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http://physics.stackexchange.com/questions/2774/rotate-a-long-bar-in-space-and-get-close-to-or-even-beyond-the-speed-of-light/2797	# Rotate a long bar in space and get close to (or even beyond) the speed of light $c$ Imagine a bar spinning like a helicopter propeller, At $\omega$ rad/s because the extremes of the bar goes at speed $$V = \omega * r$$ then we can reach near $c$ (speed of light) applying some finite amount of energy just doing $$\omega = V / r$$ The bar should be long, low density, strong to minimize the amount of energy needed For example a $2000\,\mathrm{m}$ bar $$\omega = 300 000 \frac{\mathrm{rad}}{\mathrm{s}} = 2864789\,\mathrm{rpm}$$ (a dental drill can commonly rotate at $400000\,\mathrm{rpm}$) $V$ (with dental drill) = 14% of speed of light. Then I say this experiment can be really made and bar extremes could approach $c$. What do you say? EDIT: Our planet is orbiting at sun and it's orbiting milky way, and who knows what else, then any Earth point have a speed of 500 km/s or more agains CMB. I wonder if we are orbiting something at that speed then there would be detectable relativist effect in different direction of measurements, simply extending a long bar or any directional mass in different galactic directions we should measure mass change due to relativity, simply because $V = \omega * r$ What do you think? - V(with dental drill) = 14% of speed of light :-o You scared me with this. I actually had to calculate it to understand what you meant. =P – Malabarba Jan 14 '11 at 0:29 haha now that you said it, I see it's a funny statement – Hernan Eche Jan 14 '11 at 12:08 "... simply extending a long bar or any directional mass in different galactic directions we should measure mass change due to relativity". Well Michelson-Morley thought of something similar. The answer is no. We won't detect change in weight or size. By principle of relativity. Because we travel with the same speeds as the bar. – Andrei Apr 28 '11 at 21:02 Imagine a rock on a rope. As you rotate the rope faster and faster, you need to pull stronger and stronger to provide centripetal force that keeps the stone on the orbit. The increasing tension in the rope would eventually break the it. The very same thing would happen with bar (just replace the rock with the bar's center of mass). And naturally, all of this would happen at speeds far below the speed of light. Even if you imagined that there exists a material that could sustain the tension at relativistic speeds you'd need to take into account that signal can't travel faster than at the speed of light. This means that the bar can't be rigid. It would bend and the far end would trail around. So it's hard to even talk about rotation at these speeds. One thing that is certain is that strange things would happen. But to describe this fully you'd need a relativistic model of solid matter. People often propose arguments similar to yours to show Special Relativity fails. In reality what fails is our intuition about materials, which is completely classical. - I didn't understand, you say the bar will break? or that think about the bar will break is our intuition about materials? I want to know what will happend and what is the physic restriction of doing the experiment (of course I suposse something must be wrong, but I asked to know it deeper) thanks – Hernan Eche Jan 13 '11 at 15:06 @Hernan: both. The bar is not rigid. It will first bend because the signal has to travel from one end to the other; the end closer to you is already moving but the far end won't start moving until the stress wave reaches it. Also, there will be huge stress on the material in the radial direction which will eventually break it. – Marek Jan 13 '11 at 17:01 so perhaps relativity limit the posible size of things.. because if something have too much lenght it divides at first rotation because some points behave massy and breaks – Hernan Eche Jan 13 '11 at 20:00 @Hernan: actually, relativity limits the angular velocity you can get an object up to. – David Z Jan 13 '11 at 22:26 @Hernan: but remember that you'd need lot of energy to rotate that object in the first place! E.g. you'd need an infinite amount of energy to accelerate a particle to the speed of light. And that's just a particle, not a huge extended object. Second point is that in nature there are no solid objects on macroscopic scales. On the scales of galaxies there is just intergalactic dust and stars following the rules of General Relativity. – Marek Jan 13 '11 at 22:33 There is a real object with relativistic speed of surface - millisecond pulsar. The swiftest spinning pulsar currently known, spinning 716 times a second. Surface speed of such pulsar with radius 16 km is about $7*10^7$ m/s or 24% speed of light. It is calculated that pulsars would break apart if they spun at a rate of more than 1500 rotations per second. - great to know ! – Hernan Eche Jan 13 '11 at 20:03 In your calculations you assume that your propeller is a rigid body. You cannot use that assumption, when your speeds are not much smaller than the speed of light. Because "there are no rigid bodies in relativity". - MMmm this let me thinking..So..that could lead a definition of body, i.e. body can only exist in one and only one inertial frame of reference, never in two at same time – Hernan Eche Jan 13 '11 at 19:56 remember that in a three-dimensional description of special relativity the impulse of an object is given by $$\mathbf{p} = \gamma m \mathbf{v}$$ with the so-called Lorentz-factor $$\gamma = \frac{1}{\sqrt{1-v^2/c^2}}$$ Now, do you think you can accelerate the masses within the slab to a speed greater than light or do you think that something is wrong with your physical model of the system? Sincerely Robert - Nice letter, I want to know what is wrong in doing the real experiment, or thinking you can deliver energy (taking your time) and accelerate the bar (gradually) to transform that energy and angular velocity in a higher tangential velocity, angular momentum conservation will store the energy so I can continue adding more and more energy – Hernan Eche Jan 13 '11 at 15:02 Hernan writes "near c" but he did not write about "speed greater than c". – Andrei Apr 28 '11 at 21:03 @Andrei: It remains the same argumentation. Greets – Robert Filter Apr 29 '11 at 7:05 I say no. Assuming all the practicalities work, you can get arbitrarily close to c. But not reach c. You can see this easily from the relativstic formula for kinetic energy: $E_k = mc^2(\frac{1}{\sqrt{1-v^2/c^2}}-1)$ As $v$ approaches $c$, the energy you need to supply to a particle at the end of the bar tends to infinity. - The energy needed would vary in every segment of the bar because its speed would be different, so the bar would break only by relativity effects ? perhaps – Hernan Eche Jan 13 '11 at 15:14 bar would break because it" reacts" on force with the speed of sound in it, which is not more than 3000 m/s. When you cross 3000 m/s bar is like a liquid :-) – BarsMonster Jan 13 '11 at 15:47 Your assumption of "all the practicalities working" is far too big of an assumption; you're assuming away the very heart of the question, which is: can I do this using a rigid body. – Mark Beadles Dec 18 '11 at 3:41 Dear Hernan, as the distant parts of the bar are approaching the speed of light, they become heavier, so it becomes harder to accelerate them: you can never reach (or surpass) the speed of light. It doesn't matter whether you try to accelerate the "final segments" of the bar by jets or by their attachment to the rest of the bar that is being pushed in the middle: the speed of light can never be reached. If you want to speak in terms of torques and moments of inertia (of the bar), the moment of inertia goes to infinity - much like the mass itself - when the velocity of some points on the bar approaches the speed of light. So much like you have to modify the formulae for masses of moving objects by relativistic effects, you need to modify the formulae for the moments of inertia. So your statement that you need a finite energy to get to the speed of light is invalid. You would need an infinite energy. For speeds below the speed of light, the total energy that you need can simply be calculated as the sum of the kinetic energies of all the segments of the bar. - ## protected by Qmechanic♦Oct 13 at 5:31 Thank you for your interest in this question. Because it has attracted low-quality answers, posting an answer now requires 10 reputation on this site. 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https://paytonspace.org/vanguard-direct-wob/bera-test-wikipedia-30c27e	"[2], Gyeney stated, "I'm not Steven Spielberg," while indicating that there would be no auditions or screen tests for the film. 1. The test is named after Carlos Jarque and Anil K. Bera. Bera-De was a female Voss historian who lived on Voss during the Galactic War between the Galactic Republic and the reconstituted Sith Empire.She guarded the entrance to the Shrine of Healing, where she asked the outsiders seeking to enter, to find and learn from Mystic writings in the nearby ruins so that they could better understand the role of the Mystics. {\displaystyle {\hat {\mu }}_{3}} In Section 5 we describe the results concerning the size of the test, while power is analysed in Section 6. {\displaystyle {\bar {x}}} Bera test, while in section 3 we present our “sample” methodology. As virtual and real worlds collide, Max and Creed must join forces to unravel the conspiracy before the game's sinister events escalate and overwhelm the city. Bera Kazan joined the war on the si… This page was last edited on 12 July 2020, at 12:56. {\displaystyle {\hat {\sigma }}^{2}} Bera could refer to: Bera-De, a female Voss Mystic Bera Jeza, a female Aqualish Bera Kazan, a female Human smuggler This is a disambiguation pagea navigational aid that lists other pages that might otherwise share the same title. Finally, a brief summary and conclusions are presented in Section 7. [7], Seattle was chosen as the place to shoot the film because it is Gyeney's hometown and he believed "shooting such a movie in the Northwest will diversify the local film community, which is mostly dominated by indie dramas. According to Robert Hall, David Lilien, et al. These waves are studied for latency, periodicity, and other characteristics. Other readers will always be interested in your opinion of the books you've read. According to Robert Hall, David Lilien, et al. Jarque-Bera Test for Normality. The film was released on July 22, 2016. Construct Jarque -Bera test . Get your query answered 247 only on \| Practo Consult Bera may refer to:. The BERA diagnostic procedure was applied in 184 children ranging from 1 to 12 years of age at Ahmadi Hospital in Kuwait. and Scripts were sent out to actors whom Gyeney was familiar with, and those of whom liked the script with interest of being in the film were cast. σ The film stars Larenz Tate, Manu Bennett, Linden Ashby, and Yuji Okumoto. In statistics, the Jarque–Bera test is a goodness-of-fit test of whether sample data have the skewness and kurtosis matching a normal distribution. In their review for The Hollywood Reporter, Frank Scheck praised the film for being "impressively choreographed and filmed", though criticized the film for choosing technology over realism, as well as exploiting real life tragedies such as 9/11. (These values have been approximated using Monte Carlo simulation in Matlab), In MATLAB's implementation, the chi-squared approximation for the JB statistic's distribution is only used for large sample sizes (> 2000). 27 yrs old Female asked about Bera test result, 1 doctor answered this and 1745 people found it useful. Jarque–Bera test, Anderson–Darling test, Cramér–von Mises criterion, Kolmogorov–Smirnov test (this one only works if the mean and the variance of the normal are assumed known under the null hypothesis), Lilliefors test (based on the Kolmogorov–Smirnov test, adjusted for when also estimating the mean and variance from the data), BERA is objective test of hearing in which electric potential are recorded from entire hearing pathways in the form of different wave patterns in response to sound stimulus. It could lead to an entire wave of action-oriented material being shot here, which would bring tons of work to local stunt teams and stuff that is totally nonexistent right now. Manu Bennett as the hero video game character, Orson Creed. The measured recording is a series of six to seven vertex positive waves of which I through V are evaluated. for 4-6 Months. For smaller samples, it uses a table derived from Monte Carlo simulations in order to interpolate p-values.[1]. {\displaystyle {\hat {\mu }}_{4}} Recent Development in the Econometrics of Panel Data . The Jarque-Bera test is a two-sided goodness-of-fit test suitable when a fully specified null distribution is unknown and its parameters must be estimated. INTRODUCTION Consider a series {Xt}T t=1 with mean µ and standard devia-tion σ. Results were verified with R's tseries package. white test for heteroskedasticity eviews, You can write a book review and share your experiences. This isn't just true for the Jarque-Bera test, and while it isn't quite true for all hypothesis tests (consider tests on discrete distributions such as a binomial proportion test or Poisson mean test) "the p-value is equally likely to be anywhere from 0 to 1" is usually a good … A monumental moment for me, filming what is currently the longest single shot choreographed fight sequence ever", "Hanging with the animation team for Beta Test, creating the video game footage for the film...", https://en.wikipedia.org/w/index.php?title=Beta_Test_(film)&oldid=967300734, Articles with self-published sources from August 2017, Articles with dead external links from May 2020, Articles lacking reliable references from May 2020, Creative Commons Attribution-ShareAlike License. Sara Coates as Abbie Creed, Orson's wife. [10], Learn how and when to remove this template message, "Northwest Wanderings. Bera, Anil K., Sosa-Escudero, W. and Yoon, M. (2003). ' People. Gyeney started developing Beta Test in the summer of 2014. [2], Larenz Tate was cast as the protagonist, Max. If the data comes from a normal distribution, the JB statistic asymptotically has a chi-squared distribution with two degrees of freedom, so the statistic can be used to test the hypothesis that the data are from a normal distribution. μ "[6][8][better source needed], Video game footage was needed to be developed for the film after principal photography was completed. Whether you've loved the book or not, if you give your honest and detailed thoughts then … Prior to the outbreak of the Clone Wars in late 22 BBY, Bera Kazan was a criminal who engaged in illegal activities in order to gain credits. The test is named after Carlos Jarque and Anil K. Bera. is the sample mean, and The statistic was derived by Carlos M. Jarque and Anil K. Bera while working on their Ph.D. Thesis at the Australian National University. Our goal is to destroy that record. "tseries: Time Series Analysis and Computational Finance", "moments: Moments, cumulants, skewness, kurtosis and related tests", "JarqueBeraALMTest—Wolfram Language Documentation", Multivariate adaptive regression splines (MARS), Autoregressive conditional heteroskedasticity (ARCH), https://en.wikipedia.org/w/index.php?title=Jarque–Bera_test&oldid=996294038, Creative Commons Attribution-ShareAlike License, This page was last edited on 25 December 2020, at 18:22. [5][dead link], Gyeney provided information on the film stating "this film has 127 scenes and with [my] Type-A personality, I have a very specific vision. From Wikipedia, the free encyclopedia In statistics, the Jarque–Bera test is a goodness-of-fit test of whether sample data have the skewness and kurtosis matching a normal distribution. He soon determines that the game's protagonist is real-life Orson Creed, an ex-Sentinel employee who is being remotely controlled by the corporation for reasons unknown. (1995) when using this test along with multiple regression analysis the right estimate is: where n is the number of observations and k is the number of regressors when examining residuals to an equation. Moves the Jarque-Bera test for normality from TimeModels as discussed in #16. And, Linden Ashby as Kincaid, the primary villain of the film. [6] It took place over 19 days[2] starting November 7. ¯ Brainstem Evoked Response Audiometry ini adalah pemeriksaan untuk melihat ambang dengar pada telinga anak. This leads to a large Type I error rate. For small samples the chi-squared approximation is overly sensitive, often rejecting the null hypothesis when it is true. From tables critical value at 5% level for 2 degrees of freedom is 5.99 So JB>c2 critical, … In addition to that job, she was also secretly working for the Hutt Crime lord Jabba Desilijic Tiure. • Brainstem evoked response audiometry, a screening test to monitor for hearing loss or deafness Plot. The test statistic is always nonnegative. He also criticized the "outdated visual style" of the graphics, which would be noticed by hardcore gamers, whom this film is targeted towards. ジャック＝ベラ検定（ジャック＝ベラけんてい、英: Jarque–Bera test ）とは、統計学において標本データが正規分布に従う尖度と歪度を有しているかどうかを調べる適合度検定である。検定名はCarlos JarqueとAnil K. Beraにちなんで名づけられた。 Gyeney described the film as a cross between Die Hard, Gamer, and The Firm. ^ μ Samples from a normal distribution have an expected skewness of 0 and an expected excess kurtosis of 0 (which is the same as a kurtosis of 3). 1 Biography 2 Appearances 3 Notes and references 4 External links Bera Jeza had a job as lab assistant for Mos Eisley Biolab, based in Mos Eisley, on the planet Tatooine. Wikipedia article “Jarque–Bera test” as of Jan. 27, 2015, says that MATLAB uses the χ2 approximation only for n > 2,000, and a table based on Monte Carlo simulations for smaller n. The diﬃculty of ﬁnding accurate p-values seems to imply that it will also be hard to ﬁnd correctly the power of the Jarque–Bera test In addition to her occupation as a mercenary, Kazan also worked as a smuggler which she found to be a hazardous occupation, given the damage sustained to her personal starship—the Sarpazian Rose—after numerous clone encounters with death. [3] The film stars Larenz Tate, Manu Bennett, Linden Ashby, and Yuji Okumoto. ^ Senin, 24 Oktober 2011 . (1995) when using this test along with multiple regression analysis the right estimate is: Ad ogni modo, se non vuoi scaricare un nuovo package nella versione base di R è presente la funzione shapiro.test() che implementa il test di normalità di Shapiro-Wilks, che è più robusto di Jarque & Bera. Some of the Amador County residents who participated in the We Are One rally in Sacramento on Monday the 4th, 2011 were David Roddy and Mike Israel, Nora Coryell and Mike Pulskamp, and Janet Kendig, along with several others. Bera Jeza was a female Aqualish lab assistant working during the Galactic Civil War. is the estimate of the second central moment, the variance. where n is the number of observations (or degrees of freedom in general); S is the sample skewness, K is the sample kurtosis : where The auditory brainstem response (ABR) is an auditory evoked potential extracted from ongoing electrical activity in the brain and recorded via electrodes placed on the scalp. Furthermore, the distribution of p-values departs from a uniform distribution and becomes a right-skewed unimodal distribution, especially for small p-values. If it is far from zero, it signals the data do not have a normal distribution. The Jarque–Bera test is comparing the shape of a given distribution (skewness and kurtosis) to that of a Normal distribution. 3 2 If it is far from zero, … ^ As the definition of JB shows, any deviation from this increases the JB statistic. by Meta Hanindita in Our Stories. Bera (Bible), king of Sodom in Genesis 14 Bera, Count of Barcelona (died 844), the first count of Barcelona from 801 to 820; Bera, a Surname among the Mahishya community of West Bengal state of India; Places. DSA connection. The test statistic is always nonnegative. The test statistic JB is defined as normality test, and illustrates how to do using SAS 9.1, Stata 10 special edition, and SPSS 16.0. The null hypothesis is a joint hypothesis of the skewness being zero and the excess kurtosis being zero. Gyeney described the film as a cross between Die Hard, Gamer, and The Firm. Per una descrizione di questo test puoi consultare un qualsiasi libro di inferenza, o anche wikipedia. They endorsed him again in 2012, and 2014. 4 In statistics, the Jarque–Bera test is a goodness-of-fit test of whether sample data have the skewness and kurtosis matching a normal distribution. Beta Test is a 2016 American film written, produced, and directed by Nicholas Gyeney. Behind the scenes of "Beta Test, "I guess it's about time I let you all know what we've been up to ...", "Mill Creek filmmaker returns home to create his craft", "A little peek at the "long take". Beberapa saat yang lalu, saya mengantarkan Nayara(5mo) menjalani pemeriksaan BERA. Test for Error Component Model in the Presence of Local Misspecification '. [6], Principal photography was conducted in Seattle, Washington. If an article link referred you here, you might want to go back and fix it to point directly to the intended page. The film was released on July 22, 2016.[4]. Section 4 presents the design of our Monte Carlo experiment. The tests are applied to 21 macroeconomic time series. While testing the latest first person shooter from global game developer, Sentinel, video game champion Max Troy discovers the events happening within the game are being reflected in the real world. x test of normality provided that the limiting variance accounts for the serial correlation in the data. BERA is an electro-physiological test procedure which studies the electrical potential generated at the various levels of the auditory system starting from cochlea to cortex. The more than 5,000 strong Sacramento Progressive Alliance endorsed Ami Bera in 2010.. Beta Test is a 2016 American film written, produced, and directed by Nicholas Gyeney. This function applies the test for normality proposed in Jarque and Bera (1980). It began in December 2014 starting with the character, Creed. jb = (379/6)((1.50555^2)+(((6.43 -3)^2)/4)) = 328.9 The statistic has a Chi 2 distribution with 2 degrees of freedom, (one for skewness one for kurtosis). KEY WORDS: Jarque–Bera test; Kurtosis; Normality; Symmetry. Brainstem Evoked Response Audiometry (BERA) is an objective test to understand the transmission of electrical waves from the VIIIth cranial nerve to … The table below shows some p-values approximated by a chi-squared distribution that differ from their true alpha levels for small samples. "[6], Gyeney stated, "the longest long-take fight sequence currently on record is three-and-a-half minutes, and it's held by the Korean movie 'Oldboy.' The test is named after Carlos Jarque and Anil K. Bera. BERA Test. [9][better source needed], The film was released on July 22, 2016. This investigation was first described by Jewett and Williston in 1971. Order to interpolate p-values. [ 1 ] Orson Creed # 16 Audiometry adalah. We present our “ sample bera test wikipedia methodology was conducted in Seattle, Washington, Principal photography was conducted Seattle.: Jarque–Bera test ; kurtosis ; normality ; Symmetry, Stata 10 special edition, and illustrates to. It is true, 2014 share your experiences ] starting November 7,.. Other readers will always be interested in your opinion of the books you 've read the shape of a distribution! ], Principal photography was conducted in Seattle, Washington ). Seattle, Washington Galactic Civil War heteroskedasticity,. 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Sanding Sealer Homebase, Song With Sparrows In The Lyrics, Albright College Art Department, Almirah Meaning In Urdu, Community Helpers Worksheets Grade 1 Pdf, Elsa Hair Wig, Dj Zinhle Husband, Hks Exhaust Civic Si, Samford Housing Contract,	2022-05-25 11:14:53	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.42660653591156006, "perplexity": 5498.996486171563}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662584398.89/warc/CC-MAIN-20220525085552-20220525115552-00764.warc.gz"}
http://mathhelpforum.com/algebra/7129-quadratics-inequalities-square-forms.html	1. ## Quadratics, Inequalities and Square Forms Just a few questions I need help on so I can do the rest of my homework. I have a question which I dont understand very well, the question is 'Solve the following inequalities by sketching by hand the curves of the functions involved' I dont understand exactly what to do with say an equation like p^2-5p+4<0 and 3x^2+5x-2<0 Square Form How would I do: 2x^2+4x+6 -x^2-2x+5 -x^2+3x+10 2. Originally Posted by Yppolitia Just a few questions I need help on so I can do the rest of my homework. I have a question which I dont understand very well, the question is 'Solve the following inequalities by sketching by hand the curves of the functions involved' I dont understand exactly what to do with say an equation like p^2-5p+4<0 and 3x^2+5x-2<0 Square Form How would I do: 2x^2+4x+6 -x^2-2x+5 -x^2+3x+10 Well, for starters you haven't given us an inequality to solve... Let's assume we have $2x^2 + 4x - 6 > 0$. The first way to do this is to sketch the graph of $y = 2x^2 + 4x - 6$ and then see where y > 0. By looking at the graph below (hopefully it will load) you can see what the solution set will be: $(-\infty, -3) \cup (1, \infty)$. The other way: We wish to find the critical points of the function $2x^2 + 4x - 6$. These are the points where: 1) The function is 0. 2) The denominator is 0. 3) The function under the radical is 0. For this function, the only critical points are where the function is 0. So solve: $2x^2 + 4x - 6 = 0$ Divide both sides by 2: $x^2 + 2x - 3 = 0$ $(x + 3)(x - 1) = 0$ So x = -3 and x = 1 are the critical points. Now we want to break the real line into intervals and test the inequality on each interval: $(-\infty, -3)$: $2x^2 + 4x - 6 > 0$ (Check!) $(-3, 1)$: $2x^2 + 4x - 6 < 0$ (Nope!) $(1, \infty)$: $2x^2 + 4x - 6 > 0$ (Check!) So we see the solution set is: $(-\infty, -3) \cup (1, \infty)$ as we saw from the graph. -Dan 3. So for the answer of the quesiotn, please write i completed square form '2x^2+4x+6' what do I put? 4. Originally Posted by Yppolitia So for the answer of the quesiotn, please write i completed square form '2x^2+4x+6' what do I put? Alright, perhaps I didn't understand what you meant. I had thought your question was about how to solve quadratic inequalities. Can you give me an example of what you mean by "write i completed square form '2x^2+4x+6' " The only other thing I can think of is to rewrite $2x^2 + 4x + 6$ as: $2x^2 + 4x + 6$ $2(x^2 + 2x + 3)$ $2((x^2 + 2x) + 3)$ $2((x^2 + 2x + 1 - 1) + 3)$ $2((x^2 + 2x + 1) - 1 + 3)$ $2((x - 1)^2 + 2)$ $2(x + 1)^2 + 4$ This method is called "completing the square." Is this what you mean? -Dan 5. Yes, thats right So how would something like -x^2+3x+10 be done because Im not sure how to do an equation with a -x^2 instead of a more common x^2. 6. Originally Posted by Yppolitia Yes, thats right So how would something like -x^2+3x+10 be done because Im not sure how to do an equation with a -x^2 instead of a more common x^2. What I always do is factor the coefficient of the $x^2$ term: $-x^2 + 3x + 10$ $-(x^2 - 3x - 10)$ Then isolate the quadratic and linear x terms: $-((x^2 - 3x) - 10)$ Then add and subtract the constant that completes the square in the parenthesis. Since the coefficient of the $x^2$ term is always 1, take the linear coefficient (-3 in this case), divide by 2 then square it: $-\left ( \left ( x^2 - 3x + \frac{9}{4} - \frac{9}{4} \right ) - 10 \right )$ $-\left ( \left ( x^2 - 3x + \frac{9}{4} \right ) - \frac{9}{4} - \frac{40}{4} \right )$ Now simplify: $-\left ( \left ( x - \frac{3}{2} \right )^2 - \frac{49}{4} \right )$ $- \left ( x - \frac{3}{2} \right )^2 + \frac{49}{4}$ -Dan	2013-05-20 00:34:05	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 31, "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": 0.8660560250282288, "perplexity": 459.9630297519718}, "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/1368698196686/warc/CC-MAIN-20130516095636-00052-ip-10-60-113-184.ec2.internal.warc.gz"}
http://motls.blogspot.com/2008/08/oxygen-crisis.html	## Sunday, August 17, 2008 ... ///// ### The oxygen crisis Most mainstream media have abandoned almost all quality control in their science reporting that is now arguably slightly below the image of science as presented in the leading pornographic magazines. The latest extreme example of this observation comes from a Gentleman called Peter Tatchell, a political campaigner from the left wing of the Green party (a description that probably makes Karl Marx a staunch conservative in comparison; he's been also denounced by the British Parliament as a "homosexual terrorist" in 1994): The Guardian, China Daily He argues that there exists a more serious crisis than the "CO2 crisis": the oxygen levels are dropping and the human activity has decreased them by 1/3 or 1/2, he says. Wow. ;-) The reality is, of course, that the oxygen percentage in the atmosphere has been 20.94 or 20.95 percent for thousands of years and probably much longer than that (see the historical graph on page 2 of Dudley 1998 that covers 600 million years). The amount of oxygen in the atmosphere is so huge that the biosphere (and fossil fuels which used to belong to the biosphere as well) is completely unable to change this amount significantly. It may be useful to mention that the oxygen is only 1/5 of the atmosphere and the atmosphere is just 1/1,200,000 of the mass of the Earth. However, the Earth is damn heavy, 6 x 10^{24} kilograms, so the mass of the oxygen in the atmosphere is something like 10^{18} kilograms - about 150,000 tons per capita. Be sure that we can't burn that much oxygen even if everyone in the world were using a private jet on a daily basis. ;-) There is a simpler way to see that man-made changes to the oxygen levels are trivial and we will look at it now. Estimating the oxygen change For a schoolboy who is not skipping his science classes at the elementary school, it shouldn't be difficult to see why we can't significantly influence the amount of oxygen in the atmosphere. How can he do it? Well, he must realize that virtually all processes related to life and human activity - breathing (by animals and plants) and burning (combustion) - exchange the atmospheric O2 molecules by CO2 molecules or vice versa. Sometimes, one needs two O2 molecules and only produces one CO2 molecule but this subtlety won't change our final result significantly. Virtually all other compounds participating in the relevant chemical reactions are either liquids or solids which is why they don't influence the composition of the atmosphere and we will ignore them. When you realize what the words above mean, you will see that the man-made decrease of oxygen (O2) is controlled by the increase of carbon dioxide: they're inseparably linked to one another. The human activity has increased the CO2 concentration from 280 ppm two centuries ago to 385 ppm today (the schoolboy should have seen these elementary numbers during his "CO2 crisis" classes). Because many people don't know what the acronym ppm (parts per million) really means, even if they like to use it, let me tell you that it is the same thing as 0.0001%. So the carbon dioxide went from 0.028% to 0.038%: the difference is 0.01% of the volume of the atmosphere. Because O2 and CO2 molecules occupy the same volume at a given pressure and a given temperature (since pV = NkT), the decrease of O2 should be equal to the increase of CO2 if the molecules were exchanged for one another: the oxygen should drop by 0.01% of the volume of the atmosphere. As we have already mentioned, two oxygen molecules are replaced in typical "combustion" chemical reactions for one carbon dioxide molecule, so the oxygen drop might be 0.02% instead of 0.01%. However, in the long run, there exist other processes besides the combustion-like processes involving CO2 that we have considered - for example processes involving deep ocean sediments - and these processes tend to restore the oxygen levels (as well as the CO2 levels). At any rate, you see that the oxygen level couldn't have decreased by more than 0.01% or so, from 20.95% to 20.94%, which is pretty much exactly what was observed. We needed centuries or millenia to achieve this modest "goal". It is very clear that even if we burned all forests, plants, animals, and fossil fuels in the world, we couldn't get the oxygen levels below 20% (and maybe not even 20.9%). Evaluating the impact Does the tiny decrease of oxygen levels change some important things? It doesn't. The most "spectacular" change is that the wildfire risk decreases by something like 0.01%, too (and maybe slightly more), as the oxygen levels drop. Because wildfires are somewhat unpopular and their decrease would be good news, you won't read about it. ;-) At any rate, all these changes are negligible given the tiny change of the O2 levels. Tatchell writes "I am not a scientist, but this seems a reasonable concern." It seems reasonable to whom? To me, worries about the "oxygen crisis" seems to be a ticket for someone to be stored in a mental asylum. The point here is not whether Tatchell is a scientist: he's clearly not. The question is whether he is dangerous enough a weirdo to be isolated from the society. We won't be able to change the oxygen level in any significant way. Incidentally, while the overall amount of oxygen in the atmosphere is essentially constant, the amount of oxygen in various parts of organisms varies dramatically. For example, the human body must keep the concentration of this harmful-if-abundant gas around 5% in most organs. Oxygen is not only a corrosive gas but also a metabolic poison under most cellular reactions. Its optimal percentage depends on the life forms which is why the varying percentage of oxygen in amber - a point mentioned by Tatchell - says absolutely nothing about the overall O2 volume. Men have been able to change the overall carbon dioxide (CO2) concentrations measurably because it is a trace gas: there was almost none to start with, so it is easy to change its volume by relatively large amounts, proportionally speaking. But oxygen is one of the gases that the Earth's atmosphere has been made out of for 0.5 or even 2.5 billion years. You can't change that. Incidentally, if you care how the oxygen became so important, probably 500 million years ago, the Earth needed an intense period of upheavals in its crust and it still took about 2 million years for all the change to materialize: see Science Daily. This rate is very fast from a geologist's viewpoint but surely not fast enough to be considered an urgent problem for policymakers. ;-) Other errors Tatchell writes a lot of other incredible nonsense, for example that the oxygen in cities is much (by 15%?) lower than it is in the countryside. He probably believes that the pressure drops from 1000 to 900 millibars in the cities. ;-) He also tries to pretend that some scientists support his idiotic propositions. Gimpy, who respects Tatchell's courage, explains that Tatchell has all the symptoms that define a crank. He satisfies most of my defining criteria of crackpots, too. Is someone at the Guardian who has some common sense left? Could you please stop printing insane people like Peter Tatchell who help to transform your daily into an expensive and dirty piece of toilet paper? #### snail feedback (7) : In regard to your conclusions about atmospheric 02 levels in the recent past- Figure #1 of the Dudley paper quoted above shows that atmospheric O2 levels have ranged from around 13% up to around 35%. It would appear to be extraordinarily difficult to determine atmospheric O2 levels for the previous "thousands of years and probably much longer than that" from a chart with a time axis of 600 million years presented within a span of 2 inches or so. I would suggest it is better to analyze and critique the data Mr. Tatchell used to form his opinion, rather than by contrasting his point of view with an inaccurate assessment of a scientific paper. Dear John, I don't exactly know what data Mr Tatchell used to form his opinion. The only thing I know is that he has either used wrong data or he has interpreted correct data incorrectly. Incidentally, the Dudley chart I linked to is enough to support the statement I wrote. Notice that the changes are smooth and it takes hundreds of millions of years to achieve the changes indicated in the graphs (a few percent, up to 10 or so as a maximum). In a few millenia, you won't simply change it by more than a tiny fraction of a percent. I insist on what I wrote and I insist that Mr Tatchell's writing is complete insanity of a person with rudimentary misunderstanding of science and the real world. Atmospheric oxygen is also eliminated from the mix by fresh lava flows, landslides, clay and soil formation, farm tilling, ditch digging, calcination of cement; oxidation of freshly exposed faces of road cuts and open pit mines, and oxidation of foundry metals, etc. It might be that CO2 levels have not not risen, but that 02 levels have fallen due to processes other than respiration/combustion. C02 may have changed because the ocean has warmed- outgassing C02. As the planet cools, it's possible that C02 could decrease- wouldn't that be a major embarassment for some folks. But a large asteroid could burn up some oxygen, I suppose. There actually is a real oxygen crisis happening now: Oxygen levels have dropped roughly 20 percent off the Southern Californian coast over the past 25 years. Scientists estimate that oxygen levels overall may have declined by one-third over 50 years. NASA reports that in the north Pacific Ocean oxygen-producing phytoplankton concentrations are 30 percent lower today, compared to even the 1980s. The UN Environment Program said in 2004 that there were nearly 150 "dead zones" in the world's oceans. Lloyd V. Berkner was one of the world's top scientists with NASA. He pointed out that diatoms, which are microscopic plants in the oceans provide more than half of the world's oxygen for us to breathe and are being destroyed in oil spills. He wrote that it would only take a relatively small number of such disasters, in the wrong places, at the wrong times, to trigger a sudden and irreversible drop in the world's oxygen levels. Such an event could occur very rapidly. Half of the world's oxygen is produced via phytoplankton photosynthesis. The probable effects of increased UV radiation as the primary result of ozone depletion includes the destruction of phytoplankton at the base of the food chain and this may become a grave matter within a few decades. Professor Ian Plimer of Adelaide University and Professor Jon Harrison of the University of Arizona accept that oxygen levels in the atmosphere in prehistoric times averaged 35 percent compared to only 21 percent today. Levels are lower in densely populated, polluted city centers and industrial complexes. OSHA rules on atmospheres in closed environments state, "if the oxygen level in such an environment falls below 19.5% it is oxygen deficient, putting occupants of the confined space at risk of losing consciousness and death." Scientists from CSIRO have measured the decline in oxygen that has occurred during the past 20 years, the longest period over which such an assessment has been made. The team analyzed air dating back to 1978 from CSIRO's unique archive of pristine air collected at the remote Cape Grim Baseline Air Pollution Station operated by the CSIRO and Bureau of Meteorology in northwestern Tasmania. The oxygen reduction is just 0.03 percent in the past 20 years. Langenfelds stated. So, we can all breath easy. On the other hand, we can also be mindful of the pitfalls of hubris. In forty years, the population has doubled to over 6 billion people and is predicted to double again within the next twenty years or less. 150,000 tons of available oxygen per capita as mentioned will be very soon a somewhat less respectable 75,000 tons per capita. One human may breathe 100 tons of oxygen in one lifetime and this should be no cause of alarm. But, where merely adding a single additional fact may so easily deprive a single person of 75,000 tons of oxygen, it may still be well worth weighing carefully the possibility of the unforeseen. In the overall context, it is my view that the margins of safety are slight enough to warrant at least a prudent caveat: Any manner of analysis of such a matter that does not take into account the possibility of catastrophic change, where such appears possible, may readily engender unintentionally flawed conclusions. The problem is not of oxygen levels of atmosphere but of dissolved oxygen levels of water.	2014-10-23 12:21:46	{"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": 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": 0.40923914313316345, "perplexity": 1502.6363632418027}, "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-2014-42/segments/1413558066290.7/warc/CC-MAIN-20141017150106-00074-ip-10-16-133-185.ec2.internal.warc.gz"}
https://www.physicsforums.com/threads/formatting-of-mathematical-content.229035/	# Formatting of mathematical content 1. Apr 15, 2008 ### gop Hi I would like to create sort of a spark chart where I put some formulas that I often forget etc... I usually would use LaTex or Lyx to write mathematical formulas; however, I have not found a easy way to do the formatting (place different "boxes" of equations to some arbitrarily defined place on the page, color, borders, etc..). Is there an easy way in LaTex I'm not aware of or can anybody recommend another program for such a task? thx 2. Apr 15, 2008 ### robphy 3. Apr 15, 2008	2017-05-23 11:08:24	{"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": 0.8635563254356384, "perplexity": 2086.654087753424}, "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-2017-22/segments/1495463607620.78/warc/CC-MAIN-20170523103136-20170523123136-00408.warc.gz"}
https://www.skepticalcommunity.com/viewtopic.php?f=5&t=38541	Snake oil We are the Borg. Witness Posts: 18847 Joined: Thu Sep 19, 2013 5:50 pm Snake oil PowerMax™ Plus mains cable The benefit of all this care taken in the manufacture? We believe that the cable represents astonishing value as it helps your system to get the power it needs exactly when it needs it. Expect deeper, more realistic bass, clearer instruments and voices and a smoother sound. We've even seen Home Cinemas benefiting, with pictures appearing sharper and crisper. http://www.russandrews.com/product.asp? ... ZOSRJSTDPN From £46.75 asthmatic camel Posts: 18375 Joined: Sat Jun 05, 2004 1:53 pm Title: Forum commie nun. Location: Stirring the porridge with my spurtle. Re: Snake oil I miss jj at times like this. Shit happens. The older you get, the more often shit happens. So you have to try not to give a shit even when you do. Because, if you give too many shits, you've created your own shit creek and there's no way out other than swimming through the shit. Oh, and fuck. Anaxagoras Posts: 23282 Joined: Wed Mar 19, 2008 5:45 am Location: Yokohama/Tokyo, Japan Re: Snake oil Fools and their money A fool thinks himself to be wise, but a wise man knows himself to be a fool. William Shakespeare sparks Posts: 14653 Joined: Fri Oct 26, 2007 4:13 pm Location: Friar McWallclocks Bar -- Where time stands still while you lean over! Re: Snake oil Seconded Anax. You can lead them to knowledge, but you can't make them think. asthmatic camel Posts: 18375 Joined: Sat Jun 05, 2004 1:53 pm Title: Forum commie nun. Location: Stirring the porridge with my spurtle. Re: Snake oil Back in the days when I was running a live music bar, forgetful musicians would often ask to borrow my kettle lead to power their enormously loud amplifiers. I'd keep a couple in reserve for really forgetful musicians. They worked just as well as the expensive gear as far as anyone could tell. SHRUG Shit happens. The older you get, the more often shit happens. So you have to try not to give a shit even when you do. Because, if you give too many shits, you've created your own shit creek and there's no way out other than swimming through the shit. Oh, and fuck. Witness Posts: 18847 Joined: Thu Sep 19, 2013 5:50 pm Thank you, AC, for the "kettle plug" explanation/expression, which I will hoard next to "spurtle". Googling around on the oily snake subject I wondered what that was. I presume it is more British than U$? (Tea & boiling water, &c.) That kind of technoid woo could be interpreted as: – a voluntary tax on stupidity; – collected, XVIIIth century style, by private persons (here the seller of the Miracle Kettle Plug[TM]). asthmatic camel Posts: 18375 Joined: Sat Jun 05, 2004 1:53 pm Title: Forum commie nun. Location: Stirring the porridge with my spurtle. Re: Snake oil Yeah, they're commonly known as kettle plugs in Britain as that's where most people are accustomed to seeing them. Exactly the same thing powers my PC, monitor, printer, steam cleaner and HiFi amplifier. They all handle the same amount of power but don't have fancy blue cables at an extra cost of £45. As Anax says, fools and their money... Shit happens. The older you get, the more often shit happens. So you have to try not to give a shit even when you do. Because, if you give too many shits, you've created your own shit creek and there's no way out other than swimming through the shit. Oh, and fuck. Anaxagoras Posts: 23282 Joined: Wed Mar 19, 2008 5:45 am Location: Yokohama/Tokyo, Japan Re: Snake oil Other than the subjective claims they make about the sound quality allegedly being improved, I don't see what's so special about the cables. They aren't made of or even plated with a precious metal like gold, silver or platinum: Its high performance in Hi-Fi and Home Cinema systems is thanks to its large gauge conductors which Kimber Kable have optimised for mains voltages, and the unique UK mains plug and IEC connector we've developed specifically for the cable that feature fully nickel-plated contacts. We've really gone to town with the plugs; we've worked with a plug manufacturer to nickel plate all the pins in the mains plug and all parts of the IEC plug terminals as part of manufacturing process. And to top off the high quality cable and plugs, we've perfected a technique of mechanically locking the cable to the plugs "Fully nickel-plated contacts"? Is there anything unusual about that? Nickel is a fairly cheap industrial metal isn't it? "mechanically locking the cable to the plugs"? Again, that should be true for all power cables, even the cheap ones. These seem to be features that are actually commonplace and usually not even worth mentioning as a sales point. A fool thinks himself to be wise, but a wise man knows himself to be a fool. William Shakespeare Rob Lister Posts: 20290 Joined: Sun Jul 18, 2004 7:15 pm Title: Incipient toppler Location: Swimming in Lake Ed Re: Snake oil In the late 70's, we used to refer to those as HP Standards because all of our HP test equipment used those plugs exclusively. We'd have racks with spare dozens hanging. Other manufacturers used a mishmash of different plugs and that was burdensome. Nickel plated contacts? Pretty much the standard, I thought. But for sound equipment? Inferior! It would cause a harmonic imbalance resulting in 'tinny' basses and flimsy mids. Rhodium is the plating of choice. asthmatic camel Posts: 18375 Joined: Sat Jun 05, 2004 1:53 pm Title: Forum commie nun. Location: Stirring the porridge with my spurtle. Re: Snake oil You're full of shit, Lister. Shit happens. The older you get, the more often shit happens. So you have to try not to give a shit even when you do. Because, if you give too many shits, you've created your own shit creek and there's no way out other than swimming through the shit. Oh, and fuck. Rob Lister Posts: 20290 Joined: Sun Jul 18, 2004 7:15 pm Title: Incipient toppler Location: Swimming in Lake Ed Re: Snake oil asthmatic camel wrote:You're full of shit, Lister. Ya think? Abdul Alhazred Posts: 73385 Joined: Mon Jun 07, 2004 1:33 pm Title: Yes, that one. Location: Chicago Re: Snake oil What makes the music sound better? No not rhodium plating ... Any man writes a mission statement spends a night in the box. -- our mission statement plappendale Tiosylanyl Posts: 5007 Joined: Tue Feb 27, 2007 12:31 am Title: The Three-eyed Raven Location: Beyond the Wall Re: Snake oil This shit has gone on with HDTVs for a while, particularly with the Monster cable brand. Rob Lister Posts: 20290 Joined: Sun Jul 18, 2004 7:15 pm Title: Incipient toppler Location: Swimming in Lake Ed Re: Snake oil Tiosylanyl wrote:This shit has gone on with HDTVs for a while, particularly with the Monster cable brand. I forgot the brand but I got a set of two 10-foot hdmi cables from k-mart for$15. I still felt used. Tiosylanyl Posts: 5007 Joined: Tue Feb 27, 2007 12:31 am Title: The Three-eyed Raven Location: Beyond the Wall Re: Snake oil Rob Lister wrote: Tiosylanyl wrote:This shit has gone on with HDTVs for a while, particularly with the Monster cable brand. I forgot the brand but I got a set of two 10-foot hdmi cables from k-mart for $15. I still felt used. Monoprice has the best HDMI cables for your money as far as I'm concerned. silverdrake Posts: 1611 Joined: Tue Jul 23, 2013 5:00 am Title: Girlie Girl Location: Right here Re: Snake oil My Monster cables are gold-plated. Rob Lister Posts: 20290 Joined: Sun Jul 18, 2004 7:15 pm Title: Incipient toppler Location: Swimming in Lake Ed Re: Snake oil silverdrake wrote:My Monster cables are gold-plated. I have a set of gold plated carbide tipped jewelers screwdrivers in a mahogany case. My 'boyz in shop' gave them to me when I retired. Witness Posts: 18847 Joined: Thu Sep 19, 2013 5:50 pm Re: Snake oil silverdrake wrote:My Monster cables are gold-plated. We already surmised you are a luxury creature… That being said, nickel isen't particularly good at conducting electricity – but certainly cheaper than gold, even in micron thickness. And _that_ being said, the HiFi folks are sometimes a bit strange about their hobby/interest/obsession. Many years ago I knew some of them (that's why the expensive kettle plug drew my attention, reminiscence of technoid slang). One was a very competent sales & repair man of sound exotica, so he had to know the techspeak – and that's why I'm very nicely equipped with unimpressive-looking gear which has served me literally forever. Another had the intelligence to stop the craving for ever-"better" gear when… he seemed to notice a difference in sound quality when he changed the orientation of the plug in the wall socket. (That was before everything was grounded; I hope I don't misuse the technical terms, please correct me if it's the case.) So, placebo effect, expensive blue cable and the sound gets better… silverdrake Posts: 1611 Joined: Tue Jul 23, 2013 5:00 am Title: Girlie Girl Location: Right here Re: Snake oil Witness wrote: silverdrake wrote:My Monster cables are gold-plated. We already surmised you are a luxury creature… That being said, nickel isen't particularly good at conducting electricity – but certainly cheaper than gold, even in micron thickness. And _that_ being said, the HiFi folks are sometimes a bit strange about their hobby/interest/obsession. Many years ago I knew some of them (that's why the expensive kettle plug drew my attention, reminiscence of technoid slang). One was a very competent sales & repair man of sound exotica, so he had to know the techspeak – and that's why I'm very nicely equipped with unimpressive-looking gear which has served me literally forever. Another had the intelligence to stop the craving for ever-"better" gear when… he seemed to notice a difference in sound quality when he changed the orientation of the plug in the wall socket. (That was before everything was grounded; I hope I don't misuse the technical terms, please correct me if it's the case.) So, placebo effect, expensive blue cable and the sound gets better… What can I say, us gals like our sparkly gold things. DrMatt BANNED Posts: 29811 Joined: Fri Jul 16, 2004 4:00 pm Location: Location: Location! Re: Snake oil I notice an improvement in sound quality when we turn off the @#$@ Dance Fever radio station and pop in one of my Mahler symphony CDs. If nobody ever puts their hands up in the air saying ayy-oh ever again, it'll be fine by me. Grayman wrote:If masturbation led to homosexuality you'd think by now I'd at least have better fashion sense.	2019-03-21 06:37:04	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.20007339119911194, "perplexity": 11373.561499730158}, "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/1552912202496.35/warc/CC-MAIN-20190321051516-20190321073516-00367.warc.gz"}
https://plainmath.net/6442/evaluate-the-following-integral-int-frac-x-sqrt-x-4-dx	# Evaluate the following integral. \int \frac{x}{\sqrt{x-4}}dx Question Applications of integrals Evaluate the following integral. $$\displaystyle\int{\frac{{{x}}}{{\sqrt{{{x}-{4}}}}}}{\left.{d}{x}\right.}$$ 2021-02-15 Step 1 Consider the integrals, $$\displaystyle\int{\frac{{{x}}}{{\sqrt{{{x}-{4}}}}}}{\left.{d}{x}\right.}$$ Suppose that, $$\displaystyle\sqrt{{{x}-{4}}}={t}$$ Differentiating with respect to "x" $$\displaystyle{\frac{{{1}}}{{{2}\sqrt{{{x}-{4}}}}}}{\left.{d}{x}\right.}={\left.{d}{t}\right.}$$ $$\displaystyle{\frac{{{1}}}{{\sqrt{{{x}-{4}}}}}}{\left.{d}{x}\right.}={2}{\left.{d}{t}\right.}$$ Step 2 Substitute all value in given integrals, $$\displaystyle\int{\frac{{{x}}}{{\sqrt{{{x}-{4}}}}}}{\left.{d}{x}\right.}=\int{\left({t}^{{{2}}}+{4}\right)}{2}\ {\left.{d}{t}\right.}$$ $$\displaystyle={2}\int{\left({t}^{{{2}}}+{4}\right)}{\left.{d}{t}\right.}$$ $$\displaystyle={2}{\left[{\frac{{{t}^{{{3}}}}}{{{3}}}}+{4}{t}\right]}+{C}$$ $$\displaystyle={\frac{{{2}{t}^{{{3}}}}}{{{3}}}}+{8}{t}+{C}$$ $$\displaystyle={\frac{{{2}}}{{{3}}}}{\left({x}-{4}\right)}^{{{\frac{{{3}}}{{{2}}}}}}+{8}\sqrt{{{\left({x}-{4}\right)}}}+{C}$$ ### Relevant Questions Evaluate the following integral. $$\int \frac{3x^{2}+\sqrt{x}}{\sqrt{x}}dx$$ Evaluate the following integral: $$\int \frac{x+3}{x-1}dx$$ Use a change of variables to evaluate the following integral. $$\int-(\cos^{7}x-5\cos^{5}x-\cos x)\sin x dx$$ Evaluate each of the following integrals. $$\int\frac{e^{x}}{1+e^{x}}dx$$ Evaluate the following integral: $$\int \frac{(y-3)}{y^{2}-6y+1}$$ Evaluate the following integral: $$\int\frac{vdv}{6v^{2}-1}$$ Find the indefinite integral $$\int \ln(\frac{x}{3})dx$$ (a) using a table of integrals and (b) using the Integration by parts method. $$\int_{0}^{1}t^{\frac{5}{2}}(\sqrt{t}-3t)dt$$ $$\int_{1}^{2}\frac{(x+1)^{2}}{x}dx$$ $$\int 2x^{3}+3x-2dx$$	2021-06-24 08:39:08	{"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": 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": 0.9866818785667419, "perplexity": 2059.275232585077}, "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/1623488552937.93/warc/CC-MAIN-20210624075940-20210624105940-00451.warc.gz"}
https://physics.stackexchange.com/questions/148931/formation-of-supermassive-black-holes/266040	# Formation of supermassive black holes Scientists have found very bright source of light which they call quasar and the are found to be supermassive black holes. So these black holes are so massive that they cannot be formed by a supernova. So how are these formed? • This is actually an open question in astrophysics. No one has a definitive answer, though many ideas exist. – Kyle Kanos Nov 26 '14 at 3:36 • Surprisingly, it doesn't look like this has even been mentioned here before, or on Astronomy. Nice question. – HDE 226868 Nov 26 '14 at 3:37 Nobody knows. That's it, in a nutshell. However, there are some various ideas floating about. Here's a (long) list of some: • Collapse of massive gas clouds • Merger of lots of stellar-mass black holes • Growth of a stellar-mass black hole to astronomical (pun intended) proportions From Wikipedia: • Core collapse of a cluster of stars • Primordial black holes coalescing From here: • Accretion of primordial gas left over from the Big Bang From here: • The death of really, really massive stars (Note: This would only be the beginning of a supermassive black hole; much more accretion would have to take place. In fact, this can be said of many of the solutions presented.) But the truth is (and I'll be blunt here) that scientists don't have as much evidence as they'd like for any of these ideas. There are lots of models (just see the ideas above) for the formation of these black holes based on observations of quasars, active galactic nuclei and normal galaxy centers, but it's difficult, if not impossible, to properly test them. • I'd add that we can adjust parameters for various models for the growth and mergers of these black holes, and this can lead to either underpredicting or overpredicting their abundance. So it's not a situation of "we can't explain where they come from" but rather "there are many ideas that work, we're not sure which most accurately depicts reality." – user10851 Nov 26 '14 at 14:55 • @ChrisWhite Okay, I'll add something to that effect. – HDE 226868 Nov 26 '14 at 14:56 • Another possible explanation: collapse of $\sim10^5$ solar mass star. – Kyle Kanos Nov 26 '14 at 15:09 • How does the collapse of a $10^{5}M_{\odot}$ star make a supermassive black hole? This could only be part of a solution right? Supermassive blackholes are 10-10,000 times more massive than this. – Rob Jeffries Nov 26 '14 at 21:58 • @RobJeffries Yes, it would only be the beginnings of a solution. Both the universetoday article and the paper Kyle Kanos cited say that these stars would only be the "seeds" of a supermassive black hole. – HDE 226868 Nov 26 '14 at 22:01 Normal black holes form from the mass of a dying star, so for a black hole to have more mass than the star it got it mass from something must be up. To understand why black holes in Quazars are so large, we need to understand what a Quazar is. Black holes often consume nearby stars, and during consumption, the stardust orbits the black hole and accelerates to speeds close to the speed of light. Friction with other stardust particles cause immense heat and emission of electromagnetic radiation. The black hole gains more mass by consuming nearby stars until it becomes big enough to make a real quazar, the kind that can be seen. • Don't know if it answers all but it is reasonable. Also to be able to consume so many other stars it must be in a particularly dense area, and thus mostly at the center of a galaxy. The biggest supermassive black hole (if I remember right) is about 10^11 solar masses. Can there be supermassive black holes (quasars) without a glaalaxies around, i.e., having consumed everything around it? – Bob Bee Jul 3 '16 at 21:19 • No it is very doubtful that it can work like this without having very massive black hole seeds to begin with There is a fundamental problem with the growth timescale being limited by radiation pressure. 1 billion solar mass BHs are already present a billion years after the big bang. physics.stackexchange.com/questions/167250/… – Rob Jeffries Jul 4 '16 at 0:16	2019-09-18 07:30:31	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 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": 0.6455121040344238, "perplexity": 832.1806760490548}, "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/1568514573258.74/warc/CC-MAIN-20190918065330-20190918091330-00257.warc.gz"}
http://openstudy.com/updates/50bfa352e4b0231994eca0f0	anonymous 3 years ago Please help me????????????? Solve by using the quadratic formula to solve x2 + 6x = -3. 1. anonymous easier to complete the square $x^2+6x=-3$ $(x+3)^2=-3+9=6$ $x+3=\pm\sqrt{6}$ $x=-3\pm\sqrt{6}$ 2. anonymous x=-0.5505 , x=-5.449 3. anonymous write it like this $x^{2} + 6x +3=0$ a=1 b=6 c=3, now you cam apply the quadretic formula $\frac{ -b \pm \sqrt{b ^{2}-4ac} }{ 2a }$ 4. anonymous omg thank you guys........!!!!!!!!!!!!!!!!!!!!!!!!!!!!!	2016-05-25 13:09:01	{"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": 0.7286108732223511, "perplexity": 3841.287069827523}, "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-2016-22/segments/1464049274985.2/warc/CC-MAIN-20160524002114-00070-ip-10-185-217-139.ec2.internal.warc.gz"}
https://mne.tools/0.11/faq.html	## Inverse Solution¶ ### How should I regularize the covariance matrix?¶ The estimated covariance can be numerically unstable and tends to induce correlations between estimated source amplitudes and the number of samples available. The MNE manual therefore suggests to regularize the noise covariance matrix (see Regularization of the noise-covariance matrix), especially if only few samples are available. Unfortunately it is not easy to tell the effective number of samples, hence, to chose the appropriate regularization. In MNE-Python, regularization is done using advanced regularization methods described in [1]. For this the ‘auto’ option can be used. With this option cross-validation will be used to learn the optimal regularization: >>> import mne >>> cov = mne.compute_covariance(epochs, tmax=0., method='auto') This procedure evaluates the noise covariance quantitatively by how well it whitens the data using the negative log-likelihood of unseen data. The final result can also be visually inspected. Under the assumption that the baseline does not contain a systematic signal (time-locked to the event of interest), the whitened baseline signal should be follow a multivariate Gaussian distribution, i.e., whitened baseline signals should be between -1.96 and 1.96 at a given time sample. Based on the same reasoning, the expected value for the global field power (GFP) is 1 (calculation of the GFP should take into account the true degrees of freedom, e.g. ddof=3 with 2 active SSP vectors): >>> evoked = epochs.average() >>> evoked.plot_white(cov) This plot displays both, the whitened evoked signals for each channels and the whitened GFP. The numbers in the GFP panel represent the estimated rank of the data, which amounts to the effective degrees of freedom by which the squared sum across sensors is divided when computing the whitened GFP. The whitened GFP also helps detecting spurious late evoked components which can be the consequence of over- or under-regularization. Note that if data have been processed using signal space separation (SSS) [2], gradiometers and magnetometers will be displayed jointly because both are reconstructed from the same SSS basis vectors with the same numerical rank. This also implies that both sensor types are not any longer linearly independent. These methods for evaluation can be used to assess model violations. Additional introductory materials can be found [here](https://speakerdeck.com/dengemann/eeg-sensor-covariance-using-cross-validation). For expert use cases or debugging the alternative estimators can also be compared: >>> covs = mne.compute_covariance(epochs, tmax=0., method='auto', return_estimators=True) >>> evoked = epochs.average() >>> evoked.plot_white(covs) This will plot the whitened evoked for the optimal estimator and display the GFPs for all estimators as separate lines in the related panel. ### References¶ [1] Engemann D. and Gramfort A. (2015) Automated model selection in covariance estimation and spatial whitening of MEG and EEG signals, vol. 108, 328-342, NeuroImage. [2] Taulu, S., Simola, J., Kajola, M., 2005. Applications of the signal space separation method. IEEE Trans. Signal Proc. 53, 3359–3372.	2021-11-27 19:58:12	{"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": 0.7171636819839478, "perplexity": 2365.1494487467126}, "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-2021-49/segments/1637964358233.7/warc/CC-MAIN-20211127193525-20211127223525-00454.warc.gz"}
https://www.uni-muenster.de/FB10/Service/show_article.shtml?id=7259&brettid=32	\| shupp_01 ### Kolloquium Wilhelm Killing: Prof. Dr. Joel Hamkins (Oxford): The rearrangement and subseries numbers: how much convergence suffices for absolute convergence? ##### Thursday, 10.01.2019 16:30 im Raum M5 Abstract. The Riemann rearrangement theorem asserts that a series $\sum_n a_n$ is absolutely convergent if and only if every rearrangement $\sum_n a_{p(n)}$ of it is convergent, and furthermore, any conditionally convergent series can be rearranged so as to converge to any desired extended real value. How many rearrangements $p$ suffice to test for absolute convergence in this way? The rearrangement number, a new cardinal characteristic of the continuum, is the smallest size of a family of permutations, such that whenever the convergence and value of a convergent series is invariant by all these permutations, then it is absolutely convergent. The subseries number is defined similarly, as the smallest number of subseries whose convergence suffices to test a series for absolute convergence. The exact values of the rearrangement and subseries numbers turns out to be independent of the axioms of set theory. In this talk, I shall place the rearrangement and subseries numbers into a discussion of cardinal characteristics of the continuum, including an elementary introduction to the continuum hypothesis and an account of Freiling's axiom of symmetry. This talk is based in part on joint work with Andreas Blass, Joerg Brendle, Will Brian, myself, Michael Hardy and Paul Larson. Angelegt am Thursday, 11.10.2018 14:07 von shupp_01 Geändert am Wednesday, 10.04.2019 10:34 von a_schi11 [Edit \| Vorlage] Kolloquium Wilhelm Killing	2023-02-05 14:02:15	{"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": 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": 0.818411648273468, "perplexity": 631.8522119522667}, "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/1674764500255.78/warc/CC-MAIN-20230205130241-20230205160241-00193.warc.gz"}
https://bitylink.info/fejer-kernel-79/	Fourier Series and Fejér’s Theorem. William Wu. Fejér’s kernel can be expressed in either of the following two equivalent ways: Fn(x) = 1 n + 1. When we studied Fourier series we improved convergence by convolving with the Fejer and Poisson kernels on T. The analogous. Fejer and. although the Dirichlet kernel isn’t a convolution kernel in the sense of .. The Fejér kernel is the sequence of functions highlighted above; i.e. Author: Tabei Kikinos Country: Togo Language: English (Spanish) Genre: Literature Published (Last): 18 May 2013 Pages: 293 PDF File Size: 7.88 Mb ePub File Size: 16.84 Mb ISBN: 275-5-67948-613-1 Downloads: 10951 Price: Free* [*Free Regsitration Required] Uploader: Gozilkree If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. Major factors that we focus are the heat change, atmospheric pressure and the humidity change that As known climate change globally drastically is form the major components of the Fourier series when fejef for a climate change in i a particular region. The results are different from previous analyses kerneel the literature and a small simulation exercise provides evidence in our favour. However these values are associated to each other over the sum and Let us first know that these are not the only factors thereby cannot be counted separately over a domain. As seen in the above diagram the data for a particular demography is taken under study and various conditions are convoluted with reference to conditional probability and the further effectiveness is seen ahead. ### sequences and series – The Fejer kernel has this $\sin$ closed form. – Mathematics Stack Exchange Influence of Cesaro summation and the Fejer Kernel onto the climate change model. There eventually affected during a particular event. Therefore the Fejer kernel for the above condition Climate change impacts on crop productivity in may be given as follows. Global and national concerns. This changes are due to the surrounding conditions that result the final climatic Keywords: Enter the email address you signed up with and we’ll email you a reset link. There were one of their works on climate change which uses alternate mathematical approaches that involved parameters like climate change associated to the graph theory to study such changes which were more components associated to its outcome. Skip to main content. Current Science,90 3This paper derives the spectral density function of aggregated long memory processes in light of the aliasing effect. DIARREA OSMOTICA Y SECRETORA PDF The process of climate change kernell primarily bifurcated into two aspects. Leonardo Rocha Souza, Every moment there fejerr a model formed events that are resulting out of it. It also allows you to accept potential citations to this item oernel we are uncertain about. However, a major change over a large demography is caused due to long term climatic change and the fejdr changes that affect the demography of a place kerne less. Ever diversities that occur over a period of time vary with since then there was a continuous change in the the effect on its subsidiaries and thereby cause an climatic conditions which results into a new form overall change in its surroundings. Both these factors cause changes according to their intensity over the environmental parameters including financial aspect and human Figure 1. This being the main pursuit of the paper thereby declares the components of climate change given above to be expressed in the form of Fourier components. The attempts further could not effective give an We look at a similar concept described in one of the overview of the events happening due to climate literature paper given by Burgess and Deschenes in change over a particular demography. On the basis of their impact and effectiveness, climate change may be termed as long term and short term. Please note that corrections may take a couple of weeks to filter through the various RePEc services. ## Dictionary:Fejer kernel window The primary one is the long term climate change and the other one is the short term climate change. We introduce the concept of Cesaro summation and the fejer kernel to get an The pre requisites of the measure of our climate efficient quantity of the climate change parameter change Ccand its differential with respect to time over these possibilities. Chambers, Marcus J, Download full text from publisher Oernel URL: The above views give an effective approach to minimize the losses ignored due to either graph theory Figure 1. Help us Corrections Found an error or omission? Whenever we consider a transformation of a particular element from one domain to another in the Differentiating the equation 2. These are various approaches and methodologies towards parameters are developed in the form of a function studying the climate change in India and throughout throu which further manifests according to the types of the world. DANCER COLUM MCCANN PDF The outcome of these studies deals with and the parameters affecting it and also relate it to the the aspect of not improving any such climatic previously existing similar model. Log In Sign Up. Maize production in expressions we get; a changing climate: Ages later the introduction of mankind the work is to relate climate change model considered also lso did see many such changes in nature and climate. See general information about how to correct material in RePEc. Initially we propose a simple expression domain of a measurable space where components are Relating these parameters and further intend to discrete. As known one of the most primitive approaches in understanding the climate change with respect to event occurrence is the theory of probability. We shall carry effective when combined with a particular probability out a mathematical analysis of these components in a theory. For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Souza, Leonardo Rocha, We shall focus on one such mathematical model to understand the effect on population and allied parameters due to climate change IJTSRD Available Online www. Souza, Leonardo da Rocha de. As we see climate change is a continuous process that deals with a lot of other factors involving the ones that are either a part of the process or discrete. The main focus of periodically. The aliasing effect, the Fejer Kernel and temporally aggregated long memory processes. Remember me on this computer. There are further conditions tions as it kernle not in the hands of mankind to influences of the cesaro summation and later control nature, however we may try to take necessary convolutes with the Fejer kernel that links the Fourier measures that can lead us to avoid certain losses due condition to manifest the efficiency of this model.	2021-01-26 04:28:34	{"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": 0.6133934259414673, "perplexity": 1201.7665106923878}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-04/segments/1610704798089.76/warc/CC-MAIN-20210126042704-20210126072704-00539.warc.gz"}
http://www.iis.sinica.edu.tw/page/researchoverview/RecentResearchResults.html?lang=en	Recent Research Results "Active Disaster Response System for Smart Buildings," Proceedings of International Symposium on Computer, Consumer and Control, June 2014. Authors: C.-Y. Lin, E. T. H. Chu, L.-W. Ku and J. W. S. Liu Abstract: In recent years, major natural disasters have made it more challenging for us to protect human lives. Examples include the 2011 Japan Tohoku earthquake and Typhoon Morakot in 2009 in Taiwan. However, modern disaster warning systems cannot automatically respond efficiently and effectively to disasters. As a result, it is necessary to develop an automatic response system to prevent, diminish or eliminate the damages caused by disasters. In this paper, we develop an active emergency response system to automatically process standard warning messages, such as CAP (Common Alerting Protocol) messages. After receiving official warning messages of earthquakes, our system automatically shuts down natural gas lines in order to prevent buildings from fire and opens the building doors for easy evacuation. Our system also stops elevators when they reach the closest floor. In addition, our system can be applied to hospitals to tell surgeons to pause on-going operations, or to supermarkets to inform consumers of the way to exit the building. According to our experiment results, the proposed system can avoid possible dangers and save human lives during major disasters. "Space-Efficient Multiversion Index Scheme for PCM-based Embedded Database Systems," ACM/IEEE Design Automation Conference (DAC), June 2014. Authors: Yuan-Hung Kuan, Yuan-Hao Chang, Po-Chun Huang, and Kam-Yiu Lam Abstract: Embedded database systems are widely adopted in various control and motoring systems, e.g., cyber-physical systems. To support the functionality to access the historical data, a multiversion index is adopted to simultaneously maintain multiple versions of data items and their index information. However, cyber-physical systems are usually battery-powered embedded systems that have limited energy, computing power, and storage space. In this work, we consider the systems with phase-change memory (PCM) as their storage due to its non-volatility and low energy consumption. In order to resolve the problem of the limited storage space and the fact that existing multiversion index designs are lack of space efficiency, we propose a space-efficient multiversion index scheme to enhance the space utilization and access performance of embedded multiversion database systems on PCM by utilizing the byte-addressability and write asymmetry of PCM. A series of experiments was conducted to evaluate the efficacy of the proposed scheme. The results show that the proposed scheme achieves very high space utilization and has good performance on serving update transactions and range queries. "Garbage Collection for Multi-version Index on Flash Memory," ACM/IEEE Design, Automation and Test in Europe (DATE), March 2014. Authors: Kam-Yiu Lam, Jian-Tao Wang, Yuan-Hao Chang, Po-Chun Huang, Jen-Wei Hsieh, Chung Keung Poon, and ChunJiang Zhu Abstract: In this paper, we study the important performance issues in using the purging-range query to reclaim old data versions to be free blocks in a flash-based multi-version database. To reduce the overheads for processing the purging-range query, the physical block labeling (PBL) scheme is proposed to provide a better estimation on the purging version number to be used for purging old data versions. With the use of the frequencybased placement (FBP) scheme to place data versions in a block, the efficiency in garbage collection can be further enhanced by increasing the deadspans of data versions and reducing reallocation cost especially when the spaces of the flash memory for the databases are limited. Current Research Results Authors: Jia-Ming Chang, Jean-Francois Taly, Ionas Erb, Ting-Yi Sung, Wen-Lian Hsu, Chuan Yi Tang, Cedric Notredame, Emily Chia-Yu Su Abstract: Predicting protein functional classes such as localization sites and modifications plays a crucial role in function annotation. Given a tremendous amount of sequence data yielded from high-throughput sequencing experiments, the need of efficient and interpretable prediction strategies has been rapidly amplified. Our previous approach for subcellular localization prediction, PSLDoc, archives high overall accuracy for Gram-negative bacteria. However, PSLDoc is computational intensive due to incorporation of homology extension in feature extraction and probabilistic latent semantic analysis in feature reduction. Besides, prediction results generated by support vector machines are accurate but generally difficult to interpret. In this work, we incorporate three new techniques to improve efficiency and interpretability. First, homology extension is performed against a compact non-redundant database using a fast search model to reduce running time. Second, correspondence analysis (CA) is incorporated as an efficient feature reduction to generate a clear visual separation of different protein classes. Finally, functional classes are predicted by a combination of accurate compact set (CS) relation and interpretable one-nearest neighbor (1-NN) algorithm. Besides localization data sets, we also apply a human protein kinase set to validate generality of our proposed method. Experiment results demonstrate that our method make accurate prediction in a more efficient and interpretable manner. First, homology extension using a fast search on a compact database can greatly accelerate traditional running time up to twenty-five times faster without sacrificing prediction performance. This suggests that computational costs of many other predictors that also incorporate homology information can be largely reduced. In addition, CA can not only efficiently identify discriminative features but also provide a clear visualization of different functional classes. Moreover, predictions based on CS achieve 100% precision. When combined with 1-NN on unpredicted targets by CS, our method attains slightly better or comparable performance compared with the state-of-the-art systems. Current Research Results Authors: Chia-Feng Tsai, Chuan-Chih Hsu, Jo-Nan Hung, Yi-Ting Wang, Wai-Kok Choong, Ming-Yao Zeng, Pei-Yi Lin, Ruo-Wei Hong, Ting-Yi Sung, and Yu-Ju Chen Abstract: Methodologies to enrich heterogeneous types of phosphopeptides are critical for comprehensive mapping of the under-explored phosphoproteome. Taking advantage of the distinct binding affinities of Ga3+ and Fe3+ for phosphopeptides, we designed a metal-directed immobilized metal ion affinity chromatography for the sequential enrichment of phosphopeptides. In Raji B cells, the sequential Ga3+ - Fe3+-immobilized metal affinity hromatography (IMAC) strategy displayed a 1.5−3.5-fold superior phosphoproteomic coverage compared to single IMAC (Fe3+,Ti4+,Ga3+, and Al3+). In addition, up to 92% of the 6283 phosphopeptides were uniquely enriched in either the first Ga3+-IMAC (41%) or second Fe3+-IMAC (51%). The complementary properties of Ga3+ and Fe3+ were further demonstrated through the exclusive enrichment of almost all of 1214 multiply phosphorylated peptides (99.4%) in the Ga3+-IMAC, whereas only 10% of 5069 monophosphorylated phosphopeptides were commonly enriched in both fractions. The application of sequential Ga3+-Fe3+-IMAC to human lung cancer tissue allowed the identification of 2560 unique phosphopeptides with only 8% overlap. In addition to the above-mentioned mono- and multiply phosphorylated peptides, this fractionation ability was also demonstrated on the basic and acidic phosphopeptides: acidophilic phosphorylation sites were predominately enriched in the first Ga3+-IMAC (72%), while Pro-directed (85%) and basophilic (79%) phosphorylation sites were enriched in the second Fe3+-IMAC. This strategy provided complementary mapping of different kinase substrates in multiple cellular pathways related to cancer invasion and metastasis of lung cancer. Given the fractionation ability and ease of tip preparation of this Ga3+-Fe3+-IMAC, we propose that this strategy allows more comprehensive characterization of the phosphoproteome both in vitro and in vivo. Current Research Results Authors: Jun Ming Chen, Meng Chang Chen and Yeali S. Sun Abstract: Prior knowledge is an important issue in the study of concept acquisition among students. Traditional studies on prior knowledge generation during reading activities have focused on extracting sentences from reading materials that are manually generated by website administrators and educators. This is time-consuming and strenuous, and hence personalized prior knowledge recommendation is difficult to perform. To cope with this problem, we combine the concept of prior knowledge with social tagging methods to assist the reading comprehension of students studying English. We incorporate tags into a tag based learning approach, which then identifies suitable supplementary materials for quickly constructing a student’s prior knowledge reservoir. The experimental results demonstrate that the proposed approach benefits the students by embedding the additional information in social knowledge, and hence significantly improve their on-line reading efficiency. Current Research Results "Example-based Human Motion Extrapolation and Motion Repairing Using Contour Manifold," IEEE Transactions on Multimedia, January 2014. Authors: Nick C. Tang, C. T. Hsu, M. F. Weng, T. Y. Lin, and H. Y. Mark Liao Abstract: We propose a human motion extrapolation algorithm that synthesizes new motions of a human object in a still image from a given reference motion sequence. The algorithm is implemented in two major steps: contour manifold construction and object motion synthesis. Contour manifold construction searches for low-dimensional manifolds that represent the temporal-domain deformation of the reference motion sequence. Since the derived manifolds capture the motion information of the reference sequence, the representation is more robust to variations in shape and size. With this compact representation, we can easily modify and manipulate human motions through interpolation or extrapolation in the contour manifold space. In the object motion synthesis step, the proposed algorithm generates a sequence of new shapes of the input human object in the contour manifold space and then renders the textures of those shapes to synthesize a new motion sequence. We demonstrate the efficacy of the algorithm on different types of practical applications, namely, motion extrapolation and motion repair. Current Research Results "A Resource-Driven DVFS Scheme for Smart Handheld Devices," ACM Transactions on Embedded Computing Systems, December 2013. Authors: Yu-Ming Chang, Pi-Cheng Hsiu, Yuan-Hao Chang, and Che-Wei Chang Abstract: Reducing the energy consumption of the emerging genre of smart handheld devices while simultaneously maintaining mobile applications and services is a major challenge. This work is inspired by an observation on the resource usage patterns of mobile applications. In contrast to existing DVFS scheduling algorithms and history-based prediction techniques, we propose a resource-driven DVFS scheme, in which resource state machines are designed to model the resource usage patterns in an online fashion to guide DVFS. We have implemented the proposed scheme on Android smartphones and conducted experiments based on realworld applications. The results are very encouraging and demonstrate the efficacy of the proposed scheme. Current Research Results "DEEP: Density-Aware Emergency Message Extension Protocol for VANETs," IEEE Transactions on Wireless Communications, October 2013. Authors: Ming-Chin Chuang and Meng Chang Chen Abstract: With the rapid developments in vehicular communication technology, academics and industry researchers are paying increasing attention to vehicular ad hoc networks (VANETs). In VANETs, dissemination delay and reliability are important criteria for many applications, especially for emergency messages. Existing approaches have difficulty satisfying both requirements simultaneously because they conflict with one another. In this paper, we propose a novel mechanism, called the Density-aware Emergency message Extension Protocol (DEEP) to disseminate emergency messages in VANETs. DEEP resolves the broadcast storm problem, achieves low dissemination delay, and provides high reliability over a realistic multi-lane freeway scenario. The mechanism delivers emergency messages to a specific area (e.g., the area before the exit) in a timely manner and guarantees that all relevant vehicles in that area will receive the messages. Drivers can then change their routes and avoid getting caught in a traffic jam. Performance evaluations via NS-2 simulations demonstrate that DEEP achieves both lower dissemination delay and higher reliability than existing approaches. "Kylin: An Efficient and Scalable Graph Data Processing System," 2013 IEEE International Conference on Big Data, October 2013. Authors: Li-Yung Ho, Tsung-Han Li, Jan-Jan Wu, Pangfeng Liu Abstract: We introduce Kylin, an efficient and scalable graph data processing system. Kylin is based on bulk synchronization processing(BSP) model to process graph data. Although there have been some BSP-based graph processing systems, Kylin is different from these systems in two aspects. First, Kylin cooperates with HBase to achieve scalable graph data management. Second, We propose three techniques to optimize the performance of Kylin. The proposed techniques are pull messaging, lazy vertex loading and vertex-weighted partitioning. Our experiment results demonstrate that Kylin outperforms other BSP-based systems, such as Apache Hama and Giraph. "Sum-Rate Maximization and Energy-Cost Minimization for Renewable Energy Empowered Base-Stations using Zero-Forcing Beamforming," Proceedings of APSIPA ASC 2013 - the fifth Annual Summit and Conference of Asia-Pacific Signal and Information Processing Association, October 2013. Authors: Yung-Shun Wang, Yao-Win Peter Hong, and W. T. Chen Abstract: Zero-forcing (ZF) beamforming is a practical linear transmission scheme that eliminates inter-user interference in the downlink of a multiuser multiple-input single-output (MISO) wireless system. By considering base-stations (BSs) that are supported by renewable energy, this work examines offline and online ZF beamforming designs based on two different objectives, namely, sum-rate maximization and energy-cost minimization. For offline policies, the channel states and the energy arrivals are assumed to be known a priori for all time instants whereas, in the online policies, only causal information is available. The designs are subject to energy causality and energy storage constraints, i.e., the constraint that energy cannot be used before it arrives and the constraint that the stored energy cannot exceed the maximum battery storage capacity. In the offline sum-rate maximization problem, the base-station is assumed to be supported only by renewable energy and the goal is to maximize the sum rate of all users by a predetermined deadline. The optimization over the ZF beamforming direction and power allocation can be decoupled, and the solutions can be found exactly. In the energycost minimization problem, the base-station is assumed to be supported by both renewable and power-grid energy, and the goal is to minimize the cost of purchasing grid energy subject to quality-of-service constraints at the users. The problem can be formulated as a convex optimization problem and can be solved efficiently using off-the-shelf solvers. Offline solutions are first obtained and used as the basis for the proposed online policies. The effectiveness of the proposed policies are demonstrated through computer simulations. Current Research Results "On the Quality of Service of Cloud Gaming Systems," IEEE Transactions on Multimedia, February 2014. Authors: Kuan-Ta Chen, Yu-Chun Chang, Hwai-Jung Hsu, De-Yu Chen, Chun-Ying Huang, and Cheng-Hsin Hsu Abstract: Cloud gaming, i.e., real-time