whole."
"Such limited comparisons are all the help we can get in understanding the Absolute and its relation to its appearances: Bradley rejects as impossible the demand for detailed explanations of how phenomena like error and evil belong to the Absolute, instead trying to shift the burden of proof to critics who express confidence in their incompatibility. His general answer is that anything that exists, even the worst of evils, is somehow real: the Absolute must comprehend both evil and good. But, just as truth admits of degrees, a judgment being less true the further it is from comprehending the whole of reality, so (consistent with ‘the identity of truth knowledge and reality’) reality itself admits of degrees, a phenomenon being the less real the more it is just a fragmentary aspect of the whole. The Absolute is in such a way further from evil than from good, but is itself neither, transcending them both as it transcends even religion — it is in a sense a Supreme Being, but not a personal God. The proper object of a complete system of metaphysics should be that of adjudicating the relative degree of reality of any fragmentary existent, yet as some critics objected, it is difficult to see how this could be carried out even in principle, given Bradley's contention that the Absolute is, strictly speaking, unknowable."
In Bradley's often rhapsodic descriptions of the Absolute, a conception of the world based both on his sceptical scrutiny of the inadequacies of philosophers' accounts of judgment — and, it is clear, on a kind of personal experience of a higher unity which in another context might have made him one of the world's revered religious mystics —, we can see why, at the start of this article, his metaphysics was described as ‘a striking combination of the rational and the mystical’. The very idiosyncrasy of this combination has meant that few subsequent philosophers have been convinced by it. Nevertheless, in its bold and direct confrontation of what he called ‘the great problem of the relation between Thought and Reality’, it stands in Western philosophy as a permanent and unsettling challenge to the capacity of discursive thought to display the world without distortion; unsettling because it arises, not from the imposition of an external standard which could be rejected as arbitrary or inappropriate, but from the demand that our mechanisms of representation meet the standards they themselves implicitly set."
### The Griceian Companion to Grice
Speranza
Roger Bishop Jones commented on "The Cambridge Companion to Grice", which was my fanciful way to refer to this "Cambridge Companion to Carnap".
Jones notes:
"Ah, well, they must have found reference to Aristotle in Carnap. It would be surprising if there were none at all."
Indeed. It is still a different issue whether, say, Aristotelian scholars would requote that quote! But then I have noticed that they hardly requote what Grice has to say about Aristotle for the Pacific Philosophical Quarterly ("Aristotle on the multiplicity of being").
### Aristotle: between Carnap and Grice -- "stone-age physics", not "metaphysics"
Speranza
Jones comment on a post on Grice, Carnap and Aristotle.
Jones writes:
"Considering Carnap's attitude towards Grice's work on Aristotle, both the status of Aristotle's metaphysics and that of Grice's analysis are relevant. Considering the former, the question is naturally whether Aristotle in his metaphysics is dealing with what Carnap would call external or internal questions. It may seem natural to think of these "big" questions as "external" and hence as nonesense to Carnap, but I am not convinced it is the case. Aristotle's metaphysics is a successor to the presocratic "metaphysicians", and his "Metaphysics" is an important source of our knowledge of those philosophers. But arguably the questions they addressed (about what substance the world is made of) is just part of physics, and quite meaningful. Aristotle's metaphysics, with its focus on "being qua being", might today be thought to belong to logic, and again to be meaningful. Grice's study of Aristotle quite possibly is purely analytic. So it is possible that there is nothing here in Aristotle or in Grice's treatment which Carnap might not find a meaningful enterprise. I'm not saying that is the case, but just that the question is not an easy one. The kinds of metaphysics which Carnap definitely repudiates are post-empiricism, and are known to be metaphysics because their originators make claims of rational knowledge into transcendent truth, and I don't know whether we see this in the ancient philosophers."
Excellent commentary.
Indeed, it is best to regard the pre-socratics as making PHYSICAL claims, and thus meaningful.
Russell said words to the effect that Aristotelian metaphysics is stone-age metaphysics.
Grice replied: "Stone-age physics" at best!
So we may throw Russell into the bargain!
Or not!
### Carnap, Popper, and Grice on the pervasiveness of misunderstanding
Speranza
We are considering a quote by Sir Karl Raimund Popper in "Unended Quest: An Intellectual Autobiography" (1976). On p. 29, he writes:
"Always remember that it is impossible to speak in such a way that you cannot be misunderstood: there will always be some who misunderstand you."
In "Re: To err Griceian?", R. B. Jones comments:
"I am inclined to agree with Popper."
-- i.e. It is impossible to speak in such
a way that you cannot be misunderstood: there
will always be some who misunderstand you.
Jones notes:
"The complaint of double negatives is mitigated by the modalities involved which make simplifying cancellations unsound."
Good point.
"As to whether it is strictly impossible or just extremely difficult or "practically impossible" I'm not sure."
Neither am I. Seeing the further context, I'm slightly irritated that Popper prefaces it with "always remember".
This seems like a gratuituous preface if what is to follow is a philosophical tautology.
"Always remember that either it is raining or it isn't."
"Always remember" seems to implicate "... since you may well forget".
---- The paraphrase that follows the dictum:
"there will always be some who misunderstand you"
seems to me too personal to be true.
Jones goes on:
"If one is allowed much liberty then the "double negatives" might be thought to have been unravelled in the following paraphrase, "It's impossibly difficult to be perfectly unambiguous"".
Which is good.
We should be reminded that indeed one of Grice's maxims (as he loved to call them JUST to 'echo' Kant) is:
-- avoid ambiguity.
And while this became ultra-famous in the 1967 William James lectures, the Oxford 1965 provide similar counterparts -- desiderata of candour and clarity, etc. -- The Oxford "Logic and Conversation" lectures now deposited in the "Grice Notes" at the UC/Berkeley library, the Bancroft.
The maxim, 'avoid ambiguity' seems to clash, somehow with the
"It's impossibly difficult to be perfectly unambiguous."
I was reminded elsewhere of Biblical hermeneutics and the thought occurred to me that alleged tautologies, like "I will what I will be" seem a good area of analysis.
The 'ambiguity' seems to lie at the level of the implicature.
This led me to reconsider Grice's account of tautology vis–à–vis implicature.
Grice's examples of tautology are two:
i. War is war.
ii. Women are women.
Grice uses a very 'narrow' (or is it 'broad'? I think it's broad) account of 'say' (I prefer 'explicate'). So that we have to allow that an utterer who utters either (i) or (ii) is literally NOT SAYING anything -- only implicating.
Yet it seems counterintuitive. It seems that an utterer of (i) or (ii) _is_ saying something, viz. that war is war or that women are women.
How this relates to 'ambiguity' is yet a different animal.
Grice's multiple examples of 'ambiguity' exploitation remain brilliant, such as the lines from the poem by William Blake -- is the 'ambiguity' designed as such. Cf. Empson, "Seven types of ambiguity".
And so on.
Thanks to R. B. Jones for his remarks.
I have just added Carnap for the record. It would seem that in an ideal language (such as the ones Carnap in some writings considers) ambiguity should NOT occur, and neither should misunderstanding. This relates to Chomsky and Grice.
Chomsky has been rightly criticised for having focuses on the 'ideal' communicators. Yet in those very Oxonian early Griceian lectures on "Logic and Conversation", Grice notes that it's best, from a philosophical point of view, to deal with 'idealised' cases -- cfr. the ideal theory of gases, say.
Or something.
## Tuesday, September 24, 2013
### To err is Griceian?
Speranza
Popper wrote:
"It is impossible to speak in such a way that you cannot be misunderstood."
I try to relate this to the writings of H. P. Grice -- and his symbolism, informal as it is -- in "Studies in the Way of Words". I try to evoke Strawson, too, who first saw 'understanding' in Griceian terms (in "Theoria").
I propose to use
for -- respectively -- "it is necessary that...", "it is possible that",
"there exists at least one...", and "every".
Also: "U" for utterer, "A" for "addressee", and suggested that
'misunderstand' be understood as 'failing to grasp Utterer's intention".
One feels that Popper's dictum carries, as my aunt Matilda would say, "one negative too many" -- or not -- and let us recall that, as double negatives cancel each other out -- one may still use, as Grice does, "~" to refer to "not" (as in "_im_possible", used by Popper))
And of course, we may need to apply predicate logic, with
"x understands y"
as a dyadic predicate -- abbreviated as "UND(x, y)", where 'x' and
'y' will range over, respectively, addressee and utterer -- and where "UNDE" is correlative to "MEAN".
And so on.
Only then we may inquire as to the _reasons_ that Popper may have for saying what he says.
We may also recall Biblical Scriptures -- or for that matter, Witters's 'Slab!'
"The language is meant to serve for communication between a builder A and
an assistant B. A is building with building-stones: there are blocks,
pillars, slabs and beams. B has to pass the stones, in the order in which A
needs them. For this purpose they use a language consisting of the words
"block", "pillar" "slab", "beam". A calls them out; — B brings the stone which
he has learnt to bring at such-and-such a call. Conceive this as a complete
primitive language" (Wittgenstein, Philosophical Investigations 2.)
-- and imagine scenarios when it is not possible to _misunderstand_ "Slab!" -- or for that matter, given, say, Papal Infallibility, the idea, that the Pope got, from somewhere, that there is only one body in heaven. Or not!
Cheers
## Monday, September 23, 2013
### Carnap and Grice on Aristotle's metaphysics
Speranza
The collocation here is "Aristotle's metaphysics", rather than "Aristotelian metaphysics", mind!
But I love Gardner!
And in any case, another case of a negative: "Carnap never looked at these diagrams".
### An Introduction to the Philosophy of Science
Rudolf Carnap, Martin Gardner - 1995 - Science
This often left the blackboard covered with diagrams explaining some aspect of Plato's or Aristotle's metaphysics. Carnap never looked at these diagrams while ...
### Aristotle: between Carnap and Grice
Speranza
Another connection:
### How the Cold War Transformed Philosophy of Science: To the Icy ...
George A. Reisch - 2005 - History
Carnap responded that his conception of semantic truth had nothing to do with an Aristotelian metaphysics of things and properties:
---
Grice discusses briefly Tarski's conception of truth in Way of Words, and he is amusing, as often (if not always).
Grice is worried that Tarski's conception needs a tweak to discuss things like:
"What the policeman said, 'that monkeys can talk', is true".
versus:
"What the policeman said was true".
### Aristotle: Carnap and Grice on the metaphysics
Speranza
Another cite seems to be:
### Otto Neurath and the Unity of Science - Page 71 - Google Books Result
John Symons, Olga Pombo, Juan Manuel Torres - 2010 - Electronic books
His attempts to convince Carnap or the mathematician Hans Hahn on the value ... Aristotelian metaphysics, “certain differences” between him and Carnap were ...
And so on!
### The Cambridge Companion to Grice
Speranza
--- does not exist! The man went to Oxford!
Yet, in
### The Cambridge Companion to Carnap
Richard Creath, Michael Friedman - 2007 - Philosophy
we do find an Aristotelian reference in connection with the master of Carnap Corner (which has R. B. Jones as custodian).
On p. 27
In his ongoing debate with Neurath about truth and semantics, Carnap stressed that the semantic conception did not commit him to Aristotelian metaphysics.
-----
which is just as well!
### Carnap and Grice on Aristotle on Metaphysics
Speranza
I once compiled a file for authors "cited by Grice", "that Grice cites". A big percentage of the file contained information such as "not cited by Grice", "does not cite Grice".
This may apply to our case in point.
Jones left a commentary to my "On first looking into Aristotle's metaphysics".
"I've not come across any reference to Aristotle in Carnaps writings."
---- So, in my filing system, this comes out as:
AUTHORS CITED BY CARNAP -- alphabetic.
Aristole -- NOT cited by Carnap.
Of course, we can not expect Aristotle to cite Carnap, either.
Jones goes on:
"If you Google for "Aristotle Carnap", one of my long forgotten abortive starts comes up, a page I started when thinking of Grice and Carnap."
OK. So in the filing system this comes out as:
AUTHORS CITING CARNAP and ARISTOTLE:
Jones -- vide 'start'.
This can be fascinating. There is no connection between H. P. Grice and J. D. Salinger (I recently saw his documentary -- he wrote "Catcher in the Rye". But I soon can create one:
Salinger says that he writes for 'himself' (or 'his-self' -- he was an aristocrat). This is anti-Gricean on the surface of it. Or anti-Griceian as I prefer. For, for Grice, to mean is to communicate.
Yet, Grice of course can allow for the fact that a writer, such as Salinger, can write for 'his self' -- and MEAN it!
There you have: A Salinger-Grice connection.
AUTHORS CITING GRICE:
Salinger -- not really, but a connection can be made, vis-a-vis Grice's 7th William James Lecture, where he speaks of 'meaning' and 'thinking'.
Oddly, Salinger's genius lies in his ability to reconstruct implicature-full conversations, notably by my hero, Holden Caulfield (with friends, etc.).
Jones goes on:
That start, Jones writes, "was intended to be "a presentation of a conception of metaphysics written as if to explain to Carnap why some useful purpose might be served by looking at Aristotle's Metaphysics", but I wrote down an action plan and never actually completed (or even started) any of the actions.
http://www.rbjones.com/rbjpub/philos/metap/xps007.html."
Well, but of course the connection is there, for as Jones was pointing out: there are various ways to regard this:
---- Aristotle's, Carnap's, and Grice's use of words such as 'real'. For Aristotle, the 'real' is the combination of 'matter and form'. A 'substance' is 'real', as it were. The first substance is the only real thing, actually, for Aristotle. Carnap dismisses the use of 'real' as nonsensical (or 'metaphysical'). And Grice is pretty tolerant when it comes to things that are real ('if it works, it exists' -- his Ontological Marxism goes).
---- Aristotle, Carnap, and Grice may allow for bigger questions ("out of the box" questions, as I call them) -- but Carnap is doubtful and thinks that bigger questions are nonsensical. So he would allow for an 'inner-question' about 'substance', and 'matter' and 'form'. For Aristotle, all questions are 'big', in that logic was not yet developed for a language-metalanguage discussion or for the idea of a calculus or system within questions can be meaningfully posed. Grice discusses the rationale, and architecture for building this or that 'system' in which 'inner' questions can be posited.
Or something like that.
----
If Carnap does not discuss Aristotle, perhaps the 'missing' like there is Heidegger. I.e. to examine in what respect Heidegger is thinking himself of improving on Aristotle's metaphysics and come up with why Carnap thought of Heidegger as a 'master of nonsense'.
The phrase 'master of nonsense' I find interesting -- and 'delightful', if I may say -- if only when I read it in connection with Edward Lear and Lewis Carroll (born C. L. Dodgson)!
----
Or something like that!
Thanks to R. B. Jones for the commentary.
## Tuesday, September 17, 2013
### On First Looking Into Aristotle's Metaphysics -- First Carnap, Then Grice
Speranza
We know Grice learned Aristotle from Hardie at Corpus Christi.
-- and the title is meant as an echo on first looking into Chapman's Homer.
"Carnap's father had risen from the status of a poor ribbon-weaver to become the owner of a ribbon-making factory."
Good.
"His mother [on the other hand\ came from academic stock."
"Her father was an educational reformer and her oldest brother was the archaeologist Wilhelm Dörpfeld."
GREEK CONNECTION -- or Grecian connection as I prefer -- cfr. my "Ode on a Griceian urn".
"As a ten-year old, Carnap accompanied his uncle on an expedition to Greece.[1]"
So we expect he read about 'philosophy' being one of the creations of that 'miracle' that Greece was, as books promote it.
Wikipedia continues:
"Carnap began his formal education at the Barmen Gymnasium."
I would assume that at the gym, Carnap read Greek.
Recall that Grice had attended Clifton were Greek was mandatory in the sixth form. I would suspect that at the gym or public school level, it would be poetical Greek, rather than philosophical Greek that would be promoted. At most, Plato. But HARDLY Aristotle, which school masters denigrate as not writing 'proper Greek' at all.
Wikipedia continues:
"From 1910 to 1914, Carnap attended the University of Jena, intending to write a thesis in physics. But he also studied carefully Kant's Critique of Pure Reason during a course taught by Bruno Bauch, and was one of very few students to attend Gottlob Frege's courses in mathematical logic. While Carnap held moral and political opposition to World War I, he felt obligated to serve in the German army."
I don't think I'm too familiar with the curriculum offered by Jena between 1910 and 1914, and perhaps I should continue reading Wikipedia to recheck when Carnap makes an early reference to Aristotle -- the metaphysician.
Interestingly, Kant was an interest of Carnap, as was of Grice who would rank "Kantotle" as his favourite philosopher ("Ariskant" being the second).
### Etymythology and Metaphysics
Speranza
L. R. Horn once lectured (if that's the word since the club is a delight of informality) on 'etymythology' at the Elizabethan Club, and the name stuck with me!
Anyway, this from wiki, as we discuss and explore with R. B. Jones the extent to which Carnap and Grice can be reconciled in such an abtuse field of study as metaphysics appears to be (and while we recall that one Grice Note in the Grice Collection reads, "a new discourse in metaphysics" -- "From Genesis to Revelations").
"The word "metaphysics" derives from the Greek words μετά (metá) ("beyond", "upon" or "after") and φυσικά (physiká) ("physics")".
"The word "metaphysics" first used, in Greek, as the title for several of Aristotle's works."
"And it was thus used because these works were usually anthologized after the works on physics in complete editions."
So it's like the novelist wrote the novel but failed to name it. Cfr. "The Catcher in the Rye" mistitled after R. Burns, or "Sideways": "I'm writing a novel". "What is it called?" "The day after yesterday". "That's today, no?".
Wiki continues:
"The prefix meta- ("beyond") indicates that these works come "after" the chapters on physics."
----
I.e. it would be a bibliographical prefix, as it were, as used by boring people such as librarians -- even if I run the Swimming-Pool Library...
---
Wiki continues:
"However, Aristotle himself did NOT [emphasis Speranza -- one of his Grice Notes] call the subject of these books "Metaphysics"."
"Rather, Aristotle referred to the subject of these books as "first philosophy.""
--
"prote philosophia"
philosophia prima
--
"The editor of Aristotle's works, Andronicus of Rhodes, is thought to have placed the books on first philosophy right after another work, Physics, and called them τὰ μετὰ τὰ φυσικὰ βιβλία (ta meta ta physika biblia) or "the books that come after the [books on] physics"."
Perhaps he thought that titling it "First Philosophy" would NOT sell?
--- (And to think this was all burned up in Alessandria depresses me).
Wiki continues:
"This [manoevure by Andronicus of Rhodes] was misread [read: MISUNDERSTOOD -- Speranza] by Latin scholiasts, who thought it meant
"the science of what is beyond the physical"".
Oxford followed suit. And they had two professors: the professor of physical philosophy, and the Waynflete professor of meta-physical philosophy (Strawson was one).
Wikipedia continues:
"However, once the name was given, the commentators sought to find intrinsic reasons for its appropriateness."
This reminds me of U. Eco and "The name of the rose". Why should be an intrinsic reason for a 'rose' to be called 'rose'?
Wikipedia continues:
"For instance, ["metaphysics" -- or trans-naturalia, in neo-Latin] was understood to mean "the science of the world beyond nature" (physis in Greek), that is, the science of the immaterial."
-- ghostly subject!
Wrong, when one knows that Aristotle was a hyle-morphist, rather; i.e. one who believed that 'shape' (morphe) ALWAYS comes attached with 'matter' -- And so, one who would DENY the immaterial per se.
Wikipedia continues:
"Again, it was understood to refer to the chronological or pedagogical order among our philosophical studies, so that the "metaphysical sciences" would mean "those that we study after having mastered the sciences that deal with the physical world" (St. Thomas Aquinas, "In Lib, Boeth. de Trin.", V, 1)".
Aquinas was TOO scholastic to my taste!
Note that this is not his Summa, but a rather 'early'? commentary on Boethius -- and thus perhaps not to be treated too seriously.
Wiki concludes the etymythological note on 'metaphysics':
"There is a widespread use of the term in current popular literature which replicates this error, i.e. that metaphysical means spiritual non-physical: thus, "metaphysical healing" means healing by means of remedies that are not physical.[8]"
----
Well, blame it on Andronicus -- of Rhodes (of all places!).
Heidegger possibly uses 'metaphysical' even differently. For one, I agree with his explication of the etymythology of philo-sophy.
Heidegger argues that 'philo-sophy' should NOT be read as the 'love' of wisdom, but the wisdom of love!
Speranza
There seems to be something repetitive in the TITLE to my post, "Unanaswerable questions? Carnap and Grice on metaphysics -- and falsifiability of internal metaphysical claims in the vernacular -- or other!" -- THIS CLUB.
Yet, R. B. Jones politely comments.
Here my commentary on his commentary.
Jones writes:
"Thank you also Speranza for your commentary, as always interesting and entertaining (I feel as if I must have written that many times)."
Thanks.
"Of course I cannot follow up on much of it for fear of becoming completely distracted, but I am interested in this question of who we should consider the principal targets of Carnap's metaphysical zeal, Aristotle or Heidegger."
Good.
I would think Carnap HEIDEGGER naturally, even if he never understood him. Carnap's contact with Aristotle seems more indirect.
A GRICE note: Grice's contact with Aristotle was directly from the Greek, when a student at Corpus Christi, under Hardie, at Oxford. Only later, when Grice moved to the United States of America, would he complain that students (his students) were unable to read Aristotle in GREEK!
---- I don't think Grice ever read Heidegger in German or English. YET: it is a fashionable gesture of his to write (or say) in "Prolegomena" to "Logic and conversation" -- who knows, in an attempt to provoke or amuse the Carnapians in the audience -- "Heidegger is the greatest living philosopher". (Heidegger was indeed a living philosopher then).
---
Jones goes on:
"In fact I didn't offer Aristotle as being one of Carnap's targets, so much as the source of the kind of philosophising which Carnap abjured, since his "Metaphysics" is the first volume in which (or rather, of which) that term is used."
But _does_ Aristotle *use* "metaphysical" in the object-language. It seems to me it's like a meta-linguistic description for him. He would prefer to refer to this or that alleged discipline as "first philosophy" rather. In which case, Carnap's attack would be against philosophy (first and foremost) rather than the special branch of metaphysics. I should recheck Wikipedia about this!
Jones goes on:
"Undoubtedly Heidegger was a better loved (hated?) target, but it was an extreme, and we might get a better sense of Carnap's opposition by considering Carnap's less exotic examples, one source of which is his recollections of student life."
Alright. I should re-check that, too. Grice went from a very classics-oriented college (as Corpus Christi was, based on the close study of Aristotle's work in Greek) to become a more 'general' philosopher at St. John's (also Oxford) where classics wasn't so strong.
Note too that Grice would associate Aristotle WITH Kant, and speak of "Kantotle". In doing so we are witnessing a more mature Grice that is expanding the scope of philosophy (as understood within the curriculum of "Literae Humaniores" that Grice followed) to include not just the classics like Aristotle, but the 'mods', like Kant.
--- never mind the contemporaries like Heidegger.
"I don't think it makes sense to go into more detail here, but I think this will come up again, in connection with Grice of course."
I'll recheck then:
-- Aristotle's use of 'metaphysical' qua adjective and his names for the field that metaphysics now comprises: first philosophy, and ontology?
-- Carnap's student days and his grasp of Aristotle as source of metaphysical external unanswerable questions.
Or not?
Cheers!
## Saturday, September 7, 2013
### A Grice Note: Etymythology of Sparrow Grass
Speranza
From today's Quinion's World Wide Words
http://www.worldwidewords.org.
"The name of [the] delightful vegetable [that asparagus is] has swung from classical Latin to rustic reinvention and back during its history in English."
"It first appears in English around 1000. Its name was taken from medieval Latin sparagus but by the sixteenth century it had come sperach or sperage. It might well have stayed like that had it not been for herbalists, who knew the classical Latin name was asparagus, itself borrowed from the Greek. Their influence meant that that name became quite widely known during the sixteenth and seventeenth centuries alongside the older names. Nicholas Culpeper, for example, headed an entry in his herbal of 1653 as “Asparagus, Sparagus, or Sperage”, thus covering all bases."
"Non-scholars had trouble with asparagus and did what the medieval Latin writers had done — leave off the unstressed initial vowel, so making it sparagus again. But they went one step further, converting it by folk etymology into forms that seemed to make more sense, either sparagrass or sparrowgrass. The latter form became common in the seventeenth and eighteenth centuries."
So home, and having brought home with me from Fenchurch Street a hundred of sparrowgrass, cost 18d.
Diary, by Samuel Pepys, 20 April 1667.
"In the eighteenth century sparrowgrass was so much the standard and polite term that John Walker commented in his Critical Pronouncing Dictionary in 1791: “‘Sparrow-grass’ is so general that ‘asparagus’ has an air of stiffness and pedantry”. In the late eighteenth and early nineteenth centuries it was also called Battersea grass, from the name of the London suburb alongside the Thames in whose market gardens it was grown."
"During the nineteenth century the wheel turned yet again, in part because of pedagogical opposition to a form considered to be no more than an ignorant mistake, bringing asparagus to the fore and relegating sparrowgrass to what the New English Dictionary rather loftily described in 1885 as “dialect or vulgar” status. This is supported by examples in fiction which attempt to render the voices of lower-class characters."
I remember my lars’ customer, the very lars’ customer that ever I ’ad. He was a Mr. Moses Gluckstein, a city gent and very pleasant and fond of sparrowgrass and chokes.
The War in the Air, by H G Wells, 1908. Chokes are artichokes.
Slavey came in while I was eating it, and caught me picking it up with my fingers. Next morning she says to my missis, so missis told me, “’Ow does master eat ’is sparrowgrass when ’e’s out with company, mum?” says she.
Lord Raingo, by Arnold Bennett, 1926. A slavey was a hard-worked live-in maidservant.
"Sparrowgrass is still around, though in print only as a historical reference, and the vegetable is still sometimes called grass in the greengrocery trade."
The Griceian point concerns more generally the pragmatics of malaprops and what Horn calls 'etymythology'.
"By uttering 'sparrow grass', he meant-nn asparagus and intentionally made a mistaken reference to 'sparrow' and 'grass' -- or not." But no implicature intended. So please disimplicate.
Cheers.
## Friday, September 6, 2013
### The Grice Notes
Speranza
Of course, "Grice notes" may be read, ambiguously, as "Grice" (the person) performs the act of noting. So, 'the' is preferable as a preface to disambiguate. It has the disadvantage of pretentiousness, since 'the' Grice notes are never 'the' -- in the sense of 'finished'.
On the other hand, "Some Grice Notes" sounds otiose -- if not silly.
### Grice Notes
Speranza
And the plural of "Grice note" is "Grice notes" -- many (or -- as Grice would say, "at least more than one") Grice notes.
----
Does this hold?
It may be argued that
"Elephants are pinks"
does NOT entail (but merely implicates) that we are referring to "at least more than one" elephant.
G. J. Warnock discusses this in "Metaphysics in Logic", and P. F. Strawson makes a similar point somewhere in one of his "Grice notes" in the rather pretentiously entitled, "Introduction to Logical Theory".
Note that musically, 'grace notes' should be distinguished from a singular 'grace note' -- or not.
### A Grice Note
Speranza
"A grace note is a kind of music notation used to denote several kinds of musical ornaments, usually printed smaller to indicate that it is melodically and harmonically nonessential. When occurring by itself, a single grace note normally indicates the intention of either an appoggiatura or an acciaccatura. When they occur in groups, grace notes can be interpreted to indicate any of several different classes of ornamentation, depending on interpretation."
On the other hand, a Grice note is a note by Grice or on Grice or under Grice -- perhaps even behind Grice.
The notation is similar.
Note that Grice was the main author of Grice notes. When his third "William James" lecture was prepared for publication -- never by himself! -- it came out as entitled:
"Further [Grice, that is] Notes on Logic and Conversation".
-----
### A Grice Note
Speranza
"A Grice Note" is obviously a pun on 'grace note'.
It may do to use it as a kind of "Ob.Grice", when we are discussing, er, Grice.
Speranza
## Tuesday, September 3, 2013
### Unanaswerable questions? Carnap and Grice on metaphysics -- and falsifiability of internal metaphysical claims in the vernacular -- or other!
Speranza
In his interesting "Pervasive metaphysics and other Grice/Carnap tensions", THIS CLUB, R. B. Jones writes:
"I don't know why I should have been surprised when Speranza pointed out the pervasiveness of metaphysics in Grice's philosophy, for surely every aspect of our language engages with its own special kinds of entity and thus involves some special metaphysics."
Well, but it's ALWAYS _nice_ to be surprised. In Greek, 'surprise' was spelt (or spelled') 'wonder', and note that anglophones nicley abuse this word, "I wonder who's kissing her now", the title of an old song goes. So, it's nice to wonder, i.e. it's nice to be surprised -- and there are, as these, 'meta-surprises, as when Jones wondered why he wondered ... (and so ad infinitum).
Jones continues:
"Naturally I ask the question whether this deals a serious blow to the prospects for our Grice/Carnap dialogue."
Good.
"The simple answer is: "not at all!", for surely this is what Carnap's principle of tolerance is all about, freedom to use languages irrespective of whatever ontology they presuppose (though I don't think that way of putting it is Carnap's), subject only to pragmatic questions (does it serve any purpose?), not the meaningless metaphysical "external questions"".
Indeed. I think Carnap's principle of Tolerance is a brilliant one, and Griceian in parts. Note that 'tolerance' was after all, the favourite (if not pet) word of Grice's favourite philosopher, John Locke.
INTERLUDE FROM WIKI:
"A Letter Concerning Toleration by John Locke was originally published in 1689. Its initial publication was in Latin, though it was immediately translated into other languages. Locke's work appeared amidst a fear that Catholicism might be taking over England, and responds to the problem of religion and government by proposing religious toleration as the answer. This "letter" is addressed to an anonymous "Honored Sir": this was actually Locke's close friend Philipp van Limborch, who published it without Locke's knowledge."
---- END OF INTERLUDE
Now, it may be a good exercise in Carnapian/Griceian linguistic botany to look for fine (if not nice) distinctions between 'tolerance' and 'toleration'!
Jones goes on:
"This kind of response, however, leaves us with a puzzle. If Carnap's positivism is so very accomodating, what is left of his rejection of metaphysics? Is this something which just melted away? On the other hand, can we be sure that the pervasive metaphysics in Grice is entirely concerned with questions which Carnap would recognise as "internal", as we might suppose by considering Grice's methods."
Good questions.
I would even go on and apply the universal quantifier and talk of Grice's
all-pervasive metaphysics!
