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https://www.physicsforums.com/threads/extraneous-roots.226349/	# Extraneous roots ## Main Question or Discussion Point Sorry for the length of the post, the problem I've included is not difficult but I wanted to have an example to help illustrate my question. solve: $$\sqrt{x}-\sqrt[4]{x} -2=0$$ . . . $$(x-16)(x-1)=0$$ The roots are 16 and 1, however when one puts them back into the original equation, 1 is found to be extraneous leaving 16 as the only solution. My question is, why do extraneous roots arise? I attempted to answer the question myself by reversing the above process and putting 1 in for x at each step to see when the equation becomes "invalid" for the extraneous root. $$(x-16)(x-1)=0$$ $$x^{2}-17x+16=0$$ $$x^{2}-17x+16+25x=25x$$ $$x^{2}+8x+16=25x$$ $$(x+4)^{2}=25x$$ $$x+4=5\sqrt{x}$$ $$x+4-4\sqrt{x}=5\sqrt{x}-4\sqrt{x}$$ $$x+4-4\sqrt{x}=\sqrt{x}$$ $$(\sqrt{x}-2)^{2}=\sqrt{x}$$ $$(\sqrt{x}-2)^{2}=\sqrt{x}$$ equation A $$\sqrt{x}-2=\sqrt[4]{x}$$ equation B $$\sqrt{x}-\sqrt[4]{x}-2=0$$ Putting 1 in for x in equation A works but B does not. It seems that going from A to B creates the problem. When one takes the square root of equation A the left side becomes $$((\sqrt{x}-2)^{2})^{\frac{1}{2}}$$ If I understood CompuChip's answer correctly to one of my previous posts, the inner to outer priority is not followed. If 1 is in for x, then -1 is the value in the first set of parenthesis and then -1 squared is 1, and then the square root is also 1. However if 1 is not in for x , since the roots are not known when one first goes through the problem, the squared to the 1/2 power gives what's in the parenthesis to the first power, which is just what's in the parenthesis. Then when 1 is in for x, we have -1 to the first power which is -1. The order of operations makes a difference for x=1 but does not for x=16. Is it true then, that extraneous roots arise because some mathematical operation is violated for that root? $$x = 5, x^2= 25, x=5, -5$$. Exactly the same as that, but more disguised =] In this same one, when you squared it, you introduced the erroneous negative square root when only the positive root applies.	2019-12-09 17:54:53	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 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": 0.8658134937286377, "perplexity": 331.23414878368317}, "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-2019-51/segments/1575540521378.25/warc/CC-MAIN-20191209173528-20191209201528-00057.warc.gz"}
https://brilliant.org/discussions/thread/23-2/	# #23 Suppose an integer $x$, a natural number $n$,and a prime number $p$ satisfy the equation $7x^2-44x+12=p^n$.Find the largest value of $p$. Note by Vilakshan Gupta 2 years, 2 months ago This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science. When posting on Brilliant: • Use the emojis to react to an explanation, whether you're congratulating a job well done , or just really confused . • Ask specific questions about the challenge or the steps in somebody's explanation. Well-posed questions can add a lot to the discussion, but posting "I don't understand!" doesn't help anyone. • Try to contribute something new to the discussion, whether it is an extension, generalization or other idea related to the challenge. MarkdownAppears as italics or _italics_ italics bold or __bold__ bold - bulleted- list • bulleted • list 1. numbered2. list 1. numbered 2. list Note: you must add a full line of space before and after lists for them to show up correctly paragraph 1paragraph 2 paragraph 1 paragraph 2 [example link](https://brilliant.org)example link > This is a quote This is a quote # I indented these lines # 4 spaces, and now they show # up as a code block. print "hello world" # I indented these lines # 4 spaces, and now they show # up as a code block. print "hello world" MathAppears as Remember to wrap math in $$ ... $$ or $ ... $ to ensure proper formatting. 2 \times 3 $2 \times 3$ 2^{34} $2^{34}$ a_{i-1} $a_{i-1}$ \frac{2}{3} $\frac{2}{3}$ \sqrt{2} $\sqrt{2}$ \sum_{i=1}^3 $\sum_{i=1}^3$ \sin \theta $\sin \theta$ \boxed{123} $\boxed{123}$ Sort by: You can Buy david burton's number theory book and arthur engel's problem solving strategies - 2 years, 2 months ago although quite expensive they are , but best books! - 2 years, 2 months ago This one i did :) - 2 years, 2 months ago did u get 47? - 2 years, 2 months ago Yep! - 2 years, 2 months ago @Md Zuhair @Vilakshan Gupta Guys , i just wanna ask that how can I improve my Number Theory and Geometry (particularly) skills? - 2 years, 2 months ago I struggled very much in Geometry! - 2 years, 2 months ago u will not get Arthur engel's in any shop. U can download its pdf and print it or simply read it. - 2 years, 2 months ago @Vilakshan Gupta Thank you so much... I'll surely get those! - 2 years, 2 months ago	2019-11-15 14:28:43	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 13, "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": 0.9922839999198914, "perplexity": 5474.0491457083135}, "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/1573496668644.10/warc/CC-MAIN-20191115120854-20191115144854-00202.warc.gz"}
http://math.stackexchange.com/questions/228636/how-come-proof-by-tautology-is-not-acceptable?answertab=active	# How come proof by tautology is not acceptable? If we show that a claim is equivalent to a tautology (which is stronger than showing the claim implies a tautology), how come that isn't a valid method of proof? - Showing that the claim implies a tautology doesn't tell you anything, since a tautology should be true anyhow. It is sufficient to show that your claim follows from a tautology, so if you show that your claim is equivalent to a tautology, you have shown that it is true. – Brett Frankel Nov 4 '12 at 3:21 What text or class did this come from? – Doug Spoonwood Nov 4 '12 at 3:29 If $T$ is a tautology, $(P\Rightarrow Q)\Leftrightarrow T$ is enough to prove $P\Rightarrow Q$, but it's overkill. All you need is $(P\Rightarrow Q)\Leftarrow T$. $(P\Rightarrow Q)\Rightarrow T$ is always true because $T$ is a tautology - it holds whether $P\Rightarrow Q$ is true or not, so it is a tautology in and of itself. On the other hand, $(P\Rightarrow Q)\Leftarrow T$ is only true when $P\Rightarrow Q$ is true, and in fact is equivalent to $P\Rightarrow Q$. - Who says it isn't valid? In what context? For what purpose? In some (actually most) mathematical contexts, for some (actually most) mathematical purposes, demonstrating that a formula is an instance of a tautology is a perfectly cromulent method of proving it. Among the exceptions is if the context is a course in formal logic and the purpose is to gain or show familiarity with a particular formal proof system and how it works. In that (fairly narrow) circumstance, appealing to tautology obviously misses the point, at least until you have formally proved in general that every tautology has a proof in the proof system at hand. - +1 for apparently producing the first-ever instance of "cromulent" on this site. – Rick Decker Nov 4 '12 at 19:27	2014-08-30 10:22:00	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.555380642414093, "perplexity": 334.10546068316364}, "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-2014-35/segments/1408500834883.60/warc/CC-MAIN-20140820021354-00090-ip-10-180-136-8.ec2.internal.warc.gz"}
https://mathoverflow.net/questions/306219/the-localization-of-the-integral-closure-of-a-valuation-ring-is-a-valuation-ring	# The localization of the integral closure of a valuation ring is a valuation ring Let $L\|K$ be a finite field extension, $v$ a non-archimedean valuation and $w$ an extension to $L.$ If $\mathcal{O}_L$ is the integral closure of the valuation ring $\mathcal{O}_v$ of $v$ in $L,$ show that the localization $\mathcal{O}_{\mathfrak{B}}$ of $\mathcal{O}_L$ at the prime ideal $\mathfrak{B} = \{\alpha \in \mathcal{O}_L \| w(\alpha) >0\}$ is the valuation ring $\mathcal{O}_w$ of $w.$ This is an exercise from Neukirch's book "Algebraic Number Theory", pg. 166 which I know how to solve. However, I feel that a more conceptual proof should be available but I seem unavailable to find one. Is there a "good" reason to see why the exercise is true? If $v$ is discrete, the exercise is obvious, and I would want some reason / solution which would be as convincing to me as I am about the veracity of the claim in that situation. I am sorry if this question is vague. I am OK with high-powered machinery to prove this theorem, in fact, I would be happy if it was used. I think (?) that we would be done if we could prove that the extension $\mathcal{O}_\mathfrak{B} \subset \mathcal{O}_w$ is integral. If we could prove directly that $\mathcal{O}_\mathfrak{B}$ is a valuation ring, we would also be done. But neither of these facts are obvious to me. For sake of convenience, I include the solution I have at the moment: It is easy to see that $\mathcal{O}_{\mathfrak{B}} \subset \mathcal{O}_w.$ Conversely, if $x \in \mathcal{O}_w$ let $$a_nx^n + a_{n-1}x^{n-1} + \cdots + a_1x + a_0 =0$$ be an algebraic equation for $x$ with coefficients in $K.$ Let $a_i$ be the coefficient farthest to the left with the lowest valuation. Let $b_j=a_j/a_i,$ and divide our equation by $a_i$ to get a new algebraic equation $$b_nx^n + b_{n-1}x^{n-1} + \cdots + b_1x+b_0=0.$$ Note that $v(b_j) >0$ if $j >i$ and that $v(b_j) \geq 0$ for all $i.$ Divide the equation with $x^i$ to get $$(b_nx^{n-i}+ \cdots + b_{n-i+1}x+1)+x^{-1}(b_{n-2}+ \cdots + b_0x^{-i+1})=0.$$ Let $w= (b_nx^{n-i}+ \cdots + b_{n-i+1}x+1)$ and $y= b_{n-2}+ \cdots + b_0x^{-i+1}.$ We then have that $x = -y/w.$ We now show that $y \in \mathcal{O}_L,$ and that $w \in \mathcal{O}_L, w \not \in \mathfrak{B},$ thus proving our inclusion. We note that $\mathcal{O}_L$ is the intersection in $L$ of all valuation rings containing $\mathcal{O}_v.$ Using this fact, one shows without too much trouble that our claim is true.	2019-04-20 05:15:04	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8815675377845764, "perplexity": 58.48007721492736}, "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-2019-18/segments/1555578528523.35/warc/CC-MAIN-20190420040932-20190420062932-00153.warc.gz"}
http://openstudy.com/updates/51d4bc65e4b08d0a48e51d74	## mitodoteira 2 years ago Prove: a^ba^c=a^(b+c) for real a, b, c. 1. mitodoteira $a,b,c \in \mathbb{R}$$Prove: a^{b}a^{c}=a^{b+c}$ 2. Noura11 Wait ! a should be a positive real ! 3. mitodoteira a>1 I forgot to say that. Facepalm. 4. Noura11 It is true for all a>0. We can say : $\Large a^ba^c=e^{\ln a^b}e^{\ln a^c}\\ ~~~~~~~~~\Large =e^{b\ln a}e^{c\ln a}\\ ~~~~~~~~~\Large=e^{b\ln a+c\ln a}\\ ~~~~~~~~~~\Large=e^{(b+c)\ln a}\\ ~~~~~~~~~~\Large=e^{\ln a^{b+c}} \\ ~~~~~~~~~~\Large=a^{b+c}$ 5. mitodoteira I can't use logs. I'm doing analysis and I'm still proving the fundamentals of real powers from the field axioms. 6. Noura11 OK ! If b and c are natural integers you can prove it using induction ! 7. mitodoteira b, c are just real. 8. Noura11 @mitodoteira My last reply is the 1st step of the proof ! 9. mitodoteira How? 10. sauravshakya I dont think we can use induction here... three variables 11. sauravshakya Isnt it the property??? I am not sure if it can be proven. example : we know ab=b*a because its a property what how to Prove it. 12. mitodoteira No, it isn't a property. 13. swissgirl hmmmmm how do you define the exponential function? 14. swissgirl http://math.stackexchange.com/questions/435751/proving-the-product-rule-for-exponents-with-the-same-base Here is the link to this particular question I asked on MSE. Take a look at both proofs. The proof using Least Upper Bound is more analytical and a touch harder to follow but I think that is the proof you are looking for.	2015-12-01 20:09:53	{"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": 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": 0.9084985852241516, "perplexity": 2796.690209908547}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-48/segments/1448398471436.90/warc/CC-MAIN-20151124205431-00035-ip-10-71-132-137.ec2.internal.warc.gz"}
https://www.hackmath.net/en/math-problem/5236?tag_id=104	# Outer angles The outer angle of the triangle ABC at the A vertex is 71°40 ' outer angle at the vertx B is 136°50'. What size has the inner triangle angle at the vertex C? Result C = 28.5 ° #### Solution: $A = 180 - (71+40/60) = \dfrac{ 325 }{ 3 } \doteq 108.3333 \ ^\circ \ \\ B = 180 - (136+50/60) = \dfrac{ 259 }{ 6 } \doteq 43.1667 \ ^\circ \ \\ C = 180 - (A+B) = 180 - (108.3333+43.1667) = \dfrac{ 57 }{ 2 } = 28.5 = 28.5 ^\circ = 28^\circ 30'$ Leave us a comment of this math problem and its solution (i.e. if it is still somewhat unclear...): Be the first to comment! ## Next similar math problems: 1. Isosceles triangle 10 In an isosceles triangle, the equal sides are 2/3 of the length of the base. Determine the measure of the base angles. 2. Propeller The aircraft propeller rotates at an angular speed of 200 rad/s. A) What is the speed at the tip of the propeller if its distance from the axis of rotation is 1.5 m? B) What path does the aircraft travel during one revolution of the propeller at a speed 3. Sides of right angled triangle One leg is 1 m shorter than the hypotenuse, and the second leg is 2 m shorter than the hypotenuse. Find the lengths of all sides of the right-angled triangle. 4. Cuboid face diagonals The lengths of the cuboid edges are in the ratio 1: 2: 3. Will the lengths of its diagonals be the same ratio? The cuboid has dimensions of 5 cm, 10 cm, and 15 cm. Calculate the size of the wall diagonals of this cuboid. 5. Body diagonal Calculate the volume of a cuboid whose body diagonal u is equal to 6.1 cm. Rectangular base has dimensions of 3.2 cm and 2.4 cm 6. Uphill garden I have a garden uphill, increasing from 0 to 4.5 m for a length of 25 m, how much is the climb in percent? 7. Positional energy What velocity in km/h must a body weighing 60 kg have for its kinetic energy to be the same as its positional energy at the height 50 m? 8. Cylinder and its circumference If the height of a cylinder is 4 times its circumference. What is the volume of the cylinder in terms of its circumference, c? 9. Reducing balance method A company buys an item having a useful life of 10 years for 1,000,000. If the company depreciates the item by the reducing balance method, a. Determine the depreciation for the first year. b. Estimate the depreciation for the second and third years. c.. 10. Compound interest 3 After 8 years, what is the total amount of a compound interest investment of \$25,000 at 3% interest, compounded quarterly? (interest is now dream - in the year 2019) 11. Blueberries 5 children collect 4 liters of blueberries in 1.5 hours. a) How many minutes do 3 children take 2 liters of blueberries? b) How many liters of blueberries will be taken by 8 children in 3 hours? 12. Before yesterday He merchant adds a sale sign in his shop window to the showed pair of shoes in the morning: "Today by p% cheaper than yesterday. " After a while, however, he decided that the sign saying: "Today 62.5% cheaper than the day before yesterday". Determine the n 13. AM of three numbers The number 2010 can be written as the sum of 3 consecutive natural numbers. Determine the arithmetic mean of these numbers. 14. Frustum of a cone A reservoir contains 28.54 m3 of water when completely full. The diameter of the upper base is 3.5 m while at the lower base is 2.5 m. Determine the height if the reservoir is in the form of a frustum of a right circular cone. 15. Surface of the cylinder Calculate the surface of the cylinder for which the shell area is Spl = 20 cm2 and the height v = 3.5 cm 16. The escalator I run up the escalator at a constant speed in the direction of the stairs and write down the number of steps A we climbed. Then we turn around and run it at the same constant speed in the opposite direction and write down the number of steps B that I climb 17. Three points 4 The line passed through three points - see table: x y -6 4 -4 3 -2 2 Write line equation in y=mx+b form	2019-12-08 13:33:17	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 1, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.500977635383606, "perplexity": 877.3176064179414}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-51/segments/1575540510336.29/warc/CC-MAIN-20191208122818-20191208150818-00456.warc.gz"}
http://computationalnonlinear.asmedigitalcollection.asme.org/article.aspx?articleid=1694103	0 Research Papers # A Model for Highly Strained DNA Compressed Inside a Protein Cavity [+] Author and Article Information Andrew D. Hirsh Research Assistant Department of Mechanical Engineering, University of Michigan, Ann Arbor, MI 48109 Todd D. Lillian Assistant Professor Department of Mechanical Engineering, Texas Tech University, Lubbock, TX 79409 e-mail: todd.lillian@ttu.edu Troy A. Lionberger Postdoctoral Research Associate Howard Hughes Medical Institute, Department of Physics, University of California, Berkeley, Berkeley, CA 94720 e-mail: talionberger@gmail.com Maryna Taranova Research Assistant e-mail: taranova.maryna@uci.edu Ioan Andricioaei Associate Professor e-mail: andricio@uci.edu Department of Chemistry, University of California, Irvine, Irvine, CA 92697 N. C. Perkins Professor Fellow ASME Department of Mechanical Engineering, University of Michigan, Ann Arbor, MI 48109 e-mail: ncp@umich.edu 1Corresponding author. Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received July 31, 2011; final manuscript received March 9, 2012; published online October 30, 2012. Assoc. Editor: Aki Mikkola. J. Comput. Nonlinear Dynam 8(3), 031001 (Oct 30, 2012) (8 pages) Paper No: CND-11-1121; doi: 10.1115/1.4007535 History: Received July 31, 2011; Revised March 09, 2012 ## Abstract Deoxyribonucleic acid (DNA) is a long and flexible biopolymer that contains genetic information. Building upon the discovery of the iconic double helix over 50 years ago, subsequent studies have emphasized how its biological function is related to the mechanical properties of the molecule. A remarkable system which highlights the role of DNA bending and twisting is the packing and ejection of DNA into and from viral capsids. A recent 3D reconstruction of bacteriophage $φ29$ reveals a novel toroidal structure of highly bent/twisted DNA contained in a small cavity below the viral capsid. Here, we extend an elastic rod model for DNA to enable simulation of the toroid as it is compacted and subsequently ejected from a small volume. We compute biologically-relevant forces required to form the toroid and predict ejection times of several nanoseconds. <> Topics: Cavities , DNA , Proteins Your Session has timed out. Please sign back in to continue. ## References Watson, J. D. and Crick, F. H. C., 1953, “Molecular Structure of Nucleic Acids – A Structure for Deoxyribose Nucleic Acid,” Nature, 171(4356), pp. 737–738. [PubMed] Calladine, C. R., Drew, H. R., Luisi, B. F., and Travers, A. A., 2004, Understanding DNA: The Molecule and How It Works, 3rd ed., Elsevier, New York. Gonzalez-Huici, V., Salas, M., and Hermoso, J. M., 2004, “The Push-Pull Mechanism of Bacteriophage Phi 29 DNA Injection,” Mol. Microbiol., 52(2), pp. 529–540. [PubMed] Phillips, R., Kondev, J., and Theriot, J., 2008. Physical Biology of the Cell, Garland Science, New York. Smith, D. E., Tans, S. J., Smith, S. B., Grimes, S., Anderson, D. L., and Bustamante, C., 2001, “The Bacteriophage Phi 29 Portal Motor Can Package DNA Against a Large Internal Force,” Nature, 413(6857), pp. 748–752. [PubMed] Tang, J., Olson, N., Jardine, P. J., Girimes, S., Anderson, D. L. and Baker, T. S., 2008. “DNA Poised for Release in Bacteriophage Phi 29,” Structure, 16(6), pp. 935–943. [PubMed] Purohit, P. K., Inamdar, M. M., Grayson, P. D., Squires, T. M., Kondev, J., and Phillips, R., 2005, “Forces During Bacteriophage DNA Packaging and Ejection,” Biophys. J., 88(2), pp. 851–866. [PubMed] Spakowitz, A. J., and Wang, Z. G., 2005, “DNA Packaging in Bacteriophage: Is Twist Important?” Biophys. J., 88(6), pp. 3912–3923. [PubMed] Petrov, A. S., and Harvey, S. C., 2008. “Packaging Double-Helical DNA Into Viral Capsids: Structures, Forces, and Energetics,” Biophys. J., 95(2), pp. 497–502. [PubMed] Goyal, S., Perkins, N. C., and Lee, C. L., 2005, “Nonlinear Dynamics and Loop Formation in Kirchhoff Rods With Implications to the Mechanics of DNA and Cables,” J. Comput. Phys., 209(1), pp. 371–389. Goyal, S., Lillian, T., Blumberg, S., Meiners, J.-C., Meyhöfer, E., and Perkins, N. C., 2007. “Intrinsic Curvature of DNA Influences LacR-Mediated Looping,” Biophys. J., 93(12), pp. 4342–4359. [PubMed] Lillian, T. D., Goyal, S., Kahn, J. D., Meyhöfer, E., and Perkins, N. C., 2008. “Computational Analysis of Looping of a Large Family of Highly Bent DNA by LacI,” Biophys. J., 95(12), pp. 5832–5842. [PubMed] Goyal, S., Perkins, N. C., and Lee, C. L., 2008. “Non-linear Dynamic Intertwining of Rods With Self-Contact,” Int. J. Nonlinear Mech., 43(1), pp. 65–73. Lillian, T. D., and Perkins, N. C., 2011, “Electrostatics and Self-Contact in an Elastic Rod Approximation for DNA,” J. Comput. Nonlinear Dyn., 6(1), p. 011008. Lillian, T. D., Taranova, M., Wereszczynski, J., Andricioaei, I., and Perkins, N.C., 2011, “A Multiscale Dynamic Model of DNA Supercoil Relaxation by Topoisomerase IB,” Biophys. J., 100(8), pp. 2016–2023. [PubMed] Goyal, S., 2006, “A Dynamic Rod Model to Simulate Mechanics of Cables and DNA,” PhD thesis, University of Michigan, Ann Arbor, MI. Schlick, T., 1995, “Modeling Superhelical DNA—Recent Analytical and Dynamic Approaches,” Curr. Opin. Struct. Biol., 5(2), pp. 245–262. [PubMed] Strick, T., Allemand, J. F., Croquette, V., and Bensimon, D., 2000, “Twisting and Stretching Single DNA Molecules,” Prog. Biophys. Mol. Biol., 74(1–2), pp. 115–140. [PubMed] Bustamante, C., Bryant, Z., and Smith, S. B., 2003. “Ten Years of Tension: Single-Molecule DNA Mechanics,” Nature, 421(6921), pp. 423–427. [PubMed] Beveridge, D. L., Young, M. A., and Sprous, D., 1998, “Modeling of DNA Via Molecular Dynamics Simulation: Structure, Bending, and Conformational Transitions,” Molecular Modeling of Nucleic Acids, American Chemical Society, Washington, DC, pp. 260–284. Wereszczynski, J., and Andricioaei, I., 2006, “On Structural Transitions, Thermodynamic Equilibrium, and the Phase Diagram of DNA and RNA Duplexes Under Torque and Tension,” Proc. Natl. Acad. Sci. U.S.A., 103(44), pp. 16200–16205. [PubMed] Hagerman, P. J., 1988, “Flexibility of DNA,” Annu. Rev. Biophys. Chem., 17, pp. 265–286. Manning, R. S., Maddocks, J. H., and Kahn, J. D., 1996. “A Continuum Rod Model of Sequence-Dependent DNA Structure,” J. Chem. Phys., 105(13), pp. 5626–5646. Balaeff, A., Mahadevan, L., and Schulten, K., 2006. “Modeling DNA Loops Using the Theory of Elasticity,” Phys. Rev. E, 73(3), p. 031919. Chung, J., and Hulbert, G. M., 1993, “A Time Integration Algorithm for Structural Dynamics With Improved Numerical Dissipation—The Generalized-Alpha Method,” J. Appl. Mech., 60(2), pp. 371–375. Howard, J., 2001, Mechanics of Motor Proteins and the Cytoskeleton, Sinauer Associates, Sunderland, MA. Rickgauer, J. P., Fuller, D. N., Grimes, S., Jardine, P. J., Anderson, D. L., and Smith, D. E., 2008, “Portal Motor Velocity and Internal Force Resisting Viral DNA Packaging in Bacteriophage Phi 29,” Biophys. J., 94(1), pp. 159–167. [PubMed] Duda, R. L., and Conway, J. F., 2008, “Asymmetric EM Reveals New Twists in Phage Phi 29 Biology,” Structure, 16(6), pp. 831–832. [PubMed] Lillian, T. D., Perkins, N. C., and Goyal, S., 2008, “Computational Elastic Rod Model Applied to DNA Looping,” Proceedings of ASME IDETC/CIE 2007, Las Vegas, NV, Sep. 4–7, Vol. 5, pp. 1449–1456. ## Figures Fig. 1 A schematic of mature bacteriophage φ29 based on the cryo-electron micoscopy reconstruction [6,28]. The toroidal DNA is contained within a cavity just below the capsid and suspected to contain 30–40 bp of DNA. The cavity is formed from the void between the connector and the lower collar. Shown inside the capsid is a cross sectional view of concentric hoops of DNA which ultimately fill the entire capsid. Fig. 2 The atomic structure of DNA superimposed with a an elastic rod with equivalent elastic properties. R→(s,t) tracks the position of the helical axis as a function of contour length s and time t with respect to the inertial frame e. We also define a body-fixed reference frame a(s,t) which is also a function of s and t. Figure adaped from [29]. Fig. 3 Side view of the 3-D cavity structure estimated from the connector and lower collar geometry in the cryo-EM images [6] with relevant dimensions labeled. We assume the cavity is symmetric about the vertical axis. Cavity grid points are spaced in stacked rings of points separated by dc above and below one another and dc along the circumference of each ring (see red arrows). Here, we have set dc to 4 Å to reduce the number of grid points by an order of magnitude (over 1 Å separation) and thereby gain computational efficiency. The shaded blue box indicates the approximate area A=dc2 surrounding each grid point. Fig. 4 The interaction forces are dependent on all pairwise vectors between rod grid points p and points q representing the cavity surface which are fixed in space Fig. 5 (a) Computational snapshots (aligned to the dots on the plot directly below) from simulating 90 bp of DNA compressed within the cavity. (b) Internal (compressive) force (pN) and elastic energy (kT) following Eq. (6) as functions of the shortening of the rod δ = L – d where L is the length of DNA (306 Å) and d is the distance between the upper and lower rod boundaries. The green box illustrates where we report internal force along the contour length. (c) Top and side view of the final toroidal structure. Fig. 6 Equilibrium conformation from Fig. 5(c) upon altering the cavity grid spacing parameter dc to (a) 8 Å, (b) 4 Å, (c) 2 Å, (d) 1 Å Fig. 7 (a) Dynamic ejection and toroid collapse. Snapshots illustrate DNA conformation at each of the 5 ns increments denoted in the figure below. (b) DNA reaction force (solid green line and circles) and torque (solid red line and circles) on the remaining capsid/DNA (upper end) as a function of time. The solid blue line represents the component of the viscous drag force (integrated over the length of the rod) acting along the z-axis (vertical axis). ## Discussions Some tools below are only available to our subscribers or users with an online account. ### Related Content Customize your page view by dragging and repositioning the boxes below. Related Journal Articles Related Proceedings Articles Related eBook Content Topic Collections • TELEPHONE: 1-800-843-2763 (Toll-free in the USA) • EMAIL: asmedigitalcollection@asme.org	2018-02-20 13:47:01	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 1, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.463495671749115, "perplexity": 12235.387119027577}, "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-2018-09/segments/1518891812959.48/warc/CC-MAIN-20180220125836-20180220145836-00203.warc.gz"}
http://www.lastfm.com.br/user/speri76/library/music/Algernon+Cadwallader/_/Look+Down+(Because+the+Ground+Is+Easier+to+Understand+and+Doesn't+Take+So+Much+Work+to+Figure+Out+But+I'd+Rather+Not+Know+Where+I'm+Standing+and+Have+An+Idea+of+What+Life+Is+All+About)?setlang=pt	# Biblioteca ## Look Down (Because the Ground Is Easier to Understand and Doesn't Take So Much Work… 40 execuções \| Ir para página da faixa Faixas (40) Faixa Álbum Duração Data Look Down (Because the Ground Is Easier to Understand and Doesn't Take So Much Work… 4:11 Jul 20 2012, 10h12 Look Down (Because the Ground Is Easier to Understand and Doesn't Take So Much Work… 4:11 Jun 13 2011, 15h32 Look Down (Because the Ground Is Easier to Understand and Doesn't Take So Much Work… 4:11 Abr 22 2011, 14h20 Look Down (Because the Ground Is Easier to Understand and Doesn't Take So Much Work… 4:11 Abr 13 2011, 16h51 Look Down (Because the Ground Is Easier to Understand and Doesn't Take So Much Work… 4:11 Jan 31 2011, 10h46 Look 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Doesn't Take So Much Work… 4:11 Jun 30 2010, 13h36 Look Down (Because the Ground Is Easier to Understand and Doesn't Take So Much Work… 4:11 Jun 21 2010, 15h43 Look Down (Because the Ground Is Easier to Understand and Doesn't Take So Much Work… 4:11 Jun 14 2010, 9h22 Look Down (Because the Ground Is Easier to Understand and Doesn't Take So Much Work… 4:11 Mai 27 2010, 18h52 Look Down (Because the Ground Is Easier to Understand and Doesn't Take So Much Work… 4:11 Mai 14 2010, 8h46 Look Down (Because the Ground Is Easier to Understand and Doesn't Take So Much Work… 4:11 Mai 11 2010, 15h53 Look Down (Because the Ground Is Easier to Understand and Doesn't Take So Much Work… 4:11 Abr 6 2010, 13h51 Look Down (Because the Ground Is Easier to Understand and Doesn't Take So Much Work… 4:11 Mar 17 2010, 15h32	2015-06-03 06:21:30	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, 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https://brilliant.org/discussions/thread/endless-palindrome/	× # Endless palindrome Usually, by reversing any number and adding it to the original one it is possible to get a palindromic number after a few steps. E.g. 64+46=110 110+011=121, which is a palindromic number.It reads the same forwards or backwards. E.g. 79+97=176 176+671=847 847+748=1595 1595+5951=7546 7546+6457=14003 14003+30041=44044 This is a palindrome. the first number took just 2 steps and the second, 5 steps. but 196 is an exception as John Walker discovered on May 2, 1990.In spite of employing a computer programme to carry out this process of reversal and addition he had to abandon the effort after 2,415,836 steps that yielded a number with one million digits.Still there was no palindrome for 196 Note by Vishal S 3 years ago MarkdownAppears as italics or _italics_ italics bold or __bold__ bold - bulleted- list • bulleted • list 1. numbered2. list 1. numbered 2. list Note: you must add a full line of space before and after lists for them to show up correctly paragraph 1paragraph 2 paragraph 1 paragraph 2 [example link](https://brilliant.org)example link > This is a quote This is a quote # I indented these lines # 4 spaces, and now they show # up as a code block. print "hello world" # I indented these lines # 4 spaces, and now they show # up as a code block. print "hello world" MathAppears as Remember to wrap math in $$...$$ or $...$ to ensure proper formatting. 2 \times 3 $$2 \times 3$$ 2^{34} $$2^{34}$$ a_{i-1} $$a_{i-1}$$ \frac{2}{3} $$\frac{2}{3}$$ \sqrt{2} $$\sqrt{2}$$ \sum_{i=1}^3 $$\sum_{i=1}^3$$ \sin \theta $$\sin \theta$$ \boxed{123} $$\boxed{123}$$ Sort by: There are many other palindrome like 592,790,394. - 2 years, 10 months ago I think 592 is also an exception. - 3 years ago	2018-01-16 09:58:43	{"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": 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": 0.9937371015548706, "perplexity": 7219.432030122767}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-05/segments/1516084886397.2/warc/CC-MAIN-20180116090056-20180116110056-00462.warc.gz"}
https://geo.libretexts.org/Bookshelves/Meteorology/Book%3A_Practical_Meteorology_(Stull)/03%3A_Thermodynamics/3.04%3A_Heat_Budget_of_an_Unsaturated_Air_Parcel	# 3.4: Heat Budget of an Unsaturated Air Parcel In this chapter, we consider a special case: unsaturated air parcels, for which no liquid or solid water is involved. The word “dry” is used to imply that phase changes of water are not considered. Nonetheless, the air CAN contain water vapor. In the next chapter we include the effects of saturation and possible phase changes in a “moist” analysis. # 3.4.1. Lagrangian Form of the First Law of Thermo The pressure of an air parcel usually equals that of its surrounding environment, which decreases exponentially with height. Thus, the last term of eq. (3.2d) will be non-zero for a rising or sinking air parcel as its pressure changes to match the pressure of its environment. But the pressure change with height was given by the hydrostatic equation in Chapter 1: ∆P/ρ = – \|g\| · ∆z. We can use this to rewrite the First Law of Thermo in the Lagrangian framework of a moving air parcel: \ \begin{align}\Delta T=-\left(\frac{\|g\|}{C_{p}}\right) \cdot \Delta z+\frac{\Delta q}{C_{p}}\tag{3.5}\end{align} Sample Application A 5 kg air parcel of initial temperature 5°C rises 1 km and thermally loses 15 kJ of energy due to IR radiation. What is the final temperature of the parcel? Given: ∆Q = –15,000 J, mair = 5 kg, ∆z = 1000 m , Find: T = ? K Convert from energy to energy/mass: ∆q = ∆Q/mair = (–15000 J)/(5 kg) = –3000 J kg–1 . With lack of humidity info, assume dry air. Cp = 1004. J·kg–1·K–1 (= units m2 s–2 K–1) Apply eq. (3.5): ∆T = –[(9.8 m s–2)/ (1004 m2 s–2 K–1)]·(1000m) + [(–3000 J kg–1) / (1004. J·kg–1·K–1)] = (– 9.76 – 3.00) K = –12.76 °C Check: Physics & units are reasonable. Exposition: Because we are working with a temperature difference, recall that 1 K of temperature difference = 1°C of temperature difference. Hence, we could replace the Kelvin units with °C. The net result is that the rising air parcel cools due to both IR radiative cooling and work done on the atmosphere as the parcel rises. Various processes can cause heat transfer (∆q). The sun could heat the air, or IR radiation could cool the air. Water vapor could condense and release its latent heat back into sensible heat. Exothermic chemical reactions or radioactive decay could occur among air pollutants carried within the parcel. Internal turbulence could dissipate into heat. Molecular conduction in the air is very weak, but turbulence could mix warmer or cooler air into the air parcel. Other processes such as convection and advection (Figure 3.2) do not change the parcel’s temperature, but can move the air parcel along with the heat that it possesses. Eq. (3.5) represents a heat budget. Namely, parcel temperature (which indicates heat possessed) is conserved unless it moves to a different height (where the pressure is different) or if heat is transferred to or from it. Thus, eq. (3.5) and the other First Law of Thermo eqs. (3.2) are also known as heat conservation equations. # 3.4.2. Lapse-rate Definition Define the lapse rate, Γ, as the amount of temperature decrease with altitude: \ \begin{align}\Gamma=-\frac{T_{2}-T_{1}}{z_{2}-z_{1}}=-\frac{\Delta T}{\Delta z}\tag{3.6}\end{align} Note that the lapse rate is the negative of the vertical temperature gradient ∆T/∆z. We separately consider the lapse rates inside the air parcel, and in the surrounding environment outside. Inside the air parcel, all the processes illustrated in Figure 3.2 could apply, causing the parcel’s temperature to change with changing altitude. The resulting ∆T/∆z (times –1) defines a process lapse rate (Figure 3.3). Outside the air parcel, assume the environmental air is relatively stationary. This is the ambient environment through which the air parcel moves. But this environment could have different temperatures at different altitudes, allowing us to define an environmental lapse rate (Figure 3.3). By sampling the ambient air at different heights using weather instruments such as radiosondes (weather balloons) and then plotting T vs. z as a graph, the result is an environmental sounding or vertical temperature profile of the environment. The environmental sounding changes as the weather evolves, but this is usually slow relative to parcel processes. Thus, the environment is often approximated as being unchanging (i.e., static). The temperature difference (Figure 3.3) between the parcel and its environment is crucial for determining parcel buoyancy and storm development. This is our motivation for examining both lapse rates. Sample Application Find the lapse rate in the troposphere for a standard atmosphere. Given: Std. Atmos. Table 1-5 in Chapter 1, , where T= –56.5°C at z = 11 km, and T = +15°C at z = 0 km. Find: Γ = ? °C km–1 Apply eq. (3.6): Γ = – (–56.5 – 15°C) / (11–0 km) = +6.5 °C km–1 Check: Positive Γ, because T decreases with z. Exposition: This is the environmental lapse rate of the troposphere. It indicates a static background state. # 3.4.3. Dry Adiabatic Lapse Rate The word adiabatic means zero heat transfer (∆q = 0). For the protected inner core of air parcels, this means no thermal energy entering or leaving the air parcel from outside (Figure 3.2). Nonetheless, internal processes are allowed. For the special case of humid air with no liquid water or ice carried with the parcel (and no water phase changes; hence, a “dry” process), eq. (3.5) gives: \ \begin{align}\frac{\Delta T}{\Delta z}=-\left(\frac{\|g\|}{C_{p}}\right)=-9.8 \mathrm{Kkm}^{-1}\tag{3.7}\end{align} Recalling that the lapse rate is the negative of the vertical temperature gradient, we can define a “dryadiabatic lapse rate Γd as: \ \begin{align}\Gamma_{d}=9.8 \mathrm{K} \mathrm{km}^{-1}=9.8^{\circ} \mathrm{C} \mathrm{km}^{-1}\tag{3.8}\end{align} (Degrees K and °C are interchangeable in this equation for this process lapse rate, because they represent a temperature change with height.) The HIGHER MATH box at left shows how this dry adiabatic lapse rate can be expressed as a function of pressure P: \ \begin{align} \frac{\Delta T}{T}=\frac{\Re_{d}}{C_{p}} \cdot\left(\frac{\Delta P}{P}\right)\tag{3.9}\end{align} or \ \begin{align} \frac{T_{2}}{T_{1}}=\left(\frac{P_{2}}{P_{1}}\right)^{\Re_{d} / C_{p}}\tag{3.10}\end{align} where ℜd/Cp = 0.28571 (dimensionless) for dry air, and where temperatures are in Kelvin. HIGHER MATH • Adiabatic Lapse Rate in Pressure Coordinates Start with the First Law of Thermodynamics (eq. 3.2d), but written more precisely using virtual temperature Tv to account for arbitrary concentrations of water vapor in the air. Set ∆q = 0 because adiabatic means no heat transfer: $$\mathrm{d} P=\rho \cdot C_{p} \cdot \mathrm{d} T_{v}$$ Use the ideal gas law ρ = P/(ℜd · Td ) to eliminate ρ: $$\mathrm{d} P=\frac{P \cdot C_{p} \cdot \mathrm{d} T_{v}}{\Re_{d} \cdot T_{v}}$$ Group temperature & pressure terms on opposite sides of the eq.: $$\frac{\mathrm{d} P}{P}=\frac{C_{p}}{\Re_{d}} \cdot \frac{\mathrm{d} T_{v}}{T_{v}}$$ Integrate from starting (P1, Tv1) to ending (P2, Tv2): $$\int_{P_{1}}^{P_{2}} \frac{\mathrm{d} P}{P}=\frac{C_{p}}{\Re_{d}} \cdot \int_{T_{v 1}}^{T_{v 2}} \frac{\mathrm{d} T_{v}}{T_{v}}$$ assuming Cp/ℜd is somewhat constant. The integral is: $$\left.\ln (P)\right\|_{P_{1}} ^{P_{2}}=\left(C_{p} / \Re_{d}\right) \cdot \ln \left(T_{v}\right)_{T_{v 1}}^{T_{v 2}}$$ Insert limits of integration. Also: ln(a) –ln(b) = ln(a/b) Thus: $$\ln \left(\frac{P_{2}}{P_{1}}\right)=\left(C_{p} / \Re_{d}\right) \cdot \ln \left(\frac{T_{v 2}}{T_{v 1}}\right)$$ Multiply both sides by ℜd /Cp : $$\left(\mathfrak{R}_{d} / C_{p}\right) \cdot \ln \left(\frac{P_{2}}{P_{1}}\right)=\ln \left(\frac{T_{v 2}}{T_{v 1}}\right)$$ Use the relationship: a·ln(b) = ln(ba): $$\ln \left[\left(\frac{P_{2}}{P_{1}}\right)^{\Re_{d} / C_{p}}\right]=\ln \left(\frac{T_{v 2}}{T_{v 1}}\right)$$ The anti-log of the equation ( eLHS = eRHS ) yields: \ \begin{align}\left(\frac{P_{2}}{P_{1}}\right)^{\Re_{d} / C_{p}}=\frac{T_{v 2}}{T_{v 1}}\tag{3.10}\end{align} Sample Application An air parcel with initial (z, P, T) = (100m, 100 kPa, 20°C) rises adiabatically to (z, P) = (1950 m, 80 kPa). Find its new T, & compare eqs. (3.7) & (3.10). Given: P1 = 100 kPa, P2 = 80 kPa, T1 = 20°C = 293K z1 = 100 m, z2 = 1950 m Find: T2 = ? °C First, apply eq. (3.7), which is a function of z: T2 = T1 + (∆z)·(–Γd) = 20°C – (1950–100m)·(0.0098°C/m) = 20°C – 18.1°C = 1.9°C. Compare with eq. (3.10), which is a function of P: T2 = (293K) · [(80kPa)/(100kPa)]0.28571 T2 = 293K · 0.9382 = 274.9 K = 1.9°C Check: Both equations give the same answer, so either equation would have been sufficient by itself. # 3.4.4. Potential-temperature Definition When an air parcel rises/sinks ”dry” adiabatically into regions of lower/higher pressure, its temperature changes due to work done by/on the parcel, even though no thermal energy has been removed/ added. Define a new temperature variable called the potential temperature θ that is proportional to the sensible heat contained in the parcel, but which is unaffected by work done by/on the parcel. Namely, potential temperature is constant for an adiabatic process (i.e., ∆q = 0) such as air-parcel ascent. Thus, we can use it as a conserved variable. θ can increase/decrease when sensible heat is added/removed. Such diabatic (non-adiabatic) heat transfer processes include turbulent mixing, condensation, and radiative heating (i.e., ∆q ≠ 0). Knowing the air temperature T at altitude z, you can calculate the value of potential temperature θ from: \ \begin{align}\theta(z)=T(z)+\Gamma_{d} \cdot z\tag{3.11}\end{align} The units (K or °C) of θ(z) are the same as the units of T(z). There is no standard for z, so some people use height above mean sea level (MSL), while others use height above local ground level (AGL). If, instead, you know air temperature T at pressure-level P, then you can find the value of θ from: \ \begin{align} \theta=T \cdot\left(\frac{P_{o}}{P}\right)^{\Re_{d} / C_{p}}\tag{3.12}\end{align} where ℜd/Cp = 0.28571 (dimensionless) and where temperatures must be in Kelvin. A reference pressure of Po = 100 kPa is often used, although some people use the local surface pressure instead. In this book we will assume that the surface pressure equals the reference pressure of Po = 100 kPa and will use z = 0 at that surface, unless stated otherwise. Both eqs. (3.11) and (3.12) show that θ = T at z = 0 or at P = Po. Thus θ is the actual temperature that an air parcel potentially has if lowered to the reference level adiabatically. A virtual potential temperature θv for humid air having water-vapor mixing ratio r but containing no solid or liquid water is defined as: \ \begin{align} \theta_{v}=\theta \cdot[1+(a \cdot r)]\tag{3.13}\end{align} where a = 0.61 gair/gwater vapor . If the air contains ice crystals, cloud drops, or rain drops, then virtual potential temperature is given by: \ \begin{align}\theta_{v}=\theta \cdot\left[1+(a \cdot r)-r_{L}-r_{I}\right]\tag{3.14}\end{align} where rL is the liquid-water mixing ratio and rI = ice mixing ratio. Mixing ratio is described in the Water Vapor chapter; it is the ratio of grams of water per gram of air. The θ and θv values in the previous three equations must be in units of Kelvin. An advantage of θv is that it can be used to calculate the buoyancy of air parcels that contain water — useful for anticipating storm characteristics. θv is constant only when there is no phase changes and no heat transfer; namely, no latent or sensible heat is absorbed or released. For air that is rising within clouds, with water vapor condensing, it is usually the case that the air is saturated (= 100% relative humidity; see the Water Vapor chapter for details). As a result, the watervapor mixing ratio r can be replaced with rs , the saturation mixing ratio. \ \begin{align} \theta_{v}=\theta \cdot\left[1+\left(a \cdot r_{s}\right)-r_{L}\right]\tag{3.15}\end{align} where a = 0.61 gair/gwater vapor , as before. However, there are other situations where the air is NOT saturated, but contains liquid water. An example is the non-cloudy air under a cloud base, through which rain is falling at its terminal velocity. For this case, eq (3.14) should be used with an unsaturated value of water-vapor mixing ratio. This situation occurs often, and can be responsible for damaging downbursts of air (see the Thunderstorm chapters). Why use potential temperature? Because it makes it easier to compare the temperatures of air parcels at two different heights — important for determining if air will buoyantly rise to create thunderstorms. For example, suppose air parcel A has temperature TA = 20°C at z = 0, while air parcel B has TB = 15°C at z = 1 km. Parcel A is warmer than parcel B. Does that mean that parcel A is buoyant (warmer and wants to rise) relative to parcel B? The answer is no, because when parcel B is moved dry adiabatically to the altitude of parcel A, then parcel B is 5°C warmer than parcel A due to adiabatic warming. In fact, you can move parcels A and B to any common altitude, and after considering their adiabatic warming or cooling, parcel B will always be 5°C warmer than parcel A. The easiest way to summarize this effect is with potential temperature. Using eq. (3.11), we find that θA = 20°C and θB = 25°C approximately. θA and θB keep their values (because θ is a conserved variable) no matter to what common altitude you move them, thus θB is always 5 °C warmer than θA in this illustration. Another application for potential temperature is to label lines on a thermodynamic diagram, such as described next. # 3.4.5. Intro to Thermo Diagrams Convection is a vertical circulation associated with “warm air rising” and “cold air sinking”. Meteorologists forecast the deep convection of thunderstorms and their hazards, or the shallow convection of thermals that disperse air pollutants. The phrase “warm air rising” relates to the temperature difference ∆T between an air parcel and its surrounding environment. Air-parcel-temperature variation with altitude can be anticipated using heatand water-conservation relationships. However, the surrounding environmental temperature profile can have a somewhat arbitrary shape that can be measured by a sounding balloon, but which is not easily described by analytical equations. So it can be difficult to mathematically describe ∆T vs. altitude. Instead, graphical solutions can be used to estimate buoyancy and convection. We call these graphs “thermodynamic diagrams”. In this book, I will abbreviate the name as “thermo diagram”. The diagram is set up so that higher in the diagram corresponds to higher in the atmosphere. In the real atmosphere, pressure decreases approximately logarithmically with increasing altitude, so we often use pressure P along the y-axis as a surrogate for altitude. Along the x-axis is air temperature T. The thin green lines in Figure 3.4 show the (P, T) basis for a thermo diagram as a semi-log graph. We can use eq. (3.10) to solve for the “dry” adiabatic temperature change experienced by rising air parcels. These are plotted as the thick orange diagonal lines in Figure 3.4 for a variety of starting temperatures at P = 100 kPa. These “dry adiabat” lines (also known as isentropes), are labeled with θ because potential temperature is conserved for adiabatic processes. If you know the initial (P, T) of the air parcel, then plot it as a point on the thermo diagram. Move parallel to the orange lines to the final pressure altitude. At that final point, read down vertically to find the parcel’s final temperature. INFO • Create Your Own Thermo Diagram One of the advantages of thermo diagrams is that you do NOT need to calculate adiabatic temperature changes, because they are already calculated and plotted for you for a variety of different starting temperatures. If the starting temperature you need is not already plotted, you can mentally interpolate between the drawn lines as you raise or lower air parcels. However, it is a useful exercise to see how such a thermo diagram can be created with a tool as simple as a computer spreadsheet. The green (or dark-grey) items in the spreadsheet below were typed directly as numbers or words. You can follow along on your own spreadsheet. (You don’t need to use the same colors — black is OK.) The orange (or light-grey) numbers were calculated by entering a formula (eq. 3.10) into the bottom leftmost orange cell, and then “filling up” and “filling right” that equation into the other orange cells. But before you fill up and right, be sure to use the dollar sign “$” as shown below. It holds the column ID constant if it appears in front of the ID letter, or holds the row constant if in front of the ID number. Here is the equation for the bottom left orange cell (B12): = ( (B$13+273) * ($A12/$A\$13)^0.28571 ) - 273 Different spreadsheet versions have different ways to create graphs. Select the cells that I outlined with the dark blue rectangle. Click on the Graph button, select the “XY scatter”, and then select the option that draws straight line segments without data points. Under the Chart, Source Data menu, select Series. Then manually switch the columns for the X and Y data for each series — this does an axis switch. On the graph, click on the vertical axis to get the Format Axis dialog box, and select the Scale tab. Check the Logarithmic scale box, and the Values in Reverse Order box. A bit more tidying up will yield a graph with 3 curves similar to Figure 3.4. Try adding more curves. Sample Application Given air at P = 70 kPa with T = –1°C. Find θ using the thermo diagram of Figure 3.4.	2021-05-05 22:23:12	{"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": 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": 12, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7763705253601074, "perplexity": 2238.0990547112992}, "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/1620243988696.23/warc/CC-MAIN-20210505203909-20210505233909-00493.warc.gz"}