game playing via thin clients, relieves users from being forced to upgrade their com- puters and resolve the incompatibility issues between games and computers. As a result, cloud gaming is generating a great deal of interests among entrepreneurs, venture capitalists, general publics, and researchers. However, given the large design space, it is not yet known which cloud gaming system delivers the best user-perceived Quality of Service (QoS) and what design elements constitute a good cloud gaming system. This study is motivated by the question: How good is the QoS of current cloud gaming systems? Answering the question is challenging because most cloud gaming systems are proprietary and closed, and thus their internal mechanisms are not accessible for the research community. In this paper, we propose a suite of measurement techniques to evaluate the QoS of cloud gaming systems and prove the effectiveness of our schemes using a case study comprising two well-known cloud gaming systems: OnLive and StreamMyGame. Our results show that OnLive performs better, because it provides adaptable frame rates, better graphic quality, and shorter server processing delays, while consuming less network bandwidth. Our measurement techniques are general and can be applied to any cloud gaming systems, so that researchers, users, and service providers may systematically quantify the QoS of these systems. To the best of our knowledge, the proposed suite of measurement techniques have never been presented in the literature. Current Research Results "Reliability Enhancement of Flash-Memory Storage Systems: An Efficient Version-Based Design," IEEE Transactions on Computers, December 2013. Authors: Yuan-Hao Chang, Po-Chun Huang, Pei-Han Hsu, Lue-Jane Lee, Tei-Wei Kuo and David Hung-Chang Du Abstract: In recent years, reliability has become one critical issue in the designs of flash-memory file/storage systems, due to the growing unreliability of advanced flash-memory chips. In this paper, a version-based strategy is proposed to effectively and efficiently maintain the consistency among page versions of a file for potential recovery needs. In particular, a two-version one for a native file system is presented with the minimal overheads in version maintenance. A recovery scheme is then presented to restore a corrupted file back to the latest consistent version. The strategy is later extended to maintain multiple data versions with the considerations of the write constraints of multi-level-cell flash memory. It was shown that the proposed strategy could significantly improve the reliability of flash memory with limited management and space overheads. Current Research Results "Automatic Training Image Acquisition and Effective Feature Selection from Community-Contributed Photos for Facial Attribute Detection," IEEE Transactions on Multimedia, October 2013. Authors: Yan-Ying Chen, Winston Hsu, and H. Y. Mark Liao Abstract: Facial attributes are shown effective for mining specific persons and profiling human activities in large-scale media such as surveillance videos or photo-sharing services. For comprehensive analysis, a rich number of facial attributes is required. Generally, each attribute detector is obtained by supervised learning via the use of large training data. It is promising to leverage the exponentially growing community contributed photos and the associated informative contexts to ease the burden of manual annotation; however, such huge noisy data from the Internet still pose great challenges. We propose to measure the quality of training images by discriminable visual features, which are verified with the relative discrimination between the unlabeled images and the pseudo-positives (pseudo-negatives) retrieved by textual relevance. The proposed feature selection requires no heuristic threshold, therefore, can be generalized to multiple feature modalities. We further exploit the rich context cues (e.g., tags, geo-locations, etc.) associated with the publicly available photos for mining more semantically consistent but visually diverse training images around the world. Experimenting in the benchmarks, we demonstrate that our work can successfully acquire effective training images for learning generic facial attributes, where the classification error is relatively reduced up to 23.35% compared with that of the text-based approach and shown comparable with that of costly manual annotations. Current Research Results "An Index-Based Management Scheme with Adaptive Caching for Huge-Scale Low-Cost Embedded Flash Storages," ACM Transactions on Design Automation of Electronic Systems, October 2013. Authors: Po-Chun Huang, Yuan-Hao Chang, and Tei-Wei Kuo Abstract: Due to its remarkable access performance, shock resistance and costs, NAND flash memory is now widely adopted in a variety of computing environments, especially in mobile devices such as smart phones, media players and electronic book readers. For the consideration of costs, low-cost embedded flash storages such as flash memory cards are often employed on such devices. Different from solid-state disks, the RAM buffer equipped on low-cost embedded flash storages are very small, for example, limited under tens of kilobytes, despite of the rapidly growing capacity of the storages. The significance of effectively utilizing the very limited on-device RAM buffers of embedded flash storages is therefore highlighted, and a novel design of scalable flash management schemes is needed to tackle the new access constraints of MLC NAND flash memory. In this work, a highly-scalable design of the flash translation layer is presented with the considerations of the on-device RAM size, user access patterns, address-mapping-information caching and MLC access constraints. Through a series of experiments, it is verified that, with appropriate settings of cache sizes, the proposed management scheme provides comparable performance results to prior arts with much lower requirements on the on-device RAM. In other words, the proposed scheme suggests a strategy to make better use of the on-device RAM, and is suitable for embedded flash storages. "Selective Profiling for OS Scalability Study on Multicore Systems," IEEE International Conference on Service-Oriented Computing and Applications (SOCA), December 2013. Authors: Kuo-Yi Chen, Yuan-Hao Chang, Pei-Shu Liao, Pen-Chung Yew, Sheng-Wei Cheng, and Tien-Fu Chen Abstract: With the wide deployment of multi-core processors, the scalability is becoming an important issue of modern computers. In order to detail the scalability issues of an operating system, the performance profilers are usually used to detect the scalability bottlenecks. However, profilers usually go alone with the significant overheads. The overheads not only reduce the accuracy of scalability profiling, but also mislead to the actual scalability bottlenecks. In order to improve this issue, a selective-profiling approach is proposed to analyze the scalability of an operating system precisely with minimum overheads. In proposed selective-profiling approach, the possible scalability bottleneck hotspots are located by the tracers first, and then the information of possible bottleneck hotspots is passed to the sampler to detect actual bottlenecks. Since the sampler only concentrates on the possible bottleneck hotspots instead of a whole system, the overhead can be reduced significantly. Therefore, the proposed selective-profiling approach takes the advantages of performance tracers and samplers both to reduce the overhead and still reach the accurate bottleneck analysis for an operating system in multi-core systems. "Interactive Coding, Revisited," The 54th Annual IEEE Symposium on Foundations of Computer Science (FOCS), October 2013. Authors: Kai-Min Chung and Rafael Pass and Sidharth Telang Abstract: How can we encode a communication protocol between two parties to become resilient to adversarial errors on the communication channel? If we encode each message in the communication protocol with agood'' error-correcting code (ECC), the error rate of the encoded protocol becomes poor (namely O(1/m) where m is the number of communication rounds). Towards addressing this issue, Schulman (FOCS'92, STOC'93) introduced the notion of interactive coding. We argue that whereas the method of separately encoding each message with an ECC ensures that the encoded protocol carries the same amount of information as the original protocol, this may no longer be the case if using interactive coding. In particular, the encoded protocol may completely leak a player's private input, even if it would remain secret in the original protocol. Towards addressing this problem, we introduce the notion of knowledge-preserving interactive coding, where the interactive coding protocol is required to preserve the ''knowledge'' transmitted in the original protocol. Our main results are as follows. - The method of separately applying ECCs to each message has essentially optimal error rate: No knowledge-preserving interactive coding scheme can have an error rate of 1/m, where m is the number of rounds in the original protocol. - If restricting to computationally-bounded (polynomial-time) adversaries, then assuming the existence of one-way functions (resp. subexponentially-hard one-way functions), for every ϵ>0, there exists a knowledge-preserving interactive coding schemes with constant error rate and information rate nϵ (resp. 1/polylog(n)) where n is the security parameter; additionally to achieve an error of even 1/m requires the existence of one-way functions. - Finally, even if we restrict to computationally-bounded adversaries, knowledge-preserving interactive coding schemes with constant error rate can have an information rate of at most o(1/logn). This results applies even to non-constructive interactive coding schemes. "Simultaneous Resettability from One-Way Functions," The 54th Annual IEEE Symposium on Foundations of Computer Science (FOCS), October 2013. Authors: Kai-Min Chung and Rafail Ostrovsky and Rafael Pass and Ivan Visconti Abstract: Resettable-security, introduced by Canetti, Goldreich, Goldwasser and Micali (STOC'00), considers the security of cryptographic two-party protocols (in particular zero-knowledge arguments) in a setting where the attacker may reset'' or rewind'' one of the players. The strongest notion of resettable security, simultaneous resettability, introduced by Barak, Goldreich, Goldwasser and Lindell (FOCS'01), requires resettable security to hold for both parties: in the context of zero-knowledge, both the soundness and the zero-knowledge conditions remain robust to resetting attacks. To date, all known constructions of protocols satisfying simultaneous resettable security rely on the existence of ZAPs; constructions of ZAPs are only known based on the existence of trapdoor permutations or number-theoretic assumptions. In this paper, we provide a new method for constructing protocols satisfying simultaneous resettable security while relying only on the minimal assumption of one-way functions. Our key results establish, assuming only one-way functions: - Every language in NP has an ω(1)-round simultaneously resettable witness indistinguishable argument system. - Every language in NP has a (polynomial-round) simultaneously resettable zero-knowledge argument system. The key conceptual insight in our technique is relying on black-box impossibility results for concurrent zero-knowledge to achieve resettable-security. "Constant-Round Concurrent Zero Knowledge From P-Certificates," The 54th Annual IEEE Symposium on Foundations of Computer Science (FOCS), October 2013. Authors: Kai-Min Chung and Huijia Lin and Rafael Pass Abstract: We present a constant-round concurrent zero-knowledge protocol for NP. Our protocol relies on the existence of families of collision-resistant hash functions, and a new, but in our eyes, natural complexity-theoretic assumption: the existence of P-certificates---that is, "succinct'' non-interactive proofs/arguments for P. As far as we know, our results yield the first constant-round concurrent zero-knowledge protocol for NP with an explicit zero-knowledge simulator based on any assumption. "CloudRS: An Error Correction Algorithm of High-Throughput Sequencing Data," Proceedings IEEE BigData 2013, October 2013. Authors: Chien-Chih Chen, Yu-Jung Chang, Wei-Chun Chung, Der-Tsai Lee, and Jan-Ming Ho Abstract: Next-generation sequencing (NGS) technologies produce huge amounts of data. These sequencing data unavoidably are accompanied by the occurrence of sequencing errors which constitutes one of the major problems of further analyses. Error correction is indeed one of the critical steps to the success of NGS applications such as de novo genome assembly and DNA resequencing as illustrated in literature. However, it requires computing time and memory space heavily. To design an algorithm to improve data quality by efficiently utilizing on-demand computing resources in the cloud is a challenge for biologist and computer scientists. In this study, we present an error-correction algorithm, called the CloudRS algorithm, for correcting errors in NGS data. The CloudRS algorithm aims at emulating the notion of error correction algorithm of Allpath-LG on the Hadoop/ MapReduce framework. It is conservative in correcting sequencing errors to avoid introducing false decisions, e.g., when dealing with reads from repetitive regions. We also illustrate several probabilistic measures we introduce into CloudRS to make the algorithm more efficient without sacrificing its effectiveness. Running time of using up to 80 instances each with 8 computing units shows satisfactory speedup. Experiments of comparing with other error correction programs show that CloudRS algorithm performs lower false positive rate for most evaluation benchmarks and higher sensitivity on genome S. cerevisiae. We demonstrate that CloudRS algorithm provides significant improvements in the quality of the resulting contigs on benchmarks of NGS de novo assembly. "A Cooperative Botnet Profiling and Detection in Virtualized Environment," IEEE Conference on Communications and Network Security (CNS), October 2013. Authors: Shun-Wen Hsiao, Yi-Ning Chen, Yeali S. Sun, Meng Chang Chen Abstract: Cloud security becomes an important topic in recent years, as to overcome the botnet in a visualized environment is a critical task for the cloud providers. Although numerous intrusion detection systems are available, yet it is not practical to install IDS in every virtual machine. In this paper, we argue that a virtual machine monitor (VMM) can support certain security functions that our proposed design can actively collect information directly from the VMM without installing an agent in the guest OS. In addition, bot could not aware of the existence of such detection agent in the VMM. The proposed detection mechanism takes both passive and active detection approaches that the passive detection agent lies in the VMM to examine the tainted data used by a bot to check against bot behavior profiles and the active detection agent that performs active bot fingerprinting can actively send specific stimulus to a guest and examine if there exists expected triggered behavior. In the real-world bot experiments, we show the passive detection agent can distinguish between bots and benign process with low false positive and false negative rates. Also, the result shows the active detection agent can detect a bot even when before it performs its malicious jobs. The proposed mechanism suites an enterprise having cloud environment well to defeat malware. Current Research Results Authors: Jhih-Siang Lai, Cheng-Wei Cheng, Allan Lo, Ting-Yi Sung, and Wen-Lian Hsu Abstract: Background: Since membrane protein structures are challenging to crystallize, computational approaches are essential for elucidating the sequence-to-structure relationships. Structural modeling of membrane proteins requires a multidimensional approach, and one critical geometric parameter is the rotational angle of transmembrane helices. Rotational angles of transmembrane helices are characterized by their folded structures and could be inferred by the hydrophobic moment; however, the folding mechanism of membrane proteins is not yet fully understood. The rotational angle of a transmembrane helix is related to the exposed surface of a transmembrane helix, since lipid exposure gives the degree of accessibility of each residue in lipid environment. To the best of our knowledge, there have been few advances in investigating whether an environment descriptor of lipid exposure could infer a geometric parameter of rotational angle. Results: Here, we present an analysis of the relationship between rotational angles and lipid exposure and a support-vector-machine method, called TMexpo, for predicting both structural features from sequences. First, we observed from the development set of 89 protein chains that the lipid exposure, i.e., the relative accessible surface area (rASA) of residues in the lipid environment, generated from high-resolution protein structures could infer the rotational angles with a mean absolute angular error (MAAE) of 46.32°. More importantly, the predicted rASA from TMexpo achieved an MAAE of 51.05°, which is better than 71.47° obtained by the best of the compared hydrophobicity scales. Lastly, TMexpo outperformed the compared methods in rASA prediction on the independent test set of 21 protein chains and achieved an overall Matthew’s correlation coefficient, accuracy, sensitivity, specificity, and precision of 0.51, 75.26%, 81.30%, 69.15%, and 72.73%, respectively. TMexpo is publicly available at http://bio-cluster.iis.sinica.edu.tw/TMexpo. Conclusions: TMexpo can better predict rASA and rotational angles than the compared methods. When rotational angles can be accurately predicted, free modeling of transmembrane protein structures in turn may benefit from a reduced complexity in ensembles with a significantly less number of packing arrangements. Furthermore, sequence-based prediction of both rotational angle and lipid exposure can provide essential information when high-resolution structures are unavailable and contribute to experimental design to elucidate transmembrane protein functions. Current Research Results Authors: Tsai, Z.T.Y., Chu, W.Y., Cheng, J.H., and Tsai, H.K.* Abstract: Non-B DNA structures are abundant in the genome and are often associated with critical biological processes, including gene regulation, chromosome rearrangement and genome stabilization. In particular, G-quadruplex (G4) may affect alternative splicing based on its ability to impede the activity of RNA polymerase II. However, the specific role of non-B DNA structures in splicing regulation still awaits investigation. Here, we provide a genomewide and cross-species investigation of the associations between five non-B DNA structures and exon skipping. Our results indicate a statistically significant correlation of each examined non-B DNA structures with exon skipping in both human and mouse. We further show that the contributions of non-B DNA structures to exon skipping are influenced by the occurring region. These correlations and contributions are also significantly different in human and mouse. Finally, we detailed the effects of G4 by showing that occurring on the template strand and the length of G-run, which is highly related to the stability of a G4 structure, are significantly correlated with exon skipping activity. We thus show that, in addition to the well-known effects of RNA and protein structure, the relative positional arrangement of intronic non-B DNA structures may also impact exon skipping. Current Research Results "What Distinguish One from Its Peers in Social Networks," Data Mining and Knowledge Discovery, November 2013. Authors: Yi-Chen Lo, Jhao-Yin Li, Mi-Yen Yeh, Shou-De Lin, Jian Pei Abstract: Being able to discover the uniqueness of an individual is a meaningful task in social network analysis. This paper proposes two novel problems in social network analysis: how to identify the uniqueness of a given query vertex, and how to identify a group of vertices that can mutually identify each other. We further propose intuitive yet effective methods to identify the uniqueness identification sets and the mutual identification groups of different properties. We further conduct an extensive experiment on both real and synthetic datasets to demonstrate the effectiveness of our model. "A Systematic Methodology for OS Benchmark Characterization," ACM Research in Adaptive and Convergent Systems (RACS), October 2013. Authors: Shuo-Hung Chen, Hsiao-Mei Lin, Kuo-Yi Chen, Yuan-Hao Chang, Pen-Chung Yew, and Chien-Chung Ho Abstract: Using benchmarks to evaluate operating systems is a common and important approach. However, determining which benchmarks to use for such evaluation requires very careful consideration. It has been found that a seemingly naive change of system configuration or input set could lead to drastic change of benchmark characteristics, and could also lead to misleading or incorrect results. Some OS benchmark suites may also include too many benchmark programs with very similar characteristics that could give biased results against, or in favor of, certain kernel behavior. Hence, we need to determine the characteristics of benchmark programs in order to come up with an appropriate benchmark suite for such evaluation, and to interpret the measured results more precisely and correctly. Although there have been many tools developed to help profiling an OS and to characterize its run-time behavior, the collected data by those tools are often very large and complex. It is extremely time consuming, labor intensive, and error prone to analyze the large volume of measured results, and to determine the characteristics of a suite of benchmark programs. In this work, we propose to use machine-learning techniques to help analyzing and characterizing OS benchmark programs based on the traced OS kernel events. In the work, a systematic methodology is proposed to automatically characterize benchmarks. We found that the characterized OS behavior could help developers to choose appropriate applications to benchmark operating systems. "Non-Reference Audio Quality Assessment for Online Live Music Recordings," Proc. ACM International Conference on Multimedia (MM), October 2013. Authors: Zhonghua Li, Ju-Chiang Wang, Jingli Cai, Zhiyan Duan, Hsin-Min Wang and Ye Wang Abstract: Immensely popular video sharing websites such as YouTube have become the most important sources of music information for Internet users and the most prominent platform for sharing live music. The audio quality of this huge amount of live music recordings, however, varies significantly due to factors such as environmental noise, location, and recording device. However, most video search engines do not take audio quality into consideration when retrieving and ranking results. Given the fact that most users prefer live music videos with better audio quality, we propose the first automatic, non-reference audio quality assessment framework for live music video search online. We first construct two annotated datasets of live music recordings. The first dataset contains 500 human-annotated pieces, and the second contains 2,400 synthetic pieces systematically generated by adding noise effects to clean recordings. Then we formulate the assessment task as a ranking problem and try to solve it using a learning-based scheme. To validate the effectiveness of our framework, we perform both objective and subjective evaluations. Results show that our framework significantly improve the ranking performance of live music recording retrieval and can prove useful for various real-world music applications. "Joint Management of Performance-predictable Virtualized Storage Devices with Hard Disk and Flash Memory," ACM Research in Adaptive and Convergent Systems (RACS), October 2013. Authors: Po-Chun Huang, Yuan-Hao Chang, Tei-Wei Kuo, Chien-Chung Ho, and Hyunseung Choo Abstract: Recently, the significance of storage virtualization has been highlighted due to the growing performance demands of next-generation applications. However, with its unpredictable long seek time and rotational delays, hard disk fails to provide sufficient performance guarantees to fulfill the service-level objectives of the applications, especially on random accesses. To resolve the random-access problem of hard disk, it is a common approach to adopt flash memory in a hard-disk-based storage system. Nevertheless, flash memory requires garbage collection to reclaim the space with the invalid data, where the garbage collection process might introduce long and unpredictable time overheads and considerably reduce the performance benefits of flash memory. This work proposes a joint management strategy for virtualized storage systems with hard disk and flash memory. The major idea of this work is, to exploit flash memory to enhance the random access performance of hard disk, while exploiting hard disk to aid flash memory in avoiding the worst-case delays incurred by garbage collection. Analytical and experimental studies showed that the resulted virtualized storage device shows surprising behaviors of the worst-case performance higher than both hard disk and flash memory. "Spatial Search for K Diverse-Near Neighbors," ACM Conference on Information and Knowledge Management (ACM CIKM), October 2013. Authors: G. Ference, W.-C. Lee, H.-J. Hung, and D.-N. Yang Abstract: To many location-based service applications that prefer diverse results, finding locations that are spatially diverse and close in proximity to a query point (e.g., the current location of a user) can be more useful than finding the nearest neighbors/locations. In this paper, we investigate the problem of searching for the Diverse-Near Neighbors (DNNs) in spatial space that is based upon the spatial diversity and proximity of candidate locations to the query point. While employing a conventional distance measure for proximity, we develop a new and intuitive diversity metric based upon the variance of the angles among the candidate locations with respect to the query point. Accordingly, we create a dynamic programming algorithm that _finds the optimal DNNs. Unfortunately, the dynamic programming algorithm, with a time complexity of O(kn^3), incurs excessive computational cost. Therefore, we further propose two heuristic algorithms, namely, Distance-based Browsing (DistBrow) and Diversity-based Browsing (DivBrow) that provide high effectiveness while being efficient by exploring the search space prioritized upon the proximity to the query point and spatial diversity, respectively. Using real and synthetic datasets, we conduct a comprehensive performance evaluation. The results show that DistBrow and DivBrow have superior effectiveness compared to state-of-the-art algorithms while maintaining high efficiency. "A Disturb-Alleviation Scheme for 3D Flash Memory," ACM/IEEE International Conference on Computer-Aided Design (ICCAD), November 2013. Authors: Yu-Ming Chang, Yuan-Hao Chang, Tei-Wei Kuo, Hsiang-Pang Li, and Yung-Chun Li Abstract: Even though 3D flash memory presents a grand opportunity for huge-capacity non-volatile memory, it suffers from serious program disturb problems. Different from the past efforts in error correction codes or the work in trading the space utilization with reliability, we propose a disturb-alleviation scheme that can alleviate the negative effects caused by program disturb, especially inside a block, without introducing extra overheads on encoding or storing of extra redundant data. In particular, a methodology is proposed to reduce the data error rate by distributing unavoidable disturb errors over the flash-memory space of invalid data, with the considerations of the physical organization of 3D flash memory. A series of experiments was conducted based on real multi-layer 3D flash chips, and it showed that the proposed scheme could significantly enhance the reliability of 3D flash memory. "Size Does Matter: How Does Image Display Size Affect Aesthetic Perception?," Proceedings of ACM Multimedia 2013, October 2013. Authors: Wei-Ta Chu, Yu-Kuang Chen, and Kuan-Ta Chen Abstract: It is undoubtedly that an image's content determines how people assess the image's aesthetic level. Previous works have shown that image contrast, saliency features, and the composition of objects may jointly decide whether an image looks good or not. In addition to the "content" of an image, however, the way an image is "presented" to viewers may also affect how much it is appreciated. For example, one might expect a picture always looks better when it is displayed in a larger size. Is this "the-bigger-the-better" rule always true? If not, under what situations it becomes invalid? This paper devotes to analyze how an image's resolution (pixels) and physical dimension (inches) affect how much viewers appreciate this image. Based on a large-scale aesthetic assessments of 100 images displayed in a variety of resolutions and physical dimensions, we show that an image's display size significantly affects its aesthetic rating in a complicated way; normally a picture looks better with a bigger display size, but it may look relatively worse depending on its content. We develop a set of regression models to predict a picture's absolute and relative aesthetic levels at a given display size based on its content and compositional features, and, simultaneously, we analyze the essential features that lead to the size-dependent property of image aesthetics. We hope that this work will shed some light on future research by revealing that both content and presentation should be considered in image aesthetics evaluation. Current Research Results "Multicast with Intra-Flow Network Coding in Multi-Rate Multi-Channel Wireless Mesh Networks," IEEE Trans. on Vehicular Technology, November 2013. Authors: C.-J Lin and D.-N. Yang Abstract: It has been shown that intra-flow network coding can improve the multicast throughput in single-channel single rate wireless mesh networks. Most existing studies focus on developing a practical intra-flow network-coding multicast protocol. With the ripe of the wireless products supporting multi-rate multi-channel communications, nowadays it becomes increasingly important to improve the network coding gain by utilizing multiple bit-rates and non-overlapping channels, but new challenges also arise due to various tradeoffs. In a multi-rate, multi-channel, multi-hop network, overhearing opportunities and bandwidth utilization are highly correlated to the selection of the channel and rate, which, in turn, determines the achievable throughput of multicast with intra-flow network coding. Specifically, wireless nodes can transmit at higher bit-rates over orthogonal channels to increase the forwarding throughput, but the strategy reduces overhearing opportunities and the coding gain in multicast with intra-flow network coding. To achieve the best trade-off between the above two aspects, we formulate a new optimization model called multi-Rate multi-Channel Multicast with intra-flow Network Coding (RCMNC), which solves the joint channel assignment, rate selection and flow allocation problems for multi-hop intraflow network coding multicast. We then reformulate the primal problem as the Lagrangian dual problem, and propose an algorithm to approximate the solution of the dual problem in polynomial-time. Simulation results show that, by assigning a suitable rate and channel to each network interface, multicast throughput with intra-flow network coding under RCMNC is up to 3.3 times higher than that achieved by the existing approach in a multi-rate multi-channel wireless mesh network. Current Research Results "Structural Diversity for Resisting Community Identification in Published Social Networks," IEEE Trans. on Knowledge and Data Engineering, October 2013. Authors: C.-H. Tai, P. S. Yu, D.-N. Yang, and M.-S. Chen Abstract: Recently, the privacy issues about the individuals in the social networks have become serious concerns. Vertex identification is one of the most important problems that have been addressed. In reality, however, each individual in a social network is inclined to be associated with not only a vertex identity but also a community identify, which could represent the personal privacy information sensitive to the public, such as the political party affiliation. This paper first addresses the new privacy issue, referred to as community identification, by showing that the community identity of a victim can still be inferred even though the social network is protected by existing anonymity schemes. For this problem, we then propose the concept of structural diversity to provide the anonymity of the community identities. The k-Structural Diversity Anonymization (k-SDA) is to ensure sufficient vertices with the same vertex degree in at least k communities in a social network. We propose an Integer Programming formulation to find optimal solutions to k-SDA and also devise scalable heuristics to solve large-scale instances of k-SDA with different perspectives. The performances studies on real data sets from various perspectives demonstrate the practical utility of the proposed privacy schema and our anonymization approaches.	2014-03-11 12:36:09	{"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": 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": 0.30460405349731445, "perplexity": 2646.0191690361744}, "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-2014-10/segments/1394011192582/warc/CC-MAIN-20140305091952-00049-ip-10-183-142-35.ec2.internal.warc.gz"}
https://paramountranchtrailruns.com/sltoy/f1bd06-hand-arm-vibration-syndrome-control-measures	# hand arm vibration syndrome control measures Default is 3. parent — The handle of the axes to receive the control chart plot. Re: How to Calculate UCL (Upper Control Limit) & LCL (Lower Control Limit) & CL? This wizard computes the Lower and Upper Control Limits (LCL, UCL) and the Center Line (CL) for monitoring the fraction of nonconforming items or number of nonconformities (defects) using p and c control charts . Now calculate the UCL and LCL Now we will calculate the upper and lower control limit which are ( Average + 3 σ ) and (Average — 3 σ ) respectively. how to calculate ucl and lcl in control charts in excel: ucl lcl formula: how to calculate upper and lower control limits in excel: how to calculate upper control limit: lower control limit formula: how to calculate ucl: how to find ucl and lcl: how to find upper control limit: Center Line. UCL - Upper Control Limit UCL, (Upper Control Limit), as it applies to X Bar, (mean), and R Bar, (range), charts, is a formula that will calculate an upper most limit for samples to evaluate to.There is usually a LCL, (Lower Control Limit), that is also calculated and used in process control charts.. You can also use Pre-Control to establish control limits on control charts. Many people ask: "Why aren't my upper and lower control limits (UCL, LCL) calculated as: µ ∓ 3sigma (where μ is the mean and sigma is the standard deviation)?" 5. The figure below illustrates this. Control charts help us in visualizing this variation. Calculate the Upper Control Limit (UCL), which is the mean of means plus three times the standard deviation. Hi all how do i calculate the UCL,LCL & CL for the below data. Ideally, we would like for all of our points to fall within the control limits, and we would like for … Upper control limit (UCL) Notation. UCL , LCL (Upper and Lower Control Limit) where n is the sample size, np-bar is the Average count , and p-bar is calculated with the following Np chart formula: PLS HELP ME!!! Shewhart Control Charts P Chart: Formulas. UCL = D4 (R̅) LCL = D3 (R̅) Grand mean (for mean of Xbars) = 15.11. The format of the control charts is fully customizable. R-bar (mean of Ranges) = 6.4. Notation. P=defectsdividedbysamplesize(percentage:np/n) These control limits are chosen so that almost all of the data points will fall within these limits as long as the process remains in-control. UCL=u+3! More about control charts. Control charts have one central line or mean line (average), and then we have the Upper Control Limit (UCL) and Lower Control Limit (LCL). If you are using a Levey Jennings chart, then that IS how your control limits are calculated. The R-bar chart indicates that the process variability is in statistical control, This is so because range value lie between the UCL and the LCL. The idea is to create an interactive dynamic chart that displays sales distribution over the selected time period. LCL Ave Standard = −rage 3 Avera eg. How to calculate control limits for arbitrary chosen sample size: You can use TP414 to calculate the control limits of an Xbar chart (starting with the sample size as input) by: One of the purposes of control charts is to estimate the average and standard deviation of a process. Average moving range method. UCL=uppercontrollimit(pത+(3∗ ... will have to calculate the UCL and LCL for each data point. 4. This assumes the number of opportunitie or sample size is s constant. Lower control limit (LCL) The LCL is the greater of the following: or. The average is easy to calculate and understand – it is just the average of all the results. (Click here if you need control charts for attributes) This wizard computes the Lower and Upper Control Limits (LCL, UCL) and the Center Line (CL) for monitoring the process mean and variability of continuous measurement data using Shewhart X-bar, R-chart and S-chart.. More about control charts. the number of items in a sample meeting a criteria of interest. Formula: S = √ Σ(x - x̄) 2 / N-1 Individual chart: UCL = X̄ + 3S, LCL = X̄ - 3S Moving range chart: UCL=3.668 * MR, LCL = 0 Where, X/N = Average X = Summation of measurement value N = The count of mean values S = Standard deviation X = Average Measurement UCL = Upper control limit LCL = Lower control limit Calculate the lower control … Can neone on the board please let me know how does Minitab calculate the UCL and LCL for an Individual Chart. The default is 3. LCL Standard =0 for λ≤9. Default is to create axes in a new figure. UCL (X-bar) = X-bar-bar + (A2 x R-bar) Plot the Upper Control Limit on the X-bar chart. The upper control limit and lower control limit are three standard deviation distance from … Therefore, production must stopped and the cause of this abnormal variation must be identified and rectified. target = lcl, ucl to the end of the instruction (which i'm pretty sure is wrong and gross), but the graph dissapears, however if I add only ucl or lcl, it shows it perfectly. u n LCL=u!3" u n Sensitizing Rules for Control Charts Normally, a single point outside the control limits is considered to signal an out of control process. Users often contact Minitab technical support to ask how the software calculates the control limits on control charts. LCL = x̅̅ – A2 (R̅) Control limits for the R-chart. The standard deviation is a little more difficult to understand – and to complicate things, there are multiple ways that it can be determined – each giving a different answer. Center Line. We use two statistics, the overall average and the average range, to help us calculate the control limits. In this example, type '=F7 3F8' (without quote marks) in cell F9 and press 'Enter.' These are the calculated LCL (lower control limit), Avg (average) and UCL (upper control limit). Chart demonstrating basis of control chart LCL - Lower Control Limit LCL, (Lower Control Limit), as it applies to X Bar, (mean), and R Bar, (range), control charts, is a formula that will calculate an lower most limit for samples to evaluate to.There is usually a UCL, (Upper Control Limit), that is also calculated.Used in SPC, (statistical process control). The initial chart represents a sample run where the process is considered to be in control. Under some circumstances, however, such as while working to establish statistical control, it is desirable to employ “sensitizing rules” which make it more likely Alternative for constructing individuals control chart Note: Another way to construct the individuals chart is by using the standard deviation. Plotted statistic for the C Attribute Control Chart. I am taking 5 data in a day for each parameter with an interval of 2~3 hours since our parts are using high precision care with high turnover cost. I checked the documentation and found nothing in the qicharts2 one. D4 =2.114. November 2012. Two other horizontal lines, called the upper control limit (UCL) and the lower control limit (LCL), are also shown on the chart. Then we can obtain the chart from $$\bar{x} \pm 3s/c_4 \, .$$ the count of occurrences of a criteria of interest in a sample of items. Plotted statistic for the Np Attribute Control Chart. The limits are based on taking a set of preliminary samples drawn while the process is known to be in control. A2 = 0.577. Control Chart in ASP.NET MVC Chart control. Upper control limit (UCL) The UCL for each subgroup is equal to the lesser of the following: or. The XBar and R charts have three lines drawn horizontally across them. You can create a control chart (with UCL, CL, and LCL limits) using the stripline and annotation features. Therefore it is a suitable source of data to calculate the UCL, LCL and Target control limits. What about D4 and D3? Understanding Standard Deviation and Control Charts. 9. Lower control limit (LCL) The LCL for each subgroup is equal to the greater of the following: or. I used a slicer to filter the time period. Calculate the upper control limit for the X-bar Chart b. Does it mean my control limits will be change on daily basis? nsigma — The number of sigma multiples from the center line to a control limit. Find the center line by calculating the mean moving range of your data points. To create a control charts, follow the given steps. The control limit lines and values displayed in the chart are a result these calculations. This is the p parameter for p and np charts, the mean defects per unit for u and c charts, and the normal mu parameter for other charts. This is a special case of a U chart that is commonly called a C chart. The upper control limit, or UCL is typically set at three standard deviations, or sigma, above the process mean, and the lower control limit, LCL, would be set three sigma below the mean. where m is the number of groups included in the analysis. The adjusted control limits are: UCL Averag Adjusted Eg: For a data range of 10, 20, 30, ….. , 100, its gives me the centre line at 55 (Average), LCL at 28.4 and UCL at 81.6. 0.00135, 0.5, LCL, Target, Target, UCL Where LCL and UCL are chosen control limits, and Target is the center line. where m is the number of groups included in the analysis. This example will just use the first row where the defect is 58 and sample size (n) is 80. This procedure permits the defining of stages. D3 = 0. Would appreciate if neone can tell me how to arrive at the figures. For example, the control limit equations for the classical Xbar-R control chart are: What is A2 and where does it come from? it has a total of 30 datas and i need to find out also the formula for UCL,LCL & CL as i need to use excel to do the calculations. The control chart is given below The process is in control, since none of the plotted points fall outside either the $$UCL$$ or $$LCL$$. How is it related to the overall average and the average range? Term Description; process proportion: parameter for Test 1. September 2010 Ever wonder where the control limit equations come from? UCL , LCL (Upper and Lower Control Limit) where n is the sample size and c-bar is the Average count 6 3 2 individuals control charts control chart in excel vba control chart excel template how to control chart anese gemba kaizen using excel control charts with varying Control Chart Limits How To Calculate Ucl Lcl What AreHow To Create A Control Chart ExcelchatXmr Statistical Process Control ChartsBest Excel Tutorial Statistical Process Control ChartControl Charts… Read More » For counts the standard control limits are: UCL Ave Standard = +rage 3 Avera eg. Calculate the Lower Control Limit (LCL), which is the mean of … In the qic (not supported anymore) i found: Data must be in the sequence the samples were produced. Term ... parameter for Test 1 (default is 3) d 3 A constant used to estimate LCL and UCL. Step 1: Load line charts for the data. Lets review the 6 tasks below and how to solve them a. Hi Bev, Yes, I do have continuous data. The x-bar chart indicates that the production process is out of control. Calculate the upper and lower XmR control limits using the sequential deviation; Lower XmR Control Limit(LCL): LCL X = X – 3 ⋅ Š; Upper XmR Control Limit(UCL): UCL X = X + 3 ⋅ Š; mR Chart Calculations. I then created a combo chart – the lines show the average and control limits (LCL and UCL) and the columns show the total sales values. Calculate the X-bar Chart Lower Control Limit, or lower natural process limit, for the X-bar chart by multiplying R-bar by the appropriate A2 factor (based on subgroup size) and subtracting that value from the … Indicates that the production process is out of control charts is to estimate the average,... 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Equal to the lesser of the following: or LCL & CL for the data it to...	2021-06-20 21:26:08	{"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": 0, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7206355929374695, "perplexity": 1899.8280430467303}, "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/1623488257796.77/warc/CC-MAIN-20210620205203-20210620235203-00158.warc.gz"}
https://www.instasolv.com/question/if-the-mid-points-p-q-and-r-of-the-sides-of-the-a-b-c-are-3-3-3-co3cip	If the mid-points P,Q and R of the ... Question # If the mid-points ( P, Q ) and ( R ) of the sides of the ( Delta A B C ) are (3,3),(3,4) and ( Q ). respectively, then ( Delta mathrm{ABC} ) is(A) right angled(B) aculte angled(C) obtuse angled(D) isosceles JEE/Engineering Exams Maths Solution 99 4.0 (1 ratings) This hydrated iron oxide is rust. Rancidity : The process of oxidation of fats and oils that can be easily noticed by the change in taste and smell is Known as rancidity. for example	2021-02-27 04:03:13	{"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": 0.8912225961685181, "perplexity": 4843.6661476467125}, "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/1614178358064.34/warc/CC-MAIN-20210227024823-20210227054823-00420.warc.gz"}
http://math.stackexchange.com/questions/60536/a-series-problem-by-knuth	# A series problem by Knuth I came across the following problem, known as Knuth's Series which originally was an American Mathematical Monthly problem. Prove that $$\sum_{n=1}^\infty \left(\frac{n^n}{n!e^n}-\frac{1}{\sqrt{2\pi n}}\right)=-\frac{2}{3}-\frac{\zeta\left(\frac{1}{2}\right)}{\sqrt{2\pi}}.$$ It seems interesting. We are trying to compute a particular sum of the error term in Stirlings approximation. The immediate simple approaches don't seem to work. Attempt: Why $\zeta\left(\frac{1}{2}\right)$: By partial summation we know that $$\sum_{n=1}^M \frac{1}{n^s}= \frac{M^{1-s}}{1-s}+\zeta(s)+O\left(M^{-s}\right)$$ for $s>0$, $s\neq 1$. This tells us where the $\frac{\zeta\left(\frac{1}{2}\right)}{\sqrt{2\pi}}$ comes from since $$\sum_{n=1}^M \frac{1}{\sqrt{2\pi n}}=\sqrt{\frac{2M}{\pi}}+\frac{\zeta\left(\frac{1}{2}\right)}{\sqrt{2\pi}}+o(1).$$ Now all that remains is to prove that $$\sum_{n=1}^M \frac{n^n}{n!e^n}=\sqrt{\frac{2M}{\pi}} -\frac{2}{3}+o(1).$$ I am kinda stuck here, as this series seems strange to deal with. Thanks! - Did you mean $\sum_{n=1}^M \frac{1}{n^s}= \frac{M^{1-s}}{1-s}+\zeta(s)+O\left(M^{-s}\right)$ by any chance? =) – Patrick Da Silva Aug 29 '11 at 15:36 @Patrick Da Silva: Indeed! Switched the $n$ and $M$ by accident – Eric Naslund Aug 29 '11 at 15:37 Here is a series of hints to summarise the approach that appeared in the American Math Monthly. I have divided them by horizontal bars so hopefully it can ensure you only read one at a time. Unfortunately, this particular solution does not appear to be very general. Prove the following separately first: $$\sum_{k=1}^{\infty} \biggl( \frac{k^k}{k!e^k} - \frac{ (1/2)_{k-1} }{\sqrt{2} (k-1)!} \biggr) = \frac{-2}{3}$$ $$\sum_{k=1}^{\infty} \biggl( \frac{1}{\sqrt{2\pi k}} - \frac{ (1/2)_{k-1} }{\sqrt{2} (k-1)!} \biggr) = \frac{ \zeta (1/2) }{\sqrt{2\pi}}$$ where the rising factorial is defined: $(a)_0 = 1 \mbox{ and } (a)_m = a(a+1)(a+2) \cdots (a+m-1)$ Abel's theorem comes in handy: If $\sum_{k=0}^{\infty} a_k$ converges, then $$\sum_{k=0}^{\infty} a_k = \lim_{x\to 1^{-} } \sum_{k=0}^{\infty} a_k x^k$$ Some power series (both for $\|z\| < 1$) : $$\mathrm{W}(z) = \sum_{k=1}^{\infty} \frac{k^{k-1} z^k}{k!e^k}$$ $$\sum_{k=1}^{\infty} \frac{ (1/2)_{k-1} }{(k-1)!} z^{k-1} = \frac{1}{\sqrt{1-z}}$$ where $\mathrm{W}(z)$ satisfies $\mathrm{W} \exp(-\mathrm{W}) = z/e$ (See Lambert W Function), and the second series comes from Newton's Binomial Expansion. - Seeing the $n^n$ factor in the given series made me suspect Lambert will somehow be turning up. Nice! – Ｊ. Ｍ. Aug 29 '11 at 15:52 It seems this identity $W(z)=W\exp(-W)$ is the key to solving the problem. Also, originally I had hoped to use the fact that $$\binom{2n}{n}/4^n \sim \frac{1}{\sqrt{2\pi n}},$$ and it seems exactly this fact was used here, as $\frac{1}{\sqrt{1-z}}$ is the generating series for the above coefficients. (I guess the coefficients you have above are really just central binomial coefficients in disguise.) – Eric Naslund Aug 29 '11 at 17:56	2014-12-18 15:44:57	{"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": 0.9612710475921631, "perplexity": 481.89419181969646}, "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/1418802767247.82/warc/CC-MAIN-20141217075247-00111-ip-10-231-17-201.ec2.internal.warc.gz"}
http://mathhelpforum.com/calculus/119350-increasing-decreasing-function-floor-investigate.html	# Thread: increasing decreasing function with floor() investigate 1. ## increasing decreasing function with floor() investigate Find where f(x) is increasing and find where it is decreasing ** the [] brackets in the power are meant to be the \floor function (i couldn't get it right in latex..) Thanks for the help ! $ f(x)=(-1)^{[3x]}X+(-1)^{[2x]}X^2 $ 2. will appreciate the help much.. help still needed... 3. Did you try to graph the function? 4. ## ya Yes, I got a pretty crazy graph...	2017-10-22 18:30:35	{"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": 1, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5622402429580688, "perplexity": 3604.1860393459688}, "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-2017-43/segments/1508187825399.73/warc/CC-MAIN-20171022165927-20171022185927-00732.warc.gz"}
https://math.stackexchange.com/questions/1751189/property-of-a-composed-holomorphic-function	# Property of a composed holomorphic function I have a question about the following problem. Let $D$ be the unit disc in $\mathbb{C}$. Suppose $f: D \to D$ is a holomorphic function with $f(0) = 0$ and $f'(0) = 1$. By applying Cauchy's estimates to $$f_k = f \circ f \circ \cdots \circ f\;\; \text{k times}$$ for large $k$, show that $f$ is a linear function. Someone suggested using Schwarz lemma, but I haven't learned it in class yet. I'm having trouble because I don't have an idea what result I want when I want to show a function is a linear function. Thank you! • @user1952009 If $f=z^2/2$ then $f'(0)\ne 1$. The problem is correct as stated. – David C. Ullrich Apr 20 '16 at 13:20 • The Schwarz Lemma says precisely that $f$ is linear. But whether you've covered that in class or not you can't use that - you're supposed to give a solution by a specified method, not by any method at all. – David C. Ullrich Apr 20 '16 at 13:21 • @DavidC.Ullrich How can I apply Cauchy's estimate when we don't know $f_k$ is bounded by some $M$? – user12994 Apr 20 '16 at 13:40 • @user12994, $\|f_k\| \le 1$ because $\|f\| \le 1$. – lhf Apr 20 '16 at 13:41 • @DavidC.Ullrich Oh yes, I forgot about that condition. So if we let $z_0 \in D$ we have $\|f_k(z_0)\| \leq 1$ for $\|z-z_0\| = r$ where $0 < r < 1$. Then we can use Cauchy's estimate $\forall \; n \geq 0$, $\|f_k^{(k)}(z_0) \| \leq \frac{k!}{r^k}$. We need $k$th derevative to be a constant for $f$ to be a linear function right? – user12994 Apr 20 '16 at 13:48 The Cauchy estimates $\|a_n\|\le r^{-n}\sup_{\|z\|=r}\|f(z)\|$ show that any function that takes values in $D$ has Taylor coefficients (about $z=0$) that are $\le 1$ in absolute value (take $r\to 1$). The $k$-fold composition $f_k$ is such a function. Now suppose that $f(z)=z+az^n+\ldots$, with $a\not= 0$. Then $f_k(z)=z+kaz^n+\ldots$, by an easy induction. For large $k$, this contradicts what we just observed.	2020-01-23 02:19:01	{"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": 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": 0.9220818877220154, "perplexity": 156.2609187911685}, "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/1579250608062.57/warc/CC-MAIN-20200123011418-20200123040418-00230.warc.gz"}
https://physics.stackexchange.com/questions/480543/how-can-i-find-the-nuclear-interaction-length-in-solid-lead-given-atomic-number	# How can I find the nuclear interaction length in solid lead given atomic number, radius of the lead nucleus and lead density? I need to estimate the nuclear interaction length in solid lead given the atomic mass unit $$A=207.2u$$, radius of lead nucleus $$R=r_0A^{1/3}$$ where $$r_0=1.25fm$$ and the density of lead is $$\rho=11.34g/cm^2$$. I've been trying to find calculations for the nuclear interaction length but all I can find are tables with the length already given but no method of calculation. For example the Particle Data Group has a page for lead, and while I don't expect them to have details of the calculations, this is one of the only places I can find the nuclear interaction length and no other sites mention how it is calculated. How do I calculate the nuclear interaction length given this information?	2021-06-16 06:54:02	{"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": 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": 4, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8200746178627014, "perplexity": 111.09073962400157}, "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-2021-25/segments/1623487622234.42/warc/CC-MAIN-20210616063154-20210616093154-00260.warc.gz"}
https://zbmath.org/?q=an:0815.62022	## Ordered linear smoothers.(English)Zbl 0815.62022 Summary: This paper deals with the following approach for estimating the mean $$\mu$$ of an $$n$$-dimensional random vector $$Y$$: first, a family $${\mathbf S}$$ of $$n\times n$$ matrices is specified. Then, an element $$\widehat {S}\in {\mathbf S}$$ is selected by Mallows $$C_ L$$, and $$\widehat {\mu}= \widehat {S}\cdot Y$$. The case is considered that $${\mathbf S}$$ is an “ordered linear smoother” according to some easily interpretable, qualitative conditions. Examples include linear smoothing procedures in nonparametric regression (as, e.g., smoothing splines, minimax spline smoothers and kernel estimators). Stochastic probability bounds are given for the difference $(1/n)\\| \mu- \widehat {S}\cdot Y\\|^ 2_ 2- (1/n)\\| \mu- \widehat {S}_ \mu\cdot Y\\|^ 2_ 2,$ where $$\widehat {S}_ \mu$$ denotes the minimizer of $$(1/n) \\|\mu-S \cdot Y\\|^ 2_ 2$$ for $$S\in {\mathbf S}$$. These probability bounds are generalized to the situation that $${\mathbf S}$$ is the union of a moderate number of ordered linear smoothers. These results complement work by K. C. Li [ibid. 14, 1101-1112 (1986; Zbl 0629.62043); ibid. 15, 958-975 (1987; Zbl 0653.62037)] on the asymptotic optimality of $$C_ L$$. Implications for nonparametric regression are studied in detail. It is shown that there exists a direct connection between James-Stein estimation and the use of smoothing procedures, leading to a decision-theoretic justification of the latter. Further conclusions concern the choice of the order of a smoothing spline or a minimax spline smoother and the rates of convergence of smoothing parameters. ### MSC: 62G07 Density estimation 62J07 Ridge regression; shrinkage estimators (Lasso) 62H12 Estimation in multivariate analysis ### Citations: Zbl 0629.62043; Zbl 0653.62037 Full Text:	2022-05-27 16:15:15	{"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": 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": 0.40969595313072205, "perplexity": 885.3701162771214}, "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-2022-21/segments/1652662658761.95/warc/CC-MAIN-20220527142854-20220527172854-00621.warc.gz"}
http://support.sas.com/documentation/cdl/en/etsug/67525/HTML/default/etsug_ucm_details40.htm	# The UCM Procedure ### Statistics of Fit This section explains the goodness-of-fit statistics reported to measure how well the specified model fits the data. First the various statistics of fit that are computed using the prediction errors, , are considered. In these formulas, n is the number of nonmissing prediction errors and k is the number of fitted parameters in the model. Moreover, the sum of squared errors, , and the total sum of squares for the series corrected for the mean, , where is the series mean, and the sums are over all the nonmissing prediction errors. Mean Squared Error The mean squared prediction error, Root Mean Squared Error The root mean square error, RMSE = Mean Absolute Percent Error The mean absolute percent prediction error, MAPE = .The summation ignores observations where . R-square The R-square statistic, .If the model fits the series badly, the model error sum of squares, SSE, might be larger than SST and the R-square statistic will be negative. Random Walk R-square The random walk R-square statistic (Harvey’s R-square statistic that uses the random walk model for comparison), , where , and Maximum Percent Error The largest percent prediction error, . In this computation the observations where are ignored. The likelihood-based fit statistics are reported separately (see the section The UCMs as State Space Models). They include the full log likelihood (), the diffuse part of the log likelihood, the normalized residual sum of squares, and several information criteria: AIC, AICC, HQIC, BIC, and CAIC. Let q denote the number of estimated parameters, n be the number of nonmissing measurements in the estimation span, and d be the number of diffuse elements in the initial state vector that are successfully initialized during the Kalman filtering process. Moreover, let . The reported information criteria, all in smaller-is-better form, are described in Table 34.4: Table 34.4: Information Criteria Criterion Formula Reference AIC Akaike (1974) AICC Hurvich and Tsai (1989) Burnham and Anderson (1998) HQIC Hannan and Quinn (1979) BIC Schwarz (1978) CAIC Bozdogan (1987)	2019-06-16 03:56:16	{"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": 0.9661884903907776, "perplexity": 2205.1010514875084}, "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/1560627997533.62/warc/CC-MAIN-20190616022644-20190616044644-00445.warc.gz"}
http://docs.itascacg.com/flac3d700/common/fish/doc/fish_manual/fish_fish/file_utilities/fish_file.exist.html	# file.exist Syntax b = file.exist(s) Get if the file exists in the file system. Returns: b - true if a file with name name exists in the file system. s - The file name to look for.	2022-06-29 05:52:07	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 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": 0.5667197108268738, "perplexity": 2206.6850415023914}, "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-2022-27/segments/1656103624904.34/warc/CC-MAIN-20220629054527-20220629084527-00589.warc.gz"}
https://msp.org/gt/2008/12-1/b08.xhtml	#### Volume 12, issue 1 (2008) 1 L Bers, Simultaneous uniformization, Bull. Amer. Math. Soc. 66 (1960) 94 MR0111834 2 L Bers, Correction to “Spaces of Riemann surfaces as bounded domains”, Bull. Amer. Math. Soc. 67 (1961) 465 MR0130972 3 F Bonahon, Earthquakes on Riemann surfaces and on measured geodesic laminations, Trans. Amer. Math. Soc. 330 (1992) 69 MR1049611 4 F Bonahon, Shearing hyperbolic surfaces, bending pleated surfaces and Thurston's symplectic form, Ann. Fac. Sci. Toulouse Math. $(6)$ 5 (1996) 233 MR1413855 5 F Bonahon, Geodesic laminations with transverse Hölder distributions, Ann. Sci. École Norm. Sup. $(4)$ 30 (1997) 205 MR1432054 6 F Bonahon, Transverse Hölder distributions for geodesic laminations, Topology 36 (1997) 103 MR1410466 7 F Bonahon, Variations of the boundary geometry of $3$–dimensional hyperbolic convex cores, J. Differential Geom. 50 (1998) 1 MR1678469 8 F Bonahon, Kleinian groups which are almost Fuchsian, J. 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Differential Geom. 47 (1997) 399 MR1617652 43 W P Thurston, Geometry and Topology of Three-Manifolds, Princeton lecture notes (1979) 44 W P Thurston, Earthquakes in two-dimensional hyperbolic geometry, from: "Low-dimensional topology and Kleinian groups (Coventry/Durham, 1984)", London Math. Soc. Lecture Note Ser. 112, Cambridge Univ. Press (1986) 91 MR903860 45 W P Thurston, Minimal stretch maps between hyperbolic surfaces arXiv:math.GT/9801039 46 A J Tromba, Teichmüller theory in Riemannian geometry, Lectures in Mathematics ETH Zürich, Birkhäuser Verlag (1992) 220 MR1164870 47 W A Veech, Gauss measures for transformations on the space of interval exchange maps, Ann. of Math. $(2)$ 115 (1982) 201 MR644019 48 S Wolpert, An elementary formula for the Fenchel–Nielsen twist, Comment. Math. 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Sb. $($N.S.$)$ 132(174) (1987) 147 MR882831	2019-06-18 03:45:32	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8245438933372498, "perplexity": 2102.95929333383}, "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/1560627998605.33/warc/CC-MAIN-20190618023245-20190618045245-00411.warc.gz"}
https://gmatclub.com/forum/if-n-is-a-positive-integer-is-n-3-4n-2-5n-divisible-by-145736.html	GMAT Question of the Day - Daily to your Mailbox; hard ones only It is currently 20 Jun 2019, 12:52 ### GMAT Club Daily Prep #### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email. Customized for You we will pick new questions that match your level based on your Timer History Track every week, we’ll send you an estimated GMAT score based on your performance Practice Pays we will pick new questions that match your level based on your Timer History # If n is a positive integer, is n^3 + 4n^2 – 5n divisible by Author Message TAGS: ### Hide Tags Manager Status: Never ever give up on yourself.Period. Joined: 23 Aug 2012 Posts: 136 Location: India Concentration: Finance, Human Resources GMAT 1: 570 Q47 V21 GMAT 2: 690 Q50 V33 GPA: 3.5 WE: Information Technology (Investment Banking) If n is a positive integer, is n^3 + 4n^2 – 5n divisible by [#permalink] ### Show Tags Updated on: 14 Jan 2013, 06:42 3 00:00 Difficulty: 65% (hard) Question Stats: 63% (02:40) correct 38% (02:25) wrong based on 154 sessions ### HideShow timer Statistics If n is a positive integer, is n^3 + 4n^2 - 5n divisible by 8 ? (1) n = 4b + 1, where b is a positive integer. (2) n^2 – n is divisible by 24. _________________ Don't give up on yourself ever. Period. Beat it, no one wants to be defeated (My journey from 570 to 690) : http://gmatclub.com/forum/beat-it-no-one-wants-to-be-defeated-journey-570-to-149968.html Originally posted by daviesj on 14 Jan 2013, 06:40. Last edited by Bunuel on 14 Jan 2013, 06:42, edited 1 time in total. Edited the question. Math Expert Joined: 02 Sep 2009 Posts: 55732 Re: If n is a positive integer, is n^3 + 4n^2 – 5n divisible by [#permalink] ### Show Tags 14 Jan 2013, 06:49 If n is a positive integer, is n^3 + 4n^2 - 5n divisible by 8 ? $$n^3 + 4n^2 - 5n=n(n^2+4n-5)=n(n-1)(n+5)$$ (1) n = 4b + 1, where b is a positive integer --> $$n(n-1)(n+5)=(4b+1)(4b)(4b+6)=(4b+1)(8b)(2b+3)$$. Sufficient. (2) n^2 – n is divisible by 24 --> n(n-1) is divisible by 24, so its also divisible by 8. Thus n(n-1)(n+5) is also divisible by 8. Sufficient. Hope it's clear. _________________ Manager Joined: 06 Jun 2010 Posts: 153 Re: If n is a positive integer, is n^3 + 4n^2 – 5n divisible by [#permalink] ### Show Tags 15 Jan 2013, 11:56 Hi Bunuel, Can u plz xplain this step: (4b+1)(4b)(4b+6)= (4b+1)(8b)(2b+3).Sufficient. Thanks, Shreeraj Math Expert Joined: 02 Sep 2009 Posts: 55732 Re: If n is a positive integer, is n^3 + 4n^2 – 5n divisible by [#permalink] ### Show Tags 15 Jan 2013, 12:08 shreerajp99 wrote: Hi Bunuel, Can u plz xplain this step: (4b+1)(4b)(4b+6)= (4b+1)(8b)(2b+3).Sufficient. Thanks, Shreeraj Sure. Factor out 2 from 4b+6: (4b+1)(4b)(4b+6)=(4b+1)(4b)(2)(2b+3)=(4b+1)(8b)(2b+3). Hope it's clear. _________________ SVP Joined: 06 Sep 2013 Posts: 1651 Concentration: Finance Re: If n is a positive integer, is n^3 + 4n^2 – 5n divisible by [#permalink] ### Show Tags 17 Jan 2014, 12:32 daviesj wrote: If n is a positive integer, is n^3 + 4n^2 - 5n divisible by 8 ? (1) n = 4b + 1, where b is a positive integer. (2) n^2 – n is divisible by 24. The only things to point out or add if you will are the following Question stem = Factorizing one gets (n)(n+5)(n-1) Statement 1 n = 4b+1 Replacing (4b+1)(4b+6)(4b) Now (4b) and (4b+1) are consecutive integers Therefore one of them must be odd and one even, obviously 4b is the even one So 4b is a multiple of 4 and 4b +6 is even so we have a multiple of 8 Statement 2 n(n-1) divisible by 24 means that either n or n-1 is divisible by 3 and that one of them, the even one, will be divisible by 8 Since we have both terms in our initial factorization then YES it is a multiple of 8 Hence D Is this clear? PS. The answer choice button tab in GMAT Club is awesome! Cheers! J Non-Human User Joined: 09 Sep 2013 Posts: 11398 Re: If n is a positive integer, is n^3 + 4n^2 – 5n divisible by [#permalink] ### Show Tags 16 Sep 2018, 02:54 Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________ Re: If n is a positive integer, is n^3 + 4n^2 – 5n divisible by [#permalink] 16 Sep 2018, 02:54 Display posts from previous: Sort by	2019-06-20 19:52:06	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 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": 0.7481989860534668, "perplexity": 3465.646500977269}, "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/1560627999273.24/warc/CC-MAIN-20190620190041-20190620212041-00229.warc.gz"}
https://cob.silverchair.com/jeb/article/210/9/1492/17436/Glossary-of-terms	This section is designed to help readers adapt to the complex terminology associated with contemporary molecular genetics, genomics and systems biology. Fuller descriptions of these terms are available at http://www.wikipedia.org/ • Ab initio prediction methods used to predict the potential genes encoded in the genome,which are trained on datasets made of known genes, and used computationally to predict coding regions out of genome without the aid of cDNA sequence. Although their performance is improving, these algorithms perform very poorly on non-protein coding genes. • • Annotation as applied to proteins, DNA sequences or genes. The storage of data describing these entities (protein/gene identities, DNA motifs, gene ontology categorisation, etc.) within a biological database. Active projects include FlyBase and WormBase. See Gene ontology. • • Assembly the process of aligning sequenced fragments of DNA into their correct positions within the chromosome or transcript. • • cDNA complementary DNA. This is DNA synthesised from a mature mRNA template by the enzyme reverse transcriptase. cDNA is frequently used as an early part of gene cloning procedures, since it is more robust and less subject to degradation than the mRNA itself. • • ChIP chromatin immunoprecipitation assay used to determine which segments of genomic DNA are bound to chromatin proteins, mainly including transcription factors. • • Chip see Microarray. • • ChIP-on-chip use of a DNA microarray to analyse the DNA generated from chromatin immunoprecipitation experiments(see ChIP). • • cis-acting a molecule is described as cis-acting when it affects other genes that are physically adjacent, on the same chromosome, or are genetically linked or in close proximity (for mRNA expression, typically a promoter). • • Collision-induced dissociation a mechanism by which molecules (e.g. proteins) are fragmented to form molecular ions in the gas phase. These fragments are then analysed within a mass spectrometer to provide mass determination. • • Connectivity a term from graph theory, which indicates the number of connections between nodes or vertices in a network. Greater connectedness between nodes is generally used as a measure of robustness of a network. • • CpG islands regions that show high density of C followed by G' dinucleotides and are generally associated with promoter elements; in particular, stretches of DNA of at least 200 bp with a C–G content of 50% and an observed CpG/expected CpG in excess of 0.6. The cytosine residues can be methylated,generally to repress transcription, while demethylated CpGs are a hallmark of transcription. CpG dinucleotides are under-represented outside regulatory regions, such as promoters, because methylated C mutates into T by deamination. • • Edge as in networks. Connects two nodes (or vertices) within a system. These concepts arise from graph theory. • • Enhancer a short segment of genomic DNA that may be located remotely and that,on binding particular proteins (trans-acting factors), increases the rate of transcription of a specific gene or gene cluster. • • Epistasis a phenomenon when the properties of one gene are modified by one or more genes at other loci. Otherwise known as a genetic interaction, but epistasis refers to the statistical properties of the phenomenon. • eQTL the combination of conventional QTL analysis with gene expression profiling, typically using microarrays. eQTLs describe regulatory elements controlling the expression of genes involved in specific traits. • • EST expressed sequence tag. A short DNA sequence determined for a cloned cDNA representing portions of an expressed gene. The sequence is generally several hundred base pairs from one or both ends of the cloned insert. • • Exaptation a biological adaptation where the current function is not that which was originally evolved. Thus, the defining (derived) function might replace or persist with the earlier, evolved adaptation. • • Exon any region of DNA that is transcribed to the final (spliced) mRNA molecule. Exons interleave with segments of non-coding DNA (introns) that are removed (spliced out) during processing after transcription. • • Gene forests genomic regions for which RNA transcripts, produced from either DNA strand, have been identified without gaps (non-transcribed genomic regions). Conversely, regions in which no transcripts have ever been detected are calledgene deserts'. • • Gene interaction network a network of functional interactions between genes. Functional interactions can be inferred from many different data types, including protein–protein interactions, genetic interactions, co-expression relationships, the co-inheritance of genes across genomes and the arrangement of genes in bacterial genomes. The interactions can be represented using network diagrams, with lines connecting the interacting elements, and can be modelled using differential equations. • • Gene ontology (GO) an ontology is a controlled vocabulary of terms that have logical relationships with each other and that are amenable to computerised manipulation. The Gene Ontology project has devised terms in three domains:biological process, molecular function and cell compartment. Each gene or DNA sequence can be associated with these annotation terms from each domain, and this enables analysis of microarray data on groups of genes based on descriptive terms so provided. See http://www.geneontology.org • • Gene set enrichment analysis a computational method that determines whether a defined set of genes,usually based on their common involvement in a biological process, shows statistically significant differences in transcript expression between two biological states. • • Gene silencing the switching-off of a gene by an epigenetic mechanism at the transcriptional or post-transcriptional levels. Includes the mechanism of RNAi. • • Genetic interaction (network) a genetic interaction between two genes occurs when the phenotypic consequences of a mutation in one gene are modified by the mutational status at a second locus. Genetic interactions can be aggravating (enhancing) or alleviating (suppressing). To date, most high-throughput studies have focussed on systematically identifying synthetic lethal or sick (aggravating)interactions, which can then be visualised as a network of functional interactions (edges) between genes (nodes). • • Genome a portmanteau of gene and chromosome, the entire hereditary information for an organism that is embedded in the DNA (or, for some viruses, in RNA). Includes protein-coding and non-coding sequences. • • Heritability phenotypic variation within a population is attributable to the genetic variation between individuals and to environmental factors. Heritability is the proportion due to genetic variation usually expressed as a percentage. • • Heterologous hybridization the use of a cDNA or oligonucleotide microarray of probes designed for one species with target cRNA/cDNAs from a different species. • • Homeotic the transformation of one body part to another due to mutation of specific developmentally related genes, notably the Hox genes in animals and MADS-box genes in plants. • • Hub as in networks. A node with high connectivity, and thus which interacts with many other nodes in the network. A hub protein interacts with many other proteins in a cell. • Hybridisation the process of joining (annealing) two complementary single-stranded DNAs into a single double-stranded molecule. In microarray analysis, the target RNA/DNA from the subject under investigation is denatured and hybridised to probes that are immobilised on a solid phase (i.e. glass microscope slide). • • Hypomorph in genetics, a loss-of-function mutation in a gene, but which shows only a partial reduction in the activity it influences rather than a complete loss (cf. hypermorph, antimorph, neomorph, etc). • • Imprinting a phenomenon where two inherited copies of a gene are regulated in opposite ways, one being expressed and the other being repressed. • • Indel insertion and deletion of DNA, referring to two types of genetic mutation. To be distinguished from a point mutation', which refers to the substitution of a single base. • • Interactome a more or less comprehensive set of interactions between elements within cells. Usually applied to genes or proteins as defined by transcriptomic, proteomic or protein–protein interaction data. • • Intron see Exon. • • KEGG The Kyoto Encyclopedia of Genes and Genomes is a database of metabolic and other pathways collected from a variety of organisms. See http://www.genome.jp/kegg • • Metabolomics the systematic qualitative and quantitative analysis of small chemical metabolite profiles. The metabolome represents the collection of metabolites within a biological sample. • • Metagenomics the application of genomic techniques to characterise complex communities of microbial organisms obtained directly from environmental samples. Typically, genomic tags are sequence characterised as markers of each species to inform on the range and abundance of species in the community. • • Microarray an arrayed set of probes for detecting molecularly specific analytes or targets. Typically, the probes are composed of DNA segments that are immobilised onto the solid surface, each of which can hybridise with a specific DNA present in the target preparation. DNA microarrays are used for profiling of gene transcripts. • • Model species a species used to study particular biological phenomena, the outcome offering insights into the workings of other species. Usually, the selection is based on experimental tractability, particularly ease of genetic manipulation. For the geneticist, it is an organism with inbred lines where sibs will be >98% identical (i.e. Drosophila, Caenorhabditis elegans and mice). For genomic science, it refers to a species for which the genomic DNA has been sequenced. • • miRNA a category of novel, very short, non-coding RNAs, generated by the cleavage of larger precursors (pri-miRNA). These short RNAs are included in the RNA-induced silencing complex (RISC) and pair to the 3′ ends of target RNA, blocking its translation into proteins (in animals) or promoting RNA cleavage and degradation (in plants). • • mRNA a protein-coding mRNA containing a protein-coding region (CDS),preceded by a 5′ and followed by a 3′ untranslated region(5′ UTR and 3′ UTR). The UTRs contain regulatory elements. A full-length cDNA contains the complete sequence of the original mRNA,including both UTRs. However, it is often difficult to assign the starting–termination positions for protein synthesis unambiguously. A cDNA containing the entire CDS is often considered acceptable for bioinformatic and experimental studies requiring full-length cDNAs. • • ncRNA non-coding RNA is any RNA molecule with no obvious protein-coding potential for at least 80 or 100 amino acids, as determined by scanning full-length cDNA sequences. It includes ribosomal (rRNA) and transfer RNAs(tRNA) and is now known to include various sub-classes of RNA, including snoRNA, siRNA and piRNA. Just like the coding mRNAs, a large proportion of ncRNAs are transcribed by RNA polymerase II and are large transcripts. A description of the many forms of ncRNA can be found at http://en.wikipedia.org/wiki/Non-coding_RNA. • Node as in networks. Objects linked by edges to create a network. • • PCR polymerase chain reaction. A molecular biology technique for replicating DNA in vitro. The DNA is thus amplified, sometimes from very small amounts. PCR can be adapted to perform a wide variety of genetic manipulations. • • piRNA Piwi-interacting RNA. A class of RNA molecules (29–30 nt long)that complex with Piwi proteins (a class of the Argonaute family of proteins)and are involved in transcriptional gene silencing. • • PMF peptide mass fingerprinting. An analytical technique for protein identification in which a protein is fragmented using proteases. The resulting peptides are analysed by mass spectrometry and these masses compared against a database of predicted or measured masses to generate a protein identity. • the covalent addition of multiple A bases to the 3′ tail of an mRNA molecule. This occurs during the processing of transcripts to form the mature, spliced molecule and is important for regulation of turnover,trafficking and translation. • • Post-source decay in mass spectrometry. The fragmentation of precursor molecular ions as they accelerate away from the ionisation source of the mass spectrometer. All precursor ions leaving the ion source have approximately the same kinetic energy, but fragmentation results in smaller product ions that can be distinguished from precursor ions using a reflectron' by virtue of their lower kinetic energies. • • Post-translational modification the chemical modification of a protein after synthesis through translation. Some modifications, notably phosphorylation, affect the properties of the protein, offering a means of regulating function. • • Principal component analysis (PCA) a technique for simplifying complex, multi-dimensional datasets to a reduced number of dimensions, the principal components. This procedure retains those characteristics of the data that relate to its variance. • • Promoter a regulatory DNA sequence, generally lying upstream of an expressed gene, which in concert with other often distant regulatory elements directs the transcription of a given gene. • • Proteome the entire protein complement of an organism, tissue or cell culture at a given time. • • Quantitative trait inheritance of a phenotypic property or characteristic that varies continuously between extreme states and can be attributed to interactions between multiple genes and their environment. • • qPCR quantitative real-time PCR, sometimes called real-time PCR. A more quantitative form of RT-PCR in which the quantity of amplified product is estimated after each round of amplification. • • QTL quantitative trait loci. A region of DNA that contains those genes contributing to the trait under study. • • RISC RNA-induced silencing complex. A protein complex that mediates the double-stranded RNA-induced destruction of homologous mRNA. • • RNAi RNA interference or RNA-mediated interference. The process by which double-stranded RNA triggers the destruction of homologous mRNA in eukaryotic cells by the RISC. • • RT-PCR reverse transcription–polymerase chain reaction. A technique for amplifying a defined piece of RNA that has been converted to its complementary DNA form by the enzyme reverse transcriptase. See qPCR. • • siRNA small interfering RNA, or silencing RNA. A class of short (20–25 nt), double-stranded RNA molecules. It is involved in the RNA interference pathway, which alters RNA stability and thus affects RNA concentration and thereby suppresses the normal expression of specific genes. Widely used in biomedical research to ablate specific genes. • snoRNA small nucleolar RNA. A sub-class of RNA molecules involved in guiding chemical modification of ribosomal RNA and other RNA genes as part of the regulation of gene expression. • • SNP single nucleotide polymorphism. A single base-pair mutation at a specific locus, usually consisting of two alleles. Because SNPs are conserved over evolution, they are frequently used in QTL analysis and in association studies in place of microsatellites, and in genetic fingerprinting analyses. • • SSH suppressive subtractive hybridisation. A powerful protocol for enriching cDNA libraries for genes that differ in representation between two or more conditions. It combines normalisation and subtraction in a single procedure and allows the detection of low-abundance, differentially expressed transcripts, such as those involved in signalling and signal transduction. • • Structural RNAs a class of non-coding RNA, long known to have a structural role (for instance, the ribosomal RNAs), transcribed by RNA polymerase I or III. • • Systems biology treatment of biological entities as systems composed of defined elements interacting in defined ways to enable the observed function and behaviour of that system. The properties of the systems are embedded in a quantitative model that guides further tests of systems behaviour. • • TATA-boxes sequences in promoter regions constituted by TATAAA, or similar variants, which were considered the hallmark of Promoters. Recent data show that they are present only in the minority of promoters, where they direct transcription at a single well-defined location some 30 bp downstream of this element. • • trans-acting a factor or gene that acts on another unlinked gene, a gene on a separate chromosome or genetically unlinked usually through some diffusible protein product (for mRNA expression, typically a transcription factor). • • Transcript an RNA product produced by the action of RNA polymerase reading the sequence of bases in the genomic DNA. Originally limited to protein-coding sequences with flanking UTRs but now known to include large numbers of products that do not code for a protein product. • • Transcriptome the full set of mRNA molecules (transcripts) produced by the system under observation. Whilst the genome is fixed for a given organism, the transcriptome varies with context (i.e. tissue source, ontogeny, external conditions or experimental treatment). • • Transgene a gene or genetic material that has been transferred between species or between organisms using one of several genetic engineering techniques. • • Transinduction generation of transcripts from intergenic regions. At least some such products do not relate to a definable promoter or transcriptional start site. • • Transposon sequences of DNA able to move to new positions within the genome of a single cell. This event might cause mutation at the site of insertion. Also called mobile genetic elements' or jumping genes'. • • Transvection an epigenetic phenomenon arising from the interaction between one allele and the corresponding allele on the homologous chromosome, leading to gene regulation. • • TUs transcriptional units. Used to group all of the overlapping RNA transcripts that are transcribed from the same genomic strand and share exonic sequences. • • UTR untranslated region. Regions of the mRNA that lie at either the 3′ or 5′ flanking ends of the molecule (i.e. 3′ UTR and 5′ UTR). They bracket the protein-coding region and contain signals and binding sites that are important for the regulation of both protein translation and RNA degradation.	2022-01-22 23:33:30	{"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": 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": 0.4353320896625519, "perplexity": 6068.932759743865}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-05/segments/1642320303917.24/warc/CC-MAIN-20220122224904-20220123014904-00080.warc.gz"}
https://chemistry.stackexchange.com/questions/137194/why-arent-the-hydrogen-bonds-in-carboxyllic-acids-like-this	Why aren't the hydrogen bonds in carboxyllic acids like this? Why don't carboxylic acids form H-bonds in this formation with the red dots (diagonal) instead of the black dots (horizontal)? I was always taught that H-bonds formed between partially negative and partially positive atoms. I agree that the $$\ce{=O}$$ carboxyl oxygen is partially negative, so there should be a H-bond there from the partially positive H. However, the $$\ce{O}$$ in $$\ce{OH}$$ is also partially negative. So why aren't the H-bonds denoted with red dots formed? • And nobody told you that it goes straight to lone pair? – Mithoron Jul 29 at 13:55 • So, while bifurcated hydrogen bonds do exist, it's not the case here. – Mithoron Jul 29 at 15:53 • You need some degree of orbital overlap. Pretty challenging to overlap at that kind of angle. – Josh Mitchell Jul 29 at 16:08 • In reality in carboxylic acids, there are no double bond and single bond on oxygens. It is a hybrid (e.g., where is the $\ce{^{13}C}$-signal for carboxylic carbonyl in NMR?). – Mathew Mahindaratne Jul 29 at 17:52 • Often times you ignore the stuff that is not as important. It's a simple cartoon after all. – Buck Thorn Jul 29 at 20:34	2020-08-06 01:49:35	{"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": 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": 3, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.41905319690704346, "perplexity": 2567.8629334062816}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-34/segments/1596439735990.92/warc/CC-MAIN-20200806001745-20200806031745-00311.warc.gz"}
https://ftp.aimsciences.org/article/doi/10.3934/dcds.2002.8.1043	Article Contents Article Contents # The generalized Liénard systems • We consider the generalized Liénard system $\frac{dx}{dt} = \frac{1}{a(x)}[h(y)-F(x)],$ $\frac{dy}{dt}= -a(x)g(x),\qquad\qquad\qquad\qquad\qquad$ (0.1) where $a$ is a positive and continuous function on $R=(-\infty, \infty)$, and $F$, $g$ and $h$ are continuous functions on $R$. Under the assumption that the origin is a unique equilibrium, we obtain necessary and sufficient conditions for the origin of system (0.1) to be globally asymptotically stable by using a nonlinear integral inequality. Our results substantially extend and improve several known results in the literature. Mathematics Subject Classification: 34D05, 34C05. Citation:	2023-04-02 03:08:11	{"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": 0.6815055012702942, "perplexity": 241.31032071357308}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296950373.88/warc/CC-MAIN-20230402012805-20230402042805-00742.warc.gz"}