Oxonian interlude:
http://oxforddictionaries.com/definition/english/all--pervasive
## all-pervasive
• occurring or having an effect through or into every part of something:the all-pervasive excitement
--- end of Oxonian interlude.
Jones goes on:
"I revisited some of the milestones in Carnap's writings on Metaphysics to clarify my thinking on the first of those puzzles, and it is interesting to see that this very question (about what is left of Carnap's proscription of metaphysics after "Empiricism, Semantics and Ontology") is answered in the statement of his position on metaphysics in the Schilpp volume.
Evidently other people had wondered, after "Empiricism, Semantics and Ontology" whether Carnap's objections to Metaphysics had not just dwindled into nothingness (Carnap is responding to Beth)."
Let's Wiki Beth for the record. Carnap, unlike Grice, was fortunate ('lucky' is perhaps too informal an epithet) that Schilpp was able to have him in his "Library of Living Philosophers". As things are, while Strawson (Grice's junior) also made it -- and Strawson's is my favourite "library-of-living-philosophers" volume -- Grice didn't, but then, there is the ever expanding Library of Dead Philosophers.
----- LONG INTERLUDE ON "THE BOOK OF DEAD PHILOSOPHERS"
by Simon Critchley
## Editorial Reviews
### Amazon.com Review
Amazon Best of the Month, February 2009: For professor Simon Critchely, how we die is possibly more important than how we lived.
In The Book of Dead Philosophers, Critchley presents a lineup of nearly 200 famous (and not so famous) philosophers and explores how, through their deaths, one might be inspired to lead a richer life. From a few words to a few pages, each great thinker's death is examined in an enlightening and entertaining manner as the author waxes on the often brutal (and odd) ways they left this mortal coil. And along with natural causes, murders, and suicides, you'll discover what dark departures from suffocating in cow dung, indigestion, and lethal insect stings have to do with how we live today. At times the "sobering power of the philosophical death" might seem more like a morbidly ironic punchline to the life each philosopher led, but Critchley writes, "My hope is that, if read from beginning to end, a cumulative series of themes will emerge that will add up to a specific argument about how philosophy might teach one how to die, and by implication, how to live." --Brad Thomas Parsons
### From Publishers Weekly
According to Cicero, to philosophize is to learn how to die. Critchley (Infinitely Demanding) illustrates this claim in his portraits of the deaths of more than 190 philosophers from the ancients to the analytics of the mid–20th century. A primer on just about every notable philosophical figure in history, this book challenges readers to learn from the philosophers' conduct in life and the circumstances of their deaths. Confucius believed that mourning underscored the value of life; accordingly, his followers grieved his death for at least three years. Thoreau, Emerson and John Stuart Mill died of ordinary ailments while relishing the natural world. Aquinas found serenity contemplating the bough of a tree, fitting consolation for the philosopher who preached the interconnectedness of nature and the soul. Dionysius spent the second half of his life rejecting Stoicism and embracing hedonism yet committed a protracted suicide by voluntary starvation. David Hume proved that atheists could die happy. The book offers an interpretation of death's potential as a final artistic and intellectual endeavor; it is a witty and generous gift that will leave readers perhaps a little less afraid of death and more appreciative of life. (Feb.)
### From Booklist
*Starred Review* Dismayed by the devolution of philosophy into a dry academic specialty, Critchley reconnects his discipline with the most universal of human concerns. For it is in pondering death that serious thinkers have discovered the wellsprings of wisdom. Seneca is thus voicing a persistent philosophical motif when he insists, “He will live badly who does not know how to die well.” However, because death refuses to shrink into a tidy intellectual construct, Critchley scrutinizes not only what prominent philosophers have thought about the subject but also how they have actually died. Readers thus contemplate the dying Augustine reading the Hebrew psalms in tears; the doomed Nietzsche rushing into the street to embrace a horse, so signaling a final descent into syphilitic madness; the heroic Bergson contracting his fatal illness by voluntarily joining fellow Jews forced into the bitter cold of midwinter to register with Nazi authorities. Scholars may complain about the scrapbook style of (dis)organization, as the deaths and death thoughts of almost 200 philosophers pass in quick review. But most readers will recognize the aptness of the rapid-fire summary, each entry a piquant reminder of the brevity of life and a forceful rejection of the illusions of intellectual progress. A work that makes philosophy matter again. --Bryce Christensen
### Review
“A provocative and engrossing invitation to think about the human condition and what philosophy can and can't do to illuminate it.”
The Financial Times
“Rigorous, profound and frequently hilarious. . . . Critchley is an engaging, deadpan guide to the metaphysical necropolis. . . . At a time when much popular philosophy is either frivolous, dull or complacent, his is a bracingly serious and properly comic presence.”
The Daily Telegraph (UK)
Simon Critchly is Professor and Chair of Philosophy at the New School for Social Research in New York. He is the author of many books, most recently, On Heidegger's Being and Time and Infinitely Demanding: Ethics of Commitment, Politics of Resistance. The Book of Dead Philosophers was written on a hill overlooking Los Angeles, where he was a scholar at the Getty Research Institute. He lives in Brooklyn.
Pre-Socratics, Physiologists, Sages and Sophists
Philosophical thought emerged in the Greek-speaking world two and a half millennia ago. First we encounter the various sages and so- called “physiologists,” like Thales and Anaxagoras, who attempted to explain the origins of the universe and the causes of nature. We will then turn to the sometimes shadowy figures, like Pythagoras, Heracleitus and Empedocles, who define the world of thought prior to the birth of Socrates and the struggle between philosophy and sophistry in Athens during the Classical period of the fifth and fourth centuries bc.
Of course, one might with some justice claim that the Sphinx was the first philosopher and Oedipus the second. This would also have the merit of making philosophy begin with a woman and continuing with an incestuous parricide. The Sphinx asks her visitors a question, which is also a riddle, and perhaps even a joke: what goes on four legs in the morning, on two legs at noon, and on three legs in the evening? If they get the answer wrong, she kills them. Furthermore, when Oedipus guesses the right answer to the riddle—man crawls on all fours as a baby, walks on two legs as an adult and with a cane in old age—the Sphinx commits philosophical suicide by throwing herself to the ground from her high rock.
Thales
(flourished in the sixth century bc)
Thales came from the once mighty port of Miletus, close to the present Turkish coast, whose harbour long ago dried up thanks to the unending attention of silt.
Thales was the possible originator of the saying “know thyself,” who famously predicted the solar eclipse of May 585 bc. He believed that water was the universal substance and once fell into a ditch when he was taken outdoors by a Thracian girl to look at the stars. On hearing his cry, she said, “How can you expect to know about all the heavens, Thales, when you cannot even see what is just beneath your feet?” Some feel—perhaps rightly—that this is a charge that philosophy never entirely escaped in the following two and a half millennia.
Thales died at an advanced age of heat, thirst and weakness while watching an athletic contest. This inspired Diogenes Laertius to the following execrable verse:
As Thales watched the games one festal day The fierce sun smote him and he passed away.
Solon
(630–560 bc)
Solon was a famed Athenian legislator who repealed the bloody laws of Dracon (although it was Dracon whose name was turned into an adjective). Plutarch remarks that Solon suggested that brides should nibble a quince before getting into bed. The reason for this is unclear. When Solon was asked why he had not framed a law against parricide, he replied that he hoped it was unnecessary. He died in Cyprus at the age of eighty.
Chilon
(flourished in the sixth century bc)
A Spartan to whom the saying “know thyself” is also sometimes attributed. He died after congratulating his son on an Olympic victory in boxing.
Periander
(628–588 bc)
Like Thales, Solon and Chilon, Periander of Corinth was considered one of the Seven Sages of Greece. To others, like Aristotle, he was simply a tyrant. However, there is a bizarre story about the lengths to which Periander went in order to conceal his place of burial: he instructed two young men to meet a third man at a predetermined place and kill and bury him. Then he arranged for four men to pursue the first two and kill and bury them. Then he arranged for a larger group of men to hunt down the four. Having made all these preparations, he went out to meet the two young men for he, Periander, was the third man.
Epimenides
(possibly flourished in the sixth century,
possibly a mythical figure)
A native of Crete, the setting for Epimenides’ famous paradox. Epimenides’ original statement was “Cretans, always liars.” He appears to have intended this literally, as the great Cretan lie is the belief that Zeus is mortal, whereas every sensible person knows that he is really immortal. However, in logic, this paradox takes on a more acute form. Consider the sentence “This statement is not true.” Now, is this statement true? If it is, then it is not; if it is not, then it is. This is a perfect example of a paradox. That is, it is a proposition whose truth leads to a contradiction and the denial of its truth also leads to a contradiction.
Legend has it that Epimenides was sent into the countryside by his father to look after some sheep. But instead of tending to the sheep, he fell asleep in a cave for fifty-seven years. Upon waking, he went in search of the sheep, believing that he had only taken a short nap. When he returned home, everything (unsurprisingly) had changed and a new owner had taken possession of his father’s farm. Eventually, he found his younger brother, by now an elderly man, and learnt the truth.
Epimenides’ fame spread and it was believed thereafter that he possessed the gift of prophecy. Diogenes tells of how the Athenians sent for him when the city was suffering from the plague. He again took some sheep and went to the Areopagus, the high rock in the centre of Athens. He commanded that a sacrifice be made at each spot where a sheep decided to lie down. In this way, apparently, Athens was freed from the plague.
According to Phlegon in his work On Longevity, Epimenides lived to be 157 years old. This makes him a centurion, excluding his long nap in the cave. The Cretans claim that he lived to be 259 years old. But, as we all know, Cretans are always liars.
Anaximander
(610–546/545 bc)
Anaximander somewhat obscurely claimed that the Unlimited or that which is without boundaries (apeiron) is the original material of all existing things. He discovered his own limit at the age of sixty-four.
Pythagoras
(580–500 bc)
Sadly, it is now almost universally assumed by classical scholars that Pythagoras never existed. It seems that there was a group of people in southern Italy called Pythagoreans who invented a “Founder” for their beliefs who, accordingly, lived and died in a manner consistent with those beliefs. But let’s not allow Pythagoras’ mere non-existence to deter us, as the stories that surround him are so compelling. They are also illustrative of the wider point that disciples of a thinker will often simply invent stories and anecdotes that illustrate the life of the master in whom they want to believe. Perhaps we should be suspicious of this desire for a master.
Be that as it may, Pythagorean doctrines were bound by an oath of secrecy, so we know very little prior to the version of them that appears in Plato. These include a belief in the immortality and transmigration of the soul and the view that the ultimate reality of the universe consists in number. Pythagoreans regarded even numbers as female and odd numbers as male. The number 5 was called “marriage” because it was the product of the first even (2) and odd (3) numbers (the ancient Greeks considered the number 1 a unit and not a proper number, which had to express a multiplicity). Pythagoreans also believed that their master had established the ratios that underlie music. This had huge influence in the notion of musica universalis or music of the spheres, where the entire cosmos was the expression of a musical harmony whose key was given in mathematics.
However, the Pythagoreans also observed a number of other, more worldly doctrines, involving food in particular. They abstained from meat and fish. For some reason red mullet is singled out for especial prohibition, and Plutarch notes that they considered the egg taboo, too. Pythagoras and his followers also inherited from the Egyptians a strong revulsion to beans, because of their apparent resemblance to the genitalia. Apparently, “bean” may have been a slang term for “testicle.” But there are many other possible reasons for this dislike of beans.
There are some fascinating remarks in the Philosophumena [Philosophizings] or the Refutation of All Heresies by the Christian Bishop Hippolytus written around ad 220. According to him, if beans are chewed and left in the sun, they emit the smell of semen. Even worse, if one takes the bean in flower and buries it in the earth and in a few days digs it up, then, “We shall see it at first having the form of a woman’s pudenda and afterwards on close examination a child’s head growing with it.” Of course, as many of us know to our cost, beans should be avoided as they produce terrible flatulence. Oddly, it was because of beans that Pythagoras is alleged to have met his end. But I am getting ahead of myself.
So the legend goes, Pythagoras left his native Samos, an island off the Ionian coast, because of a dislike of the policies of the tyrant Polycrates. He fled with his followers to Croton in southern Italy and extended considerable influence and power in the region of present-day Calabria. Porphyry, in his Life of Pythagoras, relates how a certain Cylo, a rich and powerful local figure, felt slighted by the haughtiness with which Pythagoras treated him. As a consequence, Cylo and his retinue burnt down the house in which Pythagoras and his followers were gathered. The master only escaped because his followers bridged the fire with their own bodies. He got as far as a field of beans, where he stopped and declared that he would rather be killed than cross it. This enabled his pursuers to catch up with him and cut his throat.
Yet, there is another story, related by Hermippus, that when the cities of Agrigentum and Syracuse were at war, the Pythagoreans sided with the Agrigentines. Unbelievably, Pythagoras was killed by the Syracusans as he was trying to avoid a beanfield. Thirty-five of his followers were subsequently burnt at the stake for treachery.
------ END OF LONG INTERLUDE, and add "Grice" to Critchley's book of dead philosophers.
Jones goes on about Carnap's reply to Beth which reminds me that I should wiki Beth:
---- INTERLUDE ON BETH:
Evert Willem Beth (7 July 1908 – 12 April 1964) was a Dutch philosopher and logician, whose work principally concerned the foundations of mathematics.
Beth was born in Almelo, a small town in the eastern Netherlands. His father had studied mathematics and physics at the University of Amsterdam, where he had been awarded a Ph.D. Evert Beth studied the same subjects at Utrecht University, but then also studied philosophy and psychology. His 1935 Ph.D. was in philosophy.
In 1946, he became professor of logic and the foundations of mathematics in Amsterdam. Apart from two brief interruptions – a stint in 1951 as a research assistant to Alfred Tarski, and in 1957 as a visiting professor at Johns Hopkins University – he held the post in Amsterdam continuously until his death in 1964. His was the first academic post in his country in logic and the foundations of mathematics, and during this time he contributed actively to international cooperation in establishing logic as an academic discipline.
He died in Amsterdam.
## Contributions to logic
### Definition theorem
The definition theorem states that a predicate (or function or constant) is implicitly definable if and only if it is explicitly definable.
### Semantic tableaux
Semantic tableaux are a proof method for formal systems. Cf. Gentzen's natural deduction and sequent calculus, or even J. Alan Robinson's resolution and Hilbert's axiomatic systems. It is considered by many to be intuitively simple, particularly for students not acquainted with the study of logic (Wilfrid Hodges for example presents semantic tableaux in his introductory textbook, Logic, and Melvin Fitting does the same in his presentation of first-order logic for computer scientists, First-order logic and automated theorem proving).
One starts out with the intention of proving that a certain set $\Gamma \,$ of formulae imply another formula $\varphi\,$, given a set of rules determined by the semantics of the formulae's connectives (and quantifiers, in first-order logic). The method is to assume the concurrent truth of every member of $\Gamma \,$ and of $\neg \varphi$ (the negation of $\varphi\,$), and then to apply the rules to branch this list into a tree-like structure of (simpler) formulae until every possible branch contains a contradiction. At this point it will have been established that $\Gamma \cup \{ \neg \varphi \}$ is inconsistent, and thus that the formulae of $\Gamma\,$ together imply $\varphi \,$.
### Beth models
These are a class of relational models for non-classical logic (cf. Kripke semantics).
## Books
• Evert W. Beth, The foundations of mathematics. A study in the philosophy of science. XXVΊ + 722 pp. Amsterdam, North-Holland 1959.
• Evert W. Beth, Epistemologie mathematique et psychologie (with J. Piaget). 352 pp. Paris P.U.F. 1961.
• Evert W. Beth, Formal Methods: An introduction to symbolic logic and to the study of effective operations in arithmetic and logic. D. Reidel Publishing Company / Dordecht-Holland, 1970. ISBN 90-277-0069-9.
## References
• Francella, Miriam (1999). "Evert Willem Beth's Scientific Philosophy". Grazer Philosophische Studien 57: 221–236. doi:10.5840/gps19995712.
• Heyting, Alan (1966). "In memoriam: Evert Willem Beth (1909–1964).". Notre Dame Journal of Formal Logic 7 (4): 289–295.
• Mooij, J J A. "Beth, Evert Willem (1908–1964)". Biographical Dictionary of the Netherlands: 1880–2000. Retrieved 22 April 2013.
In his "Annotated Snark", M. Gardner -- an interesting philosopher, mathematical philosopher, even -- thinks, with other authors he quotes, that 'greens' there is a coded reference to the Hegelian philosopher of the "Absolute", Thomas Hill Green.
INTERLUDE:
Thomas Hill Green (7 April 1836 – 15 March 1882) was an English philosopher, political radical and temperance reformer, and a member of the British idealism movement. Like all the British idealists, Green was influenced by the metaphysical historicism of G.W.F. Hegel. He was one of the thinkers behind the philosophy of social liberalism.
----
Jones goes on:
"With this clarification in mind we may ask again how Grice's work might have appeared in Canap's eyes. The question then becomes, is Grice's interest in metaphysics exclusively relative to some language (presumably English), or does he get into more absolute questions? That's a question for JL perhaps, but I shall speculate a little myself. It seems to me that Grice's species of ordinary language philosophy is not so exclusively concerned with the analysis of language as would be needed for there not to be an issue here. For Grice "ordinary language" is not an exclusive subject matter, but rather an ubiquitous source of insight. In at least some of his metaphysical enterprises the object of his studies does not seem to be language."
Indeed, and my caveats here would be:
Grice's 'idio-' "lectal" practices
-- his "deutero-Esperanto".
For a time, it was unfashionable in Oxford to speak of Grice as a philosopher of language. He was rather, merely concerned with 'mean' and 'meaning'. I think it was
C. A. B. PEACOCKE
the first (as I like to think) who started to take the questions of 'language' seriously. Notably in a colloquium organised by Evans and McDowell. M. K. Davies later followed suit, as did B. F. Loar and others. Even Schiffer.
But there is a gap between Grice's analysis of what an Utterer means (what he is interested at elucidating, and which occupies most of the pages of his WoW -- Way of Words) and what an expression in a Language (for a Population P) means.
For the more or less explicit and formal definitions of 'meaning in a language for a population' then I refer to Peacocke, who incidentally, succeeded Strawson as Oxford's Waynflete Professor of Metaphysical Philosophy (as he should! -- for this is ALL metaphysics we are talking about!). I'll try to re-trace some of Peacocke's most formal definitions.
Add to that the Grice-oriented type of scepticism as to what a language is (or isn't) as per Davidson's "Nice Derangement". This paper, unfortunately, was published by Davidson separately (what's the use of providing an essay for a festschrift if you're going to publish it elsewhere) but it merited an intertesting reply by Hacking, and (of all people) Dummett -- and they all more or less shared Davidson's sceptical approach to this abstraction that Ferdinand de Saussure called 'Language' -- even "natural".
Jones goes on:
"In some cases the point might be exegetical, [Grice] might be excavating the metaphysics of philosophers (Aristotle perhaps). This would not fit Carnap's narrow conception of philosophy, but at least it would not be the proscribed metaphysics."
Indeed. Grice can get to be over-exegetical, as in "Aristotle on the multiplicity of 'being'" (Pacific Philosophical Quarterly, published posthumously in 1988) which is Grice's reply to Owen's rather rude remark that, in Aristotle, 'being' is polysemous! ("einai" in Greek -- The Griceian result is the outcome well known to Jones of distinguishing izzing from hazzing)
Jones goes on:
"I think however, that even when considering, say, some aspect of Aristotelian metaphysics, Grice is not purely, or even primarily. exegetical, rather he seeks to take up and progress some aspect of the problem which Aristotle was addressing."
-- while criticising Owen.
For 80% of Grice's pleasure derived from providing arguments to his seniors. Owen ended up writing the obituary of Gilbert Ryle, and he says words to this effect: "I am often asked: what group exercised the bigger mysticism? Ryle's group, or Austin's group, later led by Grice. And I would say Austin's and Grice's -- Their 'Play Group' acquired a cult status that the group that Ryle led and to which I belonged never did".
Owen's essay is nicely entitled, "The snares of ontology", for he thinks that Aristotle is precisely trapped in 'external' questions to the Greek language (of which he only spoke a 'lower' dialect, some say!).
Jones goes on:
"Aristotle is of course one of the early sources of just those metaphysical "pseudo-problems" which Carnap criticised, and so it seems likely that Grice may well in this way find himself crossing Carnap's line."
Good. I would think Carnap's IMMEDIATE target of attack was Heidegger with his things like, "Nothing noths", but it's true that Aristotle could go over the top, and invent a 'category' when he couldn't find it!
Jones wonders:
"Why should we care whether Carnap would have found the problems which Grice addressed genuine? What was the point of fantasising about a conversation between these two philosophers. There is more than one, but in this domain it seems to me that what is happening is that we are stripping away those kinds of metaphysics to which it is easy to give meaning (say, descriptive metaphysics, or the exegesis of Aristotelian metaphyics) and which for that reason do not fall foul of Carnap's critique, and when focussed down on the real metaphysics (perhaps what Strawson called "revisionary" metaphysics, perhaps only a part of that), we can imagine Carnap challenging Grice to give meaning to the enterprise. To the extent that Grice succeeds in doing so, the scope of Carnap's critique would be narrowed."
Excellently put.
Jones goes on:
"There is interplay here between method and meaning. Carnap wants to see a definite meaning for a metaphysical claim, because in default of that we can have no idea how it can be verified (using that term loosely)."
And cfr. the 'entrance' of Popper with his talk on falsifiability.
INTERLUDE ON "FALSIFIABILITY" and internal metaphysical claims in the vernacular
Falsifiability or refutability is the trait of a statement, hypothesis, or theory whereby it could be shown to be false if some conceivable observation were true. In this sense, falsify is synonymous with nullify, meaning not "to commit fraud" but "show to be false". Science must be falsifiable. The scientific method can not be implemented without the theoretical possibilities of both disproof and verification.
By the problem of induction, no number of confirming observations can verify a universal generalization, such as All swans are white, yet it is logically possible to falsify it by observing a single black swan. Thus, the term falsifiability is sometimes synonym to testability. Some statements, such as It will be raining here in one million years, are falsifiable in principle, but not in practice.[1]
The concern with falsifiability gained attention by way of philosopher of science Karl Popper's scientific epistemology "falsificationism". Popper stresses the problem of demarcation—distinguishing the scientific from the unscientific—and makes falsifiability the demarcation criterion, such that what is unfalsifiable is classified as unscientific, and the practice of declaring an unfalsifiable theory to be scientifically true is pseudoscience.
In falsificationism, an unfalsifiable and thus unscientific theory is not necessarily intrinsically false or inappropriate, since metaphysical theories might be true or contain truth, but one cannot know for sure. Simply, to be scientific, a theory must entail at least one observation, which may or may not be the case. (Falsificationism is not a general epistemology, then, which for Popper is critical rationalism, aimed to be the first epistemology fully based on criticism and discarding quest for justification.)
----- END OF WIKI INTERLUDE ON "FALSIFIABILITY".
Jones goes on and concludes with what he calls two 'concessions'.
The first concession:
"Conversely, if we could say in what way such claims could be verified or refuted then those methods would suffice to give meaning to the claims. The effect of the dialogue is to extract from Grice more detail about meanings and methods, and from Carnap consequent narrowing of the scope of critique.
Further effects might be hoped for. From Carnap it seems to me one might hope for two further kinds of concession. The first is in the use of the term "metaphysics", which for Carnap is used exclusively in a perjorative, proscriptive way. We could reasonably hope that he might be persuaded to accept a wider use ot the term which embraced questions which he does not consider meaningless, e.g. to encompass descriptive metaphysics. We might suggest perhaps in the first instance that Carnap reserve the term "absolute metaphysics" for the external questions which he regards as meaningless and allow that internal ontological questions (especially ones internal to natural languages) be spoken of as a kind of meaningful metaphysics."
---- A related point would be to add 'ontological' to the vocabulary, as per Quine (yes, we know, a big critique of Carnap) alla "On what there is".
The term 'metaphysical' surely shouldn't be taken so seriously, seeing that it's merely an accidental Greek idiom for what Aristotle felt fell 'beyond the physical' books' -- or something.
"Ontological", rather, makes it explicit that what we are into is the use of 'copulative' expressions of this or that type.
The second concession Jones expresses as follows:
"A second concession which might be easy to extract is the acknowledgement that meaningfulness is not discrete, that it is the business of philosophers and particularly of metaphysicians to probe into just those areas where meaning is hard to grasp, and that one should perhaps in metaphysics accept more a more tenuous grasp on meaning that one might hope for in say, arithmetic. The concessions here, in relation to metaphysics, seem all on Carnap's side, Grice's part, clarification of meanings and methods seemingly just more of what he is ordinarily engaged in. It is in the dogmas that we seek concessions, and we have been talking here about Carnap's anti-metaphysical dogma.
The place for Grice's concessions is in his own dogmas, which is what I am here calling his Betes Noire, the various aspects of "minimalism". There is a symmetry here, for the dogmas of Carnap and those of Grice are both anti-dogmatic."
Indeed. Grice in particular, would rather be seen, to use Grandy's pun, defending the under-dogma anyday.
Jones concludes:
"Carnap rejects external questions as criteria for the acceptability of languages, because he wants to be tolerant about language forms. Grice rejects minimalism for similar reasons. He construes minimalism as a set of nominalistic dogmas and he doesn't like being deprived of any of the ontology implicit in our language. Carnap's minimalism is however a pragmatic rather than a dogmatic enterprise. Our conversation will progress more fruitfully if Grice(*) would recognise that not all minimalism is abhorrent."
Indeed. And it isn't!
Thanks for a most enlightening post! | 2017-08-20 11:38:55 | {"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": 0, "img_math": 8, "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": 0.556226372718811, "perplexity": 4785.063388423651}, "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-2017-34/segments/1502886106465.71/warc/CC-MAIN-20170820112115-20170820132115-00534.warc.gz"} |
https://math.stackexchange.com/questions/484350/how-to-compute-bochner-laplacian-delta-nabla-nabla-sum-nabla-e-i | # How to compute Bochner laplacian $\Delta=\nabla^*\nabla=\sum \nabla_{e_i}$?
I'm struggling with proving that Bochner laplacian can be described by the following formula similar to the standard laplacian formula from calculus: $$\Delta = \sum_i \nabla_i^2,$$ where $\nabla_i = \nabla_{e_i}$ for some local orthonormal basis $e_i$ and $\nabla$ is a connection satisfying any reasonable conditions (Levi-Civita on $TM$, the induced connections on $\Omega^k(M)$).
We live on a compact $C^\infty$ Riemannian manifold without boundary and the laplace operator is defined as $\nabla^*\nabla$, where $\nabla$ is viewed as a map $\Gamma(E)\to \Gamma(T^*M \otimes E)$ between spaces with scalar product and thus the adjoint operator $\nabla^*\!\!:\Gamma(T^*M \otimes E) \to \Gamma(E)$ is well defined*.
I'm new to Levi-Civita, so please be understanding if the solution is trivial...
*Actually the spaces here are neither finite dimensional nor Hilbert, so it is not clear if the adjoint operator exists... The explanation will be highly appreciated, but it can be assumed that $\nabla^*$ exists.
This calculation is done in full detail (without the assumption that the basis is orthonormal) in example $10.1.32$ of Liviu Nicolaescu's wonderful book Lectures on the Geometry of Manifolds which is freely available as a pdf from his website.