https://tex.stackexchange.com/questions/96726/bibliography-style-auth-year	# Bibliography style - [AUTH YEAR] I'm looking for a bst bibliography style that I could use, but I cannot find any site where I could see any list of styles ot theirs names. I would like my bibliography to be in a format: [ALSA 1992] Alsabbagh J.R., Raghavan V.V., A framework for multiple query optimization, w: Proc. of Intern. Conf. on Data Eng., 1992, s. 157 − 162. [BATO 1986] Batory D.S., et al, Extensible cost model and query optimization in Genezis, IEEE Database Eng., vol.9, No.4, 1986, s. 30 − 37. I found only a similar style that is called wmaainf. Does anyone know where I could find a style that I described earlier? • I'm using BibTeX (using \bibliographystyle{wmaainf}{\raggedright\sloppy\small\bibliography{bibliography}}) to include it). My language is Polish so this is why it says s. 30 - 37 as s stands for strona. I found wmaainf here: link – krajol Feb 4 '13 at 15:52 2. Adapt the style that comes closest to your taste. Suppose we start with wmaainf. Note that this style forbids any modification. In good TeX tradition that might mean that you are allowed to copy the style to a differently named file, and modify your copy. But I can not give legal advise here. Suppose your are allowed to do that, and your copied style is called krajol.bst. Open that in an editor, and replace the english strings (those are enclosed in "...") to polish strings. E.g., the function format.pages contains the line { "p.~" pages n.dashify * }. Changing that to { "s.~" pages n.dashify * } would now give the desired s. for strona. Note that more modern styles are internaionalised, meaning that they adapt to a language set with babel, but wmaainf is not one of them. 3. Make your own style from scratch with the help of custom-bib. You need to run latex makebst and you will be asked many many questions what your bibliography style should look like. At the end, you get your desired style file. But please read the manual before. One goody is that style files produced with custom-bib can be internationalised with a polski option, i.e., you can produce your style in Polish without having to translate anything.	2019-10-16 14:07:52	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4874434173107147, "perplexity": 2433.16252896329}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-43/segments/1570986668994.39/warc/CC-MAIN-20191016135759-20191016163259-00022.warc.gz"}
https://academic-accelerator.com/Manuscript-Generator/Low-Order	## However, there are some unexpected influences caused by the low order harmonic sinusoidal pulse width modulation (SPWM), such as the imbalanced submodule power in cascaded half-bridge inverter (CHB) and limited output power capability in H-bridge neutral-point-clamped (HNPC) converter. A Systematic Study on the Harmonic Overlap Effects for DC/AC Converters under Low Switching Frequency Modulation ## It is well known that the pulse width modulation selective harmonic elimination control (SHEPWM) applied to a seven-level inverter can allow the suppression of only two low order harmonics. Enhanced Harmonic Elimination Using Genetic Algorithm Optimization in Multilevel Inverters ## A benefit of this method is that is uses low order schemes iteratively to produce a high order approximation. A posteriori Error Estimation for the Spectral Deferred Correction Method ## This element uses low order interpolation functions for the seven kinematic variables. An edge-based smoothed three-node composite plate element with refined zigzag kinematics ## The results of even relatively low orders of approximation are highly accurate and can be calculated very efficiently. Approximate Representations of Shaped Pulses Using the Homotopy Analysis Method. ## Accurate results have been obtained in using a relatively low order from the perturbation series. Critical exponents from the weak-coupling, strong-coupling and large-order parametrization of the hypergeometric (k+1Fk) approximants ## A mixed-method for the order abatement of large-scale linear dynamic systems (LSLDSs) into desired low order systems is proposed. Order Abatement of Linear Dynamic Systems Using Renovated Pole Clustering and Cauer Second Form Techniques ## The fundamental voltage is obtained by solving the equations in such a way that the desired low order harmonics are eliminated. DSP Based Implementation of SHE-PWM For Cross-Switched Multilevel Inverter ## By designing parameters such as shear frequency and low order harmonic attenuation coefficient, the dynamic and static ability of position calculation is improved. Linear Hall Position Calculation Method of PMLSM Based on Type-III PLL ## However, different sources of non-linearities, including low order harmonics mapped to secondary subspaces, cross-coupling saturation and iron losses result in a notable deviation from the experimentally measured waveforms. Improved Mathematical Modeling of Six Phase Induction Machines Based on Fractional Calculus ## The goal of this work was to study the influence of low order mode responses on extreme response statistics. Extreme value statistics of flow-induced hydrofoil vibration and resonance ## Comparison of the results predicted by the procedure described in this paper with limited numerical applications, corroborates that it is successful in predicting the response of the components when these are tuned to low order modes of the carrying structure. An Analytical Approximation to the Seismic Response of Light Linear Nonstructural Components in Resonance With Linear Structures ## In the field of complex systems, it is often possible to arrive at some simple stochastic or chaotic Low Order Models (LOMs) exploiting the time scale separation between leading modes of interest and fast fluctuations. On the determination of the optimal parameters in the CAM model. ## Low order models based on the Blade Element Momentum (BEM) theory exhibit modeling issues in the performance prediction of Vertical Axis Wind Turbines (VAWT) compared to Computational Fluid Dynamics, despite the widespread engineering practice of such methods. Formulation, Validation, and Application of a Novel 3D BEM Tool for Vertical Axis Wind Turbines of General Shape and Size ## manoeuvring, gust), low order methods are known to introduce significant dissipation and dispersion errors. A Coupled HDG-FV Method for Unsteady Compressible Flows ## Besides, they are sharp at least for low order methods, if the testing moments and deflection in their right parts are found by accurate recovery procedures. A posteriori error bounds for classical and mixed FEM’s for 4th-order elliptic equations with piece wise constant reaction coefficient having large jumps ## We present differences in dissolved organic carbon (DOC) concentrations and dissolved organic matter (DOM) molecular composition within Upper Mississippi River Basin low order streams and rivers draining one of three dominant landcovers (forest, agriculture, and urban). Anthropogenic landcover impacts fluvial dissolved organic matter composition in the Upper Mississippi River Basin ## Low order streams drain a big proportion of river catchments. Controls of nitrogen cycling under gaining and losing conditions in a first order agricultural stream ## Pada tahapan mengingat (remembering), memahami (understanding), menerapkan (applying) dikategorikan sebagai kemampuan berpikir tingkat rendah atau Low Order Thinking Skill (LOTS). INTERSEKSI BERPIKIR KRITIS DENGAN HIGH ORDER THINKING SKILL (HOTS) BERDASARKAN TAKSONOMI BLOOM ## This paper addresses the question of how cognitive levels covering high, middle, and low order thinking skills are delineated in the questions seen from Bloom’s revised taxonomic framework and stimulus. Evaluating Cognitive Level of Final Semester Examination Questions Based on Bloom’s Revised Taxonomy ## Compared to previous models, these low order systems display longer turbulence lifetimes and lower transition thresholds. Structure interactions in a reduced-order model for wall-bounded turbulence ## A mixed-method for the order abatement of large-scale linear dynamic systems (LSLDSs) into desired low order systems is proposed. Order Abatement of Linear Dynamic Systems Using Renovated Pole Clustering and Cauer Second Form Techniques ## A low order network model is built to recognize the thermoacoustic modes of the combustion system. Effects of acoustic liner on thermoacoustic instabilities in a premixed swirl combustor ## Then, a low order network model is used to explain the observed behaviors. The effect of inlet boundaries on combustion instability in a pressure-elevated combustor ## The following items were examined preoperatively and 1 month postoperatively: uncorrected visual acuity (UCVA), best-corrected visual acuity (BCVA), spherical, cylinder, central corneal thickness (CCT), corneal mean curvature (CMC), total ocular aberrations (TA), total low order aberrations (tLOAs), defocus, astigmatism and total high order aberrations (tHOAs), spherical, coma, trefoil, modulation transfer function (MTF), MTF cutoff , SR, objective scatter index (OSI), point scatter function at 50 and 10% (PSF50%, PSF10%), and contrast visual acuity of 100, 20, and 9% (VA100%, VA20%, and VA9%). Comparison of early visual quality in patients with moderate myopia using different optical zones in small incision lenticule extraction (SMILE) ## As an application example, the compensations of some low order aberrations of the 2. Applications of the elastic modes of a circular plate in wavefront correction of the adaptive optics and the active optics. ## The mean dimension of a black box function of $d$ variables is a convenient way to summarize the extent to which it is dominated by high or low order interactions. Efficient estimation of the ANOVA mean dimension, with an application to neural net classification ## Interestingly, in these cases, the mapping reveals that the inferred models are essentially low order interaction models. Restricted Boltzmann Machines as Models of Interacting Variables ## With the explicit time integration and low order finite elements under the total Lagrangian framework, the proposed model is much computationally efficient for modeling the dynamic mechanical behavior of a cell colony. Continuum-based modeling of collective cell migration ## The angular and spatial derivative terms of governing equations in the cylindrical coordinate system are approximated by high order Chebyshev polynomials instead of the low order finite difference schemes. Prediction of coupled radiative and conductive heat transfer in concentric cylinders with nonlinear anisotropic scattering medium by spectral collocation method ## A low order thermal network model for the perimeter zone, validated with experimental measurements, is utilized to study various control strategies in response to changes in the electrical grid price signal, including short term (nearly reactive) changes of the order of 10–15 min notice. Model Predictive Control Strategies to Activate the Energy Flexibility for Zones with Hydronic Radiant Systems ## Our new Curie depth model differs by as much as ±20 km relative to previous models, with the largest differences arising from the low order thermal model and variable susceptibility. A global Curie depth model utilising the equivalent source magnetic dipole method ## Tensor-train (TT) decomposition has been an efficient tool to find low order approximation of large-scale, high-order tensors. Adaptive Algorithms for Tracking Tensor-Train Decomposition of Streaming Tensors ## The main features of this work include the adaptive length of the chromosome for ascending system order identification, no limitation of the order of the system to approximate, robust to the system noise, and capable of providing low order approximation to the system. A Cascaded Genetic Algorithm with Adaptive Length of the Chromosome for Blind System Order and Parameters Identification 10.13287/j.1001-9332.202101.035 ## Therefore, lake sediments could not be used to analyze the historical sedimentary model of low order PCBs. [Reconstruction of temporal and spatial trends of atmospheric pollution based on polychlorinated biphenyls concentration changes in ombrotrophic bogs]. 10.1109/TPDS.2020.3025145 ## We first formalize the CCT minimization problem into a 0-1 programming problem, then relax and solve the problem in 2 steps to obtain the coflow order and flow grouping decisions on each circuit. Minimizing Coflow Completion Time in Optical Circuit Switched Networks 10.1209/0295-5075/ac2751 ## Although quasi-resonant interactions are observed at low orders, five-wave resonant interactions are found to be the lowest-resonant order subsisting in the capillary range, and are thus probably the mechanism generating the observed 1D capillary-wave turbulence. Experimental quasi-1D capillary-wave turbulence ## The mean dimension of a black box function of $d$ variables is a convenient way to summarize the extent to which it is dominated by high or low order interactions. Efficient estimation of the ANOVA mean dimension, with an application to neural net classification 10.1007/s12046-021-01695-0 ## The simulated geometry exhibits a low order of dispersion 4. Numerical analysis on the supercontinuum generation through Al0.24Ga0.76As based photonic crystal fiber 10.1109/LDIA49489.2021.9505854 ## By designing parameters such as shear frequency and low order harmonic attenuation coefficient, the dynamic and static ability of position calculation is improved. Linear Hall Position Calculation Method of PMLSM Based on Type-III PLL 10.1109/ACCESS.2021.3069963 ## However, different sources of non-linearities, including low order harmonics mapped to secondary subspaces, cross-coupling saturation and iron losses result in a notable deviation from the experimentally measured waveforms. Improved Mathematical Modeling of Six Phase Induction Machines Based on Fractional Calculus 10.1016/J.ANUCENE.2021.108211 ## Efficacy of the acceleration iterations with varying coarse mesh size and convergence criteria of the low order problem, and their overall performance has been investigated for the 2-group LRA-BWR problem and the 7-group C5G7 problem. Comparative studies of iterative methods for solving the “optimally diffusive” coarse mesh finite difference accelerated transport equation 10.1016/j.jcp.2020.109940 ## The WENO type extrapolation maintains high order accuracy if the solution is smooth near the boundary and it becomes a low order extrapolation automatically if a shock is close to the boundary. An inverse Lax-Wendroff procedure for hyperbolic conservation laws with changing wind direction on the boundary ## manoeuvring, gust), low order methods are known to introduce significant dissipation and dispersion errors. A Coupled HDG-FV Method for Unsteady Compressible Flows 10.1088/1742-6596/1715/1/012030 ## Besides, they are sharp at least for low order methods, if the testing moments and deflection in their right parts are found by accurate recovery procedures. A posteriori error bounds for classical and mixed FEM’s for 4th-order elliptic equations with piece wise constant reaction coefficient having large jumps 10.1007/s00540-021-02915-x ## After confirming that the patient was well awake and could follow orders, she was sent to the ward. Re-sleeping after reversal of remimazolam by flumazenil 10.1016/J.EGYR.2021.03.003 ## The result shows that flow order, the co-current flow or the counter-current flow, has little influence on the engine array performance. Performance analysis of different arrangements of a new layout dish-Stirling system 10.1103/PHYSREVFLUIDS.6.034610 ## Compared to previous models, these low order systems display longer turbulence lifetimes and lower transition thresholds. Structure interactions in a reduced-order model for wall-bounded turbulence 10.1007/s12206-021-0837-0 ## With the explicit time integration and low order finite elements under the total Lagrangian framework, the proposed model is much computationally efficient for modeling the dynamic mechanical behavior of a cell colony. Continuum-based modeling of collective cell migration 10.1051/E3SCONF/202125602016 ## The proposed system consists of a high-power thyristor-based line commutated converter to contribute a majority of the dc de-icing current and a low power PWM CSC to provide a part of the dc de-icing current and to compensate the low order harmonic ac current from the TCR. A Multi-Functional De-Icing Equipment Using Hybrid Type Parallel Current Source Converters 10.1016/J.MSEB.2021.115149 ## The photocatalytic performance of ZnO nanoflowers follow order of sea urchin > rose > southern cone marigold flower. Shape selective flower-like ZnO nanostructures prepared via structure-directing reagent free methods for efficient photocatalytic performance 10.1016/J.IJHEATMASSTRANSFER.2021.121678 ## The radiant thermal source is first identified via a low order reduced model based on AROMM (Amalgam Reduced Order Modal Model) method. On-line indirect thermal measurement in a radiant furnace by a reduced modal model 10.1109/ICCWorkshops50388.2021.9473576 ## In this work, comparative experimental measurements of low order OAM, Ince-, and Hermite-Gaussian modes in turbulence are presented. Higher-Order Spatial Modes in Turbulence: Alternatives to Orbital Angular Momentum 10.1016/J.CITIES.2021.103206 ## In the urban network, resources can flow orderly and realize optimal allocation, but the crisis also can spread and even exert an amplification effect. The dynamic development process of urban resilience: From the perspective of interaction and feedback 10.1016/j.cma.2020.113556 ## The method shows good agreement with existing experimental results and superior behaviour when compared to a low order panel method. An Isogeometric Boundary Element Method for 3D lifting flows using T-splines 10.11591/IJPEDS.V12.I1.PP295-303 ## However, adding the dead-time increases the low order harmonics of the output voltage/current waveform of the inverter. Mitigating the dead-time effects on harmonics spectrum of inverter waveform by the confined band VSFPWM technique ## The goal of this work was to study the influence of low order mode responses on extreme response statistics. Extreme value statistics of flow-induced hydrofoil vibration and resonance 10.1016/J.CPC.2021.107863 ## The solver is free of any approximation (no linearisation of the scattering operator, no close-to-equilibrium approximation, full non-analytic dispersions, full account of Pauli factors, and no limit to low order scattering) \cite{Michael}. Numerical scheme for the far-out-of-equilibrium time-dependent Boltzmann collision operator: 1D second-degree momentum discretisation and adaptive time stepping ## A low order thermal network model for the perimeter zone, validated with experimental measurements, is utilized to study various control strategies in response to changes in the electrical grid price signal, including short term (nearly reactive) changes of the order of 10–15 min notice. Model Predictive Control Strategies to Activate the Energy Flexibility for Zones with Hydronic Radiant Systems 10.1016/J.JAPPGEO.2021.104401 ## These are removed via a low order eigenimage filter in which the decomposed GPR data is reconstructing without the eigenimages containing them. Resolution enhancement of deconvolved ground penetrating radar images using singular value decomposition 10.3390/app11135874 ## Low order models based on the Blade Element Momentum (BEM) theory exhibit modeling issues in the performance prediction of Vertical Axis Wind Turbines (VAWT) compared to Computational Fluid Dynamics, despite the widespread engineering practice of such methods. Formulation, Validation, and Application of a Novel 3D BEM Tool for Vertical Axis Wind Turbines of General Shape and Size 10.3934/ENERGY.2021028 ## The angular and spatial derivative terms of governing equations in the cylindrical coordinate system are approximated by high order Chebyshev polynomials instead of the low order finite difference schemes. Prediction of coupled radiative and conductive heat transfer in concentric cylinders with nonlinear anisotropic scattering medium by spectral collocation method 10.1007/s11770-021-0884-4 ## In addition, at low orders, the error range of the new optimized SGFDM could be strictly controlled within 1‱, whereas, at high orders, while ensuring accuracy, the spectrum coverage significantly improved. Optimizing staggered-grid finite-difference method based on the least-squares combination of the square window function 10.1007/S10958-021-05217-5 ## The traditional theories characterized by the low orders of approximation of transverse shears do not enable one to detect these local effects, which explains their quite rough accuracy. Refined Model of Thermoelastoplastic Bending of Layered Plates with Regular Structure. ІІ. Model Problems 10.32999/ksu2307-8030/2021-43-13 ## The application of classical methods description of the control system assumes that the control objects are described by linear dynamic links of low order. NEURO-FUZZY CONTROL SYSTEM OF NON-DETERMINED ECONOMIC OBJECT 10.5194/EGUSPHERE-EGU21-5058 ## Low order streams drain a big proportion of river catchments. Controls of nitrogen cycling under gaining and losing conditions in a first order agricultural stream 10.47813/dnit-mip3/2021-2899-109-117 ## Transformation of forecast variance and prediction intervals in case of simple (moving averages MA(q) and autoregressions AR(p) of low order) models is also considered but is a part of further work. Improvement of time series forecasting quality by means of multiple models prediction averaging 10.1007/s11075-020-00996-5 ## New simple recurrence relations of low order satisfied by dual Bernstein polynomials are given. Fast and accurate evaluation of dual Bernstein polynomials 10.3390/jmse9101139 ## The speed of this process can be accelerated by the decrease of the hollow order, topological charge, beam width, and transverse coherence width of the beam. Propagation Properties of an Off-Axis Hollow Gaussian-Schell Model Vortex Beam in Anisotropic Oceanic Turbulence 10.4236/AJCM.2021.111003 ## Specifically, we studied a dual version of the Theorem of Routh-Hurwitz and present explicit criteria for polynomials of low order and derivatives. On a Dual to the Properties of Hurwitz Polynomials I 10.21203/rs.3.rs-799351/v1 ## Comparison of the results predicted by the procedure described in this paper with limited numerical applications, corroborates that it is successful in predicting the response of the components when these are tuned to low order modes of the carrying structure. An Analytical Approximation to the Seismic Response of Light Linear Nonstructural Components in Resonance With Linear Structures 10.1109/ICMT52455.2021.9502810 ## AKA-II shows very low order of reaction and high activation energy leading to considerably long shelf life but harsh stabilizer depletion when the end of shelf life is nearing. Modeling of smokeless powders shelf life using results of multi-temperature study on stabilizer consumption 10.1007/JHEP07(2021)021 ## We work perturbatively — but to arbitrary orders — in the ratio of the heavy operator’s conformal dimension to the dual CFT2’s central charge, thus going beyond the low order results of [1] and [2]. The Regge limit of AdS3 holographic correlators with heavy states: towards the black hole regime 10.1109/TASC.2021.3058547 ## Using the available data, we analyzed the distributions of coil geometry, collared coil size, main field, and low order field errors in warm conditions. Analysis of Geometry and Field Quality Along the Series Production of the 11 T Dipole for the High Luminosity LHC 10.1109/JSEN.2021.3054870 ## A novel conductivity surface decomposition approach, based on low order bivariate polynomials and RBF networks is introduced for the efficient solution of the EIT inverse problem. Tactile Sensing Using Machine Learning-Driven Electrical Impedance Tomography 10.1016/J.PEPI.2021.106672 ## Our new Curie depth model differs by as much as ±20 km relative to previous models, with the largest differences arising from the low order thermal model and variable susceptibility. A global Curie depth model utilising the equivalent source magnetic dipole method 10.1016/J.IJMECSCI.2021.106296 ## Low order continuous equations are pursued since they avoid the need to involve extra boundary conditions. Analysis of low order non-standard continualization methods for enhanced prediction of the dispersive behaviour of a beam lattice 10.1007/JHEP04(2021)194 ## In the proposed approach, matrix model multi-point resolvents take a simplified form and some structures of the genus expansion, hardly visible at low order, may be identified and rigorously proved. On topological recursion for Wilson loops in $$\mathcal{N}$$ = 4 SYM at strong coupling 10.1016/J.GEOG.2020.11.005 ## Secondly, the paper gives a theory proof to explain why only the low orders of the coefficients are influenced by polar gaps. Analysis of limitations on recovery of gravity field based on satellite gravity gradient data 10.1007/S10878-021-00709-1 ## We allow order splitting between consecutive lots. A note on the single machine CON and CONW problems with lot scheduling 10.1007/s00334-021-00831-4 ## Pollen assemblages and vegetation correlate better in terms of richness, that is, low order diversity indices. Testing the potential of pollen assemblages to capture composition, diversity and ecological gradients of surrounding vegetation in two biogeographical regions of southeastern Europe 10.1016/j.matcom.2020.11.006 ## The results show that the NARX with low order models fit the real data very well if compared to the ARX models. Autoregressive exogenous input modelling for lipase catalysed esterification process 10.1016/j.jcp.2021.110527 ## The aim of this paper is to develop efficient recursive strategies to tackle a class of high dimensional integrals having a special product structure with low order couplings, motivated by models in lattice gauge theory from quantum field theory. Lattice meets lattice: Application of lattice cubature to models in lattice gauge theory 10.1007/S42835-020-00636-X ## A low order CP mode (TM11 Mode) and a high order CP mode (TM12 Mode) are both excited in this simple structure for the dual band operation. Dual Mode Dual-Band Circularly Polarized Modified Square Ring Antenna 10.1109/MWSCAS47672.2021.9531686 ## The filters resulted through this procedure have a precise circular shape even close to frequency plane margins and they have a very steep transition for relatively a low order, thus being very efficient. Efficient Design Procedure for Circular Filter Banks 10.3390/APP11073282 ## The optimization results show that the damping loss factor increases when the position of the patch is close to the constraint boundary, and the best strategy is to optimize the low order damping loss factor of the system under moving loads. Dynamic Response Analysis of a Thin Plate with Partially Constrained Layer Damping Optimization under Moving Loads for Various Boundary Conditions 10.1109/TPWRD.2020.3001217 ## The proposed scheme can eliminate the phase angle error during frequency drift without compromising its benefits of the low order control system. Advanced Type-1c FLL for Enhancing Converters Synchronization During Frequency Drift 10.35445/ALISHLAH.V13I1.385 ## This paper addresses the question of how cognitive levels covering high, middle, and low order thinking skills are delineated in the questions seen from Bloom’s revised taxonomic framework and stimulus. Evaluating Cognitive Level of Final Semester Examination Questions Based on Bloom’s Revised Taxonomy 10.3390/aerospace8090250 ## Although such problems might be of interest for different applications, the present study is specifically oriented to the low order modeling of high-frequency combustion instability in liquid-propellant rocket engines. A Hybrid Real/Ideal Gas Mixture Computational Framework to Capture Wave Propagation in Liquid Rocket Combustion Chamber Conditions 10.1142/S0217751X2150086X ## In the low order of the perturbation theory, matrix elements of some of QED. Quantum electrodynamics with self-conjugated equations with spinor wave functions for fermion fields 10.1177/0142331221998465 ## In order to overcome implementation problems, the low order proportional-integral-derivative (PID) type controllers, which minimize the H ∞ norm of the closed loop system, are designed in the centralized and the decentralized settings. H ∞ controller design for the mitigation of atmospheric effects on the laser beam pointing 10.1051/E3SCONF/202125201010 ## The traditional proportional feedforward control strategy can suppress the low order harmonics in the strong power grid, but in the weak power grid environment, the grid impedance will have an adverse impact on the stability of the system, resulting in the proportional feedforward control can not suppress the low order harmonics well. An improving control strategy for grid -connected current in weak grid ## While this compound suffers from a low ordering point and is a helimagnet, these difficulties are easily remedied by the substitution of appropriate amounts of cobalt for Fe, with room-temperature saturation magnetization as high as 1. Effect of atom substitutions on the magnetic properties in Ce2Fe17: Toward permanent magnet applications 10.1109/TIM.2021.3082268 ## The proposed sensor presents a high sensitivity due to low order modes that propagate in the middle single-mode fiber (SMF) cladding. A Simple Optical Sensor Based on an In-Line Mach–Zehnder Interferometer for Monitoring Single- and Two-Phase Flows in Pipelines 10.1051/E3SCONF/202125802006 ## Direct approximation of these data gives an expression for the flow order. Modern problems in assessment of hydraulic resistance 10.1051/E3SCONF/202126403038 ## The regulator is built into the pressure drop between the high and low order channels. Water flow regulator for irrigation canals 10.1051/EPJCONF/202124710023 ## With those features, this problem set could then be used for benchmarking neutron transport methods as well as its low order methods in 2D single assembly and full core configurations. A SIMPLIFIED SMAHTR BENCHMARK PROBLEM SET 10.46298/lmcs-17(3:16)2021 ## In comparison, the analogous problems for exact rational or real algebraic coefficients are known to be decidable only for linear recurrences of fairly low order. Decision problems for linear recurrences involving arbitrary real numbers 10.1016/J.AST.2021.107070 ## A low order network model is built to recognize the thermoacoustic modes of the combustion system. Effects of acoustic liner on thermoacoustic instabilities in a premixed swirl combustor 10.15598/AEEE.V19I2.4100 ## The noise component of the low order IMFs is removed with the pixel-wise Wiener filtering. BEMD Based Ultrasound Image Speckle Reduction Technique Using Pixel-Wise Wiener Filtering	2022-09-29 08:16:42	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 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": 0.45641347765922546, "perplexity": 2822.4289082677274}, "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/1664030335326.48/warc/CC-MAIN-20220929065206-20220929095206-00377.warc.gz"}
https://physics.stackexchange.com/questions/79470/gamma-in-newtons-second-law-of-motion-in-differential-form	# $\gamma$ in Newton's Second Law of Motion in Differential Form I am teaching myself Differential Equations from a website. In the website I am up to Direction Fields and an example of a differential equation is Newton's Second Law of Motion. It is written on the website like this: $$m\frac{dv}{dt}=mg-\gamma v$$ I know that $m$ is the mass, $g$ is the gravitational acceleration, $v$ is the velocity, and $t$ is the time, but what does $\gamma$ stand for? • Looks like it has something to do with viscosity. – Ruslan Oct 3 '13 at 9:52 • Comment to the question (v1): A force of the type $\vec{F}=-\gamma \vec{v}$ is known as kinetic friction, damping, or Stokes' drag, depending on the context. – Qmechanic Oct 3 '13 at 10:18 The $\gamma$ here is some coefficient/constant (which has the units $\mathrm{kg\,s^{-1}}$). This formula is saying that the resultant force $F = \mathrm{d}v/\mathrm{d}t$ is equal to the force on the mass from gravity minus some force $\gamma v$ which is dependent on velocity. To me, you are right, this does not make too much sense from a Newtonian standpoint (IMO) as this is representing a drag linearly dependent on velocity which is never the case in my experience. It would make more sense if the resistive force was written as $\lambda v^{2}$ (and the units of $\lambda$ amended accordingly for some arbitrary example case), this could then represent an air/fluid resistance where $\lambda$ is some type of 'drag coefficient'. I hope this helps. • In Stokes' law, e.g., one has drag force proportional to first power of velocity, not second one. – Ruslan Oct 3 '13 at 9:57 • This is a Newtonian equation taken at face value. A classic introduction to aerodynamic drag for basic Newtonian physics is to use $\lambda v^{2}$ and there is nothing wrong with doing so. This clearly is not an advanced equation and all I am doing it answering the question, not second guessing what the author of the equation was thinking at the time of writing. – MoonKnight Oct 3 '13 at 10:15 • The down vote is non-sense. Tell me the reason. This site makes a mockery of StackExchange. – MoonKnight Oct 9 '13 at 13:27 The general form of Newton's Law for constant mass is $$m \frac{dv}{dt} = F$$ so in your case, $F = mg - \gamma v$ is the provided force law. In your case your force happens to depend on the velocity; the greater the velocity, the more negative the force, so it is a kind of friction or drag. $\gamma$ is just the proportionality constant between the friction force $F_{fric} = -\gamma v$ and the velocity, just like $k$ is the proportionality constant between the position and the force $F_{spring} = -kx$ for a spring.	2020-01-21 03:56:36	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7325318455696106, "perplexity": 230.4576949053761}, "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/1579250601241.42/warc/CC-MAIN-20200121014531-20200121043531-00322.warc.gz"}
https://trac-hacks.org/ticket/4907	Opened 13 years ago Closed 13 years ago #4907 closed defect (fixed) Reported by: Owned by: kontakt@… Martin Scharrer normal NumberedHeadlinesPlugin minor Ryan J Ollos 0.11 Description When I want to use the first level Trac headline (=) as an unnumbered Title for the wiki page and then start numbered headings in the second level (##), skipping the first level (#), then The numbering of the second-level headlines starts with 0.1. I would rather suspect the second level to sense that there is no upper-level numbering and start the numbering in the first level that uses the numbering, so the headline descrbes above would be numbered as 1. Lorem ipsum Usually in a document I want the main title to be unnumbered. In OOo for example there is a seperate format "Title" which we don't have here. Maybe it would be intersting anyways to allow users to influence the numbering via arguments to the plugin (like specifying the id). One could add a feature to re-start the numbering at any point, or to override the depth level to use. In my case, this could look like = Document Title = comment:2 Changed 13 years ago by Ryan J Ollos Cc: Ryan J Ollos added; ryano@… removed comment:3 Changed 13 years ago by Martin Scharrer (In [6853]) Added option for numbering_starts_at_level_two. See #4907. comment:4 Changed 13 years ago by Martin Scharrer Status: new → assigned Our idea of user settings looks good, but will require much more work. In the meanwhile use revision [6853] or later with numbering_starts_at_level_two = true in the config file. See NumberedHeadlinesPlugin#Configuration. It changes the behavior globally so that the following wiki text: = Document Title = ### sub ### # Another title-like headline, unnumbered but resets numbers # ### sub ### = Another title-like headline, unnumbered and does not reset numbers = ### sub ### becomes equivalent to: <h1> Document Title </h1> <h2> 1. First numbered heading </h2> <h3> 1.1. sub </h3> <h1> Another title-like headline, unnumbered but resets numbers </h1> <h3> 1.1. sub </h3> <h1> Another title-like headline, unnumbered and does not reset numbers </h1> <h3> 2.1. sub </h3> Displayed as HTML: Another title-like headline, unnumbered and does not reset numbers comment:5 Changed 13 years ago by Martin Scharrer Resolution: → fixed assigned → closed As of [6856] there is the support to set headline numbers manually. Also leading zeros are ignored. This should resolve this ticket. Modify Ticket Change Properties	2022-05-17 20:51:35	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5960571765899658, "perplexity": 11545.759326807713}, "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/1652662520817.27/warc/CC-MAIN-20220517194243-20220517224243-00331.warc.gz"}
http://tractatusblog.blogspot.com/2007/11/6_6755.html	Tuesday, November 20, 2007 6.1203 In order to perceive a tautology as such, one can, in cases in which no sign of generality occurs in the tautology, avail oneself of the following method: I write “TpF”, “TqF”, “TrF”, etc. in stead of “p”, “q”, “r”, etc. I express the truth-combinations with brackets, e.g.: The coordination of the truth or falsity of the whole proposition and the truth-combinations of the truth-arguments with lines in the following way: T (T/F)->F" shapes="_x0000_i1026" height="96" width="128"> This sign, e.g., would therefore present the proposition p → q. Now I will investigate on the strength of that whether, e.g., the proposition ~(p. ~p) (the Law of Contradiction) is a tautology. The form “~ξ” gets written in our notation as; T, (T)->F" shapes="_x0000_i1029" height="64" width="64">T, (T)->F" shapes="_x0000_i1029" height="64" width="64">T, (T)->F" shapes="_x0000_i1029" height="64" width="64"> the form “ξ . η” thus: F (T/T)->T" shapes="_x0000_i1032"> So the proposition ~(p. ~q) goes thus: T, T/F->F" shapes="_x0000_i1033">T, T/F->F" shapes="_x0000_i1033">T, T/F->F" shapes="_x0000_i1033"> If we put here “p” instead of “q” and investigate the combination of the outermost T and F with the innermost, then we get the result that the truth of the whole proposition is coordinated with all the truth-combinations of its arguments, its falsity with none of the truth-combinations. A somewhat complicated way of demonstrating an obvious truth, but I suppose it’s the demonstration that matters here. Or maybe the point is that this is all that logic can be/do.	2018-12-19 16:28:44	{"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": 0.843938410282135, "perplexity": 4345.420500921764}, "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-2018-51/segments/1544376832559.95/warc/CC-MAIN-20181219151124-20181219173124-00394.warc.gz"}
https://davidegerosa.com/news/	# Davide Gerosa May 25, 2022 ## Which black hole formed first? Mass-ratio reversal in massive binary stars from gravitational-wave data Big stars burn everything they have, die fast, and produce big black holes. So when you see two black holes together, it’s likely that the big black hole comes from the big star. Or maybe not? Before dying, the big star can drop some mass onto the other guy, making it bigger! So now, the initially big star still produces the first black hole, but, at the end of the day, that might not be the more massive black hole anymore! This scenario is called “mass-ratio reversal” and our astrophysics friends have put together many models out there showing this is indeed possible for a good fraction of the black holes that produce gravitational-wave events. So here we ask the data: given the events LIGO and Virgo have seen so far, what’s the evidence for mass-ratio reversal in binary stars? Read Matt’s paper to find out. Matthew Mould, Davide Gerosa, Floor S. Broekgaarden, Nathan Steinle arXiv:2205.12329 [astro-ph.HE]. May 4, 2022 ## New horizons for fundamental physics with LISA Another short post today, but it’s not just astrophysics that will be awesome with LISA, but fundamental physics too! Here is the white paper of the relevant LISA working group. Get ready to test your wildest ideas, my theory friend! K. G. Arun, et al. (141 authors incl. Davide Gerosa) arXiv:2205.01597 [gr-qc]. April 26, 2022 ## PhD in gravitational physics! The University of Milano-Bicocca welcomes applications for Ph.D. scholarships. The application deadline is May 20th, 2022 for positions starting in the Fall of 2022: In particular, the theoretical astrophysics group is looking for strong, highly motivated candidates to join our activities in black-hole binary dynamics, gravitational-wave data exploitation, and numerical relativity. Faculty members with matching interests include Gerosa, Sesana, Colpi, Dotti, and Giacomazzo. The candidates will have ample opportunities to work with and visit external collaborators as well. Our PhD admission program includes a number of “open” scholarships, covering all research activities in the department (including ours!). All candidates are considered for those by default. In addition, our group sponsors two specific positions: • “Gravitational-wave data and black-hole binary dynamics”, supervised by Gerosa. Possible research directions include statistical inference from LIGO/Virgo and LISA data, application of machine-learning tools to gravitational-wave astronomy, and theoretical investigations of black-hole binaries. • “Dynamics of massive black hole binaries in dense stellar systems”, supervised by Sesana and Gualandris. This is a dual-doctorate position in partnership with the University of Surrey, UK. The main focus is the understanding of binary evolution using N-body simulations and analytical modeling. The successful candidate will spend 50% of their time at Bicocca and 50% of their time at Surrey. Candidates wishing to be considered for these additional positions should mention it explicitly in their application. More information on the astrophysics group at Bicocca can be found at astro.fisica.unimib.it. For informal inquiries please do not hesitate to contact [email protected] or [email protected]. April 22, 2022 ## Long-term research appointment in computational astrophysics at Milano-Bicocca (Italy) The University of Milano-Bicocca (Italy) invites expressions of interest for a 3+2 year research position in HPC applications to astrophysics. The astrophysics group at Milano-Bicocca provides a vibrant environment with expertise covering all aspects of gravitational-wave astronomy, relativistic astrophysics, galactic dynamics, and numerical relativity. This is embedded in a wider astronomical context including both observational and experimental activities. Our group has tight connections with the LISA Consortium, the Virgo Collaboration, the Einstein Telescope Science Board, the European Pulsar Timing Array, and the Italian National Institute for Nuclear Physics (INFN) via the TEONGRAV national initiative. Staff members with matching interests include Colpi, Dotti, Gerosa, Giacomazzo, Lupi, and Sesana. Milan is a beautiful, international city in the north of Italy. Mountains and lakes are just around the corner. Art, culture, and food are outstanding. The city hosts three international airports with worldwide connections. This recruitment campaign is part of a wider national initiative supporting HPC-related computational activities throughout the country. This is a major investment program directly supported by the European Union. It will provide the most ideal context for ambitious candidates wishing to develop and apply state-of-the-art computational and machine-learning tools to current astrophysical and gravitational-wave modeling issues. The researcher will be appointed at the so-called “RTDA” level for 3 years. The contract can also be extended for 2 more years depending on funding availability. The starting date is negotiable, with the earliest and latest dates on January 1st, 2023 and May 1st, 2023, respectively. RTDA researchers are full-time university employees (with full benefits, such as health insurance and pension plan), have limited teaching duties, and are eligible to fully supervise research MSc student projects. This is an ideal setup for early-career researchers wishing to transition toward research independence and start developing their own group. The successful candidate will have a PhD in Physics, Astronomy, Computer Science, or related discipline, strong programming skills, and previous experience in one or more of the following topics: HPC workflows, GPU software development, computational astrophysics, gravitational-wave astronomy, numerical relativity, statistical data analysis, machine learning. Applications should include a CV with a list of publications and a two-page statement covering research interests and plans. These should be sent to [email protected] by June 15th, 2022 for full consideration. Candidates should also arrange for two reference letters to be sent to [email protected] by June 15th, 2022. We strive to build a diverse and inclusive environment and welcome expressions of interest from traditionally underrepresented groups. Women are especially encouraged to apply. For inquiries please do not hesitate to contact Bruno Giacomazzo ([email protected]) or Davide Gerosa ([email protected]). April 21, 2022 ## Got an ISCRA-B supercomputer allocation! I was just awarded a large allocation on the Italian national supercomputer at CINECA. My PhD student Viola De Renzis (our parameter-estimation expert!) is the co-I on our proposal. Our award is part of the so-called ISCRA Class B program (which is their medium-size allocation scheme) and amounts to 1.2M CPUh on the Galileo cluster (that is: we’re going to have to crunch a ton of numbers now!). Viola and I will study the extraction of spin-spin couplings from black-hole binaries using gravitational-wave data and stochastic sampling techniques. Stay tuned! April 13, 2022 ## “With a little help from my friends” Workshop at JHU We’re at Johns Hopkins University (Baltimore) today, for a brainstorming workshop we organized together with the gravity groups at JHU and Penn State. A ton of interesting people, cool science, fun numerics, big black holes, future detectors, and many new exciting projects we all want to start. The idea is to get “a little help from my (gravity) friends”. Have a look at what we’re up to: davidegerosa.com/with-a-little-help-from-my-friends-workshop/ April 8, 2022 ## The last three years: multiband gravitational-wave observations of stellar-mass binary black hole Observing gravitational waves from the ground (i.e. LIGO, Virgo, etc) give us a unique view on “the last three minutes” of the life of compact objects before they merge with each other. Going to space (I’m talking to you, LISA!) will instead give us “the last three years”. Completed together with the rest of the Birmingham crowd, this paper provides a realistic view of this truly amazing landscape. LISA observations at low frequencies in the 2030s will be paired with high-frequency data from LIGO’s successors (the so-called 3rd generation detectors). Together (and that’s crucial, together!) LISA and 3g detectors will tell us the full story of the life of merging black holes. LIGO alone is like catching up with a movie because you were late at the theatre, LISA alone is like a huge cliffhanger before the series finale… multiband observations are a bingewatching experience! Antoine Klein, Geraint Pratten, Riccardo Buscicchio, Patricia Schmidt, Christopher J. Moore, Eliot Finch, Alice Bonino, Lucy M. Thomas, Natalie Williams, Davide Gerosa, Sean McGee, Matt Nicholl and Alberto Vecchio. arXiv:2204.03423 [gr-qc]. April 4, 2022 ## Constraining black-hole binary spin precession and nutation with sequential prior conditioning Daria’s new paper is out! (With key contributions from others in the group… This is also Viola’s first paper!). Here we look at sub-dominant black-hole spin effects in current data from LIGO and Virgo (yeah sorry guys… our black-hole spin obsession goes on). People have looked at spin precession before, but we’re interested in even more subtle things, namely disentangling precession and nutation. This is a tricky business, which is made complicated by the fact that this piece of information is hidden behind other parameters that are easier to measure (say the masses of the two black holes). Our paper is an attempt to formulate and systematically exploit something we called “sequential prior conditioning” (which is: mix&match priors and posteriors in Bayesian stats…). Results are weak today but strong tomorrow. Daria Gangardt, Davide Gerosa, Michael Kesden, Viola De Renzis, Nathan Steinle. arXiv:2204.00026 [gr-qc]. March 11, 2022 ## Astrophysics with the Laser Interferometer Space Antenna LISA astrophysics is awesome and everything you might ever want to know is written this paper. [Sorry for the short blog post, but there isn’t much else to say really…] A huge thanks to all the captains that put this massive community-wide effort together. Pau Amaro-Seoane, et al. (155 authors incl. Davide Gerosa). arXiv:2203.06016 [gr-qc]. March 9, 2022 ## Deep learning and Bayesian inference of gravitational-wave populations: hierarchical black-hole mergers It took a while (so many technical challenges…) but we made it! Matt‘s monster paper is finally out! Let me introduce a fully-fledged pipeline to study populations of gravitational-wave events with deep learning. If it sounds cool, well, it is cool (just look at the flowchart in Figure 1!). We can now perform a hierarchical Bayesian analysis on GW data but, unlike current state-of-the-art applications that rely on simple functional form, we can use populations inferred from numerical simulations. This might sound like a detail but it’s not: it’s necessary to compare GW data directly against stellar physics. While we don’t do that yet here (our simulations are admittedly too simple), there’s a ton of astrophysics already in this paper. Whether you care about neural networks or hierarchical black-hole mergers (or, why not, both!), sit tight, fasten your seatbelt, and read Matt’s paper. Matthew Mould, Davide Gerosa, Stephen R. Taylor. arXiv:2203.03651 [astro-ph.HE]. March 2, 2022 ## New class! Astrostatistics I just had the first lectures of a class I’m teaching for the first time: Astrostatistics and Machine Learning (sounds exciting? Well, it is!). This is an advanced course for the MSc degree in Astrophysics and Space Science at the University of Milano-Bicocca. My students and I will travel across data inference, Bayesian wonders, sampling, regression, classification, and become best friends with deep learning. All of this is applied to astrophysical datasets. The entire class is available under the form of jupyter notebooks at github.com/dgerosa/astrostatistics_bicocca_2022. The repository is hooked up with the mybinder service. February 23, 2022 ## Congrats Cecilia! Huge congrats to my student Cecilia Fabbri who got her Bachelor’s degree today. Cecilia defended (quite brilliantly!) her project titled “Constraining the black-hole irreducible mass with current gravitational-wave data”. Her work ended up in our recent draft (arxiv:2202.08848). Cecilia is continuing with a Master’s degree in astrophysics at Milano-Bicocca, stay tuned for her future successes! February 21, 2022 ## The irreducible mass of LIGO’s black holes Spinning black holes are weird (well, all black holes are weird but those that spin are the worse!). They have a funny thing called ergoregion where orbiting particles can have negative energy. Penrose was the first to realize that this can be exploited to extract energy from the black hole itself. The thing is, even if you figure out how to do it, you’re inevitably going to spin the black hole down. At the end of the day, you’re left with a fossil black hole that does not have any spin. The mass of that leftover black hole (“What’s for lunch dear? Fancy some sushi or prefer a black hole?”) is called irreducible mass. Hawking (another giant!) figured out this has to do with thermodynamics. Long story short, in this paper we compute the irreducible mass of the black holes detected in gravitational waves by LIGO. It was funny to re-discover that gravitational wave detection was indeed the motivation behind Hawking original proof of the area theorem (he had Weber‘s claimed detection in mind at the time). The story behind our paper starts as a toy calculation with my undergraduate student Cecilia and ended up in a neat, hopefully informative exploitation of LIGO data. We reparametrized LIGO’s black-hole properties using the rotational and rotational contributions to their total energy, we ranked current gravitational-wave events according to their “irreversibility”, and we compute a sort of population version of the area law. Enjoy! Davide Gerosa, Cecilia Maria Fabbri, Ulrich Sperhake. arXiv:2202.08848 [gr-qc]. January 20, 2022 ## People visiting Traveling is (kind of) coming back, and we’re having lots of visitors around, all supported by external research grants (congrats folks, you’re great!) Safe travel everyone, it’s time we move our group meetings to a larger room. January 7, 2022 ## Cariplo Foundation Grant I’m very happy to share that I was awarded a 330k EUR grant from the Cariplo Foundation. Cariplo is a trust that supports scientific research in the Lombardy region of Italy. Our proposal is titled “Deep into the relativistic two-body problem“, though arguably a better title could have been “more black-hole fun coming our way”! December 6, 2021 ## TEONGRAV My group and I are now part of TEONGRAV, which is the Italian national initiative dedicated to gravitational theory and phenomenology. TEONGRAV is run by the INFN (National Institute for Nuclear Physics) and, besides the other folks here in Milan, it counts members from Florence, Rome, Naples, Padua, Trento, and Trieste. Looking forward to new exciting collaborations, all surrounded by good Italian coffee of course! November 17, 2021 ## The Bardeen-Petterson effect in accreting supermassive black-hole binaries: disc breaking and critical obliquity Breaking things is fun! In the previous paper of this series, we looked at accretion disks around massive black-hole binaries and found things were going awry. We kept on finding configurations that our implementation could not handle… And now we know this is real! Finding disk solutions when the spin of the black hole has a large misalignment is just not possible! And that’s because the disk really breaks into different sections. We’ve now checked it with state-of-the-art hydrodynamical numerical simulations that not only confirm what we suspected but also show some funny things (like breaking being prevented by disk spirals, etc). I was serious, breaking things is real fun! Check out Rebecca’s beautiful movies! Rebecca Nealon, Enrico Ragusa, Davide Gerosa, Giovanni Rosotti, Riccardo Barbieri. Monthly Notices of the Royal Astronomical Society 509 (2021) 5608–5621. arXiv:2111.08065 [astro-ph.HE]. October 13, 2021 ## Gravitational-wave population inference at past time infinity Great Scott, a new paper! When analyzing gravitational-wave data, looking at one black hole at a time is not enough anymore, the fun part is looking at them all together. The issue Matt and I are tackling here is that one needs to be consistent with putting together different events when fitting the entire population. This is obvious for things that do not change (say the masses of the black holes, those are what they are), but becomes a very tricky business for varying quantities (say the spin directions, which is what we look at here). In that case, it’s dangerous to put together events taken at different stages of their evolution. And the solution to this problem is…. time travel! We show that but propagating binaries backward in time, one can put all sources on the same footing. After that, estimating the impact of the detector requires traveling forward in time, so going “back to the future”. After all, we all know that post-Newtonian black-hole binary integrations look like this: Matthew Mould, Davide Gerosa. Physical Review D 105 (2022) 024076. arXiv:2110.05507 [astro-ph.HE]. October 11, 2021 ## Nate is joining us! Nathan Steinle is officially starting his postdoc in the group today! Nate graduated with Mike Kesden at the University of Texas at Dallas and is now working with me and the rest of the Birmingham crowd. Welcome Nate! Hope you enjoy this side of the pond. October 4, 2021 ## Postdoctoral fellowships in gravitational-wave astronomy at Milan-Bicocca (Italy) The University of Milan-Bicocca (Italy) invites expressions of interest for postdoctoral positions in gravitational-wave astronomy. Successful candidates will join Prof. Davide Gerosa and will constitute the core team of the “GWmining” project funded by the European Research Council. Targeted investigations include applications of machine-learning techniques to gravitational-wave physics, modeling of black-hole binary populations from their stellar progenitors, relativistic dynamics, and statistical inference. Candidates will have ample opportunities to explore other areas of gravitational-wave astronomy and will be encouraged to develop independent collaborations. We anticipate awarding two positions. Appointments will be for a three-year term and come with generous research and travel budget. The starting date is negotiable. The astrophysics group at Milan-Bicocca provides a vibrant environment with expertise covering all aspects of gravitational-wave astronomy, relativistic astrophysics, and numerical relativity, as well as a wider astronomical context including observational and experimental activities. The group has tight connections with the LISA Consortium, the Virgo Collaboration, and the Italian National Institute for Nuclear Physics (INFN) via the TEONGRAV national initiative. Faculty members with matching interests include Gerosa, Sesana, Colpi, Giacomazzo, and Dotti. Milan is a beautiful, international city in the north of Italy. Mountains and lakes are just around the corner. Successful candidates will have a PhD in Physics or related discipline, strong programming skills, and previous experience in one or more of the following topics: gravitational-wave astronomy, stellar evolution, relativistic astrophysics, general relativity, machine learning, statistical inference. Applications should include a CV with a list of publications and a two-page statement covering research interests and plans. These should be sent to [email protected] by December 1st, 2021 for full consideration. Candidates should also arrange for at least two, but preferably three, reference letters to be sent to the same address by December 1st, 2021. We strive to build a diverse and inclusive environment and welcome expressions of interest from traditionally underrepresented groups. For inquiries please do not hesitate to contact Davide Gerosa at [email protected]. September 18, 2021 ## Welcome Viola! Viola De Renzis is the latest addition to our group! Viola graduated from Rome “La Sapienza” with an MSc thesis on exotic compact objects and is now starting her PhD with me at Milan-Bicocca. Viola plays guitar, arguably better than Matt (although he runs for a million miles, and that’s when he’s tired), while Daria remains by far the best fencer in the group. Welcome, we all look forward to working with you! September 8, 2021 ## SIGRAV Prize for Young Researchers It is a true honor to receive the career Prize for Young Researchers of the Italian Society for General Relativity and Gravitational Physics (SIGRAV). I was awarded the prize in the class of relativistic astrophysics. It’s amazing to be recognized in my home country; it’s great to be back! Let me thank all my mentors, advisors, collaborators, and now students who are walking with me in the adventure of science. Here is me with the president of the society Fulvio Ricci. And here are press releases from the University of Milan-Bicocca and the INFN. September 1, 2021 ## Moving (back to) Milan! We moved! I’ve had the opportunity to relocate to Milan, in the north of Italy, very close to where I’m from. I’m now an Associate Professor at the University of Milan-Bicocca, one of the two campuses in the beautiful city of the “Madonnina“. Some of the folks in my group will be visiting Milan very often, and (spoiler alert!) we’re going to have new additions soon. I’m sad to leave the amazing group in Birmingham, but also very excited at this new tremendous opportunity. August 6, 2021 ## Population-informed priors in gravitational-wave astronomy No black hole is an island entire of itself. We’ve got many gravitational wave events now. One can look at each of them individually (aka “parameter estimation”), all of them together (aka “population”), or each of them individually while they’re together. That’s what we do in this paper: we look at the properties of individual gravitational-wave events in light of the rest of the observed population. The nice thing is that all of these different ways of looking at the data are part of the same statistical tool, which is a hierarchical Bayesian scheme. Careful, heavy stats inside, don’t do this at home. Christopher J. Moore, Davide Gerosa. Physical Review D 104 (2021) 083008. arXiv:2108.02462 [gr-qc]. July 14, 2021 ## Well done Max! Huge congrats to Maciej (Max) Dabrowny, who just graduated from the University of Birmingham after a very successful research project with us (Max’s project ended up in a paper!). Well done and all the best for the future. July 11, 2021 ## Settimana dell’astronomia 2021 I was recently interviewed for the Italian Week of Astronomy (“Settimana dell’Astronomia”), a science festival organized by Fondazione Lombardia per l’Ambiente and supported by various Italian associations, universities, and research centers. Here is the nice clip they put together (I mean, I’m terrible at speaking to a camera, but they assembled it very well!). June 24, 2021 ## Modeling the outcome of supernova explosions in binary population synthesis using the stellar compactness Today we go deep into the perilous world of binary population synthesis! Using Nicola’s code MOBSE, our master student Maciej has implemented some new prescriptions for how supernovae explode and produce compact objects. In practice, we use the compactness (that’s mass over radius) of the stellar core before the explosion to decide if that specific star will form a neutron star or a black hole. This now needs to be compared carefully with gravitational-wave data, but we suggest that there are two key signatures one should look for: the lowest black hole masses and the relative merger rates between black holes and neutron stars. Maciej Dabrowny, Nicola Giacobbo, Davide Gerosa. Rendiconti Lincei. Scienze Fisiche e Naturali 32 (2021) 665–673. arXiv:2106.12541 [astro-ph.HE]. June 10, 2021 ## A new IREU friend from Missouri We have a new friend in the group! Meredith Vogel is joining us for her undergraduate summer research project. Meredith is e-visiting us from Missouri State University (but will soon start her grad school at the University of Florida) and will be working with Matt on numerical-relativity surrogate models. Meredith’s project is part of the IREU (International Summer Research) program, which is a great opportunity for US students to visit groups abroad, including us! Welcome Meredith, looking forward to seeing your great science. That’s the place were I saw a real alligator. On campus! June 10, 2021 ## Bayesian parameter estimation of stellar-mass black-hole binaries with LISA LISA is going to be great and will detect stuff from white dwarfs to those supermassive black-hole that live at the center of galaxies. If we’re lucky (yeah, who knows how many of these we will see), LISA might also detect some smaller black holes, similar to those that LIGO now sees all the time, but at a much earlier stage of their lives. But if we’re indeed lucky, the science we would take home is outstanding. Using simulated data from the LISA Data Challenge we unleash the new amazing parameter-estimation code Balrog (don’t ask what it means, it’s just a name, not one of those surreal astronomy acronyms) at this problem. Dive into the paper for some real data-analysis fun! Riccardo Buscicchio, Antoine Klein, Elinore Roebber, Christopher J. Moore, Davide Gerosa, Eliot Finch, Alberto Vecchio. Physical Review D 104 (2021) 044065. arXiv:2106.05259 [astro-ph.HE]. May 27, 2021 ## Looking for the parents of LIGO’s black holes Who are the parents of LIGO’s black holes? Stars, most likely. Things like those we see in the sky at night will eventually surrender to gravity and collapse. Some of them will form black holes. Some of them will form binary black holes. Some of them will merge. Some of them will be observed by LIGO. That’s the vanilla story at least, but it might not apply to all of the black holes that LIGO sees. For some of those, stars might be the grandparents or the great grandparents. And the parents are … just other black holes! This is today’s paper lead by Vishal Baibhav. Instead of just measuring the properties of the black holes that LIGO observes, we show we can also say something about the features of the black hole parents. Read on to explore the black-hole family tree. Vishal Baibhav, Emanuele Berti, Davide Gerosa, Matthew Mould, Kaze W. K. Wong. Physical Review D 104 (2021) 084002. arXiv:2105.12140 [gr-qc]. May 18, 2021 ## Come to Milan for a PhD! The University of Milano-Bicocca welcomes applications for Ph.D. scholarships. The application deadline is June 16th, 2021 for positions to start later in 2021: https://en.unimib.it/education/doctoral-research-phd-programmes/how-apply-phd-programme In particular, I am looking for a strong, highly motivated candidate to join my newly established research group supported by the European Research Council. The candidate will work toward interpreting the phenomenology and the astrophysics of gravitational-wave sources using innovative machine-learning techniques. My activities are embedded within the wider Astrophysics group at the University of Milano-Bicocca –a world-leading research environment in strong gravity and relativistic astrophysics. Faculty members with matching interests include Colpi, Sesana, Dotti, and Giacomazzo. The candidate will have ample opportunities to work with and visit external collaborators as well. This specific position is titled “Large catalogs of gravitational-wave events with machine learning”. Interested candidates should mention it explicitly in their application. Milan is a beautiful, international city in the north of Italy. Mountains and lakes are just around the corner. For further information and informal inquiries please do not hesitate to contact me ([email protected]). May 11, 2021 ## Hierarchical mergers of stellar-mass black holes and their gravitational-wave signatures The quest of finding their astrophysical origin of merging black-hole binaries is now a key open problem in modern astrophysics. Stars are the natural progenitor of black holes: at the end of their lives, the core collapses and leaves behind a compact object. But once those “first-generation” black holes are around, they can potentially meet again and form “second generation” LIGO events. I first got interested in this problem in 2017 and, together with many many others researchers in the community, we explored the consequences of this “hierarchical merger” scenario in terms of both gravitational-wave physics and astrophysical environments. In this Nature Astronomy review article, Maya and I tried to condense all this body of work into a few pages. The result is (we hope) a broad and informed overview of this emerging research strand, with a whopping number of more than 270 citations! Hope you like it. Davide Gerosa, Maya Fishbach. Nature Astronomy 5 (2021) 749-760. arXiv:2105.03439 [astro-ph.HE]. Review article. April 26, 2021 ## High mass but low spin: an exclusion region to rule out hierarchical black-hole mergers as a mechanism to populate the pair-instability mass gap Hierarchical mergers are the new black. LIGO is seeing black holes that are just too big to be there. The reason is that stars, which collapse and produce black holes, do some funny things when they get too massive. Notably, they start to spontaneously produce positrons and electrons instead of keeping their own photons. Long story short: those missing photons make the temperature go up, ignite an explosion that disrupts the core and prevents black-hole formation. This “mass gap” is a solid prediction from our astrophysics friends. In some previous papers, we and other groups pointed out that one can bypass stars and form black holes from previous black holes (and goodbye my dear maximum mass limit!). But now our astrophysics friends are telling us they can also evade the limit with some more elaborate astro-magic (winds, rotation, dredge-up, reaction rates, accretion). Today’s paper is about telling the two apart, with a key prediction: a black hole with large mass but low spin would raise a glass to the astro-wizards. Davide Gerosa, Nicola Giacobbo, Alberto Vecchio. Astrophysical Journal, 915 (2021) 56. arXiv:2104.11247 [astro-ph.HE]. March 31, 2021 ## Testing general relativity with gravitational-wave catalogs: the insidious nature of waveform systematics. General Relativity works well. But we still want to test it, and I guess that’s because it actually works too well (you know, all those quantum things that don’t really fit, etc). And we want to test it with gravitational-wave data, and not just because it’s the new cool thing to do (though it is!) but also because they gravitational waves give us insight into the strong-field regime of gravity where new things, if they are there at all, should show up. Now, all of this sounds great but, in practice, one has to deal with the actual model used to analyze the data. Errors in these signal models (aka waveforms), which are somewhat inevitable, can trick us into thinking we have seen a deviation from General Relativity. So, before you go out on the street and shout that Einstein was wrong, keep calm and mind your waveform. Christopher J. Moore, Eliot Finch, Riccardo Buscicchio, Davide Gerosa. iScience 24 (2021) 102577. arXiv:2103.16486 [gr-qc]. Other press coverage: indiescience, sciencedaily, phys.org, astronomy.com, physicsworld. ps. The codename for this paper was SANITY: SystemAtics usiNg populatIons to Test general relativitY. March 31, 2021 ## Group study on BH binaries in AGN disks This is a quick update some of our group activities… In the past few months we’ve been busy learning about the formation of stellar-mass black-hole binaries in the disks of active galactic nuclei. We organized a journal club and studied one paper each week on this “new” formation channel for LIGO sources. We discussed a ton of topics, going from disk accretion to migration traps, LIGO rates, AGN variability, GW counterparts, hierarchical mergers, all the way to EMRIs. Here is a log of all the sessions: davidegerosa.com/bhbin-agndisks Let me thanks all those who took part and presented papers including Daria, Matt (1), Chris, Eliot, Matt (2), Alberto, Evan, Riccardo, and Sean. March 9, 2021 ## A taxonomy of black-hole binary spin precession and nutation Here is the latest in our (by now long) series of papers on black-hole binaries spin precession. This work was is championed by two outstanding PhD students, Daria (in my group) and Nate (UT Dallas). The key idea behind this paper is that, for black-hole spins, one cannot really talk about precession without talking about nutation (although we only say “precession” all the time…). The spin of, say, the Earth also does both precession (azimuthal motion) and nutation (polar motion). But, unlike in the Earth problem, for black-hole spins the two motions happen on roughly the same timescale meaning that you cannot really take them apart. Or can you? We stress the role of five parameters that characterize the combined phenomenology of precession and nutation. The hope is now to use them as building blocks for future waveforms… stay tuned! Daria Gangardt, Nathan Steinle, Michael Kesden, Davide Gerosa, Evangelos Stoikos. Physical Review D 103 (2021) 124026. arXiv:2103.03894 [gr-qc]. ps. Stupid autocorrect! It’s nutation, not mutation. January 29, 2021 ## Eccentric binary black hole surrogate models for the gravitational waveform and remnant properties: comparable mass, nonspinning case Orbital eccentricity in gravitational-wave observations has been long neglected. And with good reasons! Gravitation-wave emission tends to circularize sources. By the time black holes are detectable by LIGO/Virgo/LISA/whatever, they should have had ample time to become circular. Unless something exciting goes on in their formation, things like clusters, triples, Kozai-Lidov oscillations, etc. And if that happens, we want to see it! This paper contains the first model for gravitational waveforms and black-hole remnants (final mass, spin) trained directly on eccentric numerical relativity simulations. Because eccentric is the new circular. Tousif Islam, Vijay Varma, Jackie Lodman, Scott E. Field, Gaurav Khanna, Mark A. Scheel, Harald P. Pfeiffer, Davide Gerosa, and Lawrence E. Kidder. Physical Review D 103 (2021) 064022. arXiv:2101.11798 [gr-qc]. January 22, 2021 ## HopBham! We are running a virtual workshop with my group (Bham) and Emanuele Berti’s group at Johns Hopkins University (Hop). It’s an attempt to feel a bit less lonely during the COVID pandemic. Hope this is the opportunity to start new projects! And we’re a funny crowd… For more: davidegerosa.com/hopbham-workshop/ December 15, 2020 ## Up-down instability of binary black holes in numerical relativity [Intro music…Now imagine one of those voices from a TV show trailer…] Up-down instability S01-E03. “Previously on the up-down instability. After finding out that the instability exists (S01-E01) and calculating its analytic endpoint (S01-E02), one terrifying prospect remains. What if it’s just PN? Can all of this disappear in the strong-field regime? This challenge now needs to be faced”. Today’s paper is the latest in our investigations of the up-down instability in binary black holes. If the primary black hole is aligned and the secondary is anti-aligned to the orbital angular momentum, the entire system is unstable to spin precession. We found this funny thing using a post-Newtonian (read: approximate) treatment but we couldn’t be 100% sure that this would still be true when the black holes merge and our approximation fails. So, we got our outstanding SXS friends on board and ask them if they could see the same effect with their numerical relativity (read: the real deal!) code. And the answer is… yes! The instability is really there! And by the way, these are among the longest numerical relativity simulations ever done. Vijay Varma, Matthew Mould, Davide Gerosa, Mark A. Scheel, Lawrence E. Kidder, Harald P. Pfeiffer. Physical Review D 103 (2021) 064003. arXiv:2012.07147 [gr-qc]. Supporting material available here. November 25, 2020 ## A generalized precession parameter chi_p to interpret gravitational-wave data Spin precession is cool, and we want to measure it. In General Relativity, the orbital plane of a binary is not fixed but moves around. This effect is related to the spin of the orbiting black holes and contains a ton of astrophysical information. The question we try to address in this paper is the following: how does one quantify “how much” precession a system has? This is typically done by condensing information into a parameter called $$\chi_{\rm p}$$, which is here generalize to include two- spin effects. There are two black holes in a binary and we received numerous complaints from the secondaries: they want to join the gravitational-wave fun! Davide Gerosa, Matthew Mould, Daria Gangardt, Patricia Schmidt, Geraint Pratten, Lucy M. Thomas. Physical Review D 103 (2021) 064067. arXiv:2011.11948 [gr-qc]. Open-source code: homepagerepository. November 16, 2020 ## Nicola joins the band It’s a great pleasure to welcome Nicola Giacobbo, who starts his postdoc with us today. Nicola completed his PhD and first postdoc year in Padova, and is an expert in population-synthesis simulations, compact binary progenitors, stellar physics, and all those funny things. Welcome Nicola! November 10, 2020 ## Inferring the properties of a population of compact binaries in presence of selection effects If you want to know what’s out there, you need to figure out what’s missing. And gravitational-wave astronomy is no exception. We are trying to infer how things like black holes and neutron stars behave in the Universe given a limited number of observations, which are somehow selected by our detectors. This is a very general problem which is common to a variety of fields of science. We provide a hopefully pedagogical introduction to population inference, deriving all the necessary statistics from the ground up. In other terms, here is what you always wanted to know about this population business everyone is talking about but never dared to ask. This document is going to be part of a truly massive “Handbook of Gravitational Wave Astronomy” soon to be published by Springer (not really a handbook I would say, you probably need a truck to carry it around). Salvatore Vitale, Davide Gerosa, Will M. Farr, Stephen R. Taylor. Chapter of “Handbook of Gravitational Wave Astronomy”; Springer Singapore (2021). arXiv:2007.05579 [astro-ph.IM]. September 25, 2020 I am truly honored to receive this year’s research prize of the Italian Culture Ministry and the Lincei National Academy. The prize is given to Italian researchers in various fields, and this year was awarded in the physical sciences. September 17, 2020 ## ERC Starting Grant I was awarded a Starting Grant from the European Research Council for my program titled “Gravitational-wave data mining”. My team and I will look into gravitational-wave data, machine-learning tools, black-hole binary dynamics, stellar-evolution simulations, etc. The total awarded amount is 1.5M EUR. Here is the press release from the Birmingham news office. Thank you Europe, you’re great. September 14, 2020 ## Daria’s PhD adventure starts here I am very happy to welcome Daria Gangardt back in my group. We worked together last summer for a short but successful summer project. Now Daria is starting her PhD. I’m honored we can be part together of the next great discoveries of our field September 11, 2020 ## Congrats to MSc students Congratulations to my Master’s students that graduate this year: Abdullah Aziz and Julian Chan from the University of Birmingham, and Beatrice Basset from the University of Lyon. Well done all, and good luck with your future adventures. July 30, 2020 ## Structure of neutron stars in massive scalar-tensor gravity And here is the latest episode in the series of our massive scalar-tensor gravity papers… After stellar collapse, we now look at how neutron stars look like in this strange theory of gravity (recap: “massive scalar-tensor” means that gravity is mediated by the usual metric plus a scalar field which as a mass). Result: not only the theory is strange, stars are strange too! If you want to get a neutron star of 40 solar masses, look no further, massive scalar-tensor is the theory for you. More seriously, we explore all the different families of static solutions, highlighting a remarkable phenomenology. This is the kind of predictions we need to test gravity with astrophysical sources! Roxana Rosca-Mead, Christopher J. Moore, Ulrich Sperhake, Michalis Agathos, Davide Gerosa. Symmetry 12 (2020) 1384. arXiv:2007.14429 [gr-qc] July 15, 2020 ## Gravitational-wave selection effects using neural-network classifiers And here is my latest lockdown effort: some experiments in the wonderful and perilous world of machine learning. The idea of this paper is to teach a computer to figure out by itself if a gravitational-wave signal will be detectable or not. The problem is very similar to that of image recognition: much like classifying if an image is more likely to contain a dog or a cat, here we classify black-hole mergers based on the imprints they have in the LIGO and Virgo detectors. This is important to quantify the so-called “selection effects”: in order to figure out what the Universe does based on what we observe, we need to know very well “how” we observe and thus what we are going to miss. Our code is built using Google’s TensorFlow and it is public on Github, feel free to play with it! Davide Gerosa, Geraint Pratten, Alberto Vecchio. Physical Review D 102 (2020) 103020. arXiv:2007.06585 [astro-ph.HE] Open-source code: homepage, repository. June 12, 2020 ## Massive black hole binary inspiral and spin evolution in a cosmological framework Supermassive black hole inspiral and spin evolution are deeply connected. In the early stages when black holes are brought together by star scattering and accretion, spin orientations can change because of interactions with the environment. Later on, when gravitational waves are driving the mergers, spins change because of relativistic couplings. In this paper we try to follow this complicated evolution in a full cosmological framework, using products of the Illustris simulation suite, a new sub-resolution model, and post-Newtonian integrations. Mohammad Sayeb, Laura Blecha, Luke Zoltan Kelley, Davide Gerosa, Michael Kesden, July Thomas. Monthly Notices of the Royal Astronomical Society 501 (2020) 2531–2546. arXiv:2006.06647 [astro-ph.GA]. May 20, 2020 ## Core collapse in massive scalar-tensor gravity If General Relativity is too boring, couple it to something else. In this paper we study what happens to stellar collapse and supernova explosions if gravity is transmitted not only with the usual metric of Einstein’s theory (aka the graviton) but also an additional quantity. If this extra scalar field has a mass, it dramatically impacts the emitted gravitational waves… Which means that maybe, one day, one can use gravitational-wave data to figure out if scalar fields are coupled to gravity. Here we try to explore all the related phenomenology of stellar collapse with a large set of simulations covering the parameter space. And the overall picture is remarkably neat and simple! Roxana Rosca-Mead, Ulrich Sperhake, Christopher J. Moore, Michalis Agathos, Davide Gerosa, Christian D. Ott. Physical Review D 102 (2020) 044010. arXiv:2005.09728 [gr-qc].	2022-07-01 05:30:13	{"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": 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": 0.3145124912261963, "perplexity": 2791.4638952920095}, "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-2022-27/segments/1656103920118.49/warc/CC-MAIN-20220701034437-20220701064437-00074.warc.gz"}
https://gmatclub.com/forum/pat-invested-x-dollars-in-a-fund-that-paid-8-percent-annual-interest-232518.html	GMAT Question of the Day - Daily to your Mailbox; hard ones only It is currently 19 Jun 2018, 22:34 ### 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 # Pat invested x dollars in a fund that paid 8 percent annual interest, Author Message TAGS: ### Hide Tags Math Expert Joined: 02 Sep 2009 Posts: 46176 Pat invested x dollars in a fund that paid 8 percent annual interest, [#permalink] ### Show Tags 20 Jan 2017, 07:08 00:00 Difficulty: 15% (low) Question Stats: 78% (00:41) correct 22% (00:41) wrong based on 67 sessions ### HideShow timer Statistics Pat invested x dollars in a fund that paid 8 percent annual interest, compounded annually. Which of the following represents the value, in dollars, of Pat's investment plus interest at the end of 5 years& A. 5(0.08x) B. 5(1.08x) C. (1+5(0.08))x D. (1.08)^5 x E. (1.08x)^5 _________________ Board of Directors Status: QA & VA Forum Moderator Joined: 11 Jun 2011 Posts: 3509 Location: India GPA: 3.5 Re: Pat invested x dollars in a fund that paid 8 percent annual interest, [#permalink] ### Show Tags 20 Jan 2017, 08:46 Bunuel wrote: Pat invested x dollars in a fund that paid 8 percent annual interest, compounded annually. Which of the following represents the value, in dollars, of Pat's investment plus interest at the end of 5 years& A. 5(0.08x) B. 5(1.08x) C. (1+5(0.08))x D. (1.08)^5 x E. (1.08x)^5 $$Amount = Principal ( 1 + \frac{Rate}{100})^{No \ of \ Years}$$ $$Amount = x ( 1 + \frac{8}{100})^5$$ $$Amount = x ( 1.08)^5$$ Hence, correct answer will be (D) $$x ( 1.08)^5$$ _________________ Thanks and Regards Abhishek.... PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS How to use Search Function in GMAT Club \| Rules for Posting in QA forum \| Writing Mathematical Formulas \|Rules for Posting in VA forum \| Request Expert's Reply ( VA Forum Only ) Intern Joined: 16 Oct 2017 Posts: 37 Re: Pat invested x dollars in a fund that paid 8 percent annual interest, [#permalink] ### Show Tags 11 Mar 2018, 13:12 Is that the formula for simple interest? I'm familiar with the compound interest formula, but never use this formula when the answer choices is an integer... usually, I just repeatedly multiply out... this question is an exception... BSchool Forum Moderator Joined: 26 Feb 2016 Posts: 2820 Location: India GPA: 3.12 Pat invested x dollars in a fund that paid 8 percent annual interest, [#permalink] ### Show Tags 11 Mar 2018, 13:31 OCDianaOC wrote: Is that the formula for simple interest? I'm familiar with the compound interest formula, but never use this formula when the answer choices is an integer... usually, I just repeatedly multiply out... this question is an exception... Hi OCDianaOC This is the formula for compound interest when done yearly $$A = P(1 + \frac{r}{100})^{n}$$ where n - number of years r - rate of interest A - Amount realized at the end of n years P - Principal invested initially Coming back to this problem Pat invests x(Principal) at 8%(R) for 5(n) years Therefore, Amount = x$$(1 + \frac{8}{100})^5$$ = x*$$(1.08)^5$$(Option D) _________________ You've got what it takes, but it will take everything you've got Intern Joined: 16 Oct 2017 Posts: 37 Re: Pat invested x dollars in a fund that paid 8 percent annual interest, [#permalink] ### Show Tags 11 Mar 2018, 14:20 Thank you! In that case, learning the simple interest formula isn't necessary for the GMAT, right? For simple interest questions, there is never the formula in the answer choices, always an integer instead? Board of Directors Status: QA & VA Forum Moderator Joined: 11 Jun 2011 Posts: 3509 Location: India GPA: 3.5 Re: Pat invested x dollars in a fund that paid 8 percent annual interest, [#permalink] ### Show Tags 12 Mar 2018, 09:56 OCDianaOC wrote: Thank you! In that case, learning the simple interest formula isn't necessary for the GMAT, right? For simple interest questions, there is never the formula in the answer choices, always an integer instead? Both are necessary, please go through this link to clear the concept https://magoosh.com/gre/2012/compound-i ... n-the-gre/ _________________ Thanks and Regards Abhishek.... PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS How to use Search Function in GMAT Club \| Rules for Posting in QA forum \| Writing Mathematical Formulas \|Rules for Posting in VA forum \| Request Expert's Reply ( VA Forum Only ) Re: Pat invested x dollars in a fund that paid 8 percent annual interest, [#permalink] 12 Mar 2018, 09:56 Display posts from previous: Sort by	2018-06-20 05:34:37	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 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": 0.6681894063949585, "perplexity": 9060.59890774769}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-26/segments/1529267863463.3/warc/CC-MAIN-20180620050428-20180620070428-00478.warc.gz"}
https://byjus.com/rd-sharma-solutions/class-11-maths-chapter-6-graphs-of-trigonometric-functions/	# RD Sharma Solutions Class 11 Graphs Of Trigonometric Functions ## RD Sharma Solutions Class 11 Chapter 6 A graph of Sine function is a continuous wave that keeps on repeating itself. The domain of the sine function comprises of real numbers in radians, therefore curves have no holes or breaks. Just like other functions in algebra, it is possible to translate and transform trig functions. Consider the basic function $f(t)=sin(t)$,, in this function the amplitude of one has graph goes one unit down and one unit up from the midline of the graph. Now explore in depth about graphs of Trigonometric functions through RD Sharma Solutions for class 11. In this section, students will have an easy access to exercise wise solved question and answers. Chapter 6 Graphs of Trigonometric Functions Graphs of Trigonometric Functions Exercise 6.1 Graphs of Trigonometric Functions Exercise 6.2 Graphs of Trigonometric Functions Exercise 6.3 #### Practise This Question The digits 1, 2, 3.... 9 are arranged in a random order, find the probability that 1, 2, 3 will appear as neighbors in the order mentioned.	2019-06-18 22:44:27	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 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": 0.40849846601486206, "perplexity": 723.5301159150348}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-26/segments/1560627998844.16/warc/CC-MAIN-20190618223541-20190619005541-00228.warc.gz"}
https://papers.nips.cc/paper/9181-on-robustness-of-principal-component-regression	# NIPS Proceedingsβ ## On Robustness of Principal Component Regression [PDF] [BibTeX] [Supplemental] [Reviews] [Author Feedback] [Meta Review] [Sourcecode] ### Abstract Consider the setting of Linear Regression where the observed response variables, in expectation, are linear functions of the p-dimensional covariates. Then to achieve vanishing prediction error, the number of required samples scales faster than pσ2, where σ2 is a bound on the noise variance. In a high-dimensional setting where p is large but the covariates admit a low-dimensional representation (say r ≪ p), then Principal Component Regression (PCR), cf. [36], is an effective approach; here, the response variables are regressed with respect to the principal components of the covariates. The resulting number of required samples to achieve vanishing prediction error now scales faster than rσ2(≪ pσ2). Despite the tremendous utility of PCR, its ability to handle settings with noisy, missing, and mixed (discrete and continuous) valued covariates is not understood and remains an important open challenge, cf. [24]. As the main contribution of this work, we address this challenge by rigorously establishing that PCR is robust to noisy, sparse, and possibly mixed valued covariates. Specifically, under PCR, vanishing prediction error is achieved with the number of samples scaling as r max(σ2, ρ−4 log5(p)), where ρ denotes the fraction of observed (noisy) covariates. We establish generalization error bounds on the performance of PCR, which provides a systematic approach in selecting the correct number of components r in a data-driven manner. The key to our result is a simple, but powerful equivalence between (i) PCR and (ii) Linear Regression with covariate pre-processing via Hard Singular Value Thresholding (HSVT). From a technical standpoint, this work advances the state-of-the-art analysis for HSVT by establishing stronger guarantees with respect to the ∥·∥2,∞-error for the estimated matrix rather than the Frobenius norm/mean-squared error (MSE) as is commonly done in the matrix estimation / completion literature.	2020-08-03 18:51:47	{"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": 0.8314943909645081, "perplexity": 1534.3338542545655}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-34/segments/1596439735823.29/warc/CC-MAIN-20200803170210-20200803200210-00588.warc.gz"}
https://socratic.org/questions/560f3512581e2a5c2e851d24	# What are imaginary numbers? Oct 3, 2015 The Real numbers can be represented as a line. The Complex numbers can be represented by a plane whose $x$ axis is the Real numbers. Imaginary numbers are the numbers on the $y$ axis of that plane. #### Explanation: Suppose we start with Whole numbers $0 , 1 , 2 , 3 , \ldots$ We can add them them quite happily and we always get another Whole number. We can solve problems like $x + 2 = 5$, but when we try to solve problems like $x + 5 = 2$ we find our Whole numbers are insufficient. So we can introduce the idea of a negative number and expand our idea of what a number is to include all of the Integers: $\mathbb{Z} = \left\{0 , 1 , - 1 , 2 , - 2 , 3 , - 3 , \ldots\right\}$ We can add and multiply any two Integers and we always get an Integer. We can solve problems like $2 x + 6 = 0$, but when we try to solve problems like $6 x + 2 = 0$ we find our Integers are insufficient. So we can introduce the idea of a Rational number and expand our idea of what a number is to include all numbers of the form $\frac{m}{n}$ where $m , n \in \mathbb{Z}$ and $n \ne 0$. ... To cut a long story short, in order to be able to solve problems like ${x}^{2} + 1 = 0$ we introduce the imaginary unit $i$, with the property ${i}^{2} = - 1$. A square root of a negative Real number is a pure imaginary number. In fact, we define the principal square root of a negative Real number as: $\sqrt{x} = i \sqrt{- x}$ Any Complex number $z \in \mathbb{C}$ can be represented as $z = a + i b$ where $a$ and $b$ are Real numbers. $a$ is called the Real part of $z$ and $i b$ the Imaginary part. This can be pictured as the point $\left(a , b\right)$ on a plane. Please note that Imaginary numbers are no more imaginary than Real numbers. Sir Isaac Newton seemed to dislike working with negative numbers, which he called "imaginary" numbers.	2021-09-26 09:37:43	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 23, "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": 0.7760036587715149, "perplexity": 130.6903750251209}, "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/1631780057857.27/warc/CC-MAIN-20210926083818-20210926113818-00422.warc.gz"}
https://plainmath.net/7772/solve-equations-inequalities-solution-inequalities-interval-notation	# Solve the equations and inequalities. Write the solution sets to the inequalities in interval notation. 5<=3+\|2x-7\| Question Solve the equations and inequalities. Write the solution sets to the inequalities in interval notation. $$\displaystyle{5}\le{3}+{\left\|{2}{x}-{7}\right\|}$$ 2020-12-17 Simplify the give expression as follows. $$\displaystyle{3}+{\left\|{2}{x}-{7}\right\|}\ge{5}$$ $$\displaystyle{3}+{\left\|{2}{x}-{7}\right\|}-{3}\ge{5}-{3}$$ (subtract 3 from both sides) $$\displaystyle{\left\|{2}{x}-{7}\right\|}\ge{2}$$ by the absolute rule, if $$\displaystyle{\left\|{u}\right\|}\ge{a}$$, a>0 then $$\displaystyle{\left\|{u}\right\|}\le-{a}{\quad\text{and}\quad}{\left\|{u}\right\|}\ge{a}$$ $$\displaystyle{2}{x}-{7}\le-{2}{\quad\text{and}\quad}{2}{x}-{7}\ge{2}$$ ($$\displaystyle\because$$ by absolute rule) $$\displaystyle{2}{x}-{7}+{7}\le-{2}{\quad\text{and}\quad}{2}{x}-{7}+{7}\ge{2}+{7}$$ (add 7 on both sides) $$\displaystyle\frac{{{2}{x}}}{{2}}\le\frac{{5}}{{2}}{\quad\text{and}\quad}\frac{{{2}{x}}}{{2}}\ge\frac{{9}}{{2}}$$ (divie by 2 onn both sides) $$\displaystyle{x}\le\frac{{5}}{{2}}{\quad\text{and}\quad}{x}\ge\frac{{9}}{{2}}$$ Therefore, the solution set of the given inequaliry is $$\displaystyle{\left(-\infty,\frac{{5}}{{2}}\right]}\cup{\left[\frac{{9}}{{2}},\infty\right)}$$. ### Relevant Questions Solve the equations and inequalities. Write the solution sets to the inequalities in interval notation. $$−x^{3}−5x^{2}+4x+20<0$$ Solve the equations and inequalities. Write the solution sets to the inequalities in interval notation. $$\displaystyle−{x}^{{{3}}}−{5}{x}^{{{2}}}+{4}{x}+{20}{<}{0}$$ Solve the equations and inequalities. Write the solution sets to the inequalities in interval notation. $$\displaystyle{\log{{2}}}{\left({3}{x}−{1}\right)}={\log{{2}}}{\left({x}+{1}\right)}+{3}$$ Solve the equations and inequalities. Write the solution sets to the inequalities in interval notation. $$5\leq3+∣2x−7∣5\leq3+∣2x−7∣$$ Solve the equations and inequalities. Write the solution sets to the inequalities in interval notation. $$3x(x−1)=x+63x(x−1)=x+6$$ Solve the equations and inequalities. Write the solution sets to the inequalities in interval notation. $$9^{2m−3}=27^{m+1}$$ Solve the equations and inequalities. Write the solution sets to the inequalities in interval notation. $$∣5x−1∣=∣3−4x∣∣5x−1∣=∣3−4x∣$$ Solve the equations and inequalities. Write the solution sets to the inequalities in interval notation. $$(x^{2}−9)^{2}−2(x^{2}−9)−35=0$$ Solve the equations and inequalities. Write the solution sets to the inequalities in interval notation. $$\frac{(x−4)}{(x+2)}\leq 0$$ Solve the equations and inequalities. Write the solution sets to the inequalities in interval notation. $$\displaystyle{5}\leq{3}+∣{2}{x}−{7}∣{5}\leq{3}+∣{2}{x}−{7}∣$$	2021-05-13 12:03:09	{"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": 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": 0.9719251394271851, "perplexity": 716.1183610242911}, "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/1620243989916.34/warc/CC-MAIN-20210513111525-20210513141525-00616.warc.gz"}