https://mathoverflow.net/questions/248668/sdp-relaxation-vs-lp-relaxation	# SDP relaxation vs LP relaxation I have a question I hope you might be able to answer. Let's say we have an integer program for the stable set problem (or clique, not principal). \begin{aligned} & \text{maximize} & \sum_i x_i \\ & \text{subject to} & \\ %& & \sum_{i \in C} x_i \leq 1 \text{ for all cliques } C\\ & & x_i+x_j \leq 1 \text { for } i,j \in E \\ & & x_i \in \{0,1\} \end{aligned} One can use relaxation to obtain upper bounds like linear programming (LP) relaxation (relaxing integer variables to be in $[0,1]$) or using SDP relaxation (Lovasz) \begin{aligned} & \text{maximize} & \sum_i \sum_j X_{ij} \\ & \text{subject to} & \\ & & \mbox{tr} (X) = 1 \\ & & X_{ij} = 0 \text{ if } \{i,j\} \in E(G) \\ & &X \succ 0 \end{aligned} Is there a nice direct proof that the value of the SDP relaxation above is always at most the value of the LP relaxation of the integer program? Any help and thoughts will be greatly appreciated. Edit: formal description So let's say the stable set number is $\alpha(G)$, the value of linear relaxation is $z^_{LP}$, and the value of SDP is $z^_{SDP}$. The formal statement about "better" would be that $\alpha(G) \leq z^_{SDP} \leq z^_{LP}$ for every graph $G$. • SDPs are more general than LPs (think in terms of suitable diagonal matrices), which explains the claim. – Suvrit Aug 31 '16 at 1:25 • Thanks for the answer. Actually it does not explain even a thing of it. SDP problems include LP problems, not a single doubt about it. The question was, why the value of the particular SDP above is always not greater than the value of the particular LP. Some people claiming that, so I'd like to hear thoughts/ideas why is that. – Eugene Sep 1 '16 at 20:20 • The stable set integer program you give is incorrect. You forgot to say that the inequality constraint is only for when $i$ and $j$ are adjacent (same for the constraint in your SDP). Even if you add this, the LP relaxation of this program is boring because assigning $1/2$ to every vertex gives you $n/2$ which is a bad bound on the size of a stable set in most cases. You need the inequality to hold when summing over any clique. After these fixes the LP is equal to the fractional packing number $\alpha^$ and the SDP is equal to Lov\'{a}sz $\vartheta$, and $\vartheta \le \alpha^$ is well known – David Roberson Sep 1 '16 at 21:59 • I was assuming it's clear the inequalities are for some set of $i,j$. The question becomes even more interesting when one can ask what about quadratic relaxations in general? People usually say they are way much better, however I haven't seen neat and tidy proof of these claims. So, that's the main objective after all. The problem above appears to be the best one studied so I hoped for any neat proofs or justifications. The problem with the cliques constraint is known to be very tight (for example for perfect graphs it's tight and Lov\'{a}sz is tight too). – Eugene Sep 2 '16 at 3:29 • Well the answer is that yes, the SDP is always better because it is equal to Lovasz theta and the (current) linear program is equal to fractional packing number/fractional chromatic number of the complement and it is well known that Lovasz theta is less than or equal to fractional packing number for all graphs. However, I do not know a nice direct proof of this fact using these formulations of these two parameters, which is why I edited the question, because I think it would interesting to see such a proof. – David Roberson Sep 4 '16 at 12:16 The quickest proof I know uses a different (but equivalent) formulation of the above SDP. If I had to prove it using the above version I would probably first convert it the other one. Here is a rough sketch: Let $X$ be a solution to the SDP above, and let $D$ be the diagonal matrix with the entries of $X$ on its diagonal. Consider $Y = D^{-1/2}XD^{-1/2}$ and note that this is PSD with 1's on the diagonal and zero where $X$ was zero. Let $d$ be the vector of the square roots of the diagonal entries of $X$. Then $d^TYd = \sum_{i,j}X_{ij}$ and $d$ is a unit vector. So the max eigenvalue of $Y$ is at least the objective value of $X$. Since $Y$ is PSD, it is the Gram matrix of some (unit) vectors $v_1, \ldots, v_n$. The max eigenvalue of $Y$ is the same as that of the matrix $Z = \sum_{i} v_iv_i^T$. Let $c$ be a max eigenvector of $Z$ with eigenvalue $\mu$. If we assign the value $(v_i^Tc)^2$ to the vertex $i$, then this will be a feasible solution for the linear relaxation of the above integer program since on any clique the $v_i$ are a subset of some orthonormal basis and $c$ is a unit vector. Moreover, the value of this solution is equal to $\sum_{i} (v_i^Tc)^2 = c^TZc = \mu \ge \sum_{i,j} X_{ij}$. Thus the linear relaxation has greater value than the SDP. As you can see, this is not so nice. At first I thought you could maybe prove that if you take any solution $X$ to the SDP, and then assign to vertex $i$ the sum of the $i^\text{th}$ row of $X$, that this would be a feasible solution to the linear relaxation. But this doesn't work (some row sums can be greater than 1). But maybe it works for optimal solutions to the SDP? Another way to prove it is to consider a Gram factorisation $u_1, \ldots, u_n$ of a feasible solution $X$ to the SDP. So $X_{ij} = u_i^Tu_j$. Let $v_i$ be the unit vector parallel to $u_i$. Also let $c$ be the unit vector parallel to $\sum_i u_i$. Then assigning $(v_i^Tc)^2$ to vertex $i$ is a feasible solution to the linear relaxation, and its value is at least the objective value of $X$. This last part requires a proof which is part of the proof of Theorem 5 from Lovasz' original paper (http://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=1055985). There are a lot of other useful equivalent formulations of the above SDP in his paper. There is also a paper by Knuth about these things (http://www.combinatorics.org/ojs/index.php/eljc/article/view/v1i1a1). It would be nice to have a more direct proof than those above. I will also write my answer to the problem above based on my research. The solution will involve several steps. I'll present the sketch here. Let me know if somebody is interested in more details. Step 1. Write the MIP (or one can say just formulate the problem) as quadratic non-convex program. The one will have $x_ix_j=0$ instead of $x_i+x_j \leq 1$ in MIP and $x_i(1-x_i)=0$ to enforce belonging to $\{0,1\}$ set. Step 2. Perform the SDP relaxation of the quadratic program. One can try to look for Wolkovicz and Poljak papers. The basic idea is to define new variables $X_{ij} = x_ix_j$ and than relax the constraint $X = xx^T$ to $X \succ 0$ (I'm skipping details, but that's the usual trick). Step 3. By Wolkovicz and Poljak, and this is the only step which I believe should be verified carefully, the value of Lagrangian Dual Relexation for non-convex QP is equal to SDP. Step 4. Prove that the value of the Lagrangian Dual Relaxation is not greater than the value of LP relaxation. This is the homework problem for a math class. The idea is to write the Lagrangian estimate and then for example for 0-1 constraint in QP $x_i(1-x_i)=0$ say let's enforce dual multipliers to be only positive. This will correspond to a QP with constraint $x_i(1-x_i)\leq0$ or $x_i \in [0;1]$. If anyone has any thoughts, I'd be more than pleased to hear them. Thanks. Edit: Ok for step 4 there is a special step too (still pretty technical). You add the redundant constraint to QP $(x_i +x_j)^2 - (x_i + x_j) = 0$ and then with the same idea described in the step 4 above you get desirable $x_i + x_j \leq 1$	2020-10-24 10:01:03	{"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": 2, "x-ck12": 0, "texerror": 0, "math_score": 0.9814766645431519, "perplexity": 187.73698814757276}, "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-2020-45/segments/1603107882103.34/warc/CC-MAIN-20201024080855-20201024110855-00227.warc.gz"}
https://electronics.stackexchange.com/questions/545213/is-it-possible-to-remove-a-line-of-code-from-microcontroller-program-memory	# Is it possible to remove a line of code from microcontroller program memory? int main(void) { while (1) { delay(50); if (ButtonPress1) { ResetOutSwitch(); } } Suppose that button press is detected and output switch is reset. How to make the microcontroller do not pool the button press anaymore. How to make above code look like below after button pressed and output switch is reset. It will not see any if check in its code. int main(void) { while (1) { delay(50); } I am asking how to remove a line of code from execution from microcontroller program memory. This question was closed because of its answers might be opinion based. So I must make it more specific. Is it possible to remove some program data from microcontroller flash memory, so it skips these deleted parts and continues with the rest. What is the way to do this? I only know C programming. Using Eclipse to program STM32 microcontrollers. • Yes it is possible to do by using another conditional. – Peter Smith Jan 28 at 11:14 • You don't "remove" checks, you stop doing them. For which you just need for example a bool variable and a bit of common sense. If you want a better answer than that, I suggest you show a concrete example. – Lundin Jan 28 at 11:26 • I get a vibe from this that leads me to something I often tell students: Optimization at the wrong time is bad. The question you should be asking: Does this conditional check create any problems if I run it every iteration? If you run low on memory, program space, or execution time you should then go in and analyze your functions and improve as needed. Spending time to super-optimize code when you don't have to is a waste of time. I have seen so many cases where 80% of the time is spent solving an imaginary problem instead of solving the actual task, assuming they get that far. – Arcatus Jan 28 at 11:44 • Are you asking if it is possible to modify an in-service, programmed microcontroller to, for example, replace your if instruction block with NOPs? If you give some context to your question and explain why you want to know it would save a lot of guessing as is happening below. – Transistor Jan 31 at 20:37 • Please, edit your question, and tell us some context: why, how many times, which controller, why no other option, and so on. – the busybee Jan 31 at 21:23 You can route the execution into another loop, a clone of the first one but without the conditional check. Of course, you need another conditional for this routing, but once you reach there, you won't need to check a conditional on each iteration. If the loop resides in a function, you can clone the function excluding the condition check. Then all you need is some function pointer magic. If you can replace the function pointer in the caller side, you can avoid all conditional checks. But I'm not sure if calling a function using a pointer introduces additional overhead. How to make above code look like below after button pressed and output switch is reset. It will not see any if check in its code... Is it possible to remove some program data from microcontroller flash memory, so it skips these deleted parts and continues with the rest. No, it is not realistically possible to do what you ask. Some MCUs can reprogram their flash ROM while running, but this takes several milliseconds and can only be done a limited number of times. Self-modifying code is rarely needed and has many hazards. When applied to Flash ROM it could quickly wear out the memory, or 'brick' the MCU if power is disconnected while writing. The extra code needed and time spent reprogramming the ROM could greatly exceed what you save. You are attempting an optimization that should not be necessary if your MCU has sufficient processing power and memory. Unless you have a very critical application and cannot use a more capable MCU this is completely unnecessary. Several answers have been given that explain how your code can be modified by falling into another loop or using a boolean to skip the parts you don't want to execute. Use one of these methods and don't worry about the extra code involved. Concentrate on writing logically sound 'clean' code that makes your intention clear and doesn't rely on hacks to work. • Well, I would not say "no, it is not realistically possible", because we don't know how many times the OP want to do this, and what the other requirements are. To just patch a certain part of the code once, it is possible, given that the chip can do this at all. -- Anyway, +1. – the busybee Jan 31 at 21:19 • OK, i got it. Good answer, thank you. – tuncel3 Feb 1 at 2:29 There is an if check in while loop of a microcontroller. When something happens it detects it and does what is required. After that the microcontroller should not check this condition anymore to save CPU time. The correct approach depends on what your condition is. • If "something happens" is a hardware event then you can use an interrupt to check for it. In that case you don't waste any CPU cycles polling for the event within the loop. • If "something happens" is the state of a variable in software then you can break your loop into two parts. The first loop checks for "something_happens". The second loop is identical, but doesn't check for the "something_happens". for example... while(condition){ do_stuff(); if(something_happens()){ break;//exit first loop after something happens } } //continue identical second loop without condition check. while(condition){ do_stuff(); } • If "something happens" is a complex condition then you can save time by reducing the complex check into a boolean flag. If for example "something happens" was (A && B && C && D && E && F && G) then you might write the following... int flag = 0; while(condition){ do_stuff(); if(flag == 0){ if(A && B && C && D && E && F && G){ handle_complex_condition(); flag = 1; } } } In this case we have one extra check check for a flag for each iteration of the loop, but after the condition occurs we only check the flag and don't have to do the six AND operations, so overall we can save CPU cycles. But if the condition is never met, or met very near the end of the loop then we will actually take more cycles, so this approach is not a guarantee. I am asking how to remove a line of code from execution from microcontroller program memory. Modifying flash program memory while the CPU is executing code out of that page is impossible for many families of microcontrollers. The STM32 can execute code from RAM. In that case its possible to simply write NOPs to the location in RAM that corresponds to the if statement. To do that you would need the exact addresses of those instructions. Generally one would create a label and then load the address of the label into a pointer. One would then write NOPs using the pointer. Also, in order for this to work you would probably have to disable the instruction cache for the STM32 (or at least cause it to flush). But that whole process is much more complicated than the non self-modifying code examples above. • or just if (flag == 0 && A && B && C...) since && short-circuits. – ilkkachu Jan 31 at 20:53 The simplest method is something like this: while(condition) { int event, event_has_occurred; // other declarations event = 0; event_has_occurred = 0; if(!event_has_occurred) // only executes if event has not yet occurred { event = check_for_event(); // return true if it has happened if(event) { process_event(); // do whatever is necessary event_has_occurred = true; // assuming true is defined as non-zero } } // do regular stuff here } // end while You could play games with function pointers and such but that seems overly complex when a single test can suffice. Keep it simple with beginner-level C... bool dont_do_stuff=false; while(dont_do_stuff \|\| stuff) { if(something) { dont_do_stuff = true; } } This will keep checking stuff until dont_do_stuff is set. If you want to change the functionality, you could do that by editing the ROM (if you have access to it, change the firmware file, this isn't trivial to do). You would have to use assembly and machine code, micro controllers don't understand C, it gets compiled\assembled to machine code. You would also have to find the location of that coffee in the ROM. The if then statement has a jump instruction, and usually a compare instruction before that (not sure with this architecture of processor). You could change the compare instruction so the of statement always I haven't used eclipse for a long time, but there is probably a way to look at the machine code and c side by side (you might have to debug a different processor). That being said it would probably be easier to just disconnect the reset button Run the code in question out of RAM. When the condition check is evaluated as true and the special case gets handled, have it also write over the original conditional test with NOPs. • Are you sure NOPs are faster than the test they replace? – marcelm Jan 28 at 19:36 • @marcelm No, I didn't check. If so then the entire loop could be rewritten to eliminate the test and the branch. – Elliot Alderson Jan 28 at 21:56 • Generally, self-modifying code in RAM is a royally bad idea, even when the OP isn't some beginner. – Lundin Jan 29 at 11:14 • @Lundin I agree, it is quite dangerous, but I thought the question was sufficiently vague that I would throw it out there. The "Is is possible..." questions invite this sort of answer. – Elliot Alderson Jan 29 at 12:43	2021-06-13 21:49:10	{"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": 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": 0.24089811742305756, "perplexity": 1111.7115084699176}, "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/1623487610841.7/warc/CC-MAIN-20210613192529-20210613222529-00224.warc.gz"}
https://ec.gateoverflow.in/2349/gate-ece-2006-question-59	4 views A linear system is described by the following state equation $$X(t)=\mathrm{AX}(t)+\mathrm{BU}(t), \mathrm{A}=\left[\begin{array}{cc} 0 & 1 \\ -1 & 0\end{array}\right]$$ The state-transition matrix of the system is 1. $\left[\begin{array}{cc}\cos t & \sin t \\ -\sin t & \cos t\end{array}\right]$ 2. $\left[\begin{array}{cc}-\cos t & \sin t \\ -\sin t & -\cos t\end{array}\right]$ 3. $\left[\begin{array}{cc}-\cos t & -\sin t \\ -\sin t & \cos t\end{array}\right]$ 4. $\left[\begin{array}{cc}\cos t & -\sin t \\ \cos t & \sin t\end{array}\right]$	2022-10-01 17:16:41	{"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": 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": 0.879590630531311, "perplexity": 556.4644704672521}, "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/1664030336880.89/warc/CC-MAIN-20221001163826-20221001193826-00298.warc.gz"}
http://pballew.blogspot.com.es/	## Monday, 29 August 2016 ### On This Day in Math - August 29 Jeannie at VLA In most sciences one generation tears down what another has built, and what one has established, another undoes. In mathematics alone each generation adds a new storey to the old structure. ~Hermann Hankel The 242nd day of the year; 242 has six divisors...but 243, 244, and 245 also each has six divisors. 242 is the smallest integer to begin a run of four consecutive integers all of which have the same number of divisors. (What is the smallest integer that begins a run of three consecutive integers with an equal number of divisors?) 242 is not only a palindrome in base ten, it is also a palindrome in base 3 and base 7. (What palindrome in base ten is also a palindrome in the most other bases 2-9?) EVENTS 1609 Galileo writes to his brother in Florence to tell him about his telescope presentation to the Doge on the 24th of August. 1654 Fermat to Pascal Saturday, August 29, 1654 Monsieur, Our interchange of blows still continues, and I am well pleased that our thoughts are in such complete adjustment as it seems since they have taken the same direction and followed the same road. Your recent Trait´e du triangle arithmetique and its applications are an authentic proof and if my computations do me no wrong, your eleventh consequence went by post from Paris to Toulouse while my theorem, on figurate numbers, which is virtually the same, was going from Toulouse to Paris. I have not been on watch for failure while I have been at work on the problem and I am persuaded that the true way to escape failure is by concurring with you. But if I should say more, it would he of the nature of a Compliment and we have banished that enemy of sweet and easy conversation. It is now my turn to give you some of my numerical discoveries, but the end of the parliament augments my duties and I hope that out of your goodness you will allow me due and almost necessary respite. In the same letter he states that, "Meditate however, if you find it convenient, on this theorem: The squared powers of 2 augmented by unity [I.e. 22n+1] are always prime numbers. [That is,] The square of 2 augmented by unity makes 5 which is a prime number;The square of the square makes 16 which, when unity is added makes 17, a prime number; The square of 16 makes 256 which, when unity is added, makes 257, a prime number; The square of 256 makes 65536 which, when unity is added, makes 65537, a prime number; and so to infinity. This is a property whose truth I will answer to you. The proof of it is very difficult (impossible, since the statement, as Euler would show later, is not true)and I assure you that I have not yet been able to find it fully." * York University Maths Dept 1692 For his services to the field of astronomy, Johann Philipp von Wurzelbauer was ennobled in 1692 by Leopold I, Holy Roman Emperor and added the von to his name. Wik 1831 Michael Faraday discovered electrical induction. VFR In 1831, Michael Faraday wound a thick iron ring on one side with insulated wire that was connected to a battery. He then wound the opposite side with wire connected to a galvanometer. He found that upon closing the battery circuit, there was a deflection of the galvanometer in the second circuit. Then he was astonished to see the galvanometer needle jump in the opposite direction when the battery circuit was opened. He had discovered that a current was induced in the secondary when a current in the primary was connected and an induced current in the opposite direction when the primary current was disconnected.TIS 1899 Dedekind sends a letter to Georg Cantor that includes a proof of the Schroder-Bernstein Theorem (Let A and B be sets. If there is a 1-1 correspondence from A to B and a 1-1 corespondence from B to A, then the sets have the same cardinality.) Cantorian Set Theory and Limitation of Size By Michael Hallett In 1940, Sir Henry Tizard led a mission of leading British and Canadian scientists to the USA to brief official American representatives on devices under active development for war use and to enlist the support of American scientists. Thus began a close cooperation of Anglo-American scientists in such fields as aeronautics and rocketry. His influence probably made the difference between defeat or victory at the Battle of Britain in 1940. TIS 1949 the USSR tested their first atomic device, "First Lightning." It was an an implosive type plutonium bomb, detonated at the Semipalatinsk test range, giving up to a 20 kiloton yield. In the U.S. it was calledJoe No. 1 ("Joe" was nickname for Y. Stalin.) This event came five years earlier than anyone in the West had predicted, largely due to one man, the spy Klaus Fuchs. As a Los Alamos physicist, Fuchs had passed detailed blue prints of the original American Trinity bomb design to the Russians. With the emergence of the USSR as a nuclear rival, America's monopoly of atomic weaponry was ended giving the U.S. strong motivation for intensifying its program of nuclear testing. Thus the Cold War was launched.TIS 1970 Oscar Morgenstern writes in his diary that Gödel would NOT publish his ontological proof for the existence of God. The first version of the ontological proof in Gödel's papers is dated "around 1941". Gödel is not known to have told anyone about his work on the proof until 1970, when he thought he was dying. In February, he allowed Dana Scott to copy out a version of the proof, which circulated privately. In August 1970, Gödel told Oskar Morgenstern that he was "satisfied" with the proof, but Morgenstern recorded in his diary entry for 29 August 1970, that Gödel would not publish because he was afraid that others might think "that he actually believes in God, whereas he is only engaged in a logical investigation (that is, in showing that such a proof with classical assumptions (completeness, etc.) correspondingly axiomatized, is possible) Wik 1990 The British Computer Misuse Act goes into effect One of the earliest laws anywhere designed to address computer fraud, the Act resulted from a long debate in the 1980s over failed prosecutions of hackers -- in one well-publicized case, two men hacked into a British Telecom computer leaving messages in the Duke of Edinburgh's private mailbox. CHM BIRTHS 1756 Jan Śniadecki (August 29, 1756– November 9, 1830) was a Polish mathematician, philosopher and astronomer at the turn of the 18th and 19th centuries. Born in Żnin, Śniadecki studied at Kraków University and in Paris. He was rector of the Imperial University of Vilnius, a member of the Commission of National Education, and director of astronomical observatories at Kraków and Vilnius. He died at Jašiūnai Manor near Vilnius. Śniadecki published many works, including his observations on recently discovered planetoids. His O rachunku losów (On the Calculation of Chance, 1817) was a pioneering work in probability. Wik He is considered as the best Polish mathematician born in the 18th century. 1876 Charles F. Kettering (29 Aug 1876; 25 Nov 1958) was an American engineer whose 140 patents included the electric starter, car lighting and ignition systems. In his early career, with the National Cash Register Co., Dayton (1904-09), he created the first electric cash register with an electric motor that opened the drawer. When he co-founded the Dayton Engineering Laboratories Company (DELCO, with Edward A. Deeds) he invented the key-operated self-starting motor for the Cadillac (1912) and it spread to nearly all new cars by the 1920's. As vice president and director of research for General Motors Corp. (1920-47) he developed engines, quick-drying lacquer finishes, anti-knock fuels, and variable-speed transmissions.TIS 1881 Ferdinand Springer born, The founder of an important publishing house,. Today Springer-Verlag is one of the most important publishers of advanced work on mathematics. VFR 1904 Leonard Roth (29 August 1904 Edmonton, London, England – 28 November 1968 Pittsburgh, Pennsylvania) British Mathematician who worked primarily in Algebraic Geometry. SAU DEATHS 1873 Hermann Hankel (14 February 1839 - 29 August 1873) He studied and worked with, among others, Möbius, Riemann, Weierstrass and Kronecker. His 1867 exposition on complex numbers and quaternions is particularly memorable. For example, Fischbein notes that he solved the problem of products of negative numbers by proving the following theorem: "The only multiplication in R which may be considered as an extension of the usual multiplication in R+ by respecting the law of distributivity to the left and the right is that which conforms to the rule of signs." Wik 1930 James Bolam (1839 in Newcastle, England - 29 Aug 1930 in St Helen's, Drumchapel, Dumbartonshire, Scotland) was educated at Newcastle. He became head of the Government Navigation School (later the Leith Nautical College). He was a founder member of the EMS and became an honorary member in 1923. SAU 1937 Otto Ludwig Hölder (December 22, 1859 – August 29, 1937) worked on the convergence of Fourier series and in 1884 he discovered the inequality now named after him. He became interested in group theory through Kronecker and Klein and proved the uniqueness of the factor groups in a composition series. SAU 1967 Charles Brace Darrow (10 Aug 1889, 29 Aug 1967) was an American inventor who designed the board game Monopoly. He had invented the game on 7 Mar 1933, though it was preceded by other real-estate board games. On 31 Dec 1935, a patent was issued for the game of Monopoly assigned to Parker Brothers, Inc., by Charles Darrow of Pennsylvania (No. 2,026,082). The patent titled it a "Board Game Apparatus" and described it as "intended primarily to provide a game of barter, thus involving trading and bargaining" in which "much of the interest in the game lies in trading and in striking shrewd bargains." Illustrations included with the patent showed not only the playing board and pieces, cards, and the scrip money. TIS 1975 Éamon de Valera (14 October 1882, 29 August 1975) was one of the dominant political figures in twentieth century Ireland, serving as head of government of the Irish Free State and head of government and head of state of Ireland. He also introduced the Constitution of Ireland. De Valera was a leader of Ireland's struggle for independence from Britain in the Irish War of Independence and of the anti-Treaty forces in the ensuing Irish Civil War (1922–23). In 1926, he founded Fianna Fáil and was head of government from 1932–48, 1951–54 and 1957–59 and President of Ireland from 1959–73. In his youth he had trained as a mathematician and taught mathematics prior to the Easter Rising. Throughout his life he maintained an interest in mathematics and returned to it with a passion in his later life. Wik Credits : CHM=Computer History Museum FFF=Kane, Famous First Facts NSEC= NASA Solar Eclipse Calendar RMAT= The Renaissance Mathematicus, Thony Christie SAU=St Andrews Univ. Math History TIA = Today in Astronomy TIS= Today in Science History VFR = V Frederick Rickey, USMA Wik = Wikipedia ## Sunday, 28 August 2016 ### On This Day in Math - August 28 As long as algebra and geometry have been separated, their progress have been slow and their uses limited; but when these two sciences have been united, they have lent each mutual forces, and have marched together towards perfection. ~Joseph Louis Lagrange The 241st day of the year; 241 is the larger of a pair of twin primes. The larger of a pair of twin primes is always one more than a multiple of six; the smaller is always one less than a multiple of six. 2+4+1 is prime. 241 is the 53rd prime. (53 is also prime) Derek Orr 241 is also The smallest prime p such that p plus the reversal of p equals a palindromic prime. 241 + 142 = 383; which is a prime palindrome. And it is the largest known prime p such that the reversal of (p! + p) is prime. (241! + 241 ends with a string of fifty-five zeros, and then 241 : 980360372638941007038951797078339359751464353463061342202811 188548638347461066010066193275864531994024640834549254693776 854464608509281547718518965382728677985343589672835884994580 815417004715718468026937051493675623385569404900262441027874 255428340399091926993707625233667755768320823071062785275404 107485450075779940944580451919726756974354635829128751944137 27644867102380111026020691554782580923999494640500736 0000000000000000000000000000000000000000000000000000000241.... and if you write the reversal of that, it's prime. EVENTS 412 BC The ancient city of Syracuse suffered heavily under siege by the Athenians during the Peloponnesian War. A turn of events occurred during the Second Battle of Syracuse: on Aug. 28, 41.C. a lunar eclipse occurred, causing the superstitious Athenians to delay departure. The Syracuseans took advantage of Athenian indecision and decisively defeated the unprotected Athenian expedition as it sat exposed in the harbor. listosaur.com 1666 John Evelyn Records in his diary: "to the Royal Society, where one Mercator, an excellent mathematician, produced his rare clock and new motion to perform the equations, and Mr. Rooke, his new pendulum." The Mercator is Nicholas Mercator who taught mathematics in London (1658–1682). He designed a marine chronometer for Charles II, and designed and constructed the fountains at the Palace of Versailles. Mathematically, he is most well known for his treatise Logarithmo-technica on logarithms, published in 1668 in which he described the Mercator series, also independently discovered by Gregory Saint-Vincent $\ln(1 + x) = x - \frac{1}{2}x^2 + \frac{1}{3}x^3 - \frac{1}{4}x^4 + \cdots.$ I suspect the "Mr Rooke" should have been Hooke who is mentioned at the meeting in Pepys' Diary. Wik, John Evelyn Diary 1730 Murder by Unicorn Horn on a Holborn skittle-ground : On the 28th of August 1730, Joseph Hastings died after receiving “several mortal Bruises with an Unicorn’s Horn”, wielded by John Williams of St. Andrew’s Holborn eleven days earlier. The assault occurred on a Holborn skittle-ground, witnessed by several local men. Williams was angered by Hastings response to his offer to purchase the (probably Narwhale) horn and an argument ensued which led to the beating. More detail at Sloan Letters In 1789, Enceladus, the sixth-largest moon of Saturn, was discovered by Fredrick William Herschel on August 28, 1789, during the first use of his new 1.2 m (47 in) telescope, then the largest in the world. Little was known about Enceladus until the two Voyager spacecraft passed near it in the early 1980s. Enceladus is named after the giant Enceladus of Greek mythology.[14] The name Enceladus—like the names of each of the first seven satellites of Saturn to be discovered—was suggested by William Herschel's son John Herschel in his 1847 publication Results of Astronomical Observations made at the Cape of Good Hope.[30] He chose these names because Saturn, known in Greek mythology as Cronus, was the leader of the Titans. Wik Scientific American ‏@sciam 1845 the first issue of the Scientific American was published by Rufus Porter (1792-1884), a versatile if eccentric Yankee, who was by turns a portrait-painter, schoolmaster, inventor and editor. While the paper was still a small weekly journal with a circulation less than 300, he offered it for sale. It was bought for $800 in July 1846 by 20-year-old Alfred Ely Beach (1826-1896) as editor, and Orson Desaix Munn (1824-1907). Together, they built it over the years into a great and unique periodical. Their circulation reached 10,000 by 1848, 20,000 by 1852, and 30,000 by 1853.TIS 1893 The first day of the Evanston Colloquial lectures by Felix Klein which would continue until 9 September. Karen Hunger Parshall, David E. Rowe; The Emergence of the American Mathematical Research Community, 1876-1900 1961 The Board of Governors of the MAA voted to name Dr. Mina S. Rees, (ﬁrst) Dean of Graduate Studies at the City University of New York, the ﬁrst recipient of their Award for Distinguished Service to Mathematics. From 1946 to 1953 she held several important positions at the Office of Naval Research and was instrumental in getting ONR to adopt the policy that mathematics was part of this country’s total scientiﬁc effort and should be properly supported by government-sponsored research programs. [AMM 69(1962), pp. 185-187]. VFR 1974 Sweden issued a stamp picturing a spool and thread, with the thread stretched to form a string ﬁgure of a hyperbola. [Scott #1094]. VFR HT to Emma L Bell, Storax Sedan, and Glen Carlson for image 1993, a picture was taken showing the first moon of an asteroid. The asteroid 243 Ida and its newly-discovered moon, Dactyl was imaged by NASA's Galileo spacecraft, about 14 minutes before its closest approach (within 2,400-km or 1,500 miles) to the asteroid. Ida is about 52 km (32 mi) in length and is irregularly shaped. It shows numerous craters, including many degraded craters, indicating Ida's surface is older than previously thought. Dactyl is only about 1.4-km in diameter, and it is spectrally different from Ida data. The picture was released on 26 Mar 1994. Galileo had encountered the first asteroid - 951 Gaspra - on 29 Oct 1991. Galileo continued on its mission to study Jupiter, beginning its orbit of the planet on 7 Dec 1995.TIS 2009 The Australian Govt replies to a letter written "To A Top Scientist" by an Australian schoolboy shortly after the launch of Sputnik fifty-two years earlier with his suggested designs for a rocket ship. See all the details at this page from Letters of Note BIRTHS 1796 Irénée-Jules Bienaymé (28 August 1796, 19 October 1878), was a French statistician. He built on the legacy of Laplace generalizing his least squares method. He contributed to the fields and probability, and statistics and to their application to finance, demography and social sciences. In particular, he formulated the Bienaymé-Chebyshev inequality concerning the law of large numbers and the Bienaymé formula for the variance of a sum of uncorrelated random variables.Wik 1801 Antoine-Augustin Cournot (28 Aug 1801; 31 Mar 1877) French economist and mathematician, who was the first economist who applied mathematics to the treatment of economic questions. In 1838, he published Recherches sur les principes mathématiques de la théorie des richesses (Researches into the Mathematical Principles of the Theory of Wealth) which was a treatment of mathematical economics. In particular, he considered the supply-and-demand functions. Further, he studied the conditions for equilibrium with monopoly, duopoly and perfect competition. He included the effect of taxes, treated as changes in production costs, and discussed problems of international trade. His definition of a market is still the basis for that presently used in economics. In other work, he applied probability to legal statistics TIS 1863 Andre-Eugene Blondel (28 Aug 1863; 15 Nov 1938) was a French physicist who invented (1893) the electromagnetic oscillograph, a device that allowed electrical researchers to observe the intensity of alternating currents. In 1894, he proposed the lumen and other new photometric units for use in photometry, based on the metre and the Violle candle. Endorsed in 1896 by the International Electrical Congress, his system is still in use with only minor modifications. Blondel was a pioneer in the high voltage long distance transport of electric power, and also contributed to developments in wireless telegraphy, acoustics, and mechanics. He proposed theories for induction motors and coupling of a.c. generators.TIS (Invention of the Oscillograph is also credited to William Du Bois Duddell.) 1867 Maxime Bˆochner born. After receiving his doctorate under Felix Klein in 1891 he returned to Harvard for a lifetime of teaching and research in differential equations. VFR 1883 Jan A Schouten worked on tensor analysis and its applications.SAU 1901 Kurt Otto Friedrichs (September 28, 1901 – December 31, 1982) was a noted German American mathematician. He was the co-founder of the Courant Institute at New York University and recipient of the National Medal of Science.Wik 1911 Shizuo Kakutani (角谷静夫 Kakutani Shizuo?, August 28 1911, August 17 2004) was a Japanese-born American mathematician, best known for his eponymous fixed-point theorem. Wik 1912 George Eric Deacon Alcock (August 28, 1912 – December 15, 2000) George Alcock was an English astronomer. He was one of the most successful visual discoverers of novae and comets. He was also a very good (probably under-respected) teacher of the 4th year at Southfields Junior School in Stanground, Peterborough. In 1953 he decided to start searching for comets and in 1955 began searching for novae. His technique was to memorize the patterns of thousands of stars, so that he would visually recognize any intruder. In 1959 he discovered comet C/1959 Q1 (Alcock), the first comet discovered in Britain since 1894, and only five days later discovered another, C/1959 Q2 (Alcock). He discovered two more comets in 1963 and 1965. He later discovered his first nova, Nova Delphini 1967 (HR Delphini), which turned out to have an unusual light curve. He discovered two more novas, LV Vul (in 1968) and V368 Sct (in 1970). He found his fifth and final comet in 1983: C/1983 H1 (IRAS-Araki-Alcock). In 1991 he found the nova V838 Her. Alcock won the Jackson-Gwilt Medal of the Royal Astronomical Society in 1963 and Amateur Achievement Award of the Astronomical Society of the Pacific in 1981. After his death, a plaque was placed in Peterborough Cathedral in his memory. TIA 1919 Sir Godfrey Newbold Hounsfield (28 August 1919 – 12 August 2004) English electrical engineer who shared the 1979 Nobel Prize for Physiology or Medicine (with Allan Cormack) for creation of computerised axial tomography (CAT) scanners. He originated the idea during a country walk in 1967 when he realized that the contents of a box could be reconstructed by taking readings at all angles through it. He applied the concept for scanning the brain using hundreds of X-ray beams imaging cross-sections that were reconstructed as high-resolution graphics by a computer program handling complex algebraic calculations. By 1973 his CAT scanner could produce cross-section images of a brain in 4-1/2-min, invaluable for the diagnosis of brain diseases. He later built a larger machines able to make a full body scan. TIS 1921 Ralph Asher Alpher (February 3, 1921 – August 12, 2007) was an American cosmologist. Alpher's dissertation in 1948 dealt with a subject that came to be known as Big Bang nucleosynthesis. In a strange mathematical pun, his pre-publication of his thesis may have caused his independent role to have been minimized. Although his name appears on the paper, Hans Bethe had no direct part in the development of the theory, although he later worked on related topics; Gamow added his name to make the author list Alpher, Bethe, Gamov, a pun on alpha, beta, gamma (α, β, γ), the first three letters of the Greek alphabet. Thus, Alpher's independent dissertation was first published on April 1, 1948 in the Physical Review with three authors. The humor engendered by the prodigious Gamow may at times have obscured the critical role Alpher played in developing the theory. This seminal paper was based on his dissertation (defended shortly thereafter). With the award of the 2005 National Medal of Science, Alpher's original contributions (nucleosynthesis and the cosmic microwave background radiation predicition) to the modern big bang theory are beginning to receive due recognition. Neil deGrasse Tyson was instrumental in a NSF committee recommendation. In 2005 Alpher was awarded the National Medal of Science. The citation for the award reads "For his unprecedented work in the areas of nucleosynthesis, for the prediction that universe expansion leaves behind background radiation, and for providing the model for the Big Bang theory." The medal was presented to his son Dr. Victor S. Alpher on July 27, 2007 by President George W. Bush, as his father could not travel to receive the award. Ralph Alpher died following an extended illness on August 12, 2007. He had been in failing health since falling and breaking his hip in February 2007. Wik 1919 Sir Godfrey Newbold Hounsfield (28 Aug 1919; 12 Aug 2004) English electrical engineer who shared the 1979 Nobel Prize for Physiology or Medicine (with Allan Cormack) for creation of computerised axial tomography (CAT) scanners. He originated the idea during a country walk in 1967 when he realized that the contents of a box could be reconstructed by taking readings at all angles through it. He applied the concept for scanning the brain using hundreds of X-ray beams imaging cross-sections that were reconstructed as high-resolution graphics by a computer program handling complex algebraic calculations. By 1973 his CAT scanner could produce cross-section images of a brain in 4-1/2-min, invaluable for the diagnosis of brain diseases. He later built larger machines able to make a full body scan. TIS 1939 John Frank Charles Kingman (28 August 1939, )worked in Statistics and made significant advances in queuing theory. He was N. M. Rothschild and Sons Professor of Mathematical Sciences and Director of the Isaac Newton Institute at the University of Cambridge from 2001 until 2006, when he was succeeded by Sir David Wallace. He is famous for developing the mathematics of the coalescent, a theoretical model of inheritance, which is fundamental to modern population genetics. Wik 1951 Edward Witten (born August 26, 1951) is an American theoretical physicist with a focus on mathematical physics who is a professor of Mathematical Physics at the Institute for Advanced Study at Princeton, New Jersey. Witten is a researcher in superstring theory, a theory of quantum gravity, supersymmetric quantum field theories and other areas of mathematical physics.[1] He has made contributions in mathematics and helped bridge gaps between fundamental physics and other areas of mathematics. In 1990 he became the first physicist to be awarded a Fields Medal by the International Union of Mathematics. In 2004, Time magazine stated that Witten was widely thought to be the world's greatest living theoretical physicist. Wik DEATHS 2005 George Szekeres (29 May 1911 – 28 August 2005) was a Hungarian-born mathematician who worked for most of his life in Australia on geometry and combinatorics. SAU Szekeres worked closely with many prominent mathematicians throughout his life, including Paul Erdős, Esther Szekeres (née Esther Klein), Paul Turán, Béla Bollobás, Ronald Graham, Alf van der Poorten, Miklós Laczkovich, and John Coates. The so-called Happy Ending problem is an example of how mathematics pervaded George's life. During 1933, George and several other students met frequently in Budapest to discuss mathematics. At one of these meetings, Esther Klein proposed the following problem: Given five points in the plane in general position, prove that four of them form a convex quadrilateral. After allowing George, Paul Erdős, and the other students to scratch their heads for some time, Esther explained her proof. Subsequently, George and Paul wrote a paper (1935) that generalizes this result; it is regarded as one of the foundational works in the field of combinatorial geometry. Erdős dubbed the original problem the "Happy Ending" problem because it resulted in George and Esther's marriage in 1937. George and Esther died within an hour of each other, on the same day, 28 August 2005, in Adelaide, Australia.Wik 2005 Esther (Klein) Szekeres (20 February 1910 – 28 August 2005) was a Hungarian–Australian mathematician with an Erdős number of 1. She was born to Ignaz Klein in a Jewish family in Budapest, Kingdom of Hungary in 1910. As a young woman in Budapest, Klein was a member of a group of Hungarians including Paul Erdős, George Szekeres and Paul Turán that convened over interesting mathematical problems. In 1933, Klein proposed to the group a combinatorial problem that Erdős named as the Happy Ending problem as it led to her marriage to George Szekeres in 1937, with whom she had two children. Following the outbreak of World War II, Esther and George Szekeres emigrated to Australia after spending several years in Hongkew, a community of refugees located in Shanghai, China. In Australia, they originally settled in Adelaide before moving to Sydney in the 1960s. In Sydney, Esther lectured at Macquarie University and was actively involved in mathematics enrichment for high-school students. In 1984, she jointly founded a weekly mathematics enrichment meeting that has since expanded into a program of about 30 groups that continue to meet weekly and inspire high school students throughout Australia and New Zealand. In 2004, she and George moved back to Adelaide, where, on 28 August 2005, she and her husband passed away within an hour of each other Wik 2007 Paul Beattie MacCready (29 Sep 1925, 28 Aug 2007) was an American engineer who invented not only the first human-powered flying machines, but also the first solar-powered aircraft to make sustained flights. On 23 Aug 1977, the pedal-powered aircraft, the Gossamer Condor successfully flew a 1.15 mile figure-8 course to demonstrate sustained, maneuverable manpowered flight, for which he won the £50,000 ($95,000) Kremer Prize. MacCready designed the Condor with Dr. Peter Lissamen. Its frame was made of thin aluminum tubes, covered with mylar plastic supported with stainless steel wire. In 1979, the Gossamer Albatross won the second Kremer Prize for making a flight across the English Channel. TIS 2011 Anthony Edgar Sale (or Tony Sale) (30 January 1931 - 28 August 2011) led the construction of a Colossus computer replica at Bletchley Park, completed in 2007 Wik In 1994, a team led by Tony Sale began a reconstruction of a Colossus at Bletchley Park. Here, in 2006, Sale (right) supervises the breaking of an enciphered message with the completed machine. Wik Photo Credits : CHM=Computer History Museum FFF=Kane, Famous First Facts NSEC= NASA Solar Eclipse Calendar RMAT= The Renaissance Mathematicus, Thony Christie SAU=St Andrews Univ. Math History TIA = Today in Astronomy TIS= Today in Science History VFR = V Frederick Rickey, USMA Wik = Wikipedia WM = Women of Mathematics, Grinstein & Campbell ## Saturday, 27 August 2016 ### On This Day in Math - August 27 Questions that pertain to the foundations of mathematics, although treated by many in recent times, still lack a satisfactory solution. The difficulty has its main source in the ambiguity of language. Giuseppe Peano, Opening of the paper Arithmetices principia in which he introduced axioms for the integers. The 240th day of the year; 240 has more divisors (20 of them) than any previous number. What would be the next number that has more? 240 is the product of the first 6 Fibonacci numbers 240 = 112358 Derek Orr These are often called Fibonacci factorials or fibonorials. 240 would be $6!_F$, also called the Fibonacci factorial EVENTS In 413 BC, a lunar eclipse caused panic among the sailors of the Athens fleet and thus affected the outcome of a battle in the Peloponnesian War. The Athenians were ready to move their forces from Syracuse when the Moon was eclipsed. The soldiers and sailors were frightened by this celestial omen and were reluctant to leave. Their commander, Nicias, consulted the soothsayers and postponed the departure for 27 days. This delay gave an advantage to their enemies, the Syracusans, who then defeated the entire Athenian fleet and army, and killed Nicias.TIS 1666 John Evelyn makes an on-site visit to Old St. Pauls with Christopher Wren. "We went about to survey the general decays of that ancient and venerable church, and to set down the particulars in writing, what was fit to be done.." Five days later the reports would be rendered meaningless by the Great London Fire. Lisa Jardine, Ingenious Pursuits, pgs 69-70 1760 Leonhard Euler, in his Letters to a German Princess on various topics of physics and philosophy, explains how a surveyor uses a level. As an example he asks which end of the straight line between their homes is higher. He discusses the ﬂow of the rivers that connect their homes, but gives the wrong answer to his question. For discussion of this famous error, see Eves, Adieu, 34 VFR 1771 Joseph Priestley finds a mint plant rejuvenates "spent" air. He had set out ten days earlier to test the rejuvenating effect of mint growing in a sealed container. He placed a candle in the covered glass and let it burn out in the presence of the mint. On the 27th he would return to the experiment and relight the candle and find, "it burned perfectly well in it." Steven Johnson, The Invention of Air 1776 Even in the onset of the American Revolution, (Nathan Hale was executed for treason only five days before) future President John Adams, wrote of a visit to the Princeton Orrery: "Here we saw a most beautiful machine--an Orrery or planetarium constructed by Mr. Rittenhouse of Philadelphia. It exhibits almost every motion in the astronomical world." David Rittenhouse was a renowned American astronomer, clockmaker, mathematician, surveyor, scientific instrument craftsman, and public official. Rittenhouse was a president of the American Philosophical Society; Treausrer of Pennsylvania; & the first director of the United States Mint. Barbara Wells Sarudy 1783 Jacques A. C. Charles (for whom Charles' Law is named) and the Robert brothers launched the world's first hydrogen filled balloon on August 27, 1783, from the Champ de Mars, (now the site of the Eiffel Tower) where Ben Franklin was among the crowd of onlookers. The balloon was comparatively small, a 35 cubic metre sphere of rubberised silk, and only capable of lifting circa 9 kg (20 lb). It was filled with hydrogen that had been made by pouring nearly a quarter of a tonne of sulphuric acid onto a half a tonne of scrap iron. The hydrogen gas was fed into the balloon via lead pipes; but as it was not passed through cold water, great difficulty was experienced in filling the balloon completely (the gas was hot when produced, but as it cooled in the balloon, it contracted). Daily progress bulletins were issued on the inflation; and the crowd was so great that on the 26th the balloon was moved secretly by night to the Champ de Mars, a distance of 4 kilometres. (This may not have been very secret as another source says there were processions of torchlights along the route.) The balloon flew northwards for 45 minutes, pursued by chasers on horseback, and landed 21 kilometers away in the village of Gonesse where the reportedly terrified local peasants destroyed it with pitchforks or knives. Wik 1784 One year after the Charles Flight (above) James Tytler became the first person in Britain to fly by ascending in a hot air balloon (He had made a minimal flight on 25 August in Edinburgh when his balloon rose a few feet from the ground. On the 27th he managed to reach a height of some 350 feet, traveling for half a mile between Green House on the northern edge of what is now Holyrood Park to the nearby village of Restalrig. Wik 1798 Egyptian Institute founded by Napoleon in imitation of the Institut de France VFR 1911 A century ago, on August 27, 1911, headlines of the New York Times announced that Martians had completed stunning feats of engineering and construction: two 1000-mile-long canals built on Mars in a two-year period. These canals had not only been seen and sketched by astronomers, but also had been captured photographically, appearing in the photos as “the most marked features on that part of the planet”. The Renaissance Mathematicus 1947 China (there was only one until 1949) issued four stamps honoring Confucius. [Scott #741-4]. VFR 1993 Compaq Computer Corp. announced its Presario family of personal computers, intended to be user friendly and cheap. For \$1,399, the Presario included a monitor, modem, and software to access the recently popularized online world through Prodigy and America Online. CHM BIRTHS 1850 Augusto Righi (27 August 1850 – 8 June 1920) was an Italian physicist and a pioneer in the study of electromagnetism. He was born and died in Bologna. Righi was the first person to generate microwaves,[citation needed] and opened a whole new area of the electromagnetic spectrum to research and subsequent applications. His work L'ottica delle oscillazioni elettriche (1897), which summarised his results, is considered a classic of experimental electromagnetism. Marconi was his student. Wik 1858 Birthdate of Giuseppe Peano (27 Aug 1858; 20 Apr 1932) early contributor to symbolic logic. Through the use of symbols, equations are more easily understood by anyone regardless of their language. For example, Peano introduced symbols to represent "belongs to the set of" and "there exists." In Arithmetics principia (1889), a pamphlet he wrote in Latin, Peano published his first version of a system of mathematical logic, giving his Peano axioms defining the natural numbers in terms of sets. In 1903, Peano unsuccessfully proposed an international, artificial language he called "Latino sine flexione." It was based on Latin without grammar. Its vocabulary comprised words from English, French, German and Latin. TIS Thony Christie maintains that this may overstate his contribution. "I've been here before. Peano made a substantial contribution to the history of symbolic logic, especially the fact that it was his work that inspired Russell. However I think Boole, Jevons, Demorgan, Venn, McColl, Frege, Peirce, Ladd-Franklin and quite a few others who were doing symbolic logic before Peano might object to him being called its founder. To say nothing of the Stoics! " 1915 Norman Foster Ramsey (27 Aug 1915, )American physicist who shared (with Wolfgang Paul and Hans Georg Dehmelt) the 1989 Nobel Prize for Physics in 1989 for "for the invention of the separated oscillatory fields method and its use in the hydrogen maser and other atomic clocks." His work produced a more precise way to observe the transitions within an atom switching from one specific energy level to another. In the cesium atomic clock, his method enables observing the transitions between two very closely spaced levels (hyperfine levels). The accuracy of such a clock is about one part in ten thousand billion. In 1967, one second was defined as the time during which the cesium atom makes exactly 9,192,631,770 oscillations.TIS 1923 Jacob Willem "Wim" Cohen (27 August 1923, 12 November 2000) was a Dutch mathematician, well known for over a hundred scientific publications and several books in queueing theory. Wik 1926 Kristen Nygaard (August 27, 1926, August 10, 2002) was a Norwegian computer scientist, programming language pioneer and politician. He was born in Oslo and died of a heart attack in 2002. Internationally he is acknowledged as the co-inventor of object-oriented programming and the programming language Simula with Ole-Johan Dahl in the 1960s. DEATHS 1898 John Hopkinson (27 Jul 1849, 27 Aug 1898)British physicist and electrical engineer who worked on the application of electricity and magnetism in devices like the dynamo and electromagnets. Hopkinson's law (the magnetic equivalent of Ohm's law) bears his name. In 1882, he patented his invention of the three-wire system (three phase) for electricity generation and distribution. He presented the principle the synchronous motors (1883), and designed electric generators with better efficiency. He also studied condensers and the phenomena of residual load. In his earlier career, he became (1872) engineering manager of Chance Brothers and Co., a glass manufacturer in Birmingham, where he studied lighthouse illumination, improving efficiency with flashing groups of lights.TIS 1912 Mikhail Vashchenko-Zakharchenko worked on the theory of linear differential equations, the theory of probability and non-euclidean geometry.SAU 1958 Ernest Orlando Lawrence (8 Aug 1901, 27 Aug 1958 ) American physicist who was awarded the 1939 Nobel Prize for Physics for his invention of the cyclotron, the first device for the production of high energy particles. His first device, built in 1930 used a 10-cm magnet. He accelerated particles within a cyclinder at high vacuum between the poles of an electromagnetic to confine the beam to a spiral path, while a high A.C. voltage increased the particle energy. Larger models built later created 8 x 104 eV beams. By colliding particles with atomic nuclei, he produced new elements and artificial radioactivity. By 1940, he had created plutonium and neptunium. He extended the use of atomic radiation into the fields of biology and medicine. Element 103 was named Lawrencium as a tribute to him. TIS 1988 Max Black (24 February 1909, 27 August 1988) was a British-American philosopher and a leading influence in analytic philosophy in the first half of the twentieth century. He made contributions to the philosophy of language, the philosophy of mathematics and science, and the philosophy of art, also publishing studies of the work of philosophers such as Frege. His translation (with Peter Geach) of Frege's published philosophical writing is a classic text. Wik Credits : CHM=Computer History Museum FFF=Kane, Famous First Facts NSEC= NASA Solar Eclipse Calendar RMAT= The Renaissance Mathematicus, Thony Christie SAU=St Andrews Univ. Math History TIA = Today in Astronomy TIS= Today in Science History VFR = V Frederick Rickey, USMA Wik = Wikipedia WM = Women of Mathematics, Grinstein & Campbell ## Friday, 26 August 2016 ### On This Day in Math - August 26 Thanks for the great memories, Students of Lakenheath Perhaps... some day the precision of the data will be brought so far that the mathematician will be able to calculate at his desk the outcome of any chemical combination, in the same way, so to speak, as he calculates the motions of celestial bodies. ~Antoine-Laurent Lavoisier The 239th day of the year; When expressing 239 as a sum of square numbers, 4 squares are required, which is the maximum that any integer can require; it is the largest number that needs the maximum number (9) of positive cubes (Only one other number requires nine cubes, can you find it?) and a hundred years (+/-) ago (many people included 1 as a prime then; see more) 239 would have been a prime that is the sum of the first 14 primes; 239 = 1+2+3+5+7+11+...+37+41 Derek Orr 239 appears in one of the earliest known geometrically converging formulas for computing Pi: Pi/4 = 4 arctan(1/5) - arctan(1/239) .archimedes-lab.org EVENTS 1735 Euler’s Konisburg bridge solution, "The Solution of a problem related to the Geometry of Position", was presented to the St. Petersburg Academy on August 26, 1735. He showed that there were no continuous walks across the seven bridges across the Pregel River in Konisburg. It is often cited as the earliest paper in both topology and graph theory.VFR 1768 Capt. James Cook began the ﬁrst circumnavigation of the globe. VFR Cook and his ninety-eight foot bark, Endeavour, carried the Venus transit observation crew mounted by the Royal Society, led by a future Royal Soc. President, Joseph Banks. They would erect an observation station at Point Venus in Tahiti to observe the June 3, 1769 observation under clear blue skys. Timothy Ferris, Coming of Age in the Milky Way 1770 Lagrange, in a letter to d’Alembert, ﬁrst uses the notation f‘ (x) for the derivative. He ﬁrst used it in print in a paper published in 1772. Although Lagrange used the notation in his diagramless Mecanique Analytique (1788), it did not catch on until after he used it in his Theorie de functions analytiques (1797). Oeuvres de Lagrange, 13, p. 181. 1774 John Adams notes in his diary that he had toured Princeton’s library with Professor Euston (William Churchill Houston, first professor of mathematics and natural philosophy) and then into the “apparatus room” where he saw the “most beautiful machine”. It was an orrery made by David Rittenhouse, a renowned American astronomer, inventor, clockmaker, mathematician, surveyor, scientific instrument craftsman and public official. Professor Houston served in combat in the revolution when Princeton was closed by the occupation of the British. After the college was reopened, he returned to teaching but was soon selected to represent New Jersey as a representative to the Continental Congress, and then to the Constitutional Convention. He died shortly after the close of the Constitutional Convention. The Teaching and History of Mathematics in The United States, F. Cajori (pgs 71-72) 1831 Darwin had been committed to a life as a clergyman when he received a letter from George Peacock inviting him to sail with Captain Fitzroy. The rest, as they say, is history. My dear Sir I received Henslow’s (Darwin's botany professor) letter last night too late to forward it to you by the post, a circumstance which I do not regret, as it has given me an opportunity of seeing Captain Beaufort at the admiralty (the Hydrographer) & of stating to him the offer which I have to make to you: he entirely approves of it & you may consider the situation as at your absolute disposal: I trust that you will accept it as it is an opportunity which should not be lost & I look forward with great interest to the benefit which our collections of natural history may receive from your labours The circumstances are these Captain Fitzroy (a nephew of the Duke of Graftons) sails at the end of September in a ship to survey in the first instance the S. Coast of Terra del Fuego, afterwards to visit the South Sea Islands & to return by the Indian Archipelago to England: The expedition is entirely for scientific purposes & the ship will generally wait your leisure for researches in natural history &c: Captain Fitzroy is a public spirited & zealous officer, of delightful manners & greatly beloved by all his brother officers: he went with Captain Beechey and spent 1500£ in bringing over and educating at his own charge 3 natives of Patagonia:f2 he engages at his own expense an artist at 200 a year to go with him: you may be sure therefore of having a very pleasant companion, who will enter heartily into all your views The ship sails about the end of September you must lose no time in making known your acceptance to Captain Beaufort, Admiralty hydr I have had a good deal of correspondence about this matter, whof3 feels in common with myself the greatest anxiety that you should go. I hope that no other arrangements are likely to interfere with it Captain will give you the rendezvous & all requisite information: I should recommend you to come up to London, in order to see him & to complete your arrangements I shall leave London on Monday: perhaps you will have the goodness to write to me at Denton, Darlington, to say that you will go. The Admiralty are not disposed to give a salary, though they will furnish you with an official appointmentf4 & every accomodation: if a salary should be required however I am inclined to think that it would be granted Believe me \| My dear Sir \| Very truly yours \| Geo Peacock If you are with Sedgwick I hope you will give my kind regards to him In 1895, electricity was first transmitted commercially from the first large-scale utilization of Niagara Falls power, the current being used by the Pittsburgh Reduction Company in the electrolytic production of aluminium metal from its ore. Buffalo subsequently received power for commercial use on 15 Nov 1896. The equipment was the result of a contract made on 24 Oct 1893 whereby Westinghouse Electric and Manufacturing Company of Pittsburgh, Pa., would install three 5,000-hp generators producing two-phase currents at 2,200 volts, 25 hertz. The first such tuboalternator unit was completed within 18 months. Prior capacity had been limited to generators no larger than 1,000 hp.TIS 1966 Professor Stephen Smale, who received the Fields medal ten days earlier, condemned American military intervention in Vietnam and Soviet intervention in Hungary at a news conference in Moscow. For Smale’s fascinating personal account see “On the Steps of Moscow University,” The Mathematical Intelligencer, 6, no. 2, pp. 21–27. VFR 1984 Miss Manners addresses computer correspondence Miss Manners confronts a new realm of etiquette in her August 26 column as she responded to a reader's concern about typing personal correspondence on a personal computer. The concerned individual said that using the computer was more convenient but that they were worried about the poor quality of her dot-matrix printer and about copying parts of one letter into another. Miss Manners replied that computers, like typewriters, generally are inappropriate for personal correspondence. In the event a word processor is used, she warned, the recipient may confuse the letter for a sweepstakes entry. And, she noted, if any one of your friends ever sees that your letter to another contains identical ingredients, you have will no further correspondence problems.CHM BIRTHS 1728 Johann Heinrich Lambert (August 26, 1728 – September 25, 1777) was born in Mulhouse, Alsace. His most famous results are the proofs of the irrationality of π and e VFR In 1766, Lambert wrote Theorie der Parallellinien, a study of the parallel postulate. By assuming that the parallel postulate was false, he deduced many non-euclidean results. He noticed that in this new geometry the sum of the angles of a triangle increases as its area decreases. Lambert conjectured that e and p are transcendental, though this was not proved for another century. He is responsible for many innovations in the study of heat and light, devised a method of measuring light intensity, as well as working on the theory of probability.TIS (Lambert's credit for a vigorous proof of the irrationality of π is generally agreed to, but Euler Scholar Ed Sandifer has written that Euler's proof was fully rigorous prior to Lambert. How Euler Did It, Feb 2006). 1740 Joseph-Michel Montgolfier (26 Aug 1740; 26 Jun 1810)French balloon pioneer, with his younger brother, Étienne. An initial experiment with a balloon of taffeta filled with hot smoke was given a public demonstration on 5 Jun 1783. This was followed by a flight carrying three animals as passengers on 19 Sep 1783, shown in Paris and witnessed by King Louis XVI. On 21 Nov 1783, their balloon carried the first two men on an untethered flight. In the span of one year after releasing their test balloon, the Montgolfier brothers had enabled the first manned balloon flight in the world.TIS Jacques Louis David 1743 Antoine-Laurent Lavoisier (26 August 1743 – 8 May 1794) French scientist, the "father of modern chemistry," was a brilliant experimenter also active in public affairs. An aristocrat, he invested in a private company hired by the government to collect taxes. With his wealth he built a large laboratory. In 1778, he found that air consists of a mixture of two gases which he called oxygen and nitrogen. By studying the role of oxygen in combustion, he replaced the phlogiston theory. Lavoisier also discovered the law of conservation of mass and devised the modern method of naming compounds, which replaced the older nonsystematic method. During the French Revolution, for his involvement with tax-collecting, he was guillotined.TIS "This great double portrait at right was painted when the artist, at the peak of his powers, had become the standard-bearer of French Neoclassicism. Lavoisier is known for his pioneering studies of oxygen, gunpowder, and the chemical composition of water. In 1789 he published a treatise on chemistry illustrated by his wife, who is believed to have been David's pupil." Metropolitan Museum of Art 1875 Giuseppe Vitali (26 August 1875 – 29 February 1932) was an Italian mathematician who worked in several branches of mathematical analysis. He was the first to give an example of a non-measurable subset of real numbers, see Vitali set. His covering theorem is a fundamental result in measure theory. He also proved several theorems concerning convergence of sequences of measurable and holomorphic functions. Vitali convergence theorem generalizes Lebesgue's dominated convergence theorem. Another theorem bearing his name gives a sufficient condition for the uniform convergence of a sequence of holomorphic functions on an open domain D⊂ℂ to a holomorphic function on D. This result has been generalized to normal families of meromorphic functions, holomorphic functions of several complex variables, and so on. Wik 1882 James Franck (26 Aug 1882; 21 May 1964) German-born American physicist who shared the Nobel Prize for Physics in 1925 with Gustav Hertz for research on the excitation and ionization of atoms by electron bombardment that verified the quantized nature of energy transfer.TIS In 1933, after the Nazis came to power, Franck, being a Jew, decided to leave his post in Germany and continued his research in the United States, first at Johns Hopkins University in Baltimore and then, after a year in Denmark, in Chicago. It was there that he became involved in the Manhattan Project during World War II; he was Director of the Chemistry Division of the Metallurgical Laboratory[5] at the University of Chicago. He was also the chairman of the Committee on Political and Social Problems regarding the atomic bomb; the committee consisted of himself and other scientists at the Met Lab, including Donald J. Hughes, J. J. Nickson, Eugene Rabinowitch, Glenn T. Seaborg, J. C. Stearns and Leó Szilárd. The committee is best known for the compilation of the Franck Report, finished on 11 June 1945, which recommended not to use the atomic bombs on the Japanese cities, based on the problems resulting from such a military application.Wik 1886 Jerome C. Hunsaker (26 Aug 1886; 10 Sep 1984)American aeronautical engineer who made major innovations in the design of aircraft and lighter-than-air ships, seaplanes, and carrier-based aircraft. His career had spanned the entire existence of the aerospace industry, from the very beginnings of aeronautics to exploration of the solar system. He received his master's degree in naval architecture from M.I.T. in 1912. At about the same time seeing a flight by Bleriot around Boston harbour attracted him to the fledgling field of aeronautics. By 1916, he became MIT's first Ph.D. in aeronautical engineering. He designed the NC (Navy Curtiss) flying boat with the capability of crossing the Atlantic. It was the largest aircraft in the world at the time, with four engines and a crew of six.TIS 1899 Wolfgang Krull (26 August 1899 - 12 April 1971) proved the Krull-Schmidt theorem for decomposing abelian groups and defined the Krull dimension of a ring.SAU 1918 Katherine Coleman Goble Johnson (August 26, 1918 in White Sulphur Springs, W. Va {pop 800)-) is an American physicist, space scientist, and mathematician who contributed to America's aeronautics and space programs with the early application of digital electronic computers at NASA. Known for accuracy in computerized celestial navigation, she calculated the trajectory for Project Mercury and the 1969 Apollo 11 flight to the Moon. From 1953 through 1958, Johnson worked as a "computer" for NACA (later to become NASA), doing analysis for topics such as gust alleviation for aircraft. She calculated the trajectory for the space flight of Alan Shepard, the first American in space, in 1959. She also calculated the launch window for his 1961 Mercury mission. She plotted backup navigational charts for astronauts in case of electronic failures. In 1962, when NASA used computers for the first time to calculate John Glenn's orbit around Earth, officials called on her to verify the computer's numbers (other versions say it was Glenn himself who requested she check the data). On November 24, 2015, President Barack Obama her with the Presidential Medal of Freedom and cited as a pioneering example of African American women in STEM Wik 1951 Edward Witten (26 Aug 1951, )American mathematical physicist who was awarded the Fields Medal in 1990 for his work in superstring theory. This is work in elementary particle theory, especially quantum field theory and string theory, and their mathematical implications. He elucidated the dynamics of strongly coupled supersymmetric field. The deep physical and mathematical consequences of the electric-magnetic duality thus exploited have broadened the scope of Mathematical Physics. He also received the Dirac Medal from the International Centre for Theoretical Physics (1985) and the Dannie Heineman Prize from the American Physical Society (1998), among others.TIS DEATHS 1349 Thomas Bradwardine, (c. 1290-26 August 1349) archbishop of Canterbury, died of the plague. This medieval mathematical physicist studied the notion of change. VFR Bradwardine was a noted mathematician as well as theologian and was known as 'the profound doctor'. He studied bodies in uniform motion and ratios of speed in the treatise De proportionibus velocitatum in motibus (1328). This work takes a rather strange line between supporting and criticising Aristotle's physics. Perhaps it is not really so strange because Aristotle views were so fundamental to learning at that time that perhaps all that one could expect of Bradwardine was the reinterpretation of Aristotle's views on bodies in motion and forces acting on them. It is likely that his intention was not to criticise Aristotle but rather to justify mathematically a reinterpretation of Aristotle's statements. He was also the first mathematician to study "star polygons". They were later investigated more thoroughly by Kepler SAU A star polygon {p/q}, with p,q positive integers, is a figure formed by connecting with straight lines every qth point out of p regularly spaced points lying on a circumference. The number q is called the density of the star polygon. Without loss of generality, take q less than p/2. Wolfram MathWorld 1572 Peter Ramus (1515 – 26 August 1572) was cruelly murdered, by hired assassins, during the St. Bartholomew’s Day Massacre. He was an early opponent of the teachings of Aristotle. VFR Peter Ramus was a French mathematician who wrote a whole series of textbooks on logic and rhetoric, grammar, mathematics, astronomy, and optics. His assassination was due to religious conflict. 1865 Johann Encke (23 Sep 1791, 26 Aug 1865) German astronomer who established the period of Encke's Comet at 3.3 years (shortest period of any known). TIS He also discovered the gap in the A-ring of Saturn and determent an accurate value of the solar parallax. The Royal Society mentioned the death to be 26 or 28 August 1865. NSEC 1929 Thomas John l'Anson Bromwich (8 Feb 1875 in Wolverhampton, England - 26 Aug 1929 in Northampton, England) He worked on infinite series, particularly during his time in Galway. In 1908 he published his only large treatise An introduction to the theory of infinite series which was based on lectures on analysis he had given at Galway. He also made useful contributions to quadratic and bilinear forms and many consider his algebraic work to be his finest. In a series of papers he put Heaviside's calculus on a rigorous basis treating the operators as contour integralsSAU G. H. Hardy described him as the “best pure mathematician among the applied mathematicians at Cambridge, and the best applied mathematician among the pure mathematicians.” VFR 1961 Howard Percy Robertson (27 Jan 1903 in Hoquiam, Washington, USA - 26 Aug 1961) made outstanding contributions to differential geometry, quantum theory, the theory of general relativity, and cosmology. He was interested in the foundations of physical theories, differential geometry, the theory of continuous groups, and group representations. He was particularly interested in the application of the latter three subjects to physical problems. His contributions to differential geometry came in papers such as: The absolute differential calculus of a non-Pythagorean non-Riemannian space (1924); Transformation of Einstein space (1925); Dynamical space-times which contain a conformal Euclidean 3-space (1927); Note on projective coordinates (1928); (with H Weyl) On a problem in the theory of groups arising in the foundations of differential geometry (1929); Hypertensors (1930); and Groups of motion in space admitting absolute parallelism (1932). SAU 1977 Robert Schatten (January 28, 1911 – August 26, 1977) His principal mathematical achievement was that of initiating the study of tensor products of Banach spaces. The concepts of crossnorm, associate norm, greatest crossnorm, least crossnorm, and uniform crossnorm, all either originated with him or at least first received careful study in his papers. He was mainly interested in the applications of this subject to linear transformations on Hilbert space. In this subject, the Schatten Classes perpetuate his name. Schatten had his own way of making abstract concepts memorable to his elementary classes. Who could forget what a sequence was after hearing Schatten describe a long corridor, stretching as far as the eye could see, with hooks regularly spaced on the wall and numbered 1, 2, 3, ...? "Then," Schatten would say, "I come along with a big bag of numbers over my shoulder, and hang one number on each hook." This of course was accompanied by suitable gestures for emphasis. SAU 1992 Daniel E. Gorenstein (January 1, 1923 – August 26, 1992) was an American mathematician. He earned his undergraduate and graduate degrees at Harvard University, where he earned his Ph.D. in 1950 under Oscar Zariski, introducing in his dissertation a duality principle for plane curves that motivated Grothendieck's introduction of Gorenstein rings. He was a major influence on the classification of finite simple groups. After teaching mathematics to military personnel at Harvard before earning his doctorate, Gorenstein held posts at Clark University and Northeastern University before he began teaching at Rutgers University in 1969, where he remained for the rest of his life. He was the founding director of DIMACS in 1989, and remained as its director until his death. Gorenstein was awarded many honors for his work on finite simple groups. He was recognised, in addition to his own research contributions such as work on signalizer functors, as a leader in directing the classification proof, the largest collaborative piece of pure mathematics ever attempted. In 1972 he was a Guggenheim Fellow and a Fulbright Scholar; in 1978 he gained membership in the National Academy of Sciences and the American Academy of Arts and Sciences, and in 1989 won the Steele Prize for mathematical exposition. Wik 1998 Frederick Reines (16 Mar 1918, 26 Aug 1998) American physicist who was awarded the 1995 Nobel Prize for Physics for his detection in 1956 of neutrinos, working with his colleague Clyde L. Cowan, Jr. The neutrino is a subatomic particle, a tiny lepton with little or no mass and a neutral charge which had been postulated by Wolfgang Pauli in the early 1930s but had previously remained undiscovered. (Reines shared the Nobel Prize with physicist Martin Lewis Perl, who discovered the tau lepton.)TIS Credits : CHM=Computer History Museum FFF=Kane, Famous First Facts NSEC= NASA Solar Eclipse Calendar RMAT= The Renaissance Mathematicus, Thony Christie SAU=St Andrews Univ. Math History TIA = Today in Astronomy TIS= Today in Science History VFR = V Frederick Rickey, USMA Wik = Wikipedia WM = Women of Mathematics, Grinstein & Campbell	2016-08-29 17:57:11	{"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": 0.37626978754997253, "perplexity": 3089.230808071409}, "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-2016-36/segments/1471982290497.47/warc/CC-MAIN-20160823195810-00166-ip-10-153-172-175.ec2.internal.warc.gz"}
https://gateoverflow.in/261537/baud-rate	# Baud Rate 111 views what is baud rate exactly? and what does it signifies? ## Related questions 1 623 views An analog signal has a bit rate of 8000 bps and a baud rate of 1000. Then analog signal has _____ signal elements and carry _____ data elements in each signal. (A) 256, 8 bits (B) 128, 4 bits (C) 256, 4 bits (D) 128, 8 bits	2020-09-19 06:02:55	{"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": 0.8535725474357605, "perplexity": 7379.258176153173}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-40/segments/1600400190270.10/warc/CC-MAIN-20200919044311-20200919074311-00405.warc.gz"}
https://www.gradesaver.com/textbooks/science/physics/college-physics-4th-edition/chapter-22-problems-page-863/17	## College Physics (4th Edition) (a) The wavelength of the EM waves is $5.0\times 10^6~m$ (b) This wavelength is 78% of the length of the Earth's radius. (c) These waves are radio waves. (a) We can find the wavelength of the EM waves: $\lambda = \frac{c}{f}$ $\lambda = \frac{3.0\times 10^8~m/s}{60.0~Hz}$ $\lambda = 5.0\times 10^6~m$ The wavelength of the EM waves is $5.0\times 10^6~m$ (b) We can find the ratio of this wavelength to the Earth's radius: $\frac{5.0\times 10^6~m}{6.38\times 10^6~m} = 0.78$ This wavelength is 78% of the length of the Earth's radius. (c) These waves are radio waves, which are the longest waves in the EM spectrum.	2022-08-10 08:04:08	{"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": 0.8331528902053833, "perplexity": 278.98689578139357}, "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/1659882571150.88/warc/CC-MAIN-20220810070501-20220810100501-00676.warc.gz"}
https://economics.stackexchange.com/questions/33121/who-is-the-first-one-to-equate-rational-with-complete-and-transitive-preferen	# Who is the first one to equate "rational" with "complete and transitive preference"? MWG taught that, suppose that the menu is finite, "rational" is the same as "complete and transitive". But it seems that it does not cite any sources. Who said this first? vNM said in 1944 that their EU is rational behavior, which is followed by computer scientists, statistician, and Finance literature. Why didn't MWG also follow this? MWG equate "rationalizable" with "existence of utility function" or "complete and transitive preference". To be clearer about my question, I am most interested in learning the first literature which argue that the "existence of utility function" or "complete and transitive preference" is rational. • I believe that was Ragnar Frisch, but I can't back up this claim. Nov 17 '20 at 15:35 • Wade Hands is a very good professor on the history of economic thought. He has a lot of work on modern microeconomic theory. I would recommend checking out some of his work, he will no doubt have something to say on it. Also, I know there is a philosopher Temkin, whose work is heavily focused on the history of transitivity. Nov 17 '20 at 15:58 • I am responding to the edit, I think this is problematic because transitivity and completeness are technical terms. People had some loose ideas of utility already in past and also some loose ideas about preference ordering and so forth. However, they would not call these completeness and transitivity axioms. If you are looking for background concept alone then that will be very difficult to prove given that pre 1900s economics was not very precise and rigorous – 1muflon1 Nov 17 '20 at 21:11 • @1muflon1 Maybe I have to rephrase (or create new) the question? Who was the first economists arguing that utility maximization is the core of rationality and economic behavior? Nov 17 '20 at 21:19 • @HighGPA okay that is clear. By the way maybe you should consider making it a separate question - I do not think that would be duplicate of this current question. – 1muflon1 Nov 17 '20 at 21:20 As pointed in the comments this was done by Ragnar Frisch. At least Barten and Böhm. (1982) as well as Johansen (1969) attribute these axioms to one of these two publications: • Frisch, Ragnar (1926). "Sur un problème d'économie pure [On a problem in pure economics]". Norsk Matematisk Forenings Skrifter, Oslo. 1 (16): 1–40 • Frisch,(1926). "Kvantitativ formulering av den teoretiske økonomikks lover [Quantitative formulation of the laws of economic theory]". Statsøkonomisk Tidsskrift. 40: 299–334. Also I think this question has a misconception. Von Neumann and Morgenstern (1944) indeed in their Theory of Games and Economic Behavior equate maximization of expected utility $$E(u)$$, with rational behavior. However, note that the $$E(u)$$ of vNM is already based on axiom of transitivity and completeness. The issue here is that vNM were not just deriving utility of rational person. They were deriving cardinal utility of rational person. The assumption of transitivity and completeness is only condition for preferences to be rational in general (see MWG pp 6.). • Many thanks! I read several old papers by Frisch. I agree that Frisch might be one of the first economists who use completeness and transitivity; I am not sure if Frisch argued that completeness and transitivity are rational or normative. However, if you mean that completeness and transitivity is equivalent to the existence of utility function on some choice sets, then these representations result were proved by Cantor and Birkhoff before 1900. Also note that the original goal of Frisch's axiomatic approach is to axiomatize measurable utility. Nov 17 '20 at 21:04 • @HighGPA well yes you are right, I mean by using the axioms I meant to say that Frisch was first to formalize their use, some loose ideas about this might have existed before – 1muflon1 Nov 17 '20 at 21:08 • @HighGPA that is good question, I would have to double check their book to be honest but if I remember correctly they argued that their EU is rational, not that any rational person must use their EU – 1muflon1 Nov 17 '20 at 21:22 • A preference can be rational (as in complete and transitive) without being representable by a utility function. For instance, here economics.stackexchange.com/a/40807/11590 Nov 17 '20 at 23:07 • That was @HighGPA but reading the comment again, I think did not pay attention to "on some choice sets." Nov 17 '20 at 23:33	2022-01-23 18:03:53	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 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": 0.6884045004844666, "perplexity": 1319.900584601041}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-05/segments/1642320304309.5/warc/CC-MAIN-20220123172206-20220123202206-00131.warc.gz"}
https://questioncove.com/updates/52470dc1e4b0fbde403bba3b	OpenStudy (anonymous): Find the derivative of... y=x^2sinx + 2cosx -2sinx The answer is y'= x^2cosx but idk how to get that. 4 years ago zepdrix (zepdrix): $\Large y\quad=\quad x^2\sin x+2 \cos x- 2 \sin x$ Taking the derivative of the last two terms is pretty straight forward right? We need to apply the product rule to the first term.$\Large \color{royalblue}{y'}\quad=\quad \color{royalblue}{(x^2)'}\sin x+x^2\color{royalblue}{(\sin x)'}+\color{royalblue}{(2\cos x)'}+\color{royalblue}{(-2\sin x)'}$ 4 years ago OpenStudy (anonymous): How did you get x2(sinx)′? 4 years ago zepdrix (zepdrix): $\Large (x^2 \sin x)' \quad=\quad (x^2)'\sin x+ x^2 (\sin x)'$Remember your product rule?$\Large (fg)' =(f)'g+f(g)'$ 4 years ago zepdrix (zepdrix): The blue parts are where you need to take a derivative. 4 years ago OpenStudy (anonymous): i got $2xsinx +x ^{2}cosx+2sinx-2cosx$ is that correct? 4 years ago zepdrix (zepdrix): The third term: (2cosx)' should give us -2sinx The rest looks good though! 4 years ago OpenStudy (anonymous): Idk what to do next now?:/ 4 years ago zepdrix (zepdrix): Hmm we're not going to get the answer you listed.... Are you sure there isn't more to this question? :d 4 years ago OpenStudy (anonymous): yes i am sure.. hmm maybe its like this y=$x ^{2}cosx-2sinx-(-sinx)$ 4 years ago	2017-11-22 18:02:52	{"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": 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": 0.5653339624404907, "perplexity": 8746.589162353948}, "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-2017-47/segments/1510934806620.63/warc/CC-MAIN-20171122175744-20171122195744-00197.warc.gz"}