• It is more straightforward if the basis is orthonomal. In that case $g^{ij} = \delta^{ij}$ so things simplify quite a bit. – Michael Albanese Sep 4 '13 at 22:46 | 2019-08-24 18:33:48 | {"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": 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": 0.9365085363388062, "perplexity": 103.06658781656544}, "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-2019-35/segments/1566027321351.87/warc/CC-MAIN-20190824172818-20190824194818-00446.warc.gz"} |
http://www.funpecrp.com.br/parliament-constituencies-vmgpy/5519d8-perchlorate-ion-lewis-structure | . Hence it is very important to learn how to draw Lewis Dot structure correctly for an atom, ion, molecule, polyatomic ion and an ionic compound. So, like oxygen it is also very happy with zero formal charge on it. Formal charge is the charge assigned to an atom in a molecule or ion on the basis of the difference in valence electrons and electrons used by the atom in the Lewis dot structure. First group elements (H and He) cannot have more than 2 electrons, since they have only 1s orbitals in their configurations. Valence electrons of Nitrogen atom and Chlorine atom. Now let us try Lewis dot structure of Sulfide ion ( S2-).Two negative charges means sulfur atom has gained two electrons so its electronic configuration is with 18 electrons (instead of 16). Dès qu’elles ont eu connaissance de rejets de perchlorate d’ammonium dans l’environnement en provenance d’un industriel, les ARS d’Aquitaine et de Midi-Pyrénées ont recherché les perchlorates dans l’eau du robinet produite à partir de captages d’eau situés en aval de ces rejets. Chlorine does not follow the octet rule. Lewis structure is very important in chemistry, because they are used in many important concepts of general chemistry such as chemical bonding, resonance, valence shell electron pair repulsion theory, prediction of the polarity of the molecules and understanding of reaction mechanisms. For an example, let’s find the Lewis dot structure of a nitride ion ( N3-).Three negative charges means nitrogen atom has gained three electrons so its electronic configuration is with 10 electrons (instead of 7). Drawing the Lewis Structure for ClO 4- (Perchlorate Ion) Perchlorates (salts with the ClO 4-) are used in rocket fuel (NH 4 ClO 4) and to treat hyperthyroidism (NaClO 4). Formal charge on N= Valence electrons – no of bonds – 2*Lone pairs, Formal charge on H = Valence electrons – no of bonds – 2*Lone pairs, Total valence electrons = 7(Cl) + 4*6 (4 SO)+1 (due to one negative charge) = 32, Central atom is Cl because O is more electronegative than Cl (check the periodic table). Here is a table that depicts electronegativity trends in the periodic table. Total valence electrons of given by four oxygen atoms,chlorine atom and negative charge are considered to draw the ClO 4- lewis structure. Hence all 24 valence electrons are used up . As the size of the atom increases bonded electrons move away from the nucleus of the atom and hence nucleus of atom will have less pull on the electrons. Experts are waiting 24/7 to provide step-by-step solutions in as fast as 30 minutes! Chlorate when accompanied by a Roman numeral in parentheses, e.g. So you need to draw that Lewis structure first. from http://treefrog.fullerton.edu/chem/LS/ClO4neg1LS.html, The perchlorate ion cannot be satisfactorily represented by just one. The perchlorate ion cannot be satisfactorily represented by just one Lewis Dots structure. After determining how many valence. Be belongs to group number 2 and its valence electrons are also 2. 5 point Using formal charges, determine which Lewis structure is the preferred one for the perchlorate ion. Electronegativity (EN) is the tendency of an atom to pull a shared pair electrons which results in the polarity (charge separation) in the bond. Remember Cl can have maximum 7 bonds around it because it has 7 valence electrons. Instead, it is often thought of as a hybrid of multiple resonance structures : Preparation [ edit ] Laboratory [ edit ] So this can be taken care if we replace one double bond of oxygen with a single bond and complete the octet of O with one lone pair. This structure is wrong because N cannot have more than 8 electrons around it .In the above structure we have made 6 bonds around Nitrogen means 6*2 (2 electrons in each bond) =12 electrons .Now we need to replace two of the double bonds of the oxygen atom with nitrogen into single bond .To complete the octet of these oxygen, we need to put one extra lone pair on each of them and in the structure you can see two singly bonded oxygen atoms with three lone pairs. Formal charge comes from the Lewis structure for the molecule or ion you are interested in. Phosphorus has 5 valence electrons so like nitrogen it is also very happy with zero formal charge on it. Consider the lewis structure of perchlorate ion as follows: formal charge = valence electrons - lone pairs electrons - bonding pairs electrons/2 The compound has two oxygen's with a -1 view the full answer. Now let us complete the octet of the most electronegative element O first with minimum formal charge. perchlorate ion lewis structure . Hence it is very important to learn how to draw Lewis Dot structure correctly for an atom, ion, molecule, polyatomic ion and an ionic compound. So, like oxygen it is also very happy with zero formal charge on it. Formal charge is the charge assigned to an atom in a molecule or ion on the basis of the difference in valence electrons and electrons used by the atom in the Lewis dot structure. First group elements (H and He) cannot have more than 2 electrons, since they have only 1s orbitals in their configurations. Valence electrons of Nitrogen atom and Chlorine atom. Now let us try Lewis dot structure of Sulfide ion ( S2-).Two negative charges means sulfur atom has gained two electrons so its electronic configuration is with 18 electrons (instead of 16). Dès qu’elles ont eu connaissance de rejets de perchlorate d’ammonium dans l’environnement en provenance d’un industriel, les ARS d’Aquitaine et de Midi-Pyrénées ont recherché les perchlorates dans l’eau du robinet produite à partir de captages d’eau situés en aval de ces rejets. Chlorine does not follow the octet rule. Lewis structure is very important in chemistry, because they are used in many important concepts of general chemistry such as chemical bonding, resonance, valence shell electron pair repulsion theory, prediction of the polarity of the molecules and understanding of reaction mechanisms. For an example, let’s find the Lewis dot structure of a nitride ion ( N3-).Three negative charges means nitrogen atom has gained three electrons so its electronic configuration is with 10 electrons (instead of 7). Drawing the Lewis Structure for ClO 4- (Perchlorate Ion) Perchlorates (salts with the ClO 4-) are used in rocket fuel (NH 4 ClO 4) and to treat hyperthyroidism (NaClO 4). Formal charge on N= Valence electrons – no of bonds – 2*Lone pairs, Formal charge on H = Valence electrons – no of bonds – 2*Lone pairs, Total valence electrons = 7(Cl) + 4*6 (4 SO)+1 (due to one negative charge) = 32, Central atom is Cl because O is more electronegative than Cl (check the periodic table). Here is a table that depicts electronegativity trends in the periodic table. Total valence electrons of given by four oxygen atoms,chlorine atom and negative charge are considered to draw the ClO 4- lewis structure. Hence all 24 valence electrons are used up . As the size of the atom increases bonded electrons move away from the nucleus of the atom and hence nucleus of atom will have less pull on the electrons. Experts are waiting 24/7 to provide step-by-step solutions in as fast as 30 minutes! Chlorate when accompanied by a Roman numeral in parentheses, e.g. So you need to draw that Lewis structure first. from http://treefrog.fullerton.edu/chem/LS/ClO4neg1LS.html, The perchlorate ion cannot be satisfactorily represented by just one. The perchlorate ion cannot be satisfactorily represented by just one Lewis Dots structure. After determining how many valence. Be belongs to group number 2 and its valence electrons are also 2. 5 point Using formal charges, determine which Lewis structure is the preferred one for the perchlorate ion. Electronegativity (EN) is the tendency of an atom to pull a shared pair electrons which results in the polarity (charge separation) in the bond. Remember Cl can have maximum 7 bonds around it because it has 7 valence electrons. Instead, it is often thought of as a hybrid of multiple resonance structures : Preparation [ edit ] Laboratory [ edit ] So this can be taken care if we replace one double bond of oxygen with a single bond and complete the octet of O with one lone pair. This structure is wrong because N cannot have more than 8 electrons around it .In the above structure we have made 6 bonds around Nitrogen means 6*2 (2 electrons in each bond) =12 electrons .Now we need to replace two of the double bonds of the oxygen atom with nitrogen into single bond .To complete the octet of these oxygen, we need to put one extra lone pair on each of them and in the structure you can see two singly bonded oxygen atoms with three lone pairs. Formal charge comes from the Lewis structure for the molecule or ion you are interested in. Phosphorus has 5 valence electrons so like nitrogen it is also very happy with zero formal charge on it. Consider the lewis structure of perchlorate ion as follows: formal charge = valence electrons - lone pairs electrons - bonding pairs electrons/2 The compound has two oxygen's with a -1 view the full answer. Now let us complete the octet of the most electronegative element O first with minimum formal charge.
# perchlorate ion lewis structure
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Is it linear or bent? Electronegativity Part 4 – Polarity of bonds in organic molecules based on hybridization ,oxidation number and formal charges. ClO4- Lewis Structure (Perchlorate ion) Lewis Structure of ClO 4- (Perchlorate ion) Lewis structure of ClO 4- ion is drawn step by step in this tutorial. May cause ignition when in contact with organic materials. (b) State the hybridization of the central Natom in the azide ion. All the bonds are the same length and must be thought of as a hybrid of multiple resonance structures. So, the equation can be re-written as: FC = Group No – No of bonds – 2*No of lone pairs. (b) Cl 2 will be like F 2, except that the basis functions are 3s and 3p rather than 2s and 2p. L'ion chlorate, dans lequel le chlore est hypervalent, ne peut être représenté par une unique structure de Lewis car les trois liaisons Cl–O ont la même longueur (149 pm dans le chlorate de potassium KClO 3). Want to see the full answer? When that happens, we usually assign formal charges to the bonded atoms to help determine the correct Lewis structure. 9.nitrate ion: 10 electrons around the N atom. 2. Add them together. It has 4 valence electrons so it is very happy with four bonds and no lone pairs in the Lewis dot structures. The Lewis structure is: This also predicts a single bond. Check out a sample textbook solution. Step 3 is already taken care of ,as N has 8 electrons around it and each H is with two electrons on it . 7. COMPLETE THE OCTET OF THE MOST ELECTRONEGATIVE ATOM WITH MINIMUM FORMAL CHARGES. A step-by-step explanation of how to draw the ClO4-Lewis Structure (Perchlorate Ion). Now, let’s take an element which can have an expanded octet. Want to see this answer and more? Similarly for every lone pair it uses a pair of electrons. google_ad_slot = "2147476616"; Chapter 12, Problem 115AP. Let’s practice step one “count the total valence electrons’ on molecules and polyatomic ions. Lewis dot structure of all atoms of the main periodic table. Do not skip or try to rearrange any step during your learning process, as it is important to understand and implement each step to correctly design these structures. STEP 2 : MAKE A SKELETON OF THE STRUCTURE. Here phosphorus is with 10 electrons around it (expanded octet and extra electrons are accommodated in the empty 3d orbitals of Phosphorous). Metal chlorates can be prepared by adding chlorine to … For the Lewis structure below, what are the formal charges on C, S, and N? arrow_forward. It will hold more than 8 electrons. (c) How many $\sigma$ bonds and how many $\pi$ bonds does the central nitrogen atom make in the azide ion? Previous question Next question Transcribed Image Text from this Question. It has 6 valence electrons so it is very happy with two bonds and two lone pairs in the Lewis dot structures, However if Oxygen has one bond with three lone pairs in Lewis dot structure, then, It has 5 valence electrons so it is very happy with three bonds and one lone pair in the Lewis dot structures, However if there are 4 bonds around N which we generally see in many ammonium compounds than it will acquire a formal positive charge. Trends of Electronegativity in periodic table Part 2, Measurement systems a brief introduction: Part 1, SAT Chemistry Exam : A brief introduction, Chemistry Homework Problems : Tips and Strategies to Conquer Them. For example. The VSEPR predicts a tetrahedral shape. Les perchlorates, en tant que propulsifs (Propergol composite à perchlorate d'ammoniums ou de potassium principalement) solides … perchlorate ion , ClO 4 − c . However for molecules and polyatomic ions we need to consider many more factors before drawing a correct Lewis dot structure. The VSEPR predicts a tetrahedral shape. Let’s take nitrate ion as the next example. However, unlike oxygen it has more different combinations to get a zero formal charge. The polyatomic ion is treated just like the negative nonmetals we have been using already. STEP 1 : COUNT THE TOTAL VALENCE ELECTRONS. //-->. Hence it is very important to learn how to draw Lewis Dot structure correctly for an atom, ion, molecule, polyatomic ion and an ionic compound. So, like oxygen it is also very happy with zero formal charge on it. Formal charge is the charge assigned to an atom in a molecule or ion on the basis of the difference in valence electrons and electrons used by the atom in the Lewis dot structure. First group elements (H and He) cannot have more than 2 electrons, since they have only 1s orbitals in their configurations. Valence electrons of Nitrogen atom and Chlorine atom. Now let us try Lewis dot structure of Sulfide ion ( S2-).Two negative charges means sulfur atom has gained two electrons so its electronic configuration is with 18 electrons (instead of 16). Dès qu’elles ont eu connaissance de rejets de perchlorate d’ammonium dans l’environnement en provenance d’un industriel, les ARS d’Aquitaine et de Midi-Pyrénées ont recherché les perchlorates dans l’eau du robinet produite à partir de captages d’eau situés en aval de ces rejets. Chlorine does not follow the octet rule. Lewis structure is very important in chemistry, because they are used in many important concepts of general chemistry such as chemical bonding, resonance, valence shell electron pair repulsion theory, prediction of the polarity of the molecules and understanding of reaction mechanisms. For an example, let’s find the Lewis dot structure of a nitride ion ( N3-).Three negative charges means nitrogen atom has gained three electrons so its electronic configuration is with 10 electrons (instead of 7). Drawing the Lewis Structure for ClO 4- (Perchlorate Ion) Perchlorates (salts with the ClO 4-) are used in rocket fuel (NH 4 ClO 4) and to treat hyperthyroidism (NaClO 4). Formal charge on N= Valence electrons – no of bonds – 2*Lone pairs, Formal charge on H = Valence electrons – no of bonds – 2*Lone pairs, Total valence electrons = 7(Cl) + 4*6 (4 SO)+1 (due to one negative charge) = 32, Central atom is Cl because O is more electronegative than Cl (check the periodic table). Here is a table that depicts electronegativity trends in the periodic table. Total valence electrons of given by four oxygen atoms,chlorine atom and negative charge are considered to draw the ClO 4- lewis structure. Hence all 24 valence electrons are used up . As the size of the atom increases bonded electrons move away from the nucleus of the atom and hence nucleus of atom will have less pull on the electrons. Experts are waiting 24/7 to provide step-by-step solutions in as fast as 30 minutes! Chlorate when accompanied by a Roman numeral in parentheses, e.g. So you need to draw that Lewis structure first. from http://treefrog.fullerton.edu/chem/LS/ClO4neg1LS.html, The perchlorate ion cannot be satisfactorily represented by just one. The perchlorate ion cannot be satisfactorily represented by just one Lewis Dots structure. After determining how many valence. Be belongs to group number 2 and its valence electrons are also 2. 5 point Using formal charges, determine which Lewis structure is the preferred one for the perchlorate ion. Electronegativity (EN) is the tendency of an atom to pull a shared pair electrons which results in the polarity (charge separation) in the bond. Remember Cl can have maximum 7 bonds around it because it has 7 valence electrons. Instead, it is often thought of as a hybrid of multiple resonance structures : Preparation [ edit ] Laboratory [ edit ] So this can be taken care if we replace one double bond of oxygen with a single bond and complete the octet of O with one lone pair. This structure is wrong because N cannot have more than 8 electrons around it .In the above structure we have made 6 bonds around Nitrogen means 6*2 (2 electrons in each bond) =12 electrons .Now we need to replace two of the double bonds of the oxygen atom with nitrogen into single bond .To complete the octet of these oxygen, we need to put one extra lone pair on each of them and in the structure you can see two singly bonded oxygen atoms with three lone pairs. Formal charge comes from the Lewis structure for the molecule or ion you are interested in. Phosphorus has 5 valence electrons so like nitrogen it is also very happy with zero formal charge on it. Consider the lewis structure of perchlorate ion as follows: formal charge = valence electrons - lone pairs electrons - bonding pairs electrons/2 The compound has two oxygen's with a -1 view the full answer. Now let us complete the octet of the most electronegative element O first with minimum formal charge. | 2021-05-14 04:25:49 | {"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": 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": 0.5709930658340454, "perplexity": 2511.4879801019233}, "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-2021-21/segments/1620243991737.39/warc/CC-MAIN-20210514025740-20210514055740-00188.warc.gz"} |
https://probabilityexam.wordpress.com/2013/05/01/exam-p-practice-problem-71-estimating-claim-frequency/ | # Exam P Practice Problem 71 – Estimating Claim Frequency
Problem 71-A
An auto insurer issued policies to a large group of drivers under the age of 40. These drivers are classified into five distinct groups by age. These groups are equal in size.
The annual claim count distribution for any driver being insured by this insurer is assumed to be a binomial distribution. The following table shows more information about these drivers.
$\displaystyle \begin{bmatrix} \text{Age}&\text{ }&\text{ }&\text{Mean} &\text{ }&\text{ }&\text{Variance} \\\text{Group}&\text{ }&\text{ }&\text{Of Claim Count} &\text{ }&\text{ }&\text{Of Claim Count} \\\text{ }&\text{ }&\text{ } &\text{ }&\text{ } \\ \text{16-17}&\text{ }&\text{ }&\displaystyle \frac{5}{2}&\text{ }&\text{ }&\displaystyle \frac{5}{4} \\\text{ }&\text{ }&\text{ } &\text{ }&\text{ } \\ \text{18-24}&\text{ }&\text{ }&\displaystyle 2&\text{ }&\text{ }&\displaystyle 1 \\\text{ }&\text{ }&\text{ } &\text{ }&\text{ } \\ \text{25-29}&\text{ }&\text{ }&\displaystyle \frac{3}{2}&\text{ }&\text{ }&\displaystyle \frac{3}{4} \\\text{ }&\text{ }&\text{ } &\text{ }&\text{ } \\ \text{30-34}&\text{ }&\text{ }&\displaystyle 1&\text{ }&\text{ }&\displaystyle \frac{1}{2} \\\text{ }&\text{ }&\text{ } &\text{ }&\text{ } \\ \text{35-39}&\text{ }&\text{ }&\displaystyle \frac{1}{2} &\text{ }&\text{ }&\displaystyle \frac{1}{4} \end{bmatrix}$
An insured driver is randomly selected from this large pool of insured and is observed to have one claim in the last year.
What is the probability that the mean number of claims in a year for this insured driver is greater than 1.5?
$\text{ }$
$\displaystyle (A) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \frac{14}{67}$
$\displaystyle (B) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \frac{13}{57}$
$\displaystyle (C) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \frac{3}{5}$
$\displaystyle (D) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \frac{51}{67}$
$\displaystyle (E) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \frac{50}{64}$
$\text{ }$
$\text{ }$
$\text{ }$
$\text{ }$
______________________________________________________________________
Problem 71-B
An auto insurer issued policies to a large group of drivers under the age of 40. These drivers are classified into five distinct groups by age. These groups are equal in size.
The annual claim count distribution for any driver being insured by this insurer is assumed to be a geometric distribution. The following table shows more information about these drivers.
$\displaystyle \begin{bmatrix} \text{Age}&\text{ }&\text{ }&\text{Mean} &\text{ }&\text{ }&\text{Variance} \\\text{Group}&\text{ }&\text{ }&\text{Of Claim Count} &\text{ }&\text{ }&\text{Of Claim Count} \\\text{ }&\text{ }&\text{ } &\text{ }&\text{ } \\ \text{35-39}&\text{ }&\text{ }&\displaystyle 1 &\text{ }&\text{ }&\displaystyle 2 \\\text{ }&\text{ }&\text{ } &\text{ }&\text{ } \\ \text{30-34}&\text{ }&\text{ }&\displaystyle 2&\text{ }&\text{ }&\displaystyle 6 \\\text{ }&\text{ }&\text{ } &\text{ }&\text{ } \\ \text{25-29}&\text{ }&\text{ }&\displaystyle 3&\text{ }&\text{ }&\displaystyle 12 \\\text{ }&\text{ }&\text{ } &\text{ }&\text{ } \\ \text{18-24}&\text{ }&\text{ }&\displaystyle 4&\text{ }&\text{ }&\displaystyle 20 \\\text{ }&\text{ }&\text{ } &\text{ }&\text{ } \\ \text{16-17}&\text{ }&\text{ }&\displaystyle 5&\text{ }&\text{ }&\displaystyle 30 \end{bmatrix}$
An insured driver is randomly selected from this large pool of insured and is observed to have one claim in the last year.
What is the probability that the mean number of claims in a year for this insured driver is greater than 2.5?
$\text{ }$
$\displaystyle (A) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 0.49$
$\displaystyle (B) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 0.51$
$\displaystyle (C) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 0.55$
$\displaystyle (D) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 0.57$
$\displaystyle (E) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 0.60$
______________________________________________________________________
$\text{ }$
$\text{ }$
$\text{ }$
$\text{ }$
$\text{ }$
$\text{ }$
$\text{ }$
$\text{ }$
______________________________________________________________________
______________________________________________________________________
$\copyright \ 2013 \ \ \text{Dan Ma}$ | 2019-08-18 05:33:38 | {"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": 0, "img_math": 27, "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": 0.3747941851615906, "perplexity": 838.1799672424032}, "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/1566027313617.6/warc/CC-MAIN-20190818042813-20190818064813-00276.warc.gz"} |
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# According to the Tristate Transportation Authority, making
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According to the Tristate Transportation Authority, making [#permalink]
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22 Apr 2013, 07:20
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According to the Tristate Transportation Authority, making certain improvements to the main commuter rail line would increase ridership dramatically. The authority plans to finance these improvements over the course of five years by raising automobile tolls on the two highway bridges along the route the rail line serves. Although the proposed improvements are indeed needed, the authority's plan for securing the necessary funds should be rejected because it would unfairly force drivers to absorb the entire cost of something from which they receive no benefit.
Q. Which of the following, if true, would provide the authority with the strongest counter to the objection that its plan is unfair?
(A) Even with the proposed toll increase, the average bridge toll in the tristate region would remain less than the tolls charged in neighboring states.
(B) Any attempt to finance the improvements by raising rail fares would result in a decrease in ridership and so would be self-defeating.
(C) Automobile commuters benefit from well-maintained bridges, and in the tristate region bridge maintenance is funded out of general income tax revenues to which both automobile and rail commuters contribute.
(D) The roads along the route served by the rail line are highly congested and drivers benefit when commuters are diverted from congested roadways to mass transit.
(E) The only alternative way of funding the proposed improvements now being considered is through a regional income tax surcharge, which would affect automobile commuters and rail commuters alike.
[Reveal] Spoiler: OA
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Re: Improvements to the main commuter rail line [#permalink]
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22 Apr 2013, 07:39
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D suits the bill in best way------> it gives a reason to understand why i ,as an automobile rider ,might agree to pay for the development of rail road . the fact that this money put by me will ultimately help to reduce the congestion ,which is in fact a big problem at the moment , might become a solid reason as why i sud contribute (in terms of money ) to the development of this project
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Re: Improvements to the main commuter rail line [#permalink]
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22 Apr 2013, 11:40
CharuKapoor wrote:
According to the Tristate Transportation Authority, making certain improvements to the main commuter rail line would increase ridership dramatically. The authority plans to finance these improvements over the course of five years by raising automobile tolls on the two highway bridges along the route the rail line serves. Although the proposed improvements are indeed needed, the authority's plan for securing the necessary funds should be rejected because it would unfairly force drivers to absorb the entire cost of something from which they receive no benefit.
Q. Which of the following, if true, would provide the authority with the strongest counter to the objection that its plan is unfair?
(A) Even with the proposed toll increase, the average bridge toll in the tristate region would remain less than the tolls charged in neighboring states.
(B) Any attempt to finance the improvements by raising rail fares would result in a decrease in ridership and so would be self-defeating.
(C) Automobile commuters benefit from well-maintained bridges, and in the tristate region bridge maintenance is funded out of general income tax revenues to which both automobile and rail commuters contribute.
(D) The roads along the route served by the rail line are highly congested and drivers benefit when commuters are diverted from congested roadways to mass transit.
(E) The only alternative way of funding the proposed improvements now being considered is through a regional income tax surcharge, which would affect automobile commuters and rail commuters alike.
hi charu..
i think the answer must be D..
If I m nt wrong u chose B....if that is the case..than u shud think..conclusion is "its unfair to charge drivers for financing the rail project" We need to weaken the conclusion"so if we say that we do not have any other alternative to raise the fund ...that does not weaken......if there is none who could be charged...than why these truck drivers shud be a safe bait.....ti does not make sense to say , if nthn works than we are goin to ask truck drivers...."
On ther hand D says there are cases, where the drivers have benefited , if there is no congestion on the highway...so it make us to think that when the rail system will be improved the mass transit will be less and drivers will be those who will benifit max out f it..
Consider kudos if my post helps!!!!!!
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Re: According to the Tristate Transportation Authority, making [#permalink]
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17 Jun 2013, 16:04
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According to the Tristate Transportation Authority, making certain improvements to the main commuter rail line would increase ridership dramatically. The authority plans to finance these improvements over the course of five years by raising automobile tolls on the two highway bridges along the route the rail line serves. Although the proposed improvements are indeed needed, the authority's plan for securing the necessary funds should be rejected because it would unfairly force drivers to absorb the entire cost of something from which they receive no benefit.
Q. Which of the following, if true, would provide the authority with the strongest counter to the objection that its plan is unfair?
(A) Even with the proposed toll increase, the average bridge toll in the tristate region would remain less than the tolls charged in neighboring states. irrelevant (no mention of other states)
(B) Any attempt to finance the improvements by raising rail fares would result in a decrease in ridership and so would be self-defeating.
it is about why drivers have to pay not why rail riders must not.
(C) Automobile commuters benefit from well-maintained bridges, and in the tristate region bridge maintenance is funded out of general income tax revenues to which both automobile and rail commuters contribute. stimules states why drivers have to absorb the ENTIRE COST.Hence we need to choose option which impacts either automobile drivers or rail riders.
(D) The roads along the route served by the rail line are highly congested and drivers benefit when commuters are diverted from congested roadways to mass transit.CORRECT
(E) The only alternative way of funding the proposed improvements now being considered is through a regional income tax surcharge, which would affect automobile commuters and rail commuters alike.same as C
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Re: According to the Tristate Transportation Authority, making [#permalink]
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18 Jun 2013, 18:29
CharuKapoor wrote:
According to the Tristate Transportation Authority, making certain improvements to the main commuter rail line would increase ridership dramatically. The authority plans to finance these improvements over the course of five years by raising automobile tolls on the two highway bridges along the route the rail line serves. Although the proposed improvements are indeed needed, the authority's plan for securing the necessary funds should be rejected because it would unfairly force drivers to absorb the entire cost of something from which they receive no benefit.
Q. Which of the following, if true, would provide the authority with the strongest counter to the objection that its plan is unfair?
(A) Even with the proposed toll increase, the average bridge toll in the tristate region would remain less than the tolls charged in neighboring states.
(B) Any attempt to finance the improvements by raising rail fares would result in a decrease in ridership and so would be self-defeating.
(C) Automobile commuters benefit from well-maintained bridges, and in the tristate region bridge maintenance is funded out of general income tax revenues to which both automobile and rail commuters contribute.
(D) The roads along the route served by the rail line are highly congested and drivers benefit when commuters are diverted from congested roadways to mass transit.
(E) The only alternative way of funding the proposed improvements now being considered is through a regional income tax surcharge, which would affect automobile commuters and rail commuters alike.
In order to answer this question , think about how automobile owners benefit from the toll increase. D clearly answers that.
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Re: According to the Tristate Transportation Authority, making [#permalink]
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19 Jun 2013, 09:38
CharuKapoor wrote:
According to the Tristate Transportation Authority, making certain improvements to the main commuter rail line would increase ridership dramatically. The authority plans to finance these improvements over the course of five years by raising automobile tolls on the two highway bridges along the route the rail line serves. Although the proposed improvements are indeed needed, the authority's plan for securing the necessary funds should be rejected because it would unfairly force drivers to absorb the entire cost of something from which they receive no benefit.
Q. Which of the following, if true, would provide the authority with the strongest counter to the objection that its plan is unfair?
(A) Even with the proposed toll increase, the average bridge toll in the tristate region would remain less than the tolls charged in neighboring states.
(B) Any attempt to finance the improvements by raising rail fares would result in a decrease in ridership and so would be self-defeating.
(C) Automobile commuters benefit from well-maintained bridges, and in the tristate region bridge maintenance is funded out of general income tax revenues to which both automobile and rail commuters contribute.
(D) The roads along the route served by the rail line are highly congested and drivers benefit when commuters are diverted from congested roadways to mass transit.(E) The only alternative way of funding the proposed improvements now being considered is through a regional income tax surcharge, which would affect automobile commuters and rail commuters alike.
we have to counter the claim that asking drivers to pay is unfair specifically because drivers get no benefit. Thus, the best way to counter this is to show how drivers would benefit D shows exactly how they would benefit while the other answers focus on other topics that are irrelevant.
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Re: According to the Tristate Transportation Authority, making [#permalink]
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05 Jul 2013, 07:08
Conclusion: Although the proposed improvements are indeed needed, the authority's plan for securing the necessary funds should be rejected because it would unfairly force drivers to absorb the entire cost of something from which they receive no benefit.
What we need to do:
1. Should not be rejected
2. Explain why: because there can be a benefit to the drivers
(D) answers it perfectly. drivers benefit when commuters are diverted from congested roadways to mass transit. - In Scope and weakens the conclusion.
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Re: According to the Tristate Transportation Authority, making [#permalink]
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07 Mar 2016, 09:25
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Re: According to the Tristate Transportation Authority, making [#permalink] 07 Mar 2016, 09:25
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Display posts from previous: Sort by | 2016-09-25 14:59:55 | {"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": 0.22354133427143097, "perplexity": 6586.3633754031525}, "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-2016-40/segments/1474738660214.50/warc/CC-MAIN-20160924173740-00298-ip-10-143-35-109.ec2.internal.warc.gz"} |
https://gharpedia.com/paint-sagging-defect/ | Paint Sagging: Common Defect Observed on the Painted Surface
Painting your home’s exterior and interior always adds value to your house. New paint can change the mood of a space and gives the feeling of newness and freshness to your house. However, after some time several defects might appear, during or after the paint application, i.e. chalking, brush marks, sagging, cracking, etc. Among them, sagging is the most common paint defects observed on the painted surface on the walls of your house.
Also Read: Difference between Interior and Exterior Paint
When paint runs downward after application on the surface is called sagging. Paint sagging is defined as downward movement of the paint film between the time of application and drying resulting in an uneven coating. This paint defect is more prominent if a thick layer of paint is applied on a vertical or inclined surface. The excess paint runs down and gives an uneven surface and thick lower edge.
Courtesy - 123rf
Paint sagging occurs if pigment gets separated from the paint and gets settled down at the bottom of the container. Pigment gets separated if those containers are stored for very long time or under too much heat or faulty thinning, or if stirring or shaking has been not done properly before taking in use.
There are various reasons why paint sagging occurred i.e.
• Too much of paint applied on the surface (Excessive thick coat)
• Poor workmanship painted by unskilled labour during painting
• Poor surface preparation before painting (at a certain location)
• Viscosity of the paint is less (paint too thin), or by using a wrong thinner
• Spraying of paint carried out too close or at a high pressure
• Applying paint in cold or humid weather
Always apply paint according to recommended spread rate and avoid thick paint layer. Therefore you need to take care during paint application so that this type of paint defects cannot occur on the painted surface.
Material Exhibition
Explore the world of materials. | 2019-01-20 09:38:12 | {"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": 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": 0.3258083760738373, "perplexity": 3574.293664404465}, "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-2019-04/segments/1547583705091.62/warc/CC-MAIN-20190120082608-20190120104608-00607.warc.gz"} |
http://mathhelpforum.com/algebra/33899-help-needed.html | 1. Help needed
Can anyone tell me easiest way to solve questions like
1) Area b/w graphs->f(x)=||x|-2|+||x|-4|;g(x)=|x|+||x|-6|
2)No of values satisfying the inequation-->|x|+|x-1|+|x+3|<6
3)Equations in more than one variable like--> no of values satisfying the equation |x+1|+|y+1|<4
Explain the method as well
Cheerz!!!
2. For the first one
Originally Posted by nikunj14_83
Can anyone tell me easiest way to solve questions like
1) Area b/w graphs->f(x)=||x|-2|+||x|-4|;g(x)=|x|+||x|-6|
2)No of values satisfying the inequation-->|x|+|x-1|+|x+3|<6
3)Equations in more than one variable like--> no of values satisfying the equation |x+1|+|y+1|<4
Explain the method as well
Cheerz!!!
find which is greater on the domain they are bounded by...to do this first find $g(x)=f(x)$....then set up an integral with limits of integration based on your finds...then you must find $f(x)>g(x)$ on the interval...if that is true the area between is $\int_a^{b}f(x)-g(x)dx$...if $f(x) on the interval...then it is the negative of the integral I gave you | 2016-10-21 20:34:35 | {"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": 4, "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": 0.812934160232544, "perplexity": 1694.6684924489803}, "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-2016-44/segments/1476988718303.21/warc/CC-MAIN-20161020183838-00078-ip-10-171-6-4.ec2.internal.warc.gz"} |
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An explicit Eulerian method for multiphase flow with contact line dynamics and insoluble surfactant
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Numerical Analysis, NA. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.ORCID iD: 0000-0001-7425-8029
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Numerical Analysis, NA. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Numerical Analysis, NA. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
2014 (English)In: Computers & Fluids, ISSN 0045-7930, E-ISSN 1879-0747, Vol. 101, p. 50-63Article in journal (Refereed) Published
##### Abstract [en]
The flow behavior of many multiphase flow applications is greatly influenced by wetting properties and the presence of surfactants. We present a numerical method for two-phase flow with insoluble surfactants and contact line dynamics in two dimensions. The method is based on decomposing the interface between two fluids into segments, which are explicitly represented on a local Eulerian grid. It provides a natural framework for treating the surfactant concentration equation, which is solved locally on each segment. An accurate numerical method for the coupled interface/surfactant system is given. The system is coupled to the Navier-Stokes equations through the immersed boundary method, and we discuss the issue of force regularization in wetting problems, when the interface touches the boundary of the domain. We use the method to illustrate how the presence of surfactants influences the behavior of free and wetting drops.