https://www.jobilize.com/online/course/4-3-multiply-and-divide-mixed-numbers-and-complex-fractions-by-opensta?qcr=www.quizover.com&page=1	# 4.3 Multiply and divide mixed numbers and complex fractions (Page 2/4) Page 2 / 4 Translate the phrase into an algebraic expression: “the quotient of $3x$ and $8.”$ ## Solution The keyword is quotient ; it tells us that the operation is division. Look for the words of and and to find the numbers to divide. $\text{The quotient}\phantom{\rule{0.2em}{0ex}}\text{of}\phantom{\rule{0.2em}{0ex}}3x\phantom{\rule{0.2em}{0ex}}\text{and}\phantom{\rule{0.2em}{0ex}}8\text{.}$ This tells us that we need to divide $3x$ by $8.$ $\frac{3x}{8}$ Translate the phrase into an algebraic expression: the quotient of $9s$ and $14.$ $\frac{9s}{14}$ Translate the phrase into an algebraic expression: the quotient of $5y$ and $6.$ $\frac{5y}{6}$ Translate the phrase into an algebraic expression: the quotient of the difference of $m$ and $n,$ and $p.$ ## Solution We are looking for the quotient of the difference of $m$ and , and $p.$ This means we want to divide the difference of $m$ and $n$ by $p.$ $\frac{m-n}{p}$ Translate the phrase into an algebraic expression: the quotient of the difference of $a$ and $b,$ and $cd.$ $\frac{a-b}{cd}$ Translate the phrase into an algebraic expression: the quotient of the sum of $p$ and $q,$ and $r.$ $\frac{p+q}{r}$ ## Simplify complex fractions Our work with fractions so far has included proper fractions, improper fractions, and mixed numbers. Another kind of fraction is called complex fraction , which is a fraction in which the numerator or the denominator contains a fraction. Some examples of complex fractions are: $\frac{\phantom{\rule{0.2em}{0ex}}\frac{6}{7}\phantom{\rule{0.2em}{0ex}}}{\phantom{\rule{0.2em}{0ex}}3\phantom{\rule{0.2em}{0ex}}}\phantom{\rule{1.8em}{0ex}}\frac{\phantom{\rule{0.2em}{0ex}}\frac{3}{4}\phantom{\rule{0.2em}{0ex}}}{\phantom{\rule{0.2em}{0ex}}\frac{5}{8}\phantom{\rule{0.2em}{0ex}}}\phantom{\rule{1.8em}{0ex}}\frac{\phantom{\rule{0.2em}{0ex}}\frac{x}{2}\phantom{\rule{0.2em}{0ex}}}{\phantom{\rule{0.2em}{0ex}}\frac{5}{6}\phantom{\rule{0.2em}{0ex}}}$ To simplify a complex fraction, remember that the fraction bar means division. So the complex fraction $\frac{\phantom{\rule{0.2em}{0ex}}\frac{3}{4}\phantom{\rule{0.2em}{0ex}}}{\phantom{\rule{0.2em}{0ex}}\frac{5}{8}\phantom{\rule{0.2em}{0ex}}}$ can be written as $\frac{3}{4}÷\frac{5}{8}.$ Simplify: $\frac{\phantom{\rule{0.2em}{0ex}}\frac{3}{4}\phantom{\rule{0.2em}{0ex}}}{\phantom{\rule{0.2em}{0ex}}\frac{5}{8}\phantom{\rule{0.2em}{0ex}}}.$ ## Solution $\frac{\phantom{\rule{0.2em}{0ex}}\frac{3}{4}\phantom{\rule{0.2em}{0ex}}}{\phantom{\rule{0.2em}{0ex}}\frac{5}{8}\phantom{\rule{0.2em}{0ex}}}$ Rewrite as division. $\frac{3}{4}÷\frac{5}{8}$ Multiply the first fraction by the reciprocal of the second. $\frac{3}{4}·\frac{8}{5}$ Multiply. $\frac{3·8}{4·5}$ Look for common factors. $\frac{3·4̸·2}{4̸·5}$ Remove common factors and simplify. $\frac{6}{5}$ Simplify: $\frac{\phantom{\rule{0.2em}{0ex}}\frac{2}{3}\phantom{\rule{0.2em}{0ex}}}{\phantom{\rule{0.2em}{0ex}}\frac{5}{6}\phantom{\rule{0.2em}{0ex}}}.$ $\frac{4}{5}$ Simplify: $\frac{\phantom{\rule{0.2em}{0ex}}\frac{3}{7}\phantom{\rule{0.2em}{0ex}}}{\phantom{\rule{0.2em}{0ex}}\frac{6}{11}\phantom{\rule{0.2em}{0ex}}}.$ $\frac{11}{14}$ ## Simplify a complex fraction. 1. Rewrite the complex fraction as a division problem. 2. Follow the rules for dividing fractions. 3. Simplify if possible. Simplify: $\frac{-\frac{6}{7}}{3}.$ ## Solution $\frac{-\frac{6}{7}}{3}$ Rewrite as division. $-\frac{6}{7}÷3$ Multiply the first fraction by the reciprocal of the second. $-\frac{6}{7}·\frac{1}{3}$ Multiply; the product will be negative. $-\frac{6·1}{7·3}$ Look for common factors. $-\frac{3̸·2·1}{7·3̸}$ Remove common factors and simplify. $-\frac{2}{7}$ Simplify: $\frac{-\frac{8}{7}}{4}.$ $-\frac{2}{7}$ Simplify: $-\frac{\phantom{\rule{0.2em}{0ex}}3\phantom{\rule{0.2em}{0ex}}}{\phantom{\rule{0.2em}{0ex}}\frac{9}{10}\phantom{\rule{0.2em}{0ex}}}.$ $-\frac{10}{3}$ Simplify: $\frac{\phantom{\rule{0.2em}{0ex}}\frac{x}{2}\phantom{\rule{0.2em}{0ex}}}{\phantom{\rule{0.2em}{0ex}}\frac{xy}{6}\phantom{\rule{0.2em}{0ex}}}.$ ## Solution $\frac{\phantom{\rule{0.2em}{0ex}}\frac{x}{2}\phantom{\rule{0.2em}{0ex}}}{\phantom{\rule{0.2em}{0ex}}\frac{xy}{6}\phantom{\rule{0.2em}{0ex}}}$ Rewrite as division. $\frac{x}{2}÷\frac{xy}{6}$ Multiply the first fraction by the reciprocal of the second. $\frac{x}{2}·\frac{6}{xy}$ Multiply. $\frac{x·6}{2·xy}$ Look for common factors. $\frac{\mathrm{x̸}·3·2̸}{2̸·\mathrm{x̸}·y}$ Remove common factors and simplify. $\frac{3}{y}$ Simplify: $\frac{\phantom{\rule{0.2em}{0ex}}\frac{a}{8}\phantom{\rule{0.2em}{0ex}}}{\phantom{\rule{0.2em}{0ex}}\frac{ab}{6}\phantom{\rule{0.2em}{0ex}}}.$ $\frac{3}{4b}$ Simplify: $\frac{\phantom{\rule{0.2em}{0ex}}\frac{p}{2}\phantom{\rule{0.2em}{0ex}}}{\phantom{\rule{0.2em}{0ex}}\frac{pq}{8}\phantom{\rule{0.2em}{0ex}}}.$ $\frac{4}{q}$ Simplify: $\frac{2\frac{3}{4}}{\frac{1}{8}}.$ ## Solution $\frac{2\frac{3}{4}}{\frac{1}{8}}$ Rewrite as division. $2\frac{3}{4}÷\frac{1}{8}$ Change the mixed number to an improper fraction. $\frac{11}{4}÷\frac{1}{8}$ Multiply the first fraction by the reciprocal of the second. $\frac{11}{4}·\frac{8}{1}$ Multiply. $\frac{11·8}{4·1}$ Look for common factors. $\frac{11·4̸·2}{4̸·1}$ Remove common factors and simplify. $22$ Simplify: $\frac{\frac{5}{7}}{1\frac{2}{5}}.$ $\frac{25}{49}.$ Simplify: $\frac{\frac{8}{5}}{3\frac{1}{5}}.$ $\frac{1}{2}$ ## Simplify expressions with a fraction bar Where does the negative sign go in a fraction? Usually, the negative sign is placed in front of the fraction, but you will sometimes see a fraction with a negative numerator or denominator. Remember that fractions represent division. The fraction $-\frac{1}{3}$ could be the result of dividing $\frac{-1}{3},$ a negative by a positive, or of dividing $\frac{1}{-3},$ a positive by a negative. When the numerator and denominator have different signs, the quotient is negative. If both the numerator and denominator are negative, then the fraction itself is positive because we are dividing a negative by a negative. what is Nano technology ? write examples of Nano molecule? Bob The nanotechnology is as new science, to scale nanometric brayan nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale Damian Is there any normative that regulates the use of silver nanoparticles? what king of growth are you checking .? Renato What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ? why we need to study biomolecules, molecular biology in nanotechnology? ? Kyle yes I'm doing my masters in nanotechnology, we are being studying all these domains as well.. why? what school? Kyle biomolecules are e building blocks of every organics and inorganic materials. Joe anyone know any internet site where one can find nanotechnology papers? research.net kanaga sciencedirect big data base Ernesto Introduction about quantum dots in nanotechnology what does nano mean? nano basically means 10^(-9). nanometer is a unit to measure length. Bharti do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment? absolutely yes Daniel how to know photocatalytic properties of tio2 nanoparticles...what to do now it is a goid question and i want to know the answer as well Maciej Abigail for teaching engĺish at school how nano technology help us Anassong Do somebody tell me a best nano engineering book for beginners? there is no specific books for beginners but there is book called principle of nanotechnology NANO what is fullerene does it is used to make bukky balls are you nano engineer ? s. fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball. Tarell what is the actual application of fullerenes nowadays? Damian That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes. Tarell what is the Synthesis, properties,and applications of carbon nano chemistry Mostly, they use nano carbon for electronics and for materials to be strengthened. Virgil is Bucky paper clear? CYNTHIA carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc NANO so some one know about replacing silicon atom with phosphorous in semiconductors device? Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure. Harper Do you know which machine is used to that process? s. how to fabricate graphene ink ? for screen printed electrodes ? SUYASH What is lattice structure? of graphene you mean? Ebrahim or in general Ebrahim in general s. Graphene has a hexagonal structure tahir On having this app for quite a bit time, Haven't realised there's a chat room in it. Cied A soccer field is a rectangle 130 meters wide and 110 meters long. The coach asks players to run from one corner to the other corner diagonally across. What is that distance, to the nearest tenths place. Jeannette has $5 and$10 bills in her wallet. The number of fives is three more than six times the number of tens. Let t represent the number of tens. Write an expression for the number of fives. What is the expressiin for seven less than four times the number of nickels How do i figure this problem out. how do you translate this in Algebraic Expressions why surface tension is zero at critical temperature Shanjida I think if critical temperature denote high temperature then a liquid stats boils that time the water stats to evaporate so some moles of h2o to up and due to high temp the bonding break they have low density so it can be a reason s. Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)= . After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?	2019-10-18 07:08:27	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 80, "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": 0.7670285105705261, "perplexity": 1806.6308660171526}, "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-2019-43/segments/1570986677964.40/warc/CC-MAIN-20191018055014-20191018082514-00351.warc.gz"}
https://3dprinting.stackexchange.com/questions/13530/how-can-i-determine-the-current-value-of-a-defined-variable	# How can I determine the current value of a #defined variable? I previously set up my Ender 3 with a precompiled binary of Marlin that already had the correct X and Y offsets for the attached BLTouch. Now I'm compiling my own, and rather than measure for myself I'd like to just use the same numbers. When I send M851 through the terminal, it gives me the current value for the probe's Z offset from the extruder. I know I can also use M851 to set the X and Y offset, but there doesn't seem to be a way to read the current values. Is there any way to query the printer for the current values of X_PROBE_OFFSET_FROM_EXTRUDER and Y_PROBE_OFFSET_FROM_EXTRUDER? Or, ideally, for any other arbitrary variable?	2022-05-26 23:20:59	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5544483065605164, "perplexity": 744.0703752233405}, "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/1652662627464.60/warc/CC-MAIN-20220526224902-20220527014902-00020.warc.gz"}
http://mathhelpforum.com/pre-calculus/222398-find-all-possible-values-inequality-print.html	# Find all possible values for the inequality. • Sep 29th 2013, 03:21 PM turbozz Find all possible values for the inequality. Question: What are the possible values of \|2x3\| when 0<\|x1\|<2? My solution: We know x1 becomes x-1 if x-1≥0 and -(x-1) if x-1<0. Now consider two cases. Case 1: 0<x-1<2 1<x<3 -1<2x-3<3. Case 2: 0<-x+1<2 -1<x<1 -2<2x<2 -5<2x-3<-1 Then the possible value include \|2x-3\|<3. Am I solving this problem correctly ?? Note, -5<\|2x-3\|<-1 would not work since the \|2x-3\| is bounded between two negative values. Am I solving this problem correctly ?? The solution seems so incomplete? • Sep 29th 2013, 04:59 PM HallsofIvy Re: Find all possible values for the inequality. If 0< \|x- 2\|< 2 then -2< x- 2< 2 (with $x- 2\ne 0$). Adding 2 to each part, 0< x< 4 (with $x\ne 2$). Multiplying by 2, 0< 2x< 8 (with $2x\ne 4$). Subtracting 3, -3< 2x- 3< 5 (with 2x- 3\ne 1). That is, if 0< \|x- 2\|< 2, 2x- 3 can be any number strictly between -3 and 5, except 1. • Sep 29th 2013, 05:11 PM chiro Re: Find all possible values for the inequality. Hey turbozz. Take a look at this thread: http://mathhelpforum.com/calculus/22...conundrum.html • Sep 29th 2013, 05:13 PM Soroban Re: Find all possible values for the inequality. Hello, turbozz! Quote: $\text{What are the possible values of }\|2x-3\|\,\text{ when }\,0 < \|x-1\| < 2\,?$ $\begin{array}{ccccccc}\text{Given: } & 0 & < & \|x-1\| & < & 2 \\ \\ \text{Then:} & \text{-}2 & < & x-1 & < & 2 \\ \\ \text{Add 1:} & \text{-}1 & < & x & < & 3 \\ \\ \text{Times 2} & \text{-}2 & < & 2x & < & 6 \\ \\ \text{Minus 3:} & \text{-}5 &<& 2x-3 &<& 3 \end{array}$ • Sep 29th 2013, 05:19 PM turbozz Re: Find all possible values for the inequality. Quote: Originally Posted by HallsofIvy If 0< \|x- 2\|< 2 then -2< x- 2< 2 (with $x- 2\ne 0$). Adding 2 to each part, 0< x< 4 (with $x\ne 2$). Multiplying by 2, 0< 2x< 8 (with $2x\ne 4$). Subtracting 3, -3< 2x- 3< 5 (with 2x- 3\ne 1). That is, if 0< \|x- 2\|< 2, 2x- 3 can be any number strictly between -3 and 5, except 1. I don't understand why your using 0<\|x-2\|<2 ?? How does this relate to the inequality at hand? • Sep 29th 2013, 05:23 PM turbozz Re: Find all possible values for the inequality. Quote: Originally Posted by Soroban Hello, turbozz! $\begin{array}{ccccccc}\text{Given: } & 0 & < & \|x-1\| & < & 2 \\ \\ \text{Then:} & \text{-}2 & < & x-1 & < & 2 \\ \\ \text{Add 1:} & \text{-}1 & < & x & < & 3 \\ \\ \text{Times 2} & \text{-}2 & < & 2x & < & 6 \\ \\ \text{Minus 3:} & \text{-}5 &<& 2x-3 &<& 3 \end{array}$ how to do go from 0 <\|x-1\|<2 to -2<x-1<2 ? And x=1 wouldn't work since it wouldn't satisfy 0<\|x-1\|<2. • Sep 29th 2013, 11:50 PM Prove It Re: Find all possible values for the inequality. Quote: Originally Posted by turbozz Question: What are the possible values of \|2x3\| when 0<\|x1\|<2? My solution: We know x1 becomes x-1 if x-1≥0 and -(x-1) if x-1<0. Now consider two cases. Case 1: 0<x-1<2 1<x<3 -1<2x-3<3. Case 2: 0<-x+1<2 -1<x<1 -2<2x<2 -5<2x-3<-1 Then the possible value include \|2x-3\|<3. Am I solving this problem correctly ?? Note, -5<\|2x-3\|<-1 would not work since the \|2x-3\| is bounded between two negative values. Am I solving this problem correctly ?? The solution seems so incomplete? The triangle inequality works nicely here to get an upper bound: \displaystyle \begin{align} \|a + b\| \leq \|a\| + \|b\| \end{align} So \displaystyle \begin{align} \|2x - 3\| &= \|2x - 2 - 1\| \\ &\leq \|2x - 2\| + \|-1\| \\ &= 2\|x - 1\| + 1 \\ &< 2(2) + 1 \textrm{ since } \|x - 1\| < 2 \\ &= 5 \end{align} So we can say \displaystyle \begin{align} \|2x - 3\| < 5 \end{align}. Also, the reverse triangle inequality is useful here to get a lower bound. \displaystyle \begin{align} \left\| \|a\| - \|b\| \right\| \leq \|a - b\| \end{align}. So that means \displaystyle \begin{align} \|2x - 3\| &= \|2x - 2 - 1\| \\ &\geq \left\| \|2x - 2\| - \|1\| \right\| \textrm{ by the Reverse Triangle Inequality} \\ &= \left\| 2\|x - 1\| - 1 \right\| \\ &> \left\| 2(0) - 1 \right\| \textrm{ since } \|x - 1\| > 0 \\ &= \|-1\| \\ &= 1 \end{align} So that means we have \displaystyle \begin{align} 1 < \|2x - 3\| < 5 \end{align}. • Sep 30th 2013, 03:48 AM Plato Re: Find all possible values for the inequality. Quote: Originally Posted by turbozz Question: What are the possible values of \|2x−3\| when 0<\|x−1\|<2? This question and the resulting discussion need a comment on the logic of the question. In my view reply #4 is correct. Here is the reason. This is a simple implication, an if-then question. If $0<\|x-1\|<2$ then what are the possible values of $\|2 x-3\|~?$ If $P$ is true then $Q$ must be true. Note that means that if $0<\|x-1\|<2$ then $\|2x-3\|<5$. If $a=1.5$ then $0<\|a-1\|<2$ as well as $\|2a-3\|=0<5$ Note that if $0<\|x-1\|<2$ it is possible that $\|2x-3\|<1$, example $x=1.8$. It is also worth noting that if $x=1$ then $0<\|x-1\|<2$ is a false statement. BUT that means that if $0<\|x-1\|<2$ then $\|2x-3\|<5$ is still a true statement. • Sep 30th 2013, 06:24 AM turbozz Re: Find all possible values for the inequality. Quote: Originally Posted by Prove It The triangle inequality works nicely here to get an upper bound: \displaystyle \begin{align} \|a + b\| \leq \|a\| + \|b\| \end{align} So \displaystyle \begin{align} \|2x - 3\| &= \|2x - 2 - 1\| \\ &\leq \|2x - 2\| + \|-1\| \\ &= 2\|x - 1\| + 1 \\ &< 2(2) + 1 \textrm{ since } \|x - 1\| < 2 \\ &= 5 \end{align} So we can say \displaystyle \begin{align} \|2x - 3\| < 5 \end{align}. Also, the reverse triangle inequality is useful here to get a lower bound. \displaystyle \begin{align} \left\| \|a\| - \|b\| \right\| \leq \|a - b\| \end{align}. So that means \displaystyle \begin{align} \|2x - 3\| &= \|2x - 2 - 1\| \\ &\geq \left\| \|2x - 2\| - \|1\| \right\| \textrm{ by the Reverse Triangle Inequality} \\ &= \left\| 2\|x - 1\| - 1 \right\| \\ &> \left\| 2(0) - 1 \right\| \textrm{ since } \|x - 1\| > 0 \\ &= \|-1\| \\ &= 1 \end{align} So that means we have \displaystyle \begin{align} 1 < \|2x - 3\| < 5 \end{align}. I like the way you showed the solution a lot. Only one issue though shouldn't 0<\|2x-3\|<5 ? • Sep 30th 2013, 12:43 PM Plato Re: Find all possible values for the inequality. Quote: Originally Posted by turbozz Only one issue though shouldn't 0<\|2x-3\|<5 ? The answer is $\|2x-3\|<5$. Look at this: $0<\|1.5-1\|<2$ and $0=\|2(1.5)-3\|<5$.	2016-10-25 05:17:14	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 40, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 1.000008463859558, "perplexity": 1425.5387645735827}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-44/segments/1476988719908.93/warc/CC-MAIN-20161020183839-00223-ip-10-171-6-4.ec2.internal.warc.gz"}
https://zbmath.org/?q=an:07268500	# zbMATH — the first resource for mathematics The range of all regularities for polynomial ideals with a given Hilbert function. (English) Zbl 07268500 Summary: Let $$A$$ denote any polynomial ring over a field $$K$$ and $$I$$ any homogeneous ideal of $$A$$. In this paper it is proven that, given an Hilbert function $$u$$, the set of the regularities of the homogeneous ideals $$I$$ such that the $$K$$-algebra $$A / I$$ has Hilbert function $$u$$ is an interval of integers. This result is achieved by means of constructive arguments related to the minimal functions with a given Hilbert polynomial and a given regularity. ##### MSC: 13P99 Computational aspects and applications of commutative rings 14Q99 Computational aspects in algebraic geometry 68W30 Symbolic computation and algebraic computation 11Y55 Calculation of integer sequences CoCoA Full Text: ##### References: [1] Abbott, J.; Bigatti, A. M.; Robbiano, L., CoCoA: a system for doing computations in commutative algebra, available at [2] Bigatti, Anna Maria, Upper bounds for the Betti numbers of a given Hilbert function, Commun. Algebra, 21, 7, 2317-2334 (1993) · Zbl 0817.13007 [3] Bruns, Winfried; Herzog, Jürgen, Cohen-Macaulay Rings, Cambridge Studies in Advanced Mathematics, vol. 39 (1993), Cambridge University Press: Cambridge University Press Cambridge · Zbl 0788.13005 [4] Caviglia, Giulio; Sbarra, Enrico, Zero-generic initial ideals, Manuscr. Math., 148, 3-4, 507-520 (2015) · Zbl 1329.13045 [5] Chardin, Marc; Moreno-Socías, Guillermo, Regularity of lex-segment ideals: some closed formulas and applications, Proc. Am. Math. Soc., 131, 4, 1093-1102 (2003) · Zbl 1036.13014 [6] Cioffi, F.; Lella, P.; Marinari, M. G.; Roggero, M., Minimal Castelnuovo-Mumford regularity for a given Hilbert polynomial, Exp. Math., 24, 4, 424-437 (2015) · Zbl 1333.13028 [7] Dung, Le Xuan; Hoa, Le Tuan, A note on Castelnuovo-Mumford regularity and Hilbert coefficients, J. Algebra Appl., 18, 10, Article 1950191 pp. (2019) · Zbl 1423.13094 [8] Eisenbud, David, Commutative Algebra, Graduate Texts in Mathematics, vol. 150 (1995), Springer-Verlag: Springer-Verlag New York, With a view toward algebraic geometry · Zbl 0819.13001 [9] Green, Mark L., Generic initial ideals, (Six Lectures on Commutative Algebra. Six Lectures on Commutative Algebra, Mod. Birkhäuser Class. (2010), Birkhäuser Verlag: Birkhäuser Verlag Basel), 119-186 · Zbl 0933.13002 [10] Hoa, Le Tuan, Castelnuovo-Mumford regularity (2018), available at · Zbl 0816.14023 [11] Hulett, Heather A., Maximum Betti numbers of homogeneous ideals with a given Hilbert function, Commun. Algebra, 21, 7, 2335-2350 (1993) · Zbl 0817.13006 [12] Kreuzer, Martin; Robbiano, Lorenzo, Computational Commutative Algebra. 2 (2005), Springer-Verlag: Springer-Verlag Berlin · Zbl 1090.13021 [13] Mall, Daniel, Betti numbers, Castelnuovo Mumford regularity, and generalisations of Macaulay’s theorem, Commun. Algebra, 25, 12, 3841-3852 (1997) · Zbl 0908.13007 [14] Pardue, Keith, Nonstandard Borel-fixed ideals (1994), ProQuest LLC: ProQuest LLC Ann Arbor, MI, Thesis (Ph.D.)-Brandeis University [15] Roberts, Leslie G., Hilbert polynomials and minimum Hilbert functions, (The Curves Seminar at Queens, Vol. II. The Curves Seminar at Queens, Vol. II, Kingston, Ont., 1981/1982. The Curves Seminar at Queens, Vol. II. The Curves Seminar at Queens, Vol. II, Kingston, Ont., 1981/1982, Queen’s Papers in Pure and Appl. Math., vol. 61 (1982), Queen’s Univ.: Queen’s Univ. Kingston, ON), Exp. No. F, 21 · Zbl 0593.13009 [16] Rossi, Maria Evelina; Trung, Ngô Viêt; Valla, Giuseppe, Castelnuovo-Mumford regularity and extended degree, Trans. Am. Math. Soc., 355, 5, 1773-1786 (2003) · Zbl 1075.13008 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.	2021-01-25 04:21:16	{"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": 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": 0.7639822959899902, "perplexity": 4116.200387112894}, "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/1610703564029.59/warc/CC-MAIN-20210125030118-20210125060118-00099.warc.gz"}
https://proofwiki.org/wiki/Derivatives_of_PGF_of_Poisson_Distribution	# Derivatives of PGF of Poisson Distribution ## Theorem Let $X$ be a discrete random variable with the Poisson distribution with parameter $\lambda$. Then the derivatives of the PGF of $X$ with respect to $s$ are: $\dfrac {d^k} {\d s^k} \, \map {\Pi_X} s = \lambda^k e^{- \lambda \paren {1 - s} }$ ## Proof $\ds \map {\Pi_X} s$ $=$ $\ds e^{-\lambda \paren {1 - s} }$ $\ds$ $=$ $\ds e^{-\lambda + \lambda s}$ $\ds$ $=$ $\ds e^{-\lambda} e^{\lambda s}$ Exponential of Sum We have that for a given Poisson distribution, $\lambda$ is constant. From Higher Derivatives of Exponential Function, we have that: $\dfrac {\d^k} {\d s^k} \paren {e^{\lambda s} } = \lambda^k e^{\lambda s}$ Thus we have: $\ds \frac {\d^k} {\d s^k} \map {\Pi_X} s$ $=$ $\ds \frac {\d^k} {\d s^k} e^{-\lambda} \paren {e^{\lambda s} }$ $\ds$ $=$ $\ds e^{-\lambda} \frac {\d^k} {\d s^k} \paren {e^{\lambda s} }$ Derivative of Constant Multiple $\ds$ $=$ $\ds e^{-\lambda} \lambda^k e^{\lambda s}$ Higher Derivatives of Exponential Function Hence the result. $\blacksquare$	2023-03-29 12:19:27	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 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": 0.9891871809959412, "perplexity": 183.7998006431163}, "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/1679296948976.45/warc/CC-MAIN-20230329120545-20230329150545-00103.warc.gz"}
https://zbmath.org/?q=an:1273.13052	## Challenging computations of Hilbert bases of cones associated with algebraic statistics.(English)Zbl 1273.13052 Summary: We present two independent computational proofs that the monoid derived from $$5\times 5\times 3$$ contingency tables is normal, completing the classification by H. Hibi and T. Ohsugi [in: Commutative algebra and combinatorics. Part I: Computational algebra and combinatorics of toric ideals. Part II: Topics in commutative algebra and combinatorics. Proceedings of the international workshop and conference on computational algebraic geometry, Bangalore, India, December 8–13, 2003. Mysore: Ramanujan Mathematical Society. Ramanujan Mathematical Society Lecture Notes Series 4, 91–115 (2007; Zbl 1187.13024)]. We show that Vlach’s vector disproving normality for the monoid derived from $$6\times 4 \times 3$$ contingency tables is the unique minimal such vector up to symmetry. Finally, we compute the full Hilbert basis of the cone associated with the nonnormal monoid of the semigraphoid for $$\| N\|=5$$. The computations are based on extensions of the packages $$\mathtt LattE-4ti2$$ and $$\mathtt Normaliz$$. ### MSC: 13P25 Applications of commutative algebra (e.g., to statistics, control theory, optimization, etc.) 14M25 Toric varieties, Newton polyhedra, Okounkov bodies 52B20 Lattice polytopes in convex geometry (including relations with commutative algebra and algebraic geometry) 14C05 Parametrization (Chow and Hilbert schemes) Zbl 1187.13024 Normaliz; 4ti2 Full Text: ### References: [1] Bruns [Bruns and Gubeladze 09] W., Springer Monographs in Mathematics (2009) [2] Bruns [Bruns and Ichim 10] W., J. Algebra 324 pp 1098– (2010) · Zbl 1203.13033 [3] Drton [Drton et al. 09] M., Oberwolfach Seminars 39 (2009) [4] Durand [Durand et al. 99] A., Proceedings of the 24th International Symposium on Mathematical Foundations of Computer Science, LNCS 1672 pp 92– (1999) [5] Hemmecke [Hemmecke 02] R., Mathematical Software, ICMS 2002 pp 307– (2002) [6] Hemmecke [Hemmecke et al. 08] R., Comb. Probab. Comput. 17 pp 239– (2008) [7] Hemmecke [Hemmecke et al. 09] R., Contrib. Discrete Math. 4 pp 81– (2009) [8] Ohsugi [Ohsugi 10] H., Discrete Math. 310 pp 1160– (2010) · Zbl 1230.05241 [9] Ohsugi [Ohsugi and Hibi 06] H., Commutative Algebra and Combinatorics, Ramanujan Mathematical Society Lecture Note Series 4 pp 87– (2006) [10] Studen’y [Studený 05] M., Springer Series in Information Science and Statistics (2005) [11] Sturmfels [Sturmfels and Sullivant 08] B., Mich. Math. J. 57 pp 689– (2008) · Zbl 1180.13040 [12] Sullivant [Sullivant 10] S., Ann. Inst. Stat. Math. 64 pp 717– (2010) · Zbl 1440.62396 [13] Vlach [Vlach 86] M., Discrete Appl. Math. 13 pp 61– (1986) · Zbl 0601.90105 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.	2022-10-02 19:04:05	{"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": 0.813915491104126, "perplexity": 4703.04303154423}, "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/1664030337339.70/warc/CC-MAIN-20221002181356-20221002211356-00789.warc.gz"}
https://cs.stackexchange.com/questions/89936/finding-the-entropy-of-a-random-experiment-with-probability-of-frac13	# Finding the Entropy of a random experiment with probability of $\frac{1}{3}$ Entropy is the randomness collected by an operating system or application for use in Cryptography or other uses that require random data. The formula for Entropy is $$H(p_1, ..., p_k)=-\sum_{i=1}^{k} p_i\log_2(p_i)[bit]$$ So if I were to calculate the Entropy of a coin toss. it would be $$H(\frac{1}{2}, \frac{1}{2})=-(\log_2(\frac{1}{2})+\frac{1}{2}\log_2(\frac{1}{2}))=-(0-1)=1 Bit$$ But why is there a $\frac{1}{2}$ before the $\log$? Also if I were doing an experiment where the probability of an outcome is $\frac{1}{3}$ and there are $3$ outcomes, so would the entropy be $$H(\frac{1}{3}, \frac{1}{3}, \frac{1}{3})=(\log_2(\frac{1}{3})+\frac{1}{3}\log_2(\frac{1}{3})+\frac{1}{3}\log_2(\frac{1}{3}))$$ • There should be a $1/2$ before each term. Your calculation is wrong. – xskxzr Mar 29 '18 at 6:32 • @xskxzr So if the probability was $\frac{1}{3}$, would there be $\frac{1}{3}$ before each term? – Ski Mask Mar 29 '18 at 10:06 • Yes, of course. – xskxzr Mar 29 '18 at 14:22	2019-10-15 14:27:28	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9116894006729126, "perplexity": 300.20817938797035}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-43/segments/1570986659097.10/warc/CC-MAIN-20191015131723-20191015155223-00110.warc.gz"}
https://www.physicsforums.com/threads/transmission-coefficient-in-reaction-rate-theory.733330/	# Transmission coefficient in reaction rate theory 1. Jan 17, 2014 ### dsigg This question relates to rate constants of transition events. The transmission coefficient κ reduces the value of the rate constant compared to the transition state theory (TST) value. I understand κ to be defined as the probability that a reaction coordinate q will proceed to product given that is has positive velocity at the transition state. In TST, there are no frictional forces to hold q back and κ = 1. With increasing friction, there are recrossings, and κ is reduced. My question is how does k ever fall below the value of 0.5? Naively speaking, in the limit of very large friction the velocity is quickly randomized and the probabilities of falling back to reactant or moving forward to product should both be 0.5. Yet, Kramers theory and the more general Grote-Hynes theory allow for much smaller values of κ. My thoughts are either that the stated definition of κ is wrong or if κ < 0.5 a greater number of transition events "bounce-back" to the reactant state than proceed to product. Neither option seems very appealing. Can anyone set me straight? 2. Jan 18, 2014 ### DrDu I don't know Kramers theory too well, but I could imagine that for very high friction, the particle is effectively stopped at the TS. Then it has a high probability to go back to the educts. Also without friction, you can get a small kappa due to quantum mechanical effects: http://en.wikipedia.org/wiki/Rectangular_potential_barrier	2016-08-29 23:46:42	{"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": 0.8070960640907288, "perplexity": 1067.36138071203}, "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/1471982967797.63/warc/CC-MAIN-20160823200927-00215-ip-10-153-172-175.ec2.internal.warc.gz"}
https://www.nat-hazards-earth-syst-sci.net/19/1881/2019/	Journal cover Journal topic Natural Hazards and Earth System Sciences An interactive open-access journal of the European Geosciences Union Journal topic Nat. Hazards Earth Syst. Sci., 19, 1881–1893, 2019 https://doi.org/10.5194/nhess-19-1881-2019 Nat. Hazards Earth Syst. Sci., 19, 1881–1893, 2019 https://doi.org/10.5194/nhess-19-1881-2019 Research article 28 Aug 2019 Research article \| 28 Aug 2019 Efficacy of using radar-derived factors in landslide susceptibility analysis: case study of Koslanda, Sri Lanka Efficacy of using radar-derived factors in landslide susceptibility analysis: case study of Koslanda, Sri Lanka Ahangama Kankanamge Rasika Nishamanie Ranasinghe1, Ranmalee Bandara1, Udeni Gnanapriya Anuruddha Puswewala2, and Thilantha Lakmal Dammalage1 Ahangama Kankanamge Rasika Nishamanie Ranasinghe et al. • 1Department of Surveying and Geodesy, University of Sabaragamuwa, Belihuloya, 70140, Sri Lanka • 2Department of Civil Engineering, University of Moratuwa, Moratuwa, 10400, Sri Lanka Correspondence: Ahangama Kankanamge Rasika Nishamanie Ranasinghe (nishamanie@geo.sab.ac.lk) Abstract Through the recent technological developments of radar and optical remote sensing in (i) the areas of temporal, spectral, spatial, and global coverage; (ii) the availability of such images either at a low cost or free of charge; and (iii) the advancement of tools developed in image analysis techniques and GIS for spatial data analysis, there is a vast potential for landslide studies using remote sensing and GIS as tools. Hence, this study aimed to assess the efficacy of using radar-derived factors (RDFs) in identifying landslide susceptibility using the bivariate information value method (InfoVal method) and the multivariate multi-criteria decision analysis based on the analytic hierarchy process statistical analysis. Using identified landslide causative factors, four landslide prediction models – bivariate with and without RDFs as well as multivariate with and without RDFs – were generated. Twelve factors such as topographical, hydrological, geological, land cover and soil plus three RDFs are considered. The weight of index for landslide susceptibility is calculated by using the landslide failure map, and susceptibility regions are categorized into four classes as very low, low, moderate, and high susceptibility to landslides. With the integration of RDFs, boundary detection between high- and very-low-susceptibility regions are increased by 7 % and 4 % respectively. 1 Introduction Landslides are one of the major types of geo-hazards in the world as approximately 9 % of global natural disasters are recorded as landslides (Chae et al., 2017; Chalkias et al., 2014). The recent statistics on landslide disasters per continent, from year 2000 to 2017, are summarized in the Emergency Events Database (EM-DAT, 2016). The database indicates that landslides cause around 16 500 deaths and affect 4.5 million people worldwide, with property damages of about USD 3.5 million (OFDA/CRED, 2016). The spatial prediction of landslide disasters, incorporating statistical analysis to identify areas that are susceptible to future land sliding, is one the important areas of geo-scientific research. These studies are based on the knowledge of past landslide events, topographical parameters, geological attributes, and other possible environmental factors (Park et al., 2013). Presently, remote sensing has been used extensively to provide landslide-specific information for emergency managers and policy makers in terms of disaster management activities in the world (Baroň et al., 2014; Martha, 2011). The spatial resolution of space-borne optical data is now less than 1 m in panchromatic images, and at the same time synthetic aperture radar (SAR) sensors and related processing techniques have also increased. Radar is considered to be unique among the remote sensing systems, as it is all-weather, independent of the time of day, and is able to penetrate into the objects. Additionally, radar images have been shown to depend on several natural surface parameters such as the dielectric constant and surface roughness. The dielectric constant is highly dependent on soil moisture due to the large difference in dielectric constant between dry soil and water (Kseneman et al., 2012). It is accepted in the scientific community that remote sensing techniques do offer an additional tool for extracting information on the causes of landslides and their occurrences. Especially for deriving various parameters related to the landslide predisposing and triggering factors at global and regional scales, remote sensing plays a vital role (Corominas et al., 2014; Muthu et al., 2008; Pastonchi et al., 2018). Most importantly, landslide susceptibility analysis has greatly aided the prediction of future landslide occurrences, which is important for humans who reside in areas surrounded by unstable slopes. It is therefore identified that remote sensing techniques are significant in order to extract the landslide susceptibility regions by providing most suitable landslide predisposing factors at a smaller scale. There is massive potential for research by applications in the area of disaster management if conventional remote sensing data and radar are integrated. This is because each method has its inherent disadvantages and shortcomings, as well as advantages, and integrating the two potentially complement each other. As such, this study combines the predisposing factors derived from both optical and radar satellite data for landslide susceptibility analysis. Furthermore, significant landslide predisposing factors like soil moisture, surface roughness, and forest biomass are derived from radar images, and the impacts of these factors on landslide susceptibility are examined. 1.1 Methods for landslide susceptibility analysis There are inherent limitations and uncertainties in landslide susceptibility analysis, and yet several methods have been utilized and successfully applied in the past (Kanungo et al., 2009). These methods have been of both a qualitative and quantitative nature. Generally, qualitative methods are based on expert opinions while the quantitative approaches, such as statistical and probabilistic approaches, depend on the past landslide experiences. Qualitative methods simply make use of landslide inventories to identify areas with similar geological and geomorphologic properties that show susceptibility to land failures. These methods can be divided into two groups: geomorphologic analysis and map combination. In geomorphologic analysis, the landslide susceptibility is determined directly either in the field or by the interpretation of images through geomorphologic analysis (Bui et al., 2011). Map combination is based on combining a number of predisposing factor maps for landslide susceptibility analysis. However, map combination analysis comprises a semi-quantitative nature by integrating the ranking and weighting of landslide susceptibility (Ayalew et al., 2004; Kavzoglu et al., 2014; Saaty, 1980). The analyses based on the quantitative approaches depend on numerical data and statistics, expressing the relationship between instability or predisposing factors with landslides (Reis et al., 2012). These methods are categorized into two groups: bivariate and multivariate statistical analysis. The popular information value method (InfoVal) is used as bivariate and multi-criteria decision analysis (MCDA) based on analytic hierarchy process (AHP) used as multivariate. Within the context of this work, these two methods are compared with respect to its performance in landslide susceptibility analysis. 1.2 Landslide predisposing factors It is understood that landslides may occur as consequences of complex predisposing and triggering factors. Topographical and geological factors, together with local climatic conditions, lead to landslide occurrences. The selection of these factors and preparation of corresponding thematic data layers are vital for models used in landslide susceptibility analysis (Jakob et al., 2006; Lee et al., 2017). There are no universal guidelines regarding the selection of predisposing factors in landslide susceptibility analysis. Some parameters may be important factors for landslide occurrences in a certain area but not for another one. Scientists (van Westen, 1997, 2003; van Westen and Getahun, 2003) show that every study area has its own particular set of predisposal factors which condition landslides. Determination of appropriate causal factors is a difficult task, and no specific rule exists to define how many factors are sufficient for a specific landslide susceptibility analysis. Hence, the selection of predisposing factors is dependent on the nature of the study area, opinions of the experts, and the availability of data for generating the appropriate spatial and thematic information (Kavzoglu et al., 2015; Shahabi and Hashim, 2015). 2 Study area Koslanda in Sri Lanka is located at the geographical coordinates of 064400′′ N and 810100′′ E, and the elevation is around 700–1000 m a.s.l. It is a remote, hilly area with harsh weather conditions, where the monthly rainfall ranges from 60 to 200 mm, and average temperature is 20 C. The area has rains for most of the year, with a very short, dry period during the months of February to April. The population is around 5000 people, and the study area has an extent of 19 km2 within the Koslanda area. Koslanda has been the site of several massive landslides over the years, and both the Naketiya landslide in the year 1997 and Meeriyabedda landslide in the year 2014 are very distinct in Fig. 1, and within a span of 2 years major landslides have occurred three times at the same location. When considering the typology of landslides in this study area, falling, toppling, subsidence, lateral displacements, and debris flows are prominent (NBRO, 2016). Figure 1Topographical formation of Koslanda, Sri Lanka, with its previous landslide signatures. Sources © Google Earth and CNES. The geomorphology of the area is described as a gently inclined talus slope, with a thick, loosely compacted colluvium deposit at the foot of the near-vertical rocky scarp. Koslanda is situated at the middle part of the slope, with the lower area showing a fairly steep surface as well. The composition of the colluvium deposit in the area includes a randomly arranged mixture of weathered clayey and sandy materials, with the organic matter making the deposit act as a highly absorbing entity with high water content. The study area was an abandoned tea land in which the properly maintained surface drainage system has been neglected (Somaratne, 2016). Geology refers to the physical structure and the substance of the Earth. The study area consists mainly of undifferentiated charnockitic biotite gneisses and quartzites, according to the 1:10 000 geological map from the Geological Survey and Mines Bureau (GSMB), Sri Lanka. Such a geomorphological and geological formation, together with improper land use management practices, has made the area extremely vulnerable to landslide events. 3 Data The most important phases in landslide prediction analyses are the collection of data from different sources and the construction of a spatial database on a common platform (Lan et al., 2004). The data utilized for the landslide susceptibility analysis include the topographical, hydrological, geological, soil, and land cover factors. All factors are derived from optical images (Landsat-8, Sentinel-2), radar images (Sentinel-1, TerraSAR-X), the digital elevation model (DEM) derived from aerial triangulation, and other available data sources (geology, rainfall). Stereo aerial photographs from 1993 are used to generate the 7 m resolution DEM using aerial triangulation (Copernicus Open Access Hub, 2018; USGS Earth Explorer, 2018). The landslide inventory map for the study area was constructed by integrating the interpreted multi-temporal aerial photographs, satellite images, and some temporal images from Google Earth (Fig. 2). Verifications are carried out through field investigations. In this research, the predisposing factors were selected from among the most widely considered factors in the literature and opinion from the experts. Figure 2Landslide catalogue of the Koslanda area with two different training and validating samples; background map from © Google Earth. Most data are derived as primary data from remote sensing techniques for a large area with up-to-date information. As such, 15 predisposing factors are selected for the landslide susceptibility analysis by using bivariate and multivariate statistical techniques. Of these, 12 factors (elevation, slope, aspect, planar curvature, profile curvature, topographical wetness index (TWI), land use, lineament density, distance to water bodies, soil moisture, geology, and rainfall) are derived from optical images, DEM, and auxiliary data, while three more factors (soil moisture from delta index, surface roughness, and forest biomass) are derived from radar images. These factors were then combined in order to analyse the performance of this integration for landslide susceptibility analysis. Additional graphical information is available in Figs. S1, S2, and S3. 3.1 Topographical factors The topographical factors include elevation, slope, aspect, planar curvature, profile curvature, and surface roughness of the terrain. The first four factors are derived from the 7 m resolution DEM, and surface roughness is derived using a Sentinel-1 radar image. The elevation is important to study the local relief of the terrain and ranges from 446 to 1537 m above mean sea level in the study area. Since the area contains high mountains, more than a 1000 m difference in elevation can be observed. The basic parameter for the slope stability analysis is the slope angle. The slope angle of the study area ranges from 0 to 80, showing a significant increase in slope within a relatively small area. Additionally, the area with steep slopes ranging from 60–80 can be seen in the northern part of Koslanda. Aspect is defined as the direction of maximum slope of the terrain surface, or the compass direction of a particular slope. The curvature is theoretically defined as the rate of change of slope (or slope) of the focused slope. Planar curvature describes convergence and divergence of the flow across a surface, while the profile curvature refers to acceleration or deceleration of the flow across a surface. Under radar configuration, the magnitude of radar backscatter is defined as a function of surface roughness and moisture content. Similar studies from Rahman et al. (2008) and Septiadi and Nasution (2009) emphasized the extraction of surface roughness from radar data using textural analysis. Hence, to estimate the surface roughness without the use of any ancillary field data, a Sentinel-1 radar image on 12 March 2015 under dry climatic conditions was used to reduce the effect of the moisture component from the radar backscatter. The texture is the structure, or appearance, of the surface and, as such, describes the coarseness or the homogeneity of the image structure. One of the most prominent methods for texture analysis is the grey-level co-occurrence matrix (GLCM), which is based on the second-order probability density function. The GLCM describes how often a grey level occurs at a pixel located at a fixed geometric position relative to its neighbourhood pixels. The surface roughness is normally a measure of finer surface irregularity in the surface texture. These texture features extracted from the GLCM would be the best descriptors for quantifying the state of surface roughness (Septiadi and Nasution, 2009). Hence, the GLCM texture analysis is performed using a window size of 9 pixels 9 pixels, and the homogeneity or dissimilarity criterion is used to determine the surface roughness of the study area. 3.2 Hydrological factors Distance to hydrological features, rainfall, and TWI defined by Eq. (1) are selected as the hydrological factors for this landslide susceptibility analysis. Proximity to the hydrological features is an important factor when considering the landslide susceptibility analyses (Sar et al., 2016; Shahabi and Hashim, 2015). TWI is a solid index that is capable of predicting areas susceptible to saturation or wetness of land surfaces, as well as the areas that have the potential to produce an overland flow. Within the Sri Lankan context, heavy and prolonged rainfall is the main triggering factor for the landslides. The monthly average rainfall data for the years 2014 to 2016 from 10 nearby stations to Koslanda were used in this study. Monthly rainfall data from 10 rain gauge stations are averaged, and the average rainfall map for the study area is generated using the inverse distance weighting (IDW) interpolation method within the ArcGIS environment. TWI has been used to study the spatial scale effects, or topographic control, on hydrological processes. This index was developed by Beven and Kirkby (1979) and can be defined in Eq. (1) as $\begin{array}{}\text{(1)}& \mathrm{TWI}=\mathrm{ln}\left[\propto /\mathrm{tan}\mathit{\beta }\right],\end{array}$ where is the local upslope area draining through a certain point per unit of contour length, and β is the gradient of the local slope in degrees. The applicability of the TWI in the calculation and validation of landslide susceptibility analysis has been shown by Kavzoglu et al. (2014) and Sørensen et al. (2006) among others. 3.3 Soil factors The soil moisture index (SMI) defined in Eq. (2) and the delta index defined in Eq. (5) are the soil factors focused upon in this research. Surface soil moisture is one of the most important parameters in land susceptibility analysis (Carlson et al., 1994; Zhan et al., 2002). Several methods have been proposed to estimate the surface soil moisture conditions accurately with in situ measurements. However, these methods are time-consuming and costly when the area of interest is large and the scale of work is small. Hence, this research uses the universal triangle relationship between soil moisture, the normalized difference vegetation index (NDVI), and land surface temperature (LST) derived from Landsat-8 image bands as an optical remote sensing approach, as well as the delta index derived from two radar images, as wet and dry conditions, as a radar remote sensing approach. Band 5 (near-infrared, NIR; 30 m resolution), band 4 (red, 30 m resolution), and band 11 (thermal, TIR-2, 100 m resolution) of the Landsat-8 image of 3 July 2015 are processed for extracting the soil moisture index in the thermal-NDVI space. The SMI is “0” along the dry edge and “1” along the wet edge. According to the studies from Wang and Qu (2009) and Zenga et al. (2004), SMI can be defined in Eq. (1) as $\begin{array}{}\text{(2)}& \mathrm{SMI}=\frac{\left({T}_{\mathrm{max}}-T\right)}{\left({T}_{\mathrm{max}}-{T}_{\mathrm{min}}\right)},\end{array}$ where Tmax and Tmin are the maximum and minimum surface temperature for a given NDVI, and T is the remotely sensed derived surface temperature at a given pixel for a given NDVI. The simple regression relationship between T and NDVI is formulated in Eqs. (3) and (4) as $\begin{array}{}\text{(3)}& {T}_{\mathrm{max}}={a}_{\mathrm{1}}\cdot \mathrm{NDVI}+{b}_{\mathrm{1}},\text{(4)}& {T}_{\mathrm{min}}={a}_{\mathrm{2}}\cdot \mathrm{NDVI}+{b}_{\mathrm{2}},\end{array}$ where ${a}_{\mathrm{1}}=-\mathrm{5.2362}$, b1=300.14, a2=2.9254, and b2=289.11. Radar remote sensing provides advantages for extracting near-surface soil moisture (0–5 cm), including timely coverage with repeat passes during day and night, under all weather conditions. Radar imagery from space can provide broad-scale information on near-surface soil moisture as radar signal return is responsive to changes in soil moisture. Technically, the surface roughness and vegetation affect radar backscatter much more than soil moisture. Hence, both the surface roughness and vegetation have to remain unchanged during the image acquisition for soil moisture estimation (Thoma et al., 2006). The delta index is a modified, image-differencing technique, and many studies (Barrett et al., 2009; Sano et al., 1998; Thoma et al., 2004) have proven it to be a good predictor for near-surface soil moisture extraction. This index describes the change in wet scene backscatter relative to the dry scene backscatter and is defined by Thoma et al. (2004) in Eq. (5) as $\begin{array}{}\text{(5)}& \text{Delta index}=\left\|\frac{{\mathit{\sigma }}_{\mathrm{wet}}^{\mathrm{0}}-{\mathit{\sigma }}_{\mathrm{dry}}^{\mathrm{0}}}{{\mathit{\sigma }}_{\mathrm{dry}}^{\mathrm{0}}}\right\|,\end{array}$ where ${\mathit{\sigma }}_{\mathrm{wet}}^{\mathrm{0}}$ is the radar backscatter (decibels) from a pixel in the radar image representing wet soil conditions, and ${\mathit{\sigma }}_{\mathrm{dry}}^{\mathrm{0}}$ is the radar backscatter (decibels) from a pixel in the same geographic location representing dry soil conditions at a different time. Sentinel-1 images with 10 m spatial resolution and VV polarization are used in the presented study. The dry reference image was acquired on 12 March 2015 and the wet image was acquired on 24 November 2014 after the landslide in Meeriyabedda, Sri Lanka. Therefore, the topographical changes like roughness and vegetation density showed no significant changes during these 4 months. 3.4 Land use The major land uses existing in this study area are identified as tea, scrub, forest, rock, rice, water, and residential. The Sentinel-2A image from 10 October 2016 is used to extract the desired land uses from the study area by applying supervised classification. Scrub areas are typically the tea estates that are in abundance, while the residential areas are the rooms of tea workers. It is noted that most of the devastating landslides in this area had occurred within the extensive tea estates. Hence, the main reason for the continuous occurrence of these landslides can be identified as the lack of proper land use management in the area. Forest biomass is a significant factor that can control the landmass failures or landslides. The main limitations of using optical remote sensing for forest biomass estimation are the near-constant tropical cloud cover and the insensitivity of reflectance to change in the biomass in older and mixed forests. Radar has the potential to overcome the above limitations due to its all-weather, day and night capability, with the positive relationship of radar backscatter and forest biomass. The spatial, spectral, temporal, and polarization characteristics of radar backscatter have a known influence on the forest biophysical properties. Kuplich et al. (2005) and Caicoya et al. (2016) related the radar image texture derived from GLCM to the forest biomass. An experiment was conducted by Kuplich et al. (2005) with seven texture measures, but only the GLCM-derived contrast increased the correlation between the backscatter and the log of biomass in Eq. (6) as $\begin{array}{}\text{(6)}& \text{Log of biomass}=\mathrm{2.24}+\mathrm{0.33}b+\mathrm{0.0001}c,\end{array}$ where b is the radar backscatter and c represents the GLCM contrast texture for the particular radar image. A TerraSAR-X spotlight image from 2 November 2014, with 3 m resolution and dual polarization (HH and VV), was used to estimate the forest biomass in this research. 