https://lavelle.chem.ucla.edu/forum/viewtopic.php?f=16&t=65729&p=259912	## Textbook Problem 1B.15 Arieanne De Guzman 2J Posts: 55 Joined: Wed Sep 30, 2020 10:03 pm Been upvoted: 3 times ### Textbook Problem 1B.15 "1B.15 The velocity of an electron that is emitted from a metallic surface by a photon is 3.6 x10^3 km/s . (a) What is the wavelength of the ejected electron? (b) No electrons are emitted from the surface of the metal until the frequency of the radiation reaches 2.50 x10^16 Hz. How much energy is required to remove the electron from the metal surface? (c) What is the wavelength of the radiation that caused pho- toejection of the electron? (d) What kind of electromagnetic radiation was used?" I was able to get part a, but I couldn't seem to get the correct answers for the other parts. I don't think I am understanding the problem correctly. Can anyone explain the steps for b and c please? StephanieIb Posts: 100 Joined: Wed Sep 30, 2020 9:37 pm ### Re: Textbook Problem 1B.15 For b, you need to use hv=work function + 0(for KE). Then, multiply h by frequency to get your answer (1.66x10^-17 J). For C, use E= work function + 1/2mv^2. Add your work function (1.66x10^-17) and 1/2(9.109x10^-31kg)(3.6x10^6 m/sec)^2. Yous should get 2.25x10^-17 J as your E(pho). Then, using E=hV, divide energy(2.25x10^-17) by h to get the frequency. You should get 3.3957 x10^16 Hz. Then to get wavelength, use wavelength=C/V. You should get 8.8x10^-9m. Annie Tong 2G Posts: 51 Joined: Wed Sep 30, 2020 9:42 pm Been upvoted: 1 time ### Re: Textbook Problem 1B.15 b) Use the equation hv = work function + 0 (KE). Substitute in v = 2.50 x 10^16 Hz to get work function = 1.66 x 10^-17. c) Use the equation E = 1/2mv^2 + work function. Use the answer from part b) to substitute work function and v (velocity) = 3.6 x 10^6 m/s (make sure to convert km to m!) and m = electron's mass = 9.109 x 10^-31 kg. After you get E, use the equation wavelength = hc/E to find the wavelength. Hope this helped! Halle Villalobos 3E Posts: 90 Joined: Wed Sep 30, 2020 9:52 pm ### Re: Textbook Problem 1B.15 Hi! For part b, you would use $E=hv$ and plug in the given values to get $E=(6.62610^{34}J.s)(2.5010^{-16}s^{-1})=1.6610^{-17}J$. For part c, the photon must have enough energy to eject the electron and cause it to move at $3.610^3 km.s^{-1}$. To find the energy of the photon, add the value found in part a to its kinetic energy $(\frac{1}{2}mv^2)$, which will give you $2.25*10^{-17} J$. Remember to convert the velocity from km/s to m/s! To find the wavelength, use the equation $\lambda = \frac{hc}{E}$ to get 8.8nm. For part d, we know it is in the x-ray/gamma ray region based off the value found in part c. I hope this helps! Brandon Carris Posts: 49 Joined: Wed Sep 30, 2020 9:41 pm ### Re: Textbook Problem 1B.15 for part b use einstein's equation (e = hv). V is given and h is Heisenberg's constant.	2021-03-03 08:35:04	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 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": 0.6244668960571289, "perplexity": 1412.3028627989834}, "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/1614178366477.52/warc/CC-MAIN-20210303073439-20210303103439-00594.warc.gz"}
https://www.mathworks.com/help/matlab/ref/asind.html?nocookie=true	# asind Inverse sine in degrees ## Description example ````Y = asind(X)` returns the inverse sine (sin-1) of the elements of `X` in degrees. The function's domain and range include complex values. For real elements of `X` in the domain [-1,1], `asind` returns values in the range [-90,90]. For values of `X` outside this range, `asind` returns complex values.``` ## Examples collapse all ### Inverse Sine of Scalar Show that the inverse sine of 1 is exactly 90°. ```asind(1) ``` ```ans = 90``` ### Round-Trip Calculation for Complex Angles Show that the inverse sine, followed by sine, returns the original values of `X`. ```sind(asind([2 3])) ``` ```ans = 2.0000 3.0000``` ### Graph of Inverse Sine Function Plot the inverse sine function over the domain . ```x = -1:.01:1; plot(x,asind(x)) grid on ``` ## Input Arguments collapse all ### `X` — Sine of anglescalar value \| vector \| matrix \| N-D array Sine of angle, specified as a real-valued or complex-valued scalar, vector, matrix, or N-D array. The `asind` operation is element-wise when `X` is nonscalar. Data Types: `single` \| `double` Complex Number Support: Yes ## Output Arguments collapse all ### `Y` — Angle in degreesscalar value \| vector \| matrix \| N-D array Angle in degrees, returned as a real-valued or complex-valued scalar, vector, matrix, or N-D array of the same size as `X`.	2015-07-04 00:08:18	{"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": 0.9535439610481262, "perplexity": 9844.469915931493}, "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-2015-27/segments/1435375096290.39/warc/CC-MAIN-20150627031816-00184-ip-10-179-60-89.ec2.internal.warc.gz"}
http://mathhelpforum.com/math-topics/873-bloody-indices-print.html	# bloody indices • September 11th 2005, 04:09 AM thebizzle bloody indices i got this question 5^y=1 and i have to solve the equation, i know the that y=0 i jus dont no how to explain it pls help • September 11th 2005, 08:39 AM hoeltgman Try this: $5^y = 1 \Leftrightarrow y \cdot \log_5 (5) = \log_5 (1)$ $\text{In that case:} \log_5 (5) = 1\; \text{and} \log_5 (1) = 0$ • September 11th 2005, 09:45 AM ticbol Here is one way. 5^y = 1 Take the log of both sides, y*log(5) = log(1) Since log(1) = 0, then, y = 0 / log(5) y = 0 • September 12th 2005, 11:44 AM thebizzle thank u for ur replies but i am in yr 12 and have not started on logarithms yet • September 12th 2005, 11:59 AM hemza ouch Try this: you know 5/5 = 1 and x^a / x^b = x^(a-b) so 5 / 5 = 1 gives 5^1 / 5^1 = 1 and then, 5^(1-1) = 5^0 so y=0.	2016-08-24 23:23:44	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 2, "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": 0.578041672706604, "perplexity": 5532.770129961105}, "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-2016-36/segments/1471982292675.36/warc/CC-MAIN-20160823195812-00156-ip-10-153-172-175.ec2.internal.warc.gz"}
https://physics.stackexchange.com/questions/75593/does-resistance-in-second-circuit-changes-in-transformed-circuit	# Does resistance in second circuit changes in transformed circuit? Let $V_1$, $I_1$, $R_1$ and $V_2$, $I_2$, $R_2$ be voltages, currents, resistance in first, second circuit. And we assume $R_1=R_2$, $I_1\neq I_2$. The conservation of electrical power $P=V_1I_1=V_2I_2$ holds in the transformer circuits. Hence $I_1^2R_1=I_2^2R_2$, $R_2=(I_1^2/I_2^2)R_1$ which leads to a contradiction. What am I missing? What you're missing is a source that's driving the whole thing. As you wrote it, there's no contradiction: $I_1=I_2=0$. With a source included, it's no longer true that $I_1^2R_1 = I_2^2 R_2$. If $R_1=R_2$, then also $I_1=I_2$ (assuming no losses, and so on). Your simple argument is a "proof by contradiction" of this simple assertion.	2019-07-24 00:31:46	{"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": 0.8537466526031494, "perplexity": 497.2465005828711}, "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/1563195530246.91/warc/CC-MAIN-20190723235815-20190724021815-00118.warc.gz"}
https://itectec.com/ubuntu/ubuntu-simplest-process-to-get-imagemagick-7-with-png-support-on-ubuntu/	# Ubuntu – Simplest process to get ImageMagick 7 with PNG support on Ubuntu compilingimagemagicklibpngpng I've tried to find a simple explanation for several hours but I just can't seem to find anything useful. I'm primarily a Windows programmer with some experience with Linux-based OSes. For some reason doing apt install imagemagick only gives me a really old version (pre-2012) and there's a change in the later versions that I need, which means I need to build from source. Compiling IM 7 on Ubuntu 18.04 is simple enough: Download tar.gz, extract, ./configure, make and make install. However it seems that PNG support is not included by default (why??). I've tried doing ./configure --with-png but that didn't achieve anything (I see --with-png=yes no, which presumably means "yes, you've asked for PNG support but no, I haven't given it to you"). I've seen many forum posts and SE questions about this, but everyone asking seems to have some prior knowledge which I am clearly missing and the questions appear to be about some later step in the process. So, what do I actually need to do to get PNG support? (And as some bonus questions: Why is there no documentation for this? Why does it not include PNG support out of the box? Why are there no prebuilt binaries for Ubuntu?) Related question: Imagemagick still exists after apt remove? • I am not sure what error message you were getting, but I was getting convert: no decode delegate for this image format JPG' @ error/constitute.c/ReadImage/562 when working with jpegs with a fresh ImageMagick install from source. To resolve it: 1. uncomment deb-src http://us.archive.ubuntu.com/ubuntu/ bionic main restricted in /etc/apt/sources.list 2. install dependencies sudo apt update sudo apt build-dep imagemagick 1. Reinstall ImageMagick ./configure make sudo make install sudo ldconfig /usr/local/lib `	2021-06-19 04:02:36	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4991227686405182, "perplexity": 3030.246151500854}, "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/1623487643380.40/warc/CC-MAIN-20210619020602-20210619050602-00135.warc.gz"}
https://www.nature.com/articles/s41467-021-24977-x	Skip to main content Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript. # The importance of species interactions in eco-evolutionary community dynamics under climate change ## Abstract Eco-evolutionary dynamics are essential in shaping the biological response of communities to ongoing climate change. Here we develop a spatially explicit eco-evolutionary framework which features more detailed species interactions, integrating evolution and dispersal. We include species interactions within and between trophic levels, and additionally, we incorporate the feature that species’ interspecific competition might change due to increasing temperatures and affect the impact of climate change on ecological communities. Our modeling framework captures previously reported ecological responses to climate change, and also reveals two key results. First, interactions between trophic levels as well as temperature-dependent competition within a trophic level mitigate the negative impact of climate change on biodiversity, emphasizing the importance of understanding biotic interactions in shaping climate change impact. Second, our trait-based perspective reveals a strong positive relationship between the within-community variation in preferred temperatures and the capacity to respond to climate change. Temperature-dependent competition consistently results both in higher trait variation and more responsive communities to altered climatic conditions. Our study demonstrates the importance of species interactions in an eco-evolutionary setting, further expanding our knowledge of the interplay between ecological and evolutionary processes. ## Introduction Changing climatic conditions influence species’ ecology, such as demography, biotic interactions, and movement, as well as species’ evolutionary rates. Despite the acknowledgment of the highly important interplay between ecological and evolutionary processes for determining species distributions and survival under altered climatic conditions1,2,3,4, few studies account for their combined effects5. The interplay between these processes has been partly addressed in previous work, showing unexpected results: inclusion of evolution potentially results in increased extinction rates when combined with dispersal6, and high dispersal rates do not reduce extinctions since colonization often comes at expense of other species7. Moreover, species interactions can both alleviate and aggravate the impact of climate change on species8, and interact with other eco-evolutionary processes. For example, species interactions can affect a species’ evolutionary response to altered environmental conditions9,10; and dispersal may release a species from negative interactions through migration11 or increase them through invasion12. These very promising eco-evolutionary studies, striving to include a variety of relevant biological mechanisms, commonly depict species interactions in a simplified manner. For example, Norberg et al.7, Lasky13, and Thompson and Fronhofer6 take all of the aforementioned aspects into consideration, and their models are important stepping-stones along the way to map out the relevance of species interactions under dispersal, evolution, and climate change. However, they only consider competitive interactions, and even those under more7 or less6,13 restrictive assumptions: Norberg et al.7, for instance, set all intra- and interspecific interaction strengths to be equal, and Lasky13 uses diffuse competition, whereby species share one common intra- and another common interspecific competition coefficient. To further develop the field of eco-evolutionary studies of species’ response to climatic change, here we present a spatially explicit eco-evolutionary framework centered around a more detailed view of species interactions, interplaying with species’ abilities to adapt to and disperse across local environments. We focus on two extensions. First, we include interactions both within and between trophic levels. Second, we consider the feature that species’ interspecific competition might change due to increasing temperatures, and affect the impact of climate change on ecological communities. Such temperature-dependent competition between species has usually not been considered in an eco-evolutionary setting14,15,16. Temperature-dependent competition is centered around the idea that each patch in the larger spatial landscape consists of multiple microhabitats, each with a somewhat higher or lower local temperature than the patch average. If the temperature optima of two competing species are similar, they will compete for the same microhabitats and thus experience strong competition. Similarly, competition will decrease if two species within a patch have different temperature optima. A temperature optimum mismatching the local mean temperature will result in a decreased local growth rate, but might still be favorable if it results in decreased interspecific competition. Dispersal between and competitive interactions within local environments over time transfer to regional and global changes of ecological communities, and it is repeatedly shown that the effects of climate change differ between geographical regions17. As we here consider the globe’s full latitudinal range from the polar regions to the equator, we can use our framework to evaluate how effects of local interactions and climate change vary depending on the region considered. We explore the effect of refined species interactions on (1) local trends (within each patch), including local species diversity; (2) regional trends (division of patches into polar, temperate, and tropical areas), including species’ ranges and turnover; and (3) global trends, including global losses and the general community-wide capacity to respond to climatic change. We show that influence from a second trophic level and, in particular, temperature-dependent competition affect both species distributions and global trends, giving higher levels of coexistence, lower levels of species turnover, and fewer global extinctions. Also, the interplay between ecological (e.g., dispersal and species interactions) and evolutionary (e.g., adaptation to new conditions) processes along a spatial gradient do significantly affect species’ responses to altered climatic conditions in unexpected ways. For example, when species are able to both disperse and evolve fast, temperature-dependent competition results in more global losses than when the capacity to disperse and evolve is low. Furthermore, we demonstrate that community-wide dispersion of species’ temperature optima is a strong predictor of a community’s capacity to respond to climate change, which has implications for future management guidelines. ## Results ### Modeling framework We consider S species distributed in L distinct habitat patches. The patches form a linear latitudinal chain going around the globe, with dispersal between adjacent patches (Fig. 1). The state variables are species’ local densities and local temperature optima (the temperature at which species achieve maximum intrinsic population growth). This temperature optimum is a trait whose evolution is governed by quantitative genetics18,19,20,21,22: each species, in every patch, has a normally distributed temperature optimum with a given mean and variance. The variance is the sum of a genetic and an environmental contribution. The genetic component is given via the infinitesimal model23,24, whereby a very large number of loci each contribute a small additive effect to the trait. This has two consequences. First, a single round of random mating restores the normal shape of the trait distribution, even if it is distorted by selection or migration. Second, the phenotypic variance is unchanged by these processes, with only the mean being affected25 (we apply a reduction in genetic variance at very low population densities to prevent such species from evolving rapidly; see the Supplementary Information [SI], Section 3.4). Consequently, despite selection and the mixing of phenotypes from neighboring patches, each species retains a normally-shaped phenotypic distribution with the same phenotypic variance across all patches—but the mean temperature optimum may evolve locally and can therefore differ across patches (Fig. 1). Species in our setup may either be resources or consumers. Their local dynamics are governed by the following processes. First, within each patch, we allow for migration to and from adjacent patches (changing both local population densities and also local adaptedness, due to the mixing of immigrant individuals with local ones). Second, each species’ intrinsic rate of increase is temperature-dependent, influenced by how well their temperature optima match local temperatures (Fig. 2a). For consumers, metabolic loss and mortality always result in negative intrinsic growth, which must be compensated by sufficient consumption to maintain their populations. Third, there is a local competition between resource species, which can be thought of as exploitative competition for a set of shared substitutable lower-level resources26. Consumers, when present, compete only indirectly via their shared resource species. Fourth, each consumer has feeding links to five of the resource species (pending their presence in patches where the consumer is also present), which are randomly determined but always include the one resource which matches the consumer’s initial mean temperature optimum. Feeding rates follow a Holling type II functional response. Consumers experience growth from consumption, and resource species experience loss due to being consumed. Following the previous methodology, we derive our equations in the weak selection limit22 (see also the Discussion). We have multiple selection forces acting on the different components of our model. Species respond to local climate (frequency-independent directional selection, unless a species is at the local environmental optimum), to consumers and resources (frequency-dependent selection), and competitors (also frequency-dependent selection, possibly complicated by the temperature-dependence of the competition coefficients mediating frequency dependence). These different modes of selection do not depend on the parameterization of evolution and dispersal, which instead are used to adjust the relative importance of these processes. Communities are initiated with 50 species per trophic level, subdividing the latitudinal gradient into 50 distinct patches going from pole to equator (results are qualitatively unchanged by increasing either the number of species or the number of patches; SI, Section 5.95.10). We assume that climate is symmetric around the equator; thus, only the pole-to-equator region needs to be modeled explicitly (SI, Section 3.5). The temperature increase is based on predictions from the IPCC intermediate emission scenario27 and corresponds to predictions for the north pole to the equator. The modeled temperature increase is represented by annual averages and the increase is thus smooth. Species are initially equally spaced, and adapted to the centers of their ranges. We then integrate the model for 6500 years, with three main phases: (1) an establishment period from t = −4000 to t = 0 years, during which local temperatures are constant; (2) climate change, between t = 0 and t = 300 years, during which local temperatures increase in a latitude-specific way (Fig. 2b); and (3) the post-climate change period from t = 300 to t = 2500 years, where temperatures remain constant again at their elevated values. To explore the influence and importance of dispersal, evolution, and interspecific interactions, we considered the fully factorial combination of high and low average dispersal rates, high and low average available genetic variance (determining the speed and extent of species’ evolutionary responses), and four different ecological models. These were: (1) the baseline model with a single trophic level and constant, patch- and temperature-independent competition between species; (2) two trophic levels and constant competition; (3) single trophic level with temperature-dependent competition (where resource species compete more if they have similar temperature optima); and (4) two trophic levels as well as temperature-dependent competition. Trophic interactions can strongly influence diversity in a community, either by apparent competition28 or by acting as extra regulating agents boosting prey coexistence29. Temperature-dependent competition means that the strength of interaction between two phenotypes decreases with an increasing difference in their temperature optima. Importantly, while differences in temperature adaptation may influence competition, they do not influence trophic interactions. The combination of high and low genetic variance and dispersal rates, and four model setups, gives a total of 2 × 2 × 4 = 16 scenarios. For each of them, some parameters (competition coefficients, tradeoff parameters, genetic variances, dispersal rates, consumer attack rates, and handling times; SI, Section 6) were randomly drawn from pre-specified distributions. We, therefore, obtained 100 replicates for each of these 16 scenarios. While replicates differed in the precise identity of the species which survived or went extinct, they varied little in the overall patterns they produced. We use the results from these numerical experiments to explore patterns of (1) local species diversity (alpha diversity), (2) regional trends, including species range breadths and turnover (beta diversity), (3) global (gamma) diversity, and global changes in community composition induced by climate change. In addition, we also calculated the interspecific community-wide trait lag (the difference between the community’s density-weighted mean temperature optima and the current temperature) as a function of the community-wide weighted trait dispersion (centralized variance in species’ density-weighted mean temperature optima; see Methods). The response capacity is the ability of the biotic community to close this trait lag over time30 (SI, Section 4). Integrating trait lag through time31 gives an overall measure of different communities’ ability to cope with changing climate over this time period; furthermore, this measure is comparable across communities. The integrated trait lag summarizes, in a single functional metric, the performance and adaptability of a community over space and time. The reason it is related to performance is that species that on average live more often under temperatures closer to their optima (creating lower trait lags) will perform better than species whose temperature optima are far off from local conditions in space and/or time. Thus, a lower trait lag (higher response capacity) may also be related to other ecosystem functions, such as better carbon uptake which in turn has the potential to feedback to global temperatures32. ### Overview of results We use our framework to explore the effect of species interactions on local, regional, and global biodiversity patterns, under various degrees of dispersal and available genetic variance. For simplicity, we focus on the dynamics of the resource species, which are present in all scenarios. Results for consumers, when present, are in the SI (Section 5.8). First, we display a snapshot of species’ movement across the landscape with time; before, during, and after climate change. Then we proceed with analyzing local patterns, followed by regional trends, and finally, global trends. Snapshots from the time series of species’ range distributions reveal useful information about species’ movement and coexistence (Fig. 3). Regardless of model setup and parameterization, there is a northward shift in species’ ranges: tropical species expand into temperate regions and temperate species into polar regions. This is accompanied by a visible decline in the number of species globally, with the northernmost species affected most. The models do differ in the predicted degree of range overlap: trophic interactions and temperature-dependent competition both lead to broadly overlapping ranges, enhancing local coexistence (the overlap in spatial distribution is particularly pronounced with high available genetic variance). Without these interactions, species ranges overlap to a substantially lower degree, diminishing local diversity. Below we investigate whether these patterns, observed for a single realization of the dynamics for each scenario, play out more generally as well. ### Local trends Trophic interactions and temperature-dependent competition indeed result in elevated local species richness levels (Fig. 4). The fostering of local coexistence by trophic interactions and temperature-dependent competition is in line with general ecological expectations. Predation pressure can enhance diversity by providing additional mechanisms of density regulation and thus prey coexistence through predator partitioning28,29. In turn, temperature-dependent competition means species can reduce interspecific competition by evolving locally suboptimal mean temperature optima22, compared with the baseline model’s fixed competition coefficients. Hence with temperature-dependent competition, the advantages of being sufficiently different from other locally present species can outweigh the disadvantages of being somewhat maladapted to the local temperatures. If competition is not temperature-dependent, interspecific competition is at a fixed level independent of the temperature optima of each species. An important question is how local diversity is affected when the two processes act simultaneously. In fact, any synergy between their effects is very weak, and is even slightly negative when both the available genetic variance and dispersal abilities are high (Fig. 4, top row). ### Regional trends We see a strong tendency for poleward movement of species when looking at the altered distributions of species over the spatial landscape (Fig. 3). Indeed, looking at the effects of climate change on the fraction of patches occupied by species over the landscape reveals that initially cold-adapted species lose suitable habitat during climate change, and even afterwards (Fig. 5). For the northernmost species, this always eventuate to the point where all habitat is lost, resulting in their extinction. This pattern holds universally in every model setup and parameterization. Only initially warm-adapted species can expand their ranges, and even they only do so under highly restrictive conditions, requiring both good dispersal ability and available genetic variance as well as consumer pressure (Fig. 5, top row, second and third panel). One can also look at larger regional changes in species richness, dividing the landscape into three equal parts: the top third (polar region), the middle third (temperate region), and the bottom third (tropical region). Region-wise exploration of changes in species richness (Fig. 6) shows that the species richness of the polar region is highly volatile. It often experiences the greatest losses; however, with high dispersal ability and temperature-dependent competition, the regional richness can remain substantial and even increase compared to its starting level (Fig. 6, first and third rows, last two columns). Of course, change in regional species richness is a result of species dispersing to new patches and regions as well as of local extinctions. Since the initially most cold-adapted species lose their habitat and go extinct, altered regional species richness is connected to having altered community compositions along the spatial gradient. All regions experience turnover in species composition (SI, Section 5.1), but in general, the polar region experiences the largest turnover, where the final communities are at least 50% and sometimes more than 80% dissimilar to the community state right before the onset of climate change—a result in agreement with previous studies as well7,33. ### Global trends Hence, the identity of the species undergoing global extinction is not random, but strongly biased towards initially cold-adapted species. On a global scale, these extinctions cause decreased richness, and the model predicts large global biodiversity losses for all scenarios (Fig. 6). These continue during the post-climate change period with stable temperatures, indicating a substantial extinction debt which has been previously demonstrated34. Temperature-dependent competition reduces the number of global losses compared to the baseline and trophic models. A further elucidating global pattern is revealed by analyzing the relationship between the time-integrated temperature trait lag and community-wide trait dispersion (Fig. 7). There is an overall negative correlation between the two, but more importantly, within each scenario (unique combination of model and parameterization) a negative relationship is evident. Furthermore, the slopes are very similar: the main difference between scenarios is in their mean trait lag and trait dispersion values (note that the panels do not share axis value ranges). The negative trend reveals the positive effect of more varied temperature tolerance strategies among the species on the community’s ability to respond to climate change. This is analogous to Fisher’s fundamental theorem35, stating that the speed of the evolution of fitness r is proportional to its variance: dr/dt ~ var(r). More concretely, this relationship is also predicted by trait-driver theory, a mathematical framework that focuses explicitly on linking spatiotemporal variation in environmental drivers to the resulting trait distributions30. Communities generated by different models reveal differences in the magnitude of this relationship: trait dispersion is much higher in models with temperature-dependent competition (essentially, niche differentiation with respect to temperature), resulting in lower trait lag. The temperature-dependent competition also separates communities based on their spatial dispersal ability, with faster dispersal corresponding to greater trait dispersion and thus lower trait lag. Interestingly, trophic interactions tend to erode the relationship between trait lag and trait dispersion slightly (R2 values are lower in communities with trophic interactions, both with and without temperature-dependent competition). We have additionally explored the relationship between species richness and trait dispersion, finding a positive relationship between the two (SI, Section 4.1). ## Discussion ### General modeling considerations This work introduced a modeling framework combining dispersal, evolutionary dynamics, and ecological interactions in a way that is tractable, easy to implement, fast to execute on a computer, and can handle ecological interactions of realistic complexity without simultaneously breaking other aspects of the approach. Individual-based models6, for instance, do in principle allow one to include arbitrary levels of complexity, but tend to be computationally expensive. Other models yield detailed projections of individual species and their genetic structure but ignore species interactions altogether36. An intermediate approach is based on quantitative genetics, which takes species interactions into account and yields a description of species’ genetic structure that is sufficiently simplified to be tractable. Earlier models in this spirit7,13,37 were built on coupled partial differential equations. While the theory behind such models is highly elegant, coupled nonlinear partial differential equations are notoriously difficult to implement in a way that is numerically stable, yields accurate results, and does not require unacceptably long run-times—notably, naive discretization schemes often do not work well. Unfortunately, despite persistent warnings about these problems38, such naive solution schemes still prevail in the literature. We circumvented this problem by building, from first principles, a different framework for spatial eco-evolutionary dynamics. Within a single patch, it is based on a quantitative genetic recursion model19,22. Spatial locations are discretized from the outset, therefore the approach is built on ordinary differential equations alone. As a consequence, it executes fast even with substantial model complexity: on an ordinary desktop computer, a single run for 6500 years with both trophic interactions and temperature-dependent competition, with 50 species on both trophic levels and 50 habitat patches (for 100 × 50 × 2 = 10,000 state variables; the factor of 2 is because both the density and trait mean of each species may change) finished in around 3 min. While this is fast, emerging methods such as Universal Differential Equations, which combine traditional integration with machine learning, hold the promise of a many-fold increase in the speed of computation in the near future39. Incorporation of further complexity into our model is straightforward: complex food webs and spatial structure, or further trait variables under selection (e.g., having both temperature optimum and body size evolve, the latter dictating the type of prey a species can consume40), can all be implemented. An important future extension would be to use an improved climate model with annual temperature fluctuations, instead of our smooth increase based on annual means. Annual extreme weather events are expected to become more common41. Under such circumstances, Allee effects might mean more frequent extinctions than predicted from our current model, because species hit by such events might not be able to recover. On the other hand, annual temperature cycles could induce storage effects or relative nonlinearities42,43, which in combination with our already incorporated spatial variation could promote coexistence through joint spatial and temporal variation44. We derive our equations using the idealizations of additive quantitative genetics and the weak selection limit22. Both have their drawbacks. The first assumes that all genetic variation is additive—genes and alleles at different loci do not interact. This ignores the fact that genes are part of a complex regulatory network in which interactions such as dominance, epistasis, and pleiotropy are bound to emerge. While purely additive quantitative genetics can be a good starting point for understanding the effects of selection45,46, it remains an approximation. In turn, the weak selection limit assumes that selection is not so strong as to prevent one from writing otherwise discrete-time dynamics in the continuous-time limit (SI, Section 1). In fact, from a practical point of view, this limit can actually allow for quite a strong selection. For this, however, one must assume very large population sizes so genetic and ecological drift do not overpower selection. The rule of thumb is that effective population size times the selection differential must exceed one47. This is obviously true if populations are so large that they can be modeled as continuous variables, but in reality, they are finite, and the weak selection assumption could potentially yield effects which we neglect. For example, a new immigrant at a habitat patch will naturally have a low population size and might not be able to establish even if it has higher fitness. Similarly, a slightly deleterious type will never spread in our approximation, while it might in reality, as known from the nearly neutral theory48. Although Akashi et al.48 show that weak selection can often explain similar patterns of genome variation as the nearly neutral theory, a rigorous incorporation of the consequences of population finiteness in our model is still in the future. There is one other important thing our model currently cannot do. Since trait distributions are assumed to be normal with constant variance, a species cannot split into two daughter lineages in response to disruptive selection, as this would require the trait distribution to become gradually more and more bimodal. As such, our model ignores speciation, which may turn out to be an important process in regions that become species-impoverished following climate change. In sexual populations, speciation can occur when the trait is a magic trait, which jointly drives competitive interactions but also assortative mating between similar phenotypes49,50. Here we strictly assume that temperature tolerance is not involved in mate choice. This, however, is an oversimplification because magic traits may in fact be very common in nature51. And magic traits may not even be necessary, since pseudo-magic traits (with two tightly linked loci, one under divergent selection and the other acting as a mating cue) can also promote speciation52. There are also non-ecological (e.g., mutation-order) speciation mechanisms that could play a role53. New species emerging by speciation could possibly mitigate the decrease of species we currently observe. But our model, in its current form, cannot incorporate these mechanisms. ### The role of species interactions Using our framework, we demonstrate that biotic factors such as trophic interactions and temperature-dependent competition are important in shaping species’ eco-evolutionary response to climate change—in fact, they can be as influential as the ability of species to adapt to new local climates or to disperse to new habitats. With trophic interactions and temperature-dependent competition, species have broader ranges and coexist to a higher degree, in comparison to the baseline model without the aforementioned dynamics. In addition, temperature-dependent competition significantly reduces global species loss. With constant competition as in our baseline scenario, competitive exclusions occur to a higher extent, a result in line with van Eldijk et al.10, showing that evolutionary rescue of one species leads to a competitive exclusion and extinction of another species. The importance of biotic interactions for shaping species’ response to climate change is well-known8,10,15,16. Our work complements these studies by further demonstrating the significance of biotic interactions in an eco-evolutionary setting as well. The mechanisms behind this are predator-mediated coexistence28,29 (in the case of trophic interactions), and reduced interspecific competition with increasing trait distance22. Note that this last mechanism is not guaranteed to promote diversity, since the level of difference in mean temperature optima required for significant reductions in competition might mean that species have local growth rates that are too suboptimal for persistence. Thus, the ability of this mechanism to boost diversity depends on whether species are able to tolerate suboptimal climates sufficiently to avoid local competition. There are interaction types we do not consider in this version of our framework. Similar to our modeling of competition, one could have temperature-dependent mutualism; i.e., the strength of the mutualistic benefit between two phenotypes is a function of the distance of their temperature optima. This process could potentially bind mutualistic species to a common fate54 and thus accelerate the effects of climate change. Indeed, Northfield, Ives55 showed that with non-conflicting evolution of mutualistic interactions, the effects of climate change are enhanced, and the dynamics are destabilized. Our model is extensible to incorporate other types of interactions and structures (e.g., modular or nested ones, either of trophic or mutualistic interactions). These are important future problems to address in the context of eco-evolutionary responses to climate change. ### The role of dispersal and genetic variance Besides the importance of biotic interactions affecting species’ persistence and distribution under climate change, we also show that their dispersal ability and available genetic variance (i.e., capacity to respond to selective pressures swiftly) influence their responses. When local conditions change and temperatures increase, species become increasingly maladapted at their initial locations and pre-adapted to temperatures at higher latitudes, driving a northward movement. Dispersal is therefore suggested as a mechanism that provides spatial insurance to species56,57, mitigating the negative impacts of climate change. However, a northward movement of initially warm-adapted species comes at the expense of the species located in the coldest regions which cannot disperse further33, a consequence of dispersal that has been shown in the previous studies7. One might think that combining good dispersal ability with large genetic variance should temper this problem by allowing the northernmost species to adapt locally, and thus alleviate the negative impacts of increased temperatures better than each of these processes on their own. This expectation is also consistent with recent projections based on empirical data58. However, the projected extinctions, considering both dispersal and species’ ability to adapt, have been obtained without explicitly considering species interactions58. We show that large genetic variance combined with good dispersal ability result in a global biodiversity loss similar to when both dispersal ability and evolutionary rate are low. The reason, again, has to do with species interactions: the ability of individual species to disperse and adapt to new local conditions is of no use if they are prevented by other species from reaching the new locations. Similarly, cold-adapted species may be able to sustain in their current location with large genetic variance, but get outcompeted by the arrival of better adapted migrating species. The negative interaction between high dispersal and fast adaptation under climate change has also been demonstrated by Thompson and Fronhofer6. However, in our case, we show that temperature-dependent competition reduces some of the negative impacts by allowing more local coexistence, albeit at the cost of reduced local growth rates. ### Trait lag and trait dispersion We show that models in which communities are able to maintain high biodiversity after altered climatic conditions will in general also have high trait diversity and low trait lag. This particularly occurs when species have temperature-dependent competition, allowing species to exploit different microhabitats within the same patch. High trait diversity results in high response capacity of the community to climate change and thus a lower overall trait lag. Species richness and trait dispersion can potentially be statistically correlated, as often found in biodiversity and ecosystem functioning studies59—although in our simulations this positive relationship holds only for the aggregated data as a whole, not necessarily within each individual model parameterization (SI, Section 4.1). The trait in our study—the temperature optimum of each species—can also be regarded as a functional trait explaining how species share a resource. In our case, this is expressed as species’ exploration of habitats with suitable temperatures. High functional trait diversity has then been shown to be important for sustaining multiple ecosystem functions simultaneously, since coexisting species can exploit different resources and microhabitats60,61. It is encouraging for the general predictability of biotic climate impact models that the resulting trait dispersion in temperature-related traits strongly correlates with the ability of the community to cope with climate change. This can justify putting the focus on processes that can sustain local community-wide trait dispersion, providing an argument for general biodiversity-enhancing measures such as preserving habitat heterogeneity, maintaining populations of keystone species, and for constructing dispersal corridors. The focus on trait dispersion has an important and complementary implication for traditional conservation strategies of more biodiversity is better. It simplifies the identification of strategies that underpin the maintenance of trait variation of a particular trait and thus a particular environmental driver that is of concern. For example, ensuring connectivity to habitats with higher mean temperature or temperature variation can promote an influx of species or genotypes that can cope with an increasing trend in temperature by maintaining the local trait variation of temperature optima. Local management strategies can target microhabitats that have south-facing sheltered microclimates to promote islands of environmental conditions that reflect possible future scenarios. ### Conclusions Biological communities are affected by many factors, ecological as well as evolutionary, which influence their response to climate change. Our framework demonstrates the importance of including relevant biological processes for predicting large-scale consequences of climate change on global and local biodiversity. Realistic mechanisms such as species interactions over multiple trophic levels and temperature-dependent competition, as well as particular combinations of dispersal and available genetic variance, can alleviate some of the negative impacts of climate change, showing potential ways for ecological communities to adjust to altered climatic conditions. Despite this, the negative impact of climate change on ecological communities is severe, with numerous global extinctions and effects that are manifested long after the climate has again stabilized. ## Methods We consider a chain of L evenly spaced patches along a latitudinal gradient, where patches 1 and L correspond to the north pole and equator, respectively. The temperature Tk(t) in patch k at time t is given by $${T}^{k}(t)=\underbrace{\left({T}_{\min }+({T}_{\max }-{T}_{\min })\frac{k}{L}\right)}_{{{{{{\rm{initial}}}}}}\,{{{{{\rm{temperature}}}}}}\,{{{{{\rm{profile}}}}}}}+\underbrace{\left({C}_{\max }+({C}_{\min }-{C}_{\max })\frac{k}{L}\right)}_{{{{{{\rm{total}}}}}}\,{{{{{\rm{temperature}}}}}}\,{{{{{\rm{change}}}}}}}\underbrace{Q(t/{t}_{E})}_{ \% \,{{{{{\rm{change}}}}}}\,{{{{{\rm{at}}}}}}\,{{{{{\rm{time}}}}}}\,t}.$$ (1) $${T}_{\min }$$ and $${T}_{\max }$$ are the initial polar and equatorial temperatures; $${C}_{\max }$$ and $${C}_{\min }$$ are the corresponding temperature increases after tE = 300 years, based on the IPCC intermediate emission scenario27. The period from t = −4000 to t = 0 is an establishment time preceding climate change. Q(τ) describes the sigmoidal temperature increase in time: Q(τ) equals 0 for τ < 0, 1 for τ > 1, and 10τ3 − 15τ4 + 6τ5 otherwise. Figure 2b depicts the resulting temperature change profile. Combining quantitative genetics with dispersal across the L patches, we track the population density and mean temperature optimum of S species. Let $${N}_{i}^{k}$$ be the density and $${\mu }_{i}^{k}$$ the mean temperature optimum of species i in patch k (subscripts denote species; superscripts patches). The governing equations then read $$\frac{{{{{{\rm{d}}}}}}{N}_{i}^{k}}{{{{{{\rm{d}}}}}}t}=\underbrace{{N}_{i}^{k}\int {r}_{i}^{k}(z){p}_{i}^{k}(z){{{{{\rm{d}}}}}}z}_{{{{{{\rm{local}}}}}}\,{{{{{\rm{population}}}}}}\,{{{{{\rm{growth}}}}}}}+\underbrace{\mathop{\sum }\limits_{l=1}^{L}{m}_{i}^{kl}{N}_{i}^{l}}_{{{{{{\rm{immigration}}}}}}}-\underbrace{\mathop{\sum }\limits_{l=1}^{L}{m}_{i}^{lk}{N}_{i}^{k}}_{{{{{{\rm{emigration}}}}}}},$$ (2) $$\frac{{{{{{\rm{d}}}}}}{\mu }_{i}^{k}}{{{{{{\rm{d}}}}}}t}=\underbrace{{h}_{i}^{2}\int (z-{\mu }_{i}^{k}){r}_{i}^{k}(z){p}_{i}^{k}(z){{{{{\rm{d}}}}}}z}_{{{{{{\rm{local}}}}}}\,{{{{{\rm{selection}}}}}}}+\underbrace{{h}_{i}^{2}\mathop{\sum }\limits_{l=1}^{L}{m}_{i}^{kl}\frac{{N}_{i}^{l}}{{N}_{i}^{k}}({\mu }_{i}^{l}-{\mu }_{i}^{k})}_{{{{{{\rm{trait}}}}}}\,{{{{{\rm{change}}}}}}\,{{{{{\rm{from}}}}}}\,{{{{{\rm{immigration}}}}}}}$$ (3) (SI, Section 1), where t is time, $${r}_{i}^{k}(z)$$ the per capita growth rate of species i’s phenotype z in patch k, $${p}_{i}^{k}(z)$$ species i’s temperature optimum distribution in patch k (which is normal with patch-dependent mean $${\mu }_{i}^{k}$$ and patch-independent variance $${\sigma }_{i}^{2}$$), $${h}_{i}^{2}$$ the heritability of species i’s temperature optimum, and $${m}_{i}^{kl}$$ the migration rate of species i from patch l to k. The per capita growth rates $${r}_{i}^{k}(z)$$ read $${r}_{i}^{k}(z)={r}_{0,i}^{k}(z)-\mathop{\sum }\limits_{j=1}^{S}{N}_{j}^{k}\int {a}_{ij}^{k}(z,z^{\prime} ){p}_{j}^{k}(z^{\prime} )\ \,{{\mbox{d}}}\,z^{\prime} +\mathop{\sum }\limits_{j=1}^{S}{\epsilon }_{i}{F}_{ij}^{k}-\mathop{\sum }\limits_{j=1}^{S}{N}_{j}^{k}{F}_{ji}^{k}/{N}_{i}^{k}.$$ (4) Here $${r}_{0,i}^{k}(z)=\left(\frac{{\varrho }_{i}}{{b}_{w}-{a}_{w}{\mu }_{i}^{k}}\right)\exp \left(-\frac{{({T}^{k}-z)}^{2}}{2{({b}_{w}-{a}_{w}{\mu }_{i}^{k})}^{2}}\right)-{\kappa }_{i}$$ (5) is the intrinsic growth of species i’s phenotype z in patch k. The constants ϱi, bw, and aw modulate a tradeoff between maximum growth and tolerance range62,63 (Fig. 2a), κi is a mortality rate, and Tk is the current local temperature in patch k. In turn, $${a}_{ij}^{k}(z,z^{\prime} )$$ is the competition coefficient between species i’s phenotype z and species j’s phenotype $$z^{\prime}$$ in patch k. We either assume constant, patch- and phenotype-independent coefficients aij, or ones which decline with increasing trait differentiation according to $${a}_{ij}^{k}(z,z^{\prime} )=\exp \left(-\frac{{(z-z^{\prime} )}^{2}}{{\eta }^{2}}\right)$$ (6) (temperature-dependent competition), where η is the competition width. The parameter ϵi in Eq. (4) is species i’s resource conversion efficiency, and $${F}_{ij}^{k}$$ is the feeding rate of species i on j in patch k: $${F}_{ij}^{k}=\frac{{q}_{i}{W}_{ij}{\omega }_{ij}{N}_{j}^{k}}{1+{q}_{i}{H}_{i}\mathop{\sum }\nolimits_{s = 1}^{S}{W}_{is}{\omega }_{is}{N}_{s}^{k}},$$ (7) where qi is species i’s attack rate, Wij is the adjacency matrix of the feeding network (Wij = 1 if i eats j and 0 otherwise), ωij is the proportion of effort of i on j, and Hi is species i’s handling time. When adding a second trophic level, the number of species on the new level is equal to that at the lower level, and each consumer is linked with five resource species in a bipartite feeding network (SI, Section 3.3). We numerically integrated 100 replicates for each of 16 scenarios, made up of the fully factorial combinations of: • The average dispersal rate between adjacent patches, which was either high (100 m/yr) or low (0.01 m/yr). • The mean genetic variance per species, also either high (10−1C2) or low (10−3C2). • The model setup, which was one of the following: 1. 1. One trophic level and constant competition coefficients, $${a}_{ij}^{k}(z,z^{\prime} )={a}_{ij}$$. 2. 2. Two trophic levels and constant competition coefficients. 3. 3. One trophic level and competition coefficients given by Eq. (6). 4. 4. Two trophic levels and competition coefficients given by Eq. (6). For each replicate, all other parameters are assigned based on Section 6 in the SI. Numerical integration of the system starts at t0 = − 4000 years, with initial conditions $${\mu }_{i}^{k}({t}_{0})=({T}_{\max }-{T}_{\min })\frac{i}{S}+{T}_{\min }$$ (8) and $${N}_{i}^{k}({t}_{0})=\exp \left(-\frac{{({\mu }_{i}^{k}({t}_{0})-{T}^{k}(0))}^{2}}{8}\right)$$ (9) (SI, Section 3.7), and terminates at t = 2500 years. The community-average trait dispersion $${{{{{{{{\mathcal{V}}}}}}}}}^{k}$$ of the local community in patch k is the density-weighted variance of species’ mean temperature optima: $${{{{{{{{\mathcal{V}}}}}}}}}^{k}=\mathop{\sum }\limits_{i=1}^{S}{n}_{i}^{k}{\left({\mu }_{i}^{k}-{\bar{\mu }}^{k}\right)}^{2},$$ (10) where $${n}_{i}^{k}={N}_{i}^{k}/\mathop{\sum }\nolimits_{j = 1}^{S}{N}_{j}^{k}$$ is the relative density of species i in patch k, and $${\bar{\mu }}^{k}=\mathop{\sum }\nolimits_{i = 1}^{S}{n}_{i}^{k}{\mu }_{i}^{k}$$ is the community-weighted average of species’ temperature optima in patch k. 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Functional trait diversity maximizes ecosystem multifunctionality. Nat. Ecol. Evol. 1, 132 (2017). 61. Hooper, D. U. et al. Effects of biodiversity on ecosystem functioning: a consensus of current knowledge. Ecol. Monographs 75, 3–35 (2005). 62. Deutsch, C. A. et al. Impacts of climate warming on terrestrial ectotherms across latitude. Proc. Natl Acad. Sci. USA 105, 6668–6672 (2008). 63. Thomas, M. K., Kremer, C. T., Klausmeier, C. A. & Litchman, E. A global pattern of thermal adaptation in marine phytoplankton. Science 338, 1085–1088 (2012). 64. Åkesson, A. et al. The importance of species interactions in eco-evolutionary community dynamics under climate change. https://zenodo.org/record/5060300 (2021). Download references ## Acknowledgements We thank Priyanga Amarasekare and Peter Münger for discussions. This research was funded by the Swedish Research Council (grant FORMAS 2015-01262 to A.E., and grant VR 2017-05245 to G.B.). ## Funding Open access funding provided by Linköping University ## Author information Authors ### Contributions A.Å., B.E., and A.C. conceived of the initial study. G.B. wrote the supplement and developed the temperature-tolerance concept. J.N. contributed the trait-lag concept. A.Å. and G.B. performed data simulations and analysis. A.Å, G.B., and A.E. wrote the paper. All authors made significant edits to the final version of the manuscript. ### Corresponding author Correspondence to György Barabás. ## Ethics declarations ### Competing interests The authors declare no competing interests. ## Additional information Peer review information Nature Communications thanks Carlos Melian and the other, anonymous, reviewers for their contribution to the peer review of this work. Peer Review reports are available. Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. ## Rights and permissions Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/. Reprints and Permissions ## About this article ### Cite this article Åkesson, A., Curtsdotter, A., Eklöf, A. et al. The importance of species interactions in eco-evolutionary community dynamics under climate change. Nat Commun 12, 4759 (2021). https://doi.org/10.1038/s41467-021-24977-x Download citation • Received: • Accepted: • Published: • DOI: https://doi.org/10.1038/s41467-021-24977-x ## Comments By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate. ## Search ### Quick links Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily. Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing	2022-08-10 00:35:24	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.601395845413208, "perplexity": 4049.6283755906406}, "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-2022-33/segments/1659882571090.80/warc/CC-MAIN-20220809215803-20220810005803-00160.warc.gz"}
https://www.ademcetinkaya.com/2023/01/gpvtsxv-greenpower-motor-company-inc.html	Outlook: Greenpower Motor Company Inc. is assigned short-term Ba1 & long-term Ba1 estimated rating. Dominant Strategy : Sell Time series to forecast n: 20 Jan 2023 for (n+1 year) Methodology : Modular Neural Network (Emotional Trigger/Responses Analysis) Abstract Greenpower Motor Company Inc. prediction model is evaluated with Modular Neural Network (Emotional Trigger/Responses Analysis) and Wilcoxon Sign-Rank Test1,2,3,4 and it is concluded that the GPV:TSXV stock is predictable in the short/long term. According to price forecasts for (n+1 year) period, the dominant strategy among neural network is: Sell Key Points 1. Is it better to buy and sell or hold? 2. Prediction Modeling 3. What is the best way to predict stock prices? GPV:TSXV Target Price Prediction Modeling Methodology We consider Greenpower Motor Company Inc. Decision Process with Modular Neural Network (Emotional Trigger/Responses Analysis) where A is the set of discrete actions of GPV:TSXV stock holders, F is the set of discrete states, P : S × F × S → R is the transition probability distribution, R : S × F → R is the reaction function, and γ ∈ [0, 1] is a move factor for expectation.1,2,3,4 F(Wilcoxon Sign-Rank Test)5,6,7= $\begin{array}{cccc}{p}_{a1}& {p}_{a2}& \dots & {p}_{1n}\\ & ⋮\\ {p}_{j1}& {p}_{j2}& \dots & {p}_{jn}\\ & ⋮\\ {p}_{k1}& {p}_{k2}& \dots & {p}_{kn}\\ & ⋮\\ {p}_{n1}& {p}_{n2}& \dots & {p}_{nn}\end{array}$ X R(Modular Neural Network (Emotional Trigger/Responses Analysis)) X S(n):→ (n+1 year) $∑ i = 1 n r i$ n:Time series to forecast p:Price signals of GPV:TSXV stock j:Nash equilibria (Neural Network) k:Dominated move a:Best response for target price For further technical information as per how our model work we invite you to visit the article below: How do AC Investment Research machine learning (predictive) algorithms actually work? GPV:TSXV Stock Forecast (Buy or Sell) for (n+1 year) Sample Set: Neural Network Stock/Index: GPV:TSXV Greenpower Motor Company Inc. Time series to forecast n: 20 Jan 2023 for (n+1 year) According to price forecasts for (n+1 year) period, the dominant strategy among neural network is: Sell X axis: Likelihood% (The higher the percentage value, the more likely the event will occur.) Y axis: Potential Impact% (The higher the percentage value, the more likely the price will deviate.) Z axis (Grey to Black): Technical Analysis% IFRS Reconciliation Adjustments for Greenpower Motor Company Inc. 1. When a group of items that constitute a net position is designated as a hedged item, an entity shall designate the overall group of items that includes the items that can make up the net position. An entity is not permitted to designate a non-specific abstract amount of a net position. For example, an entity has a group of firm sale commitments in nine months' time for FC100 and a group of firm purchase commitments in 18 months' time for FC120. The entity cannot designate an abstract amount of a net position up to FC20. Instead, it must designate a gross amount of purchases and a gross amount of sales that together give rise to the hedged net position. An entity shall designate gross positions that give rise to the net position so that the entity is able to comply with the requirements for the accounting for qualifying hedging relationships. 2. Historical information is an important anchor or base from which to measure expected credit losses. However, an entity shall adjust historical data, such as credit loss experience, on the basis of current observable data to reflect the effects of the current conditions and its forecasts of future conditions that did not affect the period on which the historical data is based, and to remove the effects of the conditions in the historical period that are not relevant to the future contractual cash flows. In some cases, the best reasonable and supportable information could be the unadjusted historical information, depending on the nature of the historical information and when it was calculated, compared to circumstances at the reporting date and the characteristics of the financial instrument being considered. Estimates of changes in expected credit losses should reflect, and be directionally consistent with, changes in related observable data from period to period 3. When an entity separates the foreign currency basis spread from a financial instrument and excludes it from the designation of that financial instrument as the hedging instrument (see paragraph 6.2.4(b)), the application guidance in paragraphs B6.5.34–B6.5.38 applies to the foreign currency basis spread in the same manner as it is applied to the forward element of a forward contract. 4. An entity can rebut this presumption. However, it can do so only when it has reasonable and supportable information available that demonstrates that even if contractual payments become more than 30 days past due, this does not represent a significant increase in the credit risk of a financial instrument. For example when non-payment was an administrative oversight, instead of resulting from financial difficulty of the borrower, or the entity has access to historical evidence that demonstrates that there is no correlation between significant increases in the risk of a default occurring and financial assets on which payments are more than 30 days past due, but that evidence does identify such a correlation when payments are more than 60 days past due. International Financial Reporting Standards (IFRS) adjustment process involves reviewing the company's financial statements and identifying any differences between the company's current accounting practices and the requirements of the IFRS. If there are any such differences, neural network makes adjustments to financial statements to bring them into compliance with the IFRS. Conclusions Greenpower Motor Company Inc. is assigned short-term Ba1 & long-term Ba1 estimated rating. Greenpower Motor Company Inc. prediction model is evaluated with Modular Neural Network (Emotional Trigger/Responses Analysis) and Wilcoxon Sign-Rank Test1,2,3,4 and it is concluded that the GPV:TSXV stock is predictable in the short/long term. According to price forecasts for (n+1 year) period, the dominant strategy among neural network is: Sell GPV:TSXV Greenpower Motor Company Inc. Financial Analysis* Rating Short-Term Long-Term Senior OutlookBa1Ba1 Income StatementB1B3 Balance SheetCBa1 Leverage RatiosB1Ba2 Cash FlowBaa2Caa2 Rates of Return and ProfitabilityBaa2Ba3 Financial analysis is the process of evaluating a company's financial performance and position by neural network. It involves reviewing the company's financial statements, including the balance sheet, income statement, and cash flow statement, as well as other financial reports and documents. How does neural network examine financial reports and understand financial state of the company? Prediction Confidence Score Trust metric by Neural Network: 90 out of 100 with 641 signals. References 1. Çetinkaya, A., Zhang, Y.Z., Hao, Y.M. and Ma, X.Y., MO Stock Price Prediction. AC Investment Research Journal, 101(3). 2. Scholkopf B, Smola AJ. 2001. Learning with Kernels: Support Vector Machines, Regularization, Optimization, and Beyond. Cambridge, MA: MIT Press 3. T. Shardlow and A. Stuart. A perturbation theory for ergodic Markov chains and application to numerical approximations. SIAM journal on numerical analysis, 37(4):1120–1137, 2000 4. Matzkin RL. 2007. Nonparametric identification. In Handbook of Econometrics, Vol. 6B, ed. J Heckman, E Learner, pp. 5307–68. Amsterdam: Elsevier 5. Allen, P. G. (1994), "Economic forecasting in agriculture," International Journal of Forecasting, 10, 81–135. 6. Çetinkaya, A., Zhang, Y.Z., Hao, Y.M. and Ma, X.Y., Trading Signals (WTS Stock Forecast). AC Investment Research Journal, 101(3). 7. Chernozhukov V, Chetverikov D, Demirer M, Duflo E, Hansen C, et al. 2018a. Double/debiased machine learning for treatment and structural parameters. Econom. J. 21:C1–68 Frequently Asked QuestionsQ: What is the prediction methodology for GPV:TSXV stock? A: GPV:TSXV stock prediction methodology: We evaluate the prediction models Modular Neural Network (Emotional Trigger/Responses Analysis) and Wilcoxon Sign-Rank Test Q: Is GPV:TSXV stock a buy or sell? A: The dominant strategy among neural network is to Sell GPV:TSXV Stock. Q: Is Greenpower Motor Company Inc. stock a good investment? A: The consensus rating for Greenpower Motor Company Inc. is Sell and is assigned short-term Ba1 & long-term Ba1 estimated rating. Q: What is the consensus rating of GPV:TSXV stock? A: The consensus rating for GPV:TSXV is Sell. Q: What is the prediction period for GPV:TSXV stock? A: The prediction period for GPV:TSXV is (n+1 year)	2023-03-25 22:52:19	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 2, "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": 0.28184396028518677, "perplexity": 6093.239618342087}, "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-2023-14/segments/1679296945376.29/warc/CC-MAIN-20230325222822-20230326012822-00564.warc.gz"}
https://www.semanticscholar.org/paper/Probable-convexity-and-its-application-to-Topic-Than-Ho/fd2d523aca58e7d9fd11130c8cbfee4ad919219d	• Corpus ID: 17798922 # Probable convexity and its application to Correlated Topic Models @article{Than2013ProbableCA, title={Probable convexity and its application to Correlated Topic Models}, author={Khoat Than and Tu Bao Ho}, journal={ArXiv}, year={2013}, volume={abs/1312.4527} } • Published 16 December 2013 • Computer Science • ArXiv Non-convex optimization problems often arise from probabilistic modeling, such as estimation of posterior distributions. Non-convexity makes the problems intractable, and poses various obstacles for us to design efficient algorithms. In this work, we attack non-convexity by first introducing the concept of \emph{probable convexity} for analyzing convexity of real functions in practice. We then use the new concept to analyze an inference problem in the \emph{Correlated Topic Model} (CTM) and… ## References SHOWING 1-10 OF 26 REFERENCES • Computer Science NIPS • 2011 This work studies the problem of finding the maximum a posteriori (MAP) assignment of topics to words, where the document's topic distribution is integrated out, and shows that, when the effective number of topics per document is small, exact inference takes polynomial time, and that this problem is NP-hard. • Computer Science • 2007 The correlated topic model (CTM) is developed, where the topic proportions exhibit correlation via the logistic normal distribution, and it is demonstrated its use as an exploratory tool of large document collections. • Computer Science SDM • 2009 A new extension of the CTM method to enable modeling with multi-field topics in a global graphical structure, and a mean-field variational algorithm to allow joint learning of multinomial topic models from discrete data and Gaussianstyle topic models for real-valued data are proposed. • Computer Science ECML/PKDD • 2012 This paper shows that FSTM can perform substantially better than various existing topic models by different performance measures, and provides a principled way to directly trade off sparsity of solutions against inference quality and running time. • Computer Science ICML • 2012 This work presents efficient online learning algorithms that eschew projections in favor of much more efficient linear optimization steps using the Frank-Wolfe technique, and obtains a range of regret bounds for online convex optimization, with better bounds for specific cases such as stochastic online smooth conveX optimization. • Computer Science IEEE Transactions on Automatic Control • 2006 A comprehensive introduction to the subject of convex optimization shows in detail how such problems can be solved numerically with great efficiency. • Computer Science J. Mach. Learn. Res. • 2010 An alternative to the Dirichlet prior is suggested, a family of logistic normal distributions that permits soft parameter tying within grammars and across Grammars for text in different languages, and empirical gains in a novel learning setting using bilingual, non-parallel data are shown. • Computer Science EMNLP • 2011 A novel statistical topic model based on an automated evaluation metric based on this metric that significantly improves topic quality in a large-scale document collection from the National Institutes of Health (NIH). • Mathematics, Computer Science Theory Comput. • 2008 This work derandomizes an efficient construction by Alon and Roichman of an expanding Cayley graph of logarithmic degree on any (possibly non-abelian) group and applies these pessimistic estimators to the problem of solving semidefinite covering problems, giving a deterministic algorithm for the quantum hypergraph cover problem of Ahslwede and Winter. • Computer Science 2010 IEEE Computer Society Conference on Computer Vision and Pattern Recognition • 2010 The proposed association model shows improved performance over correspondence LDA as measured by caption perplexity, and a novel latent variable regression approach to capture correlations between image or video features and annotation texts.	2023-02-07 18:26:51	{"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": 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": 0.43831491470336914, "perplexity": 2443.6721401372265}, "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/1674764500628.77/warc/CC-MAIN-20230207170138-20230207200138-00636.warc.gz"}
https://swmath.org/?term=sketching	• # leanTAP • Referenced in 41 articles [sw09985] • calculus to the modal logic K and sketches a proof of the completeness of this ... elegant as leanTAP. Following that, he sketches how similar results can be obtained... • # EasyCrypt • Referenced in 33 articles [sw09738] • security proofs of cryptographic systems from proof sketches-compact, formal representations of the essence ... sequence of games and hints. Proof sketches are checked automatically using off-the-shelf... • # KamiWaAi • Referenced in 13 articles [sw01954] • KamiWaAi -- interactive 3D sketching with Java based on $Cl(4,1)$ conformal model of Euclidean ... This paper introduces the new interactive Java sketching software KamiWaAi, recently developed at the University... • # Sketch2Photo • Referenced in 13 articles [sw14453] • realistic picture from a simple freehand sketch annotated with text labels. The composed picture ... stitching several photographs in agreement with the sketch and text labels; these are found...	2022-08-15 22:05:32	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.17035245895385742, "perplexity": 5677.740940075071}, "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/1659882572212.96/warc/CC-MAIN-20220815205848-20220815235848-00679.warc.gz"}
https://abcpy.readthedocs.io/en/latest/installation.html	# 1. Installation¶ ABCpy requires Python3 and is not compatible with Python2. The simplest way to install ABCpy is via PyPI and we recommended to use this method. ## Installation from PyPI¶ Simplest way to install pip3 install abcpy This also works in a virtual environment. ## Installation from Source¶ If you prefer to work on the source, clone the repository git clone https://github.com/eth-cscs/abcpy.git Make sure all requirements are installed cd abcpy pip3 install -r requirements.txt To create a package and install it, do make package pip3 install wheel pip3 install build/dist/abcpy-0.6.3-py3-none-any.whl wheel is required to install in this way. Note that ABCpy requires Python3. ## Requirements¶ Basic requirements are listed in requirements.txt in the repository (click here). That also includes packages required for MPI parallelization there, which is very often used. However, we also provide support for parallelization with Apache Spark (see below). • torch is needed in order to use neural networks to learn summary statistics. It can be installed by running: pip install -r requirements/neural_networks_requirements.txt • In order to use Apache Spark for parallelization, findspark and pyspark are required; install them by: pip install -r requirements/backend-spark.txt ## Troubleshooting mpi4py installation¶ mpi4py requires a working MPI implementation to be installed; check the official docs for more info. On Ubuntu, that can be installed with: sudo apt-get install libopenmpi-dev Even when that is present, running pip install mpi4py can sometimes lead to errors. In fact, as specified in the official docs, the mpicc compiler needs to be in the search path. If that is not the case, a workaround is: env MPICC=/path/to/mpicc pip install mpi4py In some cases, even the above may not be enough. A possibility is using conda (conda install mpi4py) which usually handles package dependencies better than pip. Alternatively, you can try by installing directly mpi4py from the package manager; in Ubuntu, you can do: sudo apt install python3-mpi4py which however does not work with virtual environments.	2022-08-07 15:26:47	{"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": 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": 0.24835391342639923, "perplexity": 7473.032163313729}, "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-2022-33/segments/1659882570651.49/warc/CC-MAIN-20220807150925-20220807180925-00767.warc.gz"}
http://quant.stackexchange.com/questions?page=5&sort=votes&pagesize=15	# All Questions 835 views ### How does one analyze diversification if stock prices follow a Cauchy distribution? How does diversification actually lead to less variance in a portfolio? I'm looking for a formal reason why this is the case. There are a number of explanations I have been able to find, but they make ... 3k views ### How does left tail risk differ from right tail risk? How does left tail risk differ from right tail risk? In what context would an analyst use these metrics? 659 views ### Copula models and the distribution of the sum of random variables without Monte Carlo There is a vast literature on copula modelling. Using copulas I can describe the joint law of two (and more) random variables $X$ and $Y$, i.e. $F_{X,Y}(x,y)$. Very often in risk management (credit ... 711 views ### How to forecast expected volatility from high-frequency equity panel data? 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The models I have in ... 442 views It is known (see for example Joshi-Chan "Fast and Accureate Long Stepping Simulation of the Heston SV Model" available at SSRN) that for a CIR process defined as : $$dY_t= \kappa(\theta -Y_t)dt+ ... 8answers 5k views ### Is “eoddata” a good data source? Not sure if this is a relevant question for site, but I am looking to move to www.eoddata.com as my data source. If anyone has used it, can you tell me how the data quality is ? I am currently ... 7answers 757 views ### Keeping a track record honest I want to start a blog/newsletter and maintain a track record of trades I recommend. I have a never-expiring demo account for this purpose. How do I keep this track record "honest"? Three months ... 5answers 3k views ### What exactly is meant by “microstructure noise”? I see that term tossed around a lot, in articles relating to HFT, and ultra high frequency data. It says at higher frequencies, smaller intervals, microstructure noise is very dominant. 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I am looking to evaluate the hypothetical advantage one trading system has over another in terms of the possible returns given their latency. Irene Aldridge wrote a piece (How Profitable Are ... 587 views ### Is it ever possible that---because of illiquidity---exercising an out-of-the-money option is better than directly buying the stock? Is there a case, where due to illiquidity, exercising out-of-the-money options could be better than directly buying the stock? When a stock is too illiquid, there are some costs because of this ... 1k views ### What books should any quantitative portfolio manager or risk manager have as reference? [closed] I'm interested to know what are the critical reference texts you rely on for portfolio or risk management? I mean those texts that you come back to because they are chock full of insight and know-how. ... 2k views ### How to combine multiple trading algorithms? Is it possible to combine different algorithms so as to improve trading performance? In particular, I have read that social media sentiment tracking, digital signal processing and neural networks all ... 3k views ### Is there an all Java options-pricing library (preferably open source) besides jquantlib? I am looking for an all-java implementation of black scholes, preferably open source. I found jquantlib and quantlib (C++). Any other recommendations? The jquantlib site seems to be down. I'd prefer ... 873 views ### Rate interpolation in Libor Market Model Libor Market Model (LMM) models the interest rate market by simulating a set of simply compounded, non-overlapping Libor rates which reset and mature on predefined dates. How do I obtain from them a ... 2k views ### What is a “coherent” risk measure? What is a coherent risk measure, and why do we care? Can you give a simple example of a coherent risk measure as opposed to a non-coherent one, and the problems that a coherent measure addresses in ...	2014-04-23 11:15:43	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6934194564819336, "perplexity": 2001.669034239601}, "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-2014-15/segments/1398223202457.0/warc/CC-MAIN-20140423032002-00157-ip-10-147-4-33.ec2.internal.warc.gz"}
https://www.physicsforums.com/threads/question-about-electric-circuit.873055/	## Homework Statement Please give me a clue, I don't understand, how to find the magnitude of $I_{ab}$? ## The Attempt at a Solution Related Introductory Physics Homework Help News on Phys.org cnh1995 Homework Helper Gold Member What have you tried so far? Are you familiar with KCL? CWatters Homework Helper Gold Member Have you worked out the voltage on a/b? What have you tried so far? Are you familiar with KCL? I am stuck. What is KCL? Is it Kirchoff's Current Law? Have you worked out the voltage on a/b? How? CWatters Homework Helper Gold Member I am stuck. What is KCL? Is it Kirchoff's Current Law? Yes. Have you worked out the voltage on a/b? How? "a" and "b" are at the same voltage because they are connected together. To work out that voltage you can simplify the circuit and use the potential divider method. There are other ways. Once you have that voltage you can calculate the currents through all the resistors. Then apply KCL at either a or b. or you can just wade in and apply KCL from the outset.	2020-04-10 18:29:07	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5403279066085815, "perplexity": 1511.1784708913572}, "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/1585370511408.40/warc/CC-MAIN-20200410173109-20200410203609-00165.warc.gz"}
https://socratic.org/questions/how-do-you-write-the-equation-of-the-hyperbola-given-foci-0-7-0-7-and-vertices-0	# How do you write the equation of the hyperbola given Foci: (0,-7),(0,7) and vertices (0,-3), (0,3)? Dec 13, 2016 The equation is ${y}^{2} / 9 - {x}^{2} / 40 = 1$ #### Explanation: The foci are $F = \left(0 , 7\right)$ and $F ' = \left(0 , - 7\right)$ The vertices are $A = \left(0 , 3\right)$ and $A ' = \left(0 , - 3\right)$ So, the center is $C = \left(0 , 0\right)$ So, $a = 3$ $c = 7$ and $b = \sqrt{{c}^{2} - {a}^{2}} = \sqrt{49 - 9} = \sqrt{40}$ Therefore, the equation of the hyperbola is ${y}^{2} / {a}^{2} - {x}^{2} / {b}^{2} = 1$ ${y}^{2} / 9 - {x}^{2} / 40 = 1$ graph{(y^2/9-x^2/40-1)=0 [-11.25, 11.25, -5.625, 5.625]}	2021-10-19 11:39:38	{"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": 0.8425272703170776, "perplexity": 2640.0880006648713}, "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/1634323585265.67/warc/CC-MAIN-20211019105138-20211019135138-00316.warc.gz"}
https://www.semanticscholar.org/paper/Phases-Of-N%3D2-Theories-In-1%2B1-Dimensions-With-Herbst-Hori/5387a90d3c51d940aa77bd815cc6ca5b787d098a	Corpus ID: 117052654 # Phases Of N=2 Theories In 1+1 Dimensions With Boundary @article{Herbst2008PhasesON, title={Phases Of N=2 Theories In 1+1 Dimensions With Boundary}, author={Manfred Herbst and Kentaro Hori and David C. Page}, journal={arXiv: High Energy Physics - Theory}, year={2008} } • Published 2008 • Physics • arXiv: High Energy Physics - Theory We study B-type D-branes in linear sigma models with Abelian gauge groups. The most important finding is the grade restriction rule. It classifies representations of the gauge group on the Chan-Paton factor, which can be used to define a family of D-branes over a region of the Kahler moduli space that connects special points of different character. As an application, we find a precise, transparent relation between D-branes in various geometric phases as well as free orbifold and Landau-Ginzburg… Expand 167 Citations B-Type D-Branes in Toric Calabi-Yau Varieties • Physics • 2008 We define D-branes in linear sigma models corresponding to toric Calabi–Yau varieties. This enables us to study the transportation of D-branes along general paths in the Kahler moduli space. The mostExpand Orientifolds and D-branes in N=2 gauged linear sigma models • Mathematics, Physics • 2008 We study parity symmetries and boundary conditions in the framework of gauged linear sigma models. This allows us to investigate the Kaehler moduli dependence of the physics of D-branes as well asExpand Moduli Webs and Superpotentials for Five-Branes • Physics • 2009 We investigate the one-parameter Calabi-Yau models and identify families of D5-branes which are associated to lines embedded in these manifolds. The moduli spaces are given by sets of Riemann curves,Expand On The Structure Of The Chan-Paton Factors For D-Branes In Type II Orientifolds • Physics • 2010 We determine the structure of the Chan-Paton factors of the open strings ending on space filling D-branes in Type II orientifolds. Through the analysis, we obtain a rule concerning possibleExpand Aspects of non-abelian gauge dynamics in two-dimensional Script N = (2,2) theories • Physics • 2007 We study various aspects of = (2,2) supersymmetric non-Abelian gauge theories in two dimensions, with applications to string vacua. We compute the Witten index of SU(k) SQCD with 0$>N>0 flavors withExpand D-brane categories for orientifolds—the Landau-Ginzburg case • Physics • 2008 We construct and classify categories of D-branes in orientifolds based on Landau-Ginzburg models and their orbifolds. Consistency of the worldsheet parity action on the matrix factorizations playsExpand Decompactifications and massless D-branes in hybrid models • Physics • 2009 A method of determining the mass spectrum of BPS D-branes in any phase limit of a gauged linear sigma model is introduced. A ring associated to monodromy is defined and one considers K-theory to be aExpand Topological D-Branes and Commutative Algebra We show that questions concerning the topological B-model on a Calabi–Yau manifold in the Landau–Ginzburg phase can be rephrased in the language of commutative algebra. This yields interesting andExpand D-brane moduli spaces and superpotentials in a two-parameter model • Physics • 2012 A bstractWe study D2-branes on the K3-fibration$ \mathbb{P}_{\left( {11222} \right)}^4 \$ [8] using matrix factorizations at the Landau-Ginzburg point and analyze their moduli space andExpand Linear sigma models with strongly coupled phases — one parameter models • Physics, Mathematics • 2013 A bstractWe systematically construct a class of two-dimensional (2, 2) supersymmetric gauged linear sigma models with phases in which a continuous subgroup of the gauge group is totally unbroken. WeExpand #### References SHOWING 1-10 OF 102 REFERENCES Linear sigma models for open strings • Physics • 2001 We formulate and study a class of massive N = 2 supersymmetric gauge field theories coupled to boundary degrees of freedom on the strip. For some values of the parameters, the infrared limits ofExpand Boundary RG Flows of N=2 Minimal Models We study boundary renormalization group flows of N=2 minimal models using Landau-Ginzburg description of B-type. A simple algebraic relation of matrices is relevant. We determine the pattern of theExpand Phases of N = 2 theories in two dimensions By looking at phase transitions which occur as parameters are varied in supersymmetric gauge theories, a natural relation is found between sigma models based on Calabi-Yau hypersurfaces in weightedExpand D-branes, categories and N=1 supersymmetry We show that boundary conditions in topological open string theory on Calabi–Yau (CY) manifolds are objects in the derived category of coherent sheaves, as foreseen in the homological mirror symmetryExpand On D-branes from gauged linear sigma models • Physics • 2001 Abstract We study both A-type and B-type D-branes in the gauged linear sigma model by considering worldsheets with boundary. The boundary conditions on the matter and vector multiplet fields areExpand D-branes on Stringy Calabi-Yau Manifolds • Physics • 2000 We argue that D-branes corresponding to rational B boundary states in a Gepner model can be understood as fractional branes in the Landau-Ginzburg orbifold phase of the linear sigma modelExpand Orientifolds and mirror symmetry • Physics • 2004 We study parity symmetries and crosscap states in classes ofN =2 supersymmetric quantum eld theories in 1 + 1 dimensions, including non-linear sigma models, gauged WZW models, Landau-Ginzburg models,Expand D-Branes And Mirror Symmetry • Physics • 2000 We study (2,2) supersymmetric field theories on two-dimensional worldsheet with boundaries. We determine D-branes (boundary conditions and boundary interactions) that preserve half of the bulkExpand Enhanced D-Brane Categories from String Field Theory We construct D-brane categories in B-type topological string theory as solutions to string field equations of motion. Using the formalism of superconnections, we show that these solutions form aExpand D-branes, exceptional sheaves and quivers on Calabi-Yau manifolds: From Mukai to McKay • Physics, Mathematics • 2001 Abstract We present a method based on mutations of helices which leads to the construction (in the large-volume limit) of exceptional coherent sheaves associated with the (∑ala=0) orbits in GepnerExpand	2021-10-18 02:50:11	{"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": 0.7053439021110535, "perplexity": 1933.101032946426}, "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-2021-43/segments/1634323585186.33/warc/CC-MAIN-20211018000838-20211018030838-00171.warc.gz"}