##### Place, publisher, year, edition, pages
2014. Vol. 101, p. 50-63
##### Keywords [en]
Multiphase flow, Insoluble surfactant, Marangoni force, Moving contact line, Immersed boundary method
##### National Category
Fluid Mechanics and Acoustics
##### Identifiers
ISI: 000340851500005Scopus ID: 2-s2.0-84903152815OAI: oai:DiVA.org:kth-48763DiVA, id: diva2:458563
##### Funder
Swedish Research Council, 621-2007-6375
##### Note
QC 20140919. Updated from accepted to published.
Available from: 2011-11-23 Created: 2011-11-23 Last updated: 2017-12-08Bibliographically approved
##### In thesis
1. Spectral Accuracy in Fast Ewald Methods and Topics in Fluid Interface Simulation
Open this publication in new window or tab >>Spectral Accuracy in Fast Ewald Methods and Topics in Fluid Interface Simulation
2011 (English)Doctoral thesis, comprehensive summary (Other academic)
##### Abstract [en]
This work contains two separate but related parts: one on spectrally accurate and fast Ewald methods for electrostatics and viscous flow, and one on micro- and complex fluid interface problems. In Part I we are concerned with fast and spectrally accurate methods to compute sums of slowly decaying potentials over periodic lattices. We consider two PDEs: Laplace (electrostatics, the Coulomb potential) and Stokes (viscous flow, the Stokeslet'' potential). Moreover, we consider both full and planar periodicity, the latter meaning that periodicity applies in two dimensions and the third is free''. These are major simulation tasks in current molecular dynamics simulations and in many areas of computational fluid mechanics involving e.g. particle suspensions. For each of the four combinations of PDE and periodic structure, we give spectrally accurate and O(N log N) fast methods based on Ewald's or Ewald-like decompositions of the underlying potential sums. In the plane-periodic cases we derive the decompositions in a manner that lets us develop fast methods. Associated error estimates are developed as needed throughout. All four methods can be placed in the P3M/PME (Particle Mesh Ewald) family. We argue that they have certain novel and attractive features: first, they are spectral accurate; secondly, they use the minimal amount of memory possible within the PME family; third, each has a clear and reliable view of numerical errors, such that parameters can be chosen wisely. Analytical and numerical results are given to support these propositions. We benchmark accuracy and performance versus an established (S)PME method. Part II deals with free boundary problems, specifically numerical methods for multiphase flow. We give an interface tracking method based on a domain-decomposition idea that lets us split the interface into overlapping patches. Each patch is discretized on a uniform grid, and accurate and efficient numerical methods are given for the equations that govern interface transport. We demonstrate that the method is accurate and how it's used in immersed boundary, and interface, Navier-Stokes methods, as well as in a boundary integral Stokes setting. Finally, we consider a problem in complex fluidics where there is a concentration of surfactants \emph{on} the interface and the interface itself is in contact with a solid boundary (the contact line problem). We argue that the domain-decomposition framework is attractive for formulating and treating complex models (e.g. involving PDEs on a dynamic interface) and proceed with developing various aspects of such a method.
##### Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2011. p. xv, 104
##### Series
Trita-CSC-A, ISSN 1653-5723 ; 2011:19
##### National Category
Computational Mathematics
##### Identifiers
urn:nbn:se:kth:diva-48805 (URN)978-91-7501-195-0 (ISBN)
##### Public defence
2011-12-16, Salongen, KTHB, Osquars backe 25, Stockholm, 10:00 (English)
##### Funder
Swedish e‐Science Research Center
##### Note
QC 20111125Available from: 2011-11-25 Created: 2011-11-23 Last updated: 2012-05-24Bibliographically approved
2. Computational methods for microfluidics
Open this publication in new window or tab >>Computational methods for microfluidics
2013 (English)Licentiate thesis, comprehensive summary (Other academic)
##### Abstract [en]
This thesis is concerned with computational methods for fluid flows on the microscale, also known as microfluidics. This is motivated by current research in biological physics and miniaturization technology, where there is a need to understand complex flows involving microscale structures. Numerical simulations are an important tool for doing this.
The first paper of the thesis presents a numerical method for simulating multiphase flows involving insoluble surfactants and moving contact lines. The method is based on an explicit interface tracking method, wherein the interface between two fluids is decomposed into segments, which are represented locally on an Eulerian grid. The framework of this method provides a natural setting for solving the advection-diffusion equation governing the surfactant concentration on the interface. Open interfaces and moving contact lines are also incorporated into the method in a natural way, though we show that care must be taken when regularizing interface forces to the grid near the boundary of the computational domain.
In the second paper we present a boundary integral formulation for sedimenting particles in periodic Stokes flow, using the completed double layer boundary integral formulation. The long-range nature of the particle-particle interactions lead to the formulation containing sums which are not absolutely convergent if computed directly. This is solved by applying the method of Ewald summation, which in turn is computed in a fast manner by using the FFT-based spectral Ewald method. The complexity of the resulting method is O(N log N), as the system size is scaled up with the number of discretization points N. We apply the method to systems of sedimenting spheroids, which are discretized using the Nyström method and a basic quadrature rule.
The Ewald summation method used in the boundary integral method of the second paper requires a decomposition of the potential being summed. In the introductory chapters of the thesis we present an overview of the available methods for creating Ewald decompositions, and show how the methods and decompositions can be related to each other.
##### Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2013. p. viii, 39
##### Series
Trita-NA, ISSN 0348-2952 ; 2013:01
##### National Category
Computational Mathematics
##### Identifiers
urn:nbn:se:kth:diva-116384 (URN)978-91-7501-625-2 (ISBN)
##### Presentation
2013-02-19, F3, Lindstedtsvägen 26, Kungliga Tekniska Högskolan, Stockholm, 10:00 (English)
##### Note
QC 20130124
Available from: 2013-01-24 Created: 2013-01-17 Last updated: 2013-01-24Bibliographically approved
3. Fast and accurate integral equation methods with applications in microfluidics
Open this publication in new window or tab >>Fast and accurate integral equation methods with applications in microfluidics
2016 (English)Doctoral thesis, comprehensive summary (Other academic)
##### Abstract [en]
This thesis is concerned with computational methods for fluid flows on the microscale, also known as microfluidics. This is motivated by current research in biological physics and miniaturization technology, where there is a need to understand complex flows involving microscale structures. Numerical simulations are an important tool for doing this.
The first, and smaller, part of the thesis presents a numerical method for simulating multiphase flows involving insoluble surfactants and moving contact lines. The method is based on an interface decomposition resulting in local, Eulerian grid representations. This provides a natural setting for solving the PDE governing the surfactant concentration on the interface.
The second, and larger, part of the thesis is concerned with a framework for simulating large systems of rigid particles in three-dimensional, periodic viscous flow using a boundary integral formulation. This framework can solve the underlying flow equations to high accuracy, due to the accurate nature of surface quadrature. It is also fast, due to the natural coupling between boundary integral methods and fast summation methods.
The development of the boundary integral framework spans several different fields of numerical analysis. For fast computations of large systems, a fast Ewald summation method known as Spectral Ewald is adapted to work with the Stokes double layer potential. For accurate numerical integration, a method known as Quadrature by Expansion is developed for this same potential, and also accelerated through a scheme based on geometrical symmetries. To better understand the errors accompanying this quadrature method, an error analysis based on contour integration and calculus of residues is carried out, resulting in highly accurate error estimates.
##### Abstract [sv]
Denna avhandling behandlar beräkningsmetoder för strömning på mikroskalan, även känt som mikrofluidik. Detta val av ämne motiveras av aktuell forskning inom biologisk fysik och miniatyrisering, där det ofta finns ett behov av att förstå komplexa flöden med strukturer på mikroskalan. Datorsimuleringar är ett viktigt verktyg för att öka den förståelsen.
Avhandlingens första, och mindre, del beskriver en numerisk metod för att simulera flerfasflöden med olösliga surfaktanter och rörliga kontaktlinjer. Metoden är baserad på en uppdelning av gränsskiktet, som tillåter det att representeras med lokala, Euleriska nät. Detta skapar naturliga förutsättningar för lösning av den PDE som styr surfaktantkoncentrationen på gränsskiktets yta.
Avhandlingens andra, och större, del beskriver ett ramverk för att med hjälp av en randintegralformulering simulera stora system av styva partiklar i tredimensionellt, periodiskt Stokesflöde. Detta ramverk kan lösa flödesekvationerna mycket noggrant, tack vare den inneboende höga noggrannheten hos metoder för numerisk integration på släta ytor. Metoden är också snabb, tack vare den naturliga kopplingen mellan randintegralmetoder och snabba summeringsmetoder.
Utvecklingen av ramverket för partikelsimuleringar täcker ett brett spektrum av ämnet numerisk analys. För snabba beräkningar på stora system används en snabb Ewaldsummeringsmetod vid namn spektral Ewald. Denna metod har anpassats för att fungera med den randintegralformulering för Stokesflöde som används. För noggrann numerisk integration används en metod kallad expansionskvadratur (eng. Quadrature by Expansion), som också har utvecklats för att passa samma Stokesformulering. Denna metod har även gjorts snabbare genom en nyutvecklad metod baserad på geometriska symmetrier. För att bättre förstå kvadraturmetodens inneboende fel har en analys baserad på konturintegraler och residykalkyl utförts, vilket har resulterat i väldigt noggranna felestimat.
##### Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2016. p. 51
##### Series
TRITA-MAT-A ; 2016:03
##### National Category
Computational Mathematics
##### Research subject
Applied and Computational Mathematics
##### Identifiers
urn:nbn:se:kth:diva-185758 (URN)978-91-7595-962-7 (ISBN)
##### Public defence
2016-06-02, F3, Lindstedtsvägen 26, Stockholm, 10:00 (English)
##### Funder
Swedish Research Council, 2011-3178Swedish Research Council, 2007-6375
##### Note
QC 20160427
Available from: 2016-04-27 Created: 2016-04-26 Last updated: 2016-04-27Bibliographically approved
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• rtf | 2019-08-25 14:57:01 | {"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": 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": 0.4175650477409363, "perplexity": 12147.00164477469}, "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/1566027330233.1/warc/CC-MAIN-20190825130849-20190825152849-00022.warc.gz"} |
https://par.nsf.gov/biblio/10207151-unveiling-apparent-negative-capacitance-effects-resulting-from-pulse-measurements-ferroelectric-dielectric-bilayer-capacitors | Unveiling the Apparent “Negative Capacitance” Effects Resulting from Pulse Measurements of Ferroelectric-Dielectric Bilayer Capacitors
Apparent ‘Negative Capacitance’ (NC) effects have been observed in some ferroelectric-dielectric (FE-DE) bilayers by pulse measurements, and the associated results have been published that claim to be direct evidence to support the quasi-static ‘negative capacitance’ (QSNC) idea. However, the ‘NC’ effects only occur when sufficiently high voltage is applied, and even exist in stand-alone FE capacitors. These results contradict the QSNC theory, as it predicts that once stabilized (requires a DE layer), the FE remains in the ‘NC’ state regardless of the applied voltage. In this letter, by the use of Nucleation-Limited-Switching (NLS) model, we present our results obtained from simulation of pulse measurements on samples that are similar to the published ones. The simulation results indicate that reverse polarization switching occurs upon the falling edge of the pulses, which leads to the apparent hysteresis-free NC effect. This work provides an alternative interpretation of the experimental results without invoking the QSNC theory.
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The device concept of ferroelectric-based negative capacitance (NC) transistors offers a promising route for achieving energy-efficient logic applications that can outperform the conventional semiconductor technology, while viable operation mechanisms remain a central topic of debate. In this work, we report steep slope switching in MoS2transistors back-gated by single-layer polycrystalline PbZr0.35Ti0.65O3. The devices exhibit current switching ratios up to 8 × 106within an ultra-low gate voltage window of$$V_{{{\mathrm{g}}}} = \pm \! 0.5$$${V}_{g}=±\phantom{\rule{0ex}{0ex}}0.5$V and subthreshold swing (SS) as low as 9.7 mV decade−1at room temperature, transcending the 60 mV decade−1Boltzmann limit without involving additional dielectric layers. Theoretical modeling reveals the dominant role of the metastable polar states within domain walls in enabling the NC mode, which is corroborated by the relation between SS and domain wall density. Our findings shed light on a hysteresis-free mechanism for NC operation, providing a simple yet effective material strategy for developing low-power 2D nanoelectronics. | 2022-12-01 14:47:36 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 1, "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": 0.3157186508178711, "perplexity": 4112.7499803403425}, "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/1669446710813.48/warc/CC-MAIN-20221201121601-20221201151601-00487.warc.gz"} |
http://physics.stackexchange.com/questions/93336/how-much-does-lighting-of-room-effect-evaporation | # How much does lighting of room effect evaporation?
Suppose there is a wet floor under normal conditions, how much can we alter the rate of evaporation of the wet floor by trying out different types of lights ex. Incandascnet, cfl, fluorescent etc ? I assume that these lighting solutions produce all types of EM waves but they must have distributed it unsymmetrically over the spectrum, now waterhas the frequency that equals that of microwave so my first guess was that turning on the light which emits maximum microwave would produce the fastest results. But then incandescent bulb produces lots oh heat which can heat up the water and then make it evaporate, how to compare and what would be the best solution ?
-
## 1 Answer
I strongly suspect that the choice of bulb will make no noticeable difference in evaporation rate. The total energy density striking the floor due to a 100 W bulb, even assuming that all of the energy is converted to light, is on the order of 120 $\mu \mbox{W}/\mbox{cm}^2$, which is tiny, and real bulbs are only on the order of 1% to 5% efficient, with most of the rest of the energy carried away as heat via convective cooling of the lamp surface by air. So, it's probably more like at most 20 $\mu \mbox{W}/\mbox{cm}^2$, and in either case, this is a tiny power density.
In contrast, you need power densities on the order of 10,000 $\mu \mbox{W}/\mbox{cm}^2$ to be able to see radiation make a noticeable color change on thermal-sensitive liquid crystal sheets, and those are thin, unlike the floor, which is thick and thus can also dissipate heat via conductive cooling. So the radiation due to a single light bulb is unlikely to have any impact on the heating and subsequent evaporation of water on a wet floor.
Likewise, the amount of light emitted by each bulb which is on-resonance with water transitions (microwave and infrared absorption lines) is probably not relevant. This is because in the condensed phase, rotational and vibrational relaxation times (which redistribute energy from the excited states into thermal energy) are on the order of milliseconds or shorter, whereas the evaporation process takes on the order of days or longer, so the system will more or less be at thermal equilibrium. So while a few water molecules may every now and then get excited, they'll hop back down immediately and shed the energy as heat, so it probably won't be any different than the nonresonant heating.
A large room fan blowing air around, however, may speed things up noticeably.
-
Still if someone were to compare, what will be the answer ? (Assuming there are enough lights to make an effect) – Rijul Gupta Jan 12 '14 at 16:04
I have no idea, but assuming there's enough light to have a significant power density hitting the floor, and assuming the power density is the same for each lamp type, I still suspect that it wouldn't really make a measurable difference which lamp choice you used. It's the amount of total energy which counts, not the wavelength distribution, since most of the wavelengths are just getting absorbed and turned to heat. Of course, if your floor is strongly colored one particular color, then the wavelength distribution might matter, but this is all sort of moot, since 1 bulb probably won't do much. – DumpsterDoofus Jan 12 '14 at 16:10 | 2015-12-01 18:42:28 | {"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": 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": 0.6880189776420593, "perplexity": 485.88450096320065}, "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-2015-48/segments/1448398468971.92/warc/CC-MAIN-20151124205428-00041-ip-10-71-132-137.ec2.internal.warc.gz"} |
http://mathoverflow.net/questions/109649/equality-of-rational-maps | # Equality of rational maps
Hi.
Let $f,g:X\dashrightarrow\mathbb{P}^N$ be two rational maps from a complex smooth irreducible projective variety $X$ to a projective space.
Suppose that for every general point $x\in X$ we have $\overline{f^{-1}(f(x))}=\overline{g^{-1}(g(x))}$.
Is true that $\overline{f(X)}$ and $\overline{g(X)}$ are isomorphic (resp. projectively equivalent) ?
If not, is true that $\overline{f(X)}$ is smooth if and only if $\overline{g(X)}$ is smooth?
Thanks.
-
The answer all your questions is no. Let $X = \mathbb{P}^1$ and $N=2$. Let $f:X\to \mathbb{P}^2$ be $f(x:y) = (x:y:0)$ and $g:X\to \mathbb{P}^2$ be $g(x:y) = (x^2y:x^3:y^3)$. Then $f$ and $g$ are both bijective, but the image of $g$ is the singular curve $x_0^3 = x_1^2 x_2$.
EDIT. My guess is that when $f$ and $g$ are regular and both images are normal then the answer that $f(X)$ and $g(X)$ are isomorphic could be yes thanks to Zariski's Main Theorem, but I don't see an argument that would show this.
EDIT. Suppose that $f$ and $g$ are both regular. Let $Y_0 = f(X)$ and $Y_1 = g(X)$. Denote the image of $X$ in $Y_0\times Y_1$ under $(f, g)$ by $Z$. Then by your assumption $Z$ projects bijectively onto both $Y_0$ and $Y_1$. If $Y_0$ and $Y_1$ are normal, then by ZMT we have $Y_0 = Z = Y_1$. In any case (even if $f$ and $g$ are rational) we get that $Y_0$ and $Y_1$ are birational.
Read carefully my question. I am not required $\overline{f^{-1}(f(x))}\simeq \overline{g^{-1}(g(x))}$ but $\overline{f^{-1}(f(x))}= \overline{g^{-1}(g(x))}$. – gio Oct 14 '12 at 20:47
In my example we have $f^{-1}(f(x)) = g^{-1}(g(x)) = x$ since $f$ and $g$ are both bijective... – Piotr Achinger Oct 14 '12 at 21:23
@gio: Piotr Achinger answered your question. In his example the equality of the closures does hold (not just for generic points but for every point $x\in X$). Or am I missing somethig? – Qfwfq Oct 14 '12 at 21:30 | 2015-11-25 20:31:46 | {"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": 0.9699761867523193, "perplexity": 125.83792661225772}, "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/1448398445679.7/warc/CC-MAIN-20151124205405-00317-ip-10-71-132-137.ec2.internal.warc.gz"} |
https://repo.scoap3.org/record/30549 | # Bounded Collection of Feynman Integral Calabi-Yau Geometries
Bourjaily, Jacob L. (Niels Bohr International Academy and Discovery Center, Niels Bohr Institute, University of Copenhagen, Blegdamsvej 17, DK-2100, Copenhagen Ø, Denmark) ; McLeod, Andrew J. (Niels Bohr International Academy and Discovery Center, Niels Bohr Institute, University of Copenhagen, Blegdamsvej 17, DK-2100, Copenhagen Ø, Denmark) ; von Hippel, Matt (Niels Bohr International Academy and Discovery Center, Niels Bohr Institute, University of Copenhagen, Blegdamsvej 17, DK-2100, Copenhagen Ø, Denmark) ; Wilhelm, Matthias (Niels Bohr International Academy and Discovery Center, Niels Bohr Institute, University of Copenhagen, Blegdamsvej 17, DK-2100, Copenhagen Ø, Denmark)
25 January 2019
Abstract: We define the rigidity of a Feynman integral to be the smallest dimension over which it is nonpolylogarithmic. We prove that massless Feynman integrals in four dimensions have a rigidity bounded by $2\left(L-1\right)$ at $L$ loops provided they are in the class that we call marginal: those with $\left(L+1\right)D/2$ propagators in (even) $D$ dimensions. We show that marginal Feynman integrals in $D$ dimensions generically involve Calabi-Yau geometries, and we give examples of finite four-dimensional Feynman integrals in massless ${\phi }^{4}$ theory that saturate our predicted bound in rigidity at all loop orders.
Published in: Physical Review Letters 122 (2019) | 2019-02-21 17:30:21 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 6, "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": 0.6624385118484497, "perplexity": 6108.48941192145}, "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-2019-09/segments/1550247506094.64/warc/CC-MAIN-20190221172909-20190221194909-00071.warc.gz"} |
https://www.nature.com/articles/s41598-019-50323-9?error=cookies_not_supported&code=9b01e6d8-5e3e-488f-96fa-cec8229031ac | Rarity of monodominance in hyperdiverse Amazonian forests
Abstract
Tropical forests are known for their high diversity. Yet, forest patches do occur in the tropics where a single tree species is dominant. Such “monodominant” forests are known from all of the main tropical regions. For Amazonia, we sampled the occurrence of monodominance in a massive, basin-wide database of forest-inventory plots from the Amazon Tree Diversity Network (ATDN). Utilizing a simple defining metric of at least half of the trees ≥ 10 cm diameter belonging to one species, we found only a few occurrences of monodominance in Amazonia, and the phenomenon was not significantly linked to previously hypothesized life history traits such wood density, seed mass, ectomycorrhizal associations, or Rhizobium nodulation. In our analysis, coppicing (the formation of sprouts at the base of the tree or on roots) was the only trait significantly linked to monodominance. While at specific locales coppicing or ectomycorrhizal associations may confer a considerable advantage to a tree species and lead to its monodominance, very few species have these traits. Mining of the ATDN dataset suggests that monodominance is quite rare in Amazonia, and may be linked primarily to edaphic factors.
Introduction
Tropical forests contain Earth’s highest levels of biodiversity. Over 250 tree species ≥10 cm diameter can be found in a 1-ha plot of the continental lowland tropics, whereas a similar area in the most diverse temperate broadleaf forest may hold 20–30 species1,2. Within such hyperdiverse tropical forests, however, patches occur that are dominated by a single tree species (hereafter “monodominant”). The earliest reports of tropical monodominant forests in the Amazon Basin were given by the explorers Spruce and Wallace3,4,5, who noted forests highly dominated by Eperua purpurea Benth. and E. leucantha Benth. on the white sands of the Upper Rio Negro Basin. Later Hamilton-Rice6 discovered large stands dominated by Peltogyne gracilipes Ducke (Fabaceae) during a 1924–25 expedition to northern Brazil. These perplexing single-dominant forests did not fit the traditional perception of uniformly tree-diverse tropical forests6. Similarly, the botanical explorer J. G. Myers, on his trek through the Pakaraima Mountains of then British Guiana, observed forests heavily dominated by either Peltogyne sp., Micrandra glabra Schultes (Euphorbiaceae), or multi-stemmed Dicymbe corymbosa Spruce ex. Benth. (Fabaceae)7. Monodominance has since been documented in all the tropical regions8,9,10,11,12,13. A stand has traditionally been considered monodominant when the number of canopy-level trees belonging to the same species is ≥60%9,14. Monodominant forests are “persistently dominant” when the dominant species dominates all strata/age classes in the stand, and will remain monodominant through time (i.e. late-successional, and not being a dominant, but transient, earlier successional stage).
Several mechanisms have been suggested to explain monodominance but a full understanding has yet to be achieved. Monodominance remains a topic of intensive research with controversial findings e.g.15,16. The term ‘classical monodominance’ was introduced by Peh17 and is defined as the occurrence of monodominant forests with environmental conditions similar to those of adjacent mixed-forests. Several studies, however, have revealed environmental differences between these forests, previously undetected. For example, soil nutrient or moisture availability may vary between monodominant and mixed forests10,11,13,18,19,20,21. Conversely, other studies have indicated that soil characteristics cannot alone explain monodominance13,22,23,24,25,26.
Peh et al.15 summarized several of these contrasting studies on different continents and constructed a conceptual mechanistic framework that could explain monodominance in tropical forests. They suggested that monodominance is likely to emerge under a combination of mechanisms. Furthermore, the combination of traits and mechanisms leading to monodominance can differ between tree species and tropical areas11,16,21,24. Peh et al.15 hypothesized potential pathways to monodominance as based on two well-studied monodominant systems. The first pathway was based on the Afro-tropical, ectomycorrhizal (EM), monodominant canopy tree Gilbertiodendron dewevrei (De Wild.) J. Léonard. The most important mechanisms described for this species were based on seedling shade-tolerance and slow decomposition of leaves, resulting in deep leaf litter. Slow decomposition and deep leaf litter affect soil nutrient cycling and could negatively influence the survival of individuals of many species. These conditions could be advantageous for large seeded trees because they have more reserves for germination11. Trees with large seeds also tend to have shade-tolerant seedlings; seedlings of G. dewevrei are well adapted to the heavily shaded understory, resulting in a competitive advantage over non-shade tolerant pioneer species11,14. While not fully considered by Peh, et al.15, it is well-established that G. dewevrei adults are heavily EM throughout their trans-Congo range and that seedlings of the species share many EM fungal symbionts with their parents27. Gilbertiodendron dewevrei, under a minimal disturbance regime, could attain monodominance, as is described by the mechanisms of Peh, et al.15. This pathway was further examined by Kazmierczak, et al.16, who constructed a model demonstrating that species can obtain monodominance by possessing the intrinsic traits of seeds with large mass and low dispersibility.
The second example pathway was based on Dicymbe corymbosa, a Neotropical species. This species is a mast fruiting tree, which shows coppicing (the formation of sprouts at the base of the tree or on the roots) of shoots and roots28. It has been suggested that there is a link between mast seeding and EM associations that would lead to satiation of seed predators and increased seedling densities29,30,31. Henkel23 indicated that EM associations might also promote coppicing of shoots and roots by enhancing host plant nutrient supplies. Peh et al. pointed out that such positive feedbacks could, over time, result in the dominance of a tree species via competitive exclusion15. While documented examples of monodominant forests exist for the South American tropics, almost all cases are currently known from the Guiana Shield of the region’s northeast. Given the immensity of greater Amazonia, it begs the questions of how widespread monodominant forests might be, what tree species are involved, where they occur, and what environmental drivers are involved.
Here we examine the occurrence of monodominance within the context of a large plot network in Amazonia, the single largest, and arguably the richest, tropical forest on earth (Fig. S1). In line with the earlier concept of hyperdominance32, which was defined by the most common species that make up half of all trees across a region, here we call a site monodominant when a single species of tree constitutes more than half of the individual trees ≥10 cm diameter at breast height (dbh) in a stand of ~1 ha. Questions addressed were: (1) How common or rare is monodominance in Amazonia? (2) Which tree species can become monodominant? (3) Does monodominance occur more frequently in certain families? (4) Which traits characterize monodominant species? (5) In which regions do monodominant trees occur? and, 6) What environmental factors may drive monodominance? Given the paucity of published records from Amazonia, we tested not only for monodominance but also for lower dominance levels. As possible causes of monodominance, we investigated four main mechanisms:
1. 1)
Competitive exclusion. Monodominant forest in the tropics may develop when the forest does not experience large-scale disturbance over a long time period9. This mechanism is based on a study of Eggeling33, who compared tropical rainforest in Uganda in different successional stages. Eggeling showed that over the years, when no disturbance occurred, colonizing stands developed into climax stands with low species diversity, dominated by a few shade-tolerant species. This study led to the development of the intermediate-disturbance hypothesis (IDH)34. The IDH posits that a lack of (internal or external) disturbance leads to unconstrained succession and finally competitive exclusion, where the species that is best adapted to the environmental conditions will out-compete all other species and attain dominance34,35. Under such a mechanism, lowland tropical rainforests typically would not reach this endpoint due to frequent but spatiotemporally stochastic canopy-disturbing tree falls that allow influx of early-successional species into local gap areas, overall promoting persistence of high tree alpha-diversity. The IDH has been supported by evidence in some tropical rain forests36,37 but may have little effect on actual tree diversity38. If a lack of disturbance leads to competitive exclusion, we expect highest dominance in mature forests with the lowest numbers of pioneer species.
2. 2)
Traits linked to above ground competition for light and space. Functional traits may indicate a species-specific ecological strategy. For example, seed size and wood density give an indication of a species’ mode of establishment, growth rate, and survival, and have been used to characterize pioneer versus climax species37,39. If multiple functional traits of a monodominant species differ from those of non-dominant species, they could indicate a distinctive strategy leading to monodominance. However, if the functional traits differ between monodominant species, this would suggest that different mechanisms drive the trajectory to dominance9. Other hypotheses for monodominance are associated with specific competitive traits, such as seed size, where large seeds have low dispersal ability and seedlings establish near parent trees, leading to conspecific replacement over time11,16. Furthermore, the deep litter layers that have been found in monodominant forests could act as a physical barrier for seedling establishment, where large seeds have an advantage over small-seeded species, as they have ample reserves to germinate and establish root systems11. However, small-seeded monodominant species have also been documented, and studies have shown that deep leaf litter does not always affect seedling establishment of non-dominant species. This suggests that large seeds could be a contributing, but not the sole, trait for monodominance15,40. The formation of coppices has been linked to monodominance23,28,41,42. Coppicing involves the formation of multiple shoots at the base of the tree’s stem or from the root system in the absence of major crown injury. The phenomenon allows an individual to persist indefinitely in one location, as one or more shoots may take over when the original stem dies. However, coppicing has so far been found only in a handful of species of a few Amazonian tree genera. If competitive traits lead to monodominance we expect highest dominance by species with traits that are linked with competitive ability.
3. 3)
Competitive traits linked to root-soil interactions. A prominent hypothesis for how monodominance can emerge involves EM symbiosis creating a nutritional advantage for an EM-monodominant tree species with regard to establishment and survival9,43,44,45,46. The EM association consists of a mutualistic symbiosis between plant roots and fungi in which soil nutrients are provided by the fungus to the plant. It is striking that although most tropical trees are arbuscular mycorrhizal (AM), many monodominant tree species have EM associations47,48. The mechanisms behind this relationship are still not fully understood, but most likely involve plant-soil feedback mechanisms in which the local soil-litter conditions are altered in ways favouring the dominant EM tree species9,18,44,49. While both EM and AM fungi are dependent on their host plant for carbohydrate nutrition, and must obtain soil mineral nutrients for transfer to the plant, EM fungi have the enzymatic capacity to access organic forms of mineral nutrients directly from litter while avoiding major cellulolysis50. In systems dominated by EM plants, this mechanism would leave little for AM fungi, which are dependent on mineralized forms of nutrients for uptake. This implies direct competition between these fungi for mineral nutrients50,51. As a result, EM fungi may lead to slower overall decomposition (by mining of organic minerals and thus reducing the rate of saprotrophic cellulolysis) and reduced mineral nutrient availability for AM trees, this giving EM trees a competitive advantage9,52.