3.5 Geological factors Geology refers to the physical structure and the substance of the Earth. In order to investigate the land mass failures, the geological structure of that particular area has to be analysed carefully. In addition to the geology of the area, lineament density has also been considered as a factor. The geological information of the particular area is obtained from the geological map available at the Geological Survey and Mines Bureau, Sri Lanka, at a 1:100 000 scale, and seven types of different geological structures are contained in the selected study region. Primarily the undifferentiated charnockitic biotite gneisses and quartzites are prominent with garnet-sillimanite and garnetiferous quartzofeldspathic gneiss in the study area. Lineaments are extractable linear features which are correlated with the geological structures of the Earth. When considering the analysis of lineaments with respect to the landslide potentiality, lineaments exhibit the zones of weak surfaces such as faults, fractures, and joints (Adiri, et al., 2017; Kati, et al., 2018; Mandal and Maiti, 2015). This study uses the Sentinel-2 optical satellite image, with 10 m resolution, for the extraction of lineaments of the study area. 4 Methodology The InfoVal method determines the susceptibility at each point or pixel, jointly considering the weight of influence of all predisposing factors. The weight of influence is based on the landslide inventory map of the particular area. When constructing a probability model for landslide prediction, it is necessary to assume that the landslide occurrence is determined by landslide-related factors and that future landslides will also occur under the same, or almost similar, conditions as past landslides (Remondo et al., 2013; Saha et al., 2005). Hence, at the beginning of the analysis, the landslide inventory map is divided in to two samples – training and validation – enabling the use of these data for landslide susceptibility analysis and validation of results respectively as in Fig. 2. The log function is used to control the large variation of weights in calculations. The larger the weight of influence, the stronger the relationship between landslide occurrence and the given factor's attribute. This method overlays all individual predisposing factors such as thematic maps with the landslide inventory map to calculate the density of the landslide detachment zones for each class of the selected factors. The density of landslide pixels represents the weight of influence of each predisposing factor in Eq. (7) as $\begin{array}{}\text{(7)}& \begin{array}{rl}{W}_{i}& =\mathrm{Log}\left(\frac{\mathrm{Densclass}}{\mathrm{Densmap}}\right),\\ & =\mathrm{Log}\left(\frac{{N}_{\mathrm{pix}}\left({S}_{i}\right)/{N}_{\mathrm{pix}}\left({N}_{i}\right)}{{\sum }_{i=\mathrm{1}}^{n}{N}_{\mathrm{pix}}\left({S}_{i}\right)/{\sum }_{i=\mathrm{1}}^{n}{N}_{\mathrm{pix}}\left({N}_{i}\right)}\right),\end{array}\end{array}$ where Wi is the weight given to the parameter class, Densclass is the landslide density within the parameter class and Densmap is the landslide density within the entire map. Npix(Si) is the number of landslide pixels within parameter class i, and Npix(Ni) is the total number of pixels in the same parameter class. It means that, if the parameter class contains no landslide occurrence, it will have no correlation with the landslide inventory map (Bui et al., 2011; Kavzoglu et al., 2015). The MCDA method integrates all the independent predisposing factors with the inclusion of relative contribution of each factor by putting more emphasis on the predisposing factors that contribute to landslide occurrence. The same predisposing factors with or without radar are used to investigate the landslide susceptibility regions from the AHP technique within the GIS domain. In AHP, each pair of factors in a particular factor group is examined at one time, in terms of their relative importance. Relative weights for each factor are calculated based on a questionnaire survey from experts in the field (further information for the questionnaire is available in Fig. S4). These relative weights are then used to generate a pairwise comparison matrix, which is the basic measurement mode when applying the AHP procedure. The selected predisposing factors, and relevant relative weights, are used to generate the normalized matrix with final average weights. However, expert knowledge could be subjective at times, or may cause one to assign different weights for each factor, when dealing with a large number of causative factors. Hence, in order to avoid this inconsistency, the consistency ratio (CR) is calculated. For better predictive models, the CR should be less than 0.01, otherwise each factor has to be generated with the proper pairwise comparison. The calculated final weights for 12 landslide predisposing factors without RDFs such as elevation–slope, aspect, planar curvature, profile curvature, TWI, land use, lineament density, distance to water bodies, soil moisture, geology, and rainfall were 0.030, 0.172, 0.022, 0.018, 0.014, 0.074, 0.149, 0.052, 0.045, 0.094, 0.185, and 0.145, respectively. The CR is 0.089, making it less than 0.1, which is the value shown to be the reasonable level of consistency in the pairwise comparison. The final weights for 15 predisposing factors with RDFs – elevation, slope, aspect, planar curvature, profile curvature, TWI, land use, lineament density, distance to water bodies, SMI in NDVI-T domain, geology, rainfall, soil moisture (delta index), surface roughness, and forest biomass – are 0.022, 0.145, 0.016, 0.013, 0.011, 0.053, 0.126, 0.039, 0.033, 0.065, 0.153, 0.124, 0.088, 0.088, and 0.027, respectively. When considering the 15 predisposing factors, the CR is calculated as 0.092, which is less than 0.1, thereby showing a realistic level of consistency in the pairwise comparison matrix. After decisive analysis of the types of predisposing factors, the presented work proceeded to consider 15 predisposing factors that are derived from optical, radar, and other available auxiliary data sources. Three significant causative factors – surface roughness, soil moisture from the delta index, and forest biomass – were estimated by using radar satellite images. Thus, this work investigated the performance of landslide susceptibility analysis using bivariate and multivariate methods with the inclusion of RDFs and described the processing steps in Fig. 3. Figure 3Workflow of the landslide susceptibility analysis using bivariate and multivariate approaches. The weight of influence of all predisposing factors such as thematic maps is added in a bivariate and multivariate manner to obtain the contribution of all predisposing factors for landslide susceptibility analysis. After calculating the cumulative percentage of failures of the weighted susceptibility maps, value ranges for each percentage of failure are obtained from quantile classification for 10 classes. The entire study area of each landslide susceptibility map is then discretized in to four classes as 0 %, 10 %, 30 %, and 60 % of failure regions for very-low-, low-, moderate-, and high-susceptibility classes, respectively. 5 Results Four landslide prediction models, (i) bivariate without RDFs (BiNR), (ii) bivariate with RDFs (BiWR), (iii) multivariate without RDFs (MNR), and (iv) multivariate with RDFs (MWR), are discussed. The region has been analysed and classified into four (04) landslide susceptibility regions: high, moderate, low, and very low. 5.1 Bivariate analysis with and without radar-derived factors Susceptible regions are identified from the bivariate InfoVal method without RDFs as 12 % for high, 45 % for moderate, 38 % for low, and 5 % for very low as shown in Fig. 4a. Hence, 57 % of areas from the total study area are predicted to have high and moderate susceptibility to landslide hazards. Very steep slope mountains in the north, north-west, and east regions are identified as very-low-susceptibility areas, given that the area was free from historical landslides. The middle regions with 30–50 slope are detected as having a high probability of landslide occurrences. The bivariate InfoVal method with RDFs identified 19 % of failure regions for high-susceptibility, 39 % for moderate-susceptibility, 33 % for low-susceptibility, and 9 % for very-low-susceptibility regions as presented in Fig. 4b. Therefore, 58 % of the total study area is predicted to have high and moderate susceptibility to landslides. Very steep slope mountains in the north, north-west, east, and south-east regions, the area near the Eruwendumpola Oya, are identified as having very low susceptibility to landslides. Similar to the bivariate analysis without RDFs, the middle regions with 30–50 slope are detected as having a high probability of landslide occurrences, and the reason for this is mainly because of past experiences from the Naketiya and Meeriyabedda landslides that took place in the same area. Figure 4Landslide susceptibility maps from bivariate and multivariate analysis with and without RDFs. (a) Bivariate without RDFs, (b) bivariate with RDFs, (c) multivariate without RDFs, and (d) multivariate with RDFs. 5.2 Multivariate analysis with and without radar-derived factors All 15 weighted predisposing factors were grouped as with and without RDFs, and the weighted overlay is performed separately in order to obtain the landslide susceptibility regions. Figure 4c illustrates the landslide susceptibility map from the multivariate method without RDFs and is able to identify 18 % for high-, 44 % for moderate-, 36 % for low-, and 2 % for very-low-susceptibility regions. Hence, 62 % of areas from the total study area are predicted to be of high and moderate susceptibility to landslide hazards. In the landslide susceptibility map from the multivariate method with RDFs, from the total area, 21 % of the area shows a high susceptibility to landslides, with 40 % of the area as moderate, 34 % of the area as low, and 5 % of the area as having very low susceptibility as shown in Fig. 4d. Hence, 61 % of areas from the study area are predicted to have high and moderate susceptibility to landslide hazards. In a similar manner to the InfoVal method, the top of the mountains in the north, north-west, east, and south-east regions, the area near to the Eruwendumpola Oya, are identified as having a very low susceptibility to landslide hazards, while the middle regions with 30–50 slopes are detected as having high and moderate probability of landslide occurrences. 6 Discussions Landslide prediction is of utmost importance in all phases of disaster management and development activities in a country. In recent years Koslanda in Sri Lanka has been found to be significantly prone to landslide disasters. Hence, this study investigated the efficacy of radar-derived factors for landslide susceptibility analysis of a bivariate and multivariate nature. The main difference between bivariate and multivariate analysis is that in multivariate analysis the predisposing factors are weighted by considering how each of them affect landslide hazard. Four landslide susceptibility maps are produced from bivariate and multivariate analysis with and without radar-derived factors. The areas identified as having high- and moderate-susceptibility classes in these four approaches (57 %, 58 %, 62 %, and 61 % respectively in BiNR, BiWR, MNR, and MWR) are close in value but show an increase in multivariate analysis when compared with bivariate analysis as tabulated in Table 1. Moderate- and low-landslide-susceptibility areas show very small ((1–2) %) changes between these four types of analysis. With the integration of RDFs such as surface roughness, near-surface soil moisture from the delta index, and forest biomass in bivariate and multivariate analysis, the high- and very-low-susceptibility areas are increased significantly (high: 7 % – bivariate, 3 % – multivariate; very low: 4 % – bivariate, 3 % – multivariate). However, when comparing the high- and very-low-susceptibility areas from bivariate and multivariate analysis, high-susceptibility areas show a considerable increase (without radar: 6 %; with radar: 2 %) while very-low-susceptibility areas have a noteworthy decrease (without radar: 3 %; with radar: 4 %). Table 1Landslide-susceptible area comparison from bivariate and multivariate analysis with and without RDFs. BiNR – bivariate analysis without RDFs, BiWR – bivariate analysis with RDFs, MNR – multivariate analysis without RDFs, and MWR – multivariate analysis with RDFs. 6.1 Results validation The landslide susceptibility maps derived from the bivariate and multivariate analysis are validated using the selected validation samples from the landslide failure map. The most commonly used and scientifically recognized receiver operating characteristic (ROC) curves are used to analyse the prediction and validation performances. The ROC curve is a graphical plot that illustrates the performance of classification and is considered to be a powerful tool for the validation of landslide susceptibility analysis for many years (Neuhäuser et al., 2012). The areas under the curve (AUCs) for the four different approaches – bivariate and multivariate with and without RDFs – are calculated and graphed in Fig. 5. Figure 5Success rate and prediction rate curves with AUC for the bivariate and multivariate analysis with and without RDFs. The x axis denotes the cumulative percentage of susceptibility regions, and the y axis denotes the cumulative percentage of training samples. (a–d) BiNR – bivariate analysis without RDFs, BiWR – bivariate analysis with RDFs, MNR – multivariate analysis without RDFs, and MWR – multivariate analysis with RDFs. The areas under the success rate curves measure how the landslide prediction analysis fit with the training data set, while the areas under the prediction rate curves measure how well the landslide prediction models and landslide causative factors predict the landslides. If the area under the ROC curve is closer to 1, the result of the test is excellent and vice versa, and when AUC is closer to 0.5, the result of the test is fair or acceptable (Kamp et al., 2008). The AUCs of all the success rates are more-or-less near 0.80, indicating good prediction performances according to the definition. The AUCs of all the prediction rates are having values above 0.50, thereby indicating that they are within the acceptable range as per the definition. As such, they indicate that the accuracy of the prediction rate of land susceptibility and the selection of land causative factors are acceptable, but not excellent, even though the fit between the landslide prediction and the training data set is excellent as compared in Table 2. The incompleteness of the available landslide inventory map, as well as an insufficient number of validation samples in the study area, can be shown as reasons for the discrepancy. As a whole, better prediction and validation capabilities are shown by the bivariate analysis when compared with the multivariate approaches. Table 2Comparison of area under success rate and prediction rate curves for bivariate analysis without RDFs (BiNR), bivariate analysis with RDFs (BiWR), multivariate analysis without RDFs (MNR), and multivariate analysis without RDFs (MWR). 7 Conclusions This study focused on the applicability of remote sensing and GIS for rapid landslide prediction analysis at a finer scale. Furthermore, by considering the significance of radar data for landslide analysis, this study mainly investigates the efficacy of radar-derived factors for landslide prediction analysis, which is not well experimented in the current research. Most significant predisposing factors such as surface roughness, soil moisture, and forest biomass derived from radar are incorporated to examine the landslide prediction analysis. The prediction analysis is performed by using bivariate and multivariate statistical analysis. The main difference between bivariate and multivariate analysis is that in multivariate analysis selected predisposing factors are weighted by considering how each of them are influenced for landslide susceptibility. This study investigated 15 landslide predisposing factors: elevation, slope, aspect, planar curvature, profile curvature, TWI, land use, lineament density, distance to hydrology, SMI in NDVI-T domain, geology, rainfall, soil moisture (delta index), surface roughness, and forest biomass. Most of the factors are derived from radar and optical remote sensing techniques, where smaller-scale studies with up-to-date information allow the work to be conducted with metre-level accuracy and repeated analysis simultaneously. From the results obtained, it can be concluded that the bivariate and multivariate statistical analysis, with and without RDFs, can be used for landslide prediction analysis. However, with the integration of RDFs such as surface roughness, near-surface soil moisture from the delta index, and forest biomass, the detection of the boundary between the high- and very-low-susceptibility regions is increased. When comparing the bivariate analysis with multivariate, the increase of high- and very-low-susceptibility regions is higher in bivariate than multivariate. In landslide prediction analysis, the most important susceptibility classes are the high- and very-low-susceptibility classes, as they provide significant information about the danger from a disaster. Hence, with the integration of radar-derived factors, by increasing the accuracy of prediction for high-susceptibility regions, the possibility of mitigating dangers can be considerably improved. When the accuracy and prediction of very-low-susceptibility regions are increased, the use of such lands can be encouraged for residential, community places, and safe areas when a landslide occurs. Successful prediction and validation of prediction analysis via ROC curves are achieved. Even though this study was tested for a sample area, the same methodology can be applied for any landslide-prone area to investigate the landslide prediction analysis using radar-derived factors by using bivariate and multivariate analysis. This is because the radar-derived factors can be derived for any area, as long as the data are available, and at any time under any weather conditions as radar is weather independent. Additionally, the technology can be learned easily and anyone can be trained to use this methodology to predict landslide susceptibility areas, and this is especially helpful for developing countries which do not have up-to-date data at fine resolutions. With the increasing availability of free data from optical sensors, radar sensors, and DEM, it is possible to derive more landslide predisposing factors such as thematic maps. Furthermore, there are many statistical analyses developed of a qualitative and quantitative nature for spatial data analysis. Hence, further investigations have to be performed for landslide susceptibility analysis, even focusing on the changing nature of the environments. Data availability Data availability. Landsat-8 data can be freely downloaded from USGS Earth Explorer (2018), https://gisgeography.com/usgs-earth-explorer-download-free-landsat-imagery/. Sentinel-1 and Sentinel-2A data can be freely downloaded from the Copernicus Open Access Hub (2018), https://scihub.copernicus.eu/dhus/\#/home. The DEM, predisposing factors, and other auxiliary data can be obtained by contacting the corresponding author by email (nishamanie@geo.sab.ac.lk). Supplement Supplement. Author contributions Author contributions. AKRNR performed the conceptualization, data curation, formal analysis, funding acquisition, investigation, methodology, validation, visualization, and writing of the original draft; RB supervised the study and reviewed and edited the original draft of the manuscript. UGAP and TLD supervised the study. Competing interests Competing interests. The authors declare that they have no conflict of interest. Acknowledgements Acknowledgements. The authors wish to acknowledge the Sabaragamuwa University of Sri Lanka for offering an opportunity for this research and the HETC project, Ministry of Higher Education, Sri Lanka, for providing financial support under the grant number SUSL/O-Geo/N2 as well as the University of Siegen, Germany, for providing their support in collecting and initial processing of the TerraSAR-X images from DLR, Germany. The DLR, Germany, is acknowledged with appreciation for providing radar images free of charge, and the GSMB, Sri Lanka, is acknowledged for providing the geological data necessary for this research work freely. Financial support Financial support. This research has been supported by the HETC project, Ministry of Higher Education, Sri Lanka (SUSL/O-Geo/N2). Review statement Review statement. 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Zhan, X., Miller, S., Chauhan, N., Di, L., Ardanuy, P., and Running, S.: Soil Moisture Visible/Infrared Imager/Radiometer Suite Algorithm Theoretical Basis Document, Version 5, 2002.	2019-09-16 08:38:43	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 9, "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": 0.7214802503585815, "perplexity": 4774.266420079128}, "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-2019-39/segments/1568514572516.46/warc/CC-MAIN-20190916080044-20190916102044-00086.warc.gz"}
https://stats.stackexchange.com/questions/329465/assessing-a-b-test-results-using-python	# Assessing A/B test results using Python ## Problem's setting Assume having results of an A/B test. You let you users experience two variants of your website and you counted how many converted: \| \| Converted \| Total visits \| \|--------\|-----------\|--------------\| \|Control \| $c_n$ \| $c_t$ \| \|Variant \| $v_n$ \| $v_t$ \| We have that the conversion rates are: \begin{align} \mathrm{CR}_c & = \frac{c_n}{c_t}\\ \mathrm{CR}_v & = \frac{v_n}{v_t} \end{align} We may pose three null hypotheses: • Two sided/tailed: $H_0: \mathrm{CR}_c = \mathrm{CR}_v$ and thus the alternative hypothesis is: $H_a: \mathrm{CR}_c \neq \mathrm{CR}_v$ • One sided/tailed: $H_0: \mathrm{CR}_c > \mathrm{CR}_v$ (or $H_0: \mathrm{CR}_c < \mathrm{CR}_v$) and in turn the alternative hypothesis is $H_a: \mathrm{CR}_c <= \mathrm{CR}_v$ (or $H_a: \mathrm{CR}_c >= \mathrm{CR}_v$) Before moving on, here is a list of some related discussions on Cross Validate: ## Two sided case As can be learned from the linked discussions, in this case there are two possible tests that can exploited: $z$-test and $\chi^2$-test. Here is an example: data = pd.DataFrame({ "Converted": [123, 133], "Total": [231, 262] }, index=['Control', 'Var']) # Output: # \| \| Converted \| Total # \| Control \| 123 \| 231 # \| Var \| 133 \| 262 Using statsmodels the two tests can be executed as follows: ssp.proportions_ztest(count=data.Converted, nobs=data.Total, alternative='two-sided') # Output: # (0.5507210148592081, 0.5818249364318755) ssp.proportions_chisquare(count=data.Converted, nobs=data.Total) # Output: # (0.30329363620755795, 0.5818249364318744, (array([[123, 108], [133, 129]]), array([[119.95131846, 111.04868154], [136.04868154, 125.95131846]]))) Using scipy.stats, the story is a little different. For the $\chi^2$-test, the input should be a contingency matrix which can be computed using pandas.DataFrame.concat: scipy.stats.chi2_contingency( pd.concat( [data.Total - data.Converted, data.Converted], axis=1), correction=False) # (0.303293636207558, 0.5818249364318744, 1, array([[111.04868154, 119.95131846], [125.95131846, 136.04868154]])) Note that the correction is set to False. Otherwise, the Yates’ correction kicks in. It can easily be seen that the $p$-values are the same (up to some floating point operations differences). Furthermore, the square of the $z$ static is the same as the one of the $\chi^2$. In this specific case, it is clear that the resulting $p$-value are large, and thus it is impossible to reject the null hypothesis. I am afraid I cannot point you to a straightforward $z$-test using scipy. ## One sided case The one sided case can only be evaluated using the $z$-test, and thus statsmodels is used. For the sake of demonstration, I consider three results. First, the control and variation groups have almost the same conversion rate: data = pd.DataFrame({ "Converted": [100, 145], "Total": [200, 300] }, index=['Control', 'Var']) ssp.proportions_ztest( count=data.Converted, nobs=data.Total, alternative='smaller'), ssp.proportions_ztest( count=data.Converted, nobs=data.Total, alternative='larger') # ((0.3652214232606525, 0.642526936116749), # (0.3652214232606525, 0.35747306388325095)) In this case, both one-sided tests yield high $p$-values; the null hypothesis cannot be rejected. Now, have a look in a case where the control set has a much lower conversion rate: data = pd.DataFrame({ "Converted": [80, 145], "Total": [200, 300] }, index=['Control', 'Var']) ssp.proportions_ztest( count=data.Converted, nobs=data.Total, alternative='smaller'), ssp.proportions_ztest( count=data.Converted, nobs=data.Total, alternative='larger') # ((-1.8349396085439338, 0.033257319037821406), # (-1.8349396085439338, 0.9667426809621786)) Now, the first test (corresponding to the "smaller" case) yields a low $p$-value. As a matter of fact so low that we can say it is $\sim 97\%$ safe to reject the null hypothesis being that the conversion rate of the alternative treatment is smaller. The symmetric case is when the null hypothesis is that the conversion rate of the alternative treatment is larger than the one of the control group: data = pd.DataFrame({ "Converted": [130, 145], "Total": [200, 300] }, index=['Control', 'Var']) ssp.proportions_ztest( count=data.Converted, nobs=data.Total, alternative='smaller'), ssp.proportions_ztest( count=data.Converted, nobs=data.Total, alternative='larger') # ((3.669879217087869, 0.9998786674495203), # (3.669879217087869, 0.00012133255047971392)) In this case the resulting $p$-values are going the other way around, suggesting that we can reject the "larger" null hypothesis. It is important to stress that you have to be careful what exactly you want to check, pick the suitable test and make sure you interpret the results accordingly. ## Questions 1. Is the problem setting I consider is a 2-sample or 1-sample? In particular in regards to the documentation of statsmodels.stats.power.NormalIndPower and statsmodels.stats.power.GofChisquarePower. 2. Is there a $z$-test for the setting I am considering using scipy? 3. Am I using the tests provided by statsmodels and scipy correctly for the problem setting I am considering? Should I take additional aspects into consideration? 4. Is there a way to run a one-sided $\chi^2$-test? As far as I understand it doesn't make sense.	2019-06-20 07:17:40	{"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": 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": 0.6728715896606445, "perplexity": 2126.188175626035}, "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/1560627999163.73/warc/CC-MAIN-20190620065141-20190620091141-00029.warc.gz"}
https://quantumcomputing.stackexchange.com/questions/18615/initial-state-preparation-for-hadamard-test	Initial state preparation for Hadamard test I thought I understood Hadamard test but it seems to be shaky. I understand that to get the expectation value $$\langle\psi\ \| V^\dagger\|{\bf Q}\|V\|\psi\rangle$$ we need to have gate $$V$$ (in blue) below but NOT orange $$V^\dagger$$ circuit block as my initial state is $$\|V\|\psi\rangle$$. Why don't we include the orange block? 1 Answer You could almost do it. In fact, the following circuit would work: You can convince yourself that what you do is in fact applying the unitary $$\mathbf{VUV^\dagger}$$, which will allow you to evaluate the real part of $$\langle\psi\|\mathbf{V^\dagger UV}\|\psi\rangle$$. Indeed, the standard Hadamard test allows you to evaluate the real part of $$\langle\psi\|\mathbf{Q}\|\psi\rangle$$. Here, we just replaced $$\mathbf{Q}$$ by our desired unitary. We need however in this case to be careful to the order in which we apply the gates, as pointed out in the comments. However, if we now consider the following circuit: You can see this as applying a standard Hadamard test to the state $$\mathbf{V}\|\psi\rangle$$ (note that $$\mathbf{V}$$ is no longer controlled by the first qubit). As such, this will allow you to evaluate the real part of $$(\langle\psi\|\mathbf{V}^\dagger)\mathbf{U}(\mathbf{V}\|\psi\rangle)=\langle\psi\|\mathbf{V}^\dagger\mathbf{U}\mathbf{V}\|\psi\rangle$$, which is what you want. From an implementation point of view, the latter requires less controlled gates, so it is surely preferable to use it instead of the former. If you were to include $$\mathbf{V}^\dagger$$ after the controlled-$$\mathbf{U}$$ gate, then the resulting unitary is a controlled $$\mathbf{VUV^\dagger}$$ gate (since we apply $$\mathbf{VUV^\dagger}$$ if the first qubit is in state $$\|1\rangle$$ and $$\mathbf{VV^\dagger}=\mathbf{I}$$ otherwise). Thus, this circuit would also work to compute the desired quantity, since it would be equivalent to the first circuit. All in all, removing this $$\mathbf{V^\dagger}$$ gate does not yield an equivalent circuit (the states before the measurement are different), but both can be used to evaluate the real part of $$\langle\psi\|\mathbf{V^\dagger UV}\|\psi\rangle$$. • Thanks for interesting way looking this. For the bottom circuit, what would happen if we include $V^/dagger$ after U? Jul 26 at 15:34 • @JohnParker I've edited my answer, please have a look. Jul 26 at 15:55 • Thank you for the good answer but could you look at your pictures again? the first picture starts with $V^/dagger$ the bottom starts with V.? Jul 27 at 1:44 • @JohnParker You're right, I thought that this was equivalent but it's not. I've updated the pictures accordingly. Jul 27 at 6:58	2021-09-17 03:24:47	{"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": 19, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8706263899803162, "perplexity": 247.44934157686754}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-39/segments/1631780054023.35/warc/CC-MAIN-20210917024943-20210917054943-00464.warc.gz"}
https://www.wyzant.com/resources/answers/users/86173128	01/17/16 #### Electron configuration of an ion of calcium When a calcium atom loses its valence electrons, the ion formed has an electron configuration that the same as... A) Cl B) Ar C) K D) Sc 01/17/16 #### Which of the following represents a polar molecule? A) Cl2 B) H2 C) HCl D) NaCl 01/17/16 #### Which of the following bonds is the most polar in nature? Which of the following bonds is the most polar in nature? O2, HCl, NH3, or HB 01/10/16 #### Convert 3/4 to 64ths How to convert 3/4 to 64ths? 12/07/15 #### tickets to a play cost $5 at the door and$4 in advance. The theater club wants to raise at least \$400 from the play. Write and graph an inequality for the numb Write and graph an Inequality for the number of theater tickets the theater club needs to sell to reach their goal. ## Still looking for help? Get the right answer, fast. Get a free answer to a quick problem. Most questions answered within 4 hours. #### OR Choose an expert and meet online. No packages or subscriptions, pay only for the time you need.	2021-10-19 22:18:54	{"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": 0.2017078548669815, "perplexity": 4948.514899686357}, "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/1634323585281.35/warc/CC-MAIN-20211019202148-20211019232148-00121.warc.gz"}
https://zbmath.org/?q=an%3A1365.90212	## A polynomially solvable case of the pooling problem.(English)Zbl 1365.90212 Summary: Answering a question of Haugland, we show that the pooling problem with one pool and a bounded number of inputs can be solved in polynomial time by solving a polynomial number of linear programs of polynomial size. We also give an overview of known complexity results and remaining open problems to further characterize the border between (strongly) NP-hard and polynomially solvable cases of the pooling problem. ### MSC: 90C26 Nonconvex programming, global optimization 90C60 Abstract computational complexity for mathematical programming problems Full Text: ### References: [1] Alfaki, M; Haugland, D, A multi-commodity flow formulation for the generalized pooling problem, J. Glob. Optim., 56, 917-937, (2013) · Zbl 1272.90103 [2] Alfaki, M; Haugland, D, Strong formulations for the pooling problem, J. Glob. Optim., 56, 897-916, (2013) · Zbl 1272.90054 [3] Audet, C; Brimberg, J; Hansen, P; Digabel, S; Mladenović, N, Pooling problem: alternate formulations and solution methods, Manag. Sci., 50, 761-776, (2004) · Zbl 1232.90349 [4] Ben-Tal, A; Eiger, G; Gershovitz, V, Global minimization by reducing the duality gap, Math. Program., 63, 193-212, (1994) · Zbl 0807.90101 [5] Boland, N; Kalinowski, T; Rigterink, F; Weber, T (ed.); McPhee, MJ (ed.); Anderssen, RS (ed.), Discrete flow pooling problems in coal supply chains, 1710-1716, (2015), Gold Coast [6] Boland, N; Kalinowski, T; Rigterink, F, New multi-commodity flow formulations for the pooling problem, J. Glob. Optim. Adv. Online Publ., (2016) · Zbl 1369.90132 [7] Boland, N., Kalinowski, T., Rigterink, F., Savelsbergh, M.: A special case of the generalized pooling problem arising in the mining industry. Optimization Online e-prints. (2015). http://www.optimization-online.org/DB_HTML/2015/07/5025.html · Zbl 1360.90258 [8] Buck, RC, Partition of space, Am. Math. Mon., 50, 541-544, (1943) · Zbl 0061.30609 [9] Witt, CW; Lasdon, LS; Waren, AD; Brenner, DA; Melhem, SA, OMEGA: an improved gasoline blending system for texaco, Interfaces, 19, 85-101, (1989) [10] Dey, SS; Gupte, A, Analysis of MILP techniques for the pooling problem, Oper. Res., 63, 412-427, (2015) · Zbl 1327.90351 [11] Gupte, A., Ahmed, S., Dey, S. S., Cheon, M. S.: Relaxations and discretizations for the pooling problem. J. Glob. Optim., to appear. Preprint: http://www.optimization-online.org/DB_HTML/2015/04/4883.html · Zbl 1392.90117 [12] Haugland, D; Casado, LG (ed.); García, I (ed.); Hendrix, EMT (ed.), The hardness of the pooling problem, 29-32, (2014), Spain [13] Haugland, D, The computational complexity of the pooling problem, J. Glob. Optim., 64, 199-215, (2015) · Zbl 1360.90258 [14] Haugland, D; Hendrix, EMT, Pooling problems with polynomial-time algorithms, J. Optim. Theory Appl., (2016) · Zbl 1346.90681 [15] Haverly, CA, Studies of the behavior of recursion for the pooling problem, SIGMAP Bull., 25, 19-28, (1978) [16] Rigby, B; Lasdon, LS; Waren, AD, The evolution of texaco’s blending systems: from OMEGA to starblend, Interfaces, 25, 64-83, (1995) [17] Tawarmalani, M., Sahinidis, N.V.: Convexification and Global Optimization in Continuous and Mixed-Integer Nonlinear Programming. Nonconvex Optimization and its Applications, vol. 65. Springer, New York (2002) · Zbl 1031.90022 [18] Visweswaran, V; Floudas, CA (ed.); Pardalos, PM (ed.), MINLP: applications in blending and pooling problems, 2114-2121, (2009), New York This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.	2022-08-08 21:50:32	{"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": 0.8276607990264893, "perplexity": 14625.926476791778}, "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/1659882570879.1/warc/CC-MAIN-20220808213349-20220809003349-00227.warc.gz"}
https://stats.stackexchange.com/questions/225970/interpretation-of-lasso-regression-coefficients	Interpretation of LASSO regression coefficients I'm currently working on building a predictive model for a binary outcome on a dataset with ~300 variables and 800 observations. I've read much on this site about the problems associated with stepwise regression and why not to use it. I've been reading into LASSO regression and its ability for feature selection and have been successful in implementing it with the use of the "caret" package and "glmnet". I am able to extract the coefficient of the model with the optimal lambda and alpha from "caret"; however, I'm unfamiliar with how to interpret the coefficients. • Are the LASSO coefficients interpreted in the same method as logistic regression? • Would it be appropriate to use the features selected from LASSO in logistic regression? EDIT Interpretation of the coefficients, as in the exponentiated coefficients from the LASSO regression as the log odds for a 1 unit change in the coefficient while holding all other coefficients constant. https://stats.idre.ucla.edu/other/mult-pkg/faq/general/faq-how-do-i-interpret-odds-ratios-in-logistic-regression/ • Can you fill in a little what you mean by "interpreted in the same way as logistic regression"? I'd be very useful to know exactly what interpretations you'd like to generalize. – Matthew Drury Jul 27 '16 at 19:04 • @Matthew Drury - Thank you so much for taking the time in assisting me, as my coursework never gone over LASSO. In general, from what I was taught during my graduate courses, the exponentiated coefficients from a logistic regression yields the log odds of a 1 unit increase in the coefficient while holding all the other coefficients constant. – Michael Luu Jul 27 '16 at 19:16 • In "caret" you select $\alpha$ and $\lambda$. Where does $\alpha$ come from? Is it probably a hyperparameter of an elastic net (the relative weight of LASSO versus ridge penalty) (in which case you would actually be using elastic net rather than LASSO)? – Richard Hardy Jul 27 '16 at 19:33 • As far as I can tell, significance testing for coefficients has not been introduced in most LASSO implementations. So could a difference not be that while we can determine statistically significant variables in OLS, we cannot do so with LASSO except making a weaker statement that the LASSO coefficients of corresponding variables selected are the "important" variables to consider? – godspeed Jul 27 '16 at 20:30 Are the LASSO coefficients interpreted in the same method as logistic regression? Let me rephrase: Are the LASSO coefficients interpreted in the same way as, for example, OLS maximum likelihood coefficients in a logistic regression? LASSO (a penalized estimation method) aims at estimating the same quantities (model coefficients) as, say, OLS maximum likelihood (an unpenalized method). The model is the same, and the interpretation remains the same. The numerical values from LASSO will normally differ from those from OLS maximum likelihood: some will be closer to zero, others will be exactly zero. If a sensible amount of penalization has been applied, the LASSO estimates will lie closer to the true values than the OLS maximum likelihood estimates, which is a desirable result. Would it be appropriate to use the features selected from LASSO in logistic regression? There is no inherent problem with that, but you could use LASSO not only for feature selection but also for coefficient estimation. As I mention above, LASSO estimates may be more accurate than, say, OLS maximum likelihood estimates. • Thank you so much for this response! Makes alot of sense! Please excuse my limited knowledge in this matter. As you have mentioned in another comment that I may be using elastic net rather than LASSO via caret as it chooses the optimal lambda and alpha. Would the same apply in regards to the coefficients? – Michael Luu Jul 27 '16 at 20:10 • Yes, it would. The basic logic remains the same. – Richard Hardy Jul 28 '16 at 5:42 • You write "interpretation remains the same". Could you help me understand this point? It seems to be me that the interpretation of OLS coefficients in a multiple regression setting relies on partial regression plots. However, this property does not hold for lasso coefficients, leading me to believe the interpretation would be different. – user795305 Oct 22 '17 at 13:37 • @Ben, If we assume an underlying statistical model, we can estimate its parameters in different ways, two popular ones being OLS and lasso. The estimated coefficients target the same targets, and both have some estimation error (which, if squared, can be decomposed into bias and variance), so in this sense their interpretation is the same. Now of course the methods are not the same, so you get different estimated coefficient values. If you care about the methods and their algebraic and geometrical interpretations, than these are not the same. But subject-matter interpretations are the same. – Richard Hardy Oct 22 '17 at 18:17 • @RichardHardy Ah, okay, I think I better understand what you're saying. It's certainly true that lasso may beat OLS in estimation error, but, at the end of the day, like you say, these are just estimators for the same target. Would any estimator be interpreted in the same way that OLS is interpreted? For instance, would the (nonrandom) estimator $(1, \dots, p)^T$ be interpreted that way? or the estimator with iid uniform(0,1) entries? (etc) It does seem (to me) that properties of the estimator need to be directly used in its interpretation, and even subject-matter interpretations would change. – user795305 Oct 22 '17 at 18:49	2021-01-24 13:14:47	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7949625849723816, "perplexity": 584.4920647792833}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-04/segments/1610703548716.53/warc/CC-MAIN-20210124111006-20210124141006-00678.warc.gz"}
http://openstudy.com/updates/55a4724fe4b0f93dd7c3af5f	## anonymous one year ago Write 4,500 in scientific notation. 1. jim_thompson5910 place the decimal point between the first two digits (4 and 5) 4.5 now we must move the decimal point $$\large \color{red}{3}$$ places to the right to get back to 4,500 so that is why $\Large 4,500 = 4.5 \times 10^{\color{red}{3}}$ Find more explanations on OpenStudy	2017-01-19 17:11:14	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6752698421478271, "perplexity": 787.8997898328985}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-04/segments/1484560280723.5/warc/CC-MAIN-20170116095120-00039-ip-10-171-10-70.ec2.internal.warc.gz"}
https://www.physicsforums.com/threads/thin-film-interference.401457/	# Homework Help: Thin-Film Interference 1. May 7, 2010 ### aaronb 1. The problem statement, all variables and given/known data A soap film with different thicknesses at different placers has an unknown refractive index n and air on both sides. In reflected light it looks multicolored. One region looks yellow because destructive interference has removed blue (($$\lambda_{vacuum}$$=469nm)) from the reflected light, while anotyher loks magenta because destructive interference has removed green (($$\lambda_{vacuum}$$=555nm)). In these regions the film has the minimum thickness t required for the destructive interference to occur. Find the ration t$$_{magenta}$$/t$$_{yellow}$$ 2. Relevant equations $$\lambda_{film}$$ = $$\lambda_{vacuum}$$/ n 3. The attempt at a solution i know from the problem that m =1 because it says minimum thickness. But after that I do not know how I should set up the problem using algebra or physics.	2018-07-20 15:58:15	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 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": 0.236704021692276, "perplexity": 1396.1862465980498}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-30/segments/1531676591718.31/warc/CC-MAIN-20180720154756-20180720174756-00423.warc.gz"}
http://math.stackexchange.com/questions/100981/on-the-use-of-the-topology-on-tangent-bundles/100987	# On the Use of the Topology on Tangent Bundles On learning about how to define smooth vector fields on a manifold $M$, I learned that one should first define a tangent bundle , $T(M)$, as $\cup T_p(M)$ together with a topology(smooth structure). And then, a smooth vector field $X$ would be a smooth map from $M \rightarrow T(M)$ s.t. $\pi \circ X=id_M$ However, it is obvious that the use of the auxilary manifold $T(M)$ should not be confined to merely offering a good def. of "smooth" vector fields. Well, at least you would not be using the global topology of $T(M)$. (Since the checking of "smoothness" is done locally) I am inclined to believe that the global topology of $T(M)$ may play a more important role in determining the properties of vectorfields on $M$. So here are my two questions: 1. Can you give an example where the global topology of $T(M)$ is used to control certain properties(possibly about vec. fields) on $M$? 2. If the global topology on $T(M)$ is indeed important, how do we set about determining it? I have only seen trivial examples where for $M=S^1 or \mathbb{R}^n$, $T(M)=M\times \mathbb{R}^n$. But surely, there are examples where $T(M)\neq M\times \mathbb{R}^n$. And how do we determine the topology in that case? - Let's consider the tangent bundle $T(S^2)$ of the $2$-dimensional sphere $S^2$. Note that $T(S^2)$ is not trivial bundle, i.e. $T(S^2)\not\simeq S^2\times\mathbb{R}^2$. To see this, let $X$ be a vector field of $T(S^2)$. Then, as you said, $X$ is a section of the tangent bundle $T(S^2)$, i.e. $X:S^2\rightarrow T(S^2)$ such that $\pi\circ X=id_{S^2}$. By Poincare-Hopf's theorem, $X$ must have a zero, i.e. there exists $p\in S^2$ such that $X(p)=0$. Therefore, $T(S^2)\neq S^2\times\mathbb{R}^2$; otherwise, if $T(S^2)\simeq S^2\times\mathbb{R}^2$, then there would exist a non-vanishing vector field $X$. More precisely, if $\pi: S^2\rightarrow T(S^2)\simeq S^2\times\mathbb{R}^2$, $X(p)=(p,(1,0))$ where $p\in S^2$ and $(1,0)\in\mathbb{R}^2$ is a non-vanishing vector field. From the above example, we can see that the topology of $T(S^2)$ (the property that $T(S^2)$ is non-trivial) gives property on the vector field. - About the next to last sentence, it seems to me that the non-existence of not vanishing vector fields on $S^2$ implies the non-triviality of $TS^2$, rather than the viceversa. – Giuseppe Tortorella Jan 21 '12 at 13:35 Ah, the Hairy Ball Theorem then confirms the non-triviality of $T(S^2)$. So I guess one could use the technique to find more manifolds with the "Hairy Ball" property given that if you could systematically calculate their tangent bundles! – Michael Luo Jan 21 '12 at 14:37 Of course the global topology of $T(M)$ is important. It controls, for example, the existence of globally-defined vector fields with certain properties. Conversely, the non-existence of certain vector fields tells us that the global topology of $T(M)$ is non-trivial. Consider the sphere $S^2$. By the hairy ball theorem, there are no continuous vector fields $S^2 \to T(S^2)$ which are nowhere vanishing. But if $T(S^2) \cong S^2 \times \mathbb{R}^2$ then by choosing a continuous basis of the tangent space at each point, we could obtain a continuous nowhere-vanishing vector field $S^2 \to T(S^2)$ — a contradiction. So $T(S^2) \ncong S^2 \times \mathbb{R}^2$. In the case of an embedded manifold $T(M)$ defined as the vanishing of some smooth function $F : \mathbb{R}^N \to \mathbb{R}^k$, it is easy to describe the tangent bundle as another embedded manifold $T(M)$: it is (diffeomorphic to) the submanifold $$\{ (x, \vec{v}) \in \mathbb{R}^N \times \mathbb{R}^N : F(x) = 0, D_x F (\vec{v}) = 0 \}$$ where $D_x F : \mathbb{R}^N \to \mathbb{R}^k$ is the Jacobian matrix of $F$ evaluated at $x$. So, for example, $$T(S^2) = \{ (x, y, z, u, v, w) \in \mathbb{R}^6 : x^2 + y^2 + z^2 = 1, 2 x u + 2 y v + 2 z w = 0 \}$$ It is an amusing exercise to show that $$T(S^n) \cong \{ (z_0, \ldots, z_n) \in \mathbb{C}^{n+1} : {z_0}^2 + \cdots + {z_n}^2 = 1 \}$$ In other words, $T(S^n)$ has the structure of a complex manifold! But of course some work still has to be done. It is not at all obvious from this calculation that $T(S^3) \cong S^3 \times \mathbb{R}^3$, which is a consequence of the existence of a Lie group structure on $S^3$. (All Lie groups have trivial tangent bundle.) - Dear Zhen Lin In your second sentence, I think that the two occurrences of $S^2\to\mathbb{R}^2$ should be replaced by $S^2\to T(S^2)$. – Giuseppe Tortorella Jan 21 '12 at 13:45 @Giuseppe: Quite right, thank you! – Zhen Lin Jan 21 '12 at 13:54 -Thanks for giving a way to actually compute $T(M)$, I can see how to make it rigorous.- Though I don't think I'm in a position to show $T(S^3)=S^3\times R^3$, I'll keep it in mind for future encounters. – Michael Luo Jan 21 '12 at 14:44 Every manifold with trivial tangent bundle is orientable: this is immediate from the definition. Hence every non-orientable manifold is an example of a manifold with non-trivial tangent bundle. Easy examples are the Möbius band, the real projective plane $\mathbb P^2(\mathbb R)$ and the Klein bottle. The point of view of orientability has the advantage that it is completely elementary and self-contained: no input from topology id s needed. (This is definitely not meant as a criticism of Paul's and Zhen's great answers which I have just upvoted: the theorems they allude to are quite interesting and should eventually be learned too) Edit Let me show you how easy it is to prove non-orientability! 1) A useful remark If $M$ is orientable and if $(U,x)$ and $(V,y)$ are two charts with connected domains $U,V$ , then the change of coordinates $\phi =y\circ x^{-1}: x(U\cap V) \to y(U\cap V)$ has a jacobian $Jac(\phi) =det (\frac {\partial y_i}{\partial x_j})$ which does not change sign on $x(U\cap V)\subset \mathbb R^n$. [This is remarkable because $U\cap V$ and $x(U\cap V)$ need not be connected even though $U$ and $V$ are] 2) Application: $\mathbb P^2(\mathbb R)$ is not orientable Consider the two charts $x :U\to \mathbb R^2:[1:v:w]\mapsto (v,w)$ and $y :V\to \mathbb R^2:[u:1:w]\mapsto (u,w)$ , where the domain $U$ (resp. $V$) is the set of $[u:v:w]\in \mathbb P^2(\mathbb R)$ with $u\neq 0$ (resp. $v\neq 0$). The change of coordinates is the diffeomorphism $$\phi=y\circ x^{-1}: \mathbb R^\times \mathbb R \to \mathbb R^\times \mathbb R:(u,v)\mapsto (\frac {1}{u},\frac {v}{u})$$ whose jacobian $(Jac (\phi))(u,v)= -\frac {1}{u^3}$ does change sign on its (disconnected!) domain $\mathbb R^*\times \mathbb R$. Hence $\mathbb P^2(\mathbb R)$ is not orientable according to the useful remark above. - I am a little hazy on the definition of orientability, is it: Given any loop starting and ending at P, a smooth change of tangent basis along the loop, the basis ending at P would have a positive determinant expressed as the basis starting at P? – Michael Luo Jan 21 '12 at 14:55 Dear @Michael: there are many definitions of orientable. The most elementary and operational is that you can find an atlas whose charts give rise to changes of coordinates with positive jacobian. I'll write an edit to show you how easily we can work with that definition. – Georges Elencwajg Jan 21 '12 at 16:45 Thanks for the elaboration! Turns out(from the Orientable and Hairy Ball thm example), the story is that properties of vec.fields on $M$ are somehow characterized in the topologies of $T(M)$ – Michael Luo Jan 21 '12 at 18:09	2015-05-27 23:01:50	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 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": 0.8994482755661011, "perplexity": 221.36939032345202}, "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/1432207929171.55/warc/CC-MAIN-20150521113209-00120-ip-10-180-206-219.ec2.internal.warc.gz"}
https://undergroundmathematics.org/trigonometry-compound-angles/r7021	Review question # Using angles in a pentagon... Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource Ref: R7021 ## Question $ABCDE$ is a regular pentagon. By projecting the broken line $AED$ on the line $AB$, or otherwise, show that $\cos\dfrac{\pi}{5}-\cos\dfrac{2\pi}{5}=\frac{1}{2}.$ Hence, or otherwise, show that $\cos\dfrac{\pi}{5} = \dfrac{\sqrt{5}+1}{4}$. Show further that $\cos\dfrac{3\pi}{5} = -\dfrac{\sqrt{5}-1}{4}$.	2018-09-26 11:40:19	{"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": 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": 0.21864007413387299, "perplexity": 1465.1805518654082}, "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-2018-39/segments/1537267164750.95/warc/CC-MAIN-20180926101408-20180926121808-00337.warc.gz"}