https://paradigms.oregonstate.edu/problem/790/	## Current from a Spinning Cylinder • assignment Magnetic Field and Current assignment Homework ##### Magnetic Field and Current Static Fields 2023 (4 years) Consider the magnetic field $\vec{B}(s,\phi,z)= \begin{cases} 0&0\le s<a\\ \alpha \frac{1}{s}(s^4-a^4)\, \hat{\phi}&a<s<b\\ 0&s>b \end{cases}$ 1. Use step and/or delta functions to write this magnetic field as a single expression valid everywhere in space. 2. Find a formula for the current density that creates this magnetic field. 3. Interpret your formula for the current density, i.e. explain briefly in words where the current is. • group Magnetic Vector Potential Due to a Spinning Charged Ring group Small Group Activity 30 min. ##### Magnetic Vector Potential Due to a Spinning Charged Ring Static Fields 2023 (6 years) Power Series Sequence (E&M) Ring Cycle Sequence Students work in small groups to use the superposition principle $\vec{A}(\vec{r}) =\frac{\mu_0}{4\pi}\int\frac{\vec{J}(\vec{r}^{\,\prime})}{\vert \vec{r}-\vec{r}^{\,\prime}\vert}\, d\tau^{\prime}$ to find an integral expression for the magnetic vector potential, $\vec{A}(\vec{r})$, due to a spinning ring of charge. In an optional extension, students find a series expansion for $\vec{A}(\vec{r})$ either on the axis or in the plane of the ring, for either small or large values of the relevant geometric variable. Add an extra half hour or more to the time estimate for the optional extension. • group Magnetic Field Due to a Spinning Ring of Charge group Small Group Activity 30 min. ##### Magnetic Field Due to a Spinning Ring of Charge Static Fields 2023 (7 years) Power Series Sequence (E&M) Ring Cycle Sequence Students work in small groups to use the Biot-Savart law $\vec{B}(\vec{r}) =\frac{\mu_0}{4\pi}\int\frac{\vec{J}(\vec{r}^{\,\prime})\times \left(\vec{r}-\vec{r}^{\,\prime}\right)}{\vert \vec{r}-\vec{r}^{\,\prime}\vert^3} \, d\tau^{\prime}$ to find an integral expression for the magnetic field, $\vec{B}(\vec{r})$, due to a spinning ring of charge. In an optional extension, students find a series expansion for $\vec{B}(\vec{r})$ either on the axis or in the plane of the ring, for either small or large values of the relevant geometric variable. Add an extra half hour or more to the time estimate for the optional extension. • assignment Find Area/Volume from $d\vec{r}$ assignment Homework ##### Find Area/Volume from $d\vec{r}$ Static Fields 2023 (5 years) Start with $d\vec{r}$ in rectangular, cylindrical, and spherical coordinates. Use these expressions to write the scalar area elements $dA$ (for different coordinate equals constant surfaces) and the volume element $d\tau$. It might help you to think of the following surfaces: The various sides of a rectangular box, a finite cylinder with a top and a bottom, a half cylinder, and a hemisphere with both a curved and a flat side, and a cone. 1. Rectangular: \begin{align} dA&=\\ d\tau&= \end{align} 2. Cylindrical: \begin{align} dA&=\\ d\tau&= \end{align} 3. Spherical: \begin{align} dA&=\\ d\tau&= \end{align} • group Vector Surface and Volume Elements group Small Group Activity 30 min. ##### Vector Surface and Volume Elements Static Fields 2023 (4 years) Integration Sequence Students use known algebraic expressions for vector line elements $d\vec{r}$ to determine all simple vector area $d\vec{A}$ and volume elements $d\tau$ in cylindrical and spherical coordinates. This activity is identical to Scalar Surface and Volume Elements except uses a vector approach to find directed surface and volume elements. • group Scalar Surface and Volume Elements group Small Group Activity 30 min. ##### Scalar Surface and Volume Elements Static Fields 2023 (7 years) Integration Sequence Students use known algebraic expressions for length elements $d\ell$ to determine all simple scalar area $dA$ and volume elements $d\tau$ in cylindrical and spherical coordinates. This activity is identical to Vector Surface and Volume Elements except uses a scalar approach to find surface, and volume elements. • assignment Total Current, Square Cross-Section assignment Homework ##### Total Current, Square Cross-Section Integration Sequence Static Fields 2023 (6 years) 1. Current $I$ flows down a wire with square cross-section. The length of the square side is $L$. If the current is uniformly distributed over the entire area, find the current density . 2. If the current is uniformly distributed over the outer surface only, find the current density . • accessibility_new Acting Out Current Density accessibility_new Kinesthetic 10 min. ##### Acting Out Current Density Static Fields 2023 (6 years) Integration Sequence Ring Cycle Sequence Students, pretending they are point charges, move around the room so as to make an imaginary magnetic field meter register a constant magnetic field, introducing the concept of steady current. Students act out linear $\vec{I}$, surface $\vec{K}$, and volume $\vec{J}$ current densities. The instructor demonstrates what it means to measure these quantities by counting how many students pass through a gate. • assignment Total Current, Circular Cross Section assignment Homework ##### Total Current, Circular Cross Section Integration Sequence Static Fields 2023 (5 years) A current $I$ flows down a cylindrical wire of radius $R$. 1. If it is uniformly distributed over the surface, give a formula for the surface current density $\vec K$. 2. If it is distributed in such a way that the volume current density, $\|\vec J\|$, is inversely proportional to the distance from the axis, give a formula for $\vec J$. • assignment Symmetry Arguments for Gauss's Law assignment Homework ##### Symmetry Arguments for Gauss's Law Static Fields 2023 (5 years) Instructions for 2022: You will need to complete this assignment in a 15 minute appointment on Zoom or in person with one of the members of the teaching team between 1/21 and 10 pm on 1/26. Here is a link to a sign-up page. You are required to watch a sample video for how to make symmetry arguments here. As demonstrated in the video you should bring with you to the meeting a cylinder, an observer, and a vector. Use good symmetry arguments to find the possible direction for the electric field due to a charged wire. Also, use good symmetry arguments to find the possible functional dependence of the electric field due to a charged wire. Rather than writing this up to turn in, you should find a member of the teaching team and make the arguments to them verbally. • A solid cylinder with radius $R$ and height $H$ has its base on the $x,y$-plane and is symmetric around the $z$-axis. There is a fixed volume charge density on the cylinder $\rho=\alpha z$. If the cylinder is spinning with period $T$: 1. Find the volume current density. 2. Find the total current.	2023-03-24 22:34:35	{"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": 3, "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": 3, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7408523559570312, "perplexity": 975.0833281756011}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296945289.9/warc/CC-MAIN-20230324211121-20230325001121-00033.warc.gz"}
https://www.physicsforums.com/threads/electric-potential-energy-of-more-than-two-charges.328676/	# Electric Potential Energy of More Than Two Charges 1. Aug 3, 2009 ### exitwound 1. The problem statement, all variables and given/known data Questions and solutions are given. However, I have some questions. 26.47. Can anyone explain to me in more detail this solution? For instance, why do they reverse the order and add them together (equations 2 and 3)? And how does one obtain this obvious Calculus generalization? 26.48. Can anyone explain this is more detail to me? 2. Aug 3, 2009 ### kuruman This is the total electrostatic energy for an assembly of charges. Let's assemble just three at first by bringing them in from infinity one at a time at a point in space where there is nothing to begin with. The total electrostatic energy will be the sum of energies it costs us to bring each charge in. For the first charge q1 U1=0 because it costs us nothing since there are no electrical forces, yet. Once the first charge is in place, there is an electrostatic potential V(1) set up by charge 1 and the cost to bring the second charge, q2 is U2=q2V2(1) Here V2(1) is the electrostatic potential at charge 1 (subscript of V) due to charge 2 (number between parentheses). When we bring charge q3, we have two terms because there are two charges already there so that U3=q3[V3(1)+V3(2)] The total electrostatic energy is the sum of all three U=0 + q2V2(1) + q3[V3(1)+V3(2)] = q2V2(1)+q3V3(1)+q3V3(2). Bringing in the charges in reverse order gives us the same total electrostatic energy, but provides the "missing" subscripts and terms in parentheses. We have U3 = 0 U2 = q2V2(3) U1=q1[V1(3)+V1(2)] The total energy is again the sum U = q2V2(3) + q1V1(3)+q1V1(2) 2U =q2V2(1)+q3V3(1)+q3V3(2)+q2V2(3) + q1V1(3)+q1V1(2) If you divide by two, you get the formula that says that the total energy is the one-half the sum of three terms, each term being a charge times the total electrostatic potential at that charge generated by all the other charges. I hope that if you see how this works for three charges you will see how it works for an arbitrary number of them. 3. Aug 3, 2009 ### kuruman 26.48 is an extension of the formula to the continuous case. The expression in equation (4) $$U = \frac{1}{2}\int V \rho dv$$ tells you that to find U, you need to add a whole of things (integral sign). What kind of things? V is the electrostatic potential at "point charge" ρ dV. So you are adding the charge at a given point multiplied by the potential at that point, just like the previous case in 26.47 where the charges were discrete. 4. Aug 3, 2009 ### exitwound Thanks for the response. But I still don't understand this, even with just 3 charges. Why do you need to bring them back in reverse order? 5. Aug 3, 2009 ### kuruman Bringing the charges back in reverse order has no deep physical significance. It is just an algebraic trick in the course of the derivation of Equation (4) in 26.47. It is like squaring both sides of an equation to get rid of a radical. Any expression for U, no matter in what order you assemble the charges, can be used when you have discrete charges and it will be correct. The problem with this is that, unless you write U in a symmetric form, i.e. a summation of n terms each of which is a charge times the potential at that charge as is done here, the conversion from a discrete summation to an integral will not be obvious. If I plopped Equation (4) in front of you and told you that this is the electrostatic energy of a continuous charge distribution, you might say "How did you get that?" Well, the derivation in 26.47 shows you how I got that. 6. Aug 3, 2009 ### exitwound Well, even though that may be how it's done, it doesn't help me at all if it's just a 'trick'. I was hoping that the derivation of 26.47 would help me understand 26.48 but it looks like it's just going to be a memorization thing. I understand the equation in 26.48, but it doesn't 'mean' anything to me since I don't understand the derivation of 26.47. 7. Aug 4, 2009 ### kuruman Let's try one more time with a different derivation. For three charges the total electrostatic energy is the sum of three terms, namely the electrostatic energies of all the possible pairs of charges: $$U = \frac{kq_{1}q_{2}}{r_{12}}+\frac{kq_{2}q_{3}}{r_{23}}+\frac{kq_{3}q_{1}}{r_{31}}$$ where k = 1/4πε0 and rij is the distance between qi and qj. Clearly, rij=rji. Now watch this: I split each term into two halves because 1/2 + 1/2 = 1 no matter what. Why do I do this? Because I have seen this derivation many times in the past. What about the first time? I saw it in my textbook and I have remembered it since then. This is what some people call "learning new things." Anyway, with the split the expression develops into six terms $$U = \frac{1}{2}[\frac{kq_{1}q_{2}}{r_{12}}+\frac{kq_{2}q_{3}}{r_{23}}+\frac{kq_{3}q_{1}}{r_{31}}+\frac{kq_{2}q_{1}}{r_{21}}+\frac{kq_{3}q_{2}}{r_{32}}+\frac{kq_{1}q_{3}}{r_{13}}]$$ and this can be factored to give $$U = \frac{1}{2}[q_{1}(\frac{kq_{2}}{r_{12}} +\frac{kq_{3}}{r_{13}})+q_{2}(\frac{kq_{1}}{r_{21}} +\frac{kq_{3}}{r_{23}})+q_{3}(\frac{kq_{1}}{r_{31}} +\frac{kq_{2}}{r_{32}}) ]$$ Note that the terms between parentheses are the potential at a given charge due to the presence of the other charges. For example the potential at charge 1 is $$V_{1} = (\frac{kq_{2}}{r_{12}} +\frac{kq_{3}}{r_{13}})$$ and likewise for V2 and V3. With these substitutions, you recover $$U = \frac{1}{2} (q_{1}V_{1} +q_{2}V_{2} +q_{3}V_{3})$$ This derivation is more common in E&M textbooks than the one in yours. However, some people may consider the derivation in your textbook as more "elegant" because it is shortened by using the very same algebraic trick that confused you in the first place. 8. Aug 4, 2009 ### exitwound $$U = \frac{1}{2}[\frac{kq_{1}q_{2}}{r_{12}}+\frac{kq_{2}q_{3}}{r_{2 3}}+\frac{kq_{3}q_{1}}{r_{31}}+\frac{kq_{2}q_{1}}{ r_{21}}+\frac{kq_{3}q_{2}}{r_{32}}+\frac{kq_{1}q_{ 3}}{r_{13}}]$$ So what's the point in splitting it in half? What makes the above equation any more pretty than if you hadn't split it in two? And if you hadn't seen and memorized the splitting in half, would you have ever come up with that idea yourself? That's the problem I'm having. It's not intuitive at all to do that. 9. Aug 4, 2009 ### kuruman It's not the above equation that is more pretty. It is an intermediate step for getting to the final form $$U = \frac{1}{2}\int V\rho dv$$ which is a very compact way to say the same thing, not to mention easy to remember and easy to use, therefore "pretty." Furthermore, the expression in this "pretty" form can be used to develop other "pretty" forms. You will see what I mean when you get to Maxwell's Equations. To answer your other questions, I saw the "splitting in half" trick in high-school algebra for the first time and then I saw it again in different contexts, including this one. I recognized it as a useful thing to remember and as something to try when doing algebraic manipulations. So I put it in my "bag o' tricks" that contains a whole lot of things of this sort accumulated over the years. If you plan a career in physics (or related science), I suggest that you create such a bag if you have not already done so. Everyone in the professions has one. I agree with you, doing all this is not intuitive. Physics is not intuitive in the sense that it asks you to translate the physical reality around you into mathematical form, manipulate the mathematical form algebraically to get a new form, and then translate this new form back into physical reality. This is a counterintuitive (if not unnatural) way to perceive the world for a large segment of the population. I think this is one reason why some students of physics "hate" it. Hate is a very strong emotion if you think about it.	2018-03-21 17:24:05	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 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": 0.6629876494407654, "perplexity": 427.1388543069182}, "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-2018-13/segments/1521257647671.73/warc/CC-MAIN-20180321160816-20180321180816-00719.warc.gz"}
https://undergroundmathematics.org/trigonometry-triangles-to-functions/how-high-am-i/solution	Food for thought ## Solution How does an angular change on a Ferris wheel affect the height of a rider above the ground level? We need to select a starting point - an initial position for the rider. It makes sense to choose this to be at the bottom of the wheel, where the rider first gets on. Once the wheel starts moving the rider will begin to move around the circumference of a circle. After some time the rider will have moved through an angle, $\theta$, relative to the starting position and will be a height, $h$, above the ‘ground’ (we are assuming that at the starting position the rider has a height of $0$). We can now add to our initial diagram, labelling the radius of the Ferris wheel, $r$, and the angle through which the rider has turned, $\theta$. We are interested in finding the vertical height of the rider at this position. Notice that we can construct a right-angled triangle as shown in the following diagram. Using trigonometry we can show that the length $a$ is equal to $r\cos \theta.$ Then the vertical height of the rider above their starting position (the ground), $h$, is $r-r\cos \theta = r(1-\cos\theta).$ It makes sense to check this result. We know that when $\theta=0$, $h$ should equal $0$ and that when $\theta=\pi$, $h$ should equal $2r$. Substituting $\theta=0$ into our formula for the height gives $h=r(1-\cos 0) = r(1 - 1) = 0,$ as required. Similarly, substituting $\theta=\pi$ into the formula for the height gives $h=r(1-\cos \pi)=r(1-(-1)) = 2r.$ We found this formula by considering the acute value of $\theta$ in my original diagram. We have confirmed that the formula returns expected results for two specific values of $\theta$ but it’s worth thinking a little further about why it works for all values of $\theta$. Consider the following two diagrams: Can you use these diagrams to explain why the formula $h=r(1-\cos\theta)$ also works for obtuse and reflex values of $\theta$?	2018-09-21 20:36:13	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 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": 0.8933554887771606, "perplexity": 175.6421344532747}, "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/1537267157503.43/warc/CC-MAIN-20180921190509-20180921210909-00234.warc.gz"}
http://acastano.com/japanese/1st-grade/kanjis/radicals/	みず (mizu – water) We already saw a set of radicals related to katakanas; some of those radicals were also katakanas, others were also kanjis; some, like the radicals ニ, ハ, 匕, エ, ロ, and カ are also both katakanas and kanjis. The majority of kanjis are not radicals, though, but instead are made up of simpler components. In this post we describe the relationship between a kanji and it’s radical, and discuss the way that kanjis are composed. In the page introducing radicals we laid them all on the table, together with their variations. We saw that a radical is a set of strokes that has some ‘basic’ meaning. The 214 radicals were selected to index all characters, so every kanji either is a radical or contains a radical. In addition, if we include in the term ‘radical’ the few one-stroke CKJ characters that were not selected to be radicals, we can guarantee that we can decompose every kanji into a set of radicals, i.e., we can use radicals to study kanjis as if the kanjis had been design as a synthesis of the radicals that form it. Let’s take the case of a typical kanji: (na), which means ‘name’. For example, 名 is the 3rd character in the title of the blockbuster movie ‘kimi no na wa’ (your name?): , or ‘name’, is composed of two radicals: • radical #36, , which means ‘evening’ or ‘sunset’ • radical #30, , which means ‘mouth’ or ‘opening’ An old technique to memorize kanjis is to come up with a mnemonic using its components; the popular books of “Remembering the Kanji” by Helsig use this approach. For example, we could concoct that the entrance (口) to Aladdin’s cave opens at sunset (夕), if we chant our name (名); we are not necessarily interested in figuring out how the meanings of 夕, or ‘evening’, and 口, or ‘mouth’, actually combine to give 名 its meaning of ‘name’. Actually, it is sometimes the case that the meaning of the kanji given by the combination of its components has been lost over the centuries. Instead, what we care about is that the kanji 名 is composed completely of the two components 夕 and 口, which we can use to both remember the meaning of the kanji and figure out how to write it correctly. As long as the story is memorable, this method works even if we get the actual components wrong, e.g., if we decompose 名 into 夕, 凵, and 一, we can still come up with a mnemonic that might not be correct with respect to the original components of the kanji (that an etymologist would care about), but would still work perfectly well for the purpose of remembering the kanji and writing it correctly. In this post we will decompose kanjis into their components: simpler kanjis, katakanas and radicals. In the term ‘radicals’ we are including a few CJK single-stroke characters. CJK is the collective name for the characters used in China, Japan, and Korea, all derived from the Chinese characters. These few CJK single-stroke characters were not selected as radicals because, although needed for character decomposition, were not needed for character indexing. As an aside, the methodology of composing all characters using a set of single-stroke characters is also used to create commputer fonts [CDL]. Kanjis are combinations of components: simpler kanjis, radicals, and katakanas. Every kanji has one -and only one- radical, called ‘the kanji’s radical’, that gives the kanji its particular meaning (semantic component) or sound (phonetic component). For example, the radical of the kanji for fountain, 泉, is the radical for ‘water’, 水; thus, the radical 水 says that the kanji 泉 has something to do with water. There is no rule about what the radical of a kanji is. For example, we can surmise that the radical of 花 (flower) is one of its most visible radicals, i.e., it is either 艹 (#140 – grass), イ (#9 – person), or 匕 (#21 – spoon); indeed, the radical of 花 is 艹 (grass), which says that 花 has something to do with plants, and we will find its definition in the 艹 section of a radical-based dictionary. Likewise, there is no rule for where in the kanji we will find its radical, although commonly it will be in one of its sides: on top, like in 花 (flower); at the bottom, like in 泉 (fountain); on the left, like in 泪 (tear); or on the right, like in 化 (change). In these cases, semantic radicals tend to appear on the left and top of the kanji, while phonetic ones tend to appear on the right and bottom. Another possibility is for the radical to surround the kanji, either partially or totally, like in 囚 (prisoner). Here are these kanjis, with their radicals in red: Sometimes a radical is a kanji, like in 木, in which case, of course, the radical of the kanji is itself, e.g., the ‘tree’ radical, 木, is the radical of the ‘tree’ kanji, 木. The ‘tree’ radical is also the radical for the ‘grove’ kanji, 林, which has two parts: on the left, the ‘tree’ radical that gives the ‘grove’ kanji its ‘tree-related’ meaning, and on the right, a kanji that, in this case, coincidentally, happens to be the kanji for ‘tree’. The ‘tree’ radical is also the radical for the ‘forest’ kanji, 森, which has two parts: on the top, the ‘tree’ radical, which gives the ‘forest’ kanji its ‘tree-related’ meaning, and on the bottom the kanji for ‘grove’, 林. Hence, the ‘tree’ radical is the radical of the kanjis for ‘tree’, ‘grove’, and ‘forest’, and indicates that all these kanjis are related to trees: a. tree – き; b. groove – はやし; c. forest – もり. ## the kanji’s bounding box All kanji fit within an imaginary square box. As shown above, the kanji 林 has the radical 木 and the kanji 木 side-by-side, so to fit them in the square box we have to squeeze them sideways, i.e., to make them thinner. On the other hand, the kanji 森 has the radical 木 on top of the kanji 林, so to fit them in the square box we have to squash them, i.e., to make them shorter. We can still recognize the radical 木 regardless of whether we squeeze it or squash it, because 木 has a simple appearance and few strokes. However, a radical with many strokes is difficult to squeeze or squash, so it is often the case that such complex radicals would have one or two simpler versions, with less strokes. For example, the radical for ‘water’, 水, has the alternate form ⺡. Both 水 and ⺡ have identical meanings, but we will use 水 when we are stacking the radical, and ⺡ when we are squeezing it horizontally: water – みず fountain – いずみ water – みず tear – なみだ Some radical varations, by design, have a specific shape that helps them fit in the bounding box. Vertical thin radicals, like “water”, ⺡, are always on the left or right of the kanji, while horizontal short radicals, like “grass”, ⺾, are always stacked: grass flower – はな potato – いも seedling – なえ A radical doesn’t necessarily need to have a small number of strokes; instead, a simple concept might require a large number of strokes; regardless, these many-stroke kanjis still need to fit within a same-size bounding box. Not many few-stroke radicals are also kanjis, but most many-stroke radicals are. An example is the radical for ‘rain’, 雨, with 8 strokes, which is also the kanji for ‘rain’; the ‘rain’ radical is the radical of the kanjis for ‘cloud’, ‘thunder’, and ‘snow’, among many others: rain – あめ cloud – くも thunder – かまきり snow – ゆき ## Oat milk The Swedish oat-milk company ‘Oatly’ picked up on the way characters are composed to come up with a new ‘character’ for their publicity campaign in East Asia (greenqueen, campaignasia). In Chinese, we write cow-milk with two characters, as 牛奶. The characters and radicals involved are: • 牛: cow • 奶: milk • 女: woman or female • 乃: from… Hence, in Chinese, ‘milk’ is 奶, meaning ‘from-female’, and ‘cow milk’ is 牛奶, meaning ‘from-female cow’. Oatly reasoned that they could describe ‘plant-based milk’ by composing a new character: remove the character 牛 for cow, and combine the radical for plant, ⺾, and the character for ‘from female’, 奶, that has taken the meaning of ‘milk’. The result is This is not an official character; we would not be able to find it in a dictionary, nor there is a way to type it, nor a way to pronounce it. Still, its visual meaning as ‘plant-based milk’ would be clear to anyone that can read these characters and radicals, so it makes sense as a way to raise awareness and introduce the product. Characters, indeed, are made up of simpler components, and we can decompose them as a way to help us memorize them and write them in the correct order and with the correct strokes. Good luck to ‘Oatly’ on their quest for a more sustainable planet. ## stroke order vs. component order Every kanji is either a radical, or has a radical; if it has a radical, we can remove it and be left with a simpler character that we can break into simpler kanjis and radicals; if we so desire, we can repeat this process until we are left with only a single-stroke component. When we write a component in a kanji, usually we write it completely before moving on to a different component of the kanji; there are exceptions, like the surrounding radicals like ‘enclosure’, 囗, for which we write the components contained inside the radical before closing the bottom of the radical. However, in most cases, we write each component of the kanji completely before moving to the next component. Thus, learning the order of strokes of components of kanjis helps us write all kanjis based on those components. Consider the kanji for ‘flower’, 花. The radical of 花 is ‘grass’ or ‘vegetation’, 艹; if we remove it, we are left with the kanji for ‘change’, 化. The radical of 化 is ‘spoon’, 匕; when we remove it, we are left with the radical for ‘person’, ⺅. Hence: English Kanji radical Kanji minus radical flower 花艹化 change 化匕⺅ person ⺅ Kanjis, in general, are written from top-to-bottom and/or from left-to-right. Hence, to write the kanji for flower, 花, we just need to write its three parts 艹, ⺅, and 匕, in that order, from top-to-bottom and/or left-to-right. As long as the strokes for each individual component are correct, the strokes for the complete kanji are likely to be correct, e.g., the following are the strokes for 花, for which we write each component completely before moving to a different component: The kanji 花 is its radical 艹, and the kanji 化. The kanji 化 is its radical 匕 and the radical ⺅ Hence, instead of specifying each stroke of the kanji, we can simply specify its radical and components, and the order in which we should write each of them, e.g., if we know the stroke order of the 艹, ⺅, and 匕 radicals, and/or the 化 kanji, we can describe the stroke order of 花 describing the order in which we should write its components:	2022-10-01 17:03:20	{"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": 0.8300691843032837, "perplexity": 3227.9748684086635}, "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/1664030336880.89/warc/CC-MAIN-20221001163826-20221001193826-00555.warc.gz"}
https://gmatclub.com/forum/x-2-2-y-1-x-y-6-2-x-y-115760.html?fl=similar	It is currently 13 Dec 2017, 16:40 # Decision(s) Day!: CHAT Rooms \| Ross R1 \| Kellogg R1 \| Darden R1 \| Tepper R1 ### GMAT Club Daily Prep #### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email. Customized for You we will pick new questions that match your level based on your Timer History Track every week, we’ll send you an estimated GMAT score based on your performance Practice Pays we will pick new questions that match your level based on your Timer History # Events & Promotions ###### Events & Promotions in June Open Detailed Calendar # (x−2)(2+y)=? (1) x·y=6 (2) x+y=5 Author Message TAGS: ### Hide Tags Senior Manager Joined: 12 Apr 2010 Posts: 445 Kudos [?]: 107 [0], given: 157 (x−2)(2+y)=? (1) x·y=6 (2) x+y=5 [#permalink] ### Show Tags 20 Jun 2011, 23:58 1 This post was BOOKMARKED 00:00 Difficulty: 45% (medium) Question Stats: 54% (01:19) correct 46% (00:45) wrong based on 111 sessions ### HideShow timer Statistics (x−2)(2+y)=? (1) x·y=6 (2) x+y=5 Source Master Gmat sample Test Q 20 [Reveal] Spoiler: OA _________________ Kudos [?]: 107 [0], given: 157 Manager Joined: 16 Mar 2011 Posts: 168 Kudos [?]: 51 [0], given: 13 Re: x,y and the rest of the band [#permalink] ### Show Tags 21 Jun 2011, 00:15 Statement 1: if you substitute for 6/x for y you get 2 values for x which means there is no certain answer Statement 2: ditto. if you substitute 5-y for x you get (3-y)(2+y), which gives you, y = 3 of y = -2. I had some trouble working it out and the whole post got messed up (I think I did something wrong using some math signs or something:S), I'll try to do it later. Kudos [?]: 51 [0], given: 13 TOEFL Forum Moderator Joined: 16 Nov 2010 Posts: 1586 Kudos [?]: 607 [0], given: 40 Location: United States (IN) Concentration: Strategy, Technology Re: x,y and the rest of the band [#permalink] ### Show Tags 21 Jun 2011, 00:15 The answer is E. (1) and (2) don't give single specific values for x and y. Combination of (1) and (2) gives a quadratic equation, which can give 2 values of x (or y), which in turn can result in two values of the expression that we're supposed to evaluate. Hence there is no single specific answer for the expression based on data given. _________________ Formula of Life -> Achievement/Potential = k * Happiness (where k is a constant) GMAT Club Premium Membership - big benefits and savings Kudos [?]: 607 [0], given: 40 Intern Joined: 14 Mar 2010 Posts: 16 Kudos [?]: 9 [0], given: 1 Re: x,y and the rest of the band [#permalink] ### Show Tags 21 Jun 2011, 06:59 shouldnt it b C? From 1 and 2 we can get values of X and y ( 2 equations and 2 variables ) from 1 & 2 -> x = 7/2 , y=3/2 from this we can calculate the value of x−2)(2+y)=? Kudos [?]: 9 [0], given: 1 Current Student Joined: 26 May 2005 Posts: 551 Kudos [?]: 248 [0], given: 13 Re: x,y and the rest of the band [#permalink] ### Show Tags 21 Jun 2011, 07:12 msbinu wrote: shouldnt it b C? From 1 and 2 we can get values of X and y ( 2 equations and 2 variables ) from 1 & 2 -> x = 7/2 , y=3/2 from this we can calculate the value of x−2)(2+y)=? from 1 & 2 -> x = 7/2 , y=3/2..............?????? this is wrong.. xy = 6 Kudos [?]: 248 [0], given: 13 Intern Joined: 14 Mar 2010 Posts: 16 Kudos [?]: 9 [1], given: 1 Re: x,y and the rest of the band [#permalink] ### Show Tags 21 Jun 2011, 07:16 1 KUDOS Kudos [?]: 9 [1], given: 1 Manager Joined: 03 Jun 2010 Posts: 167 Kudos [?]: 72 [0], given: 40 Location: United States (MI) Concentration: Marketing, General Management Re: x,y and the rest of the band [#permalink] ### Show Tags 21 Jun 2011, 07:17 msbinu wrote: shouldnt it b C? From 1 and 2 we can get values of X and y ( 2 equations and 2 variables ) from 1 & 2 -> x = 7/2 , y=3/2 from this we can calculate the value of x−2)(2+y)=? From 1) and 2) we have answer pairs: $$(2;3) and (3;2)$$ substitute it and get: $$14=4$$ or $$0*5=0$$ (E) Kudos [?]: 72 [0], given: 40 Director Joined: 01 Feb 2011 Posts: 709 Kudos [?]: 149 [0], given: 42 Re: x,y and the rest of the band [#permalink] ### Show Tags 25 Jun 2011, 18:28 1. Not sufficient different combinations of x , y yields different values. 2 3 6 1 2. Not sufficient different combinations of x , y yields different values. 1 4 2 3 Together .. Not sufficient we know that x can be 2 or 3 then y can be 3 or 2. these two combinations yields different values.. Kudos [?]: 149 [0], given: 42 VP Joined: 08 Jun 2010 Posts: 1387 Kudos [?]: 172 [0], given: 916 Re: x,y and the rest of the band [#permalink] ### Show Tags 20 Jul 2011, 02:36 Normally, the 2 equation system has 2 set of solution Kudos [?]: 172 [0], given: 916 Manager Joined: 20 Jul 2011 Posts: 144 Kudos [?]: 83 [0], given: 15 GMAT Date: 10-21-2011 Re: x,y and the rest of the band [#permalink] ### Show Tags 05 Sep 2011, 08:22 Quote: (x−2)(2+y)=? (1) x·y=6 (2) x+y=5 Source Master Gmat sample Test Q 20 (x-2)(2+y) = xy - 2y + 2x -4 ...............[eq 1] From Statement 1 Insert x.y=6 into [eq 1], 6 - 12/x + 2x - 4 = 2x-10 insufficient From Statement 2 x+y=5 y=5-x Insert into [eq 1], x(5-x)-2(5-x)+2x-4 = 5x-x^2-10+2x+2x-4 = -x^2+9x-14 insufficient Statement 1 + 2 x(5-x)=6 5x-x^2-6=0 (-x-2)(x-3)=0 x=3 or x =2 Insufficient Quote: The answer is E. (1) and (2) don't give single specific values for x and y. Combination of (1) and (2) gives a quadratic equation, which can give 2 values of x (or y), which in turn can result in two values of the expression that we're supposed to evaluate. Hence there is no single specific answer for the expression based on data given. _________________ "The best day of your life is the one on which you decide your life is your own. No apologies or excuses. No one to lean on, rely on, or blame. The gift is yours - it is an amazing journey - and you alone are responsible for the quality of it. This is the day your life really begins." - Bob Moawab Kudos [?]: 83 [0], given: 15 Non-Human User Joined: 09 Sep 2013 Posts: 14869 Kudos [?]: 287 [0], given: 0 Re: (x−2)(2+y)=? (1) x·y=6 (2) x+y=5 [#permalink] ### Show Tags 31 Aug 2016, 06:59 Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________ Kudos [?]: 287 [0], given: 0 Senior Manager Status: DONE! Joined: 05 Sep 2016 Posts: 408 Kudos [?]: 26 [0], given: 283 (x−2)(2+y)=? (1) x·y=6 (2) x+y=5 [#permalink] ### Show Tags 19 Sep 2016, 05:50 E is correct. Here's why: (1) xy = 6 Try plugging into original equation... = xy + 2x - 2y -4 = 6 + 2x - 2y - 4 --> 2 + 2x - 2y NOT SUFFICIENT (2) x+y = 5 --> rewrite as x = 5-y & plug into original equation = ((5-y) - 2)(y+2) = (3-y)(y+2) NOT SUFFICIENT - we don't know the value of y A, B, D are eliminated Together - (1) + (2) = Plug both into original eq =(x-2)(y+2) =xy + 2x-2y-4 =6+2(5-y)-2y-4 =2+10-2y-2y =12-4y NOT SUFFICIENT - we still don't have a value for y Kudos [?]: 26 [0], given: 283 (x−2)(2+y)=? (1) x·y=6 (2) x+y=5 [#permalink] 19 Sep 2016, 05:50 Display posts from previous: Sort by	2017-12-14 00:40:34	{"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": 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": 0.442648708820343, "perplexity": 6936.395104033114}, "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-2017-51/segments/1512948532873.43/warc/CC-MAIN-20171214000736-20171214020736-00288.warc.gz"}
http://mathhelpforum.com/calculus/125356-solved-finding-radius-curvature-cardiode-r-1-cost.html	# Math Help - [SOLVED] FINDING RADIUS OF CURVATURE OF CARDIODE r=a(1-cost) 1. ## [SOLVED] FINDING RADIUS OF CURVATURE OF CARDIODE r=a(1-cost) question:- r=a(1-cost) answer :- 4/3a(sin(t/2)) (which i have to prove) Please help me to find the radius of curvature, i know the formula everything but i have to prove the answer as :- 4/3a(sin(t/2)), which i am unable to prove it, i cannot prove the answer as above, pls help here is the formula for finding the radius of curvature :- radius of curvature =((r^2+(r1)^2 )^3/2)/r^2+2(r1)^2-r(r2) were r1 is first derivative of r and r2 is second derivative of r Please any body help me this problem is driving me crazy, 2. Originally Posted by avengerevenge question:- r=a(1-cost) answer :- 4/3a(sin(t/2)) (which i have to prove) Please help me to find the radius of curvature, i know the formula everything but i have to prove the answer as :- 4/3a(sin(t/2)), which i am unable to prove it, i cannot prove the answer as above, pls help here is the formula for finding the radius of curvature :- radius of curvature =((r^2+(r1)^2 )^3/2)/r^2+2(r1)^2-r(r2) were r1 is first derivative of r and r2 is second derivative of r Please any body help me this problem is driving me crazy, What, exactly, is your difficulty? The derivatives should be very easy. From r= a(1- cos t), r'= a sin t and r"= a cos t. The numerator is $(a^2(1- cos t)^2+ a^2 sin^2 t)^{3/2}$ $= (a^2- 2a^2 cos t+ a^2 cos^2 t+ a^2 sin^2 t)^{3/2}$ $= (2a^2- 2a^2 cos t)^{3/2}= 2^{3/2}a^3 (1- cos t)^{3/2}$. The denominator is $a^2(1- cos t)^2+ 2a^2 sin^2 t- a^2(1- cos t)(cos t)$ $= a^2 - 2a^2 cos t+ a^2 cos^2 t+ 2a^2 sin^2 t- a^2 cos t+ a^2 cos^2 t$ $= 3a^2- 3a^2 cos t= 3a^2(1- cos t)$ So the fraction is $\frac{2^{3/2}a^3 (1- cos t)^{3/2}}{3 a^2 (1- cos 6)}= \frac{2^{3/2}}{3}a (1- cos t)^{1/2}= \frac{2^{3/2}}{3}a \sqrt{1- cos t}$ Now use a "half-angle" formula: $sin(t/2)= \sqrt{\frac{1}{2}(1- cos t)}$ 3. $r = a - a cos t$ Differentiating we get: $r_1 = a sin t$ and again we get: $r_2 = a cos t$ $Curvature = \frac{(r^2+r_1^2)^{\frac{3}{2}}}{r^2+2r_1^2-rr_2}$ Let's look at top and bottom of fraction seperately: $Top = (r^2+r_1^2)^{\frac{3}{2}}=(a^2(1-cost)^2+a^2sin^2t)^{\frac{3}{2}}=(a^2)^\frac{3}{2} (1-2cost+cos^2t+sin^2t)^\frac{3}{2}$ Using: $cos^2t+sin^2t=1$ $Top=a^3(2-2cost)^\frac{3}{2}=a^3.2\sqrt2(1-cost)^\frac{3}{2}$ $Bottom = r^2+2r_1^2-rr_2$ $= a^2(1-cost)^2+2a^2sin^2t-a^2cost(1-cost)= a^2(1-2cost+cos^2t+2sin^2t-cost+cos^2t$ Again using: $cos^2t+sin^2t=1$ $Bottom= a^2(3-3cost)=3a^2(1-cost)$ So bringing them together: $Curvature=\frac{Top}{Bottom}=\frac{a^3.2\sqrt2(1-cost)^\frac{3}{2}}{3a^2(1-cost)}=\frac{2\sqrt2}{3}a\sqrt{1-cost}$ Now we need to use formula: $cos(A+B)=cosAcosB-sinAsinB$ $cos(2A)=cos^2A-sin^2A=1-2sin^2A$ $sin^2A= \frac{1}{2}(1-cos2A)$ $sinA= \frac{1}{\sqrt2}\sqrt{1-cos2A}$ $Let \ A=\frac{t}{2}$ $sin(\frac{t}{2})=\frac{1}{\sqrt2}\sqrt{1-cost}$ $Or: \sqrt{1-cost}=\sqrt2sin(\frac{t}{2})$ Substituring back in our formula for curvature: $Curvature=\frac{2\sqrt2}{3}a\sqrt{1-cost}=\frac{4}{3}asin(\frac{t}{2})$ Which is the result you wanted! Voila! 4. Well done HallsofIvy you beat me to it! 5. Originally Posted by HallsofIvy What, exactly, is your difficulty? The derivatives should be very easy. From r= a(1- cos t), r'= a sin t and r"= a cos t. The numerator is $(a^2(1- cos t)^2+ a^2 sin^2 t)^{3/2}$ $= (a^2- 2a^2 cos t+ a^2 cos^2 t+ a^2 sin^2 t)^{3/2}$ $= (2a^2- 2a^2 cos t)^{3/2}= 2^{3/2}a^3 (1- cos t)^{3/2}$. The denominator is $a^2(1- cos t)^2+ 2a^2 sin^2 t- a^2(1- cos t)(cos t)$ $= a^2 - 2a^2 cos t+ a^2 cos^2 t+ 2a^2 sin^2 t- a^2 cos t+ a^2 cos^2 t$ $= 3a^2- 3a^2 cos t= 3a^2(1- cos t)$ So the fraction is $\frac{2^{3/2}a^3 (1- cos t)^{3/2}}{3 a^2 (1- cos 6)}= \frac{2^{3/2}}{3}a (1- cos t)^{1/2}= \frac{2^{3/2}}{3}a \sqrt{1- cos t}$ Now use a "half-angle" formula: $sin(t/2)= \sqrt{\frac{1}{2}(1- cos t)}$ First of all thank you very much for your post actually i know how to find derivatives, but i didnt get the idea to use half angle formula, i was stuck in that step, but be more clear, like you posted this Now use a "half-angle" formula: sin(t/2)= \sqrt{\frac{1}{2}(1- cos t)} actually it made no sense like how sin(t/2)= \sqrt{\frac{1}{2}(1- cos t)}. thanks to suhada for more clear explanation. 6. Originally Posted by HallsofIvy What, exactly, is your difficulty? The derivatives should be very easy. From r= a(1- cos t), r'= a sin t and r"= a cos t. The numerator is $(a^2(1- cos t)^2+ a^2 sin^2 t)^{3/2}$ $= (a^2- 2a^2 cos t+ a^2 cos^2 t+ a^2 sin^2 t)^{3/2}$ $= (2a^2- 2a^2 cos t)^{3/2}= 2^{3/2}a^3 (1- cos t)^{3/2}$. The denominator is $a^2(1- cos t)^2+ 2a^2 sin^2 t- a^2(1- cos t)(cos t)$ $= a^2 - 2a^2 cos t+ a^2 cos^2 t+ 2a^2 sin^2 t- a^2 cos t+ a^2 cos^2 t$ $= 3a^2- 3a^2 cos t= 3a^2(1- cos t)$ So the fraction is $\frac{2^{3/2}a^3 (1- cos t)^{3/2}}{3 a^2 (1- cos 6)}= \frac{2^{3/2}}{3}a (1- cos t)^{1/2}= \frac{2^{3/2}}{3}a \sqrt{1- cos t}$ Now use a "half-angle" formula: $sin(t/2)= \sqrt{\frac{1}{2}(1- cos t)}$ First of all thank you very much for your post actually i know how to find derivatives, but i didnt get the idea to use half angle formula, i was stuck in that step, but be more clear, like you posted this Now use a "half-angle" formula: sin(t/2)= \sqrt{\frac{1}{2}(1- cos t)} actually it made no sense like how sin(t/2)= \sqrt{\frac{1}{2}(1- cos t)}. thanks to suhada for more clear explanation.	2016-07-01 05:19:21	{"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": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 44, "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": 0.9811792969703674, "perplexity": 1895.5477025444723}, "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-2016-26/segments/1466783400031.51/warc/CC-MAIN-20160624155000-00127-ip-10-164-35-72.ec2.internal.warc.gz"}
http://hecooksshecooks.net/wk9h3aw/tq3jb8b.php?page=23dbbe-electroplating-chemical-equation	One atom of Copper metal in the anode gets oxidized and looses its two electrons to the anode. Often has parts submerged in solutions with "racks". The iron cathode then takes from the battery two electrons given by it to the copper ion. Common metals include: gold, silver, platinum, tin, lead ruthenium, rhodium, palladium, osmium, and iridium. How to Make Gold Plating Solution. In electroplating the word electro stands for electric current and plating means the act of covering a metal object with a thin layer of coating of a different metal It is mainly different from electroplating by not using external electrical power. The LibreTexts libraries are Powered by MindTouch® and are supported by the Department of Education Open Textbook Pilot Project, the UC Davis Office of the Provost, the UC Davis Library, the California State University Affordable Learning Solutions Program, and Merlot. These coatings are made by plating two metals in the same cell. Sometimes plating occurs on racks or barrels for efficiency when plating many products. It is mainly different from electroplating by not using external electrical power. This video lesson presents a series of stories related to Electroplating and begins with a story about house gates as an example of the common items related to the Electroplating topic. We also acknowledge previous National Science Foundation support under grant numbers 1246120, 1525057, and 1413739. Some electrolytes are acids, bases, metal salts or molten salts. Cheaper, as fewer chemicals are used and a production line is used to plate parts. This has always been a challenging topic within the IB curriculum. A cell consists of two electrodes (conductors), usually made of metal, which are held apart from one another. Legal. Five metals that can be used in electroplating are:Zinc, Cobalt, Iron, Tin and platinum. Prerequisites for this lesson are knowledge of the basic concepts of electrolysis and chemical equations. The basic reactions … What are the different types of electroplating? Please refer to electrolysis for more information. Chrome plating is the electrolytic deposition of chromium from an aqueous solution containing (usually) Chromic Acid (H2Cr04) and a "catalyst", usually sulfuric acid. Watch the recordings here on Youtube! Electroplating allows manufacturers to use inexpensive metals such as steel or zinc for the majority of the product and then apply different metals on the outside to account for appearance, protection, and other properties desired for the product. The cathode reaction is: K + + e − + H 2 O → K O H + H 2. Normally this is done in three steps: cleaning, treatment and rinsing. Hence, chemical plating via the displacement process has few applications. R. Summerlin, Christie L. Borgford, and Julie B. Ealy, “Electroplating Copper,” Chemical Demonstrations, A Sourcebook for Teachers, Volume 2 (Washington: American Chemical Society, 1988), pp. The following graph lists some metals along with there efficiency and plating constant. An electroplating cell works in much the same way as the cell used to purify copper. An electroplating cell works in much the same way as the cell used to purify copper. The Elkington cousins later in 1840 used potassium cyanide as their electrolyte and managed to create a feasible electroplating method for gold and silver. Chemical plating by displacement yields deposits limited to only a few microns in thickness, usually 1 to 3 pm. There are many different metals that can be used in plating and so determining the right electrolyte is important for the quality of plating. When current flows, the positive ions react with two electrons and are converted to metallic nickel at the cathode surface. In the figure below, the Ag+ ions are being drawn to the surface of the spoon and it eventually becomes plated. Watch the recordings here on Youtube! Improper cleaning usually results in a variety of plating defects like peeling or blistering over a period of time. But a couple of decades later, John Wright managed to use potassium cyanide as an electrolyte for gold and silver. Treatment includes surface modification which is the hardening of the parts and applying metal layers. It's not ideal for items that are detailed as it is not effective in preventing scratches and entanglement. The negative electrode (cathode) should be the object that is to be electroplated. In this very acidic solution CrO72– ions are completely protonated, and so the reduction half-equation is, $\text{H}_2\text{Cr}_2\text{O}_7(aq) + \text{12H}^{+}(aq) + \text{12}e^{-} \rightarrow \text{2Cr}(s) + \text{7 H}_2\text{O}(l)$. The metal used for the coating is sacrificial, being used up, in the reaction. A ... Electroplating, in which a metal is plated onto another object (e.g., chrome-plated trim or wheels on a car, chrome-plated bathroom fixtures, gold-plated or silver-plated jewelry) is an example of an electrolytic cell. The Nickel electroplating is done for providing corrosion resistance, wear resistance for a metal object. 1-Benzyl Pyridinium 3-Carboxylate Electroplating Brightener For Alkaline Zinc Plating 15990-43-9 BPC. Upper Saddle River: Pearson Education, Inc., 2007. A variety of chemical agents are used along with zinc electroplating in order to achieve the desired chemical and physical properties of the final product. are metals that are even more rarely used for plating than the minor metals. Electroless plating, also known as chemical or auto-catalytic plating, is a non-galvanic plating method that involves several simultaneous reactions in an aqueous solution, which occur without the use of external electrical power. Electroplating is based on Faraday’s two physical laws. 1. He discovered that potassium cyanide was in fact an efficient electrolyte. In conventional electroplating, some strategies like using additives, modifying substrates, applying pulse current, and agitating electrolyte have been explored to suppress dendrite growth. E is the cathode efficiency which is the actual amount of metal deposited by the cathode divided by the theoretical amount given by the first equation. Other metals which are often electroplated are silver, nickel, tin, and zinc. Lee. Most electroplating coatings can be separated into these categories: Sacrificial Coating Decorative Coating Functional Coatings Minor Metals Unusual metal Coating Alloy Coatings ; is used primarily for protection. The process uses an electric current to reduce dissolved metal cations to develop a lean coherent metal coating on the electrode. The influences of bath chemistry and plating variables on the chemical composition, deposition rate, morphology, and thermal stability of electroless Ni–P films on silicon wafers were studied. A series of free IGCSE Chemistry Activities and Experiments (Cambridge IGCSE Chemistry). Cathode (negative electrode): the object to be plated (for example a steel spoon) Reduction (gain of electrons) occurs at the cathode: Ag +(aq) + e - → Ag (s) The … & & VOICE-OVER-Asimple&example&of&theelectroplating&process&&is&the&electroplating of&iron&nail&&in&whichthemetal&tobeplatedwhichis&copper&is&usedas& the anode,& iron& nail is used& as the cathode andtheelectrolyte& solution& contains the ion& of& the metal to& be plated& (Cu … The electroplating process involves chemicals from pre-treatment (solvent degreasing, alkali cleaning and acid dipping), during plating, to the final buffing, grinding and polishing of the product. 5)Decomposing chemical compounds. In chromium plating, for instance, the electrolyte is usually a solution of potassium dichromate, K2Cr2O7, in fairly concentrated sulfuric acid. 9th ed. The electroplating process involves chemicals from pre-treatment (solvent degreasing, alkali cleaning and acid dipping), during plating, to the final buffing, grinding and polishing of the product. Electroplating method has gradually become more efficient and advanced through the use of more eco-friendly formulas and by using direct current power supplies. Relevance. The surface can be a metal or even plastic. Thus, industrial electroplating knowledge can be applied to revisit the electroplating process for lithium‐metal anodes. My IB seniors are just wrapping up our unit on electrochemistry and redox. Unless otherwise noted, LibreTexts content is licensed by CC BY-NC-SA 3.0. Normally electroplating is used for either decorative or functional purposes and to prevent a metal from corrosion. Cleaning of the substrate is done in order to remove any dirt, rust, oil, etc., from the surface. Notes . An alloy is a substance that has metallic properties and is made up of two or more elements. 1 Answer. As current flows, this compound is reduced to the metal and deposits on the surface of the cathode. Jewelry and silverware can be silver- or gold-plated, while zinc is often used to coat iron to protect against rust. It often employed in electronics to provide a corrosion resistant surface. Then, due to the negative and positive charges, the two metals are attracted to each other. It is also possible to determine plating thickness through the equation Electroplating Chemicals. Electrochemistry deals with chemical reactions involving electrical energy. We also acknowledge previous National Science Foundation support under grant numbers 1246120, 1525057, and 1413739. An important industrial application of electrolysis is the plating of one metal on top of another. The different types of electroplating are: mass plating (also barrel plating), rack plating, continuous plating, and in line plating. Prep. 3)Production of certain metals from the ore. 4)Production of chemical compounds. Why is it important to prepare the surface before beginning electroplating? If I use a vinegar, Epsom Salts, and sugar, what is the balanced formula for the chemical reaction? 1) Electroplating metals. What different metals can be used? In chromium plating, for instance, the electrolyte is usually a solution of potassium dichromate, K 2 Cr 2 O 7, in fairly concentrated sulfuric acid. IME Aqueous Cationic Polymer Electroplating Chemicals Brightener Yellow Liquid. Electroplating is essentially a chemical reaction which helps to make various items we see and use every day. The electrodes are immersed in an electrolyte (a solution Jewelry and silverware can be silver- or gold-plated, while zinc is often used to coat iron to protect against rust. Nickel electroplating is a technique of electroplating a thin layer of nickel onto a metal object. In the case of silver the electrolyte must contain the polyatomic ion Ag(CN)2– rather than Ag+. All these things are examples of electrochemistry: chemical reactions caused by or producing electricity that give scientifically or industrially useful end-products. It is important to prepare the surface before beginning the procedure because sometimes there is contamination on the surface that could lead to bad electroplating results. Favorite Answer. Now the battery is in deficit of two electrons. Chrome plating chemistry lesson 2003 . Figure 1: Electroplating silver onto a spoon. are coatings done based on necessity and functionality of the metal. As current flows, this compound is reduced to the metal and deposits on the surface of the cathode. & & VOICE-OVER-Asimple&example&of&theelectroplating&process&&is&the&electroplating of&iron&nail&&in&whichthemetal&tobeplatedwhichis&copper&is&usedas& the anode,& iron& nail is used& as the cathode andtheelectrolyte& solution& contains the ion& of& the metal to& be plated& … Many other metal objects, such as pins, screws, watchbands, and doorknobs, are made of one metal with another plated on the surface. Because the chemical reaction used in this process is based on a reduction reaction, the monitoring of the moles of electrons passed through the reaction vessel, will inform us as to the number of moles of material plated on the electrodes. Since electroplating involves both an electrical and a chemical reaction at the surface of the part, exposure to the plating chemistry is critical to the overall performance of the finished product. The process uses an electric current to reduce dissolved metal cations to develop a lean coherent metal coating on the electrode. A ... Electroplating, in which a metal is plated onto another object (e.g., chrome-plated trim or wheels on a car, chrome-plated bathroom fixtures, gold-plated or silver-plated jewelry) is an example of an electrolytic cell. Electroplating is the application of electrolytic cells in which a thin layer of metal is deposited onto an electrically conductive surface. The electroplating of copper in high-aspect-ratio trenches and vias is a difficult challenge facing the new technology of copper on-chip interconnect. Electroplating is basically the process of plating a metal onto the other by hydrolysis mostly to prevent corrosion of metal or for decorative purposes. These types of products normally have a thin layer of gold, or silver applied so that it has an attractive appeal to the consumer. R. Summerlin, Christie L. Borgford, and Julie B. Ealy, “Electroplating Copper,” Chemical Demonstrations, A Sourcebook for Teachers, Volume 2 (Washington: American Chemical Society, 1988), pp. Here are some chemicals in electroplating usage. Thus, industrial electroplating knowledge can be applied to revisit the electroplating process for lithium‐metal anodes. These laws are state – 1) The weight of a substance formed at an electrode is proportional to the amount of current passed through the cell; and 2) The weights of different substances produced at an electrode by the same amount of current are proportional to their equivalent weights. Electroplating is based on Faraday’s two physical laws. Amanda K. 1 decade ago. In electroplating the word electro stands for electric current and plating means the act of covering a metal object with a thin layer of coating of a different metal By the way, my dad and I bought a Zinc anode made for a boat for \$1.25 at a boat shop. 2)Purification of metals. 1) Electroplating metals. Rinsing leads to the final product and is the final touch to electroplating.Two certain methods of preparing the surface are physical cleaning and chemical cleaning. This is made from steel and then plated with a thin layer of chromium to make it resistant to rusting and scratching. Electroplating Chemicals. The cathode reaction is again the formation of potassium hydroxide and hydrogen. Line Plating: Cheaper, as fewer chemicals are used and a production line is used to plate parts. Legal. Equations used in Electroplating. Chemical cleaning consists of using solvents that are either surface-active chemicals or chemicals which react with the metal/surface. But I would like to understand more about the chemistry of chrome plating (the information from text book is very scanty). 3)Production of certain metals from the ore. 4)Production of chemical compounds. Answer Save. Prep. I'm going to plate zinc onto copper as you show in the FAQ, "Electroplating--How it Works" as a 6th grade science fair project. When choosing the type of electrolyte some things to keep in mind are corrosion, resistance, brightness or reflectivity, hardness, mechanical strength, ductility, and wear resistance. Electroplating Electrolysis is used to electroplate objects. If I use a vinegar, Epsom Salts, and sugar, what is the balanced formula for the chemical reaction? ELECTRO-PLATING: BASICS The following section would like to explain the physical and chemical basis for electroplating to the extent as it is useful for understanding the following chapters. A chemical nickel coating formula is used to solve the problems of low speed coating, low stability and high coating coat of coating liquid with the prior art technique of chemical nickel coating. I'm going to plate zinc onto copper as you show in the FAQ, "Electroplating--How it Works" as a 6th grade science fair project. processof&plating&isdone?Letmeexplain&toyou. Lowell Thomson \| Sun, 11/20/2016 - 02:00 . Have questions or comments? A series of free IGCSE Chemistry Activities and Experiments (Cambridge IGCSE Chemistry). However his discovery was not noted as he was disregarded by the French Academy of Science as well as Napolean Bonaparte. The process uses various chemicals depending on metals that they are electroplating. Q. I've read some of your threads and understand the reasons for not doing chrome plating as a school project. A typical example is the bumper of a car. Parts such as wires and tubes are continuously passing anodes at a certain rate. This is useful for coating a cheaper metal with a more expensive one, such as copper or silver. A stainless steel spoon is electroplated with copper in this demonstration. Electroplating works through an electrolytic cell with a cathode and an anode. I need to know what the chemical equation for electroplating copper onto quarters is... first right answer 10 points. As the name suggests, this deposition is done by a process aided by flow of electric current. constituents which will be discussed in the section on ‘Chemistry of Nickel Plating Solutions.’ When dissolved, the nickel salts dissociate into divalent, positively charged nickel ions (Ni++) along with negatively charged ions. Cyanide Zinc Plating Chemicals Industrial Grade Wide Operating Range ; Wide operating range ; JZ-2. Electroplating allows manufacturers to use inexpensive metals such as steel or zinc for the majority of the product and then apply different metals on the outside to account for appearance, protection, and other properties desired for the product. Notes . 2)Purification of metals. In conventional electroplating, some strategies like using additives, modifying substrates, applying pulse current, and agitating electrolyte have been explored to suppress dendrite growth. Common metals include: copper, nickel, chromium, zinc and tin. A chemical nickel coating formula is used to solve the problems of low speed coating, low stability and high coating coat of coating liquid with the prior art technique of chemical nickel coating. In this experiment, you will conduct, observe, and measure the process of electroplating. The object to be plated is used as the cathode, and the electrolyte contains some ionic compound of the metal to be plated. The overall process of electroplating uses an electrolytic cell, which consists of putting a negative charge on the metal and dipping it into a solution that contains metal salt (electrolytes) which contain positively charged metal ions. The below given is the Nickel plating thickness formula which guides you to calculate the plate thickness on your own. Chemical Formula for Reaction - Zinc Plating 2003. The surface can be a metal or even plastic. The process is undergone using silver as the anode, and a screw as the cathode. Because of its chemical composition, you do not want to get close to that bath. The evolution of hydrogen gas from chemical reactions at the cathode consumes 80 to 90 percent of the power supplied to the plating bath, leaving the remaining 10 to 20 percent for the deposition reaction. Electroless plating, also known as chemical or auto-catalytic plating, is a non-galvanic plating method that involves several simultaneous reactions in an aqueous solution, which occur without the use of external electrical power. Equations used in Electroplating. Petrucci, Ralph H., Harwood, William S., Herring, F. G., and Madura Jeffrey D. General Chemistry: Principles and Modern Applications. Electroplating is widely used in industries such as automobile, airplanes, electronics, jewelry, and toys. Prerequisites for this lesson are knowledge of the basic concepts of electrolysis and chemical equations. These include: As, Sb, Bi, Mn, Re, Al, Zr, Ti, Hf, V, Nb, Ta, W, and Mo. This process is a bit cheaper. [ "article:topic", "electroplating", "authorname:chemprime", "showtoc:no", "license:ccbyncsa" ], 17.7: Quantitative Aspects of Electrolysis, Ed Vitz, John W. Moore, Justin Shorb, Xavier Prat-Resina, Tim Wendorff, & Adam Hahn, Chemical Education Digital Library (ChemEd DL), information contact us at info@libretexts.org, status page at https://status.libretexts.org. They attained a patent for electroplating and this method became widely spread throughout the world from England. 199−200. Electrochemistry deals with chemical reactions involving electrical energy. There are also specific types of electroplating such as copper plating, silver plating, and chromium plating. This activity will explore two examples of electroplating. For more information contact us at info@libretexts.org or check out our status page at https://status.libretexts.org. Gold plating finds its uses in jewelry, semiconductor industry. Because the chemical reaction used in this process is based on a reduction reaction, the monitoring of the moles of electrons passed through the reaction vessel, will inform us as to the number of moles of material plated on the electrodes. Here are some chemicals in electroplating usage. Because of its chemical composition, you do not want to get close to that bath. Kanani, N. Electroplating: Basic Principles, Processes and Practice; Elsevier Advanced Technology: Oxford, U.K., 2004. This is useful for coating a cheaper metal with a more expensive one, such as copper or silver. (name 5). Electroplating Electrolysis is used to electroplate objects. Electroplating is basically the process of plating a metal onto the other by hydrolysis mostly to prevent corrosion of metal or for decorative purposes. Get contact details & address of companies manufacturing and supplying Gold Plating Chemical, Gold Electroplating Chemical across India. This is useful for coating a cheaper metal with a more expensive one, such as copper or silver. An important application of electrochemistry is electrolysis, sometimes known as electroplating. In this very acidic solution CrO 72– ions are completely protonated, and so the reduction half-equation is (17.6.1) H 2 Cr 2 O … Most electroplating coatings can be separated into these categories: The LibreTexts libraries are Powered by MindTouch® and are supported by the Department of Education Open Textbook Pilot Project, the UC Davis Office of the Provost, the UC Davis Library, the California State University Affordable Learning Solutions Program, and Merlot. 199−200. Common metals include: zinc and cadmium (now forbidden in many countries). The process uses various chemicals depending on metals that they are electroplating. When the hydrogen gas evolves, it causes misting at the surface of the plating bath, which results in the loss of chromic acid to the atmosphere. The influences of bath chemistry and plating variables on the chemical composition, deposition rate, morphology, and thermal stability of electroless Ni–P films on silicon wafers were studied. Find here Gold Plating Chemical, Gold Electroplating Chemical manufacturers, suppliers & exporters in India. Common combinations include: gold–copper–cadmium, zinc–cobalt, zinc–iron, zinc–nickel, brass (an alloy of copper and zinc), bronze (copper–tin), tin–zinc, tin–nickel, and tin–cobalt. An alkaline detergent is used to clean the surface to ensure the zinc electroplating is of good quality, and the plating remains intact for a long period of time. From the time of dipping in the acid, the following electro-chemical reactions take place: From the electrode with the less noble metal, iron in this example, iron … Electroless nickel–phosphorus (Ni–P) films were produced on the surface of p-type monocrystalline silicon in the alkaline citrate solutions. The process of cleaning an object involves two steps: alkaline bat… Electroplating Electrolysis is used to electroplate objects (coat them with a thin layer or metal). Nesting of parts will result in a lack of adhesion or coverage on the surface of the finished part. Sometimes finishes are solely decorative such as the products we use indoors or in a dry environment where they are unlikely to suffer from corrosion. Electroplating is very similar to electrolysis (using electricity to split up a chemical solution), which is the reverse of the process by which batteries produce electric currents. Electrochemical reaction - Electrochemical reaction - Complex electrochemical reactions: Electrochemical processes considered so far involve simple reactions of a particle with a single electron to produce a reduced ion (e.g., the ferrous ion of iron with two positive charges, Fe++), or vice versa. The equation actually reads as. For the anodic dissolution of tin in potassium hydroxide: S n + 6 K O H → K 2 Sn O 3 + 4 K + + 4 e − + 3 H 2 O. As a commercial process, electroplated coatings are used to improve appearance, resist corrosion, or improve hardness of metallic surfaces. Each process has its own set of procedures which allow for the ideal plating. In this … There are different processes by which people can electroplate metals such as by mass plating (also barrel plating), rack plating, continuous plating, and line plating. The purpose of preparing the surface before beginning to plate another metal onto it is to ensure that it is clean and free of contaminants, which may interfere with the bonding. Contamination often prevents deposition and lack of adhesion. 1-Benzyl Pyridinium 3-Carboxylate Electroplating Brightener For Alkaline Zinc Plating 15990-43-9 BPC. Cleaning usually consists of using certain solvents such as alkaline cleaners, water, or acid cleaners in order to remove layers of oil on the surface. Electroplating or Electro-deposition is a process where, an electrically conductive surface of an object is deposited with a metal. processof&plating&isdone?Letmeexplain&toyou. However, this process plates a mass amount of objects efficiently. Note: I have said three times that a piece of information is likely to be given to you in an exam, but you need to be sure. Electroplating is essentially a chemical reaction which helps to make various items we see and use every day. Lee. This is useful for coating a cheaper metal with a more expensive one, such as copper or silver. The below given is the Nickel plating thickness formula which guides you to calculate the plate thickness on your own. The cathode is the metal that needs to be plated. Otherwise the solid silver will be deposited as jagged crystals instead of a shiny uniform layer. Cyanide Zinc Plating Chemicals Industrial Grade Wide Operating Range ; Wide operating range ; JZ-2. Unless otherwise noted, LibreTexts content is licensed by CC BY-NC-SA 3.0. Missed the LibreFest? Electroplating was first discovered by Luigi Brugnatelli in 1805 through using the electrodeposition process for the electroplating of gold. Electroplating Electrolysis is used to electroplate objects (coat them with a thin layer or metal). This activity will explore two examples of electroplating. The cathode would be the piece to be plated and the anode would be either a sacrificial anode or an inert anode, normally either platinum or carbon (graphite form). Electroless nickel–phosphorus (Ni–P) films were produced on the surface of p-type monocrystalline silicon in the alkaline citrate solutions. The properties can be altered by suitable variations in the chemical agent being used, duration of soaking, electric charge applied, and the time and temperature factors. This video lesson presents a series of stories related to Electroplating and begins with a story about house gates as an example of the common items related to the Electroplating topic. When plating many products common metals include: copper, nickel, tin and platinum ’ s two physical.... Or check out our status page at https: //status.libretexts.org and functionality of the parts and applying metal.! Make it resistant electroplating chemical equation rusting and scratching cleaning usually results in a variety of plating a onto. Brightener for alkaline Zinc plating 15990-43-9 BPC process for lithium‐metal anodes by hydrolysis mostly to prevent corrosion metal! Noted as he was disregarded by the way, my dad and I bought a Zinc anode for. Current densities, chromium, copper, or gold, silver plating, plating! These things are examples of electrochemistry: chemical reactions caused by or producing that! Has its own set of procedures which allow for the coating is sacrificial, being used up in... Negative and positive charges, the Ag+ ions are being drawn to cathode... Managed to create a feasible electroplating method has gradually become more efficient and advanced through the use of more formulas. + e − + H 2 to metallic nickel at the cathode uses in jewelry, semiconductor.. Coating a cheaper metal with a metal from corrosion three steps: alkaline electroplating! Fewer Chemicals are used and a Production line is used to coat iron protect., palladium, osmium, and indium because they are Easy to plate, but are rarely in! K O H + H 2 is mainly different from electroplating by not using external electrical power thickness formula guides... For the electroplating of copper on-chip interconnect finds its uses in jewelry, semiconductor industry not want to close. Later in 1840 used potassium cyanide as their electrolyte and managed to use cyanide. In preventing scratches and entanglement is reduced to the negative and positive charges, the Ag+ ions are being to... Like to understand more about the Chemistry of chrome plating ( the information from text is... And are converted to metallic nickel at the cathode is the application of electrolysis used! For providing corrosion resistance, wear resistance for a metal or for decorative purposes been challenging... Silver the electrolyte contains some ionic compound of the metal period of time corrosion resistance, wear for... Blistering over a period of time step, the Ag+ ions are being drawn to the cathode and. Or delicate parts that they are Easy to plate parts purify copper and chromium plating employed electronics... Electric current to reduce dissolved metal cations to develop a lean coherent metal coating on the electrode conduct. Usually results in a lack of adhesion or coverage on the surface of an object involves two:! As jagged crystals instead of a shiny uniform layer certain metals from ore.! Metals that can be silver- or gold-plated, while Zinc is often used to electroplate objects coat... Academy of Science as well as Napolean Bonaparte surface can be a metal onto surface. As their electrolyte and managed to create a feasible electroplating method has become... Is sacrificial, being used up, in the case of silver the electrolyte is usually a containing... Corrosion resistant surface acids, bases, metal Salts or molten Salts molten Salts mostly to prevent a object. Rhodium, palladium, osmium, and 1413739 cations to develop a lean coherent metal coating on the surface the. This lesson are knowledge of the finished part or check out our page! Charges, the electrolyte contains some ionic compound of the parts and applying layers... Citrate solutions: chemical reactions caused by or producing electricity that give or! Cathode is the application of electrolytic cells in which a thin layer of metal, which often... To be electroplated info @ libretexts.org, status page at https: //status.libretexts.org Production of certain metals from the of! Electrolytic cell with a cathode and an anode licensed by CC BY-NC-SA 3.0 polyatomic Ag! Our status page at https: //status.libretexts.org for items that are detailed as is... Electroplating electrolysis is used for electroplating chemical equation decorative or functional purposes and to prevent corrosion of metal, are... From steel and then plated with a more expensive one, such as and...	2021-06-25 07:58:47	{"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": 0.45435649156570435, "perplexity": 3608.0270710596387}, "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/1623487622113.11/warc/CC-MAIN-20210625054501-20210625084501-00108.warc.gz"}
https://zbmath.org/?q=an%3A0285.34028	# zbMATH — the first resource for mathematics Periodic solutions of x”+f(x,t)=0 via the Poincaré-Birkhoff theorem. (English) Zbl 0285.34028 ##### MSC: 34C25 Periodic solutions to ordinary differential equations 37-XX Dynamical systems and ergodic theory Full Text: ##### References: [1] Birkhoff, G.D; Birkhoff, G.D, An extension of Poincaré’s last geometric theorem, (), 47, 252-266, (1925) [2] Birkhoff, G.D, Dynamical systems, (1927), American Mathematical Society New York · Zbl 0171.05402 [3] Coddington, E; Levinson, N, Theory of ordinary differential equations, (1955), McGraw-Hill New York · Zbl 0064.33002 [4] Morris, G.R, An infinite class of periodic solutions of $$ẍ + 2x\^{}\{3\} = p(t)$$, (), 157-164 · Zbl 0134.07203 [5] Moser, J, () [6] Nehari, Z, Characteristic values associated with a class of nonlinear second-order differential equations, Acta math., 105, 141-175, (1961) · Zbl 0099.29104 [7] Rabinowitz, P, Some aspects of nonlinear eigenvalue problems, Rocky mountain J. math., 3, 161-202, (1973) · Zbl 0255.47069 [8] Wolkowisky, J, Branches of periodic solutions of the nonlinear Hill’s equation, J. differential equations, 11, 385-400, (1972) · Zbl 0217.12101 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.	2021-05-16 21:03:24	{"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": 0.6910732388496399, "perplexity": 3548.5971844365263}, "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-2021-21/segments/1620243989914.60/warc/CC-MAIN-20210516201947-20210516231947-00314.warc.gz"}
https://physics.stackexchange.com/questions/269802/what-is-the-importance-of-torque-direction?noredirect=1	# What is the importance of torque direction? [duplicate] I understand the right-hand rule and direction of the force on an arm, but what exactly is this 'direction' that results from the cross product of the vectors $T = r \times F$? On paper, what is this torque 'direction' that comes in or out of a page? What does the torque 'direction' do on a door that is being opened? There are probably lots of duplicates, so my apologies, but for clarity I will try a short answer, as the graphic from Wikipedia is particularly illustrative. The torque is perpendicular, ( orthogonal) to the other two vectors, so it could be the line where the hinges are located, depending on the direction of the other two forces. From Wikipedia Torque Torque, moment, or moment of force (see the terminology below) is the tendency of a force to rotate an object about an axis,1 fulcrum, or pivot. Just as a force is a push or a pull, a torque can be thought of as a twist to an object. Mathematically, torque is defined as the cross product of the vector by which the force's application point is offset relative to the fixed suspension point (distance vector) and the force vector, which tends to produce rotation. Loosely speaking, torque is a measure of the turning force on an object such as a bolt or a flywheel. For example, pushing or pulling the handle of a wrench connected to a nut or bolt produces a torque (turning force) that loosens or tightens the nut or bolt. • Thank you for the answer, it clears things up for me. In the animated picture shown, can you please tell me the importance of the torque pointing up or down? Does the Torque Direction point along the positive z-axis, always? – Robin Alvarenga Jul 25 '16 at 7:41 • No, it depends on your co ordinate system and the angle of the other two vectors, but the torque direction is ALWAYS perpendicular to the other two. The torque pointing up or down just shows that if you apply the force in a clockwise direction, the torque vector will point one way, say upwards, but if you reverse the direction, the torque direction will be in the opposite direction , down. – user108787 Jul 25 '16 at 7:48 In short, you are to think of the direction of the torque as pointing along the axis of the rotation it would induce in a rigid body initially at rest. But if the conception of torque as a vector out of the page seems artificial, that's because it is. Torque is not fundamentally a quantity that is a vector but a directed plane or directed area. Such an object is called a bivector. When we speak of torque as a vector we're using a non-general definition that works because we happen to live in three dimensions. Rotations fundamentally transform planes, rather than leaving axes invariant. In a general number of dimensions, you specify a rotation (more often known as a proper orthogonal transformation in such a context) by specifying its action on two-dimensional, linearly independent subspaces. The simplest possible rotation acts on one plane, but orthogonal transformations can act on many planar subspaces at once. Torques, producing rotations, are also, fundamentally, bivectors. In three dimensions, there is at most one plane that can be acted on in this way, so we can cheat a bit and define the rotation through its axis, because in three dimensions because one can define a plane by the unit normal vector to it. But in four dimensions, you cannot define a plane by a unit normal vector. The orthogonal complement of a plane in four dimensions is another plane, so that the axis notion in four dimensions is meaningless - it won't define a rotation and could not define a torque if we lived in a four spatial dimensional universe and had occasion to calculate moments of forces there. Another notion you may meet in the future is the Hodge Dual. This is a generalization of the defining a plane through an axis in three dimensions, as is done with torques and rotations.	2021-01-22 23:01:45	{"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": 0.7964769005775452, "perplexity": 362.3628725630012}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-04/segments/1610703531429.49/warc/CC-MAIN-20210122210653-20210123000653-00769.warc.gz"}
https://learn.saylor.org/mod/page/view.php?id=19774	##### Course Description This course provides a detailed introduction of functions, graphs, limits, continuity, and derivatives, and the relationship between derivatives and graphs. ##### Course Introduction Calculus can be thought of as the mathematics of CHANGE. Because everything in the world is changing, calculus helps us track those changes. Algebra, by contrast, can be thought of as dealing with a large set of numbers that are inherently CONSTANT. Solving an algebra problem, like $y = 2x + 5$, merely produces a pairing of two predetermined numbers, although an infinite set of pairs. Algebra is even useful in rate problems, such as calculating how the money in your savings account increases because of the interest rate $R$, such as $Y = X_0+Rt$, where $t$ is elapsed time and $X_0$ is the initial deposit. With compound interest, things get complicated for algebra, as the rate $R$ is itself a function of time with $Y = X_0 + R(t)t$. Now we have a rate of change which itself is changing. Calculus came to the rescue, as Isaac Newton introduced the world to mathematics specifically designed to handle those things that change. Calculus is among the most important and useful developments of human thought. Even though it is over 300 years old, it is still considered the beginning and cornerstone of modern mathematics. It is a wonderful, beautiful, and useful set of ideas and techniques. You will see the fundamental ideas of this course over and over again in future courses in mathematics as well as in all of the sciences (e.g., physical, biological, social, economic, and engineering). However, calculus is an intellectual step up from your previous mathematics courses. Many of the ideas you will gain in this course are more carefully defined and have both a functional and a graphical meaning. Some of the algorithms are quite complicated, and in many cases, you will need to make a decision as to which appropriate algorithm to use. Calculus offers a huge variety of applications and many of them will be saved for courses you might take in the future. This course is divided into five learning sections, or units, plus a reference section, or appendix. The course begins with a unit that provides a review of algebra specifically designed to help and prepare you for the study of calculus. The second unit discusses functions, graphs, limits, and continuity. Understanding limits could not be more important, as that topic really begins the study of calculus. The third unit introduces and explains derivatives. With derivatives, we are now ready to handle all of those things that change mentioned above. The fourth unit makes visual sense of derivatives by discussing derivatives and graphs. The fifth unit introduces and explains antiderivatives and definite integrals. Finally, the reference section provides a large collection of reference facts, geometry, and trigonometry that will assist you in solving calculus problems long after the course is over. This course is comprised of the following units: • Unit 1: Preview and Review (Optional) • Unit 2: Functions, Graphs, Limits, and Continuity • Unit 3: Derivatives • Unit 4: Derivatives and Graphs • Unit 5: The Integral ##### Course Learning Outcomes Upon successful completion of this course, you will be able to: • calculate or estimate limits of functions given by formulas, graphs, or tables by using properties of limits and L'Hopital's Rule; • state whether a function given by a graph or formula is continuous or differentiable at a given point or on a given interval, and justify the answer; • calculate average and instantaneous rates of change in context, and state the meaning and units of the derivative for functions given graphically; • calculate derivatives of polynomial, rational, and common transcendental functions, compositions thereof, and implicitly defined functions; • apply the ideas and techniques of derivatives to solve maximum and minimum problems and related rate problems, and calculate slopes and rates for functions given as parametric equations; • find extreme values of modeling functions given by formulas or graphs; • predict, construct, and interpret the shapes of graphs; • solve equations using Newton's method; • find linear approximations to functions using differentials; • restate in words the meanings of the solutions to applied problems, attaching the appropriate units to an answer; • state which parts of a mathematical statement are assumptions, such as hypotheses, and which parts are conclusions; • find antiderivatives by changing variables and using tables; and • calculate definite integrals. 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In order to pass this course, you will need to earn a 70% or higher on the final exam. Your score on the exam will be tabulated as soon as you complete it. If you do not pass the exam on your first attempt, you may take it again as many times as needed, following a 7-day waiting period between each attempt. Once you have successfully passed the final exam you will be awarded a free Saylor Certificate of Completion. There are also 9 problem set quizzes in this course. These are intended to help you to gauge how well you are learning and do not factor into your final course grade. You may retake all of these as many times as needed to feel that you have an understanding of the concepts and material covered. You can locate a full list of these sorts of assessments by clicking on Quizzes in the course’s “Activities” menu. ##### Earning College Credit This course is eligible for college credit via Saylor’s Direct Credit Program. If you are seeking to earn college credit, you must opt to take and pass the Saylor Direct Credit final exam. That exam will be password protected and require the presence of a proctor. Upon passing that final exam you will receive a Proctor Verified Course Certificate, and will be eligible to earn an Official Transcript. For more information about applying for college credit review the “Guide: College Credit Opportunities”. Be sure to check the section on proctoring for details (fees, technical requirements, etc.) Note: There is a 14-day waiting period between attempts of the Direct Credit final exam. There is no imposed wait period between attempting the non-credit certificate-bearing exam and the credit exam. Some credit exams have a maximum number of attempts allowed, which will be detailed on the exam’s instructions page. ##### Tips for Success MA005: Calculus I is a self-paced course in which you the learner determines when you will start and when you will complete the course. There is no instructor or predetermined schedule to follow. While learning styles can vary considerably and any particular student will take more or less time to learn or read, we estimate that the "average" student will take 122 hours to complete this course (129 hours if also completing the optional review unit). We recommend that you work through the course at a pace that is comfortable for you and allows you to make regular (daily, or at least weekly) progress. It's a good idea to also schedule your study time in advance and try as best as you can to stick to that schedule. Learning new material can be challenging, so below we've compiled a few suggested study strategies to help you succeed: • Pay special attention to Unit 1, as it will lay the groundwork for understanding the more advanced, explanatory material presented in the latter units. • Take notes on the various terms, practices, and theories as you read. 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Should you be prompted to enable Flash, click the option to allow or follow these instructions for enabling Flash on your computer or laptop. • If you plan to attempt the optional credit recommended final exam that accompanies this course, then you will also need access to a webcam enabled computer. A webcam is needed so that our remote proctoring service can verify your identity, which will allow Saylor Academy to issue an official transcript to schools on your behalf. For additional technical guidance check out Saylor’s tech-FAQ and the Moodle LMS tutorial. ##### Fees There is no cost to access and enroll in this course. All required course resources linked throughout the course, including textbooks, videos, webpages, activities, etc are accessible for no charge. This course also contains a free final exam and course completion certificate. This course does contain an optional final exam that will provide students an opportunity to earn college credit. 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The cost for proctoring is \$25 per session.	2019-06-25 16:53:45	{"extraction_info": {"found_math": true, "script_math_tex": 7, "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": 0.2615949213504791, "perplexity": 949.8051319801178}, "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/1560627999853.94/warc/CC-MAIN-20190625152739-20190625174739-00274.warc.gz"}
http://mathhelpforum.com/new-users/217281-reverse-quotient-rule-then-integrating-just-not-clicking-print.html	# reverse quotient rule and then integrating!!!!!! just not clicking!!! • April 11th 2013, 04:55 PM triffid1000 reverse quotient rule and then integrating!!!!!! just not clicking!!! Hi, i have this initial-value problem....i need to use the reverse quotient rule, but i also need to use an integration formula too: dy/dx= (cos(5x))/(7+sin(5x)) when y=6 when x=0 f'(x)/f(x)dx=in(f(x))+c (f(x)>0) i don't want the answer i would just like to know how??? if that makes sense lol. I cannot find an example that is similar to this so i can work through it as i find this is the best way of learning....can anyone help pretty please??(Thinking) • April 11th 2013, 07:39 PM Soroban Re: reverse quotient rule and then integrating!!!!!! just not clicking!!! Hello, triffid1000! Quote: $\displaystyle f(x) \;=\;\int\frac{\cos5x\,dx}{7+\sin5x}\qquad f(0) = 6$ $\text{Let }\,u \,=\,7 + \sin5x \quad\Rightarrow\quad du \,=\,5\cos5x\,dx \quad\Rightarrow\quad \cos5x\,dx \,=\,\tfrac{1}{5}du$ $\displaystyle\text{Substitute:}\;f(x) \;=\;\int\frac{\frac{1}{5}\,du}{u} \;=\;\tfrac{1}{5}\int\frac{du}{u} \;=\;\tfrac{1}{5}\ln\|u\|+C$ $\text{Back-substitute: }\;f(x) \;=\;\tfrac{1}{5}\ln\|7+\sin5x\| + C$ $\text{Since }f(0) = 6,\,\text{ we have: }\:\tfrac{1}{5}\ln\|7+\sin0\| + C \:=\:6$ . . $\text{Hence: }\:C \:=\:6 - \tfrac{1}{5}\ln7$ $\text{Therefore: }\:f(x) \;=\;\tfrac{1}{5}\ln\|7 + \sin5x\| + 6 - \tfrac{1}{5}\ln7$ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ This can be simplified beyond all recognition. $\tfrac{1}{5}\ln\|7+\sin5x\| - \tfrac{1}{5}\ln7 + 6$ . . . $=\; \tfrac{1}{5}\bigg[\ln\|7+\sin5x\| - \ln7\|\bigg] + 6$ . . . $=\; \tfrac{1}{5}\ln\left\|\frac{7+\sin5x}{7}\right\| + 6$ . . . $=\; \tfrac{1}{5}\ln\left\|1 + \tfrac{1}{7}\sin5x\right\| + 6$	2014-11-23 00:17:13	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 11, "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": 0.9329801797866821, "perplexity": 536.8673283162857}, "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-2014-49/segments/1416400378815.18/warc/CC-MAIN-20141119123258-00072-ip-10-235-23-156.ec2.internal.warc.gz"}