Reliance on the “EM mechanism” to explain tropical monodominance is, however, fraught with difficulties, as (1) EM is not exclusively found in monodominant species; (2) monodominant species also occur without EM; (3) some monodominant species possess a combination of EM and AM; and (4) EM may not necessarily slow decomposition rates in tropical forests18,44,53,54. Therefore, we also tested other root-soil interactions including nitrogen (N-) fixation and aluminium accumulation that have yet to be linked to monodominance but could confer competitive advantages on nutrient poor or toxic soils. In the tropics, N-fixation occurs primarily in Fabaceae. While fixation leads to higher nitrogen in leaves of N-fixing species, especially in the wet tropics55, N-fixing Fabaceae do not dominate the most oligotrophic Amazonian ecosystems56, instead appear to have the greatest advantage in tropical dry successional forests57. Aluminium accumulation is found predominantly in a select number of families (e.g. Rubiaceae, Melastomataceae, Myrtaceae and Vochysiaceae [for Amazonian families])58,59,60,61, including a relation with monodominance (Vochysia divergens) in wet areas in the Brazilian Pantanal62. Large numbers of non-monodominant aluminium accumulators are found in the dry Cerrado areas e.g.61. If root-soil interactions are important drivers of competition, we expect EM, nodulating or aluminium accumulating species to be monodominant more frequently than expected by chance.
4. 4)
Area. All Amazon soil types present one or more stress factors to trees. For example, white sand soils are often dry and always low in nutrients, igapó and várzea both experience a single pulse of short to long-term flooding (up to 300 days), igapó soils are nutrient poor, várzea soils are nutrient rich, swamp soils are nearly permanently flooded or waterlogged with low oxygen tension, and terra firme soils are high in potentially toxic iron and aluminium. Because of several trade-offs, a tree species cannot be a good competitor on all of these soils e.g.63,64. Consequently, most common Amazonian tree species have a demonstrable preference for one of these soil types32. These tests often fail for rare species, either because they are non-preferential or are too infrequent to allow for a quantitative test32. With an assumption that all species in Amazonia have a near perfect habitat preference, we should expect that the total area of the soil types (and their level of fragmentation) has an effect on their tree species richness, with larger areas having more species65,66,67. Thus, a fourth possible mechanism for monodominance could be related to species-area relationships, where area is a controlling factor for species richness and dominance66,68. If the area of a distinct ‘edaphic forest type’ controls species richness, we expect monodominance to be more often found in plots in forests types that are small in total areal extent.
Because domestication has previously been linked to dominance in Amazonia69, we also investigated whether domesticated species are linked to monodominance.
Results
Only 50 plots (2.6% of all plots) had levels of dominance over 50% of individuals >10 cm dbh of a single tree species (Fig. 1A) - for classical monodominance [>60%] these numbers were 19 plots (0.98%). In fact only 350 plots (18% of all plots) had dominance levels over 20%. Only 26 species (0.50% of all species) attained levels of dominance of ≥50%: Eschweilera tenuifolia, Micrandra glabra, Ruizterania retusa, Pachira nitida, Machaerium hirtum, Spirotropis longifolia, Tabebuia aurea, Mauritia flexuosa, Brosimum rubescens, Lueheopsis hoehnei, Micrandra sprucei, Dicymbe corymbosa, Eperua falcata, Triplaris weigeltiana, Phyllanthus elsiae, Digomphia densicoma, Mora excelsa, Vitex cymosa, Euterpe oleracea, Oxandra polyantha, Macrolobium multijugum, Tachigali vaupesiana, Pachira brevipes, Astrocaryum macrocalyx, Attalea speciosa, Astrocaryum murumuru (for species authorities see ter Steege, et al.70). The great majority of species (4863, 97%) did not attain 20% dominance or more. Stand-level dominant species, thus, account for a tiny minority of the tree species in Amazonia (Fig. 1B). Data by species and plot are given in Appendix S1.
Twelve out of 117 tree families had species which showed monodominance: Annonaceae, Arecaceae, Bignoniaceae, Euphorbiaceae, Fabaceae, Lamiaceae, Lecythidaceae, Malvaceae, Moraceae, Phyllanthaceae, Polygonaceae, Vochysiaceae (Appendix S2). Although Fabaceae species are a very prominent component of Amazonian forests32, the family had only seven monodominant species in the plots (Machaerium hirtum, Spirotropis longifolia, Eperua falcata, Dicymbe corymbosa, Mora excelsa, Macrolobium multijugum, Tachigali vaupesiana). Although this was the highest number of monodominant species by family, the number was not higher (nor lower) than expected by chance based on the number of species of Fabaceae in all plots (780). Arecaceae species are among the most hyperdominant in Amazonia32 and had five monodominant species in the plots (Mauritia flexuosa, Euterpe oleracea, Astrocaryum macrocalyx, Attalea speciosa, Astrocaryum murumuru). The randomization tests suggested that the number of families found with monodominant species did not deviate from a random expectation, except in the case of dominance over 20% and over 80%. Subsequent tests with Bonferroni correction suggested that only Arecaceae and Bignoniaceae have more species with dominance higher than 20% and only Vochysiaceae higher than 80%. Thus with monodominance defined at 50% or higher no family has more monodominant species than expected by chance. Based on the tests with Bonferroni correction alone Arecaceae showed more often dominance from 20–50%. There was no consistent family pattern in the dominance classes of 60% and higher.
Dominance by plot appeared affected by the percentage of pioneer species (Fig. 2). While there was a weak (but significant) linear relationship between the two variables (p 0.001), maximum dominance appeared constrained more by a larger number of pioneers, as exemplified by a quantile regression for the upper 10% of the data (Tau = 0.9, p = 0.035), than did the average dominance (Fig. 2). Monodominance was found only on plots with less than 0.8% pioneers. However, this result was influenced by the low number of observations that had a high abundance of pioneers. We resampled the data 10,000 times taking 40 plots randomly from the ranges 0; 0–0.2; 0.2–0.4; 0.4–0.6; 0.6–0.8 and over 0.8% of pioneers. The average slope of the upper 10% quantile was -9.2, still showing a negative relationship but the 95% c.i. of the mean included also zero slope. Hence we could not detect a significant relationship between percentage of pioneers and maximum dominance.
Community weighted wood density and community weighted seed mass class had little effect but the average maximum dominance was highest with the lowest and highest values of each, consistent with the traits being part of the pioneer-climax continuum (Fig. 3). Monodominance was found in 14 genera, EM in ten, nodulation in 66, aluminium accumulation in 35, and coppicing in five (Dimorphandra, Dicymbe, Euterpe, Pentaclethra, and Spirotropis). The combination of monodominance and EM was found in Dicymbe (p = 0.16); monodominance and nodulation in the three genera Machaerium, Spirotropis, and Tachigali (p = 0.46); monodominance and aluminium accumulation in Ruizterania (p = 0.35), and monodominance and coppicing in two genera (Dicymbe and Spirotropis, p = 0.007). Thus, in our data, the only ecological trait significantly linked to monodominance was coppicing. On 201 plots one of the 85 recognized Amazonian domesticated species69 was the most abundant species (Appendix S3). In almost all cases (173 plots) and in all cases with a dominance over 30% this most dominant species was an Arecaceae species (Appendix S3). Theobroma cacao was the most dominant species on 10 plots.
The highest percentages (outliers) of trees belonging to potential EM genera were found in white sand forest (PZ) and/or the Guiana Shield (Fig. 4). This forest type and region had both the highest median values as well as most of the high values for percentage EM. However, forest type explained only 2.6% (p 0.001) of the variation in EM percentage, and region 1.1% (p 0.001).
Maximum dominance was highest on those soil types with the smallest area in Amazonia (Fig. 5A). Each of the smaller forest types had higher median maximum dominance than terra firme. Forest type explained 28% (p 0.001) of the maximum dominance by plot (ANOVA). Median dominance was strongly related (power function) to area (Fig. S5). Region had only a very small effect (3% explained variation, p 0.001, Fig. 5B).
Discussion
Monodominance (defined here as ≥50% of individuals ≥10 cm dbh in a stand belong to a single tree species) appears to be quite rare over the greater Amazonian region. In the ATDN analysis presented here, a very small percentage of all plots (2.6%) and species (0.5%) exhibited monodominance by the above definition, and even less, at 1.0% and 0.3%, respectively, under the definition of classical monodominance sensu Peh, et al.15. Even dominance between 20% and 50% was not common. The overall scarcity of monodominance at plot and species level may partially be a reflection of lack of specific sampling throughout the ATDN dataset. If tree plots were not set up to capture stands with clearly dominant tree species but rather set up to capture tree-diverse forest types, the dominant stands would be “missed”. Some ATDN plots, however, were set up to study monodominance, such as those dominated by Brosimum rubescens13, Dicymbe corymbosa23, Spirotropis longifolia42 and studies of plant communities in white sand systems of Guyana and Suriname71. In general we believe most plots were not selected on the basis of selecting or avoiding monodominance. Records do exist for some dominant tree species that were not confirmed as monodominant or were not captured in the ATDN plot data. For example, Dicymbe altsonii and Dicymbe jenmanii are each dominant to monodominant in parts of Guyana46,72,73, as well as Pakaraimaea dipterocarpacea in W. Guyana/E. Venezuela72,74, Aldina spp. in N. Brazil/S. Venezuela/W. Guyana75,76,77,78, and Pseudomonotes tropenbosii in E. Colombia (Aida Vasco-Palacios pers. comm.). All of these genera are confirmed EM46,75. Several ATDN plots have been established in peat swamps, the habitat type that probably accounts for the largest area of monodominant forests in Amazonia, within which only Mauritia flexuosa and Pachira nitida were able to attain monodominance79. Micrandra spp. (Euphorbiaceae) are also known to strongly dominate poorly-drained soils in W. Guyana80,81, T.W. Henkel pers. obs. and adjacent Venezuela82. All told, the overall ranking of dominance suggests a rather smooth transition across all dominance levels (Fig. 1).
Only two families had more species at dominance classes over 20% than expected by chance. The most consistent family with significant dominance (based on Bonferroni correction alone) from 20% to 50% is Arecaceae, including 20/74 species in our data. This is consistent with Arecaceae also having a five times higher than expected number of hyperdominant species32, reflecting their regularly high local dominance. Palms may reach high dominance because they are competitive in large wet areas but they must also be fairly resistant to frequency dependent mortality, as should other hyperdominant and monodominant species. For all other families the monodominance level is rather unpredictable, so we have no reason to suggest that certain families have a predisposition for monodominance in Amazonian forests.
Disturbance, as measured by its proxy pioneer abundance, and traits related to the pioneer-climax continuum had no significant effect on dominance or diversity, contrary to findings in an earlier Afro-tropical study in Ghana38 and a study of the effects of gap-scale disturbance in Amazonian forest that found a very small effect of disturbance on diversity or dominance83. Two French Guiana studies that used pioneer species as surrogates for disturbance regime found a stronger relationship36,84. Thus as in our data monodominance was only observed in plots with very low abundance of pioneers (Fig. 2), this was not a significant pattern.
In our analysis coppicing was the only trait significantly linked to monodominance. Coppicing occurs in many species after logging or clear felling but many coppices eventually die (HtS pers. obs.). Coppicing is not common as a natural means of regeneration and has been observed mainly in species of Fabaceae genera (Dimorphandra, Dicymbe, Pentaclethra, Spirotropis), one palm (Euterpe oleracea), Humiria and Theobroma cacao85. In Dimorphandra and Humiria coppicing is a rapid response to fire damage and species of each can become dominant in Guyana and Suriname in fire-prone savannah-forest ecotones86. In closed-canopy forest they are also found as non-coppicing tall trees. Dicymbe species exhibit both EM and very pronounced coppicing in the absence of mechanical disturbance, especially in D. corymbosa, and to a lesser extent D. altsonii87. Woolley, et al.28 hypothesised that the coppicing in D. corymbosa was an evolved response to persistent infections with heart-rot fungi, the adaptive significance being that the coppicing insures persistence of the individual beyond that which would occur with a heart-rotted, single-bole tree. Thus, while coppicing was observed as an important reproduction strategy for some Amazonian tree species or as a major regeneration process in secondary growth forests, none of the above can answer the obvious question as to why more species do not spontaneously coppice in mature forest.
Similar questions can be asked for the EM habit. Seedlings of species with access to an EM network may have higher survivorship, growth and reduced density-dependent mortality relative to AM trees45. Ectomycorrhizal associations may also provide a competitive edge by directly accessing organic forms of nutrients in litter, leaving little for saprotrophic fungi or AM mycorrhizae88. However, Mayor & Henkel (2006) used reciprocal litter transplants in Dicymbe monodominant forest and mixed AM-dominated forests and found no differences in litter decomposition rate between the forest types, or within the Dicymbe forest between trenched (EM-absent) and non-trenched (EM-present) plots. Conversely, McGuire, et al.89 found slower litter decomposition in monodominant Dicymbe forest, and lower richness of saprotrophic fungi than in adjacent mixed forest. Although EM has often been linked mechanistically to monodominance9,43,44,45,46, we did not find a significant relationship between monodominance and EM in the ATDN analysis. This contrasts with the review of Corrales, et al.48 in which both monodominance and confirmed mycorrhizal type were linked in both the Paleo- and Neotropics, and the majority of fully documented monodominant tree species were EM.
Neither nodulation nor aluminium accumulation were significantly related to monodominance. While N-fixing arguably should confer a large benefit on nitrogen-limited soils, none of the monodominant Fabaceae fix nitrogen, as is the case in the Fabaceae in the wet Afrotropics, where in contrast to Amazonia most dominant Fabaceae are EM e.g.90. At an Amazonia-wide scale Fabaceae dominance and N-fixing appear negatively correlated, and N-fixing Fabaceae do not dominate the most oligotrophic Amazonian ecosystems56. N-fixing is more prominent in forests richer in species56 and appears to have the greatest advantage in tropical dry successional forests57. Aluminium accumulation is found predominantly in a select number of families (e.g. Rubiaceae, Melastomataceae, Myrtaceae and Vochysiaceae; see references in Introduction) and one species (Ruizteranea retusa) was found as monodominant in our plots in southern Amazonia, while another monodominant species, Vochysia divergens, has been observed in the Brazilian Pantanal62. While aluminium accumulators are found abundantly in the Cerrado south of Amazonia e.g.61, they appear rare in wet Amazonian forests.
Although domesticated species were the most dominant species on 201 of the 1946 plots, in almost all cases these were Arecaceae, which tend to dominate large stretches of swamp forest in Amazonia (Oenocarpus bataua, Euterpe oleracea, Mauritia flexuosa) and in the case of monodominance only Euterpe oleracea and Mauritia flexuosa. With regard to Mauritia flexuosa this species had already attained high prominence in the Amazonian landscape prior to the arrival of humans91,92.
Area had a strong effect on dominance. The ‘forest type’ with the smallest areal coverage had by far the highest mean dominance (Fig. S5). It has been argued before that smaller ecosystems in Amazonia would have lower overall tree diversity and more dominant species66,93. This would be in line with ecological theories where equilibria of immigration and extinction maintain diversity94,95. Connell and Lowman9 noted that “Single-species dominance is of less interest in regions that have smaller species pools” and did “not consider tropical forests at high altitudes, on small islands, or with low or very seasonal rainfall and/or extreme soil conditions, for example, frequently flooded freshwater swamps or mangrove forests, all habitats with few species”. In the Amazon, however, this may be the most common road to monodominance. Nascimento, et al.19 also argued that drainage and other edaphic factors drive monodominance of Peltogyne gracilipes in one Amazonian forest. Similarly, Draper, et al.79 argued that the extreme environmental conditions of Amazonian peatland forests (waterlogging and low fertility), contributed to monodominance of Mauritia flexuosa and Pachira nitida. In the case of classical monodominance of the Congolian G. dewevrei, the discussion is ongoing. Kearsley, et al.21 suggested that “environmental filtering prevailed in the monodominant G. dewevrei forest, leading to lower functional diversity in this forest type, with the dominant species showing beneficial traits related to its common riverine locations and with reduced soil N and P availability found in this environment, both co-regulating the tree community assembly”. Others, however, found no edaphic differences between the monodominant G. dewevrei forest and adjacent mixed forest25,26, a result also found with monodominant D. corymbosa in Guyana23,46. Environmental filtering would also not explain the extreme monodominance of G. dewevrei over hundreds of km2 of upland area in the Congo region11,96.
We were unable to test for basal area monodominance here as the majority of plots in the ATDN lack stem diameter measurements. Instead we used the number of individuals as our metric to determine monodominance. While this is an easily available measure, others have taken basal area and estimates of above-ground biomass as metrics. Monodominant species can differ at the plot level, e.g. D. corymbosa can have less than 60% of all individuals ≥ 10 cm dbh in some plots, but exhibit 80–90% basal area dominance, due to its complete dominance of individuals in the very large size classes23. Such a stand is still most definitely monodominant, in terms of a single species commanding the majority of site resources, and in these same stands conspecifics will always be dominant in the seedling and sapling classes. Connell and Lowman9 pointed out that monodominance can be defined as a single species comprising >60% of individuals >10 cm dbh, or >60% of stand basal area, or both, and be considered “monodominant”.
While seed mass, shade tolerance, and longevity may theoretically lead to monodominance15,16, we find little support for these traits as being causal to monodominance. While monodominance can be mechanistically related to EM and coppicing, very few tree species have used these traits to dominate Amazonian forests. Large stands dominated by single species appear linked primarily to edaphic factors, such as swamps (e.g. many palm species), nutrient poor floodplains (Eschweilera tenuifolia, Macrolobium, Triplaris, Symphonia) and soils with poor drainage (Micrandra spp.)80, white sands (Dicymbe, Eperua, Aldina), soil chemical constraints (Peltogyne, Brosimum), or may be related to fire history (Dimorphandra).
In summary, we found that monodominance, as defined by stem abundance, is extremely rare in Amazonian tropical forests, at least within the extensive ATDN dataset, and found little support for a single mechanism for monodominance. The occurrence of monodominance was most strongly linked to metacommunity dynamics of small rare ecosystems, such as white sands, peats and flooded areas. Because the edaphic differences of the forest types with smaller fragmented areas (white sand forests, Várzea, Igapó and swamp forests) with the major forest type in the Amazon (terra firme), the “forest types” in Amazonia have their to a large extent a distinct tree flora. Within these areas dominance may be in part attributed to chance – the smaller and more fragmented the forest type area, the higher the chance for local dominance.
Material and Methods
All tree data were derived from the Amazon Tree Diversity Network (ATDN, http://atdn.myspecies.info/), comprised of a long-term data set now containing >2000 tree inventory plots across Amazonia. Our analyses were based on 1946 plots, comprised of 127 families, 798 genera, and 5027 identified tree species. All analyses were performed using the R programming language97.
Firstly, dominance was calculated by plot. Dominance was defined as the relative abundance of the most abundant tree species within the community and was calculated as:
$$Dominance={N}_{d}/{N}_{tot}$$
where Nd is the number of individuals of the most abundant species and Ntot the total number of individuals in the tree plot (Dominance calculated this way is also known as the Berger-Parker index). We calculated rank dominance curves for dominance based on plots and mapped dominance across Amazonia. To study which families have more dominant species than expected by chance we listed all species with dominance over eight dominance classes (20–90%) by family. Then, with a Monte Carlo randomization test (1000 randomizations) we determined which tree families have more dominant/competitive species in each dominance class than expected by chance (based on the total number of tree species in the family). Maximum relative abundance of each species was also calculated, thus including species that were never the most dominant species in a plot. As we carried out as many tests as there are families at an error level of 5%, we can expect that at least 5% of the families may become false positives. We tested this by calculating for each of the 1000 randomizations how many families met this criterion and calculated mean and standard deviation. If the number of families found was significantly higher than this mean we applied Bonferroni correction (adjusting p as (p/number of families)), to find those families that were most likely to be the true positives of this test.
To test for competitive exclusion as a mechanism for dominance we used the percentage of pioneer species (log transformed to normalize the data) at plot level, as a proxy for disturbance36,38,84,98,99. We identified pioneers by combining low wood density and low seed mass under the condition (WD < 0.7 Λ SMC < 4, Fig. S2) sensu99. We used a loess regression to test for a relationship between the disturbance proxy and dominance at plot level.
To test if particular traits are linked to monodominance we examined two traits, wood density and seed mass, that are generally linked to longevity and dominance39,100. We calculated the community weighted average for both wood density and seed size as follows:
$$CWA=\sum {N}_{i}^{\ast }trait/\sum N$$
where CWA is the community weighted average, ∑Ni is the sum of the number of individuals with trait data, trait is the corresponding trait value on genus level for either wood density or seed mass class and ∑N is the total number of individuals in the tree community. We then carried out a loess regression to assess the relationship between the CWA of the functional traits and dominance.
To test if an EM association may lead to dominance we checked the most recent literature for confirmed EM tree species101. We tested if EM is more abundant on monodominant plots and if EM species are more likely to be monodominant. For a similar test for nodulation we used Sprent102 and Soltis, et al.103. For aluminium accumulation we used Jansen et al. (2002, 2003) and references therein. There is no single source for intrinsic coppicing, a means of persistence once an individual is established, in tropical trees - this information was collected from observations on our plots. We tested the association with Monte Carlo randomizations (n = 10,000).
To test if an area effect may lead to (mono-)dominance we used ANOVA to test if monodominance is more common in the forest types that have a smaller extent in Amazonia: white sand forest (4.6%)104, igapó and várzea (10%)104,105 and swamps (1.7%)106, compared to terra firme which covers most of the remaining area.
The datasets generated during and/or analysed during the current study are available from the corresponding author on reasonable request.
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Acknowledgements
This paper is the result of the work of hundreds of different scientists and research institutions in the Amazon over the past 80 years. Without their hard work this analysis would have been impossible. We thank Charles Zartman for the use of plots from Jutai. HtS and RS were supported by grant 407232/2013-3 - PVE - MEC/MCTI/CAPES/CNPq/FAPs; CB was supported by grant FAPESP 95/3058-0 - CRS 068/96 WWF Brasil - The Body Shop; DS, JFM, JE, PP and JC benefited from an “Investissement d’Avenir” grant managed by the Agence Nationale de la Recherche (CEBA: ANR-10-LABX-25-01); Floristic identification in plots in the RAINFOR forest monitoring network have been supported by the Natural Environment Research Council (grants NE/B503384/1, NE/ D01025X/1, NE/I02982X/1, NE/F005806/1, NE/D005590/1 and NE/I028122/1) and the Gordon and Betty Moore Foundation; B.M.F. is funded by FAPESP grant 2016/25086-3. The 25-ha Long-Term Ecological Research Project of Amacayacu is a collaborative project of the Instituto Amazónico de Investigaciones Científicas Sinchi and the Universidad Nacional de Colombia Sede Medellín, in parternship with the Unidad de Manejo Especial de Parques Naturales Nacionales and the Center for Tropical Forest Science of the Smithsonian Tropical Research Institute (CTFS). The Amacayacu Forest Dynamics Plot is part of the Center for Tropical Forest Science, a global network of large-scale demographic tree plots. We acknowledge the Director and staff of the Amacayacu National Park for supporting and maintaining the project in this National Park. We also thank two anonymous reviewers for their helpful, constructive comments.
Author information
Authors
Contributions
D.S., B.H.M., B.M. and H.t.S. initiated the study; H.t.S. and N.H. carried out the analyses, H.t.S., T.H. and N.H. wrote the manuscript, D.S., B.H.M., B.M., A.H. and J.G. gave continuous input to the writing team and comments on the analyses. All members of ATDN provided tree inventory data. All authors reviewed and added comments and additions on/to the manuscript.
Corresponding author
Correspondence to Hans ter Steege.
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ter Steege, H., Henkel, T.W., Helal, N. et al. Rarity of monodominance in hyperdiverse Amazonian forests. Sci Rep 9, 13822 (2019). https://doi.org/10.1038/s41598-019-50323-9
• Accepted:
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Scientific Reports (2020) | 2020-06-01 14:27:56 | {"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": 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": 0.6495141386985779, "perplexity": 14775.668438041741}, "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-2020-24/segments/1590347417746.33/warc/CC-MAIN-20200601113849-20200601143849-00576.warc.gz"} |
https://electronics.stackexchange.com/questions/175728/calculate-voltage-of-led-driver-required-for-a-given-amount-of-leds | # Calculate voltage of Led driver required for a given amount of led's
I have built some LED lights for my fish tank using six of these LED lamps:
http://www.ebay.co.uk/itm/261813680886?_trksid=p2057872.m2749.l2649&ssPageName=STRK%3AMEBIDX%3AIT
I have tried using this power supply:
http://www.ebay.co.uk/itm/291074673667?_trksid=p2057872.m2749.l2649&var=590234643632&ssPageName=STRK%3AMEBIDX%3AIT
When I connected the original six white LED lamps they flashed to indicate the 12v 60w driver was being overloaded. I changed it to four LED's two on each string so the circuit was well within the drivers current parameters; however They still flashed, at this point I took a voltage measurement of between 7 and 8 volts when the lights flashed. It did however work with only two LED's connected.
The driver seems to have a fixed voltage at 12v and from what I have read I need a new driver one that compensates for the drop in voltage.
I asked the person from who I bought the LED lamps what the power requirements if the chip were and he said it would be 12v per chip so around 66V? This left me a little confused because the 12v driver worked with two chips.
Is this the correct way to calculate the voltage of the driver required? Please note I found another source for these chips who states the reserve voltage if 5v; however I believe this may be a typo from the Chinese chap and he probably meant reverse voltage. Also; constant current driver so no resistor suggestions please.
Many Thanks,
Ross.
• Gotta agree with Andy. There's no part number on the E-bay site and no data sheet - not for the power supply, and not for the LEDs, either. Without accurate data, one guess is as good as another and just as likely to lead to a dead power supply or a dead LED. – JRE Jun 16 '15 at 14:58
Somewhere between 9V and 12V the LED will take a current of 900mA. If it does this at 9V and you apply 12V you might be getting a forward current of 3 amps thru the LED. There is no data sheet for the device (that I can find) so it's impossible to be exact.
But, realistically you probably need to put in a current limiting resistor for each LED. What makes you think it has a constant current circuit built into it?
The ebay link is really-really crappy at giving details - for example it states that the output power is 10 watts - this of course is rubbish!
• Hello very many thanks for the answers I appreciate it; so I do in fact have the right voltage but the current is too high? Here is a link to the other power supply I tried it with which states it is a constant current but is also dimmable. The original post only allowed me 2 links. ebay.co.uk/itm/… I have wired the whole thing up using terminal blocks so getting some sort of inline resistor might be the answer? I used similar but higher voltage chips before and they worked fine with a CC driver? – Ross Crowther Jun 17 '15 at 20:29
• No I think you might need current limiting resistors. – Andy aka Jun 17 '15 at 21:14
• I should add, the power supply of the higher voltage chips that worked had a variable voltage between 22-38v and it was definatley a constant current supply. Would the right constant current supply work though? I am reluctant to add more parts into the unit because I am running out of space too. – Ross Crowther Jun 17 '15 at 21:20
• My main message to you is good luck and next time, buy parts with full data sheets. – Andy aka Jun 18 '15 at 7:04
• Thanks Andy, I listened to some of your music. Your singing voice isn't that bad. – Ross Crowther Jun 18 '15 at 10:04
The LEDs need a constant current feed.
The power supply is a constant voltage supply.
You can PROBABLY get an OK result as follows.
Operate ONE LED from the supply with a resistor between supply V+ and LED Vin+.
The power supply is rated at 5A max.
For 6 LEDs the current per LED is 5A/6 ~= 830 mA
Let's work on 800 mA = 0.8A.
LED spec says 9 to 12V.
9V is worst case so start there.
PSU = 12V.
LED = 9V
Resistor = 12-9 = 3V R = V/I = 3V/.8A = 3.75 Ohms.
A standard value is 3.9 Ohms.
R dissipation = V x I = 3V x 0.8A = 2.4W
R needs to be 3.8 Ohm and say 5W (10 W even better).
Wire PSU+ve - Resistor - LED+ve - LED- - PSU -ve.
ie current flows through resistor and through LED.
Get voltmeter (eg in DMM)
Set to 20V range.
Turn on as above.
Measure voltage across resistor.
Target is 3V.
A bit more [tm] - say up to maybe 3.3V is OK
Lower is better than higher.
Say V across R was 2.9V. Iactual = V_across_R / R
= 2.9V / 3.9 Ohms ~= 745 mA = OK
If I is too high use a larger R - say 4.7 Ohms
If I is too low use a smaller R BUT be careful - say 3.3Ohms.
Once you have this working OK repeat for all LEDs in parallle.
One R per LED. R's are cheap, LEDS are not (although yours are a good price)
LEDs will vary in current somewhat. You can fine tine as above if desired.
## NBNBNBNB
LEDS MUST have heat sinks.
They will get very hot and die in no time with no heatsinks. This can be a simple large metal plate of available. Be sure not to short power supply when connecting LEDs to heat sink.