https://physics.stackexchange.com/questions/477814/time-evolution-using-the-dirac-equation	# Time evolution using the Dirac equation In non-relativistic qantum mechanics, the energy eigenstates (i.e.e eigensattes of the hamiltonian) evolve in phase according to their eigenenergies $$\phi_(t) = e^{-iE_nt}\phi_n(0)$$ using natural units. I am taking a course in particle physics, and there was a section on neutrino oscillations. In the caluclation of the probability of finding a neutrino in a diffrent state, the neutrino mass eigensates were assumed to evolve as above. However we are working with realtivitstic quantum mechnaics now. It is not clear to me why the states evolve in the same way.	2019-07-16 02:23:07	{"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": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 1, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9102658033370972, "perplexity": 695.2905767258623}, "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/1563195524475.48/warc/CC-MAIN-20190716015213-20190716041213-00259.warc.gz"}
https://includestdio.com/tag/shebang	# shebang 2020-12-13 ## shell – Should I put #! (shebang) in Python scripts, and what form should it take? The Question : 909 people think this question is useful Should I put the shebang in...	2022-11-27 18:39:45	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 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": 0.46630343794822693, "perplexity": 3736.567005758954}, "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-2022-49/segments/1669446710417.25/warc/CC-MAIN-20221127173917-20221127203917-00680.warc.gz"}
https://www.answers.com/Q/What_is_the_equivalent_fraction_for_1_fifth	Percentages, Fractions, and Decimal Values # What is the equivalent fraction for 1 fifth? ###### Wiki User The equivalent fraction for a fifth is 2/10 3/15 4/20 5/25 ect. 🙏🏿 0 🤨 0 😮 0 😂 0 25/125 🙏🏿 0 🤨 0 😮 0 😂 0 ## Related Questions ### Equivalent decimal of fraction one fifth? The decimal equivalent of the vulgar fraction 1/5, or one fifth, is equal to 0.2. ### What is the equivalent fractions for 1 fifth? One fifth = 1/5 Multiply the numerator (top) and the denominator (bottom) of the fraction by any non-zero integer. You will have an equivalent fraction. ### What will be an equivalent fraction be for one fifth? An equivalent fraction for one fifth would be two tenth if you multiply it by two. ### What is the equivalent fraction of 2025? An equivalent fraction is 2025/1.An equivalent fraction is 2025/1.An equivalent fraction is 2025/1.An equivalent fraction is 2025/1. ### What fraction is equivalent to 4over20? Expressed as a proper fraction in its simplest form, 4/20 is equal to 1/5 or one fifth. ### What is one fifth as a fraction? 1/5 is a fraction.One fifth is a fraction, so it is equal to 1/5 ### What fraction is one fifth equal to? One fifth is a fraction, so it's equal to one fifth or 1/5. ### What is the lowest equivalent fraction of 7 over 35? If you divide both sides of the fraction by 7, 7/35 becomes 1/5, or one fifth. ### Write an equivalent fraction for one-fifth? Equivalent fractions for 1/5 include: 2/10 3/15 4/20 Or any two integers where the division sum will equal 0.2. ### What fraction is equivalent to 7 and 8? The fraction equivalent to 7 is 7/1 while the fraction equivalent to 8 is 8/1. ### What is 1 fifth as a fraction in simplest terms? Any fraction with 1 as the numerator is in its simplest form. ### How many number in one-fifth? one-fifth = 1/5 as a fraction or 0.2 as a decimal ## Still have questions? Trending Questions What are fat burning foods? Asked By Wiki User What is half of 16? Asked By Wiki User Do potatoes have genders? Asked By Wiki User Previously Viewed	2021-02-28 04:45:57	{"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": 0.8668940663337708, "perplexity": 2374.9786351653115}, "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/1614178360107.7/warc/CC-MAIN-20210228024418-20210228054418-00279.warc.gz"}
https://zbmath.org/?q=an:1114.46041	# zbMATH — the first resource for mathematics A Kurosh-type theorem for type II$$_1$$ factors. (English) Zbl 1114.46041 One may assume that the von Neumann algebras referred to in this article are ultraweak closures of exact C-algebras, as for instance are the group von Neumann algebras of discrete exact groups. All tensor products referred to are von Neumann tensor products. The author’s §3 deals with Kurosh’s theorem and tensor products of the group von Neumann algebras. His §4 is concerned with crossed products and solidity results. A von Neumann algebra is called diffuse if it has no minimal projections. A type II$$_{1}$$ factor is prime if it is not isomorphic to a tensor product of any two type II$$_{1}$$ factors. e.g., group factors for free groups are prime. A type II$$_{1}$$ factor which is injective is also prime. A. Kuroš [Math. Ann. 109, 647–660 (1934; JFM 60.0082.02)] proved that for a sequence of groups $$\{ \Gamma_{i} \}$$ their free product can be expressed as a free product of a free group and conjugates of the $$\Gamma_{i}$$. In particular every subgroup $$\Lambda$$ of a free product $$\Gamma_{1} \Gamma_{2}$$ of groups is itself a free product of a free group $$F$$ and conjugates of subgroups of $$\Gamma_{i}$$ or $$\Gamma_{2}$$. The author proves an analogous result for the free product $$M$$ of von Neumann algebras $$M_{i}$$, viz., if $$N$$ is a non-prime non-injective subfactor of the free product $$M_{1} * M_{2}$$, whose relative commutant is a factor, then there exists a unitary $$u \in M$$ such that $$u^{}Nu$$ is contained in $$M_{1}$$ or $$M_{2}$$. It follows that $$M$$ is prime unless one of the $$M_{i}$$ is trivial or if both $$M_{i}$$ are isomorphic to $$\mathbb{M}_{2}(\mathbb{C})$$. The author’s theorem is a bit more general in that it holds also when he takes the above $$N$$ to be any injective type II$$_{1}$$ subfactor of the free product. The author calls a von Neumann algebra solid if for any diffuse von Neumann subalgebra the relative commutant is injective, following N. Ozawa [Acta Math. 192, No. 1, 111–117 (2004; Zbl 1072.46040)]. A weak version, for a finite von Neumann algebra, is semi-solidity, viz., the relative commutant of any type II$$_{1}$$ subalgebra is injective. The author considers the class, denoted by $$\mathcal{S}$$, of countable discrete groups $$\Gamma$$ such that the right and left actions of $$\Gamma \times \Gamma$$, on the ‘boundary’ of the Stone-Čech compactification of $$\Gamma$$, are amenable. The von Neumann group algebra of such a group $$\Gamma$$ is solid. This class of groups is attributed to G. Skandalis [K-Theory 1, No. 6, 549–573 (1988; Zbl 0653.46065)] because of his use of the boundary. The wreath product of groups $$\Delta$$ and $$\Gamma$$ involves $$\Gamma$$ acting on $$\Delta^{\Gamma}$$, a direct sum of $$\Delta$$’s indexed by $$\Gamma$$. Here $$\Gamma$$ acts on $$\Delta^{\Gamma}$$ by left translation, like a Bernoulli-shift action. The author uses the term ‘Bernoulli product’ of group algebras as a von Neumann algebra analogue of the wreath product. He constructs the crossed-product (or covariance) von Neumann algebra for the dynamical system made up of a von Neumann algebra $$A$$ with faithful trace $$\tau$$ and a trace-preserving action $$\alpha$$ as automorphims of a group $$\Gamma \in\mathcal{S}$$. The author now follows his methods used to prove solidity in N. Ozawa, loc. cit. He shows that if $$\Gamma$$ is exact (which relates to an amenable boundary as in Proposition 4.1) and for copies, indexed by $$\Gamma$$, of the hyperfinite type II$$_{1}$$ factor $$\mathcal{R}$$, for any diffuse von Neumann algebra $$Q \in \bigotimes_{\Gamma}$$$$\mathcal{R}$$ the relative commutant of $$Q$$ in the Bernoulli product is injective. He shows also that for a commutative ($$A.\tau)$$, $$\Gamma \in$$$$\mathcal{S}$$. The crossed product, not necessarily a II$$_{1}$$-factor, is semi-solid. For the commutative von Neumann algebra $$L^{\infty}([0,1])$$ and a measure preserving action of $$\Gamma \in {\mathcal S}$$, the Bernoulli shift implemented in the crossed product corresponds to the group measure space von Neumann algebra. The author mentions that solid type II$$_{1}$$ factors do not necessarily have Murray and von Neumann’s property $$(\Gamma)$$ but that the latter example, which is semi-solid, does has property $$(\Gamma)$$, cf., V. Jones’ and K. Schmidt’s [Am. J. Math. 109, 91–114 (1987; Zbl 0638.28014)] result that the cross-product factor does not have the property $$(\Gamma)$$ if and only if the action is ergodic but not strongly ergodic. In the case of the von Neumann algebra $$L^{\infty}([0,1])$$ and a measure preserving action of $$\Gamma \in \mathcal{S}$$ the crossed product corresponds to the group measure space; cf., the Bernoulli or topolopical Markov measure space as constructed in ergodic theory or in Shannon’s information theory. ##### MSC: 46L10 General theory of von Neumann algebras 46L55 Noncommutative dynamical systems 46L09 Free products of $$C^$$-algebras 20E06 Free products of groups, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations 46L35 Classifications of $$C^*$$-algebras ##### Citations: Zbl 1072.46040; Zbl 0653.46065; Zbl 0638.28014; JFM 60.0082.02 Full Text:	2022-01-25 08:51:07	{"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": 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": 0.7828226089477539, "perplexity": 283.64977676025046}, "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/1642320304798.1/warc/CC-MAIN-20220125070039-20220125100039-00571.warc.gz"}
https://socratic.org/questions/what-is-the-standard-form-of-y-x-3-x63-5-3x-4-5	# What is the standard form of y= (x-3)(x^3-5)-3x^4-5? Jun 4, 2017 Multiply through and collect like terms to find the solution: $y = - 2 {x}^{4} - 3 {x}^{3} - 5 x + 10$ #### Explanation: y=(x−3)(x^3−5)−3x^4−5 Multiply the two sets of brackets using the 'FOIL - firsts, outers, inners, lasts' rule. It's a simple way to ensure that we don't forget any of the necessary multiplications: y=(x^4-3x^3-5x+15)−3x^4−5 Now collect like terms to find the solution: $y = - 2 {x}^{4} - 3 {x}^{3} - 5 x + 10$ Note that the terms are written in decreasing orders of powers of $x$.	2022-05-26 17:54:01	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 5, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6221413612365723, "perplexity": 1049.9135646894379}, "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-2022-21/segments/1652662619221.81/warc/CC-MAIN-20220526162749-20220526192749-00283.warc.gz"}
http://www.sleipnirstuff.com/forum/viewtopic.php?f=83&p=303846	[ X ] Resizing a map using the OpenRA utility exe a retard guide for retarded window users... Page 1 of 1 Author Message noobmapmaker Level: 65 Position: Registered User Joined: 10 Dec 2014 Posts: 953 Kel: 296 [ Donate ] Online Status: Offline Posted: Fri Aug 04, 2017 7:42 pm Post subject: Resizing a map using the OpenRA utility exe And so that I dont forget it Somehow the guide doesnt help me to actually open the utility program and even when you've opened it there are a couple things that can make this frustrating if you don't know what needs to be done. So if you want to resize a Red Alert map: - Open CMD - Enter: cd [the path of the main OpenRA game]. Example: cd C:\Program Files (x86)\OpenRA - Enter: [the path of the main OpenRA game]>openra.utility.exe Example: C:\Program Files (x86)\OpenRA>openra.utility.exe ra This opens all commands available, but we are going to use the --resize-map command. Lets say we want to change Singles. First you can go to Skirmish in the OpenRA client to see the actual size of the map. In this case 108x50 cells (= width x height). Lets say you want to change it to 116x60. You'll allready have C:\Program Files (x86)\OpenRA> - Enter: openra.utility.exe ra --resize-map [the path to the map]\singles.oramap 116 60 find the map in your folder, then copy-paste the path followed by the name of the map, including the .oramap file extension. Example: C:\Program Files (x86)\OpenRA>openra.utility.exe ra --resize-map C:\Users\NoobMapMaker\Documents\OpenRA\maps\ra\release-20170527\themapthatIwanttoresize.oramap 128 96 C:\Program Files (x86)\OpenRA>openra.utility.exe ra --resize-map C:\Program Files (x86)\OpenRA\mods\ra\maps\themapthatIwanttoresize.oramap 128 96 Enter and wait... now check the folder that contained the original map. Don't forget to make a backup of your map before you play around with it! Note by Lucian: always add +2 cells to the size you're aiming for because on every edge of the map you'll have a 1 cell border where units cannot go. Yes, I am a retard and this is a retards' guide to resizing an OpenRA map._________________Post your fun replays online Gamereplays.org/openra Consider supporting OpenRA by setting a bounty or by donating for a serverLast edited by noobmapmaker on Wed Aug 09, 2017 8:39 am; edited 10 times in total 3.Lucian Level: 23 Position: Registered User Joined: 27 Dec 2016 Posts: 34 Kel: 29 [ Donate ] Online Status: Offline Posted: Mon Aug 07, 2017 2:53 am Thanks man, I have tried to do this in the past without success, I will try this again tonight when i get home. very, very useful! 3.Lucian Level: 23 Position: Registered User Joined: 27 Dec 2016 Posts: 34 Kel: 29 [ Donate ] Online Status: Offline Posted: Tue Aug 08, 2017 10:01 am Ah, was having some trouble, but I worked it out. In your examples you have written 128 x 96, it should be 128 96. 3.Lucian Level: 23 Position: Registered User Joined: 27 Dec 2016 Posts: 34 Kel: 29 [ Donate ] Online Status: Offline Posted: Tue Aug 08, 2017 10:07 am it's probably also worth mentioning what you are resizing isn't just the play area from 1,1, it's the border as well, from 0,0. i.e. you need to add 2 to each of the new numbers. if you want it 100 cells wide, you need to tell the utility to resize to 102. noobmapmaker Level: 65 Position: Registered User Joined: 10 Dec 2014 Posts: 953 Kel: 296 [ Donate ] Online Status: Offline Posted: Tue Aug 08, 2017 2:08 pm Will add and fixed the error, thanks!_________________Post your fun replays online Gamereplays.org/openra Consider supporting OpenRA by setting a bounty or by donating for a server JOo Level: 75 Position: Registered User Joined: 25 Jan 2012 Posts: 484 Kel: 81 [ Donate ] Online Status: Offline Posted: Tue Aug 15, 2017 1:01 pm Quote: a retard guide for retarded window users... noobmapmaker wrote (View Post): And so that I dont forget it Inq Level: 40 Position: Registered User Joined: 27 Sep 2015 Posts: 43 Kel: 21 [ Donate ] Online Status: Offline Posted: Tue Aug 15, 2017 2:32 pm Display posts from previous: All Posts1 Day7 Days2 Weeks1 Month3 Months6 Months1 Year Oldest FirstNewest First Page 1 of 1	2017-08-19 01:53:39	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8096871376037598, "perplexity": 6556.7367537168975}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-34/segments/1502886105291.88/warc/CC-MAIN-20170819012514-20170819032514-00280.warc.gz"}
https://www.aimsciences.org/journal/1556-1801/2013/8/1	# American Institute of Mathematical Sciences ISSN: 1556-1801 eISSN: 1556-181X All Issues ## Networks & Heterogeneous Media March 2013 , Volume 8 , Issue 1 Special issue dedicated to Hiroshi Matanoon the occasion of his 60th birthday: Part II Select all articles Export/Reference: 2013, 8(1): i-iii doi: 10.3934/nhm.2013.8.1i +[Abstract](2085) +[PDF](93.9KB) Abstract: Professor Hiroshi Matano was born in Kyoto, Japan, on July 28th, 1952. He studied at Kyoto University, where he prepared his doctoral thesis under the supervision of Professor Masaya Yamaguti. He obtained his first academic position as a research associate at the University of Tokyo. He then moved to Hiroshima University in 1982 and came back to Tokyo in 1988. He is a Professor at the Graduate School of Mathematical Sciences at the University of Tokyo since 1991. 2013, 8(1): 1-8 doi: 10.3934/nhm.2013.8.1 +[Abstract](2657) +[PDF](380.5KB) Abstract: We provide formal matched asymptotic expansions for ancient convex solutions to MCF. The formal analysis leading to the solutions is analogous to that for the generic MCF neck pinch in [1]. For any $p, q$ with $p+q=n$, $p\geq1$, $q\geq2$ we find a formal ancient solution which is a small perturbation of an ellipsoid. For $t\to-\infty$ the solution becomes increasingly astigmatic: $q$ of its major axes have length $\approx\sqrt{2(q-1)(-t)}$, while the other $p$ axes have length $\approx \sqrt{-2t\log(-t)}$. We conjecture that an analysis similar to that in [2] will lead to a rigorous construction of ancient solutions to MCF with the asymptotics described in this paper. 2013, 8(1): 9-22 doi: 10.3934/nhm.2013.8.9 +[Abstract](2931) +[PDF](427.6KB) Abstract: We analyze the evolution of multi-dimensional normal graphs over the unit sphere under volume preserving mean curvature flow and derive a non-linear partial differential equation in polar coordinates. Furthermore, we construct finite difference numerical schemes and present numerical results for the evolution of non-convex closed plane curves under this flow, to observe that they become convex very fast. 2013, 8(1): 23-35 doi: 10.3934/nhm.2013.8.23 +[Abstract](2810) +[PDF](345.9KB) Abstract: A reaction-diffusion equation with nonlinear boundary condition is considered in a two-dimensional infinite strip. Existence of waves in the bistable case is proved by the Leray-Schauder method. 2013, 8(1): 37-64 doi: 10.3934/nhm.2013.8.37 +[Abstract](2880) +[PDF](2045.6KB) Abstract: The deep quench obstacle problem $${\rm{\bf{(DQ)}}} $$\left\{ \begin{array}{l} \frac{\partial u}{\partial t}=\nabla \cdot M(u) \nabla w, \\ w + \epsilon^2 \triangle u + u \in \partial \Gamma(u), \end{array} \right.$$$$ for $(x,t) \in \Omega \times (0,T)$, models phase separation at low temperatures. In (DQ), $\epsilon>0,$ $\partial \Gamma(\cdot)$ is the sub-differential of the indicator function $I_{[-1,1]}(\cdot),$ and $u(x,t)$ should satisfy $\nu \cdot \nabla u=0$ on the free boundary'' where $u=\pm 1$. We shall assume that $u$ is sufficiently smooth to make these notions well-defined. The problem (DQ) corresponds to the zero temperature deep quench'' limit of the Cahn--Hilliard equation. We focus here on a degenerate variant of (DQ) in which $M(u)=1-u^2,$ as well as on a constant mobility non-degenerate variant in which $M(u)=1.$ Although historically more emphasis has been placed on models with non-degenerate mobilities, degenerate mobilities capture some of the underlying physics more accurately. In the present paper, a careful numerical study is undertaken, utilizing a variety of benchmarks as well as new upper bounds for coarsening, in order to clarify evolutionary properties and to explore the differences in the two variant models. 2013, 8(1): 65-78 doi: 10.3934/nhm.2013.8.65 +[Abstract](2484) +[PDF](412.5KB) Abstract: The insulin signaling pathway propagates a signal from receptors in the cell membrane to the nucleus via numerous molecules some of which are transported through the cell in a partially stochastic way. These different molecular species interact and eventually regulate the activity of the transcription factor FOXO, which is partly responsible for inhibiting the growth of organs. It is postulated that FOXO partially governs the plasticity of organ growth with respect to insulin signalling, thereby preserving the full function of essential organs at the expense of growth of less crucial ones during starvation conditions. We present a mathematical model of this reacting and directionally-diffusing network of molecules and examine the predictions resulting from simulations. 2013, 8(1): 79-114 doi: 10.3934/nhm.2013.8.79 +[Abstract](4093) +[PDF](648.5KB) Abstract: This paper deals with the existence of traveling fronts for the reaction-diffusion equation: $$\frac{\partial u}{\partial t} - \Delta u =h(u,y) \qquad t\in \mathbb{R}, \; x=(x_1,y)\in \mathbb{R}^N.$$ We first consider the case $h(u,y)=f(u)-\alpha g(y)u$ where $f$ is of KPP or bistable type and $\lim_{\|y\|\rightarrow +\infty}g(y)=+\infty$. This equation comes from a model in population dynamics in which there is spatial spreading as well as phenotypic mutation of a quantitative phenotypic trait that has a locally preferred value. The goal is to understand spreading and invasions in this heterogeneous context. We prove the existence of threshold value $\alpha_0$ and of a nonzero asymptotic profile (a stationary limiting solution) $V(y)$ if and only if $\alpha<\alpha_0$. When this condition is met, we prove the existence of a traveling front. This allows us to completely identify the behavior of the solution of the parabolic problem in the KPP case. We also study here the case where $h(y,u)=f(u)$ for $\|y\|\leq L_1$ and $h(y,u) \approx - \alpha u$ for $\|y\|>L_2\geq L_1$. This equation provides a general framework for a model of cortical spreading depressions in the brain. We prove the existence of traveling front if $L_1$ is large enough and the non-existence if $L_2$ is too small. 2013, 8(1): 115-130 doi: 10.3934/nhm.2013.8.115 +[Abstract](2686) +[PDF](458.9KB) Abstract: We consider a homogenization problem for the magnetic Ginzburg-Landau functional in domains with a large number of small holes. We establish a scaling relation between sizes of holes and the magnitude of the external magnetic field when the multiple vortices pinned by holes appear in nested subdomains and their homogenized density is described by a hierarchy of variational problems. This stands in sharp contrast with homogeneous superconductors, where all vortices are known to be simple. The proof is based on the $\Gamma$-convergence approach applied to a coupled continuum/discrete variational problem: continuum in the induced magnetic field and discrete in the unknown finite (quantized) values of multiplicity of vortices pinned by holes. 2013, 8(1): 131-147 doi: 10.3934/nhm.2013.8.131 +[Abstract](2411) +[PDF](614.8KB) Abstract: We consider a simplified 1-dimensional PDE-model describing the effect of contact inhibition in growth processes of normal and abnormal cells. Varying the value of a significant parameter, numerical tests suggest two different types of contact inhibition between the cell populations: the two populations move with constant velocity and exhibit spatial segregation, or they stop to move and regions of coexistence are formed. In order to understand the different mechanisms, we prove that there exists a segregated traveling wave solution for a unique wave speed, and we present numerical results on the stability" of the segregated waves. We conjecture the existence of a non-segregated standing wave for certain parameter values. 2013, 8(1): 149-170 doi: 10.3934/nhm.2013.8.149 +[Abstract](2880) +[PDF](3153.3KB) Abstract: The aim of this paper is first to find interactions between compartments of hosts in the Ross-Macdonald Malaria transmission system. So, to make clearer this association we introduce the concordance measure and then the Kendall's tau and Spearman's rho. Moreover, since the population compartments are dependent, we compute their conditional distribution function using the Archimedean copula. Secondly, we get the vector population partition into several dependent parts conditionally to the fecundity and to the transmission parameters and we show that we can divide the vector population by using $p$-th quantiles and test the independence between the subpopulations of susceptibles and infecteds. Third, we calculate the $p$-th quantiles with the Poisson distribution. Fourth, we introduce the proportional risk model of Cox in the Ross-Macdonald model with the copula approach to find the relationship between survival functions of compartments. 2013, 8(1): 171-190 doi: 10.3934/nhm.2013.8.171 +[Abstract](3294) +[PDF](417.7KB) Abstract: In this note we analyze a spatially structured SI epidemic model with vertical transmission, a logistic effect on vital dynamics and a density dependent incidence. The dynamics of the underlying system of ordinary differential equations are first shown to exhibit an infinite number of heteroclinic orbits connecting the trivial equilibrium with an interior equilibrium. Our mathematical study of the corresponding reaction-diffusion system is concerned with travelling wave solutions. Based on a detailed study of the center-unstable manifold around the interior equilibrium, we are able to prove the existence of an infinite number of travelling wave solutions connecting the trivial equilibrium and the interior equilibrium. 2013, 8(1): 191-209 doi: 10.3934/nhm.2013.8.191 +[Abstract](2671) +[PDF](430.8KB) Abstract: We consider pulse-like localized solutions for reaction-diffusion systems on a half line and impose various boundary conditions at one end of it. It is shown that the movement of a pulse solution with the homogeneous Neumann boundary condition is completely opposite from that with the Dirichlet boundary condition. As general cases, Robin type boundary conditions are also considered. Introducing one parameter connecting the Neumann and the Dirichlet boundary conditions, we clarify the transition of motions of solutions with respect to boundary conditions. 2013, 8(1): 211-260 doi: 10.3934/nhm.2013.8.211 +[Abstract](3197) +[PDF](3007.0KB) Abstract: The primary visual cortex (V1) can be partitioned into fundamental domains or hypercolumns consisting of one set of orientation columns arranged around a singularity or pinwheel'' in the orientation preference map. A recent study on the specific problem of visual textures perception suggested that textures may be represented at the population level in the cortex as a second-order tensor, the structure tensor, within a hypercolumn. In this paper, we present a mathematical analysis of such interacting hypercolumns that takes into account the functional geometry of local and lateral connections. The geometry of the hypercolumn is identified with that of the Poincaré disk $\mathbb{D}$. Using the symmetry properties of the connections, we investigate the spontaneous formation of cortical activity patterns. These states are characterized by tuned responses in the feature space, which are doubly-periodically distributed across the cortex. 2013, 8(1): 261-273 doi: 10.3934/nhm.2013.8.261 +[Abstract](3161) +[PDF](386.5KB) Abstract: A stochastic modulation of the safety distance can reduce traffic jams. It is found that the effect of random modulation on congestive flow formation depends on the spatial correlation of the noise. Jam creation is suppressed for highly correlated noise. The results demonstrate the advantage of heterogeneous performance of the drivers in time as well as individually. This opens the possibility for the construction of technical tools to control traffic jam formation. 2013, 8(1): 275-289 doi: 10.3934/nhm.2013.8.275 +[Abstract](3285) +[PDF](418.7KB) Abstract: In this paper, we explain in simple PDE terms a famous result of Bramson about the logarithmic delay of the position of the solutions $u(t,x)$ of Fisher-KPP reaction-diffusion equations in $\mathbb{R}$, with respect to the position of the travelling front with minimal speed. Our proof is based on the comparison of $u$ to the solutions of linearized equations with Dirichlet boundary conditions at the position of the minimal front, with and without the logarithmic delay. Our analysis also yields the large-time convergence of the solutions $u$ along their level sets to the profile of the minimal travelling front. 2013, 8(1): 291-325 doi: 10.3934/nhm.2013.8.291 +[Abstract](2557) +[PDF](976.3KB) Abstract: The Gierer-Meinhardt system is a mathematical model describing the process of hydra regeneration. This system has a stationary solution with a stripe pattern on a rectangular domain, but numerical results suggest that such stripe pattern is unstable. In [8], Kolokolnikov et al. proved the existence of a positive eigenvalue, which is called an unstable eigenvalue, for a stationary solution with a stripe pattern by the NLEP method, which implies the instability of the stripe pattern. In addition, the uniqueness of the unstable eigenvalue was shown under some technical assumptions in [8]. In this paper, we prove the existence and uniqueness of an unstable eigenvalue by using the SLEP method without any extra conditions. We also prove the existence of a single-spike solution in one-dimension. 2013, 8(1): 327-342 doi: 10.3934/nhm.2013.8.327 +[Abstract](2417) +[PDF](403.9KB) Abstract: A reaction diffusion system with a distributed time delay is proposed for virus spread on bacteria immobilized on an agar-coated plate. A distributed delay explicitly accounts for a virus latent period of variable duration. The model allows the number of virus progeny released when an infected cell lyses to depend on the duration of the latent period. A unique spreading speed for virus infection is established and traveling wave solutions are shown to exist. 2013, 8(1): 343-378 doi: 10.3934/nhm.2013.8.343 +[Abstract](3096) +[PDF](644.1KB) Abstract: We adapt (ray-based) geometrical optics approaches to encompass the formal asymptotic analysis of front propagation in a Fisher-KPP equation with slowly varying spatial inhomogeneities. The wavespeed is shown to be selected by two distinct (and fully constructive) mechanisms, depending on whether the source term is an increasing or decreasing function of the spatial variable. Canonical inner problems, analogous to those arising in the geometrical theory of diffraction, are formulated to give refined expressions for the wavefront location. Additional phenomena, notably the initiation of new fronts and the transitions that occur when the source term is a non-monotonic function of space, are shown to be amenable to the same asymptotic approaches. 2013, 8(1): 379-395 doi: 10.3934/nhm.2013.8.379 +[Abstract](2629) +[PDF](435.2KB) Abstract: It is well known that a competition-diffusion system has a one-dimensional traveling front. This paper studies traveling front solutions of pyramidal shapes in a competition-diffusion system in $\mathbb{R}^N$ with $N\geq 2$. By using a multi-scale method, we construct a suitable pair of a supersolution and a subsolution, and find a pyramidal traveling front solution between them. 2013, 8(1): 397-432 doi: 10.3934/nhm.2013.8.397 +[Abstract](2388) +[PDF](647.9KB) Abstract: In analogy to the analysis of minimal conditions for the formation of diffusion driven instabilities in the sense of Turing, in this paper minimal conditions for a class of kinetic equations with mass conservation are discussed, whose solutions show patterns with a characteristic wavelength. The related linearized systems are analyzed, and the minimal number of equations is derived, which is needed for specific patterns to occur. 2020 Impact Factor: 1.213 5 Year Impact Factor: 1.384 2020 CiteScore: 1.9	2021-10-27 06:04:44	{"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": 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": 1, "x-ck12": 0, "texerror": 0, "math_score": 0.7400677800178528, "perplexity": 540.7200463606375}, "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/1634323588102.27/warc/CC-MAIN-20211027053727-20211027083727-00558.warc.gz"}
https://mirror.uncyc.org/wiki/Talk:N00b	# Talk:N00b ${\displaystyle Y_{o}u_{a}r_{e}w_{e}l_{c}o_{m}e_{!}!_{!}}$ FYI I was serious. -- 21:16, 24 June 2006 (UTC) I replaced the european noob section with something a little better. The original was just an outright attack. -Flyberius 16:59, 17 July. ## Runescape WTF is up with the runescape BS? No one fucking cares about RS, except maybe the person who wrote this article.The preceding unsigned comment was added by 217.209.112.102 (talk • contribs) HA HA HA HA! NO0B! I PWN U!!! 15:22, 12 May 2009 ## Locks ```locks are so not n00bie, I demand to have this removed! 88.108.58.38 15:26, 6 July 2007 (UTC) ``` My brother (tehklinger) added the over exaggerated "g0bl1n v1llag3" thing a day before the lock. ## Greenday? Why is everything linked to Greenday? Any reson? Yeah... One or more IP-users thinking they're god's gift to humor. Either they thought wrong, or they need to change religions... -- 09:19, 7 May 2006 (UTC) ## quotes Why where 80% of all the quotes removed? This should of been discussed first.--Scott 21:28, 1 November 2006 (UTC) Nobody checks the talk page of this thing. Except maybe me. Anyways, some of the quotes are redundant, repetitive, unfunny and lack humour. By "some", I mean 80%. -- [sire] EMC [TALK] 02:59, 4 November 2006 (UTC) Also: There's no Oscar Wilde. I don't think that's acceptable. be creative --88.159.88.176 12:48, 2 August 2008 (UTC) ## Genuine 100% real N00b quote Just to let you know I actually mangled that n00b quote and left it there on purpose emc - it seemed like a good one to do that with to illustrate the actions of the n00b in the wild. I'm not all that bothered, but if you feel like adding it back then it's up to you. I'll just go and get rid of what that n00b aftjimmy kimmel was here er me actually added... -- (but) Untrue Whhhy?Whut?How? Back from the dead 23:42, 5 February 2007 (UTC) Yes, yes indeed...adding it back, I shall. -- [sire] EMC [TALK] 17:08, 6 February 2007 (UTC) We forgot the spelling of the word n00b/etc... that is N00bz0rc0pt3r. ## Pictures I'm sure we could have much better pictures on this page, mainly talking about the how to spot a noob section (where I added one) and the "What a noob sees everyday" section. Skyl3lazer 00:25, 31 March 2007 (UTC) I am a good reader of uncyclopedia for a long time, but there is no doubt that right now i am a n00b writer too:D but as i always dreamed about, i would like to make a contribution to this article..feel free to use :P A n00b expressing his good feelings.. --OMG That's the Funky Shit!! 23:07, October 18, 2009 (UTC) ## Does this guy seem like a noob? www.pleke.co.uk - He thinks he's so hard ;P Srslylol 12:19, 4 November 2007 (UTC) I'm a stupind n00b. Sry. --84.231.37.171 17:27, 21 December 2007 (UTC) ## Wikipedia? h3y guyz is this wikepedia/??!?!?!!1111oneoneelevelone!11! ok i think we should make a artical about my band we're awesome my frend scott he plays gitar and he can do a c scal!!11111oneone ^The very DEFENITION of n00b. The One and Only... NecroBlade [STFU] Live And Learn... ## Finally, my first major edit.. Plus contribution points! Ahhhhahahaha! Victory! At last, a days work done, and I.. Probably didn't really do that much. <_<; Fixed a bunch of spelling errors, made some sections make more sense, while not changing what the author said (Because im not a douche), but some of it... I just don't get. There are comments in there, if you don't feel like fixing it yourself to make it spek engleshlawl, then maybe you could just explain it to me, I'll fix it tomorrow about 8am-ish PST. ~GG~ Thorium Brotherhood Is Not 19:19, 17 June 2008 (UTC) Awesome. Glad you are enjoying editing here. MrN http://images.wikia.com/uncyclopedia/images/4/4e/HalIcon.png 19:22, Jun 17 ## Famous Quotes. "Let me Crush the N00BZ under my royal boot." Alexander the Great "Madness? This Is Halo!!!!" Leonidas, before he took 1337 Spartans to war against the MLGs (Man Love Group) "And He Brought Forth the BanHammer, And the N00BZ jizzed" The Pope --Demonic Rabbit Fiddler 19:59, March 14, 2010 (UTC) ## The Roman N00b Games did you know that in ancient rome (despite what most history books tell us) n00bs where thrown to the lions or fought as gladitors (this derives from a a mistake in translations of ancient texts, the latin for christian is Sarcalogos... the actual text read Suckalogos, the latin for n00b) the emporor at the time, at the end of the fight would either put his thumb down for "kill this fucking n00b" or put his thumb up for "kill this fucking n00b" --Gr33nmag1k 20:01, March 14, 2010 (UTC)	2019-08-25 14:41:15	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 1, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5171338319778442, "perplexity": 8985.468125593112}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-35/segments/1566027330233.1/warc/CC-MAIN-20190825130849-20190825152849-00071.warc.gz"}
http://pinboard.in/u:daguti/t:explanation-simplification/	daguti + explanation-simplification 93 « earlier The Secret Reason Why Outlets Have Three Prongs Really good explanation. I knew most of what they said here, but the fact that some new appliances only have two prongs always made me think, until I read the explanation here: "So, why is it that some electronic devices still only use two prongs? Devices with only two prongs tend to fall into three categories: they’re old, they don’t use enough electricity to cause lethal harm, or they have sufficient insulation and a non-conductive exterior (i.e. a plastic outer shell instead of a metal one) so that you’re unlikely to be electrocuted even if there’s a malfunction." energy-electricity explanation-simplification february 2018 by daguti Razor REVAMP Service This place seems to know what they're talking about with regard to fixing and refinishing razors. ===== In regards to marketing, this is exactly the kind of content that companies need to be producing. The other good thing is that they gave the service a name "Razor Revamp" which is not known in the industry. This way, when people try to find a competing service, they A) won't find a competitor because no one is using that term and B) even when competitors (or forums) start using that term, there's always some doubts in the prospect's head about whether the service is a 1:1 comparison. Note that I bookmarked a Shavenook.com thread on 2018-01-25 that lists various other competitors, in case you're looking for other places. It seems to say that RazorEmporium didn't do a great job and that Reliable Electroplating in Mass. can do a good job. shaving Reference marketing-good-content-examples explanation-simplification january 2018 by daguti Not All Projectors Are Created Equal - YouTube A great explanation of why 3LCD projectors are worth the money and 1chip or 1LCD projectors are not. Fantastic. I had no idea about this, but now I want to buy a 3LCD projector. keywords: 3 led , 3led, 3 lcd , 3lcd video marketing-good-content-examples explanation-simplification filmmaking-technique marketing-tactics--educating-or-content-marketing may 2016 by daguti This Facebook bug could have allowed hackers to take over your account – Naked Security The first few paragraphs offer a simple explanation of XSS a.k.a. Cross-site scripting. explanation-simplification programming january 2016 by daguti How Eco-Friendly is Bamboo Fabric, Really? \| Ecouterre Bamboo fiber: Vicose is essentially Rayon, which is a regenerated cellulose fiber, which means that a natural raw material is converted through a chemical process into a fiber that falls into a category between naturals and synthetics. The source of cellulose can be wood, paper, cotton fiber, or in this case bamboo. ............... Be sure to read the comments where some people talk about bad information in the article. It's not really bad info, in my opinion, just people being picky, but still good to know. clothing explanation-simplification december 2015 by daguti Next time you laugh at an infomercial! - Album on Imgur Tumblr asserts that infomercial products are actually meant for disabled people, but that's such a tiny market segment, that they sell them in infomercials so that the people who actually need them can get them and everyone else covers the cost of production that would have been too astronomical if they had only been sold in specialty stores/catalogs for the disabled. explanation-simplification tumblr december 2015 by daguti Guy Kawasaki - This is a 2,000 word masterclass on typography,... This bit of copy that Guy Kawasaki wrote in his post about the article is what convinced me to click: "This is a 2,000 word masterclass on typography, guaranteed to improve your design ability." ................... Just goes to show the power of copy writing. I never would have clicked if it had said "Learn Typography In Seconds!" or "Typography for Beginners!" --- this reiterates the point that different people have to hear things in different ways for it to click. Hence, you can reuse the same article multiple times with different introduction or caption text to draw in different readers. people-guy-kawasaki marketing-tactics--writing-copy explanation-simplification fonts-related-to design getting-started howto november 2015 by daguti It's all a hoax - Album on Imgur A great way of presenting to reel in those that believe global warming is a hoax. It starts by calling it "Global Hoax" instead of "Global Warming" and then presents each argument for why global warming is a hoax. It slowly destroys each point and shows the real culprit: Greenhouse gasses. ........... See the comments that raise valid points: "downvoting, not because warming is not real, but for shit science. Google global temperature chart 10000 years for a better picture" and "humands are 100% a contributor.. but a graph that starts in 1880 shows nothing..." climate climate-global-warming environment visualization explanation-simplification november 2015 by daguti Squatty Potty - This Unicorn Changed the Way I Poop business-executing, ideas-stolen = The reason I'm bookmarking this is that this is a perfect example of flawless execution. Others that could go in this category of flawless execution are simple ideas like 5 Hour Energy, Monster Energy Drinks, bottled water (Poland Spring), Dunkin Donuts, Starbucks, Goya, McDonald's... or just about any "regular" non-high-tech business. .......... strategy = Important to note on a strategic level that they started in the caveman/paleo crowd, but eventually branched out to the mass market. Same with 5 Hour Energy. I noticed how their commercials evolved from targeting people who need a morning wakeup to people who need an afternoon pep-me-up to ... I forgot the other market segments, but they definitely changed the messaging over time. ..... GODDAM! I just watched the whole ad and noticed that it explains why it works and they use testimonials, too. It's like they incorporated every best practice into a single ad. BRAVO SQUATTY POTTY! november 2015 by daguti ▶ You Are Now Less Dumb, David McRaney - YouTube Great example of what I could do with the 100 Words project. april 2015 by daguti Zero G Anti-Gravity iPhone Case - Available on Kickstarter - YouTube Harry Price posted on Internet Marketing Super Friends: " How to Sell Without Selling A case study about turning desire into demand. Hey, Supers. This is a link to a video: Zero G Anti-Gravity iPhone Case - Available on Ki…: http://youtu.be/VDWfn5ej2uo I'm not affiliated to this Kickstarter campaign. I've also never been so excited to buy a PRODUCT (the iPhone 6) from reviewing a video for a PRODUCT ACCESSORY. This video has it all. How can you learn from it? Here's a few ways I noted below. #1: It shows REAL average people doing normal, average, everyday things while using the accessory to make experiences more intuitive. #2: It has an upbeat song that encapsulates the mood of the experience, so you literally feel like you want to be a part of the craze. #3: There's no 'selling' involved, except for creating desire to be like one of the individuals who seems to be enjoying their purchase. Buying power is a strong force." video explanation-simplification filmmaking-technique april 2015 by daguti Men Custom Suits & Custom Shirts \| Tailor4Less I like how they have taken the complicated process of measuring a suit and simplified it. We could use this as a model for doing other products, including "What is a cappucino?" Or "What is a latte?" and other such things. clothing fashion explanation-simplification website-examples projects-w-ted-rocknjoe shopping april 2015 by daguti I don't know or care about wrestling, but this made me watch the whole 24 minutes. Really well done. marketing-good-content-examples explanation-simplification video filmmaking-technique marketing-tactics--educating-or-content-marketing march 2015 by daguti Meat and Antibiotics - 2013 Meat Eaters Guide \| Meat Eater's Guide to Climate Change Health \| Environmental Working Group "A significant contributor to the looming superbug crisis, according to scientists and health experts, is unnecessary antibiotic usage by factory farms that produce most of the 8.9 billion animals raised for food in the U.S. every year. Industrial livestock producers routinely dose their animals with pharmaceuticals, mostly administered with limited veterinary oversight and frequently without prescriptions, to encourage faster growth or prevent infection in crowded, stressful and often unsanitary living conditions." ............................ explanation-simplification = See the 4-step infographic "Superbugs From Farm To Work" medicine-pharmaceuticals-drugs-prescriptions food food-factory-farming warnings explanation-simplification december 2014 by daguti Also see comment by Sohyessofresh, starting "I suspect that this comment might..." war explanation-simplification countries-iraq december 2014 by daguti Facebook is now accessible through the Deep Web video, explanation-simplification = See the video at the bottom (which I think I've bookmarked in the past anyway...) facebook new-features startups-going-above-and-beyond news 2014 security-computer hiddeninfo explanation-simplification video october 2014 by daguti Economists Say We Should Tax The Rich At 90 Percent: "A 90 percent top marginal tax rate doesn’t mean that if you make $450,000, you are going to pay$405,000 in federal income taxes. Americans have a well-documented trouble understanding the notion of INSIGHT: And this is how the rich & rich apologists take advantage to spread their retarded message: They take advantage of the fact that people don't understand marginal tax rates, estate taxes, other things and they make it sound like everyone pays those taxes. It's the only way they can get non-wealthy (i.e. the majority) to side with them. Grimy bastards. .............. "Economists Say We Should Tax The Rich At 90 Percent: "A 90 percent top marginal tax rate doesn’t mean that if you make $450,000, you are going to pay$405,000 in federal income taxes. Americans have a well-documented trouble understanding the notion of marginal tax rates."" ............................... poverty = Lots of the top comments discussing poverty. ............... One of the best explanations of marginal tax rate & deductions: http://www.reddit.com/r/politics/comments/2k05zr/economists_say_we_should_tax_the_rich_at_90/clh6cgz explanation-simplification wealth-income-distribution poverty me-stuff me-stuff-foundational-influence taxes-as-a-concept october 2014 by daguti What My Bike Has Taught Me About White Privilege \| A Little More Sauce I thought I was going to hate this, but the analogy is particularly well suited to the purpose. Perhaps because I've ridden in traffic and know just how dangerous "good, well intentioned drivers" can be - never mind the ones high out of their mind or the ones who actively hate you. --------------------- wealth-income-distribution = Although this guy is talking about race, I think the analogy is perfectly suited to discussing middle class privilege and how anyone middle class or above sees the poor. It's not just about "trying harder" or "working longer", there are active issues that keep you down, unable to work longer, get places you need to go, etc. race bicycle explanation-simplification wealth-income-distribution me-stuff september 2014 by daguti Adobe Voice: A Happy App for Making Explainer Videos Wow, an easy way to make explainer videos with an Adobe app called Adobe Voice. (only for iPad right now) may 2014 by daguti A Review of the MovNat One-Day Fundamentals Workshop \| Mark's Daily Apple explanation-simplification = See the paragraph near the end, starting with "Three of the pillars of MovNat..." meetup-movnat exercise-movnat explanation-simplification may 2014 by daguti Leverage Points: Places to Intervene in a System - The Donella Meadows Institute 2nd of 2 resources on systems. 1st was "Systemantics"/CoolTools bookmarked 2014-03-01 ............ 2015-09-29: I've found myself coming back to this time and again --> "The systems analysis community has a lot of lore about leverage points. Those of us who were trained by the great Jay Forrester at MIT have all absorbed one of his favorite stories. “People know intuitively where leverage points are,” he says. “Time after time I’ve done an analysis of a company, and I’ve figured out a leverage point — in inventory policy, maybe, or in the relationship between sales force and productive force, or in personnel policy. Then I’ve gone to the company and discovered that there’s already a lot of attention to that point. Everyone is trying very hard to push it IN THE WRONG DIRECTION!”" ....... "Counterintuitive. ... Leverage points are not intuitive. Or if they are, we intuitively use them backward, systematically worsening whatever problems we are ..." (saved as PDF in \media\text..\business) april 2014 by daguti lXnxcwK.gif (GIF Image, 480 × 480 pixels) How QR Codes Work - a GIF that shows the different parts of the QR code, what each section does and how it works. reference explanation-simplification codes-qr-codes howto april 2014 by daguti Simplifying Website Usability: The 3 Step Approach \| Webdesigner Depot The 3 step approach to explaining what people are supposed to do when they come to your site. website-examples explanation-simplification website-improvement march 2014 by daguti ▶ Math Sucks, but this little animation is super-fun - YouTube A commercial for a tutor - ThatTutorGuy.com -- What PERFECT copy. Convincing, hits all the right pain points and entertaining. explanation-simplification video teaching marketing-tactics--writing-copy filmmaking-technique march 2014 by daguti Cool Tools – Systemantics 1st of 2 resources, the other is a blog post bookmarked 4/25/2014 with these same tags minus "gifts" ---------------------------------------------- hacking = Taking something apart, understanding it and putting it back together again. .................................. This would be a great gift for someone like Rob. --------------------------- Avail on Amazon: http://www.amazon.com/dp/B00AK1BIDM/cooltools-20 --------------- http://www.amazon.com/dp/0961825170/cooltools-20 march 2014 by daguti Programs like TrueCrypt and KeePass ask you to move your mouse randomly in order to increase password strength. This reddit comment explains how that process works. explanation-simplification encryption companies-reddit january 2014 by daguti When Cheeseburger = Walking, Will We Eat Less? : The Salt : NPR visualization = This is not a visualization, but the act of showing food as "hours of work needed to work it off" is taking food from a calorie number to a "visual" representation. visualization fitness food health explanation-simplification april 2013 by daguti I live here and I still don't get it - Imgur Infographic showing what geographic territories are included in various terms like "British Isles", "Great Britain", "United Kingdom", etc visualization geography maps countries explanation-simplification countries-united-kingdom march 2013 by daguti Viral Video Shows the Extent of U.S. Wealth Inequality The matter of wealth inequality in the United States is well known, but this video shows you the extent of that inequality in dramatic and graphic fashion. money wealth-income-distribution wealth video explanation-simplification march 2013 by daguti How Rooting Works — A Technical Explanation of the Android Rooting Process I have always been curious how rooting actually worked behind the scenes. After recently acquiring a new Eee Pad Slider, a Honeycomb tablet that so far no one has been able to root, the frustration of being locked out of this amazing piece of hardware with so much potential led me to finally sit down and figure out what exactly rooting means, what it entails from a technical perspective, and how hackers out in the wild are approaching the rooting of a new device. Although all this information is out there, I have not been able to find a good [...] february 2013 by daguti Jeff Jarvis - Google+ - Really superb NPR visualization of campaign spending. It's… http://www.kickstarter.com/projects/928340467/ormr-the-smart-image-editor and Jeff Jarvis' comment was: "Really superb NPR visualization of campaign spending. It's also a magnificent demonstration of what I tell NPR people all the time: No, your value is not making great audio. It's explaining the world well." visualization filmmaking video explanation-simplification people-jeff-jarvis november 2012 by daguti New Timothy Ferriss Book, '4-Hour Chef', Has A Great Trailer (VIDEO) For when you are out of ideas about how to encapsulate a 300+ page book in an exciting, 1 minute video... explanation-simplification filmmaking-technique video people-tim-ferriss november 2012 by daguti	2019-03-26 04:01:40	{"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": 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": 0.18043263256549835, "perplexity": 5323.852568803896}, "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-2019-13/segments/1552912204790.78/warc/CC-MAIN-20190326034712-20190326060712-00110.warc.gz"}