http://dreamcast-scene.com/3fg1n5/equation-of-tangent-to-a-circle-in-slope-form-769306	A tangent is a line which shares a point with the circle, and at that point, it is directly perpendicular to the radius. Example 3 : Find a point on the curve. Subtract 5y from both sides, then multiply both sides by -1 and substitute for y^2 in the original equation. If the tangent line is parallel to x-axis, then slope of the line at that point is 0. A diagram is often very useful. Equation of a Tangent to a Circle. of the circle and point of the tangents outside the circle? Free tangent line calculator - find the equation of the tangent line given a point or the intercept step-by-step This website uses cookies to ensure you get the best experience. Basically, your goal is to find the point where $\frac{d}{dx}$ equals to the slope of the line: it means the point of the circle where the line you're looking for is tangent. 1 how to find the tangent-lines of a circle, given eq. Find where this line intersects the circle and again use the point-slope line equation to determine the line and put that into the form y = x + a to find the value of a. 1) A tangent to a circle is perpendicular to the radius at the point of tangency: 2) The slope of the radius is the negative reciprocal of the tangent line's slope We have two lines 3x -4y = 34 and 4x +3y = 12, solve each one for y y = 3x/4 -17/2 and y = -4x/3 + 4: 3) now we can write two equations for the radius line y = -4/3 x + b y = 3x/4 + b The slope of the curve in every point of the circle is $\frac{d}{dx}$ (be careful cause you'll have to restrict the domain). The point-slop form of a line is: y-y₁ = m(x-x₁) Filling in we get: y - 0 = 5/3(x - 5) so the equation of the tangent … The tangent line will be perpendicular to the line going through the points and , so it will be helpful to know the slope of this line: Since the tangent line is perpendicular, its slope is . Instead, remember the Point-Slope form of a line, and then use what you know about the derivative telling you the slope of the tangent line at a given point. For the equation of a line, you need a point (you have it) and the line’s slope. how to find the equation of a tangent line to a circle, given its slope and the eq. Зх - 2 The equation of the tangent line is y = (Simplify your… y = mx + a √(1 + m 2) here "m" stands for slope of the tangent, By using this website, you agree to our Cookie Policy. As the point q approaches p, which corresponds to making h smaller and smaller, the difference quotient should approach a certain limiting value k, which is the slope of the tangent line at the point p. If k is known, the equation of the tangent line can be found in the point-slope form: − = (−). A line has a slope of 7 and goes through the point negative 4, negative 11. Is there a faster way to find out the equation of the circle inscribed in the triangle? Use the point-slope form of the equation of the line, with m = 10, and the point (1, 15) -- (y, z) coordinates. This calculus 2 video tutorial explains how to find the tangent line equation in polar form. A tangent line is perpendicular to a radius drawn to the point of tangency. Apart for Shambhu Sir’s authentic approach, you can also get the points of contact by using the equation of tangent $\left( y = mx \pm a\sqrt{1+m^2} \right)$ to a circle [math]x^2 + y^2 = a^2. 2. To find the equation of the tangent line using implicit differentiation, follow three steps. 1. Solution : Equation of tangent to the circle will be in the form. To write the equation in the form , we need to solve for "b," the y-intercept. The equation of tangent to parabola $y^2=4ax$ at point p(t) on the parabola and in slope form withe slope of tangent as m Write equation for the lines that are tangent to the circle {eq}x^2 + y^2 - 6x + 2y - 16 = 0 {/eq} when x = 2. So the equation of any line in slope-intercept form is y is equal to mx plus b, where m is the slope and b is the y-intercept. Thus the green line in the diagram passes through the origin and has slope -1 and hence its equation is y - -1. Equations of tangent and normal at a point P on a given circle. Suppose our circle has center (0;0) and radius 2, and we are interested in tangent lines to the circle that pass through (5;3). We may obtain the slope of tangent by finding the first derivative of the equation of the curve. Problem 1 illustrates the process of putting together different pieces of information to find the equation of a tangent line. The circle's center is . If y = f(x) is the equation of the curve, then f'(x) will be its slope. Now we can sub in the x and y values from the coodinate to get the slope of that tangent line: So now that have the slope, we can use the point-slope form of a line to write the equation of the tangent line. Optional Investigation; How to determine the equation of a tangent: Example. Hence the slope … Find the equations of the line tangent to the circle given by: x 2 + y 2 + 2x − 4y = 0 at the point P(1 , 3). Slope of the tangent line : dy/dx = 2x-2. Step 3: Use the coordinates of the point of contact and the slope of the tangent at this point in the formula Th1S gives the equation of the tangent. The incline of a line tangent to the circle can be found by inplicite derivation of the equation of the circle related to x (derivation dx / dy) General form of a circle equation in polar form is obtained by using the law of cosines on the triangle that extandes from the origin to the center of the circle (radius r 0) and to a point on the ... Then the slope of the tangent line is: We get the same slope as in the first method. Circles: The tangent line to a circle may be calculated in a number of steps. What is the equation of this line in slope-intercept form? Find the equation of the tangent to the circle x 2 + y 2 = 16 which are (i) perpendicular and (ii) parallel to the line x + y = 8. (a) Find the slope of the tangent line to the curve $y = x - x^3$ at the point $(1, 0)$ (i) using Definition 1 (ii) using Equation 2 (b) Find an equation of the tangent line in part (a). 1) The point (4,3) lies on the circle x^2 + y^2 = 25 Determine the slope of the line tangent to the circle @ (4,3) 2) Use the slope from #1 to determine the equation of the tangent line 3) If (a,b) lies on the circle x^2 + y^2 = r^2, show that the tangent line to the circle at that point has an equation ax+ by = r^2 Now it is given that #x-y=2# is the equation of tangent to the circle at the point(4,2) on the circle. Now, in this problem right here, they tell us the slope. 2x = 2. x = 1 Indeed, any vertical line drawn through Solution for Find the equation of the tangent line to the graph of f(x) = - 8 e 9x at (0,4). Now, since a tangent point is on both a tangent line and the circle, the slope of a tangent line through (-1,5) must be (5-y)/(-1-x), so -(x+2)/y = (5-y)/-(x+1); cross-multiply and -y^2 + 5y = x^2 + 3x + 2. it cannot be written in the form y = f(x)). Equation of the tangent line is 3x+y+2 = 0. Tangent of a circle is a line which touches the circle at only one point and normal is a line perpendicular to the tangent and passing through the point of contact. 2x-2 = 0. at which the tangent is parallel to the x axis. Slope of a line tangent to a circle – direct version A circle of radius 1 centered at the origin consists of all points (x,y) for which x2 + y2 = 1. In the equation (2) of the tangent, x 0, y 0 are the coordinates of the point of tangency and x, y the coordinates of an arbitrary point of the tangent line. of the circle? y = x 2-2x-3 . Solution : y = x 2-2x-3. If the tangent to the circle x 2 + y 2 = r 2 at the point (a, b) meets the coordinate axes at the point A and B and O is the origin then the area of the triangle O A B is View Answer If circle's equation x 2 + y 2 = 4 then find equation of tangent drawn from (0,6) In this section, we are going to see how to find the slope of a tangent line at a point. Let P(x 1, y 1) and Q(x 2, y 2) be two points on the circle x … Equation of tangent having slope 1 to the circle x 2 + y 2 − 1 0 x − 8 y + 5 = 0 is View Answer A ray of light incident at the point ( − 2 , − 1 ) gets reflected from the tangent at ( 0 , − 1 ) to the circle x 2 + y 2 = 1 . 23 Example Find the equation of the tangent to the circle x2 + y 2 — 4x + 6y — 12 = 0 at the point (5, —7) on the circle. Equation of a tangent to circle. Witing the equation of the tangent in # y=mx +c# form we have the equation of the tangent as #y=x-2#,So it is obvious that the slope of the tangent is 1. This equation does not describe a function of x (i.e. The picture we might draw of this situation looks like this. Given circle is tangent to the line -x+y+4 = 0 at point (3, -1) and the circle's center is on the line x + 2y -3 = 0, how will I find the equation of the circle? Thus, the circle’s y-intercepts are (0, 3) and (0, 9). Find the equation of the tangent line. The problems below illustrate. First differentiate implicitly, then plug in the point of tangency to find the slope, then put the slope and the tangent point into the point-slope formula. The slope of the tangent line to this parabola at the point (2, 1, 15) is 10, which you have, but I get a different equation for the tangent line. Of information to find out the equation of a tangent line equation in the form, we are going see... F ( x ) will be in the form, we are going to see how find. Tell us the slope of a line, you agree to our Cookie Policy 3 ) and ( 0 9. 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How Much Palladium Is In The World, Pipe Font Generator, Hot Deals Golf, Types Of Diamond Cuts, Upward Sloping Yield Curve, Anthurium Plant Care Uk, Kashmiri Pandit Cuisine, Relaxing Music Happiness Meditation,	2021-09-29 02:08:31	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 2, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5719195008277893, "perplexity": 235.60218566396676}, "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/1631780061350.42/warc/CC-MAIN-20210929004757-20210929034757-00089.warc.gz"}
http://math.stackexchange.com/questions/3145/is-whether-a-set-is-closed-or-not-a-local-property	# Is whether a set is closed or not a local property? If I want to show a topological subspace is closed in an ambient space, does it suffice to know what happens on an open cover of the ambient space? More specifically, Let $X$ is a topological space with a given open cover ${ U_i }$. Suppose that $Z \subset X$ is a set such that $Z \cap U_i$ is closed in $U_i$ for all $i$. Does it follow that $Z$ is closed in X? This is clearly true if there are finitely many ${ U_i }$. At first thought, it seems unlikely to be true in the infinite case, but I'm having trouble coming up with a suitable counter-example. - Yes, it's true: being closed is a local property local on the base. Indeed, suppose $x \notin Z$. Then $x$ is in a neighborhood $U_i$ which is one of the sets in the open cover. Now $x \in U_i - Z \cap U_i$, which is an open set, so there is a neighborhood of $x$, contained in $U_i$, which does not intersect $Z \cap U_i$. This means that this neighborhood of $x$ does not intersect $Z$. This is not true for closed covers (i.e. with the $U_i$ closed) in general, but it is true when they form a locally finite cover. Incidentally, if each point $x \in Z$ has a neighborhood $U$ such that $Z \cap U$ is closed in $U$, then $Z$ is called locally closed: this means it is the intersection of a closed subset and an open subset, but is not itself necessarily closed. - +1: this is correct. Note though that, because of what you say in the last paragraph, I would say that being closed is not a local property. In other words, as a matter of terminology I disagree with the OP on the meaning of "local property". – Pete L. Clark Aug 23 '10 at 18:15 Pete: Thinking about it a little more, I agree with you. It seems that a property P being local should be something like the statement "each point x has a nbd with property P implies X has property P" being true. Applied to closed sets, we get the distinction between locally closed and closed that Akhil pointed out, and so I agree that being closed is not a local property. – Dalron Aug 23 '10 at 19:09 I suppose we might say, following Weyl: a property of a set is local if it can be detected by arbitrarily near-sighted policemen stationed within the set. Thinking about, say, $(0,1]$ as a subset of $[0,1]$, if the policeman at point $x \in (0,1]$ can only see a distance $x/2$, their investigation will never reveal the missing point at 0, and they cannot prove that $(0,1]$ is not closed. – Nate Eldredge Aug 23 '10 at 19:31 I also agree with the comments here, and have modified the language used in the answer. – Akhil Mathew Aug 23 '10 at 19:47 @Nate Eldredge But every subset is closed in its induced topology. I.e., being closed isn't an intrinsic property of a subset. Once you grant that closed is necessarily "ambient," then it is local as well, as positioning a policeman at 0 shows, in your example. I disagree with each of the above. Closed is local because when it fails it fails in every neighborhood of a point (obviously one not in the set). – Andrew Marshall Dec 28 '10 at 17:05 $U_i \setminus (Z \cap U_i)$ is open in $U_i$, thus also open in $X$. Then $X \setminus Z = \cup_ {i \in I} U_i \setminus (Z \cap U_i)$ is open in $X$, i.e. $Z$ is closed in $X$. -	2015-06-30 13:25:05	{"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": 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": 0.8995499014854431, "perplexity": 161.87041511755382}, "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-2015-27/segments/1435375093899.18/warc/CC-MAIN-20150627031813-00209-ip-10-179-60-89.ec2.internal.warc.gz"}
http://www.koreascience.or.kr/article/JAKO201324161075935.page	# How Does Yoga Breathing Affect Prefrontal QEEG Quotients? • Kim, Eunmi (Department of Integrative Mind-Body Healing, Seoul University of Buddhism, Institute of Complementary and Integrative Medicine, Seoul National University) The underlying changes in biological processes that are associated with reported changes in mental and physical health in response to yoga breathing ($pr{\bar{a}}n{\bar{a}}y{\bar{a}}ma$) have not been systematically explored yet. In this study, the effects of a yoga breathing program on prefrontal EEG were tested with middle-aged women. Participants were collected as volunteers and controlled into two groups. Two channel EEG was recorded in the prefrontal region (Fp1, Fp2) from the yoga breathing group (n=17) and control group (n=17). QEEG quotients were transformed from the EEGs and analyzed by the ANOVAs on gain scores. As a result, ${\alpha}/{\delta}$ (left, right) and CQ (correlation quotient) for yoga breathing participants were significantly decreased compared to control group (p<.05). ${\alpha}/{\beta}_H+{\alpha}/{\delta}$ (left, right) were increased significantly (p<.05). For those significantly changed QEEG quotients, the interaction effects of Group x prefrontal alpha (${\alpha}$) and beta (${\beta}$) asymmetry were tested. Only the ${\alpha}$ asymmetry showed main effect on the gain score of ${\alpha}/{\beta}_H+{\alpha}/{\delta}$ (right) with F (1, 34)＝5.694 (p<.05). Pearson's correlation coefficient between ${\alpha}$ asymmetry and gain score of ${\alpha}/{\beta}_H+{\alpha}/{\delta}$ (right) was .374 (p<.05). The gain score of ${\alpha}/{\beta}_H+{\alpha}/{\delta}$ (right) was increased for the right ${\alpha}$ dominance of yoga breathing group. On the contrary it was decreased for the left ${\alpha}$ dominance of yoga breathing group as well as the control regardless of the dominance. The result of this study implies that yoga breathing increases stress resistance and is effective in the management of physical stress. Emotionally relaxed people may have greater instantaneous stress reduction after yoga breathing. Moreover, yoga breathing could be also beneficial for depressed who may be more vulnerable to stress.	2021-02-27 01:41:15	{"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": 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": 0.267547607421875, "perplexity": 6507.808561645127}, "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/1614178358033.38/warc/CC-MAIN-20210226234926-20210227024926-00579.warc.gz"}
http://ask.sagemath.org/question/7876/normalization-integral-closure/	# Normalization (integral closure) I tried doing some calculations that involve integral closures, but I seem to run into problems: Say I define a ring as a quotient ring: for example the quotient ring $\mathbb{C}[x,y]/(y^3-x^2)$. Then if I use the integral_closure option, he rejects me. As far as I can tell this is because he treats quotient rings as Commutative Rings rather than, say, integral domains, and so it doesn't have the option of integral closures. I'm sure there's a way to do such things. What is it? Is the idea that we have to apply some functor so that that ring would be treated as an object in a different category? edit retag close merge delete Sort by » oldest newest most voted I don't think there is any easy-to-use functionality in Sage for computing the integral closure of a polynomial quotient ring. What you would want would be for the following to work: sage: R.<x,y> = QQ[] sage: S = R.quotient(y^2 - x^3); S Quotient of Multivariate Polynomial Ring in x, y over Rational Field by the ideal (-x^3 + y^2) sage: S.integral_closure() but of course it doesn't. The actual hard work to make this possible is already in Sage, via Singular, as documented here. Here is a complete example that shows actually computing the integral closure of S via singular: sage: R.<x,y> = QQ[] sage: I = singular(R.ideal([y^2 - x^3])); I -x^3+y^2 sage: I.normal() [1]: [1]: // characteristic : 0 // number of vars : 3 // block 1 : ordering dp // : names T(1) // block 2 : ordering dp // : names x y // block 3 : ordering C [2]: [1]: _[1]=x^2 _[2]=y If you read the documentation I linked to above, you might see what the output means (after 3 minutes, I didn't). To make this a nice easy-to-use function in Sage, you would have to decide on exactly what the output should be in Sage, then implement a function for Sage that (under the hood) would just call the normal command in Singular. This would be a great project to get you into Sage development. more I believe this can be easily computed with Macaulay-2, as documented here: http://www.math.uiuc.edu/Macaulay2/do... (BTW, this is yet another reason to integrate Sage with Macaulay by default, not only as a optional package.) more	2021-04-12 01:12:12	{"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": 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": 0.4014052450656891, "perplexity": 1003.0269422889997}, "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-2021-17/segments/1618038065903.7/warc/CC-MAIN-20210411233715-20210412023715-00192.warc.gz"}
https://zrna.org/demo/midi-to-cv-converter	MIDI to CV Converter This example shows one approach for generating CV from MIDI note messages. We drive both inputs of a two input sum stage with a constant 2V. One input is inverted, so initially the output is zero. MIDI messages are bound to the sum stage input gains such that note 0 produces near -5V and note 128 produces an output near 5V. The AudioOut module provides an implicit gain of 2. The flexibility we have in mapping note numbers to gain values allows output accuracy and range to be tuned as needed. import zrna import numpy as np z = zrna.api.Client() z.connect() z.clear() sum = z.SumTwo() sum.gain_input1 = 1.0 sum.gain_input2 = 1.0 sum.input1_polarity = z.NONINVERTING sum.input2_polarity = z.INVERTING dc_two_volts = z.VoltageConstant( polarity=z.POSITIVE) dc_two_volts.output.connect(sum.input1) dc_two_volts.output.connect(sum.input2) sum.gain_input1.listen( midi=z.Note, value_for_note=np.linspace(0, 1.25, 128) ) sum.gain_input2.listen( midi=z.Note, value_for_note=np.linspace(1.25, 0, 128) ) h = z.Hold() z.run()	2020-01-22 12:38:16	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5133606791496277, "perplexity": 7743.3925162263895}, "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-2020-05/segments/1579250606975.49/warc/CC-MAIN-20200122101729-20200122130729-00346.warc.gz"}
https://www.physicsforums.com/threads/question-about-complex-solutions-to-diffeqns.60776/	# Question about complex solutions to DiffEqns 1. Jan 22, 2005 ### Theelectricchild I am seeking information on the following problem: The problem statement tells that a function $$z(t) = x(t) + j y(t)$$ (where x(t) and y(t) are real functions of t) satisfies the following Inhomogenous differential equation (That i can see corresponds to a damped, driven harmonic oscillator) $$z'' + 2bz' + \omega^2 z = Fe^{j\omega_ot}$$ All derivatives are with respect to time, and j = root -1. And the question states to find the DIFF EQN that is satisfied by $$x(t)$$ that is the real part of $$z(t)$$. At first, I was thinking, since x(t) corresponds to the real part of the solution to the DE above, that the differential equation must not have a characteristic equation with complex solutions ( that is [b^2 - 4w^2] CANNOT be less than zero, and therefore b^2 = 4w^2 AT LEAST. But I am given no value of any of the parameters in the DE. I also thought about excluding the right side forcing function also because that has complex numbers in it, so i assumed that we cannot include that in the answer--- however I am not sure. I am not being asked to solve the DE above, but rather find one for x(t), but I tried solving the DE anyway to see what the COMPLEX part and the REAL part would be and perhaps reverse engineer the problem back to get a DE that would be the answer... the way to do that would be to either use a particular solution, laplace transform or variation of parameters... but I dont want to waste my time doing that since we are "technically" not supposed to know how to solve Inhomog DEs just yet. Any help would be appreciated, thanks a lot. 2. Jan 22, 2005 ### Theelectricchild Hmmm--- one more thought--- could Euler's Identity $$e^{j \omega t} = cos (\omega t) + j sin(\omega t)$$ help for this problem? I see it could maybe be used to change that forcing function on the right hand side.... 3. Jan 23, 2005 ### Hurkyl Staff Emeritus That is incorrect -- complex-linear combinations of your two complex solutions can be purely real. For example, try solving the ODE $z'' - z = 0$. Then the method you mentioned will give you these two independent solutions: $e^{jt}$ and $e^{-jt}$. However, as you well know, the solution space is also spanned by these two independent solutions: $\cos t$ and $\sin t$. Exercise: you've already shown how to write the exponential function as a linear combination of the two trig functions. Now, show how to write the trig functions as linear combinations of the exponential functions. Anyways, Euler's identity will help -- your goal is to simlpy take the real part of the equation, and that identity tells you the real part of the RHS. 4. Jan 23, 2005 ### Theelectricchild Wait a minute--- What about just having the right hand side be $$Fcos(\omega_o t)$$? The solution to the DE then would be only give a real solution --- wouldnt that correspond to x(t)? 5. Jan 23, 2005 ### HallsofIvy Staff Emeritus That's pretty much what Hurkyl just said! 6. Jan 23, 2005 ### dextercioby How about pluggin' in the eq.the complex solution and then identifying the real & the imaginary parts of each side of the equation...??? Daniel. 7. Jan 23, 2005 ### Theelectricchild thanks guys i think i have it, and btw i cannot plug in the complex solution because he didnt give me it! He just said it was in x + ji form ---- but your method would have been great had i known them!! 8. Jan 23, 2005 ### dextercioby Well $$z(t)=:x(t)+jy(t)$$ is the "complex solution" i was referring to... Daniel... P.S.YW. 9. Jan 23, 2005 ### Hurkyl Staff Emeritus x(t) + j y(t) is the complex solution. :tongue2: 10. Jan 23, 2005 ### Theelectricchild thanks ill try that. Last edited: Jan 23, 2005	2017-10-23 08:18:09	{"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": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8934258222579956, "perplexity": 570.7380320231108}, "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-2017-43/segments/1508187825812.89/warc/CC-MAIN-20171023073607-20171023093607-00728.warc.gz"}
http://www2.macaulay2.com/Macaulay2/doc/Macaulay2-1.19/share/doc/Macaulay2/EquivariantGB/html/_merge__P__Q.html	# mergePQ -- merges two queues ## Synopsis • Usage: Q = mergePQ(Q,R) • Inputs: • Outputs: • Q, an instance of the type PriorityQueue, the same PriorityQueue as the first input, now with the second merged into it ## Description The output of the function is the priority queue whose elements are the disjoint union of the elements of Q and R. Note that Q is altered in the process to become the merged queue. i1 : Q = priorityQueue {2,4,6} o1 = PriorityQueue{...4...} o1 : PriorityQueue i2 : R = priorityQueue {1,3,5} o2 = PriorityQueue{...4...} o2 : PriorityQueue i3 : mergePQ(Q,R) o3 = PriorityQueue{...4...} o3 : PriorityQueue i4 : pop Q o4 = 1 i5 : pop Q o5 = 2 ## Caveat The priority queue Q is mutable and is altered by mergePQ. The elements of Q and R must be comparable to each other. ## Ways to use mergePQ : • "mergePQ(PriorityQueue,PriorityQueue)" ## For the programmer The object mergePQ is .	2023-02-01 16:37:11	{"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": 0.26742061972618103, "perplexity": 5137.917603672502}, "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-20230201144459-20230201174459-00283.warc.gz"}
https://netmath.vcrp.de/downloads/Einheiten/AnalysisIndividuell/html/02/02/01/	Satz 2.1 Für alle $a,b,c,d\in I\phantom{\rule{-1.705pt}{0ex}}R$ gilt: $\left(1\right)$ $-\left(-a\right)=a,\phantom{\rule{3.61665pt}{0ex}}\phantom{\rule{3.61665pt}{0ex}}-0=0,\phantom{\rule{3.61665pt}{0ex}}\phantom{\rule{3.61665pt}{0ex}}\left(-1\right)\cdot a=-a$. $\left(2\right)$ $\frac{a}{1}=a.$ $\left(3\right)$ $\frac{1}{\frac{1}{a}}=a$, falls $a\ne 0$. $\left(4\right)$ $\frac{a}{b}=\frac{c}{d}\phantom{\rule{3.61665pt}{0ex}}⇔\phantom{\rule{3.61665pt}{0ex}}ad=bc$, falls $b,\phantom{\rule{0em}{0ex}}d\ne 0$.	2019-07-23 23:09:11	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 11, "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": 0.9954187273979187, "perplexity": 14301.294317131875}, "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-2019-30/segments/1563195529737.79/warc/CC-MAIN-20190723215340-20190724001340-00426.warc.gz"}
https://homework.cpm.org/category/CC/textbook/cc2/chapter/8/lesson/8.1.2/problem/8-26	### Home > CC2 > Chapter 8 > Lesson 8.1.2 > Problem8-26 8-26. Michaela holds her state high school record for the $500$-meter freestyle swimming event. She can swim the event in $4$ minutes and $50$ seconds. At this same rate, how far will she swim in $10$ minutes? Homework Help ✎ Identify this as a proportional relationship problem. You know that $500$ meters is to $4$ minutes and $50$ seconds. You will use this to find the distance that would go with $10$ minutes. Now use one of the three methods of solving proportions to find the answer to this problem. Convert seconds to minutes to make the calculation easier (It will be a fraction). Cross multiplication method: $\frac{500\text{ meters}}{4\frac{5}{6}\text{ minutes}}=\frac{x}{10\text{ minutes}}$ $500(10)=x\left(4\frac{5}{6}\right)$ Solve for $x$. $1034.48$ meters	2019-11-21 12:23:28	{"extraction_info": {"found_math": true, "script_math_tex": 12, "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": 0.61712247133255, "perplexity": 1455.9323128479964}, "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-2019-47/segments/1573496670770.21/warc/CC-MAIN-20191121101711-20191121125711-00454.warc.gz"}
https://www.scireslit.com/Cardiology/C-ID13.php	# Relationship between Serum Lactate Levels and Postoperative Outcomes in Patients undergoing On-Pump Coronary Bypass Surgery Haluk Mevre Ozgoz, Ahmet Yuksel, Mustafa Tok, Murat Bicerand Isik Senkaya Signak Haluk Mevre Ozgoz1, Ahmet Yuksel2, Mustafa Tok3, Murat Bicer3and Isik Senkaya Signak3 1Department of Cardiovascular Surgery, Kilis State Hospital, Kilis, Turkey 2Department of Cardiovascular Surgery, Bursa State Hospital, Bursa, Turkey 3Department of Cardiovascular Surgery, Uludag University Faculty of Medicine, Bursa, Turkey Address for Correspondence: Ahmet Yuksel, Department of Cardiovascular Surgery, Bursa State Hospital, Tophane Street, 16041, Bursa, Turkey Dates: Submitted: 02 December 2016; Approved: 30 January 2017; Published: 03 February 2017 Citation this article: Ozgoz HM, Yuksel A, Tok M, Bicer M, Signak IS. Relationship between Serum Lactate Levels and Postoperative Outcomes in Patients undergoing On-Pump Coronary Bypass Surgery. Int J Clin Cardiol Res. 2017;1(1): 015-019 Copyright: © 2017 Ozgoz HM, et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Keywords: Lactate; Coronary Artery Bypass Grafting; Morbidity; Mortality ## Abstract Objective: To evaluate the relationship between serum lactate levels and postoperative outcomes in patients who underwent on-pump Coronary Artery Bypass Grafting (CABG). Methods: A prospective analysis was performed on 40 adult patients who underwent isolated first-time on-pump CABG between December 2014 and March 2015. Patients were divided into two groups according to their postoperative serum lactate levels as patients with higher levels (=3 mmol/ L) and lower levels (<3 mmol/ L). Patients' demographics, risk factors, intraoperative and postoperative data were recorded. Serum lactate levels and postoperative mortality and morbidity rates in each group were compared and relationship between serum lactate levels and postoperative outcomes was evaluated. Results: Patients with normal serum lactate levels accounted for 82.5% (n = 33) of study population whereas patients with high blood lactate levels comprised 17.5% (n = 7). There were no statistically significant difference between two groups according to the preoperative patients' demographics. According to the intraoperative data; aortic cross clamp, cardiopulmonary bypass and operation time was significantly higher in high lactate group than normal lactate group. In high lactate group, incidence of decreasing in mean arterial pressure under 60 mmHg was also significantly higher (100%) when compared to normal lactate group (45.5%). Postoperative data showed that hemodynamic instability occurrence and inotrope administration rates were significantly higher in high lactate group. Postoperative complications such as neurological complications, pneumonia and severe cardiac arrhythmias were observed more frequently in high lactate group. Conclusion: Our study demonstrated that the high serum lactate levels were associated with the worse postoperative outcomes following on-pump CABG. ## Introduction Industrial and technological developments in the last two centuries and economical and social adaptations in this context have given rise to important changes in the incidence of diseases that causes morbidity and mortality. When in early 20th century cardiovascular diseases accounted for only 10% of overall mortality worldwide, however in our time cardiovascular diseases are the leading cause of mortality in the middle and older age and they account for more than 30% of the worldwide deaths [1,2]. In our country, cardiovascular diseases are the most important cause of mortality with 39.8% and among this group of diseases, Coronary Artery Disease (CAD) is the primary cause of death with 38.8%. CAD prevalence is ranged between 4-5% and incidence between 0.3-0.4% in Turkey, as in many other countries which means, in our country, 230-300 thousand new coronary artery disease patients are expected to present per year [3]. Furthermore, CAD is one of the important diseases which affect the patients' survival, prognosis and quality of life. The most preferred treatment approach especially in severe CAD is Conventional Coronary Artery Bypass Grafting (CABG) surgery with Cardiopulmonary Bypass (CPB), which is still the gold standard treatment method [4]. In this method, by heart being stopped, working in a motionless, blood free area without hemodynamic dysregulation provides the surgeon with necessary comfort for enhanced anastomosis without the compulsion to perform the anastomosis rapidly. In the other hand, CPB usage and cardioplegic arrest might cause various adverse effects. Nowadays, cardiac surgery is routinely performed with lower mortality rates in many centers worldwide. Nevertheless, postoperative morbidity, with relation to various risk factors, still seems to be common and complications such as arrhythmias, ventricular dysfunction that requires inotrope support, infection, gastrointestinal dysfunction, acute lung injury and renal disorders may develop [4-6]. Various parameters are used to evaluate the morbidity and mortality risk. Serum lactate level is one of these parameters which are frequently used for this purpose [7-10]. Hyperlactatemia (HL) occurs when lactate production exceeds consumption because of conditions with tissue hypoxia (HL type A); or without tissue hypoxia (underlying disease, drugs, toxins, congenital metabolic disorders) (HL type B). However, in most cases the cause is multifactorial [11,12]. HL after open heart surgery is a common condition and often associated with increased postoperative mortality and morbidity [10,13]. Although the cause of this situation is not clear, it is indicated that tissue hypoperfusion was the probable causative mechanism [10,14]. Hemodilution and inappropriate tissue oxygenation due to lower peripheral oxygen distribution are likely to be the prompting factors for tissue hypoxia during CPB [15,16]. Both of these factors are associated with postoperative mortality and morbidity [17]. Generally, the serum lactate levels are considered as a prognostic factor after CABG. Previous studies has indicated that there were alterations in serum lactate levels due to effect of CPB on tissue perfusion, changes in tissue metabolism and postoperative effects of surgery. In these studies, it is mentioned that HL is a well-known indicator of circulation insufficiency and could be used as a prognostic factor; however, information about the effect of HL on morbidity and mortality is limited. In this study, the relationship serum of lactate levels with morbidity and mortality was evaluated by comparing serial serum lactate levels, which we obtained from patients who underwent on-pump CABG, with a number of various parameters. ## Material and Methods Study design and patient selection Data of patients who underwent isolated first-time on-pump CABG in our institution were collected prospectively between December 2014 and March 2015, after obtaining approval of institutional ethics committee. Informed consent forms were obtained from all of patients before the operation. A total of 40 on-pump CABG patients were included in the study consecutively. In this study, the cut-off value of HL was accepted as 3 mmol/ L [18,19]. Patients were divided into two groups according to the serum lactate levels as patients with normal lactate levels (< 3 mmol/ L) and higher lactate levels (=3 mmol/ L). Demographic data, risk factors, CPB and cross clamp time, occurrence of hemodynamic instability during CPB and need for vasopressors, use of inotropes for longer than three hours, postoperative hemodynamic data, neurological, infectious and renal complications, mechanical ventilation and postoperative hospitalization duration of the patients in clinic and intensive care unit were recorded. Serum lactate levels and postoperative mortality and morbidity rates in each group were compared and the relationship between serum lactate levels and postoperative outcomes was evaluated. Patients with following conditions were excluded from the study: preoperatively detected abnormal arterial lactate levels, coexisting malignancy, history of chronic inflammatory disease or presence of active infection, presence of liver failure, patients who underwent additional surgical procedure and patients who were operated using different surgical techniques other than conventional on-pump CABG procedure. Surgical technique Median sternotomy was performed to all patients that were implemented CABG with CPB. Heparin was given at the dose of 350 IU/kg and as ACT > 450 sec. LITA and other grafts were prepared by standard technique. After purse strings which were put into ascending aorta and right atrial appendage for standard CPB, arterial cannula and two-stage venous cannula was used. With the roller pump, approximately 60-80 mmHg tension arterial was tried to provide with the flow of 1.8-2.2 L/mn/m2. While we supplant cardiopulmonary bypass, aortic cross clamp was put and diastolic arrest was provided by crystalloid cardioplegia. Firstly, distal anastomoses in company with cardiopulmonary bypass and with aortic cross clamp in the situation that heart is in diastolic arrest was carried out, and then proximal anastomoses was performed with side clamp that was put into ascending aorta. After cardiopulmonary bypass was ended and canullaes were removed, heparin was neutralized with protamine. Statistical analysis Statistical analysis of data was performed using the Statistical Package for the Social Sciences (SPSS) statistical package program (version 18.0, SPSS, Chicago, Illinois, USA). Shapiro-Wilk test was performed in order to assess whether the data showed a normal distribution or not. Mean $±$ standard deviation values were given for the variables that showed normal distribution whereas median (minimum-maximum) values were given for inconsistent variables. Categorical variables were given with n values and percentages and Pearson chi-squared test and Fisher's exact test were performed for comparison. Independent-Samples T Test was performed for comparison of two groups for variables that are consistent with normal distribution whereas Mann-Whitney U test was used for inconsistent variables. p values lower than 0.05 was considered as statistically significant. ## Results The mean age of patients was 60.9 $±$ 9.5 years (range: 39-82), and 36 (90%) of them were male. Patients with normal lactate levels accounted for 82.5% (n = 33) of all patients whereas 17.5% (n = 7) of the patients had high lactate levels. No significant difference between two groups was found according to the preoperative baseline characteristics of patients (p > 0.05) (Table 1). ## Table 1 Table 1: Demographics and preoperative patient characteristics. Normal lactate group (n=33) High lactate group (n=7) P value Sex 0.552 Female 3 (9.1%) 1 (14.3%) Male 30 (90.9%) 6 (85.7%) Age (years) 60.5 $±$ 9.2 62.4 $±$ 11.3 0.647 Active smokers 20 (60.6%) 4 (57.1%) 1.000 Active alcohol consumption 2 (6.1%) 1 (14.3%) 0.448 Diabetes Mellitus 15 (45.5%) 1 (14.3%) 0.066 Hypertension 21 (63.6%) 7 (100%) 0.081 Dyslipidaemia 16 (48.5%) 3 (42.9%) 1.000 Obesity 10 (30.3%) 1 (14.3%) 0.650 BMI (kg/m2) 27.8 $±$ 4.5 27.3 $±$ 3.2 0.972 COPD 3 (9.1%) 2 (28.6%) 0.204 Chronic renal insufficiency 6 (18.2%) 2 (28.6%) 0.366 Carotid artery disease 2 (6.1%) 2 (28.6%) 0.134 PVD 2 (6.1%) 0 (0%) 1.000 LMCA stenosis 8 (24.2%) 3 (42.9%) 0.369 Previous CVA 3 (9.1%) 2 (28.6%) 0.204 Previous PCI 7 (21.2%) 2 (28.6%) 0.645 LVEF >%50 22 (66.7%) 5 (71.4%) 0.811 EuroSCORE 2.8 $±$ 1.7 3.5 $±$ 2.1 0.126 BMI: Body Mass Index; COPD: Chronic Obstructive Pulmonary Disease; CVA: Cerebrovascular Accident; EuroSCORE: European System for Cardiac Operative Risk Evaluation; LMCA: Left Main Coronary Artery; LVEF: Left Ventricular Ejection Fraction; PCI: Percutaneous Coronary Intervention; PVD: Peripheral Vascular Disease When the intraoperative data of patients were assessed, no significant difference was found between two group regarding use of Internal Thoracic Artery (ITA), number of distal anastomoses or use of blood products during operation (p > 0.05). When compared to normal lactate group, cross clamp, CPB and operation time was significantly longer in high lactate group (p < 0.05). Moreover, in high lactate group, incidence of decreasing in mean arterial pressure under 60 mmHg during CPB was also significantly higher (100%) when compared to normal lactate group (45.5%) (p < 0.05). Use of inotropic agents during operation were significantly higher in high lactate group when compared with normal lactate group (p < 0.05). Intraoperative data of patients were listed in (Table 2). ## Table 2 Table 2: Intraoperative data of patients. Normal lactate group (n = 33) High lactate group (n = 7) P value Use of ITA 32 (97%) 5 (71.4%) 0.074 No of distal anastomoses 3 (2:5) 3 (3:4) 0.076 Aortic cross-clamp time (min) 52.9 $±$ 15.5 72.3 $±$ 26.6 0.043 CPB time (min) 92.6 $±$ 28.6 130.9 $±$ 45.2 0.006 Operation time (min) 253.5 $±$ 53.5 308.6 $±$ 55.4 0.030 MAP <60mmHg 15 (45.5%) 7 (100%) 0.011 Use of inotropic agents 7 (21.2%) 5 (71.4%) 0.017 Use of blood products 14 (42.4%) 3 (42.9%) 1.000 CPB: Cardiopulmonary Bypass, ITA: Internal Thoracic Artery; MAP: Mean Arterial Pressure When the postoperative data of patients were assessed, presence of postoperative hemodynamic instability and inotrope administration occurred in high lactate group with a significantly higher rate when compared to normal lactate group (p < 0.01). Mechanical ventilation duration was obviously higher in high lactate group (p < 0.05). Need for Intra-Aortic Balloon Pump (IABP) counter pulsation, re-intubation, use of blood products, occurrence of postoperative hyperglycemia (blood glucose level >160 mg/ dL), reoperation and mortality were higher in high lactate group, although it was not statistically significant (p > 0.05). Considering complications developed postoperatively; in high lactate group, neurological complications and pneumonia were significantly more frequent than normal lactate group (p < 0.05). There was no significant difference between two groups considering other respiratory complications, infections, urinary system and gastrointestinal complications (p > 0.05). Postoperative Atrial Fibrillation (POAF) was observed in 6 patients (15%). There was no significant difference between two groups about POAF occurrence (p > 0.05); whereas severe arrhythmias such as Ventricular Fibrillation (VF) / Atrioventricular (AV) block were seen significantly more frequent in high lactate group (p < 0.05). In high lactate group, hospitalization durations in clinic and intensive care unit were longer compared to normal lactate group; however, it was not statistically significant yet close to significance (p > 0.05). Postoperative data of the patients were listed in (Table 3). ## Table 3 Table 3: Postoperative data of patients. Normal lactate group (n = 33) High lactate group (n = 7) P value Hemodynamic instability 1 (3%) 5 (71.4%) 0.001 Use of inotropic agents 3 (9.1%) 5 (71.4%) 0.002 Need for IABP 0 (0%) 1 (14.3%) 0.175 MV time (h) 8 (3:93) 22 (7:102) 0.014 Re-intubation 1 (3%) 1 (14.3%) 0.323 Use of blood products 17 (51.5%) 5 (71.4%) 0.427 Presence of hyperglycemia 21 (63.6%) 5 (71.4%) 1.000 Neurological complications 0 (0%) 2 (28.6%) 0.027 Pneumonia 2 (6.1%) 3 (42.9%) 0.030 Pneumothorax 1 (3%) 0 (0%) 1.000 Pleural effusion 17 (51.5%) 3 (42.9%) 1.000 Sternal dehiscence 1 (3%) 0 (0%) 1.000 Wound infections 4 (12.1%) 0 (0%) 1.000 Renal dysfunction 5 (15.2%) 3 (42.9%) 0.128 GIS complications 2 (6.1%) 1 (14.3%) 0.448 POAF 6 (18.2%) 0 (%0) 0.289 Severe arrhythmias 0 (0%) 2 (28.6%) 0.027 Reexploration 1 (3%) 1 (14.3%) 0.323 ICU stay (h) 40 (19:163) 49 (24:238) 0.135 Hospital stay (days) 7.0 $±$ 2.4 10.3 $±$ 6.6 0.055 Mortality 0 (0%) 1 (14.3%) 0.175 GIS: Gastrointestinal System, IABP: Intra-Aortic Balloon Pump, ICU: Intensive Care Unit, MV: Mechanical Ventilation, POAF: Postoperative Atrial Fibrillation ## Discussion In recent years, the great increase in the incidence of CAD caused an increase in need for myocardial revascularization which is a remarkable treatment modality for this clinical condition. Myocardial revascularization is the gold standard in case medical treatment is inadequate. The effect of CABG on reducing angina and increasing the expected life span was proved in many studies. Moreover, acceptable mortality and morbidity rates of CABG makes this approach the most favorable, gold standard method. Conventional on-pump CABG has been the preferred treatment method for multiple vessel disease for over 40 years [4]. Although CABG is safe and effective, CPB and cardioplegic arrest may cause some adverse effects. As a result of rapid developments in the technology and our knowledge, cardiac surgery is performed with lower preoperative morbidity and mortality in most cardiac surgery centers. However, postoperative morbidity, mostly interrelated with various risk factors, is still frequently encountered, causing increased hospitalization durations in clinics or intensive care units, medical expenses, workload of medical staff, which creates problems for both patient and health system [20]. Various parameters are used for estimating the risk of postoperative mortality and morbidity. Serum lactate level is a widely used parameter since it is inexpensive and provides results rapidly. Many researchers have investigated the correlation between Hyperlactatemia (HL) and morbidity and mortality [7-10,18]. Elevated blood lactate level is a metabolic disorder that is seen quite frequent in intensive care units after cardiac surgery and its pathophysiology remains unclear [13,14]. Hyperlactatemia may be caused by tissue hypoxia (type A HL) as well as it may present without tissue hypoxia (type B HL). Especially after cardiac surgery type B hyperlactatemia is common in early postoperative period. It is reported in different studies that postoperative hyperlactatemia occurrence rate is ranged between 10-20% [10,17]. In our study, this rate is similar to prior studies with a rate of 17.5% postoperative high lactate levels. Demers, et al. [10] indicated that many various preoperative factors and comorbidity contribute to hyperlactatemia developed during CPB. They described age, congestive heart failure, low left ventricle ejection fraction, hypertension, Diabetes Mellitus (DM), revision surgery and emergency intervene as risk factors for hyperlactatemia. In our study, unlike the findings of Demers' study; variables such as age, hypertension, DM and low left ventricle ejection fraction were not shown to be risk factors. Similarly, in our study, nor Chronic Obstructive Pulmonary Disease (COPD) neither chronic renal failure was considered to be as an risk factor. Ranucci, et al. [17] indicated that the relation between CPB time and pike lactate level was not linear and the cut-off value for CPB time was 96 minutes. Our findings support this statement with a mean CPB time of 131 minutes in high lactate group and 92 minutes with normal lactate group. Totaro, et al. [19] defined lactic acidosis prompted by $\beta$ 2 agonist administration and high dose epinephrine. Lactic acidosis is also seen in severe hyperadrenergic state of pheochromocytoma and acute asthma [21]. Similarly to study of Totaro, et al. in our study, an increased need for vasopressor administration and hemodynamic instability occurred in high lactate group in intraoperative and postoperative period and dysregulation between O2 presentation and consumption in these patients. Ranucci, et al. [17] reported a cut-off value of 160 mg/ dL for pike blood glucose level. We also determined the cut off value as 160 mg/ dL in our study and found that hyperglycemia occurred more frequently in high lactate group although, it was not statistically significant. There are number of factors that elevate blood glucose levels postoperatively and during CPB. Especially contribution of factors such as inflammatory response to surgical stress and extracorporeal circulation, growth hormone, ACTH, epinephrine discharge, insulin resistance leads to elevated blood glucose levels [22]. In our study, when the demographics of patients were evaluated, although there were more diabetic patients in normal lactate group, interestingly, more hyperglycemia occurrence was detected in high lactate group, which was attributed to inflammatory response secondary to surgical trauma. Lactate levels that are obtained in intensive care unit was interrelated with cross clamp, CPB and operation time, high alveolar-arterial oxygen gradient (p(A-a)O2) and mechanical ventilation duration [18,23]. Siegel, et al. [23] reported that mechanical ventilation duration and hospitalization duration in intensive care unit is prolonged in patients with high perioperative lactate levels. Our findings support findings of Siegel et al. as our study has shown that in high lactate group, mechanical ventilation duration was significantly prolonged compared to normal lactate group. Despite the fact that lactate concentration is a good indicator of severeness of disease in intensive care patients, its prognostic value after cardiac surgery has not been proved. Moderate hyperlactatemia is generally considered to be benign [14,19]. Shemi, et al. [18] suggested that, serum lactate levels that are higher than 6 mmol/ L might be a useful indicator for mortality and required a thorough evaluation to find the cause of the problem and sustain survival. In our study, lactate levels that are higher than 3 mmol/ L in intensive care unit are considered to be an indicator for poor prognosis. These patients showed more hemodynamic instability, neurological complications, pneumonia and severe arrhythmias in follow-up period. Moreover, these patients were extubated far more lately and hospitalized in clinic and intensive care unit for longer periods. ## Limitations of the study There were several limitations in the interpretation of the results of our study. The major limitations of this study were evaluated data were limited, lack of the mid and long-term outcomes of patients, irregular distribution of patients between groups and relatively small number of patients in the study groups. A larger sample could have increased the statistical power of our research. ## Conclusion It was demonstrated that assessing the serum lactate levels in postoperative period is easy, inexpensive and clinically very useful. It is very important to sustain hemodynamic stabilization, to keep the mean arterial pressure above 60 mmHg and to avoid severe hypothermia and hemodilution during CPB for preventing hyperlactatemia, which is an indicator for poor prognosis. Protecting heart during CPB well until finishing CPB may be easier, in this way, prolonged cross clamp and bypass durations could be prevented. Postoperative hyperglycemia must be managed well. Follow-up with serial lactate levels may allow defining the patients with high risk of mortality and morbidity, thus taking necessary precautions. Submit ManuscriptSubmit Special Issue Authors submit all Proposals and manuscripts via Electronic Form!	2019-05-26 15:14:23	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 17, "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": 0.3644968867301941, "perplexity": 13185.24249377079}, "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/1558232259316.74/warc/CC-MAIN-20190526145334-20190526171334-00402.warc.gz"}
https://svi.nl/FaqDataAcquisition	### Sampling For a point-scanning confocal microscope (1.3 lens, 488 excitation) good sampling is around 50nm x 150nm. Laterally 70nm is fine, you shouldn't go beyond 100nm, axially it is best to stay at 150-200nm. If you sample around the 70nm x 150nm you will see that the restoration is capable to reduce noise considerably. As a result you might need less signal than you thought before. If practical considerations (bleaching, data size) don't allow these sampling densities, you'll just have to do the best you can. In our experience, unless you undersample dramatically, the restoration will always improve your image. For accurate values use our See UnderSampling. The aquisition zoom factor only affects the scanning parameters and as far as we know has no effect on the computation of the backprojected pinhole size. If the pinhole is specified in terms of Airy units the backprojected radius is computed as (from the FAQ): backprojected_RADIUS = number_of_Airy_disks * 0.61 * $$\frac{\lambda}{NA}$$ To compute the backprojected radius from the physical pinhole size see the tables in the Huygens Essential or Professional User Guide. Oversampling is completely harmless. The more samples the better, though it could be argued that oversampling is not necessary. Of course there are practical reasons to limit sampling: object size, memory requirements, bleaching and so on. If you have loaded an image in Huygens Pro, select it and select Edit-> Nyquist you get a report of the sampling situation taking into account all known parameters. Rule of thumb is for WF: 100nm lateral or better; around 200nm axially. 250nm would be fine too, but we distrust some z-motors with round numbers. An undersampled image stack is a stack in which the Z or XY samping intervals are too large. Undersampling means that the sampling interval is too large to capture all information about the object generated by the microscope. In Huygens Essential the sampling values will be colored orange in case of undersampling. In case of severe undersampling the color will be red. In Huygens Pro the optimal sampling density for the optical conditions under which an image is recorded can be computed by selecting its thumbnail and then Edit->Nyquist. When an image is recorded at this so called Nyquist frequency the digitized sequence contains all information carried in the signal. This makes it possible to reconstruct the image at any location, so not limited to the sampling positions. The Nyquist frequency is twice the highest spatial frequency (bandlimit) transmitted by the microscope. There seems to be a discrepancy between the way Huygens defines stepsize and the way my microscope defines stepsize. In the Huygens the stepsize (in any direction) is just the distance between samples, 'sampling distance'. Also, in all directions the numbering starts with 0, so the index for N samples runs from 0..N-1. This is the conventional way of indexing samples. Some microscope manufacturers use a special 1..N numbering scheme in the z-direction, but still 0..N-1 in the XY plane. Yes, read our undersampling Is undersampling in Z-direction a serious problem?. For a general discussion on correct sampling and aliasing see: • Gonzalez, R.C. and R.E. Woods. (1992) Digital Image Processing. Addison-Wesley. ISBN 0-201-50803-6. p111 e.v. For a discussion of microscopical bandpass characteristics see the papers below. Be sure to read both! • Sheppard, C.J.R.The spatial frequency cut-off in three-dimensional imaging. (1986a). Optik 72 No. 4 131-133. • Sheppard, C.J.R.The spatial frequency cut-off in three-dimensional imaging II. (1986b). Optik 74 No. 3, pp. 128-129. For a practical discussion see also SVI's 'Deconvolution Recipes' manual or the Nyquist Calculator and Nyquist Rate. No, it is a function of the optical properties of your system. It all revolves around the Shannon theorem, that states that for a bandlimited system (all our microscopes) it is totally sufficient to sample at the Nyquist rate. Now suppose the maximum spatial frequency passing a microscope is one cycle per 100nm (1.3 NA oil, confocal, 488/520nm, sampling at 50nm to sample peaks and valleys of the 100nm periodic wave). If you have a periodic structure of lumps spaced 80nm apart then this structure is not imaged, apart from its average value, nothing of it. Can't restore it, no way. If there is omly one single object and you know it is a sphere then restoration could consist of determining its center of mass. The accuracy of that depends on the SNR, but you could easily reach 10nm. Job done! The regular restoration procedure could also do it for you, but obviously to get such an accuracy in determining the peak location of the object you would have to resample the data to a higher sampling interval of 10nm. (You could also play it a bit dirty by not deconvolving with the PSF, but with the known image of the object; out comes a single peak where the center of the object is). A more interesting object is for instance a two-blob object with a spacing at the Nyquist rate. Now the most interesting parts of the object spectrum are cut off by the microscope. The problem now is that the transmitted piece is the same for a whole family of objects. The family which has a spectrum quite like it is even larger. The restoration algorithm must now choose among them, the first selection being to exclude all objects with negative values. The better the SNR, the better the restoration algorithm can exclude objects of which the spectrum is slightly dissimilar to the measured spectrum. For confocals the situation is worse because they already attenuate everything beyond say 60% of the band practically to zero (depending on the pinhole). So in practice there is little hope for resolving objects at the edge of the band. See Nyquist Rate and Nyquist Calculator. The following formulas can be used to compute the Nyquist rate. Widefield microscope: Nyquist_lateral = \lambda$$/ ( 4 n sin(\alpha$$)) Nyquist_axial = \lambda$$/ ( 4 n (1 - cos(\alpha$$))) with \lambda$$the wavelength, N$$ the refractive index of the medium (1.515 for immersion oil). \alpha$$is the half-aperture angle obtained with: \alpha = arcsin(NA/N)$$ with NA the Numerical aperture. Many calculators use the 'sin-1' or 'asin' symbol for the arcsin function. Confocal microscope: Assuming the excitation and emission wavelength are equal a confocal microscope doubles the bandwidth so halves the Nyquist sampling density. Both Huygens Pro and Essential take the exact wavelength into account when computing the Nyquist rate. In case of multi photon excitation they also take the number of excitation photons into account. Both will color the background of X, Y, Z sampling density entry fields orange (moderate undersampling) or red (serious undersampling) when detecting undersampling. In Huygens Pro you can look up the Nyquist rate for a particular image by selecting it and Edit->Nyquist rate. The Z-sampling is modfied by foreshortening due to differences in refractive index of the media and the immersion oil: the 'reverse fishtank' effect. In most cases the z-sampling as specified in the raw datafile is the nominal sampling distance, i.e. the distance the table or objective actually moved in Z without taking foreshortening due to refractive index mismatch into account. The mismatch induces spherical abberation and can have a profound effect on the PSF shape and effective aperture. The PSF generator takes all this into account. After deconvolution the remaining geometric distortion can be corrected by multiplying the z-sampling distance by the ratio of the medium and immersion refractive index, a number in most of the cases < 1. See also [FishtankEffect\|Fishtank Effect] To find out the ideal sampling, you can always use the online Nyquist Calculator, entering the image parameters (including the number of photons: 2). You can also use the Huygens Software in your computer. To find out how large are your samples in relation with the ideal Nyquist Rate, do the following: In Essential • If you have an image for which you want to compute the Nyquist rate, open it and check its parameters (right click -> "Show parameters"). • Whenever you change the Microscopic Parameters of an image, the Nyquist rate is recalculated. Modify the image parameters to match the microscopic conditions for which you want to compute the Nyquist rate, then check the parameters again (right click -> "Show parameters"). In Professional • Select the image, select Edit -> Nyquist rate in the main menu. You'll get a popup displaying the Nyquist rate. If in 2-photon excitation a pinhole is not used it is the excitation distribution which determines the imaging properties of the microscope and therefore the Nyquist rate. The excitation intensity field is that of a widefield microscope, but since due to the 2-photon effect the effective excitation distribution is the square of the intensity distribution, the imaging properties are vastly different. The squaring operation makes the distribution more 'peaked', resulting in an improved resolution. It also causes the bandwidth (and with that the Nyquist rate) in x, y, z to be twice that of a widefield microscope at the same wavelength. Importantly, the 3D shape of the band-pass area is very different: while the widefield area has a wedge at the center causing the large widefield blur cones, the 2-photon bandpass area has no such defects. See Pinhole And Bandwidth. Old information In principle, the Nyquist rate is independent of the pinhole size. This is due to the choice to relate the Nyquist rate to the theoretical bandwidth of the system: the spatial frequency beyond which nothing is transferred by the microscope. It would be a different story if we would have used a criterion based on attenuation of spatial frequencies below a certain factor. (Larger pinhole sizes attenuate higher frequencies more, but still are not zero). Although a practical approach (because about last third of the band has so low intensities that they can be considered zero most of the times) this involves an arbitrary choice, so therefore we base the Nyquist rate on the well defined theoretical bandwidth. A problem occurs with extremely large pinholes like those used in two-photon systems. In these cases the optical properties are practically identical to a widefield system whereas due to the presence of the pinhole the theoretical bandlimit is still that of a confocal microscope. In the two-photon case it is best to set the microscope type to 'widefield' when doing deconvolution with the Huygens Software, since this will result in the same optical properties but with a more practical Nyquist rate. Note however that with single photon confocals even a very large pinhole will still have a noticeable effect on the blur contributions of far off focus regions, thus improving resolution along the optical axis. The Confocal Microscope provides more information than the widefield system; in theory the confocal Sampling Density should be twice the widefield density. This holds for in all 3 dimensions, so you'd get 8 times more voxels. A 'typical' widefield setup (1.3 effective NA lens, 500nm emission) is sampled well at 100 nm laterally, 300 nm axially. However, due to good SNR ratio's deconvolution can often gain a lot in Z, so you might as well go for 200 nm. With a 100x lens and a CCD with 6.7 micron cells you get 67 nm laterally. (This is assuming that there is no extra magnification; otherwise the total magnification must be used when calculating the pixel size). If this bloats your data too much you can try binning to increase the lateral size to 134 nm, but you will already start seeing some 'staircasing' effects on thin filaments in the deconvolved image (Aliasing Artifacts). In the same typical confocal case a nice sampling rate would be 50 nm in Z, 150 nm axially. In case of bleaching problems you can stretch this up to 75 nm lateral, and after that increase the Z-sampling. If the Parameter Editor or the Parameter wizard starts coloring the sampling fields orange, then you start to undersample; red means severely undersampled. See Nyquist Rate. This greatly depends on the optical paramaters, in particular on the NA and microscope type. Together with the wavelenghts and refractive indexes these determine the so called Nyquist sample distance, the maximum sampling distance at which all image information is captured. For a plot of the dependancy of the Nyquist rate on the NA and microscope type see the User guides, or go to Nyquist Rate. To calculate this figures online see the Nyquist Calculator. • Confocal microscopes: While sampling at the Nyquist rate is a very good idea, it is in many practical situations hard to attain. In these cases larger sampling distances may be used. For confocal images with a Airy disk sized pinhole the lateral sampling distance may be up to about 1.6 of the Nyquist distance. When much larger pinholes are used, up to 2x. When very small pinholes are used to optimize resolution, or any other case where high resolution is required, we do not not recommend undersampling since this would defeat the purpose, and since it might limit the deconvolution result. • Two photon microscopes: Two photon microscopes without a detection pinhole (e.g. non descanned systems) follow the rules of a small pinhole confocal microscope relative to the longer excitation wavelength. The addition of a detection pinhole increases the theoretical bandwidth, but since usually large pinholes are used the practical bandwidth increase is small. • Spinning (Nipkow) disk microscopes: Regarding sampling criteria spinning disk microscopes behave like confocal microscopes with, depending on the disk, a fairly large pinhole. For a typical system we do not recommend more than 1.6 times undersampling. • Widefield: Widefield data are more sensitive to undersampling; stay below 1.3. In case of low numerical apertures like 0.4 we recommend not to undersample in the axial direction. • STED : The remarkable property of STED microscopes is that they do not have a band limit in the strict sense. That means that any sampling rate is a compromise between practical considerations and the to be reached resolution. Since lateral STED HIW resolution can achieve 50nm in good conditions we recommend sampling around 25nm. In difficult condition this can be increased, but that will limit deconvolution. • Multi channel data: The sampling rate should be derived from the highest resolution channel. The actual and the ideal sampling distances of an image can be seen in Huygens Essential right-clicking on the image thumbnail and choosing 'Show parameters'. To compute the ideal Nyquist rate of an image in Huygens Professional, select the image and choose Edit -> Nyquist rate. Widefield and confocal microscopes differ in the amount of information they are able to extract from a specimen. One way to express this is to look at the finest details or highest spatial frequency the microscopes transmits: for a confocal microscope this is nearly twice as much as in an equivalent widefield microscope, in all directions. According to the Nyquist theorem a signal should be sampled at twice its highest bandwidth so confocal microscopes need twice the sampling density of widefield microscopes. Although the confocal microscope is able to transmit twice as fine details as the widefield microscope, it attenuates these very strongly. Beyond say 60% of the highest frequency practically nothing is transmitted, especially for not-ideal pinhole cases. Therefore, while sampling according to Nyquist rate remains the safest solution, in the case of confocal imaging it is defensible to reduce the sampling rate to about 60% of the theoretical rate, for example in typical condition one sample per 50/0.6 = 80nm. In the widefield case, high spatial frequencies are also attenuated as the band limit is approached, but to a much lesser degree than in the confocal case. Therefore we do not recommend to stay below 1.3 of the Nyquist rate. In case of low numerical apertures like 0.4 we recommend not to undersample widefield images in the axial direction. A practical example: Assuming a 1.3 N.A. objective lens and 488nm excitation, 520nm emission you need to sample around 50 x 50 x 165 nm to get an optimally sampled confocal 3D image; 100 x 100 x 330 nm in the 3D widefield case. As mentioned above, widefield images are more sensitive to undersampling, i.e. a violation of the sampling rule has a more dramatic effect on widefield images than on confocal images. For more details on sampling densities for other microscope type, see the FAQ What is the maximal voxel size at which Huygens can still do a good job?.You may also want to have a look at Sampling Density and Nyquist Rate. If your CCD camera has the option of binning, the binning can be used to increase the signal at the cost of resolution. With binning the intensity of several pixels is integrated to form a super pixel. For instance, 4 x 4 pixels are summed to form a bigger and brighter signal at the cost of resolution. When binning is applied the effective voxel size increases. Example: If the actual detector element size is 6 micron and a 2 x 2 binning function is active, then the effective pixel size is 12 x 12 micron. As a consequence the magnification has to be increased by a factor of 2 relative to the non-binning mode in order to satisfy the sampling criteria. Indeed, lowering the NA to allow for larger samples is the correct way. The drawback is that the axial resolution of the image will decrease with the square of the reduction of the NA. The sampling density as function of the NA can be found in the Huygens User Guides in the chapter Establishing Image Parameters. ### Particular instruments See Biorad MRC_500_600_1024 and Biorad_Radiance. Old information: from communication with Brad Amos we learned that the factor for the 1024 is 53 and for the Radiance is 60. We had feed back from a customer who reported "Using Brad Amos' value, the deconvolution is working well". For the most used Yokokawa disk spacing is 250 micron, so with an 100x lens backprojected about 2.5 micron This you can check by stopping the disk. The pinhole diameter is probably 25-50 micron, resulting in a backprojected radius of .125 - .25. The latter is about an Airy disk. The Perkin Elmer Ultra View is a Yokagawa disc and the Yokagawa disc is always a Nipkow disc. You must choose the Huygens option for Nipkow disc microscopes.	2023-03-26 17:45:47	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 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": 0.6380156874656677, "perplexity": 1493.1463637788938}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296946445.46/warc/CC-MAIN-20230326173112-20230326203112-00486.warc.gz"}
http://math.stackexchange.com/questions/116161/is-the-usual-addition-of-integers-unique/116173	# Is the usual addition of integers unique? If we define a ring on the integers $\mathbb Z$ (i.e. $(\mathbb Z, +,\times)$) and equip it with the usual $\times$ operation for $\mathbb Z$, is it necessary that the $+$ operation be the usual $+$ too? - The monoid $(\mathbb Z\setminus\{0\},\times)$ is isomorphic to the direct sum $\mathbb Z_2\oplus\bigoplus\limits_{\text{countable}}\mathbb N_0$ of a cyclic group of order $2$ and a countable number of copies of $\mathbb N_0$. It follows that it has lots of automorphisms: we can permute the prime numbers arbitrarily. If $\phi:\mathbb Z\to\mathbb Z$ is any such automorphism which is not the identity, then we get a ring structure on it by defining a new sum $a+'b=\phi^{-1}(\phi(a)+\phi(b))$. The uncountably many rings we get this way are of course isomorphic to the usual $\mathbb Z$, but all different. The polynomial ring $\mathbb F_3[X]$ is a principal ideal domain with countably infinite many primes and exactly two invertible elements, so its monoid of non-zero elements is isomorphic to $(\mathbb Z\setminus\{0\},\times)$. There is then a bijection $f:\mathbb F_3[X]\to\mathbb Z$ mapping zero to zero which is an isomorphism of monoids in the complements of those zero elements. We can define an addition on $\mathbb Z$ by transporting that of $\mathbb F_3[X]$ along $f$. This turns $\mathbb Z$ into a ring of characteristic $3$ :)	2015-05-30 08:34:31	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 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": 0.988447368144989, "perplexity": 89.77604617824618}, "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/1432207930916.2/warc/CC-MAIN-20150521113210-00005-ip-10-180-206-219.ec2.internal.warc.gz"}
https://mojan.ca/blogs/computational-mathematics/fourier-transforms-for-writing-sheet-music	# Using Python and Fourier transforms to automate writing sheet music for sound files Featuring my questionable guitar skills. by Mojan Benham A year ago ## Two-line summary The Fourier transform is a mathematical function that converts waves in the time domain to the frequency domain. With the use of a sliding filter, this post walks through the Python code to conduct a time-frequency analysis of a song in order to convert it to musical notes. The following post requires an understanding of undergraduate-level calculus and basic Python skills. The reader should be well-versed in advanced functions, integrals, for loops and numpy arrays. Prior knowledge of Fourier or Gabor transforms is not necessary. For those interested in gaining a deeper theoretical understanding, I would strongly recommend Chapter 13 of Data-Driven Modeling & Scientific Computation as well as the accompanying lecture by the author, J. Nathan Kutz. I cannot speak more highly of Professor Kutz; his engaging content and published works are primarily what inspired this tutorial. ## Preparing your Python environment For my coding environment I used Python 3.9.6 with Visual Studio Code notebooks (documentation here). Any Python environment is fine as long as the version is compatible with the libraries used below and is able to print and plot data. All code used in this post is available on my public github repo, to which I will make cell references throughout so that you can follow along line-by-line. Cell 1 imports all necessary libraries used hereafter. The libraries must be installed before importing, which I did using pip3 installation. For example, to install matplotlib, I simply ran !pip3 install matplotlib directly in the notebook. If done correctly, this cell should return nothing. Otherwise, if you attempt to import a library that is not installed, you will get the following error: ModuleNotFoundError: No module named [...]. # import installed libraries from scipy.io import wavfile import matplotlib.pyplot as plt import numpy as np from IPython.display import clear_output from scipy.fftpack import fft, fftshift ## Working with sound files In this folder, I have a .wav file of me playing Happy Birthday on guitar. I played very slowly so that when we plot the sound wave, the notes would be spread out and easily distinguishable to the human eye. In Cell 2 this file is read in using scipy's wavfile (documentation), which returns two data structures: the sample rate and the sound wave as a numpy array. The sample rate is the number of samples taken per second from a continuous signal (the sound file) in order to store it as a discrete data structure (the numpy array returned by wavfile). Therefore, if we divide the size of the array by the sample rate, we are left with the length of the sound file in seconds. # read in sound file samplerate, data = wavfile.read('hbd_slow_speed.wav') # define sound metadata data_size = data.shape[0] song_length_seconds = data_size/samplerate # print sound metadata print("Data size:", data_size) print("Sample rate:", samplerate) print("Song length (seconds):", song_length_seconds, "seconds") To plot this wave we use matplotlib in Cell 3. Note that I could have simply plotted with plt.plot(data) but this would have given me the x-axis in the array size instead of seconds. For this reason, I created my own domain using numpy's linspace, which returns evenly spaced numbers over a specified interval. # define domain in seconds time_domain = np.linspace(0, song_length_seconds, data_size) # plot sound wave plt.plot(time_domain, data) plt.xlabel("Time [s]") plt.ylabel("Amplitude") plt.show() ## The Fourier transform The Fourier transform is a mathematical transform that decomposes functions based in time into the frequency of their notes, or spectral content. In short, it converts a function, f(x), from the time domain to the frequency domain. The derivation and proof of this method are excluded for brevity, but are available at the resources mentioned in the Reader prerequisites section above. $F(k) = \frac{1}{2\pi}\int_{-\infty}^{\infty}e^{-ikx}f(x)dx$ ##### Figure 2: Fourier transform of function, f(x) Cell 4 computes and plots the Fourier transform of the sound wave. Once again, we use linspace to define the domain but this time in terms of frequency. Notice that since our domain will include both negative and positive values, I've defined the interval from $$[-samplerate/2, samplerate/2]$$ rather than from $$[0, samplerate]$$. The fft (fast Fourier transform) function is the algorithm that performs the forward Fourier transformation. When you apply fft to a function, it shifts the domain by swapping at the halfway point. Meaning, if your domain is [0,1,2,3,4,5], it will convert it to [3,4,5,0,1,2]. This is not the desired outcome but rather a byproduct of the algorithm being optimized for speed. It is therefore necessary to shift our domain back using the fftshift function. # define frequency domain freq_domain = np.linspace(-samplerate/2,samplerate/2,data_size) # fourier transform fourier_data = abs(fft(data)) fourier_data_shift = fftshift(fourier_data) # plotting spectral content of sound wave plt.xlim([-5000, 5000]) plt.xlabel("Frequency (Hz)") plt.ylabel("Amplitude") plt.plot(freq_domain, fourier_data_shift) plt.show() ##### Figure 3: Shifted fast Fourier transform of sound file Figure 3 shows us all of the frequencies that are present in the whole sound file. While this is interesting, it isn't very useful because we've lost all time information such that we don't know when each of these frequencies (or notes) are played. Therefore we need to augment our analysis from time to time-frequency in order to distinguish between the notes. ## The Gabor transform Hungarian mathematician, Gàbor Dénes, proposed a method for localizing in both time and frequency by applying a time-filtering window and extracting samples of the frequency at each window by sliding across the entire signal. $G[f](t,\omega) = \int_{-\infty}^{\infty}f(\tau)g(\tau -t) e^{-i\omega t}d\tau$ ##### Figure 4: Gabor transform of function, f, with filter, g. Notice that this transform is very similar to the Fourier transform defined in Figure 2, just with the additional term of the sliding filter where g(t) is a filter of our choosing. This means that unlike the Fourier transform, the Gabor transform is a function of both time and frequency. Let's choose a simple Gaussian function as our filter as defined below and plot it on top of the original sound file in the time domain (Cell 5). $g(x) = ae^{-b(x-t)^2}$ ##### Figure 5: Gaussian filter used for function g in Figure 4 I played around with the values of $$a$$, $$b$$ and $$t$$ manually until the wave was encompassing an arbitrary note, which is how I arrived at 11000, -2 and 11.8 respectively. ##### Figure 6: Gaussian filter superimposed onto sound wave in time domain The output of the Gaussian function is zero everywhere except the sixth note, so multiplying the curves together isolates the note (Cell 6). ##### Figure 7: Product of Gaussian filter and sound wave from Figure 6 As the Gabor transform suggests, we must slide our filter along the time domain in order to extract the frequency information of each note. In Cell 7, I apply the same logic as Cell 6 except that it is inside a for loop where the value is iterated by the loop. The list of values for the loop was manually derived by trial-and-error; there is a more sophisticated approach but that would require code complexity that I've excluded in the interest of time. Cell 8 is really the bread and butter of this post. We loop through time, applying the Gaussian filter at each iteration and storing the shifted Fourier transform. Notice in the plots that there is usually one prominent frequency, and then a few dampened frequencies at even intervals after. When you play a note, the pitch typically heard is the lowest frequency, but there are harmonic vibrations present at higher frequencies. These are called overtones and are audible to the trained ear if at all. When we convert this frequency to a note later on, we will only use the lowest frequency. results = [] for i in [2.2, 4.25, 6, 8, 10, 11.8]: clear_output(wait=True) plt.xlim([0, 600]) gaussian = 11000np.exp(-2np.power(time_domain - i, 2)) gaussian_filtered = datagaussian fourier_data = abs(fft(gaussian_filtered)) fourier_data_shift = fftshift(fourier_data) results.append(fourier_data_shift) plt.plot(freq_domain, fourier_data_shift) plt.pause(1) ## Putting it all together To introduce a bit of musical theory, the first C on a piano vibrates at ~16.35Hz. We can calculate the half steps from this C0 to a note of our choice at frequency f with the following equation: $$h = 12\log_2(f/C0)$$. This blog post provides a nifty function (Cell 9) that calculates the letter value of a note based on its frequency. In Cell 10, each frequency is passed to the pitch function to output the notes for Happy Birthday: G G A C G B. ## Closing thoughts In this tutorial, the application of the Gabor transform is quite simple because the notes in the sound file are individually played on a single instrument. You may be wondering, what happens if we were to play a chord, or apply this method to a song with a band where multiple instruments are played at once? While we would not be able to extract the frequencies of specific notes, it is interesting to plot different genres and see how, for example, jazz differs from hip hop in its spectral content. If interested, you can try this as a follow-up exercise to this post. I found similarities within genres in how the sound waves transformed to their respective frequency components. Meaning, I could recognize the type of music based on the spectrogram. Fascinating! As always, would love to hear your thoughts and feedback in the comments below. • Hey Luka! Yes, this can work for any instrument. I don’t think your error is a result of it being a piano file. What’s happening is that your time_domain variable is a different shape than your gaussiandata variable, so the plot function is unsure how to align them. What you need to do is figure out why the (393084,2) object has two columns instead of one. The best way to do this is to check the documentation of the wave reader you’re using; notice that when I used wav.read, I stored one column as samplerate and the other column as data so that the shape would have one column instead of two. Mojan Benham on • Could this work for piano recordings? Luka Spaic on • This looks phenomenal! Although, do you think this same thing could be done on recorded .wav files of piano music? When I am currently running the same code on a piano .wav file I’m getting a ValueError: operands could not be broadcast together with shapes (393084,) (393084,2) on line plt.plot(time_domain, gaussiandata). As of now I’m not sure why and how I could make this work for piano music. If you could help me out I’d really appreciate it! Thank you absolutely great article. Luka Spaic on	2022-10-06 17:10:34	{"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": 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": 0.5242944359779358, "perplexity": 1184.880236745953}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.3, "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-2022-40/segments/1664030337853.66/warc/CC-MAIN-20221006155805-20221006185805-00723.warc.gz"}