• Thanks for the in-depth answer. I have little graphics card heat sinks though I have only been testing at the moment so they are not wired up, but it would be a bad idea to wire them to the same parallel circuit? I provided a link in response to another post to a constant current power supply I used. I am prepared to solder if resistors are a must. However just to complicate things I would like to add four of these LED’s to add a bit of colour: kiwilighting.com/10w-red-blue-led-emitter. – Ross Crowther Jun 17 '15 at 21:10
• Sorry I ran out of characters: Given I will now be buying a new power supply; if I bought the right one would I get away without having to do all that soldering? I made a 10w x 10 parallel circuit with some similar lamps before but had the right power supply and it is still going strong without any resistors. – Ross Crowther Jun 17 '15 at 21:10
• @RossCrowther If you parallel LEDs at CV (constant voltage) resistors are needed EXCEPT if the supply hits its limit and starts to sag and approximates a CC (constant current) source. With a CC supply, if supply max oc voltage is > LED specified voltage then N LEDS will share the rated CC at what ever V it takes to force it down their throats. So eg LEDs that are rated at 1A each with a 10A supply - > 10 LEDS average 1A each, 5 LEDS average 2A each, 2 LEDS average 5A each !!! | BUT even if a CC supply is used and average current is OK, LEDS will not share exactly due to production .... – Russell McMahon Jun 18 '15 at 3:19
• @RossCrowther ... variations. How much it varies deep-ends on LED maker, whether there is any internal series R etc. AND mixing eg red-blue and white almost guarantees that Vf (forward voltage = operating voltage) will vary at rated current amongst LEDS If you parallel red-blue with white and white say 10-12V opn and red-blue say 9-11V then odds are the RB will get over driven and the Wh underdriven deep-ending (again) how many of each. Also the rated Vf may not be as said quite because it is a sellers rough guesstimate. | If your 10 x 10W worked well without resistors works well for .... – Russell McMahon Jun 18 '15 at 3:24
• .... you I'm (genuinely) pleased for you and many people have agood enough experience - IF all LEDs are run at less than full spec and cooled well then all should be well enough and current imbalance may be ok for your app. || From the RB picture you probably have 3 strings of 4r+3W + 4r. 3Wh x 3.3V ~= 9.9V. Tp balance this 4r would need to be 9.9/4 = 2.5V/red LED which is usually high BUT if LED were chosen for low Vf at 3V then 3 x 3V = 9V/4 = 2.25V red. They MAY tailor red & white Vfs to suit or may not care. Guess which is more likely.| Adding an R per LED is rather quick ... – Russell McMahon Jun 18 '15 at 3:29
simulate this circuit – Schematic created using CircuitLab
The bulb does light up. I took the measurements again and voltage fluctuated quite widely as the LED heated up. I don't have my heat sinks wired up at the moment; the plan is to use the same power source if there is any current to spare. I used the 10A setting on my multi-meter, swapping the leads over to the appropriate terminals. I also bypassed the resistor with a wire and measured the voltage across the led as 11.87v, not sure if that helps.
Been looking at this ohms law solver: http://www.ohmslawcalculator.com/led-resistor-calculator and it confirms I need a 3.9 ohm resistor. I think I will go buy a bunch of them, wire the whole thing up, then measure again hopefully that will take me in the right direction.
• $3.9\Omega \cdot {2.2\text{A}}^2 \approx 18.9\text{W}$ – Ignacio Vazquez-Abrams Jun 23 '15 at 17:47
• P.S. The lower voltage reading from the PSU came because I connected the LED this time. – Ross Crowther Jun 23 '15 at 17:54
• @Russell McMahon I should mention that the full circuit of six LEDs splits into two at one of the terminal blocks. With two on one string and four in the other. If this is the cause of the imbalance and why they won't all light up, might experimenting with stringing a few of the superfluous resistors together correct the imbalance on one side? – Ross Crowther Jun 24 '15 at 17:52 | 2020-08-15 00:19:47 | {"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": 0.35762110352516174, "perplexity": 2017.3227435579142}, "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/1596439740343.48/warc/CC-MAIN-20200814215931-20200815005931-00173.warc.gz"} |
https://brilliant.org/problems/its-seca/ | # Its SecA
Geometry Level 3
Find the number of real roots of the quadratic equation $$8\sec^2 A-6\sec A +1=0$$.
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http://math.stackexchange.com/questions/123709/why-is-mathbbh-otimes-mathbbh-cong-textend-mathbbr-mathbbh | # Why is $\mathbb{H}\otimes\mathbb{H}\cong\text{End}_\mathbb{R}\mathbb{H}$?
When I first learned of the quaternion algebra $\mathbb{H}$, the most concrete way to get a grip on the ring of its endomorphisms $\operatorname{End}_\mathbb{R}(\mathbb{H})$ was to view them as $4\times 4$ matrices with real entries.
It was mentioned to me that $\operatorname{End}_\mathbb{R}(\mathbb{H})\cong\mathbb{H}\otimes_\mathbb{R}\mathbb{H}$ too, but this isomorphism is not as clear to me as the isomorphism to matrices. Is there a clear justification for this isomorphism with the tensor product?
Thank you,
-
I guess by $\text{End}_{\mathbb{R}}$ you mean endomorphisms as an $\mathbb{R}$-vector space. In that case, $\mathbb{H}$ acts as endomorphisms of itself (as an $\mathbb{R}$-vector space) in two ways: left multiplication and right multiplication. That is, we have an $\mathbb{R}$-bilinear map $$\mathbb{H} \times \mathbb{H} \ni (q_1, q_2) \mapsto (x \mapsto q_1 x q_2) \in \text{End}_{\mathbb{R}}(\mathbb{H}).$$
The second action of $\mathbb{H}$ is a right action and not a left action, but we can fix this by conjugating to get $$\mathbb{H} \times \mathbb{H} \ni (q_1, q_2) \mapsto (x \mapsto q_1 x \overline{q_2}) \in \text{End}_{\mathbb{R}}(\mathbb{H}).$$
By the universal property of the tensor product (of algebras!) this gives an algebra map $$\mathbb{H} \otimes_{\mathbb{R}} \mathbb{H} \to \text{End}_{\mathbb{R}}(\mathbb{H})$$
and the question is to show that this map is an isomorphism. Since both algebras have dimension $16$, it suffices to show that this map is either surjective or injective. Surjectivity follows from the Jacobson density theorem, for example.
-
Iyt is more traditional to $(-)^{\mathrm{op}}$ the second factor of the domain to avoid the conjugation and get an iso of algebras. – Mariano Suárez-Alvarez Mar 23 '12 at 22:01
Thank you very much Qiaochu! – Tiffany Hwang Apr 9 '12 at 23:29
The algebra isomorphism sends $q_1 \otimes q_2$ to the endomorphism taking q to $q_1q\bar q_2$. Not sure of the best way of showing it is injective (or equivalenty surjective by dimensionality). One way is explicity computing the kernel using the tensor product basis of the standard 1,i,j,k basis of H.
-
Inversion isn't an algebra map; you need to conjugate. – Qiaochu Yuan Mar 23 '12 at 19:50
This answer is confusing... – Samuel Reid Mar 23 '12 at 22:37
@Qiaochu thanks ive edited it – Eric O. Korman Mar 23 '12 at 22:57 | 2015-11-25 04:21:14 | {"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": 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": 0.9790663123130798, "perplexity": 339.43974597877366}, "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/1448398444228.5/warc/CC-MAIN-20151124205404-00019-ip-10-71-132-137.ec2.internal.warc.gz"} |
https://zenodo.org/record/3971729/export/csl | Conference paper Open Access
# A Low-Complexity Dual Trellis Decoding Algorithm for High-Rate Convolutional Codes
Son Le, V.; Abdel Nour, C.; Douillard, C.; Boutillon, E.
### Citation Style Language JSON Export
{
"publisher": "Zenodo",
"DOI": "10.5281/zenodo.3971729",
"language": "eng",
"title": "A Low-Complexity Dual Trellis Decoding Algorithm for High-Rate Convolutional Codes",
"issued": {
"date-parts": [
[
2020,
8,
4
]
]
},
"abstract": "<p>Decoding using the dual trellis is considered as a potential technique to increase the throughput of soft-input soft-output decoders for high coding rate convolutional codes. However, the dual Log-MAP algorithm suffers from a high decoding complexity. More specifically, the source of complexity comes from the soft-output unit, which has to handle a high number of extrinsic values in parallel. In this paper, we present a new low-complexity sub-optimal decoding algorithm using the dual trellis, namely the dual Max-Log-MAP algorithm, suited for high coding rate convolutional codes. A complexity analysis and simulation results are provided to compare the dual Max- Log-MAP and the dual Log-MAP algorithms. Despite a minor loss of about 0.2 dB in performance, the dual Max-Log-MAP algorithm significantly reduces the decoder complexity and makes it a first-choice algorithm for high-throughput high-rate decoding of convolutional and turbo codes.</p>",
"author": [
{
"family": "Son Le, V."
},
{
"family": "Abdel Nour, C."
},
{
"family": "Douillard, C."
},
{
"family": "Boutillon, E."
}
],
"id": "3971729",
"event-place": "Virtual Conference",
"type": "paper-conference",
"event": "IEEE Wireless Communications and Networking Conference 2020 (2020 IEEE WCNC)"
}
41
15
views | 2021-01-15 20:32:39 | {"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": 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": 0.5420390367507935, "perplexity": 5539.701193663321}, "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-2021-04/segments/1610703496947.2/warc/CC-MAIN-20210115194851-20210115224851-00702.warc.gz"} |
http://www.kjg65qj.cn/pvcdrom/battery-basics/standard-potential | # Standard Potential
The overall energy of the outer electrons for a material depends on the temperature of the systems and also, for a material that is not a pure solid, also depends on the concentration of the reacting species. Thus, in measuring the electrochemical potentials, both the temperature and the concentration must be specified. The standard potential, given the symbol E0, is the electrochemical potential at 25 °C, with gasses having a pressure of 1 atm and solutions a concentration of 1 Molar (1 M or 1 mol/liter).
## Hydrogen Reduction
$2{H}^{+}\left(aq\right)+2{e}^{-}\to {H}_{2}\left(g\right)$
The standard potential of the reduction /oxidation reaction pair is the sum of the standard potentials for the half reactions (to avoid continually having to say the oxidation and reduction reaction, they are more generally termed a half reactions, since they make up half of the overall redox reaction). The values of common half reactions are listed in Tables of Standard Potentials.
## Copper Reduction with Standard Potential
The zinc undergoes an oxidation reaction, so the direction of the reaction and the sign of the standard potential must be reversed to give the oxidation/reduction reaction pair is: | 2020-08-13 17:31:03 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 1, "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": 0.797875702381134, "perplexity": 669.777755549729}, "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/1596439739048.46/warc/CC-MAIN-20200813161908-20200813191908-00324.warc.gz"} |
https://math.stackexchange.com/questions/3959206/ito-isometry-proof | # Ito isometry proof
I have been reading Steven Shreve's Stochastic Calculus for Finance II. This question is from Chapter 4 Stochastic Calculus Page 129. This is theorem 4.2.2 (Proof of Ito isometry).
This theorem is about proving the following:
$$\mathbb E I^2(t)=\mathbb E\int_0^t \Delta^2(u)du$$
Here $$\Delta(t)$$ is an adapted stochastic process meaning that it is $$\mathcal{F}(t)$$- measurable for each $$t \geq 0.$$ I can't seem to understand how we got the following:
$$\Delta$$ is a simple process and is constant on $$[t_j,t_{j+1}),$$ i.e $$\Delta(t)=\Delta(t_j)$$ for all $$t \in [t_j,t_{j+1}),$$ Thus the integral $$\int_{t_j}^{t_{j+1}} \Delta^2(u)du$$ is just a Riemann integral and we have $$\int_{t_j}^{t_{j+1}} \Delta^2(u)du=\Delta^2(t_j) \int_{t_j}^{t_{j+1}} du =\Delta^2(t_j)(t_{j+1}-t_j).$$ | 2022-09-27 20:50:03 | {"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": 10, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9663316011428833, "perplexity": 100.59762348513507}, "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-2022-40/segments/1664030335058.80/warc/CC-MAIN-20220927194248-20220927224248-00744.warc.gz"} |
http://www.encyclopediaofmath.org/index.php/Bijection | # Bijection
$\def\Id {\mathop{\rm Id}}$
A function (or mapping) is called bijective if it is both one-to-one and onto, i.e., if it is both injective and surjective.
In other words, a function $f : A \to B$ from a set $A$ to a set $B$ is
a bijective function or a bijection
if and only if
$f(A) = B$ and $a_1 \ne a_2$ implies $f(a_1) \ne f(a_2)$ for all $a_1, a_2 \in A$.
#### Equivalent condition
A mapping is bijective if and only if
• it has left-sided and right-sided inverses
and therefore if and only if
• there is a unique (two-sided) inverse mapping $f^{-1}$ such that $f^{-1} \circ f = \Id_A$ and $f \circ f^{-1} = \Id_B$.
#### Application
Bijections are essential for the theory of cardinal numbers:
Two sets have the same number of elements (the same cardinality), if there is a bijective mapping between them.
By the Schröder-Bernstein theorem — and not depending on the Axiom of Choice — a bijective mapping between two sets $A$ and $B$ exists if there are injective mappings both from $A$ to $B$ and from $B$ to $A$.
#### Related notions
In certain contexts, a bijective mapping of a set $A$ onto itself is called a permutation of $A$.
A bijective homomorphism is called isomorphism, and—if domain and range coincide—automorphism.
How to Cite This Entry:
Bijection. Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Bijection&oldid=30987
This article was adapted from an original article by O.A. Ivanova (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article | 2014-08-22 13:44:34 | {"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": 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": 0.9516746997833252, "perplexity": 388.358514015678}, "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-2014-35/segments/1408500823634.2/warc/CC-MAIN-20140820021343-00074-ip-10-180-136-8.ec2.internal.warc.gz"} |
https://www.terrysmithstudios.com/period/2010s/page/4 | # 2010s
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Photography | 2021-09-23 14:28:09 | {"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": 0.9867966175079346, "perplexity": 14910.912143657533}, "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/1631780057424.99/warc/CC-MAIN-20210923135058-20210923165058-00666.warc.gz"} |
https://math.stackexchange.com/questions/963164/verify-the-following-combinatorial-identity-sum-k-0r-binommk-binom | # Verify the following combinatorial identity: $\sum_{k=0}^{r} \binom{m}{k}\binom{n}{r-k} = \binom{m+n}{r}$ [duplicate]
$$\sum_{k=0}^{r} \binom{m}{k}\binom{n}{r-k} = \binom{m+n}{r}$$
Nice, so I've proven some combinatorial identities before via induction, other more simple ones by committee selection models.... But this one is weird, induction doesn't even seem feasible here without things getting nasty, and the summation on the left is not making things easier. Can anyone help?
## marked as duplicate by Marc van Leeuwen, Davide Giraudo, Najib Idrissi, Namaste, user147263 Oct 27 '14 at 11:18
Note that there exist different $m+n$ balls and two bags.
One bag contains $m$ balls and the other has $n$.
What is the number of choosing $r$ balls ? Clearly $$_{m+n}C_r$$
But we divided into two bag. : The number of choosing $k$ balls in the first bag is $_mC_k$ And we must choose $r-k$ balls in second. The number of possibility is $_nC_{r-k}$ So we have $$_mC_k\ _nC_{r-k}$$
This is a classic double counting argument. We will count how many ways we can choose $r$ balls from $m+n$ balls.
If we place $m+n$ balls in a single urn, then the right hand side counts the number of ways we can select $r$ balls from the urn containing $m+n$ balls.
Suppose now we place $m$ balls in one urn and $n$ balls in the other. I can select a total of $r$ things from these two two urns by choosing $k$ balls from the first urn and $r-k$ balls from the second urn. Thus there are $\binom{m}{k}\binom{n}{r-k}$ ways for this selection to happen. Summing over all possible values of $k$ will tell us the total number of ways we can choose $r$ balls from $m+n$ balls.
• This approach is direct, I understand it as well. – Aspiring Mathematician Oct 8 '14 at 3:44
Using the binomial theorem, we have \begin{align} (1+x)^m(1+x)^n &=\sum_{j=0}^m\binom{m}{j}x^j\sum_{k=0}^n\binom{n}{k}x^k\\ &=\sum_{k=0}^{m+n}\color{#C00000}{\sum_{j=0}^k\binom{m}{j}\binom{n}{k-j}}x^k \end{align} and \begin{align} (1+x)^{m+n} &=\sum_{k=0}^{m+n}\color{#C00000}{\binom{m+n}{k}}x^k \end{align} Compare the coefficients of $x^k$.
• Same idea simultaneously :) – mvggz Oct 9 '14 at 12:15
Here is a short inductive proof, that may however not be as illuminating as a combinatorial argument:
Theorem. For all nonnegative integers $r$, $m$ and $n$, there holds Vandermonde's identity $$\sum_{k=0}^{r}\binom{m}{k}\binom{n}{r-k}=\binom{m+n}{r}.$$
Proof. Let $f(m,n,r)=\sum_{k=0}^{r}\binom{m}{k}\binom{n}{r-k}$, and use the convention that $\binom{m}{k}=0$ unless $0\leq k\leq m$. Note that $f(0,n,r)=\binom{n}{r}$. Assume now that $$f(m,n,r)=\binom{m+n}{r}$$ for fixed $m$, and for all $n$ and $r$. From this and from Pascal's rule $\binom{m+1}{k}=\binom{m}{k-1}+\binom{m}{k}$, we find \begin{eqnarray*} f(m+1,n,r)&=&f(m,n,r-1)+f(m,n,r) \\ &=&\binom{m+n}{r-1}+\binom{m+n}{r}=\binom{m+n+1}{r}.\Box \end{eqnarray*}
An other way to proceed is to write:
$(x+1)^{m+n} = (x+1)^n*(x+1)^m$
Then you develop each term using the binomial formula and you evaluate the coefficient of the term $x^r$ on the right, knowing that the one on the left is $C_{n+m}^r$. The proof is quite straightforward when you go down this path.
You get a double sum with two index i,j and to find the coefficient of $x^r$ you take each term that verifies i+j=r .
Does that help? | 2019-10-16 09:17:29 | {"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": 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": 2, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9796026349067688, "perplexity": 227.31552491576565}, "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/1570986666959.47/warc/CC-MAIN-20191016090425-20191016113925-00287.warc.gz"} |
https://www.dsprelated.com/blogs-1/nf/all/Matlab.php | ## Modeling Anti-Alias Filters
September 26, 2021
Digitizing a signal using an Analog to Digital Converter (ADC) usually requires an anti-alias filter, as shown in Figure 1a. In this post, we’ll develop models of lowpass Butterworth and Chebyshev anti-alias filters, and compute the time domain and frequency domain output of the ADC for an example input signal. We’ll also model aliasing of Gaussian noise. I hope the examples make the textbook explanations of aliasing seem a little more real. Of course, modeling of...
## Sampling bandpass signals
Sampling bandpass signals 1.1 Introduction
It is known [1], [3] that bandpass signals can be sampled with a sampling frequency which is lower than the sampling frequency according to the sampling theorem.
## A Narrow Bandpass Filter in Octave or Matlab
The design of a very narrow bandpass FIR filter, coded in either Octave or Matlab, can prove challenging if a computationally-efficient filter is required. This is especially true if the sampling rate is high relative to the filter's center frequency. The most obvious filter design methods, using either window-based or Remez ( Parks-McClellan ) functions, can easily result in filters with many thousands of taps.
The filter to be described reduces the computational effort (and thus...
## Second Order Discrete-Time System Demonstration
Discrete-time systems are remarkable: the time response can be computed from mere difference equations, and the coefficients ai, bi of these equations are also the coefficients of H(z). Here, I try to illustrate this remarkableness by converting a continuous-time second-order system to an approximately equivalent discrete-time system. With a discrete-time model, we can then easily compute the time response to any input. But note that the goal here is as much to...
## Design IIR Butterworth Filters Using 12 Lines of Code
While there are plenty of canned functions to design Butterworth IIR filters [1], it’s instructive and not that complicated to design them from scratch. You can do it in 12 lines of Matlab code. In this article, we’ll create a Matlab function butter_synth.m to design lowpass Butterworth filters of any order. Here is an example function call for a 5th order filter:
N= 5 % Filter order fc= 10; % Hz cutoff freq fs= 100; % Hz sample freq [b,a]=...
## Use Matlab Function pwelch to Find Power Spectral Density – or Do It Yourself
In my last post, we saw that finding the spectrum of a signal requires several steps beyond computing the discrete Fourier transform (DFT)[1]. These include windowing the signal, taking the magnitude-squared of the DFT, and computing the vector of frequencies. The Matlab function pwelch [2] performs all these steps, and it also has the option to use DFT averaging to compute the so-called Welch power spectral density estimate [3,4].
## Delay estimation by FFT
Given x=sig(t) and y=ref(t), returns [c, ref(t+delta), delta)] = fitSignal(y, x);:Estimates and corrects delay and scaling factor between two signals Code snippet
This article relates to the Matlab / Octave code snippet: Delay estimation with subsample resolution It explains the algorithm and the design decisions behind it.
Introduction
There are many DSP-related problems, where an unknown timing between two signals needs to be determined and corrected, for example, radar, sonar,...
## Design IIR Bandpass Filters
In this post, I present a method to design Butterworth IIR bandpass filters. My previous post [1] covered lowpass IIR filter design, and provided a Matlab function to design them. Here, we’ll do the same thing for IIR bandpass filters, with a Matlab function bp_synth.m. Here is an example function call for a bandpass filter based on a 3rd order lowpass prototype:
N= 3; % order of prototype LPF fcenter= 22.5; % Hz center frequency, Hz bw= 5; ...
This article shows how to implement a Butterworth IIR lowpass filter as a cascade of second-order IIR filters, or biquads. We’ll derive how to calculate the coefficients of the biquads and do some examples using a Matlab function biquad_synth provided in the Appendix. Although we’ll be designing Butterworth filters, the approach applies to any all-pole lowpass filter (Chebyshev, Bessel, etc). As we’ll see, the cascaded-biquad design is less sensitive to coefficient...
## Digital PLL's -- Part 1
1. Introduction
Figure 1.1 is a block diagram of a digital PLL (DPLL). The purpose of the DPLL is to lock the phase of a numerically controlled oscillator (NCO) to a reference signal. The loop includes a phase detector to compute phase error and a loop filter to set loop dynamic performance. The output of the loop filter controls the frequency and phase of the NCO, driving the phase error to zero.
One application of the DPLL is to recover the timing in a digital...
## Time Machine, Anyone?
Abstract: Dispersive linear systems with negative group delay have caused much confusion in the past. Some claim that they violate causality, others that they are the cause of superluminal tunneling. Can we really receive messages before they are sent? This article aims at pouring oil in the fire and causing yet more confusion :-).
Introduction
## Plotting Discrete-Time Signals
A discrete-time sinusoid can have frequency up to just shy of half the sample frequency. But if you try to plot the sinusoid, the result is not always recognizable. For example, if you plot a 9 Hz sinusoid sampled at 100 Hz, you get the result shown in the top of Figure 1, which looks like a sine. But if you plot a 35 Hz sinusoid sampled at 100 Hz, you get the bottom graph, which does not look like a sine when you connect the dots. We typically want the plot of a...
## TCP/IP interface (Matlab/Octave)
Communicate with measurement instruments via Ethernet (no-toolbox-Matlab or Octave)
Purpose
Measurement automation is digital signal processing in a wider sense: Getting a digital signal from an analog world usually involves some measurement instruments, for example a spectrum analyzer. Modern instruments, and also many off-the-shelf prototyping boards such as FPGA cards [1] or microcontrollers [2] are able to communicate via Ethernet. Here, I provide some basic mex-functions (compiled C... | 2021-10-17 00:34:45 | {"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": 0.7307294607162476, "perplexity": 2357.384103495069}, "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/1634323585045.2/warc/CC-MAIN-20211016231019-20211017021019-00663.warc.gz"} |
https://communities.sas.com/t5/SAS-Procedures/Manual-Iterative-solution-of-survey-weighting/td-p/196049?nobounce | ## Manual Iterative solution of survey weighting
Regular Contributor
Posts: 228
# Manual Iterative solution of survey weighting
Dear all, hope you are doing well.
I wish to generate survey weights by 'Manual Iterative Solution' as stated here Introduction to Survey Weights — PRI Help
or below
Example with three characteristics A, S, E
1. Compute A weight (wA) and weight data by this weight
Generate the weighted frequency table for S
2. Compute S weight (wS) and weight by wA*wS
Generate the weighted frequency table for E
3. Compute E weight (wE) and weight by wA*wS*wE
Generate the weighted frequency for A
4. Compute a second A weight( wA2) and weight by wA*wS*wE*wA
Generate the weighted frequency for S
5. Compute a second S weight (wS2) and weight by wA*wS*wE*wA2*wS2
Generate the weighted frequency for E
6. Compute a second E weight (wE2) and weight by wA*wS*wE*wA2*wS2*wE2
Continue process until the weighted frequencies and the population frequencies don’t change. Usually converge after two or three iterations (or less)
My question is how are the second weights generated starting from step 4? I understand wA is the population proportion A over the sample proportion A.
Your help is greatly appreciated. Thank you very much.
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• 1 in conversation | 2017-11-21 08:13:16 | {"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": 0.9121853709220886, "perplexity": 7564.25487388277}, "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-2017-47/segments/1510934806327.92/warc/CC-MAIN-20171121074123-20171121094123-00315.warc.gz"} |
https://www.transtutors.com/questions/home-loans-typically-involve-points-which-are-fees-charged-by-the-lender-each-point--2605866.htm | Home loans typically involve “points,” which are fees charged by the lender. Each point charg...
Home loans typically involve “points,” which are fees charged by the lender. Each point charged means that the borrower must pay 1% of the loan amount as a fee. For example, if the loan is for $170,000 and 4 points are charged, the loan repayment schedule is calculated on a$170,000 loan but the net amount the borrower receives is only \$163,200. Assume the interest rate is .75% per month. What is the effective annual interest rate charged on such a loan, assuming loan repayment occurs over 156 months? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places. Use a financial calculator or Excel.) | 2019-11-12 21:15:25 | {"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": 0.5055431723594666, "perplexity": 2249.057031957577}, "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-2019-47/segments/1573496665767.51/warc/CC-MAIN-20191112202920-20191112230920-00429.warc.gz"} |
https://www.physicsforums.com/threads/cancelling-the-signs.734158/ | # Cancelling the signs
1. Jan 22, 2014
1. The problem statement, all variables and given/known data
This is the simplest problem you would ever get.
$\frac{-fu}{s-f}=\frac{fu}{-s+f}$
This is true.
So the signs can be cancelled.What are the rules for doing that?
I guess I was not listening to the teacher when I first learned algebra.
3. The attempt at a solution
Don't think that I don't know algebra.I just want to know the rules of THAT.
2. Jan 22, 2014
### Tanya Sharma
Multiplying numerator and denominator of a rational number by a non zero number keeps it unchanged .The non zero number in this case is -1.
3. Jan 22, 2014 | 2017-10-24 03:16:12 | {"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": 0.8298056125640869, "perplexity": 951.2520227386239}, "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/1508187827853.86/warc/CC-MAIN-20171024014937-20171024034937-00266.warc.gz"} |
http://tatome.de/zettelkasten/zettelkasten.php?standalone&reference=balslev-et-al-2012 | # Show Reference: "Eye Proprioception Used for Visual Localization Only If in Conflict with the Oculomotor Plan"
Eye Proprioception Used for Visual Localization Only If in Conflict with the Oculomotor Plan The Journal of Neuroscience, Vol. 32, No. 25. (20 June 2012), pp. 8569-8573, doi:10.1523/jneurosci.1488-12.2012 by Daniela Balslev, Marc Himmelbach, Hans-Otto Karnath, Svenja Borchers, Bartholomaeus Odoj
@article{balslev-et-al-2012,
abstract = {Both the corollary discharge of the oculomotor command and eye muscle proprioception provide eye position information to the brain. Two contradictory models have been suggested about how these two sources contribute to visual localization: (1) only the efference copy is used whereas proprioception is a slow recalibrator of the forward model, and (2) both signals are used together as a weighted average. We had the opportunity to test these hypotheses in a patient ({R.W}.) with a circumscribed lesion of the right postcentral gyrus that overlapped the human eye proprioceptive representation. {R.W}. was as accurate and precise as the control group (n = 19) in locating a lit {LED} that she viewed through the eye contralateral to the lesion. However, when the task was preceded by a brief (<1 s), gentle push to the closed eye, which perturbed eye position and stimulated eye proprioceptors in the absence of a motor command, {R.W}.'s accuracy significantly decreased compared with both her own baseline and the healthy control group. The data suggest that in normal conditions, eye proprioception is not used for visual localization. Eye proprioception is, however, continuously monitored to be incorporated into the eye position estimate when a mismatch with the efference copy of the motor command is detected. Our result thus supports the first model and, furthermore, identifies the limits for its operation.},
author = {Balslev, Daniela and Himmelbach, Marc and Karnath, Hans-Otto and Borchers, Svenja and Odoj, Bartholomaeus},
day = {20},
doi = {10.1523/jneurosci.1488-12.2012},
issn = {1529-2401},
journal = {The Journal of Neuroscience},
keywords = {biology, eye-movements, localization, motor},
month = jun,
number = {25},
pages = {8569--8573},
pmid = {22723697},
posted-at = {2012-06-25 16:28:29},
priority = {2},
publisher = {Society for Neuroscience},
title = {Eye Proprioception Used for Visual Localization Only If in Conflict with the Oculomotor Plan},
url = {http://dx.doi.org/10.1523/jneurosci.1488-12.2012},
volume = {32},
year = {2012}
} | 2019-01-17 04:58:59 | {"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": 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": 0.471904993057251, "perplexity": 7145.195369239625}, "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-2019-04/segments/1547583658702.9/warc/CC-MAIN-20190117041621-20190117063621-00469.warc.gz"} |
http://www.sciforums.com/threads/is-there-a-simple-way-to-detect-gravitational-waves.149731/page-3 | # Is there a simple way to detect gravitational waves?
Discussion in 'Pseudoscience' started by jcc, Jun 10, 2015.
1. ### jccRegistered Senior Member
Messages:
412
let's see, photon has no mass no charge, yet it carries em fields and energy?
electrons can relax? can emit photons? red and blue photons? is red photon vibrating 4 x 10^14 times per second? or is red photon passing a point 4 x 10^14 times per second?
exited atoms do vibrate and produce gravitation waves, it is fact. is gravitation radiation propagating at c speed? is it has frequency? is its energy inversely proportional to r^2?
3. ### AlexGLike nailing Jello to a treeValued Senior Member
Messages:
4,304
jcc, this is crank bullshit.
5. ### AlexGLike nailing Jello to a treeValued Senior Member
Messages:
4,304
Tiassa, you might consider treating this thread the same way. Locked and in the cesspool.
7. ### TiassaLet us not launch the boat ...Staff Member
Messages:
36,374
Mod Hat ― Closure and Redirect
I'm getting sick of this.
8. ### jccRegistered Senior Member
Messages:
412
can't handle the truth?
i don't blame you.
9. ### James RJust this guy, you know?Staff Member
Messages:
34,574
jcc:
We can't detect the gravitational waves from the sun. Not yet, anyway.
Most of the energy in the hot gases in the sun goes nowhere. It stays right there in the sun. Some energy escapes from the surface of the sun as light, which carries some energy away. We detect it as light and other forms of electromagnetic radiation on Earth. The Sun also emits lots of charged particles.
That's part of it. A lot of the sun is a plasma, though.
There's constant absorption and emission happening in the sun, so you end up with radiation in thermal equilibrium with the matter. This leads to a blackbody spectrum.