http://clay6.com/qa/27511/find-speed-of-light-in-medium-a-if-speed-of-light-in-medium-b-is-large-frac	Browse Questions # Find speed of light in medium 'a' if speed of light in medium 'b' is $\large\frac{c}{3}$ where $c=$ Speed of light in vaccum and light refracts from medium 'a' to medium 'b' making $45^{\circ}$ and $60^{\circ}$ respective with normal. $(a)\;Va= \frac{\sqrt 2}{\sqrt 3}C \\ (b)\;Va= \frac{\sqrt 2}{3 \sqrt 3}C \\ (c)\;Va= \frac{3 \sqrt 2}{\sqrt 3}C \\ (d)\; Va=\sqrt {\frac{3}{2}}C$ By Snell's law $\mu_a \sin \theta_a = \mu b \sin \theta_b$ $\large\frac{c}{V_a}$$\sin \theta_a=\large\frac{C}{Vp}$$ \sin \theta_b$ $\large\frac{C}{V_a} $$\sin 45^{\circ}=\large\frac{c}{c/3}$$\sin 60^{\circ}$ $Va= \large\frac{\sqrt 2}{3 \sqrt 3}$$C$ Hence b is the correct answer.	2017-05-27 02:24:03	{"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": 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": 0.480217307806015, "perplexity": 2813.2997228231357}, "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/1495463608765.79/warc/CC-MAIN-20170527021224-20170527041224-00188.warc.gz"}
http://www.reference.com/browse/Tetragonal+crystal+system	Definitions # Tetragonal crystal system In crystallography, the tetragonal crystal system is one of the 7 lattice point groups. Tetragonal crystal lattices result from stretching a cubic lattice along one of its lattice vectors, so that the cube becomes a rectangular prism with a square base (a by a) and height (c, which is different from a). There are two tetragonal Bravais lattices: the simple tetragonal (from stretching the simple-cubic lattice) and the centered tetragonal (from stretching either the face-centered or the body-centered cubic lattice). The point groups that fall under this crystal system are listed below, followed by their representations in international notation and Schoenflies notation, and mineral examples. Name International Schoenflies Example ditetragonal bipyramidal $frac4mmm$ D4h rutile ditetragonal pyramidal $4mm$ C4v diaboleite tetragonal bipyramidal $frac4m$ C4h scheelite tetragonal pyramidal 4 C4 wulfenite ditetragonal alternating $overline\left\{4\right\}2m$ D2d chalcopyrite tetragonal trapezohedral 422 D4 phosgenite tetragonal alternating $overline\left\{4\right\}$ S4 cahnite ## References • Hurlbut, Cornelius S.; Klein, Cornelis, 1985, Manual of Mineralogy, 20th ed., pp. 73 - 78, ISBN 0-471-80580-7 Search another word or see Tetragonal crystal systemon Dictionary \| Thesaurus \|Spanish Copyright © 2014 Dictionary.com, LLC. All rights reserved. • Please Login or Sign Up to use the Recent Searches feature	2014-09-01 13:45:06	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 5, "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": 0.2794298231601715, "perplexity": 12319.914237573617}, "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-2014-35/segments/1409535919066.8/warc/CC-MAIN-20140901014519-00454-ip-10-180-136-8.ec2.internal.warc.gz"}
https://mathematica.stackexchange.com/questions/212855/how-do-i-add-an-error-band-to-a-plot	# How do I add an error band to a plot? I have two plots, one generated with Plot and the other generated by ListLinePlot. Both plots look the same. I am trying to plot the error band of 5% around Sin[[π x]. How to do this? I have tried IntervalMarkers, but that did not work. Plot[Sin[π x], {x, 0, 1}] x = Table[i, {i, 0, 1, 0.01}]; y = Table[Sin[πx[[i]]], {i, 1, Length[x]}]; data = Transpose[{x, y}]; ListLinePlot[data] I am trying to get something like this • Can you show your attempt at IntervalMarkers? – Lukas Lang Jan 14 at 9:33 • yy = Table[ Quantity[Around[y[[i]] \[PlusMinus] 0.05y[[i]], x[[i]]], "USDollars"], {i, 1, Length[x]}]; ListLinePlot[prices, IntervalMarkers -> "Bands", InterpolationOrder -> 3, Sequence[PlotTheme -> "Scientific", PlotRange -> All]] – acoustics Jan 14 at 9:47 • Your syntax is off: The first argument of Around is the value, the second one should be the error. It doesn't understand ± for errors. Each data point should be {x, Around[y, yerr]}, so yy = Table[{x[[i]],Quantity[Around[y[[i]],0.05y[[i]]],"USDollars"]},{i,1,Length[x]}] does the trick. – Lukas Lang Jan 14 at 11:49 • I tried your suggestion, but not working – acoustics Jan 14 at 12:04 IntervalMarkers and Around can be used in a much simpler and more concise way to generate the same plot as Lucas Lang gets. Like so: ListLinePlot[Table[{i, With[{y = Sin[π i]}, Around[y, .05 y]]}, {i, 0, 1, 0.01}], IntervalMarkers -> "Bands", PlotTheme -> "Scientific"] Note: The code below is a fixed version of the attempt made by the OP (given in the comments of the question) without any additional changes. For a much cleaner solution, see @m_goldberg's answer instead. You can use IntervalMarkers and Around like this: x = Table[i, {i, 0, 1, 0.01}]; y = Table[Sin[πx[[i]]], {i, 1, Length[x]}]; yy = Table[ {x[[i]], Quantity[Around[y[[i]], 0.05y[[i]]], "USDollars"]}, {i, 1, Length[x]}]; ListLinePlot[yy, IntervalMarkers -> "Bands", InterpolationOrder -> 3, Sequence[PlotTheme -> "Scientific", PlotRange -> All]] • Basically you have the right idea, but I don't understand why you introduced all the unneeded stuff into the code, like Quantity and Sequence and options like PlotRange and InterpolationOrder. Sorry, but. because of these things I can't upvote this answer – m_goldberg Jan 14 at 13:47 • @m_goldberg That's because I simply took the code OP gave in the comments of the question and made the minimum amount of changes to get it working (i.e. to demonstrate what was wrong with theirs, instead of showing completely different code) - but you are right, the code as is is not very nice. I have added a note saying as much to the answer. – Lukas Lang Jan 14 at 14:17 • OK, I now see you picked up the OP's code from a comment. I have upvoted. – m_goldberg Jan 14 at 14:21 One way would be to use Filling. data = Table[{x, Sin[Pi x]}, {x, 0, 2, 0.01}]; ndat = Length[data]; err = Table[0.2, {i,ndat}];(you can get it from a list also) ListLinePlot[{ Table[{data[[i, 1]], data[[i, 2]]}, {i, ndat}], Table[{data[[i, 1]], data[[i, 2]] + err[[i]]/2}, {i, ndat}], Table[{data[[i, 1]], data[[i, 2]] - err[[i]]/2}, {i, ndat}]}, PlotStyle -> {{Thick, Orange}, Orange, Orange}, Filling -> {2 -> {3}} (from 2nd to third line) ] When error is a fraction of the y value err = Table[(15/100)data[[i, 2]], {i,ndat}];(15%) ListLinePlot[{Table[{data[[i, 1]], data[[i, 2]]}, {i, ndat}], Table[{data[[i, 1]], data[[i, 2]] + err[[i]]/2}, {i, ndat}], Table[{data[[i, 1]], data[[i, 2]] - err[[i]]/2}, {i, ndat}]}, PlotStyle -> {{Thick, Orange}, Orange, Orange}, Filling -> {2 -> {3}}] • What is the percentage of error? Where you mentioned it? – acoustics Jan 14 at 12:26 • I leave it to you ;). err is the table for the error. I choose uniform error 0.2. You can make it a percentage of the y value, say, 0.05*data[[n,2]] or a random number. – Sumit Jan 14 at 14:28	2020-01-27 13:14:27	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.170183464884758, "perplexity": 4111.4025904682385}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-05/segments/1579251700675.78/warc/CC-MAIN-20200127112805-20200127142805-00420.warc.gz"}
https://zbmath.org/authors/?q=ai:michler.ruth-i	# zbMATH — the first resource for mathematics ## Michler, Ruth I. Compute Distance To: Author ID: michler.ruth-i Published as: Michler, Ruth; Michler, Ruth I. External Links: Wikidata Documents Indexed: 12 Publications since 1994, including 1 Book Biographic References: 3 Publications #### Co-Authors 10 single-authored 1 Lejeune-Jalabert, Monique 1 Melles, Caroline Grant #### Serials 2 Communications in Algebra 2 Journal of Pure and Applied Algebra 2 Proceedings of the American Mathematical Society 1 Rocky Mountain Journal of Mathematics 1 Contemporary Mathematics all top 5 #### Fields 12 Algebraic geometry (14-XX) 8 Commutative algebra (13-XX) 1 General mathematics (00-XX) 1 Category theory, homological algebra (18-XX) 1 $K$-theory (19-XX) 1 Several complex variables and analytic spaces (32-XX)	2019-07-21 14:04:45	{"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": 0.18906044960021973, "perplexity": 14884.749536413725}, "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/1563195527000.10/warc/CC-MAIN-20190721123414-20190721145414-00272.warc.gz"}
https://math.stackexchange.com/questions/1674600/calculating-int-0-infty-frac-sinxx-frac-sinx-3x-3-frac-si	# Calculating $\int_0^\infty \frac{\sin(x)}{x} \frac{\sin(x / 3)}{x / 3} \frac{\sin(x / 5)}{x / 5} \cdots \frac{\sin(x / 15)}{x / 15} \ dx$ I found the following result on this webpage: $$\int_0^{\infty } \left(\prod _{k=0}^7 \frac{\sin \left(\frac{x}{2 k+1}\right)}{\frac{x}{2 k+1}}\right) \, \mathbb{d}x= \frac{\pi}{2} - \frac{6879714958723010531}{935615849440640907310521750000} \pi$$ However, I can't determine how to prove it. • For anyone not clicking the link or bothering to read the non-formatted math therein, the surprise is that $\displaystyle \int_0^\infty \prod_{k = 0}^N \frac{\sin\big(x/(2k + 1)\big)}{x/(2k+1)}\ dx = \frac{\pi}{2}$ for $N = 0, 1, \ldots, 6$, which is really quite wild! Feb 27 '16 at 18:06 • Massive integration by parts? Feb 27 '16 at 18:15 • See this MO answer (+ the comments) for some background: mathoverflow.net/questions/11517/computer-algebra-errors/…. The proof uses the Fourier transform: products of sincs become convolutions of step functions on the transform side. Feb 27 '16 at 18:18 • Also related: math.stackexchange.com/questions/999944/… Feb 27 '16 at 18:20 ## 4 Answers I have a visual explanation, why its below $$\frac{\pi}{2}$$ In 2001, the Borwein Brothers surprised their readers with the trick you referred to: The pattern suggests that the definite integral of the sinc function ($$=\pi/2$$), does not alter when this sinc is multiplied with other sincs having lower frequencies. But unexpectedly, they show that the eighth integral is about one billionth of a percent smaller. How is that possible? French mathematician Fourier allows us to look behind the scenes. From his perspective, we see a rectangular pedestal that gradually erodes: although in the beginning only its corners are rounded, inevitably the middle of the plateau will be affected as well, thereby lowering its actual height. To understand this, let's first recollect some Fourier theory: Five familiar Fourier facts 1. The Fourier transform of a sinc, is a rectangular function (SINC-RECT pair). For the Borwein Integrals, it is instructive to see each sinc-function as the frequency spectrum of a rectangular signal. 2. The 'Uncertainty Principle' tells us: 'the wider the sinc, the narrower the block'. Thus the decreasing frequency of each new sinc factor, translates in a decreasing width of its corresponding rectangular pulse. 3. The Convolution Theorem tells us: a multiplication of spectra is equivalent to the convolution of two signals. Therefore, we can understand the multiplication of these sincs, as a convolution of their corresponding block pulses. 4. The inverse Fourier Transform tells us, that the integral of a spectrum is the central value in the time domain (similar as the integral of a signal, is the central component in the Frequency domain). Therefore these Borwein Integrals are proportional to the central value of the convolution outcome of the corresponding block pulses. 5. The convolution of two equivalent block pulses (equal width), results in a triangular function (an isosceles): the left and right corner of the rectangle are completely eroded (see animation below), but the center of the plateau is preserved (which btw explains why $$\int_0^{\infty} \operatorname{sinc}(x)^2 dx = \frac{\pi}{2}$$ (see: integralOfSquaredSincs)) source: enter link description here Convolving a wide rectangle with a narrow one With this theory in mind, let's look at the second Borwein Integral. The product of the first two sincs, is equivalent to convolving a rectangle having unit width (image below, left lower graph) with a (1/3)-kernel (upper graph in the middle). The result is a trapezoid, in which only two third of the initial unit plateau width is preserved, and one third is eroded: Why? Because in the interval [-1/3, 1/3], the (1/3)-kernel was completely embedded within the unit block. Just outside this domain, however, an increasing part of the kernel is not 'matched', resulting in two downward slopes moving out of the center. However, since the center of the initial plateau is not (yet) affected, the second Borwein integral equals still $$\frac{\pi}{2}$$. The result after some more convolutions: In the third Borwein integral, the resulting trapezoid is convolved with an (1/5)-kernel, which takes away another 20% of the original plateau width. Therefore the new residual plateau is reduced to 1 - 1/3 - 1/5 = 7/15 part of the initial plateau width: With each new convolution, the residual plateau gets smaller and smaller: (which is not that well visible, because each convolution also 'smoothens' the outcome, exactly how the probability distribution of a coin flipping experiment gets smoother when more coins are flipped) Not enough plateau left to completely match the (1/15)-kernel Once the outcome of the (1/11)-convolution in turn is convolved with the (1/13)-kernel, the residual plateau equals: $$1 - \frac{1}{3}-\frac{1}{5}-...-\frac{1}{13}= \frac{2021}{45045}<\frac{1}{15}$$ which is for the first time smaller than the next convolution kernel. So for the eighth Borwein integral, the remaining plateau is too small to completely match the (1/15)-kernel in the center, resulting in a slightly lower integration outcome for the main frequency component. And since this main frequency component is proportional to this eighth integral: $$\int_0^\infty \frac{\sin(x)}{x}\frac{\sin(x/3)}{x/3}\cdots\frac{\sin(x/15)}{x/15}dx$$ we now see why it's for the first time slightly below $$\frac{\pi}{2}$$. 1. Borwein, David; Borwein, Jonathan M. (2001), "Some remarkable properties of sinc and related integrals" Link to article The great reference is: Borwein, David; Borwein, Jonathan M. "Some remarkable properties of sinc and related integrals." Ramanujan J. 5 (2001) 73–89. DOI 10.1023/A:1011497229317 • Feb 27 '16 at 18:22 Job Bouwman's answer in terms of convolutions can be framed nicely in terms of probability. In that answer, $\mathop{\rm sinc}(t) = \frac{\sin(t)}{t}$ plays the role of the Fourier transform of the indicator function of an interval. This indicator function can be interpreted as the probability density function of a uniformly distributed random variable. Then its Fourier transform is the characteristic function of that random variable. Convolution of probability density functions corresponds to addition of independent random variables, which in turn corresponds to multiplication of their characteristic functions. Specifically, let $X_0, X_1, X_2, \dots$ be independent and uniformly distributed in $[-1,1]$. As in Job Bouwman's answer, we care about the value at $x=0$ of the convolution of the density functions of $X_0$, $X_1/3$, $X_2/5$, and so on. So we're interested in the value at $x=0$ of the probability density function of $$X_0 + \frac13 X_1 + \frac15 X_2 + \dots + \frac1{2N+1} X_N.$$ That is, how likely is that sum to land in a small interval centered at $0$, compared to the size of that small interval? Up to a factor of 2, this is the same as asking how likely the sum $$Y = \frac13 X_1 + \frac15 X_2 + \dots + \frac1{2N+1} X_N$$ is to land in the interval $[-1, 1].$ Since each $X_i$ has absolute value at most $1$, this happens with probability $1$ when $N<7$, but with probability slightly less than $1$ when $N \geq 7$. Explicitly, let $f$ denote the probability density function of $Y$ and $\varphi$ denote the characteristic function of $Y$. We have \begin{align} \mathop{\mathbb P}(Y \in [-1,1]) &= \int_{-1}^1 f(x)\,dx\\ &= \int_{\mathbb R} \chi_{[-1,1]}(x)\, f(x)\,dx\\ &= \frac1{2\pi} \int_{\mathbb R} 2 \mathop{\rm sinc}(t)\, \varphi(t)\,dt, \end{align} where the last equality is due to the fact that Fourier transforms preserve the inner product between functions, up to a factor of $2\pi$. We also have $$\varphi(t) = \mathop{\mathbb E}(e^{itY}) = \prod_{k=1}^N \mathop{\mathbb E}(e^{i\,t/(2k+1)\,X_k}) = \prod_{k=1}^N \mathop{\rm sinc}\left(\frac{t}{2k+1}\right).$$ Hence \begin{align} \mathop{\mathbb P}(Y \in [-1,1]) &= \frac1{2\pi} \int_{\mathbb R} 2 \mathop{\rm sinc}(t)\, \prod_{k=1}^N \mathop{\rm sinc}\left(\frac{t}{2k+1}\right)\,dt\\ &= \frac2{\pi} \int_0^\infty \prod_{k=0}^N \mathop{\rm sinc}\left(\frac{t}{2k+1}\right)\,dt\\ &= \frac2{\pi} B_N, \end{align} where $B_N$ is the integral we're interested in. So $B_N = \pi/2$ when $N<7$ and $B_n$ is just a little bit less than $\pi/2$ when $N \geq 7$. Note that even if you take $N$ to infinity, the probability that $$Y = \frac13 X_1 + \frac15 X_2 + \frac17 X_3 + \dots$$ is outside $[-1, 1]$ is still quite small, and $$B_\infty = \int_0^\infty \prod_{k=0}^\infty \mathop{\rm sinc}\left(\frac{t}{2k+1}\right)\,dt = \int_0^\infty \prod_{j=1}^\infty \cos\left(\frac{t/2}{j}\right)\,dt = 2\int_0^\infty \prod_{j=1}^\infty \cos\left(\frac{u}{j}\right)\,du$$ is still quite close to $\pi/2$, correct to four digits I believe. You can observe an even more striking version of this behavior by evaluating the probability density function of $$X_0 + \frac13 X_1 + \frac15 X_2 + \dots + \frac1{2N+1} X_N$$ at $x = 1$ rather than $x = 0$. Up to a factor of $2$, this is the probability that $$Y = \frac13 X_1 + \frac15 X_2 + \dots + \frac1{2N+1} X_N$$ lands in the interval $[0,2]$. By symmetry around the origin, when $N < 56$, this probability is exactly $1/2$, but when $N \geq 56$, it is very slightly smaller than $1/2$. Translating this into facts about integrals, we get that $$C_N = \frac12 \int_{\mathbb R} e^{it} \prod_{k=0}^N \mathop{\rm sinc}\left(\frac{t}{2k+1}\right)\,dt = \int_0^\infty \cos(t)\, \prod_{k=0}^N \mathop{\rm sinc}\left(\frac{t}{2k+1}\right)\,dt$$ is exactly $\pi/4$ when $N < 56$ and very slightly smaller when $N \geq 56$. And because the probability that $$\frac13 X_1 + \frac15 X_2 + \frac17 X_3 + \dots$$ falls outside $[-2, 2]$ is miniscule but nonzero, we have that $$C_\infty = \int_0^\infty \cos(t)\,\prod_{k=0}^\infty \mathop{\rm sinc}\left(\frac{t}{2k+1}\right)\,dt = 2\int_0^\infty \cos(2u) \prod_{j=1}^\infty \cos\left(\frac{u}{j}\right)\,du$$ is incredibly close to $\pi/4$, correct to more than forty digits! As for the original question of calculating $B_7$ exactly, it boils down to calculating the exact probability $p$ that $$\frac13 X_1 + \frac15 X_2 + \frac17 X_3 + \frac19 X_4 + \frac1{11} X_5 + \frac1{13} X_6 + \frac1{15} X_7 > 1.$$ Up to a factor of $2^7$, this is the volume of a tetrahedral section of the 7-dimensional cube $[-1, 1]^7$, sliced off by the plane $x_1 / 3 + \dots + x_7/15 = 1$. This tetrahedron has orthogonal sides of length $3s, 5s, \dots, 15s$, where $$s = \left(\frac13 + \frac15 + \dots + \frac1{15}\right) - 1 = \frac{44190}{15!!}.$$ Hence, $$p = \frac{1}{2^7} \frac{1}{7!} 3s \dots 15s = \frac{15!! s^7}{2^7 7!} = \frac{44190^7}{2^7 7! (15!!)^6}$$ and $$B_7 = \frac\pi2 (1-2p) = \frac\pi2\left(1 - \frac{44190^7}{2^6 7! (15!!)^6} \right).$$ $$\newcommand{\S}{\operatorname{sinc}}$$ A 'brute force' solution to a beautiful problem. I don't claim this answer is as insightful as the others and the question is somewhat old, but I feel it is relevant and unique enough to merit posting. As usual, we will let $$\S(x) = \sin(x)/x$$ with $$\S(0)=1$$. The big idea: use angle-addition, Taylor series, and integration by parts to 'revert' the integral to a bunch- $$128$$, to be precise- of weighted integrals of the form $$\int_0^{\infty}\sin(a x)/x\,dx$$, each of which is $$\pi/2$$. Then we just add up the weights to produce the answer. 1. Angle-addition. Recall that \begin{align} 2\sin(\theta)\sin(\phi)=\cos(\theta-\phi)-\cos(\theta+\phi)\\ 2\sin(\theta)\cos(\phi)=\sin(\theta-\phi)-\sin(\theta+\phi)\\ 2\cos(\theta)\cos(\phi)=\cos(\theta-\phi)+\cos(\theta+\phi)\\ \end{align} For instance, this tells us $$\S(x)\S(x/3) = \frac{3}{2}x^{-2}(\cos(2x/3)-\cos(4x/3))$$. You probably see what lies ahead, even if it's somewhat unappetizing. We have $$\S(x)\S(x/3)\cdots \S(x/15) =$$ $$\frac{1\cdot 3\cdots 15}{2^7 x^8} \sum_{e_i\in\{\pm 1\}} (-1)^{\#(e_i=-1)} \cos\left( x(1+e_1 \cdot 1/3 + e_2\cdot 1/5 +\cdots +e_7 \cdot 1/15)\right)$$Thus, if we denote $$W=(1\cdot 3\cdot \cdots \cdot 15)/2^7$$, we have to evaluate $$128$$ integrals that look like $$\displaystyle{W \int_0^{\infty}\frac{\cos(a x)}{x^8}\,dx}$$, for some constant $$a$$. The trouble is that none of them are improperly integrable near $$x=0$$, which brings us to the second step in the process. 1. Taylor series. The idea here is to add and subtract the same number of lower-order terms of the Taylor series of each $$\cos(a x)$$ to make the integrals converge. For example, $$\displaystyle{\int_0^{\infty}\frac{\cos(x)}{x^8}\,dx}$$ does not converge but $$\displaystyle{\int_0^{\infty}\frac{\cos(x)-(1-x^2/2+x^4/24-x^6/720)}{x^8}\,dx}$$ does. Since the sum of the arguments of the cosines is zero (check! A short explanation is that the $$+$$ and $$-$$ signs are equal in number) we will add and subtract up to the degree six terms to make the integrals convergent. Therefore, we have to evaluate $$\int_0^{\infty}\frac{\cos(a x)-(1-(ax)^2/2+(ax)^4/24-(ax)^6/720)}{x^8}\,dx$$ 1. Integration by parts. We have $$\int_0^{\infty}\frac{\cos(a x)-(1-(ax)^2/2+(ax)^4/24-(ax)^6/720)}{x^8}\,dx$$ \begin{align} &=\left.-\frac{\cos(a x)-(1-(ax)^2/2+(ax)^4/24-(ax)^6/720)}{8x^7}\right\|_0^{\infty}\\ &+\frac{1}{7}\int _0^{\infty} \frac{-a\sin(ax)+a^6 x^5/120 - a^4 x^3/6 + a^2 x }{x^7}\,dx \end{align}The boundary terms vanish: at $$\infty$$, the denominator is a greater power and at $$0$$ the cosine series is $$O(x^8)$$. Continue this procedure until the denominator is just $$x$$: $$\cdots = \frac{a^7}{7!}\int_0^{\infty}\frac{\sin(ax)}{x}\,dx = \frac{a^7}{7!}\cdot\frac{\pi}{2}$$ 1. Add 'em up. All that's left is to add up these values for all $$128$$ values of $$a$$ corresponding to the $$2^7$$ terms of the sum. This becomes $$W \cdot \frac{\pi}{2}\cdot \frac{1}{7!} \cdot \sum_{e_i\in\{\pm 1\}} (-1)^{\#(e_i=-1)} (1+e_1 \cdot 1/3 + e_2\cdot 1/5 +\cdots +e_7 \cdot 1/15)^7$$A somewhat tedious but routine calculation gives the final answer of $$\frac{467807924713440738696537864469 \pi}{935615849440640907310521750000}$$ For clarity, I'll do a smaller example (the three sinc case) that will evaluate to $$\pi/2$$. $$\int _0^{\infty} \S(x)\S(x/3)\S(x/5)\,dx = 15 \int_0^{\infty} \frac{\sin(x)\sin(x/3)\sin(x/5)}{x^3}\,dx$$ $$=\frac{15}{4} \int_0^{\infty} \frac{-\sin(7/15 x)+\sin(13/15 x)+\sin(17/15 x)-\sin(23/15 x)}{x^3}\,dx$$ $$=\frac{15}{4} \int_0^{\infty} \frac{-\sin(7/15 x)+\sin(13/15 x)+\sin(17/15 x)-\sin(23/15 x) }{x^3}+\frac{7/15 x-13/15 x-17/15 x+23/15 x}{x^3}\,dx$$I'll just pick one of these, say the first one; the others are exactly the same. $$=\int_0^{\infty} \frac{-\sin(7/15 x)+7/15 x}{x^3}\,dx$$ $$= \left.\frac{-\sin(7/15 x)+7/15 x}{-2x^2}\right\|_0^{\infty} + \int_0^{\infty} \frac{-7/15 \cos(7/15 x)+7/15}{2x^2}\,dx$$ $$=0+0 + \frac{(7/15)^2}{2} \int _0^{\infty}\frac{\sin(7/15 x)}{x}\,dx =\frac{(7/15)^2}{2} \cdot \frac{\pi}{2}$$So the total is $$\frac{15}{4}\cdot \frac{\pi}{2}\left(\frac{(7/15)^2}{2}-\frac{(13/15)^2}{2}-\frac{(17/15)^2}{2}+\frac{(23/15)^2}{2}\right)= \frac{\pi}{2}$$ Of course, this method is merely computational: it has none of the theoretical trappings of the other answers. Nevertheless, the method could easily be generalized to other products and is quite amenable to reproduction on software. For instance, Mathematica thought long and hard about the original integral, but was able to perform the $$128$$ sub-integrals much quicker. As a final remark, I'm reminded of the idea of quadrature from numerical analysis. It seems these integral-sinc-products, and more importantly their corresponding series, are 'exact' for the first seven until an error is introduced in the eighth. Perhaps I will investigate this further. • fascinating. what does # mean in this line of your answer though? $\frac{1\cdot 3\cdots 15}{2^7 x^8} \sum_{e_i\in\{\pm 1\}} (-1)^{\#(e_i=-1)} \cos\left( x(1+e_1 \cdot 1/3 + e_2\cdot 1/5 +\cdots +e_7 \cdot 1/15)\right)$ Jun 24 '21 at 19:54 • It counts the number of $e_i$ that are equal to $-1$. There is probably a better way to write this; maybe something like $\prod_i e_i$. Jun 24 '21 at 20:28	2022-01-26 00:15:59	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 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": 50, "wp-katex-eq": 0, "align": 2, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9721332788467407, "perplexity": 432.16416357695897}, "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-2022-05/segments/1642320304876.16/warc/CC-MAIN-20220125220353-20220126010353-00277.warc.gz"}
https://www.jiskha.com/display.cgi?id=1362516890	# Chemistry posted by . If you have 1.90 mol of H_2 , how many grams of NH_3 can be produced? • Chemistry - ## Similar Questions 1. ### Chemistry Could someone please check my answers/work for the following questions. EQUATION: 3H2+N2 -->2NH3 1) How many grams of NH3 can be produced from 3.98 mol of N2? 2. ### chemistry If you have 1.90 moles of H_2 How many grams of NH_3 can be produced? 3. ### chemistry If you have 1.50 moles {\rm H_2}, how many grams of {\rm NH_3} can be produced? 4. ### college chemistry Hydrogen gas is produced when zinc reacts with sulfuric acid: Zn(s)+H_2SO_4(aq)---ZnSO_4(aq)+H_2(g) If 160 mL of wet H_2 is collected over water at 24 Celsius and a barometric pressure of 739 torr, how many grams of Zn have been consumed? 5. ### Chemistry How many moles of H_2 are needed to produce 13.27g of NH_3? 6. ### chem how many gramss of HCl to dassolve 2,5 g Fe in a lock and how much H_2 would be produced Fe(s)+2HCl(aq)-FeCl_2(aq)+H_2(g) 7. ### Chemistry If you have 1.90 mol of H_2 , how many grams of NH_3 can be produced? 8. ### Chemistry I need help I can't seem to get the right answer. Please help! 1/2 H_2 (g) + 1/2 Cl_2 (g) --> HCl (g) -92.3 kJ/mol Na(s) + 1/2 O_2(g) + 1/2H_2(g) --> NaOH(s) -426.8 kJ/mol NaCl(s) --> Na(s) + 1/2Cl_2(g) 411.1 kJ/mol H_2O(l) … 9. ### Chemistry NH4NO3(s) ¡æ N2O(g) + 2H2O(§¤). How much water is produced if 22.9 g of N2O is produced in this reaction? 10. ### chemestry How many molecules (not moles) of NH3\rm NH_3 are produced from 8.21×10−4gg of H2\rm H_2 More Similar Questions	2017-10-22 00:53:35	{"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": 0.8323238492012024, "perplexity": 13106.884050106793}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-43/segments/1508187824931.84/warc/CC-MAIN-20171022003552-20171022023552-00794.warc.gz"}
https://physics.stackexchange.com/questions/77784/motivation-to-introduce-von-neumann-algebras-in-addition-to-calgebras	# Motivation to introduce von Neumann algebras in addition to $C^$algebras? Observables are self-adjoint elements of a $C^$algebra. As such, this structure seems sufficient to describe physics. A theorem by Gelfand and Naimark says that a $C^$algebra can always be faithfully represented as a subalgebra of bounded operators on a Hilbert space, $B(H)$. One can then introduce different topologies, and a von Neumann algebra can be seen as a $C^$subalgebra of $B(H)$ that is in addition closed in one of those topologies. In another question of Physics stack exchange Why are von Neumann Algebras important in quantum physics? someone also talks about the Borel functional calculus, and one also compare von Neumann algebra to "non commutative" measure theory vs "non commutative" for $C^$algebras. My question is, is the introduction of von Neumann algebra only a technical thing or has it physical consequences? • Just a personal view. In matters of relevance to physics one is usually concerned with studying a particular observable ( like momentum, energy etc) or at most a finite algebra of observables (like spin algebra). I personally haven't seen any physics question whose answer is to be found in studying the set of all operators at once. For a physicist the statement "an observable should be Hermitian" is more useful than the statement "set of all operators form Von Neumann algebra (or whatever)" – user10001 Sep 18 '13 at 15:37 • Maybe a more specific question is, has the different topologies on bounded operator any physical relevance. It is indeed not exactly physic question but more a conceptual. The focus is not on the set of all operators but on the structure that you have on it, and then, what is well defined or not with that structure. Think about the algebra consisting of an operator position and momentum satisfying the usual commutation relation, one cannot define a norm on it!! Or even in more basis quantum mechanics lesson, why do we need to consider Hilbert space and not pre-hilbert: it allows to write inf – Noix07 Sep 18 '13 at 16:26 • inite sums. sometimes these seemingly insignificant details are essential. – Noix07 Sep 18 '13 at 16:27 • I feel I didn't finish expressing my idea on the position and momentum operator. One can realize the algebra generated by it on an infinite dimensional hilbert space, where they are unbounded operators, but not on any finite dimensional space. The choice of $L^2$ space had bothered be since my very first encounter with quantum mechanics and here was the reason – Noix07 Sep 20 '13 at 15:21 • Perhaps another reason is the connection between Connes' Embedding Conjecture concerning $II_1$ factors and Tsirelson's Problem concerning quantum correlation functions of bipartite systems. – Eli Bashwinger Dec 12 '18 at 23:41 I had the same question, when studying the subject. Let me tell you, what I was told - it relates to the functional calculus: Recall that in quantum mechanics, as we usually learn it, a measurement is a projective measurement, i.e. the outcomes of a measured observables are eigenvalues of the observable and we "update" the state according to the knowledge obtained (i.e. we project it into the Hilbert space). We can of course use the whole formalism of POVMs instead if you know about this, but still, projective measurements remain important special cases. For this reason, we don't actually need our Hermitian observables, but we need the spectral calculus and the spectral theorem. You want all spectral projections of an observable to belong to your space, since if you measure the observable, your results will be updated according to the eigenprojections. And here is the problem: C-algebras in generally do not contain all their projections, von Neumann algebras do. So the "physical consequence" is that you actually have all your measureable quantities inside the algebra of operators you call "observables". I believe that is as physical as it gets. Since von Neumann algebras can always be seen as closures of C-algebras in some topology, I would not expect there to be a much deeper reasons, although I'd love to know them myself, if there are. Other reasons mentioned to me refer to the structure of von Neumann algebras (and its lattice of projections) and how this enters different scenarios in physics, but in this case, I would say that the reason to study von Neumann algebras is rather technical than physical. Finally, let me point out that it is not a priori clear why we should study C-algebras at all - I mean, the only physical quantities are the Hermitian operators, but generically, our algebras will contain many nonhermitian elements. In my view, this means there is no reason to study either C-algebras or von Neumann algebras, but one would actually have to study Jordan algebras (the set of Hermitian elements of the bounded operators on some Hilbert space forms such a Jordan algebra, or more precisely, a Jordan operator algebra). Since these algebras are however nonassociative (which is inconvenient) and can nearly always be embedded into some associative algebra, we study the associative algebras. So, in a sense, studying C-algebras is already "a technical thing". • Thanks. I've heard of the fact that projectors given by the spectral theorem are not necessarily in the C* algebra, but I didn't check out the details seriously. Also I asked the exact same question in math, and thought about another idea math.stackexchange.com/q/498653 As for jordan algebra, I've heard that historically it was the first candidate, but then people switch to C* algebra, there must be a reason – Noix07 Sep 30 '13 at 17:54 • Well, yes, there is a reason why people consider C* algebras (or von Neumann algebras) instead of Jordan algebras. The reason is that every Jordan algebra of the type relevant for quantum mechanics can be embedded into a C- or a von Neumann algebra (with one exception, the 3x3 Hermitian matrices over the octonions). Since nonassociative algebras are really inconvenient, this means we can just as well work with the associative envelope. – Martin Sep 30 '13 at 19:27 • There are (at least) two books (of which I only read the preface or intro...) which detail what additional structures are required to built a C-algebra from the convex set of state and also the link Jordan vs. C-algebras: "Geometry of State Spaces of Operator Algebras" and "State Spaces of Operator Algebras" by Erik M. Alfsen and Frederic W. Shultz – Noix07 May 28 '15 at 9:53 List (to be completed with more references and/or items, details of the relation to physics) • there is a notion of positive energy representation (cf. Haag-Kastler axiom, "Spectrum" or "stability" condition) in which generators of translations can be choosen in the von Neumann algebra associated to the representation of the observables, but not necessarily in the C-algebra itself. cf this lecture notes, section II.4, Borchers-Arveson Theorem p.37. • The quasi-local algebra (Haag-Kastler framework) is defined as the inductive limit, of a net of local algebras (possibly von Neumann), in the category of C-algebras. Haag insists on this in "Local Quantum Physics", p.132 in the first paragraph, p.142 in the remark paragraph. (Also mentionned p.12 "quasi-local vs. global", Introduction to Algebraic Quantum Field Theory, S. S. Horuzhy) The quasi-local algebra is in turn important for the theory of superselection sectors which can be defined as an equivalence class (with quasi-equivalence of representations) of primary(=factor) representations (=minimal folium) of the quasi-local algebra (superselection sectors cannot be defined from representations of the local algebras alone). (Inductive limits in the category of von Neumann algebras do exist, Proposition 7.I p.49, "Sur la catégorie des algèbres de von Neumann", Alain Guichardet) • There is a way to take into accound unbounded operators which goes under the name of affiliated operator, this is already present in the first point. The idea is that the spectral theorem holds in the framework of von Neumann algebras (the projections of the resolution of the identity are not in the C-algebra in general), so if one has an unbounded self-adjoint operator, one can define approximations. (ref?? I remembered this while re-reading this answer) Points to check/develop/clarify (the different points are probably related): • there are different faithful representations of a C-algebra even up to quasi-equivalence, but only one for a von Neumann algebra. Or in the same vein, there is a classification of all von Neumann algebras and not of representations of C-algebras. • for the algebra $\mathcal{B}(\mathcal{H})$, one can associate a projection to each vector state, i.e. an observable asking if an arbitrary state has an overlap with this particular state or not. I wonder if a statement of the form "to all pure state is associated a projection observable" is true for all C-algebras or if there could be a distinction for C / W-algebras. More generally to a density matrix state, is the density matrix operator in the algebra? and is there a distinction between the situation of C- and that of W-algebras? • Another point about projections: the set of projections of a von Neumann is a lattice and it generates the algebra which is not the case in general for a C-algebra (cf. nevertheless this question) and i have recently learned that this is an essential structure in quantum logic. A reason I could think is this: the expectation values in quantum mechanics are of the form, $$\langle x\|Ay\rangle$$. We seek a notion of convergence on observables. If we have a set of observables $$\{A_n\}$$ converging to some other observable $$A$$ what we expect is the expectation value of the observable to converge. This is my motivation for weak operator topology. We hence expect the algebra of observable to be closed under weak topology. These are the Von Neumann algebras. [Page 113 of Haag's book] • It's a good argument. I would just add as a comment "polarization identity" to related bilinear maps $(x,y) \mapsto \langle x \| A\| y \rangle$ to quadratic forms $x \mapsto \langle x \| A\| x \rangle$. I give myself more time to think about the question as I don't really know what answer I expect in fact. – Noix07 Jun 14 '17 at 12:47 • I like the ultraweak topology more than the weak topology. It makes more direct relation to physics. I have heard that they are the same in some cases – Boltzee Jun 14 '17 at 14:22	2019-10-19 05:06:01	{"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": 3, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7776278257369995, "perplexity": 348.5094247871165}, "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-2019-43/segments/1570986688826.38/warc/CC-MAIN-20191019040458-20191019063958-00357.warc.gz"}
https://stats.stackexchange.com/questions/396018/is-s-02-an-unbiased-variance-estimator-for-a-distribution-that-is-symmetric-a	# Is $s_0^2$ an unbiased variance estimator for a distribution that is symmetric around zero? Let $$X_i$$ be a random variable, and define the following statistic $$s^2_? = \frac{1}{n} \sum _i X_i ^2$$ • Suppose that the $$X_i$$ comes from a symmetric distribution, is $$s^2_?$$ an unbiased estimator of the variance ($$\sigma^2$$) of $$X_i$$? I tried the following: $$E[s^2_?]=E[\frac{1}{n} \sum _i X_i ^2]=E[\frac{1}{n}\sum _i (X_i-\mu) ^2+2\mu X_i -\mu^2 ]$$ Considering a $$\mu$$ which satisfies $$\mu= E[X_i]=0$$ Then for the linearity of the expectation $$E[s^2_?]=E[\frac{1}{n}\sum _i (X_i-\mu) ^2] + \frac{2\mu}{n}E[\sum_i X_i]+\frac{\mu^2}{n} E[\sum_i 1]$$ So $$E[s^2_?]=\sigma^2+ \frac{2\mu}{n}E[\sum_i X_i]+\mu^2 E[\sum_i 1]$$ And, been that $$\mu=0$$ $$s^2_? = \sigma^2$$ In case that the derivation is correct: How to adapt this to the case in which $$X$$ is autocorrelated? The condition of symmetry is not required here. If you have known mean $$\mu = 0$$ then, following the working you used (but with standard notation), you get: \begin{aligned} \mathbb{E}(S_\mu^2) = \mathbb{E}\Big( \frac{1}{n} \sum_{i=1}^n X_i^2 \Big) &= \mathbb{E}\Big( \frac{1}{n} \sum_{i=1}^n (X_i - \mu)^2 \Big) \\[6pt] &= \frac{1}{n} \sum_{i=1}^n \mathbb{E}\Big((X_i - \mu)^2 \Big) \\[6pt] &= \frac{1}{n} \sum_{i=1}^n \mathbb{V}(X_i) \\[6pt] &= \frac{1}{n} \sum_{i=1}^n \sigma^2 \\[6pt] &= \frac{1}{n} \cdot n \sigma^2 = \sigma^2. \\[6pt] \end{aligned} The above working is perfectly valid in the case where the random variables are correlated. (We can still write the expectation of the sum as the sum of the expectations, etc.) This is because the true mean is assumed known in this case, so correlation between the observable values has no effect on the expected value of the estimator. That means that this estimator is an unbiased estimator of the variance, for the case where $$\mu = 0$$, regardless of the correlation between the observable variables. It is important to bear in mind that correlation between the values affects the variance of the estimator, and so confidence intervals are affected. There are other questions on this site that look at adjustments to the effective sample size (and consequent standard error of the estimator) for autocorrelation (see e.g., here). Roughly speaking, negative autocorrelation induces higher sample variance (relative to the true variance) in the series and positive autocorrelation induces lower sample variance (relative to the true variance). This necessitates adjustments to the standard error estimator, which can be calculated by deriving the variance of the estimator. • +1. Thank you. Could you comment about the case in which the random variable is autocorrelated? – user1420303 Mar 6 '19 at 23:35 • I have added additional discussion of correlation. – Ben Mar 7 '19 at 0:19 I think it's a good idea to state it more clearly and simplify the solution a little bit. Let $$X_1,\dots,X_n$$ be a random sample from a symmetric distribution with finite variance $$\sigma^2$$. The variance estimator $$\hat{\theta}=\frac{1}{n}\sum_{i=1}^n X_i^2$$ is unbiased, because $$\text{E}[\hat{\theta}] = \frac{1}{n} \sum_{i=1}^n \text{E}[X_i^2] = \frac{1}{n} \sum_{i=1}^n \left(\text{Var}[X_i] + \underbrace{\text{E}^2[X_i]}_{=\;0}\right)= \sigma^2.$$ • +1. Thank you. Could you comment about the case in which the random variable is autocorrelated? – user1420303 Mar 6 '19 at 23:35 Or, alternatively: If $$\mu=0$$, then: $$\sigma^2 = E(X^2)+E(X)^2 = E(X^2)$$ and $$E(\dfrac{1}{n} \sum_iX_i^2) = E(\bar{X^2}) = \bar{X^2} = E(X^2)$$ Then, by equating: $$\sigma^2 = E(\dfrac{1}{n} \sum_iX_i^2)$$ Thus, $$s_?^2$$ is an unbiased estimator of $$\sigma^2$$. • +1. Thank you. Could you comment about the case in which the random variable is autocorrelated? – user1420303 Mar 6 '19 at 23:35 • The last equation sign in this working is incorrect, and should be replaced with an approximation sign --- there is a difference between the second raw moment of a random variable and the corresponding sample estimator. In general, it is not true that $S_\mu^2 = \sigma^2.$ – Ben Mar 7 '19 at 0:20 • That's correct. I clarified my answer to avoid confusion. – Kuma Mar 8 '19 at 13:47	2021-05-05 22:07:58	{"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": 27, "wp-katex-eq": 0, "align": 0, "equation": 1, "x-ck12": 0, "texerror": 0, "math_score": 0.9916961789131165, "perplexity": 297.1892088029644}, "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/1620243988696.23/warc/CC-MAIN-20210505203909-20210505233909-00446.warc.gz"}
https://www.math.tolaso.com.gr/	## Bernstein limit Let be real numbers. Consider the function: as well as the polynomial . Evaluate the limit . Solution The polynomial is nothing else than a Bernstein one. is Riemann integrable on and is a discontinuity of a first kind. Thus, where and . ## An iteration limit Let be a natural number and let where the number of ‘s in the definition of is . For example: Evaluate the limit: Solution We easily see by induction that as well as Thus, and thus does not exist. ## Double summation Let be a real number. Evaluate the series: Solution Since the summands are all positive , we can sum by triangles. Thus, where is the Riemann zeta function. ## Inequality of a function Let be a differentiable function with continuous derivative. Prove that: Solution For it holds that Taking absolute values and using basic properties of the integral we get Integrating we have: (1) Working similarly on we get (2) Adding equations we get the result. ## An arccotangent integral Let denote the Riemann zeta function. Prove that Solution Background: I have always been of the opinion that integrals of this form diverged when integrated from something to infinity. Apparently, this is not the case since the above not only converges but it has a nice closed form involving the Riemann zeta function. The technique to break it down , is pretty simple actually. Integration by parts! Yep! We combine IBP along with Fourier series and voilà. However, somewhere in the middle of this evaluation process we will come across a famous constant , , coming literally out of nowhere. But this is what to expect when reducing trigonometric integrals to logarithmic ones. We begin our evaluation by stating two lemmata: Lemma 1: It holds that . Proof: Successively, we have that: where is the Catalan’s constant. Also, which is the known Fourier series expansion of the function. Lemma 2: It holds that . Proof: Successively, we have that: Hence, ### Who is Tolaso? Find out more at his Encyclopedia Page.	2019-06-18 17:06:33	{"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": 0.9704928398132324, "perplexity": 1175.0600076708986}, "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/1560627998808.17/warc/CC-MAIN-20190618163443-20190618185443-00468.warc.gz"}
http://mathhelpforum.com/math-challenge-problems/1618-reader-vs-writer.html	1. ## The Reader Vs. The Writer This riddle is created by me, and is a hypothetical scenario. It's fairly hard, at least for those without university maths I recon. The hard part was constructing the functions, especially the cubic equation was a good and interesting challenge. The Writer is writing a book, and as soon as one page is done The Reader reads it. And so it goes on. A clever mathematician has figured out functions to represent the speed at which The Writer writes at and The Reader reads at. $ W(d) = 200(\sin{d})+200 $ $ d = <0, \infty> $ $ W(d) = <0, 400> $ This writer is so commited to this endless book, that he only refrains himself from writing 6 days in a full year. All other days, he writes. If there is a leap year he takes 29th of February off as well. $ R(h)=\frac{1500}{91}(\frac{1}{3}h^3-\frac{9}{4}h^2+\frac{95}{6}) $ $ h = <0, 6> $ $ R(h) = <0, \frac{25800}{91}> $ This function should be treated as a (non-continuous and)cycling function within the bounds of h as stated above. In other words, from $h = <0, 1>$ is all the reading the reader does on Monday to Tuesday, and $h = <5, 6>$ is Friday to Saturday. The Reader reads 6 out of 7 days a week. Sunday isn't a reading day for the reader. When, if ever, will The Reader catch up with The Writer? If so, at what rate? If, The Reader will never catch The Writer, how much faster does The Writer write than The Reader read?	2017-09-22 04:49:06	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 8, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3891609013080597, "perplexity": 1537.3022689640152}, "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-2017-39/segments/1505818688208.1/warc/CC-MAIN-20170922041015-20170922061015-00288.warc.gz"}