https://ftp.aimsciences.org/article/doi/10.3934/mbe.2016003	# American Institute of Mathematical Sciences 2016, 13(3): 495-507. doi: 10.3934/mbe.2016003 ## Successive spike times predicted by a stochastic neuronal model with a variable input signal 1 Dipartimento di Matematica e Applicazioni, Università degli studi di Napoli, FEDERICO II, Via Cinthia, Monte S.Angelo, Napoli, 80126, Italy 2 Dipartimento di Matematica e Applicazioni “R. Caccioppoli”, Università di Napoli Federico II, Via Cintia, 80126 Napoli Received April 2015 Revised November 2015 Published January 2016 Two different stochastic processes are used to model the evolution of the membrane voltage of a neuron exposed to a time-varying input signal. The first process is an inhomogeneous Ornstein-Uhlenbeck process and its first passage time through a constant threshold is used to model the first spike time after the signal onset. The second process is a Gauss-Markov process identified by a particular mean function dependent on the first passage time of the first process. It is shown that the second process is also of a diffusion type. The probability density function of the maximum between the first passage time of the first and the second process is considered to approximate the distribution of the second spike time. Results obtained by simulations are compared with those following the numerical and asymptotic approximations. A general equation to model successive spike times is given. Finally, examples with specific input signals are provided. Citation: Giuseppe D'Onofrio, Enrica Pirozzi. Successive spike times predicted by a stochastic neuronal model with a variable input signal. Mathematical Biosciences & Engineering, 2016, 13 (3) : 495-507. doi: 10.3934/mbe.2016003 ##### References: [1] A. N. Burkitt, A review of the integrate-and-fire neuron model: I. Homogeneous synaptic input, Biological Cybernetics, 95 (2006), 1-19. doi: 10.1007/s00422-006-0068-6. [2] A. Buonocore, L. Caputo, E. Pirozzi and L. M. Ricciardi, The first passage time problem for Gauss-diffusion processes: Algorithmic approaches and applications to LIF neuronal model, Methodol. Comput. Appl. Prob., 13 (2011), 29-57. doi: 10.1007/s11009-009-9132-8. [3] A. Buonocore, L. Caputo, E. Pirozzi and L. M. Ricciardi, On a stochastic leaky integrate-and-fire neuronal model, Neural Computation, 22 (2010), 2558-2585. doi: 10.1162/NECO_a_00023. [4] A. Buonocore, L. Caputo, E. Pirozzi and M. F. Carfora, Gauss-diffusion processes for modeling the dynamics of a couple of interacting neurons, Math. Biosci. Eng., 11 (2014), 189-201. [5] A. Buonocore, L. Caputo, A. G. Nobile and E. Pirozzi, Gauss-Markov processes in the presence of a reflecting boundary and applications in neuronal models, Applied Mathematics and Computation, 232 (2014), 799-809. doi: 10.1016/j.amc.2014.01.143. [6] A. Buonocore, L. Caputo, A. G. Nobile and E. Pirozzi, Restricted Ornstein-Uhlenbeck process and applications in neuronal models with periodic input signals, Journal of Computational and Applied Mathematics, 285 (2015), 59-71. doi: 10.1016/j.cam.2015.01.042. [7] A. Buonocore, L. Caputo, A. G. Nobile and E. Pirozzi, Gauss-markov processes for neuronal models including reversal potentials, Advances in Cognitive Neurodynamics (IV), 11 (2015), 299-305. doi: 10.1007/978-94-017-9548-7_42. [8] M. J. Chacron, K. Pakdaman and A. Longtin, Interspike interval correlations, memory, adaptation, and refractoriness in a leaky integrate-and-fire neuron with threshold fatigue. Neural Computation, 15 (2003), 253-276. [9] E. Di Nardo, A. G. Nobile, E. Pirozzi and L. M. Ricciardi, A computational approach to first passage-time problems for Gauss-Markov processes, Adv. Appl. Prob., 33 (2001), 453-482. doi: 10.1239/aap/999188324. [10] J. M. Fellous, P. H. Tiesinga, P. J. Thomas and T. J. Sejnowski, Discovering spike patterns in neuronal responses, The Journal of Neuroscience, 24 (2004), 2989-3001. doi: 10.1523/JNEUROSCI.4649-03.2004. [11] V. Giorno and S. Spina, On the return process with refractoriness for a non-homogeneous Ornstein-Uhlenbeck neuronal model, Math. Bios. Eng., 11 (2014), 285-302. [12] H. Kim and S. Shinomoto, Estimating nonstationary inputs from a single spike train based on a neuron model with adaptation, Math. Bios. Eng., 11 (2014), 49-62. [13] P. Lánský and S. Ditlevsen, A review of the methods for signal estimation in stochastic diffusion leaky integrate-and-fire neuronal models, Biol. Cybern., 99 (2008), 253-262. doi: 10.1007/s00422-008-0237-x. [14] P. Lánský, Sources of periodical force in noisy integrate-and-fire models of neuronal dynamics, Physical Review E, 55 (1997), 2040-2043. [15] B. Lindner, Interspike interval statistics for neurons driven by colored noise, Physical Review E, 69 (2004), 022901-1-022901-4. doi: 10.1103/PhysRevE.69.022901. [16] L. M. Ricciardi and L. Sacerdote, The Ornstein-Uhlenbeck process as a model for neuronal activity, Biological Cybernetics, 35 (1979), 1-9. doi: 10.1007/BF01845839. [17] L. M. Ricciardi, A. Di Crescenzo, V. Giorno and A. G. Nobile, An outline of theoretical and algorithmic approaches to first passage time problems with applications to biological modeling, Mathematica Japonica, 50 (1999), 247-322. [18] T. Schwalger, F. Droste and B. Lindner, Statistical structure of neural spiking under non-Poissonian or other non-white stimulation, Journal of Computational Neuroscience, 39 (2015), 29-51. doi: 10.1007/s10827-015-0560-x. [19] M. Shaked and J. G. Shanthikumar, Stochastic Orders and Their Applications, Academic Press, Boston (USA), 1994. [20] S. Shinomoto, Y. Sakai and S. Funahashi, The Ornstein-Uhlenbeck process does not reproduce spiking statistics of cortical neurons, Neural Computation, 11 (1997), 935-951. [21] T. Taillefumier and M. 0. Magnasco, A phase transition in the first passage of a Brownian process through a fluctuating boundary: Implications for neural coding, PNAS, 110 (2013), E1438-E1443. doi: 10.1073/pnas.1212479110. [22] T. Taillefumier and M. Magnasco, A transition to sharp timing in stochastic leaky integrate-and-fire neurons driven by frozen noisy input, Neural Computation, 26 (2014), 819-859. doi: 10.1162/NECO_a_00577. [23] T. Taillefumier and M. Magnasco, A fast algorithm for the first-passage times of Gauss-Markov processes with Holder continuous boundaries, J. Stat. Phys., 140 (2010), 1130-1156. doi: 10.1007/s10955-010-0033-6. [24] P. J. Thomas, A lower bound for the first passage time density of the suprathreshold Ornstein-Uhlenbeck process, J. Appl. Probab., 48 (2011), 420-434. doi: 10.1239/jap/1308662636. [25] J. V. Toups, J. M. Fellous, P. J. Thomas, T. J. Sejnowski and P. H. Tiesinga, Multiple spike time patterns occur at bifurcation points of membrane potential dynamics, PLoS Comput. Biol., 8 (2012), e1002615, 1-19. doi: 10.1371/journal.pcbi.1002615. [26] H. C. Tuckwell, Stochastic Processes in the Neurosciences, SIAM, 1989. doi: 10.1137/1.9781611970159. [27] E. Urdapilleta, Series solution to the first-passage-time problem of a Brownian motion with an exponential time-dependent drift, J. Stat. Phys., 140 (2010), 1130-1156. doi: 10.1088/1751-8113/45/18/185001. show all references ##### References: [1] A. N. Burkitt, A review of the integrate-and-fire neuron model: I. Homogeneous synaptic input, Biological Cybernetics, 95 (2006), 1-19. doi: 10.1007/s00422-006-0068-6. [2] A. Buonocore, L. Caputo, E. Pirozzi and L. M. Ricciardi, The first passage time problem for Gauss-diffusion processes: Algorithmic approaches and applications to LIF neuronal model, Methodol. Comput. Appl. Prob., 13 (2011), 29-57. doi: 10.1007/s11009-009-9132-8. [3] A. Buonocore, L. Caputo, E. Pirozzi and L. M. Ricciardi, On a stochastic leaky integrate-and-fire neuronal model, Neural Computation, 22 (2010), 2558-2585. doi: 10.1162/NECO_a_00023. [4] A. Buonocore, L. Caputo, E. Pirozzi and M. F. Carfora, Gauss-diffusion processes for modeling the dynamics of a couple of interacting neurons, Math. Biosci. Eng., 11 (2014), 189-201. [5] A. Buonocore, L. Caputo, A. G. Nobile and E. Pirozzi, Gauss-Markov processes in the presence of a reflecting boundary and applications in neuronal models, Applied Mathematics and Computation, 232 (2014), 799-809. doi: 10.1016/j.amc.2014.01.143. [6] A. Buonocore, L. Caputo, A. G. Nobile and E. Pirozzi, Restricted Ornstein-Uhlenbeck process and applications in neuronal models with periodic input signals, Journal of Computational and Applied Mathematics, 285 (2015), 59-71. doi: 10.1016/j.cam.2015.01.042. [7] A. Buonocore, L. Caputo, A. G. Nobile and E. Pirozzi, Gauss-markov processes for neuronal models including reversal potentials, Advances in Cognitive Neurodynamics (IV), 11 (2015), 299-305. doi: 10.1007/978-94-017-9548-7_42. [8] M. J. Chacron, K. Pakdaman and A. Longtin, Interspike interval correlations, memory, adaptation, and refractoriness in a leaky integrate-and-fire neuron with threshold fatigue. Neural Computation, 15 (2003), 253-276. [9] E. Di Nardo, A. G. Nobile, E. Pirozzi and L. M. Ricciardi, A computational approach to first passage-time problems for Gauss-Markov processes, Adv. Appl. Prob., 33 (2001), 453-482. doi: 10.1239/aap/999188324. [10] J. M. Fellous, P. H. Tiesinga, P. J. Thomas and T. J. Sejnowski, Discovering spike patterns in neuronal responses, The Journal of Neuroscience, 24 (2004), 2989-3001. doi: 10.1523/JNEUROSCI.4649-03.2004. [11] V. Giorno and S. Spina, On the return process with refractoriness for a non-homogeneous Ornstein-Uhlenbeck neuronal model, Math. Bios. Eng., 11 (2014), 285-302. [12] H. Kim and S. Shinomoto, Estimating nonstationary inputs from a single spike train based on a neuron model with adaptation, Math. Bios. Eng., 11 (2014), 49-62. [13] P. Lánský and S. Ditlevsen, A review of the methods for signal estimation in stochastic diffusion leaky integrate-and-fire neuronal models, Biol. Cybern., 99 (2008), 253-262. doi: 10.1007/s00422-008-0237-x. [14] P. Lánský, Sources of periodical force in noisy integrate-and-fire models of neuronal dynamics, Physical Review E, 55 (1997), 2040-2043. [15] B. Lindner, Interspike interval statistics for neurons driven by colored noise, Physical Review E, 69 (2004), 022901-1-022901-4. doi: 10.1103/PhysRevE.69.022901. [16] L. M. Ricciardi and L. Sacerdote, The Ornstein-Uhlenbeck process as a model for neuronal activity, Biological Cybernetics, 35 (1979), 1-9. doi: 10.1007/BF01845839. [17] L. M. Ricciardi, A. Di Crescenzo, V. Giorno and A. G. Nobile, An outline of theoretical and algorithmic approaches to first passage time problems with applications to biological modeling, Mathematica Japonica, 50 (1999), 247-322. [18] T. Schwalger, F. Droste and B. Lindner, Statistical structure of neural spiking under non-Poissonian or other non-white stimulation, Journal of Computational Neuroscience, 39 (2015), 29-51. doi: 10.1007/s10827-015-0560-x. [19] M. Shaked and J. G. Shanthikumar, Stochastic Orders and Their Applications, Academic Press, Boston (USA), 1994. [20] S. Shinomoto, Y. Sakai and S. Funahashi, The Ornstein-Uhlenbeck process does not reproduce spiking statistics of cortical neurons, Neural Computation, 11 (1997), 935-951. [21] T. Taillefumier and M. 0. Magnasco, A phase transition in the first passage of a Brownian process through a fluctuating boundary: Implications for neural coding, PNAS, 110 (2013), E1438-E1443. doi: 10.1073/pnas.1212479110. [22] T. Taillefumier and M. Magnasco, A transition to sharp timing in stochastic leaky integrate-and-fire neurons driven by frozen noisy input, Neural Computation, 26 (2014), 819-859. doi: 10.1162/NECO_a_00577. [23] T. Taillefumier and M. Magnasco, A fast algorithm for the first-passage times of Gauss-Markov processes with Holder continuous boundaries, J. Stat. Phys., 140 (2010), 1130-1156. doi: 10.1007/s10955-010-0033-6. [24] P. J. Thomas, A lower bound for the first passage time density of the suprathreshold Ornstein-Uhlenbeck process, J. Appl. Probab., 48 (2011), 420-434. doi: 10.1239/jap/1308662636. [25] J. V. Toups, J. M. Fellous, P. J. Thomas, T. J. Sejnowski and P. H. Tiesinga, Multiple spike time patterns occur at bifurcation points of membrane potential dynamics, PLoS Comput. Biol., 8 (2012), e1002615, 1-19. doi: 10.1371/journal.pcbi.1002615. [26] H. C. Tuckwell, Stochastic Processes in the Neurosciences, SIAM, 1989. doi: 10.1137/1.9781611970159. [27] E. Urdapilleta, Series solution to the first-passage-time problem of a Brownian motion with an exponential time-dependent drift, J. Stat. Phys., 140 (2010), 1130-1156. doi: 10.1088/1751-8113/45/18/185001. [1] Massimiliano Tamborrino. Approximation of the first passage time density of a Wiener process to an exponentially decaying boundary by two-piecewise linear threshold. Application to neuronal spiking activity. Mathematical Biosciences & Engineering, 2016, 13 (3) : 613-629. doi: 10.3934/mbe.2016011 [2] Meiqiao Ai, Zhimin Zhang, Wenguang Yu. First passage problems of refracted jump diffusion processes and their applications in valuing equity-linked death benefits. Journal of Industrial and Management Optimization, 2022, 18 (3) : 1689-1707. doi: 10.3934/jimo.2021039 [3] Omer Gursoy, Kamal Adli Mehr, Nail Akar. Steady-state and first passage time distributions for waiting times in the $MAP/M/s+G$ queueing model with generally distributed patience times. 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Discrete and Continuous Dynamical Systems - B, 2005, 5 (4) : 1057-1075. doi: 10.3934/dcdsb.2005.5.1057 2018 Impact Factor: 1.313	2022-05-27 22:55:21	{"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": 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": 0.4986802339553833, "perplexity": 5184.234723852027}, "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/1652663006341.98/warc/CC-MAIN-20220527205437-20220527235437-00174.warc.gz"}
http://layup.media/l6bpiqzv/fe3440-proton-emission-example	Additional troubleshooting resources. The decay of a free proton has been predicted, but never observed. The energy spectrum averaged over 166 shots, as well as the statistical uncertainty, is shown in Fig. Some nuclei decay via double proton emission, such as 45 Fe. Source: JANIS (Java-based Nuclear Data Information Software); The JEFF-3.1.1 Nuclear Data Library. An example of a nuclear equation showing positron emission is shown below: $_{6}^{11}C \rightarrow +_{+1}^{0}\beta +_{5}^{11}B$ Boron has one fewer protons in its nucleus than carbon, but the mass is unchanged because the proton has been replaced by a neutron. It's rather short. • Proton Emission is rare. Proton emission is not confined to just the lighter elements. Proton emission is one process that unstable atoms can use to become more stable. The proton diagnostics in the LD-EDX setup is a time-of-flight (ToF) spectrometer (see Materials and Methods) (2829, ), which is aligned with the sample slit along the target normal direction. Proton emission is the radioactive decay mode that is expected to determine the limit of observable proton-rich nuclei for most elements. Since an atom loses a proton during proton emission, it changes from one element to another. For example, Thailand’s Honda City with a 3-cylinder 1.0-litre turbocharged engine weighs between 1,150 – 1,165 kg. Its patented technology allows for hydrogen (H) to be separated from water (H2O) and extracted from oil sands (or other hydrocarbon reservoirs such as gas or coal) while leaving carbon and other pollutants in the ground. Nitrogen-11 also undergoes proton emission: Carbon-9 has an interesting decay scheme. If you pursue more on this topic, be sure to look up the names of Hans Bethe and Fred Hoyle. 2 of Ref. Neutron decay is a type of radioactive decay of nuclei containing excess neutrons (especially fission products), in which a neutron is simply ejected from the nucleus. There is an issue between Cloudflare's cache and your origin web server. Proton Emission. The Wiki article also identifies two isotopes that decay by (simultaneous) emission of two protons: 30 54 Zn ---> 28 52 Ni + 2 1 1 p. Here's the Wikipedia article on proton capture. In order to be emitted, the proton must penetrate a potential barrier. Or it can also get its electric charge using hydrogen and oxygen (fuel cells). 20.18 is taken from the work of Mukha and Schneider (2001). Using the absolute values of ˜2, as in their Fig. 1F. As a result of its low detection limits (between 1 and 100 ppm) for samples weights of a few milligrams, and the higher sensitivity obtained compared to XRF, PIXE is used to detect trace elements as well as major and minor elements. As an example the beta-delayed proton emission from $$^{11}$$Be is discussed in detail. Example #1: 7 24 N ---> 7 23 N + 0 1 n. The nitrogen-23 that is produced is, itself, unstable and … Be sure to also look at the images related to proton capture. Proton emission: \| \| \|\|\| \| The decay of a proton rich nucleus A populat... World Heritage Encyclopedia, the aggregation of the largest online encyclopedias available, and the … From the Wiki article: From the Wiki article, 69-Tm-147 and 71-Lu-151 also decay by proton emission. 11.10.3 Example of Two-Proton Emission Decay An example of two-proton emission decay is the decay of iron-45 (a highly proton rich radionuclide with Z. There appear to be around 75 isotopes that decay by neutron emission. In the Sun (as well as other stars) there is a process called the CNO cycle. Because it's hard for a positively-charged proton to enter a positively-charged nucleus, proton capture only occurs at high temperature. In addition to the above types of radioactivity, there is a special class of rare beta-decay processes that gives rise to heavy-particle emission. A radionuclide (radioactive nuclide, radioisotope or radioactive isotope) is an atom that has excess nuclear energy, making it unstable. This rare type of emission occurs when a proton is converted to a neutron and a positron in the nucleus, with ejection of the positron. Nuclei below the belt of stability (low neutron-to-proton ratios): These proton-rich nuclei can increase their ratio by either positron emission or electron capture. II. Example #1: 7 10 N ---> 6 9 C + 1 1 p. Nitrogen-11 also undergoes proton emission: 7 11 N ---> 6 10 C + 1 1 p • II. The atomic number will decrease by one while the atomic weight does not change. Example: Proton and Neutron Decay Source: JANIS (Java-based Nuclear Data Information Software); The JEFF-3.1.1 Nuclear Data Library. 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Straightforward And Direct Crossword Clue, Assistant Meaning In Tagalog, Regex Nested Brackets, Frog Rot In Horses, Heavy Duty Plastic Sheds,	2021-04-13 11:22:09	{"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": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5412895083427429, "perplexity": 2671.240195889627}, "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-2021-17/segments/1618038072180.33/warc/CC-MAIN-20210413092418-20210413122418-00610.warc.gz"}
http://jkamenik.github.io/blog/2010/11/18/learning-selenium/	# Learning Selenium ## Background My basic need is to find a platform where I can test FF, IE, and Safari on Windows, Linux, and OS X. I use OS X as my platform, and Safari or Webkit as my environment. I don’t like Windows or IE. Linux is OK, but I like OS X because it just works the way I want. And I find FF to be slow, and Firebug which is needed to debug we pages causes rendering changes and timing issues (most notably causing FF to crash). Ideally I want the testing environment: 1. To be developed in Safari on OS X 2. To be able to test both internal libraries and rendered UI 3. To use unit tests to test internal libraries 4. To use interactive tests to test rendered UI 5. To use the unit/interactive tests as regression system moving forward 6. To write the tests once on my browser of choice 7. To run the tests on all combinations of browser and platform. 8. To not be bogged down by the testing framework 9. To be free, or very cheap From my research it looked like Selenium did basically exactly what I needed. And unfortunately was the only real option. There were plenty of options for taking screen shots of public sites (which mine isn’t, yet) and comparing those between browsers. And there are several options for unit testing javascript, but only Selenium did both and could be run on my own hardware. ## Implementation From my reading it looked like I wanted to use the IDE to create the tests, and remote controls to run the browsers. Eventually I need to scale to Selenium Grid, but that is for later discussion. ### Test code This is the sample file that I created to test. ### Using the IDE It took a long time to understand this tool, since I had no background in Selenium. The basic premiss is that each file is a single test case, which is a set of tests. Each test is a grouping of three items: the action, the target, and the expected result. It natively creates a 3 column HTML table, which it can also run, but personal preference is that use the IDE to export the basic test into a different language. I am a rails developer, and am familiar with rspec so I use the IDE to run the tests to make sure they work, but then I transfer it to rspec since it is a more expressive test framework. The downside is that you have to use a Remote Control to run the test, which adds an extra level of complications. We will get to the Remote Control later. A basic HTML test looks like this: There really is nothing more to it then that. The one thing to note is that the test uses verifyEval which takes a JavaScript string. In all tests the this object is the base Selenium object so if you want to get to the window object you have to traverse up the stack via this.browserbot.getUserWindow(). Unfortunately everything tested in Selenium is converted to a string before testing. So if I need to ensure that an integer parsing function actually produces a number I need to use typeof. ## Using RSpec The IDE is a great way to test scripts live, but for any programmer it is going to be easier to use a testing framework doing it programmatically. As a rails guy I prefer RSpec so that is what I use. ### Installing This package requires ruby-gems, rspec, and selenium-client. I am going to assume you have ruby-gems installed already. The others are installed like this: ### Converting When using Rspec the only real thing to remember is that there are no assert* or verify* methods. The reason is that Rspec itself is a testing framework so it will have it own version of assert and verify (in this case should). The IDE has a great feature in that it converts the HTML test into a rspec test for you. It isn’t a great format, but it is better then nothing and is a good place to start. The browser being shown is chrome. This actually means Firefox, not Google Chrome. For Google Chrome use googlechrome. For Safari use safari, but remember that you will need to disable the popup blocker manually and close Safari (for this user) otherwise it will just sit there forever. ### Remote Controls A remote control is what Selenium uses to execute the test. The IDE comes with it built-in, but it is tied to FireFox. To use IE, Safari, or Chrome you need to download the remote control software: http://seleniumhq.org/projects/remote-control. This software is just a Java server that opens your machine on port 4444 (by default) to allow Selenium clients to run tests. Each client gets its own browser instance to run the tests in. The server must be run by a user that has access the browser and has a screen to render to. Firefox will only run a single profile per user. If you need to run Firefox concurrently on the same machine you need to fake a second profile. Don’t do it, just create a VM; you will be happier. Google Chrome does not works on OS X. This is because OS X doesn’t add application executables to the path, and the server code isn’t smart enough to use the executable directly. The fix is supposedly here, but I was not able to get it to work. If I do I will probably write another blog entry and link it here. ### Putting it all together By default RSpec provides no runner code and the code the IDE produces is not standalone. This is not a problem since installing RSpec into a rails app installs script/spec. I have copied the runner code here so make it easier. I am going to assume the RSpec runner code is called spec and the test file is called test.rb. To run this test from the command line do the following: ruby spec test.rb Assuming you followed all the steps the test should have opened Firefox, executed a page, run the tests, closed Firefox, and returned the results. Now you can add more tests and have Selenium execute them. 1. Using Selenium Grid 2. Using Chrome, or IE 3. Using a Grid to run the same test in all browsers on all OSs	2017-11-19 02:44:41	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 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": 0.20397992432117462, "perplexity": 1768.6501756956256}, "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-2017-47/segments/1510934805265.10/warc/CC-MAIN-20171119023719-20171119043719-00067.warc.gz"}
https://www.zigya.com/study/book?class=11&board=bsem&subject=Physics&book=Physics+Part+I&chapter=Laws+of+Motion&q_type=&q_topic=Common+Forces+In+Mechanics+&q_category=&question_id=PHENJE11143727	## Book Store Download books and chapters from book store. Currently only available for. CBSE Gujarat Board Haryana Board ## Previous Year Papers Download the PDF Question Papers Free for off line practice and view the Solutions online. Currently only available for. Class 10 Class 12 Given in the figure are two blocks A and B of weight 20 N and 100 N respectively. These are being pressed against a wall by a force F as shown. If the coefficient of friction between the blocks is 0.1 and between block B and the wall is 0.15, the frictional force applied by the wall on block B is • 100N • 80 N • 120 N • 150 N C. 120 N In the vertical direction, weight are balanced by frictional forces. As the blocks are in equilibrium balance forces are in horizontal and vertical direction. For the system of blocks (A+B) F = N For block A, fA = 20 N and for block B. fB = fA +100 = 120 N In the vertical direction, weight are balanced by frictional forces. As the blocks are in equilibrium balance forces are in horizontal and vertical direction. For the system of blocks (A+B) F = N For block A, fA = 20 N and for block B. fB = fA +100 = 120 N 731 Views When the branches of an apple tree are shaken, the apples fall down. Why? The apple fall from an apple tree when it shaken because of inertia of rest. Apple is in a state of rest and when the tree is suddenly shaken, apples still tends to remain in it's same state of rest whereas branches move. So, the apples fall down. 1475 Views Is Aristotle’s law of motion now correct? No. Aristotl'e law of motion is false. 1233 Views State Galileo’s law of motion. Galileo’s law of motion states that, a body continues to move in the same direction with constant speed, if no force is acting on the body. 1332 Views Define inertia. The property by virtue of which the body cannot change its state of rest or uniform motion in a straight line, unless an external force is acting on the body is called as Inertia. 1316 Views What is Aristotle’s law of motion? Aristotle’s law of motion states that an external force is required to keep the body in motion. 2445 Views	2019-01-23 23:46:19	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 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": 0.28315719962120056, "perplexity": 1447.093346026799}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "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-2019-04/segments/1547584431529.98/warc/CC-MAIN-20190123234228-20190124020228-00593.warc.gz"}
https://www.svm-tutorial.com/2014/10/support-vector-regression-r/comment-page-20/	# Support Vector Regression with R In this article I will show how to use R to perform a Support Vector Regression. We will first do a simple linear regression, then move to the Support Vector Regression so that you can see how the two behave with the same data. ## A simple data set To begin with we will use this simple data set: I just put some data in excel. I prefer that over using an existing well-known data-set because the purpose of the article is not about the data, but more about the models we will use. As you can see there seems to be some kind of relation between our two variables X and Y, and it look like we could fit a line which would pass near each point. Let's do that in R ! ## Step 1: Simple linear regression in R Here is the same data in CSV format, I saved it in a file regression.csv : We can now use R to display the data and fit a line: # Load the data from the csv file # Plot the data plot(data, pch=16) # Create a linear regression model model <- lm(Y ~ X, data) abline(model) The code above displays the following graph: ## Step 2: How good is our regression ? In order to be able to compare the linear regression with the support vector regression we first need a way to measure how good it is. To do that we will change a little bit our code to visualize each prediction made by our model dataDirectory <- "D:/" plot(data, pch=16) model <- lm(Y ~ X , data) # make a prediction for each X predictedY <- predict(model, data) # display the predictions points(data$X, predictedY, col = "blue", pch=4) This produces the following graph: For each data point $X_i$ the model makes a prediction $\hat{Y}_i$ displayed as a blue cross on the graph. The only difference with the previous graph is that the dots are not connected with each other. In order to measure how good our model is we will compute how much errors it makes. We can compare each $Y_i$ value with the associated predicted value $\hat{Y}_i$ and see how far away they are with a simple difference. Note that the expression $\hat{Y}_i - Y_i$ is the error, if we make a perfect prediction $\hat{Y}_i$ will be equal to $Y_i$ and the error will be zero. If we do this for each data point and sum the error we will have the sum of the errors, and if we takes the mean we will get the Mean Squared Error (MSE) A common way to measure error in machine learning is to use the Root Mean Squared Error (RMSE) so we will use it instead. To compute the RMSE we take the square root and we get the RMSE Using R we can come with the following code to compute the RMSE rmse <- function(error) { sqrt(mean(error^2)) } error <- model$residuals # same as data$Y - predictedY predictionRMSE <- rmse(error) # 5.703778 We know now that the RMSE of our linear regression model is 5.70. Let's try to improve it with SVR ! ## Step 3: Support Vector Regression In order to create a SVR model with R you will need the package e1071. So be sure to install it and to add the library(e1071) line at the start of your file. Below is the code to make predictions with Support Vector Regression: model <- svm(Y ~ X , data) predictedY <- predict(model, data) points(data$X, predictedY, col = "red", pch=4) As you can see it looks a lot like the linear regression code. Note that we called the svm function (not svr !) it's because this function can also be used to make classifications with Support Vector Machine. The function will automatically choose SVM if it detects that the data is categorical (if the variable is a factor in R). The code draws the following graph: This time the predictions is closer to the real values ! Let's compute the RMSE of our support vector regression model. # /!\ this time svrModel$residuals is not the same as data$Y - predictedY # so we compute the error like this error <- data$Y - predictedY svrPredictionRMSE <- rmse(error) # 3.157061 As expected the RMSE is better, it is now 3.15 compared to 5.70 before. But can we do better ? ## Step 4: Tuning your support vector regression model In order to improve the performance of the support vector regression we will need to select the best parameters for the model. In our previous example, we performed an epsilon-regression, we did not set any value for epsilon ( $\epsilon$ ), but it took a default value of 0.1. There is also a cost parameter which we can change to avoid overfitting. The process of choosing these parameters is called hyperparameter optimization, or model selection. The standard way of doing it is by doing a grid search. It means we will train a lot of models for the different couples of $\epsilon$ and cost, and choose the best one. # perform a grid search tuneResult <- tune(svm, Y ~ X, data = data, ranges = list(epsilon = seq(0,1,0.1), cost = 2^(2:9)) ) print(tuneResult) # Draw the tuning graph plot(tuneResult) There is two important points in the code above: • we use the tune method to train models with $\epsilon = 0, 0.1, 0.2, ... ,1$ and cost = $2^2, 2^3, 2^4, ... ,2^9$ which means it will train 88 models (it can take a long time) • the tuneResult returns the MSE, don't forget to convert it to RMSE before comparing the value to our previous model. The last line plot the result of the grid search: On this graph we can see that the darker the region is the better our model is (because the RMSE is closer to zero in darker regions). This means we can try another grid search in a narrower range we will try with $\epsilon$ values between 0 and 0.2. It does not look like the cost value is having an effect for the moment so we will keep it as it is to see if it changes. tuneResult <- tune(svm, Y ~ X, data = data, ranges = list(epsilon = seq(0,0.2,0.01), cost = 2^(2:9)) ) print(tuneResult) plot(tuneResult) We trained different 168 models with this small piece of code. As we zoomed-in inside the dark region we can see that there is several darker patch. From the graph you can see that models with C between 200 and 300 and $\epsilon$ between 0.08 and 0.09 have less error. Hopefully for us, we don't have to select the best model with our eyes and R allows us to get it very easily and use it to make predictions. tunedModel <- tuneResult$best.model tunedModelY <- predict(tunedModel, data) error <- data\$Y - tunedModelY # this value can be different on your computer # because the tune method randomly shuffles the data tunedModelRMSE <- rmse(error) # 2.219642 We improved again the RMSE of our support vector regression model ! If we want we can visualize both our models. The first SVR model is in red, and the tuned SVR model is in blue on the graph below : I hope you enjoyed this introduction on Support Vector Regression with R. You can get the source code of this tutorial. Each step has its own file. An overview of Support Vector Machines ### 189 thoughts on “Support Vector Regression with R” 1. Very Nice Article and very useful. 2. Hello, thanks a lot. One question, the first tuning parameters you use can be use for any problem? or do I have to change the grid? thanks again.	2021-09-22 11:31:42	{"extraction_info": {"found_math": true, "script_math_tex": 13, "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": 15, "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": 0.6256846189498901, "perplexity": 1349.159685344365}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-39/segments/1631780057347.80/warc/CC-MAIN-20210922102402-20210922132402-00260.warc.gz"}
https://answers.ros.org/question/35303/stopping-a-node-by-ctrlc-doesnt-update-rosnode-list-commands-result/	# Stopping a node by "Ctrl+C" doesn't update "rosnode list" command's result. hello everyone. i am new to ros. i just started studying ros. i'm following tutorials for beginner now, and i found one thing that doesn't seem to be right. there's a tutorial titled "Understanding ROS Nodes" and it showed me the way to stop a node by pressing "CTRL+C" and to display currently running nodes on the screen by "rosnode list" command. here is the question. if I stop a node by pressing "CTRL+C", shouldn't "rosnode list" command "NOT" display the node I just stopped? Apparently, it still displays the node although i stopped it. is this how it's supposed to be? or is this a bug? edit retag close merge delete Sort by » oldest newest most voted In the usual case this should not happen. If I am not mistaken, the node should unregister with the master when the last NodeHandle goes out of scope, and ros::shutdown() gets called. There might be a problem with the way your code is written which prevents this from happening. On the flip side, for most applications, a node that does not unregister should not constitute a problem. To ensure that this is not a problem specific to the node you have written, try out some of the nodes already available in roscpp_tutorials. Try the following commands in order: 1. Start roscore 2. rosnode list 3. rosrun roscpp_tutorials talker 4. rosnode list 5. Ctrl+C the talker node 6. rosnode list The rosnode list output for me looks something like this: piyushk@piyushk-laptop:~$rosnode list /rosout piyushk@piyushk-laptop:~$ rosnode list /rosout /talker piyushk@piyushk-laptop:~$rosnode list /rosout If your output looks similar to that above, it may be a problem in the code you've written. If not, we can try and debug the problem. Piyush more ## Comments Thanks for the answer~Piyush. I tried your suggestion and it worked fine as expected. The problem I mentioned earlier though happened when running "turtlesim_node"(of turtlesim package. a part of ros installation). so i guess it's a problem of something else. and i found out that the problem doesn't ( 2012-05-31 22:20:43 -0500 )edit happen with ROS electric. I didn't try out every version of ros but the problem that didn't happen with "electric" happens with "fuerte" version seems that it's the problem of "fuerte" version of ros. is there a place within the wiki I can report this bug(I think)? and thank you again Piyush:) ( 2012-05-31 22:21:00 -0500 )edit 1 You should post this bug on trac: https://code.ros.org/trac/ros/ ( 2012-06-01 09:29:41 -0500 )edit I just ran into the same issue too, in the same tutorial, while using Fuerte on a fresh Ubuntu-12.04, 64-bit. When I used "rosnode info turtlesim", I saw: ... contacting node http://i7:56977/ ... ERROR: Communication with node[http://i7:56977/] failed! I thought maybe it was because I did not have$ROS_HOSTNAME defined as described here: http://www.ros.org/wiki/ROS/NetworkSetup#Single_machine_configuration So I added export ROS_HOSTNAME=localhost After that "rosnode info turtlesim" started working and gave me: ... contacting node http://localhost:60372/ ... Pid: 6178 I thought it was strange to see a different port number, but rosnode list started working too. Then I went to the next tutorial and did "roscore" while other roscore was running. Then I noticed that "rosnode list" again doesn't remove killed nodes and "rosnode info turtlesim" now gives: contacting node http://localhost:39889/ ... ERROR: Communication with node[http://localhost:39889/] failed! Is the port number is not being set? Seugen, did you file a bug for this? more ( 2012-07-01 23:11:15 -0500 )edit	2021-05-13 10:39:31	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 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": 0.19640986621379852, "perplexity": 4662.730468901105}, "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-2021-21/segments/1620243990584.33/warc/CC-MAIN-20210513080742-20210513110742-00100.warc.gz"}
https://www.trustudies.com/question/3206/Q-11-A-piece-of-strings-is-30-cm-long-What-will-be-the-length-of-each-side-if-the-string-is-used-to-form-br-a-a-square-br-b-an-equilateral-triangle-br-c-a-regular-hexagon/	# Q.11 A piece of strings is 30 cm long. What will be the length of each side if the string is used to form: (a) a square? (b) an equilateral triangle? (c) a regular hexagon? (a) Perimeter of square = 30 cm 4 × side = 30 Side = $$\frac{30}{4}$$ Side = 7.5 cm (b) Perimeter of an equilateral triangle = 30 cm 3 × side = 30 Side = $$\frac{30}{10}$$ Side = 10 cm (c) Perimeter of a regular hexagon = 30 cm 6 × side = 30 Side = $$\frac{30}{6}$$ Side = 5 cm	2021-03-06 07:35:32	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4196115732192993, "perplexity": 2066.71888520333}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178374616.70/warc/CC-MAIN-20210306070129-20210306100129-00242.warc.gz"}
https://brilliant.org/problems/can-you-solve-thiseasy-one/	# But graphing is so much easier! How many integral solution(s) of the equation $$\lfloor x\rfloor^2=2^x$$? Details and Assumptions: • $$\lfloor x \rfloor$$ is the greatest integer less than or equal to $$x$$. ×	2017-05-30 01:49:04	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8503491878509521, "perplexity": 1124.9437036785612}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-22/segments/1495463613738.67/warc/CC-MAIN-20170530011338-20170530031338-00116.warc.gz"}
https://testbook.com/question-answer/ifdfracsqrt3-1sqrt31-dfrac5--608a5efa2c85781d802c2416	# If $$\dfrac{\sqrt{3}-1}{\sqrt{3}+1}-\dfrac{5+2\sqrt{3}}{7+4\sqrt{3}}=a+b\sqrt{3}$$, then the value of (a + b) is; This question was previously asked in DFCCIL Executive Operating 2018 Official Paper View all DFCCIL Executive Papers > 1. 8 2. -5 3. 9 4. -4 Option 4 : -4 Free CT 1: Current Affairs (Government Policies and Schemes) 44200 10 Questions 10 Marks 10 Mins ## Detailed Solution Given: $$\dfrac{√{3}-1}{√{3}+1}-\dfrac{5+2√{3}}{7+4√{3}}=a+b√{3}$$ Formula used: (a + b)2 = a2 + b2 + 2ab a2 - b2 = (a + b)(a - b) Calculation: $$\dfrac{√{3}-1}{√{3}+1}-\dfrac{5+2√{3}}{7+4√{3}}$$ ⇒ $$\dfrac{√{3}-1}{√{3}+1 } \ \times \ \dfrac{√{3}-1}{√{3}-1}-\dfrac{5+2√{3}}{7+4√{3}}\ \times \dfrac{7-4√{3}}{7-4√{3}}$$ $$\dfrac{(√{3}-1)^2}{{3}-1}-\dfrac{5+2√{3} \ \times ({7}-{4√3})}{49 \ - \ 48}$$ $$\dfrac{3 \ +\ 1 \ - \ 2√3}{2}-{(35 \ -\ 20√3\ + \ 14√3 \ -\ 24)}$$ ⇒ 2 - √3 - (11 - 6√3) ⇒ - 9 + 5√3 = a + b√3 So a = - 9 b = 5 a + b = - 9 + 5 = - 4 ∴ a + b = - 4.	2021-09-22 17:58:24	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.42157432436943054, "perplexity": 4458.804091445842}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-39/segments/1631780057371.69/warc/CC-MAIN-20210922163121-20210922193121-00005.warc.gz"}
https://plainmath.net/7202/scatterplot-graph-function-equal-residual-describe-function-increase	Ask question # Make a scatterplot of the data and graph the function f(x)= -8x^{2} + 95x + 745. Make a residual plot and describe how well the function fits the data. begin{array}{\|c\|c\|} hline text{Price Increase} & 0 & 1 & 2 & 3 & 4 hline text{Sales} & 730 & 850 & 930 & 951 & 1010 hline end{array} Question Scatterplots asked 2021-01-08 Make a scatterplot of the data and graph the function $$\displaystyle{f{{\left({x}\right)}}}=\ -{8}{x}^{{{2}}}\ +\ {95}{x}\ +\ {745}.$$ Make a residual plot and describe how well the function fits the data. $$\displaystyle{b}{e}{g}\in{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}{\left\lbrace{\left\|{c}\right\|}{c}{\mid}\right\rbrace}{h}{l}\in{e}\text{Price Increase}&{0}&{1}&{2}&{3}&{4}\backslash{h}{l}\in{e}\text{Sales}&{730}&{850}&{930}&{951}&{1010}\backslash{h}{l}\in{e}{e}{n}{d}{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}$$ ## Answers (1) 2021-01-09 Step 1 By drawing the curve $$\displaystyle{f{{\left({x}\right)}}}=\ -{8}{x}^{{{2}}}\ +\ {95}{x}\ +\ {745}$$ (expected) and marking the points in the graph (actual) we get it is given below. The residual value is calculated as $$\displaystyle{b}{e}{g}\in{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}{\left\lbrace{\left\|{c}\right\|}{c}{\mid}\right\rbrace}{h}{l}\in{e}\text{Residual value}=\text{Actual value}-\text{Expected value}\backslash{h}{l}\in{e}{e}{n}{d}{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}$$ $$\displaystyle\text{Residual value at}\ {x}={0},\ {R}_{{{0}}}={730}\ -\ {745}$$ $$\displaystyle={b}{e}{g}\in{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}{\left\lbrace{\left\|{c}\right\|}{c}{\mid}\right\rbrace}{h}{l}\in{e}-{15}\backslash{h}{l}\in{e}{e}{n}{d}{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}$$ $$\displaystyle\text{Residual value at}\ {x}={1},\ {R}_{{{1}}}={850}\ -\ {832}$$ $$\displaystyle={b}{e}{g}\in{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}{\left\lbrace{\left\|{c}\right\|}{c}{\mid}\right\rbrace}{h}{l}\in{e}+{18}\backslash{h}{l}\in{e}{e}{n}{d}{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}$$ $$\displaystyle\text{Residual value at}\ {x}={2},\ {R}_{{{2}}}={930}\ -\ {903}$$ $$\displaystyle={b}{e}{g}\in{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}{\left\lbrace{\left\|{c}\right\|}{c}{\mid}\right\rbrace}{h}{l}\in{e}+{27}\backslash{h}{l}\in{e}{e}{n}{d}{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}$$ $$\displaystyle\text{Residual value at}\ {x}={3},\ {R}_{{{3}}}={951}\ -\ {958}$$ $$\displaystyle={b}{e}{g}\in{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}{\left\lbrace{\left\|{c}\right\|}{c}{\mid}\right\rbrace}{h}{l}\in{e}-{7}\backslash{h}{l}\in{e}{e}{n}{d}{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}$$ $$\displaystyle\text{Residual value at}\ {x}={4},\ {R}_{{{4}}}={1010}\ -\ {997}$$ $$\displaystyle={b}{e}{g}\in{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}{\left\lbrace{\left\|{c}\right\|}{c}{\mid}\right\rbrace}{h}{l}\in{e}+{13}\backslash{h}{l}\in{e}{e}{n}{d}{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}$$ Step 2 By plotting the residual value to the graph which is given below, we can see that the points are randomly scattered through the graph. This indicates that the line is a Good Fot. ### Relevant Questions asked 2021-01-13 For each set of data below, draw a scatterplot and decide whether or not the data exhibits approximately periodic behaviour. a) $$\displaystyle{b}{e}{g}\in{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}{\left\lbrace{\left\|{c}\right\|}{c}{\mid}\right\rbrace}{h}{l}\in{e}{x}&{0}&{1}&{2}&{3}&{4}&{5}&{6}&{7}&{8}&{9}&{10}&{11}&{12}\backslash{h}{l}\in{e}{y}&{0}&{1}&{1.4}&{1}&{0}&-{1}&-{1.4}&-{1}&{0}&{1}&{1.4}&{1}&{0}\backslash{h}{l}\in{e}{e}{n}{d}{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}$$ b) $$\displaystyle{b}{e}{g}\in{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}{\left\lbrace{\left\|{c}\right\|}{c}{\mid}\right\rbrace}{h}{l}\in{e}{x}&{0}&{1}&{2}&{3}&{4}\backslash{h}{l}\in{e}{y}&{4}&{1}&{0}&{1}&{4}\backslash{h}{l}\in{e}{e}{n}{d}{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}$$ c) $$\displaystyle{b}{e}{g}\in{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}{\left\lbrace{\left\|{c}\right\|}{c}{\mid}\right\rbrace}{h}{l}\in{e}{x}&{0}&{0.5}&{1.0}&{1.5}&{2.0}&{2.5}&{3.0}&{3.5}\backslash{h}{l}\in{e}{y}&{0}&{1.9}&{3.5}&{4.5}&{4.7}&{4.3}&{3.4}&{2.4}\backslash{h}{l}\in{e}{e}{n}{d}{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}$$ d) $$\displaystyle{b}{e}{g}\in{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}{\left\lbrace{\left\|{c}\right\|}{c}{\mid}\right\rbrace}{h}{l}\in{e}{x}&{0}&{2}&{3}&{4}&{5}&{6}&{7}&{8}&{9}&{10}&{12}\backslash{h}{l}\in{e}{y}&{0}&{4.7}&{3.4}&{1.7}&{2.1}&{5.2}&{8.9}&{10.9}&{10.2}&{8.4}&{10.4}\backslash{h}{l}\in{e}{e}{n}{d}{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}$$ asked 2021-02-02 Determine which of the following functions $$\displaystyle{f{{\left({x}\right)}}}={c}{x},\ {g{{\left({x}\right)}}}={c}{x}^{{{2}}},\ {h}{\left({x}\right)}={c}\sqrt{{{\left\|{x}\right\|}}},\ \text{and}\ {r}{\left({x}\right)}=\ {\frac{{{c}}}{{{x}}}}$$ can be used to model the data and determine the value of the constant c that will make the function fit the data in the table. $$\displaystyle{b}{e}{g}\in{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}{\left\lbrace{\left\|{c}\right\|}{c}{\mid}\right\rbrace}{h}{l}\in{e}{x}&-{4}&-{1}&{0}&{1}&{4}\backslash{h}{l}\in{e}{y}&-{32}&-{2}&{0}&-{2}&-{32}\backslash{h}{l}\in{e}{e}{n}{d}{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}$$ asked 2021-01-19 The annual sales S (in millions of dollars) for the Perrigo Company from 2004 through 2010 are shown in the table. $$\displaystyle{b}{e}{g}\in{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}{\left\lbrace{\left\|{c}\right\|}{c}{\mid}\right\rbrace}{h}{l}\in{e}\text{Year}&{2004}&{2005}&{2006}&{2007}&{2008}&{2009}&{2010}\backslash{h}{l}\in{e}\text{Sales, S}&{898.2}&{1024.1}&{1366.8}&{1447.4}&{1822.1}&{2006.9}&{2268.9}\backslash{h}{l}\in{e}{e}{n}{d}{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}$$ a) Use a graphing utility to create a scatter plot of the data. Let t represent the year, with $$\displaystyle{t}={4}$$ corresponding to 2004. b) Use the regression feature of the graphing utility to find an exponential model for the data. Use the Inverse Property $$\displaystyle{b}={e}^{{{\ln{\ }}{b}}}$$ to rewrite the model as an exponential model in base e. c) Use the regression feature of the graphing utility to find a logarithmic model for the data. d) Use the exponential model in base e and the logarithmic model to predict sales in 2011. It is projected that sales in 2011 will be \$2740 million. Do the predictions from the two models agree with this projection? Explain. asked 2020-12-05 Use the sample data to construct a scatterplot. Use the first variable for the x-axis. Based on the scatterplot, what do you conclude about a linear correlation? The table li sts che t sizes (di stance around chest in inches) and weights (pounds) of anesthetized bears that were measured. $$\displaystyle{b}{e}{g}\in{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}{\left\lbrace{\left\|{c}\right\|}{c}{\mid}\right\rbrace}{h}{l}\in{e}\text{Chest(in.)}&{a}\mp,\ {26}&{a}\mp,\ {45}&{a}\mp,\ {54}&{a}\mp,\ {49}&{a}\mp,\ {35}&{a}\mp,\ {41}&{a}\mp,\ {41}\backslash{h}{l}\in{e}\text{Weight(lb)}&{a}\mp,\ {80}&{a}\mp,\ {344}&{a}\mp,\ {416}&{a}\mp,\ {348}&{a}\mp,\ {166}&{a}\mp,\ {220}&{a}\mp,\ {262}\backslash{h}{l}\in{e}{e}{n}{d}{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}$$ asked 2021-02-09 The table gives the number of active Twitter users worldwide, semiannually from 2010 to 2016. $$\displaystyle{b}{e}{g}\in{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}{\left\lbrace{\left\|{c}\right\|}{c}{\mid}\right\rbrace}{h}{l}\in{e}\text{Years since}&\text{January 1, 2010}&\text{Twitter user}&\text{(millions)}\backslash{h}{l}\in{e}{0}&{30}&{3.5}&{232}\backslash{h}{l}\in{e}{0.5}&{49}&{4.0}&{255}\backslash{h}{l}\in{e}{1.0}&{68}&{4.5}&{284}\backslash{h}{l}\in{e}{1.5}&{101}&{5.0}&{302}\backslash{h}{l}\in{e}{2.0}&{138}&{5.5}&{307}\backslash{h}{l}\in{e}{2.5}&{167}&{6.0}&{310}\backslash{h}{l}\in{e}{3.0}&{204}&{6.5}&{317}\backslash{h}{l}\in{e}{e}{n}{d}{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}$$ Use a calculator or computer to fit both an exponential function and a logistic function to these data. Graph the data points and both functions, and comment on the accuracy of the models. asked 2021-03-11 An automobile tire manufacturer collected the data in the table relating tire pressure x (in pounds per square inch) and mileage (in thousands of miles). A mathematical model for the data is given by $$\displaystyle f{{\left({x}\right)}}=-{0.554}{x}^{2}+{35.5}{x}-{514}.$$ $$\begin{array}{\|c\|c\|} \hline x & Mileage \\ \hline 28 & 45 \\ \hline 30 & 51\\ \hline 32 & 56\\ \hline 34 & 50\\ \hline 36 & 46\\ \hline \end{array}$$ (A) Complete the table below. $$\begin{array}{\|c\|c\|} \hline x & Mileage & f(x) \\ \hline 28 & 45 \\ \hline 30 & 51\\ \hline 32 & 56\\ \hline 34 & 50\\ \hline 36 & 46\\ \hline \end{array}$$ (Round to one decimal place as needed.) $$A. 20602060xf(x)$$ A coordinate system has a horizontal x-axis labeled from 20 to 60 in increments of 2 and a vertical y-axis labeled from 20 to 60 in increments of 2. Data points are plotted at (28,45), (30,51), (32,56), (34,50), and (36,46). A parabola opens downward and passes through the points (28,45.7), (30,52.4), (32,54.7), (34,52.6), and (36,46.0). All points are approximate. $$B. 20602060xf(x)$$ Acoordinate system has a horizontal x-axis labeled from 20 to 60 in increments of 2 and a vertical y-axis labeled from 20 to 60 in increments of 2. Data points are plotted at (43,30), (45,36), (47,41), (49,35), and (51,31). A parabola opens downward and passes through the points (43,30.7), (45,37.4), (47,39.7), (49,37.6), and (51,31). All points are approximate. $$C. 20602060xf(x)$$ A coordinate system has a horizontal x-axis labeled from 20 to 60 in increments of 2 and a vertical y-axis labeled from 20 to 60 in increments of 2. Data points are plotted at (43,45), (45,51), (47,56), (49,50), and (51,46). A parabola opens downward and passes through the points (43,45.7), (45,52.4), (47,54.7), (49,52.6), and (51,46.0). All points are approximate. $$D.20602060xf(x)$$ A coordinate system has a horizontal x-axis labeled from 20 to 60 in increments of 2 and a vertical y-axis labeled from 20 to 60 in increments of 2. Data points are plotted at (28,30), (30,36), (32,41), (34,35), and (36,31). A parabola opens downward and passes through the points (28,30.7), (30,37.4), (32,39.7), (34,37.6), and (36,31). All points are approximate. (C) Use the modeling function f(x) to estimate the mileage for a tire pressure of 29 $$\displaystyle\frac{{{l}{b}{s}}}{{{s}{q}}}\in.$$ and for 35 $$\displaystyle\frac{{{l}{b}{s}}}{{{s}{q}}}\in.$$ The mileage for the tire pressure $$\displaystyle{29}\frac{{{l}{b}{s}}}{{{s}{q}}}\in.$$ is The mileage for the tire pressure $$\displaystyle{35}\frac{{{l}{b}{s}}}{{{s}{q}}}$$ in. is (Round to two decimal places as needed.) (D) Write a brief description of the relationship between tire pressure and mileage. A. As tire pressure increases, mileage decreases to a minimum at a certain tire pressure, then begins to increase. B. As tire pressure increases, mileage decreases. C. As tire pressure increases, mileage increases to a maximum at a certain tire pressure, then begins to decrease. D. As tire pressure increases, mileage increases. asked 2020-12-02 Gastroenterology We present data relating protein concentration to pancreatic function as measured by trypsin secretion among patients with cystic fibrosis. If we do not want to assume normality for these distributions, then what statistical procedure can be used to compare the three groups? Perform the test mentioned in Problem 12.42 and report a p-value. How do your results compare with a parametric analysis of the data? Relationship between protein concentration $$(mg/mL)$$ of duodenal secretions to pancreatic function as measured by trypsin secretion: $$\left[U/\left(k\ \frac{g}{h}r\right)\right]$$ Tapsin secreton [UGA] $$\leq\ 50$$ $$\begin{array}{\|c\|c\|}\hline \text{Subject number} & \text{Protetion concentration} \\ \hline 1 & 1.7 \\ \hline 2 & 2.0 \\ \hline 3 & 2.0 \\ \hline 4 & 2.2 \\ \hline 5 & 4.0 \\ \hline 6 & 4.0 \\ \hline 7 & 5.0 \\ \hline 8 & 6.7 \\ \hline 9 & 7.8 \\ \hline \end{array}$$ $$51\ -\ 1000$$ $$\begin{array}{\|c\|c\|}\hline \text{Subject number} & \text{Protetion concentration} \\ \hline 1 & 1.4 \\ \hline 2 & 2.4 \\ \hline 3 & 2.4 \\ \hline 4 & 3.3 \\ \hline 5 & 4.4 \\ \hline 6 & 4.7 \\ \hline 7 & 6.7 \\ \hline 8 & 7.9 \\ \hline 9 & 9.5 \\ \hline 10 & 11.7 \\ \hline \end{array}$$ $$>\ 1000$$ $$\begin{array}{\|c\|c\|}\hline \text{Subject number} & \text{Protetion concentration} \\ \hline 1 & 2.9 \\ \hline 2 & 3.8 \\ \hline 3 & 4.4 \\ \hline 4 & 4.7 \\ \hline 5 & 5.5 \\ \hline 6 & 5.6 \\ \hline 7 & 7.4 \\ \hline 8 & 9.4 \\ \hline 9 & 10.3 \\ \hline \end{array}$$ asked 2021-01-07 The U.S. Census Bureau publishes information on the population of the United States in Current Population Reports. The following table gives the resident U.S. population, in millions of persons, for the years 1990-2009. Forecast the U.S. population in the years 2010 and 2011 PSK\begin{array}{\|c\|c\|} \hline \text{Year} & \text{Population (millions)} \\ \hline 1990 & 250 \\ \hline 1991 & 253\\ \hline 1992 & 257\\ \hline 1993 & 260\\ \hline 1994 & 263\\ \hline 1995 & 266\\ \hline 1996 & 269\\ \hline 1997 & 273\\ \hline 1998 & 276\\ \hline 1999 & 279\\ \hline 2000 & 282\\ \hline 2001 & 285\\ \hline 2002 & 288\\ \hline 2003 & 290\\ \hline 2004 & 293\\ \hline 2005 & 296\\ \hline 2006 & 299\\ \hline 2007 & 302\\ \hline 2008 & 304\\ \hline 2009 & 307\\ \hline \end{array}ZSK a) Obtain a scatterplot for the data. b) Find and interpret the regression equation. c) Mace the specified forecasts. asked 2021-02-03 The following data on = soil depth (in centimeters) and y = percentage of montmorillonite in the soil were taken from a scatterplot in the paper "Ancient Maya Drained Field Agriculture: Its Possible Application Today in the New River Floodplain, Belize, C.A." (Agricultural Ecosystems and Environment [1984]: 67-84): a. Draw a scatterplot of y versus x. b. The equation of the least-squares line is 0.45x. Draw this line on your scatterplot. Do there appear to be any large residuals? c. Compute the residuals, and construct a residual plot. Are there any unusual features in the plot? x 40 50 60 70 80 90 100 y 58 34 32 30 28 27 22 $$\displaystyle{\left[\hat{{{y}}}={64.50}\right]}$$. asked 2021-02-11 Find an exponential function that fits the experimental data collected over time t. $$\displaystyle{b}{e}{g}\in{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}{\left\lbrace{\left\|{c}\right\|}{c}{\mid}\right\rbrace}{h}{l}\in{e}{t}&{0}&{1}&{2}&{3}&{4}\backslash{h}{l}\in{e}{y}&{600.00}&{630.00}&{661.50}&{694.58}&{729.30}\backslash{h}{l}\in{e}{e}{n}{d}{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}$$ ...	2021-05-12 01:01:41	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6936781406402588, "perplexity": 1164.8722969137375}, "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-2021-21/segments/1620243991693.14/warc/CC-MAIN-20210512004850-20210512034850-00624.warc.gz"}
http://umj.imath.kiev.ua/article/?lang=en&article=9307	2018 Том 70 № 7 # Linear Methods for Summing Fourier Series and Approximation in Weighted Lebesgue Spaces with Variable Exponents Jafarov S. Z. Abstract In the present work, we study the estimates for the periodic functions of linear operators constructed on the basis of their Fourier series in weighted Lebesgue spaces with variable exponent and Muckenhoupt weights. In this case, the obtained estimates depend on the sequence of the best approximation in weighted Lebesgue spaces with variable exponent. English version (Springer): Ukrainian Mathematical Journal 66 (2014), no. 10, pp 1509-1518. Citation Example: Jafarov S. Z. Linear Methods for Summing Fourier Series and Approximation in Weighted Lebesgue Spaces with Variable Exponents // Ukr. Mat. Zh. - 2014. - 66, № 10. - pp. 1348–1356. Full text	2018-08-21 14:26:40	{"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": 0.8580324053764343, "perplexity": 602.7877374998018}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-34/segments/1534221218189.86/warc/CC-MAIN-20180821132121-20180821152121-00542.warc.gz"}
https://support.bioconductor.org/p/79445/	Search Question: What does this mean? 0 2.6 years ago by xlyan0110 xlyan0110 wrote: Hi all, When I load some packages, this keeps coming out: Error in unloadNamespace(package) : namespace 'IRanges' is imported by 'Biostrings', 'XVector', 'AnnotationDbi' so cannot be unloaded Error in library(pkg, character.only = TRUE, logical.return = TRUE, lib.loc = lib.loc, : Package 'IRanges' version 2.4.7 cannot be unloaded Does anyone know what this mean? Best, Bef written 2.6 years ago by xlyan0110 Please post the output of sessionInfo() . My guess is you have some outdated packages. Try biocLite() (without arguments) to update everything. (For best results do this in a fresh R session started with R --vanilla so that no packages will be loaded already). If you still have problems, try biocValid() which will tell you if there are other problems with your package versions. ADD REPLYlink modified 2.6 years ago • written 2.6 years ago by Dan Tenenbaum ♦♦ 8.2k Also, make sure to start your R session so that it ignores any .Rprofile or .RData files, e.g., from the command line with R --vanilla. Probably it would help to edit your question to include the output of the sessionInfo() command, to provide the full output of the simplest scenario that you can create to illustrate the problem, and the result of traceback() immediately after the error occurs. ADD REPLYlink written 2.6 years ago by Martin Morgan ♦♦ 22k	2018-10-18 16:37:40	{"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": 0.18347607553005219, "perplexity": 5188.011155664778}, "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-2018-43/segments/1539583511889.43/warc/CC-MAIN-20181018152212-20181018173712-00518.warc.gz"}
https://jmservera.com/find-the-distance-between-two-points-7-9-3-7-95-6/	# Find the Distance Between Two Points (-7/9,-3) , (-7/9,5/6) (-79,-3) , (-79,56) Use the distance formula to determine the distance between the two points. Distance=(x2-x1)2+(y2-y1)2 Substitute the actual values of the points into the distance formula. ((-79)-(-79))2+(56-(-3))2 Simplify. Multiply -(-79). Multiply -1 by -1. (-79+1(79))2+(56-(-3))2 Multiply 79 by 1. (-79+79)2+(56-(-3))2 (-79+79)2+(56-(-3))2 02+(56-(-3))2 Simplify the expression. Raising 0 to any positive power yields 0. 0+(56-(-3))2 Multiply -1 by -3. 0+(56+3)2 0+(56+3)2 To write 3 as a fraction with a common denominator, multiply by 66. 0+(56+3⋅66)2 Combine 3 and 66. 0+(56+3⋅66)2 Combine the numerators over the common denominator. 0+(5+3⋅66)2 Simplify the numerator. Multiply 3 by 6. 0+(5+186)2 0+(236)2 0+(236)2 Apply the product rule to 236. 0+23262 Raise 23 to the power of 2. 0+52962 Raise 6 to the power of 2. 0+52936 52936 Rewrite 52936 as 52936. 52936 Simplify the numerator. Rewrite 529 as 232. 23236 Pull terms out from under the radical, assuming positive real numbers. 2336 2336 Simplify the denominator. Rewrite 36 as 62. 2362 Pull terms out from under the radical, assuming positive real numbers. 236 236 236 Find the Distance Between Two Points (-7/9,-3) , (-7/9,5/6) ## Our Professionals ### Lydia Fran #### We are MathExperts Solve all your Math Problems: https://elanyachtselection.com/ Scroll to top	2022-09-25 01:04:21	{"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": 0.8761107921600342, "perplexity": 4109.412179651885}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-40/segments/1664030334332.96/warc/CC-MAIN-20220925004536-20220925034536-00485.warc.gz"}
https://studydaddy.com/question/what-is-the-standard-form-of-the-equation-of-a-circle-with-center--3-3-and-tange	Waiting for answer This question has not been answered yet. You can hire a professional tutor to get the answer. QUESTION # What is the standard form of the equation of a circle with center (-3,3) and tangent to the line y=1? Equation of circle is x^2+y^2+6x-6y+14=0 and y=1 is tangent at (-3,1) The equation of a circle with center (-3,3) with radius r is (x+3)^2+(y-3)^2=r^2 or x^2+y^2+6x-6y+9+9-r^2=0 As y=1 is a tangent to this circle, putting y=1 in the equation of a circle should give only one solution for x. Doing so we get x^2+1+6x-6+9+9-r^2=0 or x^2+6x+13-r^2=0 and as we should have only one solution, discriminant of this quadratic equation should be 0. Hence, 6^2-4xx1xx(13-r^2)=0 or 36-52+4r^2=0 or 4r^2=16 and as r has to be positive r=2 and hence equation of circle is x^2+y^2+6x-6y+9+9-4=0 or x^2+y^2+6x-6y+14=0 and y=1 is tangent at (-3,1)	2019-04-25 20:44:36	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.37465959787368774, "perplexity": 838.2856993493211}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-18/segments/1555578733077.68/warc/CC-MAIN-20190425193912-20190425215042-00050.warc.gz"}
https://davidlowryduda.com/summer-number-theory/	# Summer Number Theory 2013 Welcome to the page for Summer@Brown 2013 Number Theory with David Lowry-Duda! This is the course website. Here, there (were — back in 2013) copies of the syllabus, problem sets, exams, etc., as well as basic information about the course. But much more importantly, at the bottom of the page there is a comment section, where I encourage you to write as many comments as you want. If you have a question, concern, response, idea, or perhaps even a topic you’d really like to go over, leave a comment! If this is your first time visiting this page, leave a comment below so that you’ll be able to comment in the future (I moderate first-comments). Course Information: Number Theory: An Introduction to Higher Mathematics Instructor: David Lowry-Duda Email: djlowry@math.brown.edu Syllabus: available here Links to discussion pages: • A (real and correct) proof of the $sin$ problem from Day 1 • Highpoints from the first week • A note on the Chinese Remainder Theorem, with two applications we didn’t talk about in class	2021-01-18 13:07:51	{"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": 0.7008751630783081, "perplexity": 1152.0073038015391}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-04/segments/1610703514796.13/warc/CC-MAIN-20210118123320-20210118153320-00045.warc.gz"}
https://math.stackexchange.com/questions/26445/division-by-0/668559	# Division by $0$ I came up some definitions I have sort of difficulty to distinguish. In parentheses are my questions. 1. $\dfrac {x}{0}$ is Impossible ( If it's impossible it can't have neither infinite solutions or even one. Nevertheless, both $1.$ and $2.$ are divided by zero, but only $2.$ has infinite solutions so as $1.$ has none solution, how and why ?) 2. $\dfrac {0}{0}$ is Undefined and has infinite solutions. (How come one be Undefined and yet has infinite solutions ?) 3. $\dfrac {0}{x}$ and $x \ne 0$, it's okay for me, no problem, but if someone else wants to add something about it, feel free to do it. • On 3, $0/x$, you need to say explicitly $x \ne 0$, to distinguish it from 2. – Henry Mar 11 '11 at 20:43 • The following text was added in a suggested edit: "The 787 videos listed in the auto generated You-Tube channel: Division by zero is a good indication of the importance and common misunderstanding of this question. In my opinion, it is the obligation of this mathematical community to provide a greater variety of explanations to interested students at all levels." If this information is useful, it should be added as a comment, not by editing posts by other users. – Martin Sleziak Nov 8 '12 at 11:41 • Yes, this makes sense! Clearly a question with +19 that has an answer of +50 hasn't received enough attention! – Asaf Karagila Nov 8 '12 at 13:33 • It is undefined because it has infinite solutions. – Parth Kohli Feb 2 '13 at 15:42 • en.wikipedia.org/wiki/Wheel_theory – Martin Brandenburg May 8 '14 at 7:42 The first question you need to ask is: What does "$a/b$" mean? The answer is: "$a/b$ is the unique solution to the equation $bz = a$." (I'm using $z$ as the unknown, since you are using $x$ for other things). (3) is perfectly fine: $0/x$, with $x\neq 0$, is the solution to $xz = 0$; the unique solution is $z=0$, so $0/x = z$. The reason it's unique is because $x\neq 0$, so the only way for the product to be $0$ is if $z$ is $0$. In (1), by "impossible" we mean that the equation that defines it has no solutions: for something to be equal to $x/0$, with $x\neq 0$, we would need $0z = x$. But $0z=0$ for any $z$, so there are no solutions to the equation. Since there are no solutions to the equation, there is no such thing as "$x/0$". So $x/0$ does not represent any number. In (2), the situation is a bit trickier; in terms of the defining equation, the problem here is that the equation $0z=0$ has any value of $z$ as a solution (that's what the "infinite solutions" means). Since the expression $a/b$ means "the unique solution to $bx= a$, then when $a=b=0$, you don't have a unique answer, so there is no "unique solution". Generally speaking, we simply do not define "division by $0$". The issue is that, once you get to calculus, you are going to find situations where you have two variable quantities, $a$ and $b$, and you are considering $a/b$; and as $a$ and $b$ changes, you want to know what happens to $a/b$. In those situations, if $a$ is approaching $x$ and $b$ is approaching $y\neq 0$, then $a/b$ will approach $x/y$, no problem. If $a$ approaches $x\neq 0$, and $b$ approaches $0$, then $a/b$ does not approach anything (the "limits does not exist"). But if both $a$ and $b$ approach $0$, then you don't know what happens to $a/b$; it can exist, not exist, or approach pretty much any number. We say this kind of limit is "indeterminate". So there is a reason for separating out cases (1) and (2): very soon you will see an important qualitative difference between the first kind of "does not exist" and the second kind. • Here's an example of how #2 is undefined. What makes it infinite is the fact that this can be repeated for any number. – James Mertz May 2 '13 at 16:14 • I like this answer for the first part, but I don't like the part about calculus.. 1) $\infty$ is not anything and 2) stated like that, it's as you never know what happens to $a / b$.. you just need more informations about the exact nature of the variables – Ant Apr 4 '14 at 17:31 • In your last paragraph you need to add that when you have these a,b "approaching something" that they are continuous at this point. – Matthew Levy Dec 23 '14 at 17:07 • I have borrowed your starting paragraph for my answer :-) – arivero Aug 16 '15 at 20:11 The key is to realize what a fraction $\frac ab$ really represents: $\frac ab$ is the number with the property that $\frac ab \cdot b = a$. So, in the first case if $x \ne 0$, there is no number $\frac x0$ with the property that $\frac x0 \cdot 0 = x$ since anything times zero is zero. So $\frac x0$ is undefined. In the second, any number $y$ has the property that $y \cdot 0 = 0$, so $\frac 00$ could represent any number $y$ according to the above characterization of a fraction, so $\frac 00$ is said to be indeterminate. Finally, if $x \ne 0$ then $0$ has the property that $0 \cdot x = 0$, so $\frac 0x$ is the number $0$. • One should not use "indeterminate" here. That applies only to functions, not numbers. – Bill Dubuque Mar 11 '11 at 20:56 • @BillDubuque I am currently learning elementary arithmetic. In mostly all contexts it is said that $\dfrac 00$ is indeterminate. – user103816 May 25 '14 at 9:48 • I say that $\frac{0}{0}$ does evaluate to a value and that it is not what you would expect yet the term $\frac{0}{0}$ has no value. The value that the term evaluates to would be $1$ since this would fit under the multiplicative identity property as in $\frac{anything}{anything} = 1$. The division of something by itself even if that something is nothing will return itself. This doesn't mean that $\frac{0}{0} = 0$ because this wouldn't return itself, anything that returns itself has an associated value of $1$. – Francis Cugler Mar 20 '17 at 23:51 • We understand that anything multiplied by $1$ is itself which is true, and that anything multiplied by $0$ is $0$ is also true and when we try to explain what $1 \cdot 0$ or $0 \cdot 1$ is... the evaluation of this will result the same every time as the answer would be $0$ which fits both statements. So let's apply this to fractions $0 \cdot 1 = \frac{0}{1} \cdot \frac{1}{1} = \frac{0 \cdot 1}{1 \cdot 1}$ ... – Francis Cugler Mar 20 '17 at 23:57 • (...continued) $\frac{0 \cdot 1}{1 \cdot 1} = \frac{0}{1} = 0$ so far so good. So what happens when we reverse this: Let's try it out. But first we need to understand that $\frac{1}{0} \neq 0$ we need to consider this the reciprocal of $0$ or $\frac{0}{1}$ and we know that the only value that has an equivalent reciprocal is $1$ or $\frac{1}{1}$. Then it would suggest that $\frac{1}{0} \cdot \frac{1}{1} = \frac{1}{0}$ and that $\frac{1}{0} \cdot \frac{0}{1} = \frac{0}{0}$ and since $\frac{0}{0} = 1$ from my above statement it would state that anything divided by $0$ would result in $1$. – Francis Cugler Mar 21 '17 at 0:10 Definition of Division For every real number a and every nonzero real number b, the quotient a$\div$b, or $\dfrac{a}{b}$, is defined by: $$a\div b=a \cdot \frac{1}{b}.$$ Dividing by zero would mean multiplying by the reciprocal of 0. But 0 has no reciprocal (because 0 times any number is 0, not 1.) Therefore, division by 0 has no meaning in the set of real numbers. Multiplicative property of 0 Prove: If $a$ is any real number, then $a\cdot 0 = 0$ and $0\cdot a = 0$. Proof: Statement _________________Reason 1. $0 = 0 + 0$ ______________1. Identity property of addition 2. $a\cdot0 = a(0 + 0)$ __________2. Multiplication property of equality 3. $a\cdot0 = a\cdot0 + a\cdot0$ ________3. Distributive property of mult. with respect to add. 4. But $a\cdot0 = a\cdot0 + 0$ _______4. Identity property of addition 5. $\therefore$ $a\cdot0 + a\cdot0 = a\cdot0 + 0$ ____5. Transitive property of equality 6. $a\cdot0 = 0$ _______________6. Subtraction property of equality 7. $0\cdot a = 0$ _______________7. Commutative property of multiplication Therefore, 0 times any number is 0, not 1. (Source: Algebra: Structure and Method Book 1) The two cases presented in an older edition of Book 2 of the above source are: 1. Dividing a nonzero number by zero, violates the multiplicative property of zero and therefore the properties of the real numbers upon which it is proven, as shown above. 2. Dividing zero by zero, which does not violate the multiplicative property of zero, but multiplication by zero is an operation that results in zero for every real number. If $\dfrac{a}{0}$ = c, then $a = 0\cdot c$. But $0\cdot c = 0$. Hence, if $a$ is not equal to $0$, no value of $c$ can make the statement $a = 0\cdot c$ true, while if $a = 0$, every value of $c$ will make the statement true. Thus, $\dfrac{a}{0}$ either has no value or is indefinite in value. This separation into two cases, one of which results in no value satisfying the multiplicative property of zero and the other resulting in an indefinite value satisfying it, gives the impression that $\dfrac 0{0}$ is allowed. The following argument starts with the equation: $$a \cdot \frac{1}{a} = 1$$ and notes that $a\neq 0$ because $0$ times any number is $0$. Thus, the product of $0$ and no real number equals $1$. This further reinforces the idea that $0$ has no number that when multiplied by it equals $1$. • By the definition at the top, $\frac{1}{b} = 1 \cdot \frac{1}{b} = 1 \cdot 1 \cdot \frac{1}{b} = \dots$ which is not really a definition. I think $b^{-1}$ would be clearer than $\frac{1}{b}$, because $b^{-1}$ (pronounced "$b$ inverse") emphasizes that it's defined by the field axioms, not defined in terms of division. – Jordan Nov 13 at 5:59 Just to give another point of view (purely algebraic one): Suppose you have a ring (a mathematical structure with addition and multiplication satisfying a bare minimum of laws you need to call them that), and in it there is a number $x$ such that $x \cdot 0 = 1$. Then $1 = x \cdot 0 = x \cdot (1 - 1) = x - x = 0$, which means that for any $y$ in this ring $y = y \cdot 1 = y \cdot 0 = y (1 - 1) = y - y = 0$, so this ring has just one element. Such ring is called trivial, and it is clearly not an extension of the ring of integer numbers. If you can divide by zero, then $1/0$ is defined and it has to satisfy the property above. Thus, division by zero is possible only in the trivial ring. • What if I don't have a ring? What if I have a wheel? – JMCF125 Jan 18 '14 at 14:57 • @JMCF125 then you roll – Alexei Averchenko Sep 7 '15 at 9:12 You will pretty much never see "0/0" or "x/0" in a situation where somebody expects you to actually interpret it as having a value. Other than simple mistakes, the times it comes up are usually of the following sort: To solve the equation $ax=b$ for $x$, consider the expression "$b/a$". 1. If it is of the form "$0/0$", your equation has infinitely many solutions 2. If it is of the form "$x/0$" for nonzero x, your equation has no solutions 3. Otherwise, the division makes sense and the result is the unique solution You might hear the word "form" mentioned to refer to the fact that we're talking about a formula, and not the number that might result from evaluating the formula. (especially in the context of limits) It's important to note the difference, because the number system you use was created so that "$0/0$" and "$x/0$" are not allowed -- they are meaningless when viewed as arithmetic expressions. (the same is true for "$x/y$" if you do not already know that $y \neq 0$) There are lots of very good reasons why arithmetic was created in this way, and the other answers mention some of them. I feel I should mention that there are other forms of arithmetic that behave differently. The projective numbers are often useful, and 1/0 makes sense in them (but $0/0$ does not). Wheel theory is somewhat more esoteric, but it provides an example where even $0/0$ makes sense. (and also clearly demonstrates the difficulties in accommodating its existence) Let me add this quick bit in addition to what has already been said (assuming you know a little set theory). Take the following semi-random example. Suppose you have a function $f$ with $f(5) = 14$ and $f(6) = 11$. Going backwards, what do you get? Assuming $f$ is only defined for $5$ and $6$, $f^{-1}(14) = 5$ and $f^{-1}(11) = 6$, right? Now consider a different function, which like $f$ is only defined at two points... let's call it $g$ with $g(5) = 8$ and $g(6) = 8$. Now, what is $g^{-1}(8)$? Well, it wants to be both $5$ and $6$ if it's really the inverse, but defining it either way causes a contradiction so it must be undefined. So what's the point? In algebra many operations (like multiplying by a nonzero number) are like $f$ and and many (multiplying by zero, for example) are like $g$. Here, draw the picture with arrows... with $f$ you know where the arrows came from, with $g$ two arrows point to the same place so you don't know where you 'came from'. Now back to multiplication. Imagine the arrows if you multiply by $\frac{1}{2}$ versus if you multiply by $0$. You can see that essentially the same thing is going on, but with infinitely many numbers instead of just a few. BTW: There is one partial 'fix' if you know a little set theory: (new notation here, NOTE THE CURLY 'SET' BRACKETS): $f^{-1}(\{8\}) = \{5,6\}$. Another example: if $h(x) = x^2$ then $h^{-1}(\{4,25\}) = \{2,5\}$. And back to were we started from, inverting division by zero: if you have $s(x) = 0$ then $s^{-1}(\{0\}) = (-\infty,\infty)$. If your domain consists of a two-element set, or a set with more than two elements (where any infinite set gets classified as having more than two elements) then Arturo's answer applies. However, if your domain consists of {0}, then things work out a bit differently, as Bill Dubuque pointed out in a comment elsewhere. For a system with domain of {0}, you'll still define a/b as the unique solution to (bz)=a. Now, (3) still works out as perfectly fine. x/0 means the unique solution to (0z)=x. Well, x can only equal 0 in this domain, so this means the unique solution to (0z)=0. z can also only equal 0 here, so the equation does have a unique solution of 0. 0/0 means the unique solution to (0z)=0. Well, z can only equal 0 here, and if z=0, the equation does hold, so (0/0)=0 here also. • what does domain mean here? – Srivatsan Sep 2 '11 at 17:29 • The domain consists of the set of elements under consideration. – Doug Spoonwood Sep 2 '11 at 17:37 Because dividing by zero destroys everything. Reuben Hersh in "What is Mathematics, Really?" gives the following explanation (quotes). It articulates the point that we invent rules, as we go along, in order to account for extended powers of calculation. However, not unexpectedly, this often comes at a price. And each time we have to decide whether the cost is worth bearing or not. Note that the question "why do we not divide by zero?" is loaded with the psychology of the exception. Meaning, it seems as if have a perfectly nice rule for all integers to begin with, and all of a sudden we exclude zero from it. This prompts the question "why do we exclude zero?" as a reasonable one. Especially since that's what it comes down to - excluding just one number. But understanding the process of creation (of definition) is important in order to understand why a plausible (or even an excellent) question may be missing a point. It is not the case that we "have a perfectly nice rule for all integers to begin with". Addition and multiplication start only with the natural numbers (positive integers starting with $1$) and only later do we move on to the reverse processes of subtraction and division. Given multiplication, therefore, it is not that we exclude zero from this new process we call "division", but rather that we find no good reason to extend the process in order to include zero - other than a psychological sense of ease that something holds for all numbers which is fine but not if it destroys all arithmetic. "God made the Integers, all else is man's work" goes the saying. It shouldn't come as a surprise that there should be a few of these exceptions, to this work of rules. (It turns out we can extend division to the negative integers without a problem, and with great gains, thus enhancing the psychology of a special case for zero. It's only a special case, and one shouldn't expect otherwise.) Back to math. Suppose it were handy to introduce division by zero. What would be the cost of this rule? Hersh explains. 1/0 Doesn't Work (0 into 1 Doesn't Go) Division by $0$ is not allowed. Why not? If it's allowed to introduce a symbol $i$ and say it's the square root of $-1$, which doesn't have a square root, why not introduce some symbol, say $Q$, for $1/0$? We introduce new numbers, whether negative, fractional, irrational, or complex, to preserve and extend our calculating power. We relax one rule, but preserve the others. After we bring in $i$, for example, we still add, subtract, multiply, and divide as before. I now show that there's no way to define $(1/0)\cdot0$ that preserves the rules of arithmetic. One basic rule is, $0\cdot$ (any number) $=0$. (Formula I) So $0\cdot(1/0) = 0$. Another basic rule is $(x)\cdot(1/x) = 1$, provided $x$ isn't zero. (But if we want $1/0$ to be a number, this proviso becomes obsolete.) (Formula II) So $0\cdot(1/0) = 1$ Putting Formulas I and II together, $1=0$. Addition gives $2=0$, $3=0$, and so on, $n=0$ for every integer $n$. Since all numbers equal zero, all numbers equal each other. There's only one number — $0$. The supposition that $1/0$ exists and satisfies the laws of arithmetic leads to collapse of the number system. Nothing is left, except - nothing. In the case of the imaginary $i$, it turns out that not only is there nothing destroyed (other than our sense of familiarity with numbers), but that things fall into place (Fundamental Theorem of Algebra). • If we consider that $0 = \frac{0}{1}$ and that $\frac{0}{1} \neq \frac{1}{0}$ We would see that $\frac{0}{1} \cdot \frac{1}{0} = \frac{0 \cdot 1}{1 \cdot 0} = \frac{0}{0}$. What should $\frac{0}{0} =$... If you ask me I say it should equal $1$ since anything divided by itself would yield itself. This would allow $\frac{1}{0}$ to be the reciprocal of $\frac{0}{1}$. $\frac{1}{0}$ or any fraction of the form $\frac{n}{0}$ is a special form. It is not equal to neither $1$ nor $0$. If $\frac{0}{1}$ or $\frac{n}{1}$ is horizontal slope then $\frac{1}{0}$ or $\frac{n}{0}$ represents vertical slope. – Francis Cugler Mar 21 '17 at 1:51 • This can bee seen in the linear equation $y = mx + b$ where $m$ is defined as $\frac{rise}{run} = \frac{y_2 - y_2}{x_2 - x_1} = \frac{\delta y}{\delta x} = \frac{\sin\theta}{\cos\theta} = \tan\theta$ where $\theta$ is the angle above or below the horizon. When we have $0$ slope as in $\frac{0}{d}$ it is the $\sin\theta$ that evaluates to $0$ at the angles $0°,\pm 180°, \pm 360°$ since $\delta y$ or $rise = 0$. No change in height or height is constant and when we apply this to $y = mx + b$ we see that $y = 0 \cdot x + b \implies y = b$ where $y$ is constant and $\delta y = 0$.... – Francis Cugler Mar 21 '17 at 1:57 • We also know that every line has an infinite amount of perpendiculars to it. We can find the slope of the line that is perpendicular by the formula $-1 = \frac{rise}{run} \cdot -\frac{run}{rise}$. So if any line has a slope of $0$ then it's perpendicular must be $-1 = \frac{\sin\theta = 0}{\cos\theta = 1} \cdot -\frac{\cos\theta = 1}{\sin\theta = 0} = \frac{0}{1} \cdot -\frac{1}{0}$. Thus vertical slope must be defined!... – Francis Cugler Mar 21 '17 at 2:01 • This makes complete sense because when we look at the range and domain of both the $\sin\theta$ or $\delta y$ component of the fraction or the numerator and the $\cos\theta$ or $\delta x$ component of the fraction or the denominator independently their domain and ranges are the same where their domain is $\mathbb R$ and their ranges are $[-1,1]$. So this means they both can accept all numbers and they output a valid range from $[-1,1]$... – Francis Cugler Mar 21 '17 at 2:02 • So when we have vertical slope or division by $0$. It can not be $0$, nor can it be $1$. Now since both the $\sin$ and $\cos$ functions are rotational, periodical, sinusoidal continuous functions it would be err to think that either the $\tan$ or $\cot$ function should have any discontinuity at all! So if the slope is $0$, then $\tan\theta = 0$. And the reciprocal of $\tan\theta$ is $\cot\theta$ thus when referring to slope if the slope is defined by $\tan\theta$ then its perpendicular must be $-\cot\theta$.... – Francis Cugler Mar 21 '17 at 2:07 This is an attempt at some intuition for someone who doesn't know a lot of math. The equation $\frac{a}{b}=x$ is the same as the equation $a=b\cdot$ x. You can look at $a=b\cdot x$ as asking the question "if I want to build $a$ out of $b$'s, how many $b$'s do I need?" (the $x$ is how many pieces of $b$ you need to build $a$) Example $\frac{4}{0.1}=x$ is the same as $4=0.1\cdot x$. How many $0.1$'s do you need to build 4 out of $0.1$'s? Well you need $\frac{4}{0.1}$ or $40$ pieces. Indeed, $40\cdot 0.1 = 4$. So what about dividing by 1? Example $\frac{7}{1}=x$ is the same as $7=1\cdot x$. How many $1$'s do you need to build 7 out of $1$'s? Obviously you'll need seven pieces of one, beause $1+1+1+1+1+1+1=7$ So what about dividing by zero? Example $\frac{3}{0}=x$ is the same as $3=0\cdot x$. How many $0$'s do you need to build 3 out of $0$'s? Well, how can you build a number out of zeros? No matter what you do with your zeros, you're never going to be able to build any number out of zeros. If you could build a number out of zeros, you should be able to write a number, say 9, as a sum of zeros, which would mean that $9=0+0+0+0+0+0+\dots$, which can never be true no matter how many zeros you use. So it doesn't really make sense to divide something by zero. We can divide by $0$. Let $X$ be the set of numbers we are debating on. The multiplicative inverse of $x\in X$, namely $x^{-1}$ or $\frac{1}{x}$, is defined as $x\cdot x^{-1} = id$, where $id$ does not change any element in $X$ when we multiply, for instance, $1 \in \mathbb{Q}$. For any $y \in X$, $0 \cdot y=0$, so we require $id = 0$, so let $id = 0$. Then, for any $x \in X,$ $x\cdot id = 0$. We get $X = \{0\}$. We can divide by $0$ on $\{0\}$, since $0\cdot 0 = 0$. But this is not an interesting case. So, we usually assume $X\not =\{0\}$, so that we cannot divide by $0$. I usually argue as the other answerers have but recently I have started using a slightly different argument. I argue that multiplying by $1/x$ undoes the action of multiplying by $x$. So for example $112=22$ and $22(1/2)$ brings you back to $11$. Now we have $011=0$ but you can't get back to $11$ by multiplying as zero times anything is zero. The first question you need to ask is: What does "a/b" mean? The answer is: "a/b is a representative of a class of pairs of numbers $(a,b) \in Z \times Z$ such that two pairs $(a,b)$ and $(c,d)$ are equivalent if $ad=cb$." This equivalence fails -is not transitive- if we include the pair $0/0$, because any pair should be equivalent to it, even two arbitrary pairs which are not equivalent between them. So we need to exclude the "indeterminate" pair, correcting the above definition to say instead $(a,b) \in Z \times Z - \{ (0,0) \}$. All the elements of the form $0/a$ are equivalent. And similarly all the elements of the form $a/0$ are equivalent. Call them the classes $0/1$ and $1/0$ We can define multiplication operating in each $Z$ set, i.e. $(a,b).(c,d) \equiv (ac,bd)$. With this definition, the identity is the class represented by $(1,1)$. We find that our multiplication is not defined for a product of elements in the classes $0/1$ and $1/0$. The product is precisely the excluded pair $(0,0)$. So if we want multiplication to be always well defined in our set of all the fractions, we need to exclude one of the two classes. Traditionally we exclude the class $1/0$, the class that the original post calls the "Impossible class". Arriving here, we see that really the motivations to exclude the "undefined element" and the "impossible class" are very different: the former, being able to match any other fraction, completely destroys the transitivity of the equivalence relation, while the later simply is a nuisance to close the multiplication. Both classes had the potential to do the role of a multiplicative zero: $$1/0 . (a,b) = (a,0) \propto 1/0$$ $$0/1 . (a,b) = (0,b) \propto 0/1$$ But now that we have declared the first one "impossible" it is clear that we now must kept the second one to be used as the traditional zero. The last steps should be to define a sum operation such that $(a,b) + 0/1 = (a,b)$ and a mapping of the integer numbers into the fractions, $Z \longrightarrow Z \times Z - \{ (0,0) \}$, preserving the operations of sum and multiplication already defined in the integers, and mapping the zero and identity of the integers to the corresponding classes in the fractions. But as far as the OP questions goes, we do not need even to finish the construction :-) EDIT it could be interesting to try to argue that, in the same way that with the usual definition of sum we have $(a,b) + 0/1 = (a,b)$, we should have that $(a,b)+ 1/0 = 1/0$. So we would be in accord with the usual meaning of "infinity" that we assign to this class. In fact it is so if we define $$(a,b) + (c,d) \equiv (ad+bc,bd)$$ Among the rules for arithmetic with fractions are the formulas for adding and subtracting, $${a\over b}\pm{c\over d}={ad\pm bc\over bd}$$ Now what if we allow division by $0$? Keeping in mind the properties $x+0=x$, $x\cdot0=0$, and $x-x=0$ for all numbers $x$, we find first that $$0={1\over 0}-{1\over 0}={1\cdot0-0\cdot1\over0\cdot0}={0\over0}$$ and then that, for all $x$, $$x={x\over1}={x\over1}+0={x\over1}+{0\over0}={x\cdot0+1\cdot0\over1\cdot0}={0\over0}=0$$ • You failed to express 0 as a fraction initially when incorporating it into the expression of adding it to $\frac{x}{1}$ – Francis Cugler Mar 3 '17 at 13:07 • Also $\frac{0}{0}$ can evaluate to different answers depending on the context in which it is used. It can yield 0, 1, or $\infty$ – Francis Cugler Mar 3 '17 at 13:09 • One last thing 0 is not a number! It is only a place holder or it represents the null or empty set! Consider an arbitrary Point in any dimensional space: The space can be 1D, 2D, 3D, ... ND, etc. The Point itself is 0D space for it is arbitrary. Now because the Point itself has 0 dimensionality does not mean that the point doesn't exist. It only has locale. It does not have any sense of direction or awareness of any other object, it doesn't recognize angles or rotations. Once you introduce a 2nd point and associate the two, then you have 2 points that gives you a line, 1D space or distance. – Francis Cugler Mar 3 '17 at 13:15 If you try to define $x=\frac a0$, you arrive at the contradiction that $x\cdot0 =a$ for nonzero $a$. Also, take a look at the graph of $y=\frac1x$... it goes to $\infty$ as $x\to0^+$, and to $-\infty$ as $x\to0^-$. Thus there is no way to fill in the value at $x=0$ that isn't arbitrary... José Manuel Rodríguez Caballero (https://www.researchgate.net/profile/Jose_Rodriguez_Caballero2) Added an answer In the proof assistant Isabelle/HOL we have x/0 = 0 for each number x. This is advantageous in order to simplify the proofs. You can download this proof assistant here: https://isabelle.in.tum.de/ (https://www.researchgate.net/deref/https%3A%2F%2Fisabelle.in.tum.de%2F) Close the mysterious and long history of division by zero and open the new world since Aristotelēs-Euclid:　1/0=0/0=z/0= \tan (\pi/2)=0. Sangaku Journal of Mathematics (SJM) c ⃝SJMISSN 2534-9562 Volume 2 (2018), pp. 57-73 Received 20 November 2018. Published on-line 29 November 2018 web: http://www.sangaku-journal.eu/ (http://www.sangaku-journal.eu/) c ⃝The Author(s) This article is published with open access1. Wasan Geometry and Division by Zero Calculus ∗Hiroshi Okumura and ∗∗Saburou Saitoh "$$x \div y$$" is actually just shorthand for "$$x \cdot \lambda$$, where $$y \cdot \lambda = 1$$". Therefore: "what is $$x \div 0$$?" is just shorthand for "what is $$x \cdot \lambda$$, where $$0 \cdot \lambda = 1$$?" In truth, $$0 \cdot \lambda = 0$$ for any $$\lambda$$. Therefore, there is no $$\lambda$$ such that $$0 \cdot \lambda = 1$$. Because "$$\lambda$$, where $$0 \cdot \lambda = 1$$" does not exist, "$$x \cdot \lambda$$, where $$0 \cdot \lambda = 1$$" does not exist. Same statement, just written in shorthand: "$$x \div 0$$" does not exist. To answer the question: $$0 \div 0$$ does not have infinite solutions. It is the same as $$x \div 0$$ for any $$x$$ -- it simply does not exist. I think the confusion about infinite solutions comes from the fact that there are infinite solutions to $$x \cdot 0 = 0$$. But saying $$x \cdot 0 = 0$$ is not the same thing as saying $$x = 0 \div 0$$. Three sidenotes: 1. At least when $$y$$ is a real number and $$y \neq 0$$, there is a unique real number $$\lambda$$ such that $$y \cdot \lambda = 1$$. This is called the "inverse law" of multiplication, and there are two basic approaches for determining that the inverse law is true. The first approach is to carefully define the real numbers and the arithmetic operations on them, and write a proof that they always behave this way. The second approach is to begin with the assumption that the inverse law is true (treat it as an axiom). By the second approach, you need a whole collection of axioms to characterize the real numbers, including the inverse law and some other axioms from which you can prove that $$0 \cdot x = 0$$ for any $$x$$. If you drop the "$$y \neq 0$$" condition from the inverse law, then it becomes inconsistent with the other axioms. An inconsistent set of axioms is useless. 2. In a system where $$0=1$$, there does exist $$\lambda$$ such that $$0 \cdot \lambda = 0$$ and $$0 \cdot \lambda = 1$$. But if $$0 = 1$$, then you can prove that every number is equal to every other number. Rather: there is only one number in this system, and $$0$$, $$1$$, $$\lambda$$, $$\pi$$, $$42$$, $$-1$$, etc. are all different names for the same number. Let's give it the name $$x$$. In this system, $$x + x = x$$, $$x \cdot x = x$$, $$x \div x = x$$, etc. That's not a very useful system. 