I'm not sure what "mechanism" you want.
Electrons change orbital when they gain or lose energy. The electromagnetic interaction creates or destroys photons in the process.
A red and a blue photon have different frequencies.
Mass and charge are not required for something to carry energy.
Photons have momentum $p=E/c$, where $E$ is the photon's energy.
It's a discrete value that the energy of a particle or other object can have.
10. ### river
Messages:
14,523
If gravity has a physical wave to it , then objects should simply ride the wave .
Hence :
Strong attraction and weak attraction at equal intervals
danshawen likes this.
11. ### danshawenValued Senior Member
Messages:
3,950
One way to produce gravity waves is by large masses orbiting other large masses (typically very slowly). These are waves of time dilation, which is one reason you are not likely to detect them using either an interferometer or with multi-ton Weber bars and attached piezoelectric sensors. The first method is nothing more than an updated Michaelson-Morely experiment, which will always have a null result for gravitational waves. The second idea operates on the same principle as the Earth-moon tides, but since the dimensions of bars are not referenced to anything that measures time not also under the influence of the same gravity waves, it will never detect anything. The Earth-moon tides work as a gravity wave detector as a sort of water clock. Water closer to the moon side of the Earth undergoes a different time dilation /acceleration than the water on the far side.
What is needed to detect gravitational waves like the ones due to planets orbiting the Sun in our solar system, is to measure time dilation effects in as many different directions as possible using a clock that is based on quantum entanglement and their rates referenced to another such entanglement clock located at a great distance from the gravitational influences you are trying to measure.
Last edited: Jun 13, 2015
12. ### Dr_ToadIt's green!Valued Senior Member
Messages:
2,527
Why the hell y'all feed this troll instead of using the ban hammer, I just don't get.
He has been banned from here more than once, yet you succumb to his anti-education fucking bullshit for page after page of hand-holding, as if you can't really believe someone could be so abysmally stupid and still goad further responses from (Your name here)?
What motivation could there be to allow this dumbass hatful of hammers to keep shitting on this forum?
Fucking ban me.
13. ### danshawenValued Senior Member
Messages:
3,950
It is true that his previous posts were lackluster, Dr Toad, but since this particular subject is one in which a lot of mainstream physics money was and is being spent, so far with nothing but null results, I, for one would be willing to give jcc the benefit of the doubt. Better and more productive to allow discussion that might bring in some better ideas than to hone dozens more LIFO mirrors and beam splitters to finer than 1 atom planar tolerances, and all of the wasted expense that process will entail.
I don't know or care whom LIFO employed for their design, but even Joe Weber, a naval engineer turned physicist, was not as wrong. Dr Weber was no crackpot. Not particularly original in his designs, but he did the best he could. When I attended U of M in the '70s, he had a pretty good cult going, and more than one big project there failed. The electron ring accelerator failed because it ran out of money to redesign its focusing magnets. Some of that team went on to much greater success in physics. Failure sometimes just means you dreamt big, and ran out of money.
Last edited: Jun 13, 2015
14. ### Q-reeusValued Senior Member
Messages:
3,647
Which theory of gravity are you referring to? It's not GR, for which the only allowed GW's have purely spatial component distortions. Time only enters as propagation parameter e.g. cos(ωt - kx).
Maybe - but not because they won't detect g_tt time distortions.
You are confusing near-field tidal variations with vastly weaker hoped-for GW's. Chalk and cheese.
danshawen likes this.
15. ### danshawenValued Senior Member
Messages:
3,950
Oh, yeah. Another case of the Minkowski version of Euclidean/Pythagorean/ hyperbolic rotation / time tacked on as an extra physical dimension / afterthought kind of relativistic reasoning that makes GR only an approximation (although in cases like bulk celestial mechanics with only a few bodies in motion, and a dominant mass, it's the best we've got). Well, that just explains a lot. You win honors and accolades for being forthright enough to provide any detail on this flawed idea.
The underlying principle of operation was evidently treated as something of a closely guarded classified U.S. Navy top secret or something in the 1970s. An easy expedient for hiding bad engineering, don't you think? Like Teller's flawed H-bomb design that would never have worked.
LIFO no doubt plays a similar game with what should be classified as basic science research.
Last edited: Jun 13, 2015
16. ### Q-reeusValued Senior Member
Messages:
3,647
Umm....I think that last bit was not a back-handed compliment. Anyway, if it helps, I actually have some sympathy for the idea that any possible GW should involve temporal distortion. Here's cut & paste from another site where GW detection came up:
danshawen likes this.
17. ### exchemistValued Senior Member
Messages:
9,654
I agree about jcc and have reported him, hoping he will eventually get banned. I expect he is accumulating the points necessary for that to happen. Meanwhile I avoid his obvious wind-ups.
18. ### krash661[MK6] transitioning scifi to realityValued Senior Member
Messages:
2,973
you exclude scale of an entity, without realizing it.
danshawen likes this.
19. ### jccRegistered Senior Member
Messages:
412
are you sure? science has to be sure.
if heat and light from the sun are gravitation waves produces by hot gasses, aren't we feel/see it all the time? why you say gravitation waves is not detectable?
20. ### jccRegistered Senior Member
Messages:
412
can we detect that heat and light from the sun?
heat and light as you said, as i suggested, are produced by exited/vibrating hot gasses/atoms on the sun?
21. ### originIn a democracy you deserve the leaders you elect.Valued Senior Member
Messages:
11,059
Yes we are sure.
They aren't so we don't.
They may be detectable but we have not detected them yet.
22. ### originIn a democracy you deserve the leaders you elect.Valued Senior Member
Messages:
11,059
I certainly can.
Actually the heat and light is from nuclear fusion and by the time the emitted gamma rays reach the surface their energy has been lowered to mostly UV, IR and the visible spectrum.
23. ### jccRegistered Senior Member
Messages:
412
are the atoms of the hot gasses on the sun vibrating?
are they produce gravitation waves?
is the energy of the gravitation wave proportional to its frequency?
where that energy goes/becomes? | 2020-08-13 02:56:03 | {"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": 0.3647558093070984, "perplexity": 3066.812911411562}, "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/1596439738950.61/warc/CC-MAIN-20200813014639-20200813044639-00505.warc.gz"} |
http://mymathforum.com/number-theory/342822-diophantine-hyperbola.html | My Math Forum Diophantine hyperbola
Number Theory Number Theory Math Forum
November 15th, 2017, 01:55 PM #1 Newbie Joined: Nov 2017 From: Mexico Posts: 1 Thanks: 0 Diophantine hyperbola I am given an integer c an and we know the sum of consecutives integers can reach this number. I reach this expression \begin{align*} c &= \dfrac{n(n+1)}{2} - \dfrac{m(m+1)}{2} \end{align*} where n > m, both are integers positive. we can reduce that to \begin{align*} 2 * c &= n^2 + n - m^2 - m \end{align*} For example if c = 1000 then one of the solutions is n = 52 and m = 27. How can I get all the integer solutions n and m ? Last edited by limboa; November 15th, 2017 at 02:04 PM. Reason: v8archie was right
November 15th, 2017, 02:01 PM #2 Math Team Joined: Dec 2013 From: Colombia Posts: 7,502 Thanks: 2511 Math Focus: Mainly analysis and algebra ${}-m$, not ${}+m$
November 15th, 2017, 02:55 PM #3 Math Team Joined: Dec 2013 From: Colombia Posts: 7,502 Thanks: 2511 Math Focus: Mainly analysis and algebra Not sure it helps, but \begin{align*}n^2+n-m^2-m&=\frac14\left((2n+1)^2 - (2m+1)^2\right) \\ &=\frac14(2n+2m+2)(2n-2m)=(n+m+1)(n-m) \end{align*}
Tags diophantine, hyperbola
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Contact - Home - Forums - Cryptocurrency Forum - Top | 2018-11-15 12:26:16 | {"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": 0.9680356383323669, "perplexity": 5331.927502118986}, "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/1542039742685.33/warc/CC-MAIN-20181115120507-20181115142507-00189.warc.gz"} |
https://stats.stackexchange.com/questions/520380/cumulative-distribution-function-of-s-n-t-where-s-n-t-is-the-time-of | # Cumulative Distribution Function of $S_{N_{t}}$ where $S_{N_{t}}$ is the time of the last arrival in $[0, t]$
I am confused on this problem. My professor gave this as the solution:
$$S_{N_{T}}$$ is the time of the last arrival in $$[0, t]$$. For $$0 < x \leq t, P(S_{N_{T}} \leq x) \sum_{k=0}^{\infty} P(S_{N_{T}} \leq x | N_{T}=k)P(N_{T}=k)$$
$$= \sum_{k=0}^{\infty} P(S_{N_{T}} \leq x | N_{T}=k) * \frac{e^{- \lambda t}*(\lambda t)^k}{k!}$$.
Let $$M=max(S_1, S_2, ..., S_k)$$ where $$S_i$$ is i.i.d. for $$i = 1,2,.., k$$ and $$S_i$$~ Uniform$$[0,t]$$.
So, $$P(S_{N_{T}} \leq x) = \sum_{k=0}^{\infty} P(M \leq x)\frac{e^{- \lambda t}*(\lambda t)^k}{k!} = \sum_{k=0}^{\infty} (\frac{x}{t})^k \frac{e^{- \lambda t}*(\lambda t)^k}{k!} = e^{- \lambda t} \sum_{k=0}^{\infty} \frac{(\lambda t)^k}{k!} = e^{- \lambda t}e^{- \lambda x} = e^{\lambda(x-t)}$$
If $$N_t = 0$$, then $$S_{N_{T}} = S_0 =0$$. This occurs with probability $$P(N_t = 0) = e^{- \lambda t}$$.
Therefore, the cdf of $$S_{N_{T}}$$ is: $$P(S_{N_{T}} \leq x) = \begin{array}{cc} \{ & \begin{array}{cc} 0 & x < 0 \\ e^{- \lambda (x-t)} & 0\leq x\leq t \\ 1 & x \geq t \end{array} \end{array}$$
I don't really understand the part of creating the variable M of the maximum of k i.i.d. random variables in order to solve the problem. Any help would be greatly appreciated, thank you!
In the future please be more careful when asking your question. The screenshot of the problem is missing so much context; how do you expect others to know how $$N_t$$ and $$S_{N_t}$$ are defined? Furthermore there are careless typos throughout your professor's solution (writing $$T$$ sometimes instead of $$t$$, missing equals signs, misplaced parentheses, mathematical typos like writing $$(\lambda t)^k$$ instead of $$(\lambda x)^k$$, and $$e^{-\lambda t} e^{-\lambda x} = e^{\lambda (x-t)}$$, etc.). I guess if these were transcriptions of your professor's handwritten notes these things might happen, but you should try your best to catch these things when studying.
I will assume that you have a Poisson process with rate $$\lambda$$, and $$N_t$$ is defined as the number of arrivals in time interval $$[0, t]$$, and $$S_i$$ is the time of the $$i$$th arrival.
$$P(S_{N_t} \le x) = \sum_{k=0}^\infty P(S_{N_t} \le x \mid N_t = k) P(N_t = k).$$ We know $$P(N_t = k) = e^{-\lambda t} (\lambda t)^k/k!$$.
The other term is the probability that the last arrival in $$[0, t]$$ happens before time $$x$$, given that there are $$k$$ arrivals in $$[0, t]$$. Your professor uses a nontrivial result about Poisson processes to compute this term.
Conditioned on the event $$N_t = k$$ (i.e. there are $$k$$ arrivals in $$[0, t]$$), the distribution of arrival times $$(S_1, S_2, \ldots, S_k)$$ are the order statistics of $$k$$ i.i.d. $$\text{Uniform}[0,t]$$ random variables.
See here for a reference, although if your professor is using this result, you may have already encountered it in class somewhere.
In particular, conditioned on $$N_t = k$$, the last arrival $$S_{N_t}$$ has the same distribution as the maximum of $$k$$ i.i.d. $$\text{Uniform}[0,t]$$ random variables $$U_1, \ldots, U_k$$. (I use $$U_i \sim \text{Uniform}[0,t]$$ to not conflate with the $$S_i$$ which are already defined as the $$i$$th arrival in the Poisson process.)
So, the term $$P(S_{N_t} \le x \mid N_t = k) = P(M \le x)$$ where $$M = \max\{U_1, \ldots, U_k\}$$.
Thus, $$P(S_{N_t} \le x) = \sum_{k=0}^\infty (x/t)^k e^{-\lambda t} (\lambda t)^k/k! = e^{-\lambda t} \sum_{k=0}^\infty (x \lambda)^k/k! = e^{-\lambda t} e^{x \lambda}.$$ | 2021-08-04 08:39:39 | {"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": 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": 50, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8946540951728821, "perplexity": 138.44471563620942}, "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-2021-31/segments/1627046154798.45/warc/CC-MAIN-20210804080449-20210804110449-00535.warc.gz"} |
http://mathhelpforum.com/advanced-algebra/81019-determinant.html | # Math Help - Determinant
1. ## Determinant
$|A| = \begin{vmatrix} 1 & 2&3&\dots&n-1&n\\-1 & 0&3&\dots & n-1&n\\-1&-2&0&\dots &n-1 &n\\ \vdots&&&&&\\ -1& -2& -3&\dots & -(n-1) & 0 \end{vmatrix}$
Show that $|A|=n!$.
2. Originally Posted by james_bond
$|A| = \begin{vmatrix} 1 & 2&3&\dots&n-1&n\\-1 & 0&3&\dots & n-1&n\\-1&-2&0&\dots &n-1 &n\\ \vdots&&&&&\\ -1& -2& -3&\dots & -(n-1) & 0 \end{vmatrix}$
Show that $|A|=n!$.
First, for $1\leqslant j\leqslant n$ you can take a factor j out of the j'th column, giving you $|A| = n!\begin{vmatrix} 1 & 1&1&\dots&1&1\\-1 & 0&1&\dots & 1&1\\-1&-1&0&\dots &1 &1\\ \vdots&&&&&\\ -1& -1& -1&\dots & -1 & 0 \end{vmatrix}$. Now add the top row of that new matrix to each of the other rows and you'll get an upper-triangular matrix with 1s on the diagonal. So its determinant is 1. | 2015-03-05 01:13:16 | {"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": 0, "img_math": 0, "codecogs_latex": 6, "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": 0.9406053423881531, "perplexity": 398.3063823400685}, "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-2015-11/segments/1424936463676.59/warc/CC-MAIN-20150226074103-00053-ip-10-28-5-156.ec2.internal.warc.gz"} |
https://primordialmachine.com/api/ring1-library/intrinsic-library/Ring1_Intrinsic_subtract | $$% Arcus cosine. \def\acos{\cos^{-1}} % Vector projection. \def\projection#1#2{{proj_{#1}\left(#2\right)}} % Vector rejection. \def\rejection#1#2{{rej_{#1}\left(#2\right)}} % Norm. \def\norm#1{{\left\|#1\right\|}} % Cross product. \def\cross#1#2{\mathit{cross}\left(#1,#2\right)} % Dot product. \def\dot#1#2{{#1 \cdot #2}} % Magnitude. \def\mag#1{{\left|#1\right}} \def\group#1{\left(#1\right)}} \def\sbgrp#1{\left\{#1\right\}}$$
## Ring1_Intrinsic_subtract
Compute the difference of two values detecting numeric overflow.
Ring1_Result Ring1_Intrinsic_subtract_suffix ( type *result, type x, type y )
The following table denotes the valid combinations of suffix and type
suffix type u8 uint8_t u16 uint16_t u32 uint32_t u64 uint64_t s8 int8_t s16 int16_t s32 int32_t s64 int64_t sz size_t
### Parameter Variables
x
The first value aka minuend.
y
The second value aka subtrahend.
result
A pointer to a variable. For the assigned value see remarks section.
### Return Values
Ring1_Result_Success on success, Ring1_Result_Failure on failure.
### Post Conditions
If this function fails, then it sets the by-thread status variable.
Below is a list of failure conditions and the status codes indicating them.
Ring1_Status_InvalidArgument
result was NULL.
Ring1_Status_NumericOverflow
a numeric overflow occurred.
### Remarks
For the function variants for uintn_t and size_t, the value assigned to the variable are the lower n bits of the mathematical sum of the minuend and the subtrahend. This means x - y is reduced modulo MAX + 1 where MAX is UINTn_MAX or SIZE_MAX, respectively.
For the function variants for intn_t, the value assigned to the variable are the lower n bits of the 2's complements difference of the minuend and the subtrahend.
Consequently, these functions can be used to perform safe subtraction of signed and unsigned integers. | 2022-09-26 03:45:02 | {"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": 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": 0.20919176936149597, "perplexity": 10797.557033872492}, "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-2022-40/segments/1664030334644.42/warc/CC-MAIN-20220926020051-20220926050051-00731.warc.gz"} |
https://msp.org/pjm/2015/273-1/p03.xhtml | #### Vol. 273, No. 1, 2015
Recent Issues Vol. 299: 1 2 Vol. 298: 1 2 Vol. 297: 1 2 Vol. 296: 1 2 Vol. 295: 1 2 Vol. 294: 1 2 Vol. 293: 1 2 Vol. 292: 1 2 Online Archive Volume: Issue:
The Journal Subscriptions Editorial Board Officers Special Issues Submission Guidelines Submission Form Contacts Author Index To Appear ISSN: 1945-5844 (e-only) ISSN: 0030-8730 (print) Other MSP Journals
Some results on the generic vanishing of Koszul cohomology via deformation theory
### Jie Wang
Vol. 273 (2015), No. 1, 47–73
##### Abstract
We study the deformation-obstruction theory of Koszul cohomology groups of ${g}_{d}^{r}$’s on singular nodal curves. We compute the obstruction classes for Koszul cohomology classes on singular curves to deform to a smooth one. In the case where the obstructions are nontrivial, we obtain some partial results for generic vanishing of Koszul cohomology groups.
##### Keywords
Koszul cohomology, general curves, deformation theory, generic vanishing, maximal rank conjecture
Primary: 14H51 | 2019-06-24 18:21:30 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 1, "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": 0.7671624422073364, "perplexity": 7581.556025855972}, "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-2019-26/segments/1560627999620.99/warc/CC-MAIN-20190624171058-20190624193058-00121.warc.gz"} |
https://codegolf.stackexchange.com/questions/128450/index-of-the-row-with-most-non-zero-elements | # Index of the row with most non-zero elements
This is a simple one: Take a matrix of integers as input, and output the index of the row with the most non-zero elements. You may assume that there will only be one row with the most non-zero elements.
### Test cases:
These are 1-indexed, you may choose if you want 0 or 1-indexed.
1
0
row = 1
---
0 -1
0 0
row = 1
---
1 1 0 0 0
0 0 5 0 0
2 3 0 0 0
0 5 6 2 2
row = 4
---
0 4 1 0
0 0 -6 0
0 1 4 -3
2 0 0 8
0 0 0 0
row = 3
# MATL, 6 bytes
!gs&X>
Input is a matrix, with ; as row separator.
### Explanation
! % Transpose
g % Logical: convert non-zeros to 1
s % Sum of each column, or sum of row if there's a single row
&X> % Arg max. Implicitly display
# Mathematica, 23 bytes
Ordering[Count@0/@#,1]&
# 05AB1E, 8 6 bytes
ΣĀO}θk
Try it online!
-2 Bytes thanks to Erik the Outgolfer
### Explanation
ΣĀO}θk
Σ } # Sort input by following code
Ā # Is element not 0? (vectorized)
O # Sum
θk # Get index of "largest" element
# Implicit print
• Use Ā instead of Ä0› for -2. Jun 26 '17 at 16:31
• Yee just realized there is probably a better way to do that part than what I had. Damn I feel like I'm learning a new 05AB1E command every day ^^ Jun 26 '17 at 16:32
# R, 31 bytes
pryr::f(which.min(rowSums(!m)))
returns an anonymous function which takes a matrix:
function(m)which.min(rowSums(!m))
rowSums sums the rows, with !m transforming 0 to 1 and everything else to 0. which.min returns the 1-based index of the first row which contains the min sum (i.e., which row has the fewest zeros).
Try it online!
• You need which.min() since non-zero elements will become FALSE with !m. Jun 26 '17 at 16:09
• @user2390246 oh, wow, I completely misread the question. Fixed, thank you. Jun 26 '17 at 16:33
snd.minimum.(zip[1..]).map(filter(==0))
Try it online!
How it works
map -- for each row
(filter(==0)) -- collect the 0s
(zip[1..]) -- pair with row index (<#0s>, <index>)
minimum -- find the minimum
snd -- extract index from pair
• Nice! Better than mine, good to learn something. Jun 27 '17 at 3:42
# C#, 69 bytes
using System.Linq;m=>m.IndexOf(m.OrderBy(r=>r.Count(n=>n!=0)).Last())
Takes a List<int[]> as input and returns the 0-indexed result.
# Actually, 9 bytes
0@♀cñ♂RmN
Try it online!
Explanation:
0@♀cñ♂RmN
0@♀c count zeroes in each row
ñ♂R enumerate and reverse each row (each row becomes [count, index] pair)
m minimum
N last element (the index)
## Python 3, 54 48 bytes
lambda a:a.index(min(a,key=lambda r:r.count(0)))
Shaved off 6 bytes. Old solution:
lambda a:min(range(len(a)),key=lambda i:a[i].count(0))
• Just noticed it matches directly with the changes to the python 2 answer now. Jun 26 '17 at 16:49
# APL (Dyalog), 11 bytes
(⊢⍳⌈/)+/0≠⎕
Try it online!
0≠⎕ Boolean matrix where non-zero
+/ sum rows
( apply the following tacit function to the list of sums
⌈/ the maximum's
index
in the argument list
)
# Brachylog, 17 bytes
{{∋0}ᶜ}ᵐA;.∋₎~⌋A∧
Try it online!
€ĀOZk
Try it online!
0-indexed.
TL$€M Try it online! 1-indexed. So many 5-byte versions... TL$€M, T€L€M, TJ$€M, T€J€M, ¬¬Ṣ€M, ṠAṢ€M, ṠAS€M, AṠṢ€M, AṠS€M, ¬ċ€0M, ... • Why do they all look like words? Jun 26 '17 at 22:33 # Haskell - 69 68 Bytes Saved one byte thanks to Siracusa! Rows are zero indexed g=filter m y=head$g((==maximum y).(y!!))[0..]
f=m.map(length.g(0/=))
## Usage
f [[1,1,0,0,0],[2,3,0,0,0],[0,5,6,2,2],[1,1,1,1,1]]
Try it online!
• Defining g=filter saves you one byte Jun 26 '17 at 17:54
Try it online!
# V, 18 bytes
òø0
jòÚDuu/"
dGؾ
Try it online!
Unlike most V answers, this is 0-indexed.
00000000: f2f8 300a 6af2 da44 7575 2f12 220a 6447 ..0.j..Duu/.".dG
00000010: d8be ..
Not bad for a language with no numeric support! ;P
I also have discovered that the uppercase variant of the count command, that is Ø, is horribly broken.
# Python 3, 92 bytes
def f(x):
for e in x:
e.sort()
y=x[:]
y.sort()
return x.index(y[-1])
First sort each row such that the entrys are [0,0,..,0,x,x,x] then sort the whole matrix, so that the last entry in y is the row we are looking for. The copy y=x[:] is necessary, since .sort() works inplace, hence we don't know the original index after sorting.
I appreciate any help how to golf this solution further. Most bytes are lost because of the whitespaces in each line. The code itself is only 68 bytes long.
Try it online!
• I don't know Python but can't you remove most of the whitespace from this? Jun 26 '17 at 16:09
• @TheLethalCoder Python uses indentation instead of brackets for codeblocks, instead of brackets or keywords (e.g. for .. end). Jun 26 '17 at 16:12
• Even then python can be golfed a fair amount. The following is equivalent to your original code: def f(a):b=list(map(sorted,a));return b.index(sorted(b)[-1]) Jun 26 '17 at 16:13
• This answer uses a for loop and a function but with no newlines so I assume you can remove a lot of them although it is Python 2 the whitespace restrictions should be similar. Jun 26 '17 at 16:14
• Don't works for lists with negative numbers
– Rod
Jun 26 '17 at 16:18
# Python 2, 64 55 52 48 bytes
• Thanks to @Rod for shaving 9 bytes!!: count 0s and use min() instead of max()
• @Rod saved yet another 3 bytes: use input() instead of def
• @ovs saved 4 bytes: use of lambda and hash-map
lambda x:x.index(min(x,key=lambda n:n.count(0)))
Try it online!
• 48 bytes
– ovs
Jun 26 '17 at 16:28
• Thanks @ovs. I didn't exactly understand how it works though. Jun 26 '17 at 16:36
• It's more or less the same logic that you had on your answer, but using min with the key parameter
– Rod
Jun 26 '17 at 18:54
# JavaScript (ES6), 62 bytes
0-indexed. Takes a 2D array as input.
a=>(a=a.map(x=>x.filter(y=>y).length)).indexOf(Math.max(...a))
• Can you add an explanation for this one? Does filter implicitly "filter" zeroes? Jun 26 '17 at 16:10
• You're supposed to return the index of the row...
– Neil
Jun 26 '17 at 16:10
• Still trying to golf some more off it, @TheLethalCoder, will be adding a demo and an explanation when I'm done. In the meantime, see here for more info on filter, keeping in mind that 0 is falsey. Jun 26 '17 at 16:28
• @Neil: Fixed now. Jun 26 '17 at 16:29
• @Shaggy I assumed that was the case with filter was just making sure. Jun 26 '17 at 16:30
# Jelly, 7 bytes
ċ0$ÞḢi@ Try it online! ċ0$ÞḢi@ Main link
Þ Sort by
ċ0$the number of occurences of 0 Ḣ Take the first element i@ Index in the original array # Pyth, 6 bytes xQh/D0 Demonstration Instead of finding the row with the most non-zero elements, I find the row with the least zero elements. /D0: Order (D) by count (/) of zeros (0). Implicitly applied to Q, the input. h: Take the first, and minimum, element. xQ: Find the index (x) in the input (Q) of that element. • This was exactly what I had a well. It felt clunky and like I was missing something, but it seems like there's just not a clean way to do it :( Jun 27 '17 at 1:29 # Retina, 46 bytes %M\b0 m(?<=(¶.+)*)$
;\$#1
O#.+
!(?<=^.+;).+
Try it online!
0-indexed. Works with positive and negative integers (and 0). Assumes no leading zeros.
# Java 8, 145 bytes
import java.util.*;m->{int t=0,s=0,i=0,r=0;for(;i<m.size();i++){List l=(List)m.get(i);for(;l.remove(0L););s=l.size();if(s>t){t=s;r=i;}}return r;}
Ugly, but it works..
Explanation:
Try it here.
import java.util.*; // Required import for List
m->{ // Method with List parameter and integer return-type
int t=0,s=0,i=0, // Temp integers
r=0; // Result integer
for(;i<m.size();i++){ // Loop over the List of Lists
List l=(List)m.get(i); // Get the inner List
for(;l.remove(0L);); // Remove all zeros
s=l.size(); // Get the size of the List
if(s>t){ // If this size is larger than the previous
t=s; // Set t to this size
r=i; // And set the result to the index of this row
}
} // End of loop
return r; // Return result-integer
} // End of method
# Java (OpenJDK 8), 119 101 bytes
m->{int i=m.length,M=0,I=0,c;for(;i-->0;){c=0;for(int x:m[i])if(x!=0)c++;if(c>M){M=c;I=i;}}return I;}
Try it online!
Java, that sweet verbose language :)
Thanks for saving 18 bytes, @KevinCruijssen ;)
• +1 nice answer. Was about to post an even more verbose answer myself.. Was doubting whether to post it, and it's a good thing I hadn't since it's 145 bytes and ugly.. ;) Here it is... EDIT: Hmm, btw, your last two test cases fail.. Jun 27 '17 at 8:46
• Checking your code just made me realize there's a bug in my answer! o_O I don't even know how my test cases pass... Jun 27 '17 at 8:49
• Good to go, I fixed it! Jun 27 '17 at 8:51
• Nice! Btw, you can golf it by using a for-each inner loop to get rid of j and other longer parts like j=m[i].length, and m[i][j] like this: m->{int i=m.length,M=0,I=0,c;for(;i-->0;){c=0;for(int x:m[i])if(x!=0)c++;if(c>M){M=c;I=i;}}return I;} (101 bytes) Jun 27 '17 at 9:01
# JavaScript (ES6), 51 Bytes
m=>m.reduce((a,e,i)=>e.filter(x=>x).length>a?i:a,0)
where m is a 2D array and the index returned is 0-indexed
Test cases:
f=
m=>m.reduce((a,e,i)=>e.filter(x=>x).length>a?i:a,0)
console.log(f([[1], [0]]))
console.log(f([[0,-1], [0,0]]))
console.log(f([[1,1,0,0,0], [0,0,5,0,0], [2,3,0,0,0], [0,5,6,2,2]]))
console.log(f([[0,4,1,0], [0,0,-6,0], [0,1,4,-3], [2,0,0,8], [0,0,0,0]]))
# Java 8, 100 bytes
m->m.indexOf(m.stream().map(z->{z.removeIf(x->x==0);return z;}).max((q,r)->q.size()-r.size()).get())
## Explanation
The power of Lists and Streams! (and without the imports, to boot!)
Let's break this little lambda down into chunks:
m.stream().map(z->{z.removeIf(x->x==0);return z;}
We turn our List of Lists (the matrix in the question) into a Stream and go through each element, removing all of those pesky zeroes from each sub-List. We need to explicitly return the sublist each time here, because Stream.map() converts each object in the Stream to whatever the mapping returns, and we don't want to change them.
.max((q,r)->q.size()-r.size()).get()
We go through our newly de-zeroed sublists, and simply check how big they are next to each other, getting us the biggest sublist. The .get() is because the Stream.max() returns an Optional, requiring that extra function call.
m.indexOf()
We take that biggest sublist, and find where it is in the main List, giving us our result!
## Notes
This breaks if the outer list is empty, but I'm taking
You may assume that there will only be one row with the most non-zero elements.
to imply that there will always be at least one row. Correct me if I'm wrong.
# Python 2, 51 bytes
def f(x,i=0):print i;x[i].remove(0);f(x,-~i%len(x))
Try it online!
This version removes 0s progressively through the arrays, printing the current index, and crashes when there are no more zeros to remove. Last printed index is the answer.
# Python 2, 57 bytes
lambda x,i=0:0in x[i]>x[i].remove(0)and f(x,-~i%len(x))|i
Try it online!