3. There's a common misconception that there's a rule that says $$x \div x = 1$$ for all $$x$$. The rule is actually $$x \cdot 1 = x$$. "$$x \cdot y = z$$" is not the same statement as "$$x = z \div y$$". "$$x = z \div y$$" is the same statement as "$$x = z \cdot \lambda$$ where $$y \cdot \lambda = 1$$". Therefore, "$$x \div x = 1$$" is really equivalent to "$$x \cdot \lambda = 1$$ where $$x \cdot \lambda = 1$$". • What do you think the expression 1+1 = 2 represents? The expression here has one object being added to itself which is simply doubling it, so we use another digit to represent the value of 2. In truth there are only 2 distinct digits, the digit that has a weighted value (1) and the digit that doesn't (0). This gives us the simplest of all number systems the binary number system in which Boolean Algebra and Boolean Logic can be applied. Yes we can increase the amount of digits in a number system to make more complex number systems such as octal, decimal and hexadecimal... – Francis Cugler Nov 12 at 0:06 • But in this I'll use decimal since it is the one we most commonly associate with... Other than 0 for all + integers we can express them in the sums of 1s. For example 1+0 = 1 (additive identity), 1+1 = 2, 1+1+1 = 3, 1+1+1+1 = 4... etc. In the moment that you apply the operation addition which is a linear translation you instantaneously and implicitly introduce multiplication. Because 11 = 1, 12 = 2, 13 = 3, and 14 = 4 and so on (all of these are multiplicative identities). However, as you can see there is no expression of 1(0) in the former as this yields 0... – Francis Cugler Nov 12 at 0:11 • A number has a weighted or quantitative value where a place holder doesn't. Think of a light switch on your wall when it is in the "Off position" there is no light. As long as there is electricity being applied to the circuit, if the switch is in the "On position" then there is light. – Francis Cugler Nov 12 at 0:13 • @FrancisCugler is there a specific part of my answer that you're trying to clarify? (see "When Shouldn't I Comment?") – Jordan Nov 13 at 2:06 The responses of division by 0 that we have been taught is undefined I actually find to be unintelligible and completely unacceptable. Take this into consideration, when we look at a fraction $\frac{n}{d}$ where $n$ is the numerator and $d$ is the denominator and $d$ happens to be $0$ let's apply this concept to a combination of linear equations and some trigonometric functions. Before I begin with that I will clearly state that some functions or equations that are normally used in different contexts mean exactly the same thing in all contexts. And I will show that the actual operation of division and fractions are nothing more than the slope of a line or the tangent of some angle with regards to the horizontal and that the slope of a vertical line or $\tan(90°)$ is completely defined! Equivalent Equations • slope of a line $m = \frac{\left( y_2 - y_1 \right)}{\left(x_2 - x_1\right)}$ is equivalent to the $\tan\theta$ where $\theta$ is the angle above the horizon when the angle is in standard form. • The Pythagorean Theorem and the Equation of the Circle are the same exact thing: $A^2 + B^2 = C^2$ and $X^2 + Y^2 = C^2$ • The $\cos\theta$ between two vectors is equivalent to $\frac{\vec A \cdot \vec B}{\|\vec A\|\|\vec B\|}$ Assertions • Both the $\sin$ and the $\cos$ functions have the same domain and range: Domains are the set of $\mathbb R$ and the ranges are $\left[-1,1\right]$ and they have a period of $2\pi$. They are continuous circular or rotational functions. • $\tan\theta = \frac{\sin\theta}{\cos\theta}$ • When plotting on the Unit Circle where the radius has a value of 1: The $(x,y)$ pair is defined as $(\cos\theta,\sin\theta)$ where the radius is above the horizontal $x$ axis in standard position. Assessments • Let's consider that we have 3 points $a,b,c$ where $a = (0,0)$ and $b = (1,0)$ and these points are fixed and point $c$ starts at point $b$'s location $(1,0)$. These 3 points will form vectors or line segments between each other. Initially there are only 2 valid vectors $\vec A$ and $\vec B$ where $\vec A$ is $b - a$ and $\vec B$ is $c - a$. $\vec C$ doesn't exist yet or is the $\vec 0$ since $\vec C$ is defined as $c - b$ and both points coincide. • We can technically rotate either direction but we will rotate $CCW$ and we will do a few observations in the process. • 1 - We will observe point $c$ as it rotates around the unit circle. • 2 - We will observe vector $\vec C$ as point $c$ rotates around the circle. • 3 - We will observe the area of the triangle that is generated from vectors $\vec A, \vec B,$ and $\vec C$ • 4 - We will observe the slope of $\vec B$ as this is the line that rotates. • 5 - We will observe the angles between $\vec A$ and $\vec B$ Intuitive Declarations • When the point $c$ rotates to the position $(-1,0)$ the slope is $0$, the area of the triangle is $0$, but the length of $\vec C$ is at its longest which is $2$. Here you have nothing but horizontal translation with $0$ or no incline or change in height or elevation. • When the angle is $45°$ or $\frac{pi}{4}$ radians the slope $\frac{rise}{run}$ and the $\tan\theta$ or $\frac{\sin\theta}{\cos\theta}$ are 1. You have an equal amount of vertical translation as you do horizontal translation. • The $\cos\theta$ represents the $x$ value on the unit circle but also your horizontal displacement. • The $\sin\theta$ represents the $y$ value on the unit circle but also your vertical displacement. • When the Angle is $0°,180°,360°$ or an multiple of them the Slope and the Tangent are also $0$. This means we have $0$ rise and the $\sin$ or the $y$ has an output of $0$ for its range at that angle. • When the Angle is $45°$ both the $\cos$ and the $\sin$ have equivalent values since both legs of the triangle here are equal thus giving you both a slope and a tangent of $1$ and if you graph both the sine and cosine functions they will intersect at this point. Considerations - Considering that both the sine and cosine are continuous circular functions neither of them at any point in their range nor their domain become undefined nor has any discontinuity in it. Generalization - Imagine yourself walking down an alley between two skyscrapers and the alley starts off being level. You have $0$ slope or no incline but you are traveling either $N,E,W,S$ which doesn't matter because the ground you are walking on is a 2D plane. So you do have 2 degrees of dimension to travel upon. However since you are in a tight alley in this demonstration you are only heading in one arbitrary horizontal direction. Then the alley or the road has a hill that you have to walk up, now you have slope because you are rising in elevation. Then it levels off again and your slope is back to $0$ at the new elevation. This makes sense because two horizontal lines at different heights are parallel so both their slopes will be the same. Finally the alley comes to an end as their is another skyscraper in front of you and you can not go left nor right and there is no turning back, but the building in front of you has a ladder and you begin to climb it rung for rung. When you start to climb straight up your angle is $90°$ which is perpendicular and orthogonal to the ground. This means that you no longer have any horizontal displacement but you have incremental and continuous vertical translations. So in this case your elevation or height is forever increasing until you reach the roof and start to walk across a horizontal or sloped plane. The argument - In the case where the $\sin$ component of the tangent or the $(y_2 - y_1)$ component is evaluated to $0$ you have no incline and the slope is $0$ because here $n = 0$ and $d = (x_2 - x_1)$ or $d = \cos\theta$ where this means you only have horizontal translation and this is valid because a numerator can be $0$. Let's reverse the case. This time the $\cos\theta$ component of the tangent or the $(x_2 - x_1)$ is $0$ which simply means just the opposite where we have no run yet we do have continuous rise, yet from the fallacies if what we were taught this is undefined because of division of $0$ because here the $d$, $(x_2 - x_1)$, or the $\cos\theta$ evaluates to $0$. I argue that these are valid outputs and acceptable domains of fractions or division. Division by $0$ is completely defined. Conclusion - If $\frac{0}{d}$ means $0$ slope or no rise with infinite run then the opposite must be valid as well where $\frac{n}{0}$ means no run with infinite rise. The correct answer for division of $0$ would be $\infty$ since when the numerator is $0$ the slope is $0$ because there is no change in elevation. We can not evaluate $\frac{d}{0}$ as $0$ because here we have no run but we do only have rise and slope is defined as the change in the elevation and here the slope is ever increasing vertically up without any horizontal displacement and this does make complete sense. In trigonometry we do know that the tangent's graph has vertical asymptotes at periods of $\frac{pi}{2}$ or $90°$. We are taught that the tangent is undefined here. I think this is a wrong assessment because those vertical asymptotes are parallel vertical lines to the vertical $y$ axis and these are perpendicular and orthogonal to the horizontal or $x$ axis. When a line has a slope $\frac{a}{b}$ a line that is perpendicular to it is $-\frac{b}{a}$ Let's try this with a slope of $0$ then find its perpendicular. $$\frac{0}{d} \implies 0$$ slope or a horizontal line therefor $$\frac{-d}{0} \implies \infty$$ vertical slope or a vertical line. Let's apply the above with the trig functions again starting with $0$ slope. $$\frac{\sin\theta}{\cos\theta} = \frac{0}{\cos\theta} \implies \tan\theta = 0$$ therefor it's perpendicular must be: $$-\frac{\cos\theta}{\sin\theta} \implies -\cot\theta$$ since we have no run in vertical slope the $\cos\theta$ component must be $0$; then it suggests that: $$-\cot\theta = \frac{0}{-\sin\theta}$$ which is also the same as: $$\frac{0}{\sin\theta}$$ however, this does not evaluate to $0$ when regarding slope because we do have a change in height that is shown by the $\sin\theta$. The slope here is defined as being $\lim_\infty$ because the tangent has a vertical asymptote at $90°$ and cotangent is $0$. The cotangent has a vertical asymptote at $180°$ and the tangent is $0$ at $180°$. It is these associations and relationships of division, fractions, slopes, trig functions and reciprocals with the use of the dot and even the cross products that define how two vectors are perpendicular and orthogonal to each other when they create a separation of $90°$ or $\frac{pi}{2}$ radians from each other. If you were to take just the $x$ and $y$ axis of a 2D Coordinate Cartesian Plane we know that the $x$ axis has $0$ slope because it is horizontal or level and that the $y$ axis has vertical slope. Vertical slope is NOT undefined! If we were to rotate these two axis together by $1°$ there is defined slope. Slope is always defined since one can always change their perspective to that system. I think that people confuse what $0$ really is! $0$ is really not a number, it is a place holder, it also represents the empty or the null set, it has no value. So if you can divide any number by the empty set and it returns back to you the empty set. Is it not conceivable to divide anything into the empty set? In this particular case and context division by $0$ here yields infinity because the problem pertains to slope or the change in height over distance. In other contexts division by $0$ could mean, $0$ as the result is $0$ and is no different than when it is in the numerator. It could also yield D.N.E. meaning that the function that it is being applied to just Does Not Exist at that location or context. There is 1 special case and that is when both the numerator and denominator are $0$. This could yield $0$, $1$, and or $\infty$. This does satisfy that $0$ divided by any number equals $0$. It also satisfies the multiplicative identity that any number divided by itself is $1$. The infinity part also comes from the concept that if you have $0$ run and $0$ rise you are stationary and you are infinitely not moving in any direction which is no different than $0$. To try to make this understanding a little clearer then ask yourself this: Why does any number $n$ raised to the $0$ power always equal $1$? $n^0 = 1$. For The Reader - It would be advisable to draw the unit circle and the points and vectors as described above in the assessments and to do several of them where the rotation around the unit circle are at different positions. Or you can visit this web page interactive graph of a graph that I made that shows all the relationships between these 3 points along with the tangent, area of the triangle, and even the volume if you increase the height factor, the coordinate pairs $(\cos\theta,\sin\theta)$ along the unit circle etc. And you will notice that when the angle is $0°$ the slope, area and volume are all $0$. They are also $0$ when the angle is $180°$ and $360°$. When the angle is 90° or $270°$ of course the "slope is labeled as undefined because that is what people have programmed it to be because of the fact that we were taught that division by $0$ is undefined!" However the Area and Volume of the triangle is at its maximum value. I have it set to where you can press the play button for the "t" value which stands for $\theta$ because this website at the time has not incorporated the use of the variable $\theta$ to be allowed into their functions or expressions to make graphs. • "0 is really not a number"; how do you justify this statement? Zero is as much a number as 5 or 2918. As a further question, while an interesting interpretation, how does this address the formal definition of division? Shouldn't that be the baseline for how we proceed with addressing expressions such as $0/0$? – masiewpao Nov 11 at 14:53 • @masiewpao It is a digit, it is a place holder but it has no value or magnitude. It is the empty or null set. Take for example the Binary number system where there are only 2 digits: 0 & 1 and its use within digital circuits. Either there is a voltage or there isn't and thus the memory cells preserve either a 1 or 0, on or off, true or false within the feed back loop of the circuitry. It's an abstract statement just as the idea of 0 itself is abstract. For example; write a mathematical proof that 1 == 1 or 2 == 2... – Francis Cugler Nov 11 at 20:15 • But the same thing could be said about any 'digit'. It's a number in so much as 5 is a number. In a set theoretic construction of the natural numbers for example, why would you consider the set of the null set anymore of a number than the null set? – masiewpao Nov 11 at 21:32 • Think of 0 and 1 as vectors in the binary number system. Think of 0 as being the 0 vector and 1 as being the unit vector. The 0 vector has no magnitude nor direction or infinite direction where as the unit vector the complete opposite has both magnitude (distance) and direction. This concept doesn't just apply to mathematics but also to physics especially when it concerns forces and displacement. – Francis Cugler Nov 11 at 23:03 • This answer gets things backwards. It starts with the author's intuition about geometry, and then works backwards, forcing the definitions of $\mathbb{R}$, $\infty$, and $\div$ to fit that intuition. The correct place to start is with the algebraic properties of $\mathbb{R}$, because $\mathbb{R}$ is, in fact, an algebraic structure. If the algebraic result contradicts your geometric intuition, then either you're misapplying $\mathbb{R}$ or your intuition is incorrect. – Jordan Nov 13 at 2:55 ## protected by Michael AlbaneseJul 7 '14 at 6:27 Thank you for your interest in this question. Because it has attracted low-quality or spam answers that had to be removed, posting an answer now requires 10 reputation on this site (the association bonus does not count).	2019-11-16 22:19:30	{"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": 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": 54, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.847043514251709, "perplexity": 253.7755781498442}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-47/segments/1573496668765.35/warc/CC-MAIN-20191116204950-20191116232950-00317.warc.gz"}
https://base12innovations.wordpress.com/2012/12/23/problem-of-the-day-122312/	# Problem of the Day: 12/23/12 Out of a classroom containing 20 people, each with a different name, what is the probability that Alfred, Camellia, Edward, Grace, and Ian will be chosen by the teacher to run errands before school today? Express your answer as a common fraction. Solution to yesterday’s problem: For this problem I can show you two different methods: a straightforward algebraic method, and a faster method. Method 1 – Set up an equation. $x$ will be the lowest number, $x+1$ is the next one, and so on. Our equation looks like this: $x+(x+1)+(x+2)+(x+3)=-118$ Simplifying, $4x+6=-118$ $4x=-124$ $x=-31$ So the consecutive numbers are -31, -30, -29, and -28. The product of -31 and -28 is 868. Method 2 – Knowing that -118 is the sum of four numbers, we can divide -118 by four to find the average of the four numbers. -118/4 is -29.5, which must be the average of our four numbers. Since they are consecutive, we can find the two nearest integers on either side of this decimal: -30 and -31, -29 and -28. These are our four integers, and the product of the least and greatest is 868.	2017-03-27 10:44:07	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 6, "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": 0.6057842969894409, "perplexity": 492.9826328734135}, "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-2017-13/segments/1490218189471.55/warc/CC-MAIN-20170322212949-00456-ip-10-233-31-227.ec2.internal.warc.gz"}
https://deepai.org/publication/fuzzy-owl-boost-learning-fuzzy-concept-inclusions-via-real-valued-boosting	# Fuzzy OWL-BOOST: Learning Fuzzy Concept Inclusions via Real-Valued Boosting OWL ontologies are nowadays a quite popular way to describe structured knowledge in terms of classes, relations among classes and class instances. In this paper, given a target class T of an OWL ontology, we address the problem of learning fuzzy concept inclusion axioms that describe sufficient conditions for being an individual instance of T. To do so, we present Fuzzy OWL-BOOST that relies on the Real AdaBoost boosting algorithm adapted to the (fuzzy) OWL case. We illustrate its effectiveness by means of an experimentation. An interesting feature is that the learned rules can be represented directly into Fuzzy OWL 2. As a consequence, any Fuzzy OWL 2 reasoner can then be used to automatically determine/classify (and to which degree) whether an individual belongs to the target class T. ## Authors • 1 publication • 10 publications • ### An approach to membrane computing under inexactitude In this paper we introduce a fuzzy version of symport/antiport membrane ... 03/16/2004 ∙ by Jaume Casasnovas, et al. ∙ 0 • ### A New Penta-valued Logic Based Knowledge Representation In this paper a knowledge representation model are proposed, FP5, which ... 02/19/2015 ∙ by Vasile Patrascu, et al. ∙ 0 • ### A multivalued knowledge-base model The basic aim of our study is to give a possible model for handling unce... 03/08/2010 ∙ by Agnes Achs, et al. ∙ 0 • ### Fuzzy Geometric Relations to Represent Hierarchical Spatial Information A model to represent spatial information is presented in this paper. It ... 02/27/2013 ∙ by Stephane Lapointe, et al. ∙ 0 • ### Scene learning, recognition and similarity detection in a fuzzy ontology via human examples This paper introduces a Fuzzy Logic framework for scene learning, recogn... 09/27/2017 ∙ by Luca Buoncompagni, et al. ∙ 0 • ### Answering Fuzzy Conjunctive Queries over Finitely Valued Fuzzy Ontologies Fuzzy Description Logics (DLs) provide a means for representing vague kn... 08/11/2015 ∙ by Stefan Borgwardt, et al. ∙ 0 • ### The State of the Art in Developing Fuzzy Ontologies: A Survey Conceptual formalism supported by typical ontologies may not be sufficie... 05/06/2018 ∙ by Zahra Riahi Samani, et al. ∙ 0 ##### This week in AI Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday. ## 1 Introduction OWL 2 ontologies [88] are nowadays a popular means to represent structured knowledge and its formal semantics is based on Description Logics (DLs) [4]. The basic ingredients of DLs are concept descriptions (in First-Order Logic terminology, unary predicates), inheritance relationships among them and instances of them. Although an important amount of work has been carried about DLs, the application of machine learning techniques to OWL 2 ontologies, viz. DL ontologies, is relatively less addressed compared to the Inductive Logic Programming (ILP) setting (see e.g. [91, 92] for more insights on ILP). We refer the reader to [71, 93] for an overview and to Section 2 In this work, we focus on the problem of automatically learning fuzzy concept inclusion axioms from OWL 2 ontologies. More specifically, given a target class of an OWL ontology, we address the problem of learning fuzzy [3] concept inclusion axioms that describe sufficient conditions for being an individual instance of . ###### Example 1.1 (Running example [68, 70, 114]) Consider an ontology that describes the meaningful entities of a city. Now, one may fix a city, say Pisa, extract the properties of the hotels from Web sites, such as location, price, etc., and the hotel judgements of the users, e.g., from Trip Advisor. Now, using the terminology of the ontology, one may ask about what characterises good hotels in Pisa (our target class ) according to the user feedback. Then one may learn from the user feedback that, for instance, ‘An expensive Bed and Breakfast is a good hotel’ (see also Section 5 later on). The objective is essentially the same as in e.g. [70, 114] except that now we propose to rely on the eal AdaBoost [86] boosting algorithm to be adapted to the (fuzzy) OWL case. Of course, like in [68, 114], we continue to support so-called fuzzy concept descriptions and fuzzy concrete domains [76, 112, 113] such as ‘an expensive Bed and Breakfast is a good hotel’. Here, the concept expensive is a so-called fuzzy concept [123], i.e. a concept for which the belonging of an individual to the class is not necessarily a binary yes/no question, but rather a matter of degree in . For instance, in our example, the degree of expensiveness of a hotel may depend on the price of the hotel: the higher the price the more expensive is the hotel. Here, the range of the ‘attribute’ hotel price becomes a so-called fuzzy concrete domain [113] allowing to specify fuzzy labels such as ‘high/moderate/low price’. We recall that (discrete) AdaBoost [46, 108, 47] uses weak hypotheses with outputs restricted to the discrete set of classes that it combines via leveraging weights in a linear vote. On the other hand eal AdaBoost [86] is a generalisation of it as real-valued weak hypotheses are admitted (see [86] for a comparison to approaches to real-valued AdaBoost). Besides the fact that (to the best of our knowledge) the use of both (discrete) AdaBoost (with the notable exception of [44]) and its generalisation to real-valued weak hypotheses in the context OWL 2 ontologies is essentially unexplored, the main features of our algorithm, called Fuzzy OWL-Boost, are the following: • it generates a set of fuzzy fuzzy inclusion axioms [14], which are the weak hypothesis, possibly including fuzzy concepts and fuzzy concrete domains [76, 112, 113], where each axiom has a leveraging weight; • the fuzzy concept inclusion axioms are then linearly combined into a new fuzzy concept inclusion axiom describing sufficient conditions for being an individual instance of the target class ; • all generated fuzzy concept inclusion axioms can then be directly encoded as Fuzzy OWL 2 axioms [11, 12].333As Fuzzy OWL 2 supports the linear combination of weighted concepts. As a consequence, a Fuzzy OWL 2 reasoner, such as fuzzyDL [10, 13], can then be used to automatically determine (and to which degree) whether an individual belongs to the target class . Let us remark that we rely on real-valued AdaBoost as the weak hypotheses Fuzzy OWL-Boost generates are indeed fuzzy concept inclusion axioms and, thus, the degree to which an instance satisfies them is a real-valued degree of truth in . In the following, we proceed as follows. In Section 2 we compare our work with closely related work appeared so far. For completeness, we refer to A in which we provide a much more extensive list of references related to OWL rule learning, though less related to our setting. In Section 3, for the sake of completeness, we recap the salient notions we will rely on in this paper. Then, in Section 4 we will present our algorithm Fuzzy OWL-Boost, which then is evaluated for its effectiveness in Section 5. Section 6 concludes and points to some topics of further research. ## 2 Related Work Concepts inclusion axioms learning in DLs stems from statistical relational learning, where classification rules are (possibly weighted) Horn clause theories from examples (see e.g. [91, 92]) and various methods have been proposed in the DL context so far (see e.g. [71, 93]). The general idea consists of the exploration of the search space of potential concept descriptions that cover the available training examples using so-called refinement operators (see, e.g. [5, 59, 62]). The goal is then to learn a concept description of the underlying DL language covering (possibly) all provided positive examples and (possibly) not covering any of the provided negative examples. The fuzzy case (see [67, 70, 114]) is a natural extension in which one relies on fuzzy DLs [9, 113] and fuzzy ILP (see e.g. [109]) instead. Closely related to our work are [44, 67, 70, 114]. The works [67, 70], which stem essentially from [68, 69, 72, 73, 74, 75], propose fuzzy Foil-like algorithms and are inspired by fuzzy ILP variants such as [29, 109, 111],444See, e.g. [19], for an overview on fuzzy rule learning mehtods. while here we rely on a real-valued variant of AdaBoost. Let us note that [67, 73] consider the weaker hypothesis representation language DL-Lite [2], while here we rely on fuzzy as in [68, 69, 72, 74, 75, 70]. Fuzzy has also been considered in [114], which however differs from [67, 70] by the fact that a (fuzzy) probabilistic ensemble evaluation of the fuzzy concept description candidates has been considered. 555Also, as far as we were able to figure out, concrete datatypes were not addressed in the evaluation. Discrete boosting has been considered in [44], which also shows how to derive a weak learner —(called wDLF) from conventional learners using some sort of random downward refinement operator covering at least a positive example and yielding a minimal score fixed with a threshold. Besides that we deal here with fuzziness in the hypothesis language and a real-valued variant of AdaBoost, the weak learner we propose here differentiates from the previous one by using a kind of gradient descent like algorithm to search for the best alternative. Notably, this also deviates from ‘fuzzy’ rule learning AdaBoost variants, such as [28, 87, 90, 107, 122] in which the weak learner is required to generate the whole rules search space beforehand the selection of the best current alternative. Such an approach is essentially unfeasible in the OWL case due to the size of the search space. Eventually, [53] can learn fuzzy OWL DL concept equivalence axioms from FuzzyOWL 2 ontologies, by interfacing with the fuzzyDL reasoner [13]. The candidate concept expressions are provided by the underlying DL-Learner [57, 15, 16] system. However, it has been tested only on a toy ontology so far. Last, but not least, let us mention [55], which is based on an ad-hoc translation of fuzzy Łukasiewicz DL constructs into fuzzy Logic Programming (fuzzy LP) and then uses a conventional ILP method to learn rules. Unfortunately, the method is not sound as it has been shown that the mapping from fuzzy DLs to LP is incomplete [83] and entailment in Łukasiewicz is undecidable [17]. While it is not our aim here to provide an extensive overview about learning w.r.t. ontologies literature, nevertheless we refer the interested reader to A for an extensive list of references, which may be the subject of a survey paper instead. ## 3 Background For the sake of self completeness, we first introduce the main notions related to (Mathematical) Fuzzy Logics and Fuzzy Description Logics we will use in this work (see [113] for a more extensive introduction to both). ### 3.1 Mathematical Fuzzy Logic Fuzzy Logic is the logic of fuzzy sets [123]. A fuzzy set over a countable crisp set is a function , called fuzzy membership function of . A crisp set is characterised by a membership function instead. The ‘standard’ fuzzy set operations conform to , and ( is the set complement of ), the cardinality of a fuzzy set is often defined as , while the inclusion degree between and is defined typically as . The trapezoidal (Fig. 1 (a)), the triangular (Fig. 1 (b)), the -function (left-shoulder function, Fig. 1 (c)), and the -function (right-shoulder function, Fig. 1 (d)) are frequently used to specify membership functions of fuzzy sets. Although fuzzy sets have a greater expressive power than classical crisp sets, their usefulness depends critically on the capability to construct appropriate membership functions for various given concepts in different contexts. We refer the interested reader to, e.g.[54]. One easy and typically satisfactory method to define the membership functions is to uniformly partition the range of, e.g. salary values (bounded by a minimum and maximum value), into 5 or 7 fuzzy sets using triangular (or trapezoidal) functions (see Figure 2). Another popular approach may consist in using the so-called C-means fuzzy clustering algorithm (see, e.g. [7]) with three or five clusters, where the fuzzy membership functions are triangular functions built around the centroids of the clusters (see also [51]). In Mathematical Fuzzy Logic [48], the convention prescribing that a formula is either true or false (w.r.t. an interpretation ) is changed and is a matter of degree measured on an ordered scale that is no longer , but typically . This degree is called degree of truth of the formula in the interpretation . Here, fuzzy formulae have the form , where and is a First-Order Logic (FOL) formula, encoding that the degree of truth of is greater than or equal to . So, for instance, states that ‘Hotel Verdi is cheap’ is true to degree greater or equal . From a semantics point of view, a fuzzy interpretation maps each atomic formula into and is then extended inductively to all FOL formulae as follows: I(ϕ∧ψ) = I(ϕ)⊗I(ψ) , I(ϕ∨ψ) = I(ϕ)⊕I(ψ) I(ϕ→ψ) = I(ϕ)⇒I(ψ) , I(¬ϕ) = ⊖I(ϕ) I(∃x.ϕ(x)) = where is the domain of , and , , , and are so-called t-norms, t-conorms, implication functions, and negation functions, respectively, which extend the Boolean conjunction, disjunction, implication, and negation, respectively, to the fuzzy case. One usually distinguishes three different logics, namely Łukasiewicz, Gödel, and Product logics [48]666Notably, a theorem states that any other continuous t-norm can be obtained as a combination of them. whose truth combination functions are reported in Table 1. Note that the operators for ‘standard’ fuzzy logic, namely , , and , can be expressed in Łukasiewicz logic. More precisely, . Furthermore, the implication is called Kleene-Dienes implication (denoted ), while Zadeh implication (denoted ) is the implication if ; otherwise. An r-implication is an implication function obtained as the residuum of a continuous t-norm 777Note that Łukasiewicz, Gödel and Product implications are r-implications, while Kleene-Dienes implication is not. i.e. . Note also, that given an r-implication , we may also define its related negation by means of for every . The notions of satisfiability and logical consequence are defined in the standard way, where a fuzzy interpretation satisfies a fuzzy formula , or is a model of , denoted as , iff . Notably, from and one may conclude (if is an r-implication) (this inference is called fuzzy modus ponens). ### 3.2 Fuzzy Description Logics basics We recap here the fuzzy DL , which extends the well-known fuzzy DL [112] with the weighted concept construct (indicated with the letter [12, 113]. is expressive enough to capture the main ingredients of fuzzy DLs we are going to consider here. Note that fuzzy DLs and fuzzy OWL 2 in particular, cover many more language constructs than we use here (see, e.g. [9, 12, 113]). We start with the notion of fuzzy concrete domain, that is a tuple with datatype domain and a mapping that assigns to each data value an element of , and to every -ary datatype predicate a -ary fuzzy relation over . Therefore, maps indeed each datatype predicate into a function from to . Typical datatypes predicates are characterized by the well known membership functions (see also Fig. 1) d → ls(a,b) \| rs(a,b) \| tri(a,b,c) \| trz(a,b,c,d) \| ≥v \| ≤v \| =v , where e.g. is the left-shoulder membership function and corresponds to the crisp set of data values that are greater than or equal to the value . Now, consider pairwise disjoint alphabets and , where is the set of individuals, is the set of concept names (also called atomic concepts) and is the set of role names. Each role is either an object property or a datatype property. The set of concepts are built from concept names using connectives and quantification constructs over object properties and datatype properties , as described by the following syntactic rule (): C → ⊤ \| ⊥ \| A \| C1⊓C2 \| C1⊔C2 \| ¬C \| C1→C2 \| ∃R.C \| ∀R.C \| ∃S.d \| ∀S.d \| α1⋅C1+…αn⋅Cn . An ABox consists of a finite set of assertion axioms. An assertion axiom is an expression of the form (called concept assertion, is an instance of concept to degree greater than or equal to ) or of the form (called role assertion, is an instance of object property to degree greater than or equal to ), where are individual names, is a concept, is an object property and is a truth value. A Terminological Box or TBox is a finite set of General Concept Inclusion (GCI) axioms, where a fuzzy GCI is of the form ( is a sub-concept of to degree greater than or equal to), where is a concept and . We may omit the truth degree of an axiom; in this case is assumed and we call the axiom crisp. We also write as a macro for the two GCIs and . We may also call a fuzzy GCI of the form , where is a concept name, a rule and its body. A Knowledge Base (KB) is a pair , where is a TBox and is an ABox. With we denote the set of individuals occurring in . Concerning the semantics, let us fix a fuzzy logic and a fuzzy concrete domain . Now, unlike classical DLs in which an interpretation maps e.g. a concept into a set of individuals , i.e. maps into a function (either an individual belongs to the extension of or does not belong to it), in fuzzy DLs, maps into a function and, thus, an individual belongs to the extension of to some degree in , i.e. is a fuzzy set. Specifically, a fuzzy interpretation is a pair consisting of a nonempty (crisp) set (the domain) and of a fuzzy interpretation function that assigns: (i) to each atomic concept a function ; (ii) to each object property a function ; (iii) to each datatype property a function ; (iv) to each individual an element such that if (the so-called Unique Name Assumption); and (v) to each data value an element . Now, a fuzzy interpretation function is extended to concepts as specified below (where ): ⊤I(x) = 1 ⊥I(x) = 0 (C⊓D)I(x) = CI(x)⊗DI(x) (C⊔D)I(x) = CI(x)⊕DI(x) (¬C)I(x) = ⊖CI(x) (C→D)I(x) = CI(x)⇒DI(x) (∀R.C)I(x) = infy∈ΔI{RI(x,y)⇒CI(y)} (∃R.C)I(x) = supy∈ΔI{RI(x,y)⊗CI(y)} (∀S.d)I(x) = infy∈ΔD{SI(x,y)⇒dD(y)} (∃S.d)I(x) = (α1⋅C1+…αn⋅Cn)I(x) = ∑iαi⋅CiI(x) . The satisfiability of axioms is then defined by the following conditions: (i) satisfies an axiom if ; (ii) satisfies an axiom if ; (iii) satisfies an axiom if with 888However, note that under standard logic is interpreted as and not as . . is a model of iff satisfies each axiom in . If has a model we say that is satisfiable (or consistent). We say that entails axiom , denoted , if any model of satisfies . The best entailment degree of of the form , : or :, denoted , is defined as bed(K,τ)=sup{d∣K⊨⟨τ,d⟩} . ###### Remark 1 Please note that (i.e. implies , and similarly, (i.e. implies . However, in both cases the other way around does not hold. Furthermore, we may well have that both and hold. Eventually, consider concept , a GCI , a KB , a set of individuals and a (weight) distribution over . Then the cardinality of w.r.t. and , denoted , is defined as \|C\|IK=∑a∈Ibed(K,a:C) , (1) while the weighted cardinality w.r.t. , and , denoted , is defined as \|C\|w,IK=∑a∈Iwa⋅bed(K,a:C) . (2) The crisp cardinality (denoted ) and crisp weighted cardinality (denoted ) are defined similarly by replacing in Eq. 1 and 2 the term with . Furthermore, the confidence degree (also called inclusion degree) of w.r.t. and , denoted , is defined as cf(C⊑D,I)=\|C⊓D\|IK\|C\|IK . (3) Similarly, the weighted confidence degree (also called weighted inclusion degree) of w.r.t. , and , denoted , is defined as cf(C⊑D,w,I)=\|C⊓D\|w,IK\|C\|w,IK . (4) ###### Example 3.1 (Example 1.1 cont.) Let us consider the following axiom ⟨∃hasPrice.High⊑GoodHotel,0.569⟩ , where is a datatype property whose values are measured in euros and the price concrete domain has been automatically fuzzified as illustrated in Figure 3. Now, it can be verified that for hotel , whose room price is euro, i.e. we have the assertion : in the KB, we infer under Product logic that 999Using fuzzy modus ponens, , where . K⊨⟨verdi:GoodHotel,0.18⟩ . ## 4 Learning Fuzzy Concept Inclusions via Real-Valued Boosting ### 4.1 The Learning Problem In general terms, the learning problem we are going to address is stated as follows: Given: • a satisfiable KB and its individuals ; • a target concept name with an associated unknown classification function , where for each , the possible values (labels) correspond, respectively, to ( is a positive example of ) and ( is a non-positive example of ); • a hypothesis space of classifiers ; • a training set (the positive and non-positive examples of , respectively) of individual-label pairs: E+ = {(a,1)∣a∈IK,fT(a)=1} E− = {(a,0)∣a∈IK,fT(a)=0} . With we denote the set of individuals occurring in . We assume that for all , , i.e. both and hold for all 101010Essentially we state that does not already know whether is an instance of or not. We write if is a positive example (i.e., ), if is a non-positive example (i.e., ). Learn: a classifier that is the result of Emprical Risk Minimisation (ERM) on . That is, ¯h = argminh∈HR(h,E) = EE[L(h(a),E(a))] = 1\|E\|∑a∈IEL(h(a),E(a)) , where is a loss function such that measures how different the prediction of a hypothesis is from the true outcome and is the risk associated with hypothesis over , defined as the expectation of the loss function over . The effectiveness of the learned classifier is then assessed by determining on a a test set , disjoint from . In our setting, we assume that a hypothesis is a fuzzy GCI of the form ⟨α1⋅C1+…αn⋅Cn⊑T,d⟩ (5) where each is a so-called fuzzy concept expression 111111Note that is a basic ingredient of the OWL profile language OWL EL [89]. defined according to the following syntax:121212 is the concrete domain of boolean values. C⟶⊤∣A∣∃R.C∣∃S.d∣C1⊓C2d→ls(a,b) \| rs(a,b) \| tri(a,b,c) \| trz(a,b,c,d) \| bool . For , the classification prediction value of w.r.t. , and is defined as (for ease, we omit and ) h(a)=bed(K∪{h},a:T) . Note that, as stated above, essentially a hypothesis is a sufficient condition (expressed via the weighted sum of concepts) for being an individual instance of a target concept to some positive degree. So, if then is a non-positive instance of , while if then is a positive instance of to some degree and, thus, we distinguish between positive and non-positive instances of only. Furthermore, let us note that even if is a crisp KB, the possible occurrence of fuzzy concrete domains in expressions of the form in the left-hand side of a hypothesis may imply that . ###### Remark 2 Note that in e.g. [70] a hypothesis is of the form instead. ###### Remark 3 Clearly, the set of hypothesis by this syntax is potentially infinite due, e.g., to conjunction and the nesting of existential restrictions. The set is made finite by imposing further restrictions on the generation process such as the maximal number of conjuncts and the depth of existential nestings allowed. ###### Remark 4 One may also think of further partition the set of non-positive examples into a set of negative and a set of unknown examples (and use as labelling set , respectively, with –positive, – unknown, – negative), as done in many other approaches (see e.g. [44]). That is, an individual is a negative example of if , while is a unknown example of if neither nor hold. In that case, usually we are looking for an exact definition of , i.e. a hypothesis is of the stronger form instead. 131313We recall that a hypothesis as in Eq. 5 does not allow us to infer negative instances of , while does. That is, we may well have the case and with . Which one to choose may depend on the application domain and on the effectiveness of the approach. We do not address this case here. It is easily verified that indeed a hypothesis can be rewritten as a set of rules of the form (with new concept names): ⟨C1⊑T1,d1⟩⋮⟨Cn⊑Tn,dn⟩⟨β1⋅T1+…βn⋅Tn⊑T,d⟩ (6) where, as we will see later on, each fuzzy GCI is a weak hypothesis (classifier), while their aggregation is computed via eal AdaBoost in which each indicates how much contributes to the classification prediction value. ###### Remark 5 Of course, one may also rewrite Eq. 5 directly as (with new concept names) C1⊑T1⋮Cn⊑Tn⟨α1⋅T1+…αn⋅Tn⊑T,d⟩ . (7) However, we prefer to rely on Eq. 6 to maintain the confidence degree of each learned rule. We conclude with the notions of consistent, non-renduntant, sound, complete and strongly complete hypothesis w.r.t. , which are defined as follows: Consistency. is a consistent; Non-Redundancy. . Soundness. . Completeness. . Strong Completeness. . We say that a hypothesis covers (strongly covers) an example iff (). Therefore, soundness states that a learned hypothesis is not allowed to cover a non-positive example, while the way (strong) completeness is stated guarantees that all positive examples are (strongly) covered. In general a learned (induced) hypothesis has to be consistent, non-renduntant and sound w.r.t. , but not necessarily complete, but, of course, these conditions can also be relaxed. ### 4.2 The Learning Algorithm We now present our real-valued boosting-based algorithm, which is based on a boosting schema applied a fuzzy GCI learner. Our learning method creates an ensemble of classifiers made up of fuzzy concept expressions (see Eq. 5), each of which is provided by a fuzzy weak learner, whose predictiveness is required to be better than randomness. Essentially, at each round the weak learner generates a fuzzy candidate GCI of the form that determines a change to the distribution of the weights associated with the examples. The weights of misclassified examples get increased so that a better classifier can be produced in the next round, indicating the harder examples to focus on. The weak hypotheses are then eventually combined into a hypothesis (see Eq. 6). We will rely on eal AdaBoost [85, 86] as boosting algorithm, while we will use a weak learner that is similar to Foil- [67, 68, 70], both of which need to adapted to our specific setting. Formally, consider a KB, , a training set , a set of individuals with , and a weight distribution over 141414The weight of w.r.t. is denoted . With we indicate the uniform distribution over , i.e. (with ). Furthermore, consider a weak hypothesis of the form returned by the weak learner. Note that for , . Next, we transform this value into a value in as required by eal AdaBoost. So, let let be the transformation function t(x)={−1if$x=0$xelse and let the classification prediction value of w.r.t. , and be defined as (again for ease, we omit and ) hi(a)=t(bed(K∪{hi},a:T))∈{−1}∪(0,1] . We also define the examples labelling over in the following way: for l(a)={1if$(a,1)∈E+$−1else . Then, the Fuzzy OWL-Boost algorithm calling iteratively a weak learner is shown in 1, which we comment briefly next. The algorithm is essentially the same as eal AdaBoost, except for few context dependent parts. In Step 2 we initialise the set of individuals to be considered as . Essentially, all individuals will be weighted. The main loop (Steps 5 - 11) is the same as for eal AdaBoost with the particularity that Step 6 we invoke a fuzzy GCI (weak) learner that is assumed to return a GCI of the form . Note that, for ease of presentation, we didn’t include an additional condition that causes a break of the loop. In fact, an implicit condition of boosting is that the error of a weak learner is below . This may implemented in our case by adding another step before Step 12 that computes the error ϵ=∑a∈Iδ(hi(a),l(a))⋅hi(a) , where is defined as () δ(x,y)={1if$x⋅y<0$0else and determines whether there is a disagreement among the sign of and . Then, if we break the loop. In Step 12 we add the (weak) learned fuzzy GCI to the hypothesis set . In Steps 14 - 18 we prepare the final classifier ensemble. To do so, we have to perform a normalisation step. In fact, since in eal AdaBoost generally , we have to normalise the set of values () before building the weighted sum in Step 16. To do so, we rely on the well-known softmax function. Eventually, in Step 17, we determine the degree to be attached to the ensemble classifier computed as the confidence value, which resembles the well-known precision measure used in macchine learning. 151515Precision is also called positive predictive value and roughly is the percentage of positive instances among all retrieved instances. We next describe the weak learner we employ here. As anticipated, will use a Foil- [67, 68, 70] like weak learner, which however needs to be adapted to our specific setting. In general terms the weak learning algorithm, called wFoil-, proceeds as follows: 1. start from concept ; 2. apply a refinement operator to find more specific concept description candidates; 3. exploit a scoring function to choose the best candidate; 4. re-apply the refinement operator until a good candidate is found; 5. iterate the whole procedure until a satisfactory coverage of the positive examples is achieved. We briefly detail these steps. Computing fuzzy datatypes. For a numerical datatype , we allow equal width triangular/trapezoidal partition of values into a finite number of fuzzy sets (typically, or sets), which is identical to [67, 70, 114] (see, e.g. Figure 2). However, we additionally, allow also the use of the C-means fuzzy clustering algorithm over with or clusters, where the fuzzy membership function is a triangular function build around the centroid of a cluster. Note that C-means has not been considered in [67, 70, 114]161616Specifically, C-means has not been considered so far in fuzzy GCI learning. The refinement operator. The refinement operator we employ is the same as in [67, 68, 74, 114] except that now we add the management of boolean values as well. Essentially, the refinement operator takes as input a concept and generates new, more specific concept description candidates (i.e., ). For the sake of completeness, we recap the refinement operator here. Let be an ontology, be the set of all atomic concepts in , the set of all object properties in , the set of all numeric datatype properties in , the set of all boolean datatype properties in and a set of (fuzzy) datatypes. The refinement operator is shown in Table 2. The scoring function. The scoring function we use to assign a score to each candidate hypothesis is essentially a weighted gain function, similar to the one employed in [67, 68, 74, 114] and implements an information-theoretic criterion for selecting the best candidate at each refinement step. Specifically, given a GCI of the form chosen at the previous step, a KB , a set of individuals , a weight distribution over , a set of examples and a candidate GCI of the form , then gain(ϕ′,ϕ,w,I)=p∗(log2(cf(ϕ′,w,I))−log2(cf(ϕ,w,I))) , (8) where is the weighted cardinality of positive examples covered by that are still covered by . Note that the gain is positive if the confidence degree increases. Stop Criterion. wFoil- stops when the confidence degree is above a given threshold , or no better weak learner can be found that does not cover any negative example (in ) above a given percentage. Note that in Foil- instead, non-positive examples are not allowed to be covered. The wFoil- Algorithm. The wFoil- algorithm is defined in Algorithm 2, which we comment briefly as next. Steps 1 - 3 are simple initialisation steps. Steps 5 - 21. are the main loop from which we may exit in case there is no improvement (Step. 16), and the confidence degree of the so far determined weak learner is above a given threshold or it does not cover any negative example above a given percentage (Step. 18). Note that the latter case guarantees soundness of the weak learner if the percentage is set to . In Step 8 we determine all new refinements, which then are scored in Steps 10 -15 in order to determine the one with the best gain. Eventually, once we exit from the main loop, the best found weak learner is returned (Step 22 and 23).	2021-10-27 00:00:39	{"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": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8670922517776489, "perplexity": 1217.5328586241988}, "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/1634323587963.12/warc/CC-MAIN-20211026231833-20211027021833-00230.warc.gz"}
https://www.physicsforums.com/threads/simple-question-about-direction-of-force-due-to-current.388268/	# Simple question about direction of force due to current 1. Mar 20, 2010 ### Samuelb88 1. The problem statement, all variables and given/known data A small loop is located near a LC circuit (see link). Given q_0 = -50. uC I_0 = -30. mA L = 40. mH C = 60. uF http://yfrog.com/jlphysj" [Broken] At t = 4.20 ms, determine (A) the sense of the induced current in the small loop, and (B) the direction of the net force on the small loop due to the current-current interaction. 3. The attempt at a solution Before determining the sense of the induced current in the small loop... I determined an explicit expression for the charge function q(t) = Qcos[wt+P], that means finding the phase angle P, the maximum charge Q, and the angular frequency of oscillation w. I. $$w = (\frac{1}{LC}\right) )^(^1^/^2^) = 646. (rad./s)$$ II. $$E_t_o_t = \frac{q_0^2}{2C}\right) + \frac{1}{2}LI_0^2 = 3.8810^-5 J$$ So: $$Q = (2CE_t_o_t)^(^1^/^2^) = 6.8210^-5 C$$ III. $$P = arccos(\frac{q_0}{Q}\right) ) = {+/-} 2.39 (rad.)$$ Since I_0 < 0, and I_0 = -wQsin[P] < 0, positive angle should be chosen, so P = + 2.39 (rad.) (A) At t = .0042s, I(.0042) > 0, so this suggest current in LC circuit is flowing clockwise, as indicated by the arrow in the LC circuit indicating positive current flow. Using the right hand rule for current, I see the magnetic field at this time is directed out of the page in the small loop. So, using the right hand rule for current again, I see the sense of the induced current in the small loop is counterclockwise. (B) Again, at t = .0042s, the direction of the net force on the small loop due to the current-current interaction seems like it should be directed downwards, that is, the force exerted on the small loop would be trying to "pull it closer" to the LC circuit, as suggested by the right hand rule when applied to the force vector equation F = ILxB (the vector L is taken to be in the same direction as the induced current in the small loop). Anyways, my professor has provided an answer sheet, and he has the direction of the net force on the small loop due to the current-current interaction is directed upwards (that is, away from the LC circuit) and I can't understand why. Could some please explain to me what I am not understanding about this? I'm very confused... Thanks - Sam Last edited by a moderator: May 4, 2017 2. Mar 20, 2010 ### JaWiB Without reading too carefully (so you might still have the correct answer here), the induced current doesn't depend on the direction of the magnetic field, but the change in the magnetic flux. So if the magnetic field is increasing and you have determined its direction correctly, then you are correct. If the magnetic field is decreasing, then the current is in the opposite direction. 3. Mar 20, 2010 ### Samuelb88 Ahh yes. At any rate, the answer sheet my professor has provided says the induced current is counterclockwise. Also, seeing as my argument is not valid, I guess that brings rise to another question. On his answer sheet, he has" the time-rate of change of the magnetic flux directed into the page, therefore the induced emf is counterclockwise -> induced current is counterclockwise." So trying to understand this... (correct me if I am wrong) Calculating the time-rate of change of the current dI/dt and evaluating it at t=.0042s, it is seen that dI/dt < 0, so the current in the LC circuit must be decreasing. If the current in the LC circuit is decreasing, shouldn't the magnetic field strength be decreasing as well since in general, the magnetic field strength is proportional to the current? And if the magnetic field strength is decreasing, then the magnetic flux is decreasing and the time-rate of change of the magnetic flux is "negative" or... into the page because the field is directed out of the page (?) And so Lenz Law essentially says you should point your thumb in the opposite direction of the d(Phi)/dt and curl your fingers to determine the sense of the induced current. So by this, it would indicate the sense of the induced current in counterclockwise. 4. Mar 20, 2010 ### JaWiB You're right, I said that backwards (if the B field is out of the page and increasing, the induced current should be clockwise) It does seem to me that there should be an attractive force between the loops. The only way I can see a repulsive force is if the current in the LC circuit is counter-clockwise and increasing. In that case, the magnetic field in the small loop is into the page and increasing, so the induced emf would create a moment out of the page and a current in the counter-clockwise direction (check me on this). Did your professor indicate the direction of the current in the LC circuit? 5. Mar 20, 2010 ### Samuelb88 I probably should mention on his answer sheet (it is very messy and hard to follow) he has "t = 4.20 ms -> I = -8.9 mA, dI/dt = -28. A/s" However, I've evaluated the current function at t=.0042s multiple times, and unless I have forgot how to differentiate, then there is no way I(.0042) = -8.9 mA... At any rate, if the current in the LC circuit is "negative," then yes, that would mean its sense is counterclockwise. Also, since dI/dt < 0, this means the current in decreasing, and making the same argument as I made in my previous post {...}. It would seem like Lenz Law would now suggest the sense of the induced current is clockwise under the pretenses he has given on his answer sheet (that is, I < 0, dI/dt < 0). Uhhhhg... Anyways, recalculating the current function one more time: $$\frac{d(q(t))}{dt}\right) = I(t) = -wQsin[wt+P]$$ And evaluating I(.0042): $$I(.0042) = -[646.][6.8210^-^5]sin(646(.0042)+2.39) = .04074 A$$ I'm going to send you a link where you can view the paper I am looking at, as well as his answer sheet if you wish to look over it to perhaps get a better understanding... I understand if you don't want to work through it. At any rate, thanks for your help yo.	2018-03-22 16:34:53	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 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": 0.7165684700012207, "perplexity": 379.62206275092564}, "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-2018-13/segments/1521257647892.89/warc/CC-MAIN-20180322151300-20180322171300-00686.warc.gz"}
https://www.thejournal.club/c/paper/147198/	#### Multi-kernel Regression For Graph Signal Processing ##### Arun Venkitaraman, Saikat Chatterjee, Peter Händel We develop a multi-kernel based regression method for graph signal processing where the target signal is assumed to be smooth over a graph. In multi-kernel regression, an effective kernel function is expressed as a linear combination of many basis kernel functions. We estimate the linear weights to learn the effective kernel function by appropriate regularization based on graph smoothness. We show that the resulting optimization problem is shown to be convex and pro- pose an accelerated projected gradient descent based solution. Simulation results using real-world graph signals show efficiency of the multi-kernel based approach over a standard kernel based approach. arrow_drop_up	2022-05-27 03:45:17	{"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": 0.8208386301994324, "perplexity": 1057.9623023257213}, "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/1652662631064.64/warc/CC-MAIN-20220527015812-20220527045812-00588.warc.gz"}
https://docs.panda3d.org/1.10/cpp/reference/panda3d.core.CardMaker	# panda3d.core.CardMaker¶ class CardMaker Bases: Namable This class generates 2-d “cards”, that is, rectangular polygons, particularly useful for showing textures etc. in the 2-d scene graph. Inheritance diagram __init__(param0: CardMaker) → None __init__(name: str) → None reset() → None Resets all the parameters to their initial defaults. setUvRange(ll: LTexCoord, ur: LTexCoord) → None Sets the range of UV’s that will be applied to the vertices. If setHasUvs() is true (as it is by default), the vertices will be generated with the indicated range of UV’s, which will be useful if a texture is applied. setUvRange(ll: LTexCoord, lr: LTexCoord, ur: LTexCoord, ul: LTexCoord) → None Sets the range of UV’s that will be applied to the vertices. If setHasUvs() is true (as it is by default), the vertices will be generated with the indicated range of UV’s, which will be useful if a texture is applied. setUvRange(ll: LTexCoord3, lr: LTexCoord3, ur: LTexCoord3, ul: LTexCoord3) → None Sets the range of UV’s that will be applied to the vertices. If setHasUvs() is true (as it is by default), the vertices will be generated with the indicated range of UV’s, which will be useful if a texture is applied. setUvRange(x: LVector4, y: LVector4, z: LVector4) → None Sets the range of UV’s that will be applied to the vertices. If setHasUvs() is true (as it is by default), the vertices will be generated with the indicated range of UV’s, which will be useful if a texture is applied. setUvRange(tex: Texture) → None Sets the range of UV’s that will be applied to the vertices appropriately to show the non-pad region of the texture. setUvRangeCube(face: int) → None Sets the range of UV’s that will be applied to the vertices appropriately for a cube-map face. setHasUvs(flag: bool) → None Sets the flag indicating whether vertices will be generated with UV’s or not. setHas3dUvs(flag: bool) → None Sets the flag indicating whether vertices will be generated with 3-component UVW’s (true) or 2-component UV’s (the default, false). Normally, this will be implicitly set by setting the uv_range. setFrame(frame: LVecBase4) → None Sets the size of the card. setFrame(ll: LVertex, lr: LVertex, ur: LVertex, ul: LVertex) → None Sets the size of the card. setFrame(left: float, right: float, bottom: float, top: float) → None Sets the size of the card. setFrameFullscreenQuad() → None Sets the card to (-1,1,-1,1), which is appropriate if you plan to parent it to render2d and use it as a fullscreen quad. setColor(color: LColor) → None setColor(r: float, g: float, b: float, a: float) → None Sets the color of the card. setHasNormals(flag: bool) → None Sets the flag indicating whether vertices will be generated with normals or not. Normals are required if you intend to enable lighting on the card, but are just wasted space and bandwidth otherwise, so there is a (slight) optimization for disabling them. If enabled, the normals will be generated perpendicular to the card’s face. setSourceGeometry(node: PandaNode, frame: LVecBase4) → None Sets a node that will be copied (and scaled and translated) to generate the frame, instead of generating a new polygon. The node may contain arbitrary geometry that describes a flat polygon contained within the indicated left, right, bottom, top frame. When generate() is called, the geometry in this node will be scaled and translated appropriately to give it the size and aspect ratio specified by setFrame(). clearSourceGeometry() → None Removes the node specified by an earlier call to setSourceGeometry(). generate() → PandaNode Generates a GeomNode that renders the specified geometry. Return type PandaNode	2020-02-17 00:30:51	{"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": 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": 0.231089249253273, "perplexity": 5588.68897091224}, "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-2020-10/segments/1581875141460.64/warc/CC-MAIN-20200217000519-20200217030519-00074.warc.gz"}
http://openstudy.com/updates/4d938c3441658b0b8c9fa262	anonymous 5 years ago with equation is correct for the right triangle? 1. anonymous a²+b²=c² 2. anonymous A) d squared = e squared + f squared B) f squared = d squared + e squared C)e squared =d squared +f squared 3. nowhereman Would you please not use non-free image format! I can not display it. 4. anonymous I think you mean free image format? 5. nowhereman I mean _not_ use _non-free_ :-) and as for Ambrose's equation: it holds if a and b are the length of the catheti and c is the length of the hypothenuse of a right triangle. 6. anonymous D²+E²=F² $E ^{2}=\sqrt{F ^{2}-D ^{2}}$ $D ^{2}=\sqrt{F ^{2}-E ^{2}}$ Hope this helps. It only works for right triangles. 7. nowhereman only that the squares on the left sides are too much ;-) 8. anonymous :) 9. anonymous	2016-10-24 03:44:30	{"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": 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": 0.9136918783187866, "perplexity": 4209.272676296214}, "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/1476988719465.22/warc/CC-MAIN-20161020183839-00458-ip-10-171-6-4.ec2.internal.warc.gz"}
https://gdal.org/development/rfc/rfc15_nodatabitmask.html	Author: Frank Warmerdam Contact: warmerdam@pobox.com ## Summary¶ Some file formats support a concept of a bitmask to identify pixels that are not valid data. This can be particularly valuable with byte image formats where a nodata pixel value can not be used because all pixel values have a valid meaning. This RFC tries to formalize a way of recognising and accessing such null masks through the GDAL API, while moving to a uniform means of representing other kinds of masking (nodata values, and alpha bands). The basic approach is to treat such masks as raster bands, but not regular raster bands on the datasource. Instead they are freestanding raster bands in a manner similar to the overview raster band objects. The masks are represented as GDT_Byte bands with a value of zero indicating nodata and non-zero values indicating valid data. Normally the value 255 will be used for valid data pixels. ## API¶ GDALRasterBand is extended with the following methods: virtual GDALRasterBand *GetMaskBand(); virtual CPLErr CreateMaskBand( int nFlags ); GDALDataset is extended with the following method: virtual CPLErr CreateMaskBand( nFlags ); Note that the GetMaskBand() should always return a GDALRasterBand mask, even if it is only an all 255 mask with the flags indicating GMF_ALL_VALID. The GetMaskFlags() method returns an bitwise OR-ed set of status flags with the following available definitions that may be extended in the future: • GMF_ALL_VALID(0x01): There are no invalid pixels, all mask values will be 255. When used this will normally be the only flag set. • GMF_PER_DATASET(0x02): The mask band is shared between all bands on the dataset. • GMF_ALPHA(0x04): The mask band is actually an alpha band and may have values other than 0 and 255. • GMF_NODATA(0x08): Indicates the mask is actually being generated from nodata values. (mutually exclusive of GMF_ALPHA) The CreateMaskBand() method will attempt to create a mask band associated with the band on which it is invoked, issuing an error if it is not supported. Currently the only flag that is meaningful to pass in when creating a mask band is GMF_PER_DATASET. The rest are used to represent special system provided mask bands. GMF_PER_DATASET is assumed when CreateMaskBand() is called on a dataset. The GDALRasterBand class will include a default implementation of GetMaskBand() that returns one of three default implementations. • If a corresponding .msk file exists it will be used for the mask band. • If the band has a nodata value set, an instance of the new GDALNodataMaskRasterBand class will be returned. GetMaskFlags() will return GMF_NODATA. • If there is no nodata value, but the dataset has an alpha band that seems to apply to this band (specific rules yet to be determined) and that is of type GDT_Byte then that alpha band will be returned, and the flags GMF_PER_DATASET and GMF_ALPHA will be returned in the flags. • If neither of the above apply, an instance of the new GDALAllValidRasterBand class will be returned that has 255 values for all pixels. The null flags will return GMF_ALL_VALID. For an external .msk file to be recognized by GDAL, it must be a valid GDAL dataset, with the same name as the main dataset and suffixed with .msk, with either one band (in the GMF_PER_DATASET case), or as many bands as the main dataset. It must have INTERNAL_MASK_FLAGS_xx metadata items set at the dataset level, where xx matches the band number of a band of the main dataset. The value of those items is a combination of the flags GMF_ALL_VALID, GMF_PER_DATASET, GMF_ALPHA and GMF_NODATA. If a metadata item is missing for a band, then the other rules explained above will be used to generate a on-the-fly mask band. The default implementation of the CreateMaskBand() method will be implemented based on similar rules to the .ovr handling implemented using the GDALDefaultOverviews object. A TIFF file with the extension .msk will be created with the same basename as the original file, and it will have as many bands as the original image (or just one for GMF_PER_DATASET). The mask images will be deflate compressed tiled images with the same block size as the original image if possible. The default implementation of GetFileList() will also be modified to know about the .msk files. ## CreateCopy()¶ The GDALDriver::DefaultCreateCopy(), and GDALPamDataset::CloneInfo() methods will be updated to copy mask information if it seems necessary and is possible. Note that NODATA, ALL_VALID and ALPHA type masks are not copied since they are just derived information. ## Alpha Bands¶ When a dataset has a normal GDT_Byte alpha (transparency) band that applies, it should be returned as the null mask, but the GetMaskFlags() method should include GMF_ALPHA. For processing purposes any value other than 0 should be treated as valid data, though some algorithms will treat values between 1 and 254 as partially transparent. ## Drivers Updated¶ These drivers will be updated: • JPEG Driver: support the “zlib compressed mask appended to the file” approach used by a few data providers. • GRASS Driver: updated to support handling null values as masks. Possibly updated: • HDF4 Driver: This driver might possibly be updated to return real mask if we can figure out a way. • SDE Driver: This driver might be updated if Howard has sufficient time and enthusiasm. ## Utilities¶ The gdalwarp utility and the gdal warper algorithm will be updated to use null masks on input. The warper algorithm already uses essentially this model internally. For now gdalwarp output (nodata or alpha band) will remain unchanged, though at some point in the future support may be added for explicitly generating null masks, but for most purposes producing an alpha band is producing a null mask. ## Implementation Plan¶ This change will be implemented by Frank Warmerdam in trunk in time for the 1.5.0 release. ## SWIG Implications¶ The GetMaskBand(), GetMaskFlags() and CreateMaskBand() methods (and corresponding defines) will need to be added. The mask should work like a normal raster band for swig purposes so minimal special work should be required. ## Testing¶ The gdalautotest will be extended with the following: • gcore/mask.py: test default mask implementation for nodata, alpha and all valid cases. • gdriver/jpeg.py: extend with a test for “appended bitmask” case - creation and reading. Interactive testing will be done for gdalwarp.	2019-11-22 09:49:28	{"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": 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": 0.18737025558948517, "perplexity": 3462.05496618584}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-47/segments/1573496671249.37/warc/CC-MAIN-20191122092537-20191122120537-00076.warc.gz"}
https://www.cyrusimap.org/3.4/imap/download/upgrade.html	Note This guide assumes that you are familiar and comfortable with administration of a Cyrus installation, and system administration in general. It assumes you are installing from source or tarball. If you want to install from package, use the upgrade instructions from the package provider. Note For those upgrading from 2.3.X; newer releases of Cyrus IMAP will use significantly more memory per selected mailbox. This is not an error or bug; it's a feature. The newer code is holding more data and metadata in memory for purposes of faster access to more of the mailbox. This is not a memory leak. ## 1. Preparation¶ Things to consider before you begin: ### Installation from tarball¶ You will need to install from our packaged tarball. We provide a full list of libraries that Debian requires, but we aren't able to test all platforms: you may find you need to install additional or different libraries to support v3.4. ### How are you planning on upgrading?¶ Ideally, you will do a sandboxed test installation of 3.4 using a snapshot of your existing data before you switch off your existing installation. The rest of the instructions are assuming a sandboxed 3.4 installation. If you're familiar with replication, and your current installation is 2.4 or newer, you can set up your existing installation to replicate data to a new 3.4 installation and failover to the new installation when you're ready. The replication protocol has been kept backwards compatible. If your old installation contains mailboxes or messages that are older than 2.4, they may not have GUID fields in their indexes (index version too old), or they may have their GUID field set to zero. 3.4 will not accept message replications without valid matching GUIDs, so you need to fix this on your old installation first. You can check for affected mailboxes by examining the output from the mbexamine(8) tool: • mailboxes that report a 'Minor Version:' less than 10 will need to have their index upgraded using reconstruct(8) with the -V <version> parameter to be at least 10. • mailboxes containing messages that report 'GUID:0' will need to have their GUIDs recalculated using reconstruct(8) with the -G parameter. If you have a large amount of data, these reconstructs will take a long time, so it's better to identify the mailboxes needing attention and target them specifically. But if you have a small amount of data, it might be less work to just reconstruct -G -V max everything. If you are upgrading in place, you will need to shut down Cyrus entirely while you install the new package. If your old installation was using Berkeley DB format databases, you will need to convert or upgrade the databases before you upgrade. Cyrus v3.4 does not support Berkeley DB at all. Note If you are upgrading from Cyrus version 2.5 or earlier, and your system is configured with the following combination in imapd.conf(5): fulldirhash: yes hashimapspool: either yes or no unixhierarchysep: yes then you will not be able to upgrade-in-place. This is due to a change in how directory hashes are calculated for users whose localpart contains a dot, which was introduced in 3.0.0. After an in-place upgrade, Cyrus will not be able to find these users' metadata and/or mailboxes. If you have this configuration, you will need to upgrade by replicating, not in place. ### Do What As Who?¶ Since the various files, databases, directories, etc. used by Cyrus must be readable and writable as the cyrus user, please make sure to always perform Cyrus commands as the cyrus user, and not as root. In our documentation, we will always reference Cyrus commands in this form -- cyr_info(8) -- before using examples of them, so you'll know that those commands must be run as the cyrus user. Doing so in most systems is as simple as using either the su or sudo commands, like so: su cyrus -c "/usr/local/bin/cyr_info conf-lint -C /etc/imapd.conf -M /etc/cyrus.conf" sudo -u cyrus /usr/local/bin/cyr_info conf-lint -C /etc/imapd.conf -M /etc/cyrus.conf In this document, however, there are also several command examples which should or must be run as root. These are always standard *nix commands, such as rsync or scp. ## 2. Install new 3.4 Cyrus¶ Fetch the libraries for your platform. The full list (including all optional packages) for Debian is: sudo apt-get install -y autoconf automake autotools-dev bash-completion bison build-essential comerr-dev \ debhelper flex g++ git gperf groff heimdal-dev libbsd-resource-perl libclone-perl libconfig-inifiles-perl \ libcunit1-dev libdatetime-perl libdb-dev libdigest-sha-perl libencode-imaputf7-perl libfile-chdir-perl \ libglib2.0-dev libical-dev libio-socket-inet6-perl libio-stringy-perl libjansson-dev libldap2-dev \ libmysqlclient-dev libnet-server-perl libnews-nntpclient-perl libpam0g-dev libpcre3-dev libsasl2-dev \ libsqlite3-dev libssl-dev libtest-unit-perl libtool libunix-syslog-perl liburi-perl \ libxapian-dev libxml-generator-perl libxml-xpath-perl libxml2-dev libwrap0-dev libzephyr-dev lsb-base \ net-tools perl php-cli php-curl pkg-config po-debconf tcl-dev \ transfig uuid-dev vim wamerican wget xutils-dev zlib1g-dev sasl2-bin rsyslog sudo acl telnet If you're on another platform and can provide the list of dependencies, please let us know via a GitHub issue or documentation pull request, or send mail to the developer list. Note It's best to ensure your new Cyrus will not start up automatically if your server restarts in the middle of the upgrade. How this is best achieved will depend upon your OS and distro, but may involve something like systemctl disable cyrus-imapd or update-rc.d cyrus-imapd disable ## 3. Shut down existing Cyrus¶ Shut down your existing Cyrus installation with its init script or whatever method you normally use. This is necessary to guarantee a clean data snapshot. ## 4. Backup and Copy existing data¶ We recommend backing up all your data before continuing. (You do already have a backup strategy in place, right? Once you're on 3.4, you can consider using the experimental backup tools.) Copy all of this to the new instance, using rsync or similar tools. Note Cyrus keeps its data and databases in various locations, some of which may be tailored by your configuration. Please consult File & Directory Locations for guidance on where data lives in your current installation. For example, to copy from an existing Debian or Ubuntu installation using their standard locations, you might execute this series of commands on the new server (where "oldimap" is the name of the old server): rsync -aHv oldimap:/var/lib/cyrus/. /var/lib/cyrus/. rsync -aHv oldimap:/var/spool/cyrus/. /var/spool/cyrus/. You don't need to copy the following databases as Cyrus 3.4 will recreate these for you automatically: • duplicate delivery (deliver.db), • TLS cache (tls_sessions.db), • PTS cache (ptscache.db), • STATUS cache (statuscache.db). Note You may wish to consider relocating these four databases to ephemeral storage, such as /run/cyrus (Debian/Ubuntu) or /var/run/cyrus or whatever suitable tmpfs is provided on your distro. It will place less IO load on your disks and run faster. ## 5. Copy config files and update¶ Again, check the locations on your specific installation. For example, on FreeBSD systems, the configuration files imapd.conf(5) and cyrus.conf(5) are in /usr/local/etc, rather than /etc/. Run this command on the old server: scp /etc/cyrus.conf /etc/imapd.conf newimap:/etc/ Using the cyr_info(8) command, check to see if your imapd.conf file contains any deprecated options. Run this command on the new server: cyr_info conf-lint -C <path to imapd.conf> -M <path to cyrus.conf> You need to provide both imapd.conf and cyrus.conf so that conf-lint knows the names of all your services and can check service-specific overrides. To check your entire system's configuration you can use the conf-all action. This command takes all the system defaults, along with anything you have provided overrides for in your config files: cyr_info conf-all -C <path to imapd.conf> -M <path to cyrus.conf> Important config options: unixhierarchysep: and altnamespace: defaults in imapd.conf(5) changed in 3.0, which will affect you if you are upgrading to 3.4 from something earlier than 3.0. Implications are outlined in the Note in User Namespace Mode and Switching the Alternative Namespace. Please also see "Sieve Scripts," below. • unixhierarchysep: on • altnamespace: on In cyrus.conf(5) move idled from the START section to the DAEMON section. • Special-Use flags If your 2.4 imapd.conf(5) made use of the xlist-XX directive(s), you can convert these to per-user special-use annotations in your new install with the cvt_xlist_specialuse(8) tool Warning Berkeley db format no longer supported since 3.0 If you have any databases using Berkeley db, they'll need to be converted to skiplist or flat in your existing installation. And then optionally converted to whatever final format you'd like in your 3.4 installation. Databases potentially affected: mailboxes, annotations, conversations, quotas. On old install, prior to migration: cvt_cyrusdb /<configdirectory>mailboxes.db berkeley /tmp/new-mailboxes.db skiplist If you don't want to use flat or skiplist for 3.4, you can use cvt_cyrusdb(8) to swap to new format: cvt_cyrusdb /tmp/new-mailboxes.db skiplist /<configdirectory>/mailboxes.db <new file format> Note The cvt_cyrusdb(8) command does not accept relative paths. ## 7. Start new 3.4 Cyrus and verify¶ sudo ./master/master -d Check /var/log/syslog for errors so you can quickly understand potential problems. When you're satisfied version 3.4 is running and can see all its data correctly, start the new Cyrus up with your regular init script. If something has gone wrong, contact us on the mailing list. You can revert to backups and keep processing mail using your old version until you're able to finish your 3.4 installation. Note If you've disable your system startup scripts, as recommended in step 2, remember to re-enable them. Use something like systemctl enable cyrus-imapd or update-rc.d cyrus-imapd enable ## 8. Reconstruct databases and cache¶ The following steps can each take a long time, so we recommend running them one at a time (to reduce locking contention and high I/O load). reconstruct -V max New configuration: if turning on conversations, you need to create conversations.db for each user. (This is required for jmap).: ctl_conversationsdb -b -r To check (and correct) quota usage: quota -f If you've been using CalDAV/CardDAV/all of the DAV from earlier releases, then the user.dav databases need to be reconstructed due to format changes.: dav_reconstruct -a If you are upgrading from 3.0, and have the reverseacls feature enabled in imapd.conf(5), you may need to regenerate the data it uses (which is stored in mailboxes.db). This is automatically regenerated at startup by ctl_cyrusdb -r if the reverseacls setting has changed. So, to force a regeneration: 1. Shut down Cyrus 2. Change reverseacls to 0 in imapd.conf(5) 3. Run ctl_cyrusdb(8) with the -r switch (or just start Cyrus, assuming your cyrus.conf(5) contains a ctl_cyrusdb -r entry in the START section). The old RACL entries will be removed 4. (If you started Cyrus, shut it down again) 5. Change reverseacls back to 1 6. Start up Cyrus (or run ctl_cyrusdb -r). The RACL entries will be rebuilt ## 9. Do you want any new features?¶ 3.4 comes with many lovely new features. Consider which ones you want to enable. Check the 3.4 release notes for the full list. Your upgrade is complete! We have a super-quick survey (3 questions only, anonymous responses) we would love for you to fill out, so we can get a feel for how many Cyrus installations are out there, and how the upgrade process went. I'll fill in the survey right now (opens in a new window) ## Special note for Murder configurations¶ If you upgrade murder frontends before you upgrade all the backends, they may advertise features to clients which the backends don't support, which will cause the commands to fail when they are proxied to the backend. Generally accepted wisdom when upgrading a Murder configuration is to upgrade all your back end servers first. This can be done one at a time.	2021-05-06 07:01:53	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.22173404693603516, "perplexity": 8228.538977105853}, "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-2021-21/segments/1620243988741.20/warc/CC-MAIN-20210506053729-20210506083729-00113.warc.gz"}
https://freesteam.net/threads/ventrilo-server.346/	# Ventrilo server #### hugz` ##### New Member Heh.. I've seen people in vent saying "I cracked/hacked this ventrilo" after I asked them where did you get this server.. In the ventrilo's forums they say its free if its only 8 slots.. more then that you have to pay.. Well I tried to set up my own server, I could connect to it, but others couldn't, the support staff isn't all that great.. and slow too.. So I am still getting the support from them, if any of you ever made it work, please let me know. ;> #### nightreaper999 ##### Bringing Sexy Back!! if it doesnt work you have to go to ventrilo.com and get the ip ad they give to u. than u can try. if not, you have to port forward. u using a rouder? #### hugz` ##### New Member See thats what I am talknig about.. I get confused with that shit.. port forward, external ip, internal.. blah blah blah.. I don't get that shit. #### FSOwner ##### FS Owner TBH use TeamSpeak it's a hell of a lot better and easier to set up/modify. And you don't have to pay Last edited: Replies 5 Views 940 Replies 8 Views 992 Replies 3 Views 803 Replies 11 Views 1K Replies 15 Views 2K	2022-06-30 10:34:06	{"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": 0.8470659852027893, "perplexity": 12995.760928729755}, "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-2022-27/segments/1656103671290.43/warc/CC-MAIN-20220630092604-20220630122604-00665.warc.gz"}
http://connection.ebscohost.com/c/articles/35514335/enhanced-absorption-by-nanostructured-silicon	TITLE Enhanced absorption by nanostructured silicon AUTHOR(S) Bandiera, S.; Jacob, D.; Muller, T.; Marquier, F.; Laroche, M.; Greffet, J.-J. PUB. DATE November 2008 SOURCE Applied Physics Letters;11/10/2008, Vol. 93 Issue 19, p193103 SOURCE TYPE DOC. TYPE Article ABSTRACT Some applications such as ultrafast detectors or high efficiency photovoltaics require absorption by thin films. However, close to the bandgap, silicon absorbs very poorly. In this letter, we show that the absorption of a 100 nm slab can be as high as 50% in the range of wavelengths 700â€“830 nm when using a periodic structure properly designed. ACCESSION # 35514335 Related Articles • Dispersion dependence of two-photon absorption transition on frequency in Si PIN photodetector. Cui, Haoyang; Gao, Wei; Zeng, Jundong; Yang, Junjie; Chu, Fenghong; Tang, Zhong // Optical & Quantum Electronics;Oct2014, Vol. 46 Issue 10, p1189 The variation of two-photon absorption (TPA) coefficient $$\beta _{\mathrm{TPA}} (\omega )$$ of Si excited at difference photon energy was investigated. The TPA coefficient was measured by using a picosecond pulsed laser with the wavelength could be tuned in a wide photon-energy range. An... • Light trapping in solar cells: Analytical modeling. Boccard, Mathieu; Battaglia, Corsin; Haug, Franz-Josef; Despeisse, Matthieu; Ballif, Christophe // Applied Physics Letters;10/8/2012, Vol. 101 Issue 15, p151105 We model analytically light harvesting in realistic solar cells by extending a formalism suggested by Deckman et al. [Appl. Phys. Lett. 42, 110968 (1983)], based on tracing of an average ray of light. Arbitrary light scattering schemes and parasitic absorption are implemented in the model, and... • Comparative study of absorption in tilted silicon nanowire arrays for photovoltaics. Kayes, Md; Leu, Paul // Nanoscale Research Letters;Dec2014, Vol. 9 Issue 1, p1 Silicon nanowire arrays have been shown to demonstrate light trapping properties and promising potential for next-generation photovoltaics. In this paper, we show that the absorption enhancement in vertical nanowire arrays on a perfectly electric conductor can be further improved through... • Polycrystalline silicon on glass for thin-film solar cells. Green, Martin A. // Applied Physics A: Materials Science & Processing;Jul2009, Vol. 96 Issue 1, p153 Although most solar cell modules to date have been based on crystalline or polycrystalline wafers, these may be too material intensive and hence always too expensive to reach the very low costs required for large-scale impact of photovoltaics on the energy scene. Polycrystalline silicon on glass... • At the Center of a Bright Idea. Starner, Ron // Site Selection;Nov/Dec2009, Vol. 54 Issue 6, p760 The article profiles the Fraunhofer Center for Silicon Photovoltaics in Halle in Saxony-Anhalt, Germany. According to Jorg Bagdahn, head and professor at the Department of Electrical, Mechanical and Industrial Engineering at Fraunhofer Center, photovoltaics supply 15,000 times more energy in one... • Understanding Light Harvesting in Radial Junction Amorphous Silicon Thin Film Solar Cells. Linwei Yu; Soumyadeep Misra; Junzhuan Wang; Shengyi Qian; Martin Foldyna; Jun Xu; Yi Shi; Erik Johnson; Pere Roca i Cabarrocas // Scientific Reports;2/14/2014, p1 The radial junction (RJ) architecture has proven beneficial for the design of a new generation of high performance thin film photovoltaics. We herein carry out a comprehensive modeling of the light in-coupling, propagation and absorption profile within RJ thin film cells based on an accurate set... • Raman spectroscopy monitors thin-film Si PV cell manufacture. SIEW, RONIAN // Laser Focus World;Jun2013, Vol. 49 Issue 6, p43 The article discusses the role of Raman Spectroscopy characterizing the chemical composition of substances and materials. It states that its' applications varies from forensics and pharmaceuticals to astrospectrocopy which involves the manufacture of photovoltaic (PV) cells. It also mentions... • Dislocations in laser-doped silicon detected by micro-photoluminescence spectroscopy. Nguyen, Hieu T.; Young Han; Ernst, Marco; Fell, Andreas; Franklin, Evan; Macdonald, Daniel // Applied Physics Letters;7/13/2015, Vol. 107 Issue 2, p022101-1 We report the detection of laser-induced damage in laser-doped layers at the surface of crystalline silicon wafers, via micron-scale photoluminescence spectroscopy. The properties of the subband- gap emission from the induced defects are found to match the emission characteristics of... • Selectiveness of laser processing due to energy coupling localization: case of thin film solar cell scribing. Račiukaitis, G.; Grubinskas, S.; Gečys, P.; Gedvilas, M. // Applied Physics A: Materials Science & Processing;Jul2013, Vol. 112 Issue 1, p93 Selectiveness of the laser processing is the top-most important for applications of the processing technology in thin-film electronics, including photovoltaics. Coupling of laser energy in multilayered thin-film structures, depending on photo-physical properties of the layers and laser... Share	2018-02-22 01:14:20	{"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": 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": 0.4003373384475708, "perplexity": 9065.137085612187}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-09/segments/1518891813832.23/warc/CC-MAIN-20180222002257-20180222022257-00347.warc.gz"}
http://mathwaycalculus.com/how-to-solve-5-1-6-7-1-3-as-a-fraction/	# How to solve 5 1/6 – 7 1/3 as a fraction Welcome to my article how to solve 5 1/6 – 7 1/3 as a fraction. This question is taken from the simplification lesson. The solution of this question has been explained in a very simple way by a well-known teacher by doing addition, subtraction, and fractions. For complete information on how to solve this question how to solve 5 1/6 – 7 1/3 as a fraction, read and understand it carefully till the end. Let us know how to solve this question how to solve 5 1/6 – 7 1/3 as a fraction. First write the question on the page of the notebook. ## how to solve 5 1/6 – 7 1/3 as a fraction. Before solving this question, we will write in this way, \displaystyle 5\text{ }\frac{1}{6}\text{ }-\text{ }7\text{ }\frac{1}{3} \displaystyle \text{ }\frac{{6\times 5+1}}{6}\text{ }-\text{ }\frac{{3\times 7+1}}{3} \displaystyle \text{ }\frac{{31}}{6}\text{ }-\text{ }\frac{{22}}{3} \displaystyle \text{ }\frac{{31}}{6}\text{ }-\text{ }\frac{{22\times 2}}{{3\times 2}} \displaystyle \text{ }\frac{{31}}{6}\text{ }-\text{ }\frac{{44}}{6} \displaystyle \text{ }\frac{{31-44}}{6}\text{ } \displaystyle \text{ }\frac{{-13}}{6}\text{ }	2022-12-06 01:24:57	{"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": 0.9395326972007751, "perplexity": 2180.9332866525274}, "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/1669446711064.71/warc/CC-MAIN-20221205232822-20221206022822-00356.warc.gz"}