Wanted to try a different approach from what's already here. So here I recursively iterate over the array removing one 0 at a time until the current array no longer has any zeroes - and then output the index of that array.
# Japt, 7 bytes
0-indexed. Takes input as an array of arrays.
mè
bUrw
Test it
## Explanation
Implicit input of array U.
[[0,4,1,0],[0,0,-6,0],[0,1,4,-3],[2,0,0,8],[0,0,0,0]]
Map (m) over U returning the count of truthy (non-zero) elements in each sub-array. Implicitly assign this new array to U.
[2,1,3,2,0]
Urw
Reduce (r) array U by getting the greater of the current value and the current element.
3
b
Get the first index in U where the element equals that value and implicitly output the result.
2 | 2021-12-01 13:33:39 | {"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": 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": 0.2288862019777298, "perplexity": 4274.400256307777}, "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/1637964360803.0/warc/CC-MAIN-20211201113241-20211201143241-00516.warc.gz"} |
https://ask.sagemath.org/question/60597/weyl-character-formula-in-sagemath/ | # Weyl character formula in Sagemath
I am trying to program Weyl character formula in Sage as follows:
A2 = WeylCharacterRing("A2")
a2 = WeightRing(A2)
L = A2.space()
W = L.weyl_group()
Lambda = L.simple_roots()[1]+L.simple_roots()[2]
rho = L.rho().coerce_to_sl()
r1 = sum((-1)^(w.length())*a2(w.action(Lambda+rho)) for w in W)
r2 = prod(1-a2(-alpha) for alpha in L.positive_roots())
r3 = a2(-rho)
Now I want to compute r1*r3/r2. But there is some error: AttributeError: 'WeightRing_with_category.element_class' object has no attribute 'quo_rem'
How to fix this problem?
Also the result of r2 is:
a2(0,0,0) + a2(-2,1,1) - a2(-2,0,2) + a2(-1,-1,2) - a2(-1,1,0) - a2(0,-1,1)
How to translate r2 (and the final result of Weyl character) into a form which is easier to read? I would like to write it as a Laurent polynomial in $e^{\omega_1}, e^{\omega_2}$, where $\omega_1, \omega_2$ are fundamental weights.
Thank you very much.
edit retag close merge delete | 2022-01-20 08:16:05 | {"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": 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": 0.19817882776260376, "perplexity": 3716.1745317362033}, "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-2022-05/segments/1642320301730.31/warc/CC-MAIN-20220120065949-20220120095949-00363.warc.gz"} |
https://mydbanotebook.org/post/troubleshooting-02/ | #### What's wrong with Postgres?
##### March 22, 2020
This post is part of several blog posts (at least two!) about Troubleshooting Postgres. Last time, we found out if Postgres was running and how to start it. Please find here all the troubleshooting posts.
Here is my checklist of troubleshooting Postgres:
[] Try to start postgres (if this works, stop here) [] Locate the log file [] Look at the messages in Postgres logfile
To start Postgres, please refer to Is Postgres running.
## Locating Postgres logfile
### For Debian and friends
Debian-based distributions have these wonderful perl wrappers that extend Postgres administration tool. Use them!
pg_lsclusters
So, for me, I’ll find this:
root@ubuntu:/home/vagrant# pg_lsclusters
Ver Cluster Port Status Owner Data directory Log file
12 main 5432 online postgres /var/lib/postgresql/12/main /var/log/postgresql/postgresql-12-main.log
12 test 5433 online postgres /var/lib/postgresql/12/test /var/log/postgresql/postgresql-12-test.log
Your logfile is simply indicated there. Go find out why Postgres is not happy with you!
### For Red Hat and friends
Let’s say it straight: it won’t be easy, depending on how you (mis)configured Postgres. If Postgres is running, you can always query it like that:
postgres=# select pg_current_logfile();
But, if you’re reading that post, you might be in a situation where Postgres refuses to start and you have no idea where your logfile is.
To find your Postgres logfile, you need to find out how Postgres was configured, regarding logs. Maybe you simply don’t have a logfile at all!
#### Finding $PGDATA Red Hat and Red Hat-based distribution use systemctl to control Postgres. So the best thing you have to do is to ask directly systemctl to know where the config file is: systemctl cat postgresql-12.service | grep "PGDATA" | grep "Environment" Here’s my example: [root@centos7 vagrant]# systemctl cat postgresql-12.service | grep "PGDATA" | grep "Environment" Environment=PGDATA=/var/lib/pgsql/12/data/ #### Finding your logfile Now that you have found your $PGDATA, you’ll be able to look at your Postgres log settings to find out where your Postgres log are located.
You’ll need to find out the value of the following parameters:
[] logging_collector [] log_destination [] log_directory [] log_filename
Here’s one way to get them all:
sed -e 's/#.*$//' /var/lib/pgsql/12/data/postgresql.conf | grep -E "logging_collector|log_destination|log_directory|log_filename" If some of the parameters don’t show up, it simply means that they’re not set and the default value is taken instead. Here are the default values for each one: • logging_collector: the default is off • log_destination: the default is stderr • log_directory: the default is log meaning logs will be sent to the log directory inside $PGDATA
• log_filename: the default is postgresql-%Y-%m-%d_%H%M%S.log
Now, you need to interpret these results to understand where your logfile is. This schema might help you:
For example, if you had these results:
[root@centos7 vagrant]# sed -e 's/#.*$//' /var/lib/pgsql/12/data/postgresql.conf | grep -E "logging_collector|log_destination|log_directory|log_filename" log_destination = 'stderr' logging_collector = on log_directory = 'log' log_filename = 'postgresql-%a.log' It means you’ll find your Postgres logfile in $PGDATA/log and the name of the logfile will be postgresql-Sun.log, as today is Sunday.
Now, go look at your logfile. Postgres is pretty good at telling you what’s wrong. Be particularly attentive to the few last lines! | 2020-04-02 15:52:30 | {"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": 0.22146467864513397, "perplexity": 8820.130589879414}, "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/1585370506988.10/warc/CC-MAIN-20200402143006-20200402173006-00018.warc.gz"} |
https://wiki.kidzsearch.com/wiki/Template:Enwp_based | kidzsearch.com > wiki Explore:images videos games
# Template:Enwp based
Template documentation
This template is used on the talk page of an article to say which version of the English Wikipedia article was used as the basis for the article here.
## Format
Choose one of the following:
• {{Enwp based | url= (full link to the referenced version on the English Wikipedia) }}
• {{Enwp based | 1= (full link to the referenced version on the English Wikipedia) }}
• {{Enwp based | (full link to the referenced version on the English Wikipedia) }}
If another named parameter is used, or no parameter is given, an error will be shown.
Note: The exact version of the article which was used should be referenced, not just the article itself.
• If the most current version was used, the version link can be found by clicking "Permanent link" in the sidebar on the left hand side of the page on English Wikipedia. Use the URL that appears.
• If a previous version was used, go to the history of the article at English Wikipedia and click on the date and time of the version that was used. Use the URL that appears.
## Examples
• {{enwp based|url=http://en.wikipedia.org/w/index.php?title=Philosophical_skepticism&oldid=346768538}}
• {{enwp based|1=http://en.wikipedia.org/w/index.php?title=Philosophical_skepticism&oldid=346768538}}
• {{enwp based|http://en.wikipedia.org/w/index.php?title=Philosophical_skepticism&oldid=346768538}}
## Related templates
• {{based on}}, almost identical in function but with a few extra options, and the url parameter must be named (i.e., |url=)
• {{translated page}}, for use when the source article is from a non-English Wikipedia | 2020-07-03 13:46:43 | {"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": 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": 0.17190209031105042, "perplexity": 2472.261545466193}, "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-2020-29/segments/1593655882051.19/warc/CC-MAIN-20200703122347-20200703152347-00097.warc.gz"} |
https://zbmath.org/?q=an%3A1316.11038 | ## Period(d)ness of $$L$$-values.(English)Zbl 1316.11038
Borwein, Jonathan M. (ed.) et al., Number theory and related fields. In memory of Alf van der Poorten. Based on the proceedings of the international number theory conference, Newcastle, Australia, March 12–16, 2012. New York, NY: Springer (ISBN 978-1-4614-6641-3/hbk; 978-1-4614-6642-0/ebook). Springer Proceedings in Mathematics & Statistics 43, 381-395 (2013).
Let $$q=\exp(2 \pi i \tau)$$, where $$\tau$$ is in the upper half-plane $$\mathrm{Im} (\tau)>0$$, and let $\eta(\tau)=q^{1/24} \prod_{m=1}^{\infty}(1-q^m)=\sum_{n=-\infty}^{\infty} (-1)^n q^{(6n+1)^2/24}$ be the Dedekind eta function. Set $$\eta_k=\eta(k \tau)$$, and $L(f,m)=\frac{1}{(m-1)!} \int_{0}^{1} f \log^{m-1} q \frac{dq}{q}$ for a modular form $$f(\tau)=\sum_{n=1}^{\infty} a_n q^n$$. For the cusp form $$f(\tau)=\nu_4^2 \nu_8^2$$ (whose $$L$$-series coincide with those of a conductor $$32$$ elliptic curve) the authors prove that $L(f,2)=\frac{\pi}{8} \int_{0}^{1} \frac{x}{\sqrt{1-x^4}} \log \frac{1+x}{1-x} dx=0.9170506353\dots$ and $L(f,3)=\frac{\pi^2}{128} \int_{0}^{1} \frac{(1-\sqrt{1-x^2})^2}{(1-x^2)^{3/4}} dx \int_{0}^1 \int_{0}^1 \frac{dy dw}{1-x^2(1-(1-y^2)(1-w^2))}$ (which is $$0.9826801478\dots$$). Some further hypergeometric evaluations are also obtained.
For the entire collection see [Zbl 1266.11001].
### MSC:
11F67 Special values of automorphic $$L$$-series, periods of automorphic forms, cohomology, modular symbols 11G55 Polylogarithms and relations with $$K$$-theory
### Citations:
Zbl 1260.11062; Zbl 1378.11091
Full Text: | 2022-05-20 22:41:36 | {"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": 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": 0.7900599241256714, "perplexity": 730.4944881307249}, "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/1652662534693.28/warc/CC-MAIN-20220520223029-20220521013029-00546.warc.gz"} |
http://bootmath.com/higher-homology-group-of-eilenberg-maclane-space-is-trivial.html | # Higher homology group of Eilenberg-Maclane space is trivial
I’m trying to solve the following exercise from Algebraic Topology by Hatcher (self-study):
Show that $H_{n+1}(K(G,n);\mathbb{Z}) = 0$ if $n > 1$.
$K(G,n)$ is the Eilenberg-Maclane space.
I’m following a hint suggesting starting with a Moore space $M(G,n)$. The idea
I have is to kill homotopy groups at dimensions $> n$ by attaching cells of dimension $> n + 1$. By Hurewicz theorem the resulting space is $K(G, n)$. The problem I have is that attaching cells of dimension $n + 2$ affects $H_{n+1}$ so it’s not necessarily $0$. I don’t know whether I need to do something extra to ensure it stays $0$.
This exercise is later used to prove the surjectivity of the Hurewicz homomorphism at $n + 1$. Hence we cannot use this fact here.
Help is appreciated. Thanks
#### Solutions Collecting From Web of "Higher homology group of Eilenberg-Maclane space is trivial"
Attaching cells of dimension $(n+2)$ can indeed change $H_{n+1}(X)$ for some space $X$, but it can only make it smaller. That is, if $X^\prime$ is $X$ with the $(n+2)$ cells attached, then $H_{n+1}(X^\prime)$ is a quotient of $H_{n+1}(X)$.
This follows from looking at what happens in the long exact sequence of homology associated to the cofibre sequence $\bigsqcup S^{n+1} \rightarrow X \rightarrow X^\prime$, where the first map is the characteristic map of the cells being attached.
Also, in your case to suffices to observe that if a CW-complex $Y$ has no $k$-cells, then $H_{k}(Y) = 0$, since the cellular chain complex (which can be used to compute the singular homology) is generated in degree $k$ by the set of all $k$-cells of $Y$. | 2018-07-20 04:36:55 | {"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": 0.9270402193069458, "perplexity": 149.5479524149924}, "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-2018-30/segments/1531676591497.58/warc/CC-MAIN-20180720041611-20180720061611-00208.warc.gz"} |
http://mathhelpforum.com/trigonometry/151899-equation-quadratic-curve-three-dimensional-space.html | # Math Help - Equation for a quadratic curve in a three-dimensional space?
1. ## Equation for a quadratic curve in a three-dimensional space?
I'm not really sure if this is the right area BUT I did similar things such as this in trig so I thought this might be a good place to ask.
I'm working within a three dimensional space and I have three points that I must create a quadratic curve out of. The curve must touch all three points. In 2d the process for solving this is easy enough but in three dimensions I begin to have trouble. I built a script that can find and output the X,Y,and Z coordinates and their distance in relation to each other but I need to know a formula (or possibly two combining formulas. I'm not really sure how using two would work for programming) to plug in the values. Anyone know a formula like this?
2. Do you think this is really a question for the trigonometry sub-forum?
Best ask a mod to move it to improve the chanes of getting a proper reply.
3. A curve is one-dimensional so to write a curve in three dimensions, you need to reduce from 3 variables to one. you can do that by either using two equations in the three coordinates (so that the two equations can be solved for two of them in terms of the other one) or three equations for x, y, and z in terms of a parameter, t, say. That is, something like:
$x= at^2+ bt+ c$, $y= dt^2+ et+ f$, and $z= gt^2+ ht+ i$.
You are free to choose what values t takes at each point, although choosing values reflecting the distances between the points might simplify things. Putting the t values and the x, y, z values of the points in the parametric equations will give 9 linear equations for the nine coefficients, a, b, c, d, e, f, g, h, and i.
4. Hello, Korinkite!
I don't agree with your intial statements.
I'm working within a three-dimensional space
and I have three points that I must create a quadratic curve out of.
In 2-D the process for solving this is easy enough. . really?
Three points do not determine a quadratic curve.
General quadratic function: . $Ax^2 + Bxy + Cy^2 + Dx + Ey + F \:=\:0$
. . which has six coefficients to be determined.
We have only three points: . $(x_1,y_1),\;(x_2,y_2),\;(x_3,y_3)$
They produce this system of equations:
. . $\begin{Bmatrix}Ax_1^2 + Bx_1y_1 + Cy_1^2 + Dx_1 + Ey_1 + F &=& 0 \\ \\[-3mm]
Ax_2^2 + Bx_2y_2 + Cy_2^2 + Dx_2 + Ey_2 + F &=& 0 \\ \\[-3mm]
Ax_3^2 + Bx_3y_3 + Cy_3^2 + Dx_3 + Ey_3 + F &=& 0
\end{Bmatrix}$
. . which obviously does not have a unique solution.
5. ## Got it!
Sorry for the late reply. First to Soroban, I apologize if I wasn't being entirely clear. I didn't mean to suggest that there could be one perfect equation for a quadratic curve with three points. In the end, I did get Hallsofivy's method to work so a few screenshots might save the trouble of explaining. | 2015-04-25 04:48:10 | {"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": 6, "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": 0.7485739588737488, "perplexity": 278.53947276348316}, "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-2015-18/segments/1429246646036.55/warc/CC-MAIN-20150417045726-00290-ip-10-235-10-82.ec2.internal.warc.gz"} |
https://math.stackexchange.com/questions/2506388/how-to-build-the-equation-for-this-question | # How to build the equation for this question?
In a class, there are $20$ people. In this class, there are $4$ people who know only english, $9$ who don't know french, $7$ who don't know english. Then, how many people who know both language are there?
Here is my venn diagram
enter image description here
$$r(1) = \text {who know english}$$ $$r(3) = \text {who know french}$$ $$r(2) = \text {who know both}$$ $$r(4) = \text {who know no language}$$
I'm building the equation now
$$\sum_{i = 1} r(i) = 20$$ $$r(1) + r(2) + r(3) + r(4) = 20$$ $$r(1) = 4$$
I don't have any idea about how to find $r(2)$. What is the correct equation we ought to use?
• Let E be the number who speak English. F be the number who speak French. Then 20 - E = 4, 20 - F = 9. The r notation is too clumbsy to work with. – William Elliot Nov 5 '17 at 19:51
The fact that there are $9$ people who don't know French means that there are $9$ people outside the $F$ circle, meaning that:
$$r(1)+r(4)=9$$
Likewise, the fact that there are $7$ people who don't know English means that there are $9$ people outside the $E$ circle, meaning that:
$$r(3)+r(4)=7$$
I assume you can take it from there.
$r(1)+r(4)=9;\;r(3)+r(4)=7$
$r(1) + r(2) + r(3) + r(4) = 20$
$r(1)=4$
$r(4)=5$
$r(3)=2$
$r(2)=9$ | 2019-08-20 03:09:28 | {"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": 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": 0.658970832824707, "perplexity": 298.10331383554274}, "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/1566027315222.14/warc/CC-MAIN-20190820024110-20190820050110-00130.warc.gz"} |
https://mathematica.stackexchange.com/questions/22094/modular-arithmetic-efficiently-calculating-the-remainders-of-factorials | # Modular arithmetic - efficiently calculating the remainders of factorials
When working on this question regarding the divisibility of the sum of factorials, I decided to write some code to test "small values" of the problem using the following code.
f[p_] := Total[Mod[#!, p] & /@ Range[p - 1]];
Table[Mod[f@Prime@i, Prime@i], {i, 1, 500}]
Basically, what the code does is sum up all the factorials $$1!+2!+3!+\dots+(p-1)!$$
and find the remainder modulo $p$, for prime $p$.
Unfortunately, my code as written takes a very long time to run. Checking the first 500 primes takes 88.280966 seconds on my computer, but checking the first 2000 primes took me about 4 hours.
Is there any way to improve the code, or is it already the best we can do?
As for optimizations not involving the code, I used Wilson's Theorem, which states that for all primes $p$,
$$(p-1)!\equiv-1 \bmod p$$
Using the above theorem, we can modify the code as follows.
h[p_] := Total@Flatten[{Mod[#!, p], PowerMod[(# - 1)!*(-1)^(#), -1, p]} & /@ Range[(p - 1)/2]];
Table[Mod[h@Prime@i, Prime@i], {i, 1, 500}]
This is considerably faster than the previous code, since checking the first 500 primes takes only 25.896166 seconds. However, checking the first 2000 primes still takes an inordinately long time.
This is bit faster:
toPrime = 500;
sums = Accumulate@FoldList[Times, 1, Range[2, Prime@toPrime - 1]];
primes = Prime[Range[toPrime]];
Mod[sums[[primes - 1]], primes]
Precompute factorial sums and primes. Mod is fast on lists.
• you are way too humble! calculating your sum for even the first 2000 primes takes less than a second. However, is there a way to get around storing large numbers in sums in memory? It keeps crashing my computer when I try toPrime=5000. – Vincent Tjeng Mar 26 '13 at 6:03
• +1 (that's freaking fast!) Can you explain why Accumulate@FoldList[#1 #2 &, 1, Range[n] is so much quicker to Accumulate@Array[#! &, n] + 1? I really don't get it. – gpap Mar 26 '13 at 11:23
• @gpap Calculating factorial so many times costs a lot. Since we know we want all the factorials up to Prime[toPrime]-1, we ultimately gain a lot keeping the intermediate results with FoldList. – Michael E2 Mar 26 '13 at 12:04
• @MichaelE2 Yes, worked it out myself in the meantime - you multiply the previous result and don't calculate a factorial at every step. Thanks – gpap Mar 26 '13 at 12:11
• Is there any reason why you used #1 #2 & instead of Times? – J. M. is away Jun 15 '15 at 12:53
Let $x \equiv r_1 \bmod p$ and $y \equiv r_2 \bmod p$. Then, $x y \equiv r_1 r_2 \bmod p$. So, we can compute the sum of the factorials mod p using:
f[p_] := Mod[ Total @ FoldList[ Mod[Times[##], p]&, Range[p-1]], p]
Let's compare this to the naive implementation:
t[p_] := Mod[Sum[k!, {k, p-1}], p]
For example:
f[Prime[500]] //AbsoluteTiming
t[Prime[500]] //AbsoluteTiming
{0.00058, 1813}
{0.085628, 1813}
The nice thing about using Mod[Times[##], p] as the FoldList function is that the output should be a machine number unless you are working with very large primes. That means that f can be compiled:
fc = Compile[{{p, _Integer}},
Mod[ Total @ FoldList[ Mod[Times[##], p]&, Range[p-1]], p],
RuntimeAttributes->{Listable}
];
Let's compare for a large prime:
f[Prime[10^6]] //AbsoluteTiming
fc[Prime[10^6]] //AbsoluteTiming
{1.83041, 9308538}
{1.05449, 9308538}
Faster, but the real difference is that fc is Listable. Hence, comparing timings on a list shows a much larger difference. For example:
r1 = f /@ Prime[Range[5000, 5500]]; //AbsoluteTiming
r2 = fc[Prime[Range[5000, 5500]]]; //AbsoluteTiming
r1 === r2
{2.06691, Null}
{0.395402, Null}
True
Finally, since the list of all factorials is not stored anywhere, the memory used is much more manageable. Here is the memory and timing for the first 5000 primes:
r1 = fc[Prime[Range[5000]]]; //MaxMemoryUsed //AbsoluteTiming
{3.03463, 462848}
This is quite a bit smaller than @MichaelE2's answer:
MaxMemoryUsed[
toPrime = 5000;
sums = Accumulate@FoldList[Times, 1, Range[2, Prime@toPrime - 1]];
primes = Prime[Range[toPrime]];
r2 = Mod[sums[[primes - 1]], primes]
] //AbsoluteTiming
r1 === r2
{2.40441, 4064607008}
True
The compiled answer uses .462KB while the approach where all the factorials are precomputed takes 4GB, and the timing is not too different. | 2019-08-24 12:43:09 | {"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": 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": 0.5452675819396973, "perplexity": 3235.7443640870365}, "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/1566027320734.85/warc/CC-MAIN-20190824105853-20190824131853-00137.warc.gz"} |
https://physics.stackexchange.com/questions/483296/can-a-syringe-be-used-as-a-hanging-scale-if-needed | # Can a syringe be used as a hanging scale if needed?
FYI: This is not a homework q; I am just curious... You can assume that...
• the syringe tip cap creates a "perfect" seal, i.e., keeps air from flowing in/out!
• the syringe is completely depressed before starting the experiment.
• the outside barrel has metric ruler.
• the syringe is hung in the following way...
Is the following equation correct for determining the mass of the weight, based on how far it causes the plunger to depress...
$$m = \frac{A\cdot B\cdot x}{a\cdot L}$$
where...
• A = Surface area of the (black) stopper face.
• B = Bulk modulus of air given temperature & atmospheric pressure readings.
• x = Plunger displacement (due to suspending weight) after waiting for a "long" time.
• a = Acceleration due to gravity.
• L = Length of syringe barrel.
• Yes, I thought about the friction... The syringe manufacturers could VERY accurately measure the force ($= F_{\text{tc off}}$) required to overcome the friction between stopper & barrel (i.e., w/ the tip cap off) engraving the outcome; then my equation would look like this... $$0 = F_{\text{tc on}} + F_m \Longrightarrow 0 = \left(\frac{A\cdot B\cdot x}{L} + F_{\text{tc off}}\right) + \left(-m\cdot a\right) \Longrightarrow m = \frac{A\cdot B\cdot x}{a\cdot L} + \frac{F_{\text{tc off}}}{a}$$ Does it still look correct, after I've made the update? – Landon Jun 2 '19 at 23:42 | 2020-06-02 05:09:05 | {"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": 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": 1, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6782485842704773, "perplexity": 2375.5344517801263}, "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/1590347422803.50/warc/CC-MAIN-20200602033630-20200602063630-00208.warc.gz"} |
https://fizzylogic.nl/2018/10/07/its-easier-than-ever-to-add-machine-learning-to-your-c-program-use-ml-net/ | In the past machine learning was something exclusively for the pythonistas or data scientists that knew how to use Python or R and had studied statistics. Not anymore, it has become a lot easier for developers to use machine learning. This also goes for .NET developers.
In april this year Microsoft launched the new ML.NET library. A library with classic machine learning algorithms implemented in C#. This means if you are programming C# you now have access to a large group of machine learning algorithms that you can use in your application.
## What makes ML.NET so interesting?
Typically when you want to use machine learning in your application you have to build something in Python or R. But that means if you are writing C# you need to switch to another language to build your machine learning application.
I personally love the idea of using just one language in a project. It makes it easier for developers on the team to take on any job that we throw at them. Also, switching languages all the time is hard and annoying. I do this a lot and I can assure you, you have to retrain your muscle memory everytime you do this.
ML.NET may be young, but has a full set of machine learning algorithms. Even cooler, if you have someone on the team that made a deep learning model in Tensorflow, you can load that into ML.NET as well.
You still need to learn about different machine learning problems and how to approach them. But at least you can do it from C#.
## Getting started with ML.NET
So how do you start? ML.NET is available as a nuget package. You can add this package to your project in two ways:
dotnet add package Microsoft.ML
Or right click your project, choose Manage nuget packages and search for Microsoft.ML. Once added you can start building your machine learning pipeline.
ML.NET uses the pipeline pattern as a way to express the process of training a model. When you build a machine learning solution you typically have these steps in your program:
1. Load data from a data source
2. Preprocess the data so that it is in a format the algorithm understands
3. Use the preprocessed data to train the model
This looks like a pipeline and that's the reason why ML.NET uses this pattern. Let's take a look at how to build a training pipeline.
First step is to build a data source for the pipeline. There are a number of loaders you can use, one of them the TextLoader.
var env = new LocalEnvironment();
ctx => (
new MultiFileSource("data/train.csv"), hasHeader: true, separator: ',');
When you call CreateReader you need to provide a lambda that will tell the loader how to get data from the CSV file into a C# type. You can go strongly typed, or just use C# 7 tuples like in the sample above.
Once you have a data source, you need to convert the data so that it fits the algorithm.
Most machine learning algorithms need floating points. Which we don't have at this point in the code. So we need to extend the pipeline.
var estimator = reader.MakeNewEstimator()
.Append(row => (
price: row.price,
style: row.style.OneHotEncoding(),
condition: row.condition,
quality: row.quality,
lotArea: row.lotArea,
type: row.style.OneHotEncoding()
));
We take the reader and append a new pipeline component to it. This pipeline component takes the incoming data from the reader and transform it.
Some properties you simply need to copy as they already have the right format. Others you have to change.
For example, take a look at the style property. In my dataset this is encoded as a string representing different styles of homes. But the machine learning algorithm expects a number. So we tell the pipeline we want our style property to be one-hot encoded. The output now contains numbers representing the different values I have in my dataset.
Now that we have the values encoded, we need to make sure we have a target value to train on and a set of features to feed into the machine learning algorithm. For this you need another step in the pipeline:
estimator.Append(row => (
price: row.price,
features: row.condition.ConcatWith(
row.quality, row.style, row.type, row.lotArea).Normalize()
)
)
The price is copied to the output of the pipeline step. The features however are made by concatenating the different properties from the input into a single vector. Each column in the output vector features represents a property we loaded earlier.
Now on to the final step, let's add the step that predicts the price of a house.
var regressionContext = new RegressionContext(env);
estimator.Append(row => (
price:row.price,
predictedPrice: regressionContext.Trainers.Sdca(
row.price,
row.features,
loss: new SquaredLoss())
));
To predict the price of a house we use a regression context. The regression context contains logic to build machine learning models that are used for regression purposes.
The predictedPrice is set by the Sdca algorithm that you initialize in this step. Additionally you need to copy the original price as well. To train the model you feed in the expected price and the features from the previous step. Additionally you need to provide a loss function. This loss function is used in the optimization of the machine learning model.
To be able to evaluate the model you need to return the expected value and the predicted value in this step. We'll get back to this later on.
Because now that you have a pipeline you can train it using the Fit method.
var data = reader.Read(new MultiFileSource("data/train.csv"));
var model = estimator.Fit(data);
First load the data using the reader. Feed this data into the estimator pipeline we built earlier. This produces a trained model.
If you want to know how well the model performs, you need to use the evaluation logic provided by the regression context.
var metrics = regressionContext.Evaluate(model.Transform(data),
row => row.price, row => row.predictedPrice);
The Evaluate method needs the real price and predicted price. You can provide this information by calling Transform method on your estimator pipeline. Next you need to provide the field for the real value and the predicted value.
The output of the Evaluate method is a set of metrics. This contains the error rate for your model and other relevant metrics.
Once a model is trained you can use it to make predictions. When making a prediction you still need to use the preprocessing stops earlier. The data doesn't come from a data source like a text file, but rather from your application.
class House
{
public float condition;
public float quality;
public string style;
public string type;
public float lotArea;
public float price;
}
class PredictedPrice
{
public float predictedPrice;
}
var predictor = model.AsDynamic.MakePredictionFunction<House, PredictedPrice>(env);
You can create a prediction function by calling AsDynamic and then MakePredictionFunction with the type information for the input and the output.
The properties on both of these types should match the fields you are using in your pipeline. In my case, I need to provide all the properties I used to train the model. Additionally, I created a PredictedPrice class with a predictedPrice property that matches the predictedPrice property that I created at the end of the pipeline.
The predictor can now be used to make a prediction:
var prediction = predictor.Predict(new House
{
lotArea = 8450,
type = "1Fam",
style = "2Story",
quality = 7,
condition = 5
});
Console.WriteLine(\$"Predicted price: {prediction.predictedPrice}");
That's it, a strongly typed machine learning pipeline to predict housing prices.
## Get adventuring, try it out!
This is the part where I have to warn you about the state of ML.NET. It is still in preview, version 0.6 is up on nuget at the moment. Which means you can use it, but things will change and break.
Probably not for your next production project. But great for experiments and projects that are starting out today.
So get adventuring and try it out! | 2019-08-21 01:47:22 | {"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": 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": 0.2704014182090759, "perplexity": 932.8797439301443}, "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/1566027315695.36/warc/CC-MAIN-20190821001802-20190821023802-00303.warc.gz"} |
https://nigerianscholars.com/past-questions/economics/question/250331/ | Home » » The demand made on each other by the agriculture and industrial sector as the ec...
# The demand made on each other by the agriculture and industrial sector as the ec...
### Question
The demand made on each other by the agriculture and industrial sector as the economy grows are reflected in?
### Options
A)
backward and forward linkages
B)
horizontal and vertical linkages
C) | 2022-07-05 13:13:13 | {"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": 0.8970240354537964, "perplexity": 5106.050913602149}, "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-2022-27/segments/1656104576719.83/warc/CC-MAIN-20220705113756-20220705143756-00526.warc.gz"} |