http://threadspodcast.com/standard-error/measurement-error-vs-standard-deviation.html	Home > Standard Error > Measurement Error Vs Standard Deviation # Measurement Error Vs Standard Deviation ## Contents doi:10.4103/2229-3485.100662. ^ Isserlis, L. (1918). "On the value of a mean as calculated from a sample". The margin of error of 2% is a quantitative measure of the uncertainty – the possible difference between the true proportion who will vote for candidate A and the estimate of Another way of considering the standard error is as a measure of the precision of the sample mean.The standard error of the sample mean depends on both the standard deviation and The standard error is also used to calculate P values in many circumstances.The principle of a sampling distribution applies to other quantities that we may estimate from a sample, such as check over here The smaller standard deviation for age at first marriage will result in a smaller standard error of the mean. The standard error (SE) is the standard deviation of the sampling distribution of a statistic,[1] most commonly of the mean. Deng Chapel Hill, NC, United States 邓春勤 A Medical Doctor turned into Biostatistician in Clinical Trial and Drug Development Industry View my complete profile Useful Links Cytel's Blog on Clinical Trials Note: the standard error and the standard deviation of small samples tend to systematically underestimate the population standard error and deviations: the standard error of the mean is a biased estimator ## Standard Error Of Measurement Formula Initially, I mistakenly thought that SEM was for standard error of mean. Can anyone help? We may choose a different summary statistic, however, when data have a skewed distribution.3When we calculate the sample mean we are usually interested not in the mean of this particular sample, This also means that standard error should decrease if the sample size increases, as the estimate of the population mean improves. Later sections will present the standard error of other statistics, such as the standard error of a proportion, the standard error of the difference of two means, the standard error of Also, a very high standard deviation of the results for the same survey, for example, should make one rethink about the sample size and the survey as a whole.In physical experiments, Standard Error Of Measurement Reliability Notice that s x ¯ = s n {\displaystyle {\text{s}}_{\bar {x}}\ ={\frac {s}{\sqrt {n}}}} is only an estimate of the true standard error, σ x ¯ = σ n For a large sample, a 95% confidence interval is obtained as the values 1.96×SE either side of the mean. Standard Error Of Measurement Calculator Note that the standard error of the mean depends on the sample size, the standard error of the mean shrink to 0 as sample size increases to infinity. The standard error is also used to calculate P values in many circumstances.The principle of a sampling distribution applies to other quantities that we may estimate from a sample, such as check it out Standard error of the mean Further information: Variance §Sum of uncorrelated variables (Bienaymé formula) The standard error of the mean (SEM) is the standard deviation of the sample-mean's estimate of a Standard deviation will not be affected by sample size. Standard Error Of Measurement Spss Br J Anaesthesiol 2003;90: 514-6. [PubMed]2. However, it can clearly be seen that the properties of these two sets are different. The standard error of all common estimators decreases as the sample size, n, increases. ## Standard Error Of Measurement Calculator Comments View the discussion thread. . https://en.wikipedia.org/wiki/Standard_error From data (simulation) The next diagram takes random samples of values from the above population. Click Take Sample a few times and observe that the sample standard deviation varies from Standard Error Of Measurement Formula The sample standard deviation, s, is a random quantity -- it varies from sample to sample -- but it stays the same on average when the sample size increases. Standard Error Of Measurement Example Membership benefits: Get your questions answered by community gurus and expert researchers. Exchange your learning and research experience among peers and get advice and insight. This difference changes the meaning of what is being reported: a description of variation in measurements vs a statement of uncertainty around the estimate of the mean. check my blog Wilson Mizner: "If you steal from one author it's plagiarism; if you steal from many it's research." Don't steal, do research. . Because the 5,534 women are the entire population, 23.44 years is the population mean, μ {\displaystyle \mu } , and 3.56 years is the population standard deviation, σ {\displaystyle \sigma } The true standard error of the mean, using σ = 9.27, is σ x ¯ = σ n = 9.27 16 = 2.32 {\displaystyle \sigma _{\bar {x}}\ ={\frac {\sigma }{\sqrt Standard Error Of Measurement And Confidence Interval Please review our privacy policy. and Keeping, E.S. (1963) Mathematics of Statistics, van Nostrand, p. 187 ^ Zwillinger D. (1995), Standard Mathematical Tables and Formulae, Chapman&Hall/CRC. Retrieved Oct 17, 2016 from Explorable.com: https://explorable.com/measurement-of-uncertainty-standard-deviation . this content Terms and Conditions for this website Never miss an update!	2018-02-25 13:45:39	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8105355501174927, "perplexity": 906.8364945799324}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-09/segments/1518891816462.95/warc/CC-MAIN-20180225130337-20180225150337-00341.warc.gz"}
http://raphael.uaca.com/experiments/recurrent_visual_attention/details.md	# Recurrent visual attention model (Experiment notes) ### 2015/3/19 #### REINFORCE learning for the policy of location network In the paper, the policy is defined as multivariate gaussian pdf of position. Then the REINFORCE algorithm learns the gradient of this log probability wrt. weight of location network This never worked in my experimental setting, instead, it seems the following simple gradient can make REINFORCE work. $$\nabla_{\theta}{l_t}$$ #### Solve zero-gradient problem for gaussian pdf function in theano Consider sampled position as a constant in T.grad. Runs with theano 0.6. _tanh = nnprocessors.build_activation("tanh") wl = theano.shared(np.array([[0.2,0.3], [0.1,0.3]], dtype="float32")) h_t = T.constant(np.array([0.1,0.2])) l_t = _tanh(T.dot(h_t, wl)) sampled_l_t = _sample_gaussian(l_t, T.constant(np.array([[0.1,0],[0,0.1]]), dtype="float32")) sampled_pdf = _multi_gaussian_pdf(sampled_l_t, l_t) f = theano.function([], [l_t, sampled_pdf, g]) f() ### 2015/3/24 #### May be use gaussian distribution as policy is a bad idea If the variance is set to be a small value, then a outlier can give exploding gradient. If the variance is large, then it's hard to make the training converge. • stochacity will increase over time in the recurrent network • Clip gradients can not help much ### 2015/3/25 Backprop with RL really is non-trivial thing. More details found available in "MULTIPLE OBJECT RECOGNITION WITH VISUAL ATTENTION", including variance and zoom ratio (15%) ### 2015/3/26 • valid error: 3.64 • test error: 4.19 Differences between the model described in literal: • tanh non-linearity vs. RELU • RELU gives explosion in gradients in my experiments • Reccurent NN vs. LSTM • In this experiment, normal recurrent NN is used to save time Other insights: • Pre-training with random glimpses may be important	2017-08-16 21:32:55	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 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": 0.4510796368122101, "perplexity": 10972.070277985964}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-34/segments/1502886102663.36/warc/CC-MAIN-20170816212248-20170816232248-00685.warc.gz"}
https://www.gradesaver.com/textbooks/math/geometry/CLONE-68e52840-b25a-488c-a775-8f1d0bdf0669/chapter-5-section-5-1-ratios-rates-and-proportions-exercises-page-216/4a	## Elementary Geometry for College Students (6th Edition) 24:32 Find what 24 and 32 are both divisible by Divide by 8 24$\div$8=3 32$\div$=4 So then 3:4	2019-09-19 16:56:15	{"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": 0.378751665353775, "perplexity": 4745.6674526461575}, "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/1568514573561.45/warc/CC-MAIN-20190919163337-20190919185337-00283.warc.gz"}
https://dsp.stackexchange.com/questions/64190/fir-filter-implementation-without-padding	# FIR Filter implementation without padding Is it possible to implement FIR filtering action without padding the input and coefficients? i.e. Let's say if the input and filter coefficients are of size 4, then the output will be 7 samples. So, while implementing, we generally add 3 more zeros to both input and filter coefficients making them equal to output size. But, if the input and filter coefficients are of size 1024, then the output will be of 2047 samples. So, now, we need to add 1023 zeros to both input and filter coefficients. This is inefficient, right? So, I just want to know is there any other way to implement FIR Filtering without padding? The below code gives the idea I was talking about. int main() { int x[4],h[4],y[7]={0}; int i,j; for(i=0;i<4;i++) { x[i] = i+1; h[i] = i+1; } for(int i=0;i<7;i++) { for(int j=0;j<4;j++) { y[i+j] = y[i+j]+x[i]h[j]; //filtered signal of length M+N-1 } } for(i=0;i<7;i++) printf("%d\n", y[i]); } Output: 1,4,10,20,25,24,16 - expected But obtained results - 1,4,10,20,garbage value, garbage value, garbage value • Implementing a FIR filter in the time domain doesn't require any padding. The output length is simply N(num of samples) + M (filter kernel length) -1. – dsp_user Feb 28 at 7:41 • @dsp_user Can you modify the code to get the results without padding? I modified, but couldn't get the correct results. – rkc Feb 28 at 7:48 • There are a number of issues with that code. The output length should be N+M-1 and yet your output length is only y[M]. Also, the main inner loop should go to M so change it accordingly. Also, I have y[i+j] whereas you have y[i], which is clearly wrong. The first 4 samples only seem correct because the output is shifted by M samples but your implementation is incorrect. – dsp_user Feb 28 at 9:01 • I have kept the changes whatever you told in the comments section in the code. Kindly, have a look. I am getting only M Correct samples if I used the commented section instead of my code. – rkc Feb 28 at 10:23 • ‘i’ should run for the length of x, which is 4, not 7 – Dan Szabo Feb 28 at 19:34 As I said in a comment, no padding is necessary. A simple FIR implementation might look like (it is assumed that the filter kernel h[] has already been implemented) float y[N+M-1]; //set y[] to zero for(int i=0;i<N;i++){ //N - signal length for(int j=0;j<M;j++){ //M - filter kernel length (usually much shorter than N y[i+j] = y[i+j]+x[i]h[j]; //filtered signal of length M+N-1 } } h[] represents the filter kernel and is usually implemented as a window-sync filter of length M (in your case it's just the original signal). For your use case, you'd have int x[7],h[7],y[13]={0}; int i,j; for(i=0;i<7;i++) { if(i<4) { x[i] = i+1; h[i] = i+1; } if(i>=4) { x[i] = 0; h[i] = 0; } } for(int i=0;i<7;i++) { for(int j=0;j<7;j++) { y[i+j] = y[i+j]+x[i]h[j]; //filtered signal of length M+N-1 } } Note that since you're convolving a signal with itself (xh), you don't even need h[] but I kept it for clarity. • I could get only M samples of expected value at the output, if I use the code without padding. – rkc Feb 28 at 8:33 • Post the entire code (including the filter kernel) you're using now and I'll have a look . – dsp_user Feb 28 at 8:35 • Hi, I added the whole code with the changes you mentioned. – rkc Feb 28 at 8:48 • @rkc, no you didn't. You see that I'm using y[i+j] whereas you have y[i]. Also , change the length of y to y[N+M-1]. There might be other issues too. – dsp_user Feb 28 at 9:07 • @rkc, If you're still having difficulty implementing this, just explain which part you don't understand so that I can help. – dsp_user Feb 28 at 9:36	2020-10-26 02:06:50	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 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": 0.4564248025417328, "perplexity": 2292.502614582736}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-45/segments/1603107890108.60/warc/CC-MAIN-20201026002022-20201026032022-00179.warc.gz"}
https://jcom.sissa.it/article/pubid/JCOM_1907_2020_A08/	## 1 Introduction Would it have been easier if we could see the damn virus all around us; if it was red and prickly, and stuck to us like blackjacks? asks South African science journalist Elsabé Brits in Vrye Weekblad, an Afrikaans-language online newspaper [Brits, 2020 ]. It is reasonable that people feel aggravated by an invisible enemy that has caused global disruption and widespread hardship. The nature of viruses as an invisible, potentially deadly, threat explains our fascination with viruses and the prevalence of virus metaphors in popular culture (for example, ‘computer viruses’ or ‘viral videos’); as well as the common occurrence of lethal viruses as villains in science fiction and movies such as Outbreak and Contagion [Schell, 1997 ]. In Fever , a 2016 thriller by South African author Deon Meyer, the storyline of widespread havoc and devastation caused by a deadly virus now almost seem like a disconcertingly accurate depiction of what was to come in 2020. This article explores South African editorial cartoons in the context of COVID-19, and specifically how newspaper cartoonists illustrate the virus and use anthropomorphism as a visual rhetorical device to communicate aspects of the virus and articulate responses to it. Given that our increasingly sophisticated abilities to visualise viruses have transformed our understanding of and response to viruses, we start with a brief reference to the theory of social representation of science, followed by a concise summary of historical milestones that have paved the way for our current capabilities to visualise viruses. Next, we look at the role of editorial cartoons, and their potential contribution to public communication of science. We discuss anthropomorphism as one of the key tools used by cartoonists to engage readers. Finally, the focus of the current study is an analysis of the anthropomorphic portrayal of the novel coronavirus in South African editorial cartoons, published from January to May 2020. We analyse the incidence and nature of how the virus is anthropomorphised as an indicator of public sentiment about the novel coronavirus and COVID-19. We conclude with a discussion of the implications of anthropomorphising the coronavirus for public understanding of the science behind COVID-19. ## 2 Theoretical perspective A theoretical understanding of social representations of science helps us to understand the processes whereby abstract ideas and objects are made more concrete until they are assimilated into general culture [Moscovici, 1961 ; Moscovici, 1984 ; Höijer, 2011 ]. Bauer and Gaskell [ 1999 ] argue that things or ideas are typically ‘represented’ when they are absent or hidden from sight, adding that an original idea may take on multiple forms in different pragmatic contexts. In a reflection on social construction of scientific realities, Sismondo [ 2010 ] elaborates on how materials are manipulated in laboratories to create new shapes and beautiful objects that are created to emphasize specific characteristics and may, therefore, be very different from the original images produced in the laboratory. These processes are clearly at work when viruses are visualised by artists and/or illustrators (including cartoonists). Consequently, our current understanding of and our responses to viruses are shaped by the scientific images and artistic renditions created by scientists and artists. In the case of the novel coronavirus, visualisations often go further than scientific depictions to include artistic impressions, as in the case of editorial cartoons. In addition to providing a descriptive rendering of the virus in an accessible format to mass audiences, these cartoons articulate popular sentiment and add an interpretive layer of meaning within discursive contexts. Because they are created to appeal to a general readership, editorial cartoons about COVID-19 provide a perspective on the cultural and social meanings of such a pandemic, and the many nuances of the multifaceted relationship between a pandemic and culture. Understanding the multiple and nuanced linkages between culture and disease is a prerequisite for preventing, controlling or mitigating epidemics [Wald, Tomes and Lynch, 2002 ; Alcabes, 2009 ]. ## 3 Milestones towards visualising viruses In a reflection on how we depict COVID-19, Chatterjee [ 2020 ] describes the “cloak of invisibility” that surrounds the novel coronavirus as a fierce weapon, allowing it to multiply, invade and threaten us without being seen. It is therefore understandable that the natural history of viruses is characterised by efforts to visualise this threat. A brief look at the history of our abilities to visualise viruses highlight how historical advances have shaped this relationship and how current technologies continue to influence how we view viruses. The world first got to see images of the novel coronavirus in January 2020, about a month after the World Health Organisation (WHO) was informed of a new disease that first emerged in China [World Health Organisation, 2020 ]. Soon after, these images began circulating in the media. That detailed images of this virus could enter the public domain so swiftly, is thanks to the development of microscopic imagery over the course of several centuries, and recent advances in visualisation techniques. The earliest microscopes go back to around 1600, but these were little more than magnifying glasses and were regarded as curious toys, rather than being used for systematic observations that contributed to scientific knowledge [Ball, 1966 ]. This changed when, in the 17 ${}^{\mathrm{th}}$ century, Antony Van Leeuwenhoek crafted a single-lens microscope that could magnify up to 300 times [Fildes, 1951 ; Gest, 2004 ]. In Victorian times, gazing through microscopes became a popular hobby in Great Britain, as people were fascinated by a previously unseen world teeming with tiny living creatures [Campbell, 2018 ]. Until the mid-19 ${}^{\mathrm{th}}$ century, people had no idea that bacteria, yeasts and viruses could cause disease and death. In busy hospitals, doctors and nurses moved from one patient and surgical procedure to the next without washing their hands, unaware that they were spreading lethal infections. The idea of washing hands as a hygiene protocol was scorned by the medical profession [Tan et al., 2020 ]. In visual imagery of the time, diseases were depicted as terrifying evil spirits [Ulaby, 2020 ]. In the late 1850s, Louis Pasteur demonstrated the role of microorganisms (in this case bacteria) in fermentation and putrefaction, thereby laying the foundations for microbiology as a modern scientific discipline [Artenstein, 2012 ]. Germ theory — i.e. the notion that diseases are caused by invisible minute organisms, or germs — met with considerable public resistance, especially in the U.S. [Richmond, 1954 ; Tomes, 1997 ]. The mass media, and particularly women’s magazines, played an important role in creating public awareness and wider acceptance of germ theory and domestic hygiene practices [Tomes, 1990 ]. In Queen of the Home , published in 1889, magazine editor and author, Emma Churchman Hewitt, wrote that germ theory “placed in the hands of everyone, if not the power of destroying these germs, at least the power to prevent their proliferation” [Tomes, 1999 , p. 67]. In the early 1930s, the first transmission electron microscope was built and used to produce images of bacteria; eight years later, it was used to capture images of a virus [Ackermann, 2011 ; Buiani, 2014 ]. Current advances in microscopy allow us to see the detailed structure of viruses, thereby helping scientists to develop treatments and vaccines [Goldsmith and Miller, 2009 ]. In 1967, virologists June Almeida and David Tyrrell were the first to describe previously unknown virus particles characterised by a “distinct layer of projections” (i.e. coronaviruses) [Almeida and Tyrrell, 1967 , p. 176]. Today, we have detailed images of coronavirus particles with the characteristic fringe of protruding clumps that create the effect of a halo, or corona, around the virus [Nerlich, 2020 ]. A month after Chinese health officials informed the WHO in December 2019 of 44 patients with a mysterious form of pneumonia [World Health Organisation, 2020 ], the first images of the novel coronavirus [Gale, 2020 ] were released, with other laboratories around the world producing similar images soon afterwards (see Figure 1 a & b). Subsequently, leading laboratories around the world have created electron micrographs and artistic renditions of this virus. These images, described by Frumkin [ 2020 ] as ghostly black-and-white tracings of the invisible, bear little resemblance to the bright and colourful depictions of the novel coronavirus that were subsequently widely portrayed in the media. At first, all electron micrographs were produced in black and white and had to be stained afterwards [Weaving, 2020 ]. In 2016, scientists developed a way of capturing these images in colour by staining cellular components with metal ions that emit unique signals, which can then be rendered as vivid colours [Adams et al., 2016 ]. Alternatively, scientists add colour later to make the images clear and vivid, but the choice of colours are arbitrary as can be seen in Figure 2 a and 2 b for example. Based on the structural information obtained through sophisticated imaging techniques, artists at the Centers for Disease Control and Prevention produced a high-resolution graphic of the novel coronavirus (or SARS-CoV-2) that has been widely used in the media (see Figure 3 ). There are multiple and intricate steps in the process of transforming data retrieved from a microscope into a visible image of a virus, with several elements of interpretation involved along the way. Scientists and illustrators use artificial colours for technical reasons, but also to add aesthetic and media appeal to their pictures. Ultimately, the way the virus is drawn (or illustrated) depends on what it looks like under the microscope, as well as choices and assumptions made by the artist. These choices can affect public fears and anxieties about infectious diseases. Therefore, visualisations of viruses are more than mere illustrations; they have socio-cultural dimensions [Buiani, 2014 ; Frumkin, 2020 ]. For example, Weaving [ 2020 ] points out that, if we were willing to accept that objects captured in the sub-microscopic world (i.e. the realm that viruses inhabit) are essentially monochrome grey, viruses would seem less like hostile invaders. Instead, we typically depict viruses in bold colours which portray them as aggressive and noxious substances and contribute to a culture of fear that surrounds them [Buiani, 2014 ]. Similarly, cartoonists choose specific colours when they draw the virus in order to elicit a specific response from readers. In addition to the choice of colour, other artistic devices such as anthropomorphism contribute to the media discourse around the virus and, ultimately, articulate and shape popular understandings of science. ## 4 Anthropomorphism — origins, merits and concerns Anthropomorphism refers to the phenomenon whereby authors or artists attribute human characteristics to non-human animals and non-living or inanimate objects [Byrne, Grace and Hanley, 2009 ]. This includes physical characteristics and abilities, for example a talking dog or a dancing teapot, as well as mental characteristics and abilities, for example a sad tree or an angry virus. Scientific consensus dictates that coronaviruses are merely minute bundles of genetic material that exist only to replicate. Thus, there is no thought, intent or capacity for malice on the part of the virus; it cannot be sneaky, evil or aggressive; viruses cannot attack us or wage a war against us [Porubanova and Guthrie, 2020 ]. As stated by Philp [ 2020 ], the virus does not exist to kill or harm, those are just its side effects. But, as is true for a multitude of non-human beings and inanimate objects, people frequently attribute human-like characteristics and traits to microbial life forms and viruses, including physical and psychological features, as well as human behaviours and cognitive states [Epley, Waytz and Cacioppo, 2007 ; Wood, 2019 ]. The inclination to anthropomorphise viruses during disease outbreaks is not new. Moodley and Lesage [ 2019 ] studied how newspapers in South Africa represented the 2014 outbreak of Ebola and found that the Ebola virus was frequently portrayed as a predator and criminal. Similarly, Connelly and Macleod [ 2003 ] showed how newspaper reports afforded agency to the Aids virus, allowing for its construction as the enemy, and inciting citizens to take on a preventative and caring role. Perhaps the widespread occurrence of anthropomorphism is evidence that we, as human beings, think of ourselves as the most important beings (i.e. anthropocentrism) and that is why we interpret any experience from a human viewpoint [Byrne, Grace and Hanley, 2009 ]. Another explanation is that anthropomorphism is simply a way of reasoning about an unfamiliar entity in terms of a human framework [Epley, Waytz, Akalis et al., 2008 ]. In other words, we make sense of something by making that entity sentient, which satisfies our collective need to control our environment, a phenomenon known as effectance motivation [Waytz et al., 2010 ]. From the perspective of the cognitive processes underlying anthropomorphism, Airenti [ 2018 ] defines anthropomorphism as a relation that humans establish with non-human entities as if they were human beings. In doing so, we put the non-human entity “in the position of interlocutor in an imaginary communicative situation” [Airenti, 2018 , p. 9]. In the course of this process, we automatically attribute intentionality and social behaviour to these entities. The author argues that all of us, from young children to adults, have a basic tendency to anthropomorphise and that anthropomorphism, therefore, is a “specific human attitude, not a childish mistake” [Airenti, 2018 , p. 7]. As a literary device, anthropomorphism is particularly widespread in children’s books, and is mostly applied to animals. The use of anthropomorphism boomed when Disney started producing animated cartoon films with mice, rabbits, piglets, wolves and many other species talking, walking, dancing, arguing, and more [DoRozario, 2006 ]. Our tendency to anthropomorphise animals is not surprising, given that we have lived in close proximity to wild and domestic animals for centuries, and that we rely on animals for food, transportation and labour, but also for companionship, protection and entertainment [Breedlove and Arguin, 2015 ]. Notably, zoonoses (the transfer of diseases from animals to humans) inevitably result from these close interactions. Pedagogically, anthropomorphism can be a useful tool to humanise science, making it more accessible to learners. Hight [ 2017 ] demonstrated that, in documentary films, anthropomorphism helped viewers to recall content more accurately, without creating anthropomorphic attitudes towards the films’ content, concluding that anthropomorphism is a useful tool for communicating science, engaging audiences and increasing content absorption without compromising the integrity of the information. Wood [ 2019 ] presents a perspective on the popularity and ubiquity of anthropomorphism in Japanese culture, including its widespread use in public communication of science. Examples include talking test tubes, smiling proteins, plant hormones with personalities and atomic particles wearing hats and sunglasses. Japanese explanations of how influenza is transmitted include virus particles “represented with evil, grinning faces and pitchforks, gleefully attacking their victims” [Wood, 2019 , p. 25]. However, anthropomorphism occurs across all cultures and types of literature, including academic texts. Dealing with forms of life that people can’t see but that affect their daily lives, the field of microbiology is particularly susceptible to the use of anthropomorphic terminology [Davies, 2010 ]. Examples from microbiology research include reports of screaming yeasts [Roosth, 2009 ], hungry fungi that attack iron [Hand, 2016 ], dancing bacteria [Talib et al., 2017 ] and rock-eating bacteria [Smith, 2018 ]. While many scientists acknowledge the potential of anthropomorphism as a tool to increase empathy with non-human species, they also point out that it may lead to inaccurate understanding of biological processes in the natural world [Milman, 2016 ]. Negative judgments about anthropomorphism range from describing it as a mild vice that a well-educated person should avoid [Bruni, Perconti and Plebe, 2018 ], to viewing the phenomenon as something that is potentially misleading and even an example of bad science [Arbilly and Lotem, 2017 ]. For example, in the case of microorganisms, children’s anthropocentric conceptions are primarily related to the roles of microbes as agents of disease, resulting in a mostly negative perspective [Byrne, Grace and Hanley, 2009 ] which is appropriate for viruses, but not always correct in the case of bacteria and yeasts. In the context of disease prevention and control, it is pointed out that a view of viruses as predators that can stalk their victims is misleading, since it warps our understanding of the role that we, as humans, play as vectors for spreading the virus [Weldon, 2001 ]. ## 5 Anthropomorphising the coronavirus Two distinctive features make the coronavirus instantly recognisable: the virus is shaped like a sphere and it is surrounded by a halo of lumps. These structural features are usually more pronounced in artists’ impressions compared to the images we see in electron micrographs. In the first few months of 2020, a global explosion of artworks depicting coronavirus particles established a rendition of these ‘spikey balls’ as an iconic image of a virus that disrupted life around the globe [Gaiter, 2020 ; Nerlich, 2020 ]. When cartoonists draw the novel coronavirus, they often go a step further. In addition to bold and bright colours and exaggerated features, they add human characteristics, motivations, behaviours and emotional expressions — i.e. they anthropomorphise the virus. The attribution of anthropomorphic characteristics to invisible pathogens such as bacteria or viruses is a common occurrence, especially when we are faced with uncertainty and fear [Airenti, 2018 ]. There are many reasons why artists may choose to anthropomorphise a virus. Broadly speaking, anthropomorphism could help us to make sense of a complex, confusing and unpredictable world [Porubanova and Guthrie, 2020 ]. In the case of the coronavirus, thinking of the virus as human-like, gives us a way to grasp these unseen entities and, even if this grasp is just an illusion, it provides us with some sense of confidence and control. More specifically, depicting the coronavirus as a clever genius or devious adversary that is actively plotting against us, may help people to rally together against a common enemy [Philp, 2020 ]. If the threat is portrayed as sentient, people may be more willing to comply with precautionary measures and tolerate treatments [Schlozman, 2014 ]. Similarly, Kim and McGill [ 2011 ] demonstrated that when diseases are described as having evil intentions to hurt us, it affected the level of risk people perceived, and this, in turn, depended on their individual perceived power to control the risk. Furthermore, adding human traits to a virus, could be a way to add emotional engagement and evoke a response. For example, illustrating the virus with an evil grin or an aggressive pose clearly emphasises the threat, while drawing the virus as cute and endearing could be a way to assuage public fears [Ulaby, 2020 ]. However, it can also be misleading to draw the virus as something reassuring and friendly that almost resembles a toy [Gaiter, 2020 ]. In general, it could be argued that giving the virus a ‘face’ makes it more ‘real’ and may encourage people to adhere to hygiene protocols such as wearing masks, washing hands regularly and keeping a physical distance from others. In the South African context, cartoonists also use anthropomorphism as a tool to contextualise scientific information and reflect public sentiment within the prevailing social, political and economic contexts. By paying attention to these anthropomorphic elements, it may become evident not only what the prevailing understanding of scientific information is, but also what attitudes, anxieties, fears and misconceptions may be present in popular discourses. ## 6 Defining editorial cartoons, as well as their roles and relevance to science communication Editorial cartoons (also known as newspaper cartoons or political cartoons) are persuasive visual summaries that intelligibly condense and simplify a current issue into one depiction in a form that is easily understood by the general public [Medhurst and DeSousa, 1981 ; Wigston, 2002 ; Giarelli and Tulman, 2003 ]. Cartoonists get their ideas and inspiration from the daily flow of news, events and issues in the political, economic, cultural and societal arenas [Wiid et al., 2016 ]. Most editorial cartoons present a single message or perspective and are drawn within a single frame (or border), which differentiates them from comic strips that typically have storylines spanning a series of frames. DeSousa and Medhurst [ 1982 ] describe the primary function of (political) cartooning as showing the interrelationships of people, events and power, and add that cartoonists tap into the collective consciousness of readers, thereby reaffirming cultural values and our individual interpretations of those values. These cartoons may help readers to interpret their experiences of the world at a specific time [Greenberg, 2002 ] and reflect contemporary cultural attitudes and values [Giarelli and Tulman, 2003 ]. During difficult times, cartoonists may also offer hope and encourage solidarity [The Economist, 2020 ]. As a form of visual news discourse, editorial cartoons not only comment on current events, but also express concern, criticism and frustration, question those in power and provoke people to react against injustice, often with a satirical and/or comical slant [Kotzé, 1988 ; Kleeman, 2006 ; Knieper, 2007 ; Panneerselvan, 2020 ]. Cartoons, furthermore, are a visual record of history that helps to construct the rhetoric related to a specific topic or issue [Kelley-Romano and Westgate, 2007 ]. Reflecting on the role of cartoons from the 19 ${}^{\mathrm{th}}$ century in public health advocacy, Hansen [ 1997 ] points out that, in the second half of this century, profound changes in our understanding of infectious diseases coincided with the golden age of political cartooning. Instead of an exclusive focus on professional writing, the author suggests that cartoons are a significant source that reveal how ordinary people understand a specific health issue and provide some insight into their circumstances and challenges while facing a health issue. Hansen draws attention to the advocacy role of cartoons, and their role in identifying problems and assigning responsibility for such problems. ## 7 Analysing the socio-cultural meaning of South African cartoons on COVID-19 Around the globe, newspaper cartoonists have responded to the COVID-19 pandemic and contributed to the discourse by capturing and commenting on the political and societal impacts and responses in their work. The same is true in South Africa, a country with a strong tradition of award-winning editorial cartooning. This provided a unique opportunity to study how South African cartoonists represent a science-related issue that is closely interwoven with politics and society. The ability of editorial cartoons to capture public sentiment at a specific point in time is illustrated in South African editorial cartoons that reflect the societal impact of the pandemic on the society. Amongst the first few cases of COVID-19 in South Africa were seven people (out of a group of 10 people traveling together) who returned to Durban, South Africa, on 1 March 2020, after a ski holiday in Italy. As numbers started climbing in South Africa, journalist Sizwe Dhlomo took to social media with the claim that it was the rich who brought the coronavirus to South Africa, but the poor who would suffer the most [Entertainment Reporter, 2020 ]. This notion, of the rich infecting the poor, was depicted by cartoonist Brandan Reynolds in his cartoon ‘The rich’, which shows a jet plane seeding the virus over an informal settlement (Figure 4 ). As signalled by this cartoon, which was published early in the pandemic, the media discourse around COVID-19 in South Africa would be shaped by the socio-economic and political contexts in one of the world’s most unequal countries. This highlights the importance of understanding the public communication of science within particular contexts. Rather than relying on the provision of factual information as a way to counter disinformation and improve public understanding in a one-size-fits-all approach, science communication needs to reckon with the specific conditions of its reception and interpretation. Editorial cartoons can communicate issues that would be difficult to articulate in written texts. Previous experience in South Africa, such as during the HIV/Aids struggle, showed how cartoons can play a vital role in combating disease [Wigston, 2002 ; Horne, 2011 ]. Globally, comics and graphic novels have offered pathways to improve health literacy [e.g. Tatalovic, 2009 ; Green and Myers, 2010 ; Tarver et al., 2016 ; McNicol, 2017 ; Farinella, 2018 ]. By distilling complex issues into a form accessible to a non-expert audience [Kleeman, 2006 ; Kelley-Romano and Westgate, 2007 ; Domínguez, 2014 ], editorial cartoons constitute a form of public science communication. Representations of scientific information are, however, bound up with other contextual socio-cultural dynamics. In the context of the coronavirus pandemic, science communication was engaged in a struggle for discursive dominance over disinformation campaigns, conspiracy theories and anecdotal speculation. A cartoon from the current dataset (see Figure 5 ) draws attention to the dangerous spread of disinformation alongside the spread of the virus. The cartoon, by Jonathan Shapiro (drawing under the pen name Zapiro), depicts a virus-like figure labelled ‘Fake News Virus’, that dwarfs the coronavirus, suggesting that misinformation and conspiracy theories may pose an even bigger danger to society. This cartoon could be read as an implicit commentary on the limits of popular science communication such as editorial cartooning itself, even as it attempts to issue a warning that only authoritative, legitimate sources of information should be trusted. Cartoonists employ a variety of tools, such as paradox, irony, humour and exaggeration to deliver a specific message at a specific time [Giarelli and Tulman, 2003 ]. In the African context, cartoonists have been noted to appropriate the global conventions of caption, (indirect) allusion, exaggeration (caricature), symbolism and pseudonym, and combine them with contextual communicative norms and socio-cultural aesthetics, which may include allusions to local issues, the use of popular catch phrases, and employment of local lingua franca [Oduro-Frimpong, 2018 ]. For example, in the cartoon by Carlos published in the weekly paper the Mail & Guardian (Figure 6 ), South Africa tells the virus to “tsek!”, an expression that is a shortened version of the South African slang word “voetsek”, which means “get lost!” or “scram!”. By contextualising scientific information in a local context and communicating in a local vernacular, the informal register of editorial cartoons affords them the ability to communicate complex scientific communication to audiences in language they understand. This however implies that an element of interpretation will always be present in cartoonists’ work. Shapiro, arguably South Africa’s best known cartoonist, refers to himself as a “visual columnist” who interprets events “in a personal way”: “I’m always working with things that the public knows about and may not know about, and I occasionally start debates” [Dennill, 2017 , online]. ## 8 Objectives and research questions Our objective with this study was to determine if (and how) South African cartoonists illustrated the novel coronavirus in cartoons related to COVID-19, with a specific focus on the incidence and nature of anthropomorphism as a tool in their visual discourse about the virus. Based on the theory of caricature which suggests that cartoons represent public sentiment toward pertinent issues at a given point in time [Wiid et al., 2016 ], we assumed that cartoons about COVID-19, and the characteristics of virus illustrations, would articulate and influence public views, and help shape public perception [Kleeman, 2006 ; Greenberg, 2002 ; Panneerselvan, 2020 ]. Therefore, we also examined the emotional tone conveyed by cartoons containing illustrations of the virus. Our research set out to answer the following research questions: 1. How often do South African editorial cartoonists include illustrations of the novel coronavirus in their editorial cartoons related to the COVID-19 pandemic? 2. What are the most dominant characteristics of their virus drawings in terms of structural shape (morphology) and colour? 3. Do these cartoonists anthropomorphise their virus drawings and, if so, what human characteristics and abilities do they attribute to the virus? 4. What is the overall emotive tone (or sentiment) of the cartoons? ## 9 Methodology Our study analysed editorial cartoons published in South African newspapers (print and online) during the first five months of 2020, i.e. 1 January to 31 May. The timeframe for the study starts one day after officials from the WHO in China first reported an outbreak of a new type of coronavirus, on 31 December 2019 [World Health Organisation, 2020 ]. Over the next few weeks, COVID-19 started spreading around the world, and South Africa’s first case was confirmed on 5 March 2020 [Abdool Karim, 2020 ]. A national, five-week lockdown started on 26 March 2020; followed by a gradual phasing out of lockdown measures over many months. Using a combination of PressReader and online news sites as sources of data, we identified 15 South African newspapers that publish single-panel editorial cartoons regularly, jointly publishing the work of 14 cartoonists, as shown in Table 1 . Table 1 : Newspapers and cartoonists included in the current study. We searched for cartoons in each of these 15 newspapers or news sites in every issue and downloaded all those cartoons that were relevant to the novel coronavirus and the COVID-19 pandemic. From this group of cartoons — as far as we could establish, a census of the entire population of cartoons during this timeframe — we identified cartoons that included a depiction of one or more viruses and drew these as a purposive sample. Guided by a codebook, we coded these cartoons for the characteristics of the virus portrayals (morphology and colour), as well of for the presence of anthropomorphism. In those where anthropomorphism was present, we coded the virus drawings to analyse the type of physical characteristics resembling humans (such as facial features and limbs), emotional states (for example angry, friendly or neutral) and activity (i.e. drawings where the virus appears to be running, climbing, etc.). Finally, we coded all the cartoons containing virus drawings (where anthropomorphism was present or not) for sentiment (or emotional tone). Two coders collaborated on the development and testing of the codebook. Independent coding of 25 randomly selected cartoons resulted in an overall inter-coder reliability score of 86% between the two coders, which is higher than the generally required agreement of 80% [Bayerl and Paul, 2011 ]. ## 10 Findings To answer RQ1 (How often do South African editorial cartoonists include illustrations of the novel coronavirus in their editorial cartoons related to the COVID-19 pandemic?) we compared the total number of COVID-19-related cartoons (the population) in our data set with the number of cartoons containing virus illustrations (in our purposive sample). A total of 497 editorial cartoons relevant to COVID-19 were published between 1 January and 31 May 2020 in the 15 newspapers listed in Table 1 . Of these, 120 (24%) included an illustration of a coronavirus. Figure 7 compares the number of COVID-19-related cartoons (published per week) with the number of cartoons that illustrated the virus. Overall, the number of cartoons related to COVID-19 rose sharply during March 2020 once the first case of COVID-19 was confirmed in South Africa and case numbers started to increase. The topic remained of key importance (and had high news value) during April and May, as South Africans had to cope with stringent lockdown regulations. Once the lockdown took effect (from end March), fewer cartoons contained an illustration of the virus. Overall, 377 of the total set of 497 cartoons (76%) did not include a depiction of the virus. This is because cartoonists responded to the pandemic not only in terms of its scientific dimensions, but also focused on the political response to the pandemic and the associated societal and economic implications. It could therefore be argued that the contextual aspects of the pandemic, which include the politicisation of the outbreak and subsequent policy responses, outweighed the purely scientific elements of its portrayal in editorial cartoons. Our second research question focused on the shapes and colours that cartoonists favoured in their virus drawings. In terms of the shape, we found that cartoonists almost always used exaggeration when they drew the crown-like halo of the virus, thereby altering the appearance of the virus considerably. An example of such exaggeration of the virus’s shape, with the purpose of increasing the perception of threat, can already be seen in one of the earliest depictions of the virus in the South African media. In Die Burger ’s cartoon on 29 January 2020 (see Figure 8 ). In this cartoon, a threatening and evil-looking coronavirus is attaching itself to a worried-looking (and mask-wearing) planet Earth. In 110 of the 120 cartoons containing a drawing of the virus (i.e. in more than 90% of virus drawings) we analysed, cartoonists depicted the coronavirus as having enlarged knobs or elongated (even spikey) stalks. In contrast, in electron microscope images, the so-called halo of the coronavirus consists of tiny, rounded blobs (looking almost like a string of beads) that closely surround the central structure of the virus. Examples of such elongated stalks or spikes can be seen in Figures 8 and 11 . In cartooning, the exaggeration (or distortion) of physical features is used to make a specific point or convey a specific message. In the case of the coronavirus, the exaggeration of its protrusions could be a way to draw attention to the threat posed by the virus. As noted by Weaving [ 2020 ] the image of spherical blobs with spikes somewhat resembles an alien invader. In terms of the colours that cartoonists chose to illustrate the virus, our results show that they favoured green (n=42; 35%) or red (n=40; 33%). Keeping in mind that viruses are essentially monochrome grey, cartoonists could base their colour palette on scientific information (virus electron micrographs or scientific illustrations where ‘false’ colours have been added), but they also use colour as a visual tool to make their illustrations more persuasive. Their strong preference for green and red (see Figures 9 a, b & c) adds to the rhetoric of the viral threat. In this context, green is a distasteful colour (associated with sickness and slime), while red spells danger, but there is a risk that the overuse of these colours could fuel public fears unnecessarily [Weaving, 2020 ]. In our third research question, we explored the presence and incidence of anthropomorphism in the virus drawings, as well as the type of human characteristics that cartoonists attributed to the virus. Anthropomorphism was present in more than half of the 120 cartoons where the virus was illustrated (n=70; 58%). Figure 10 shows that cartoonists applied anthropomorphism to their drawings throughout the study period. In those cartoons where anthropomorphism was present (n=70), the virus was almost always attributed with typical human facial features such as eyes and/or nose and/or mouth (n=68; 97%). Of these 68 cartoons, 38 (56%) had visible teeth, while 34 (50%) had human-like limbs (arms/hands and/or legs/feet). In terms of the facial expressions of the virus, most were evil-looking (n=46; 68%). In a few cases, the virus had a friendly expression (n=4; 6%) or looked sad (n=3; 4%), while the rest were neutral. The evil-looking facial expressions were frequently exacerbated by pointy teeth, dripping with slime (see Figure 11 as an example). We were interested to see how often anthropomorphism was taken to a higher level by giving the virus the ability to speak, crediting it with consciousness and intentionality [Alden, 2004 ]. In 16 cartoons (23% of the 70 cartoons where the virus was anthropomorphised) the virus “spoke”. In 57 of the 70 anthropomorphised virus drawings (81%), the virus performed an activity, such as walking, running, often including threatening behaviour. These types of anthropomorphism are illustrated in two cartoons by Dr Jack & Curtis (Figure 12 a & b). The image used in Figure 12 a made use of the ‘monster’ trope and alludes to the dark comedy musical film Little Shop of Horrors (1986). The South African president, Cyril Ramaphosa, is seen to feed the insatiable virus with jobs, the economy, small and medium enterprises (SMEs) and individual freedoms. While providing a memorable ‘hook’ into popular culture, this cartoon links the anthropomorphic depiction of the virus with broader socio-economic concerns about economic devastation and debates about the erosion of democratic freedoms during the stringent lockdown regulations. Another example of a cartoonist’s impression of how the coronavirus intentionally and maliciously disrupted global events such as the Olympic Games, is illustrated in Figure 13 . Research question 4 focused on the overall emotive tone of all the cartoons included in this study where the virus was illustrated (n=120). The most dominant tone was fear (n=76; 63.3%) as illustrated in Figure 14 . Only 28 (23.3%) of the cartoons where the virus was illustrated had a humorous tone, with the rest (n=16; 13.3%) considered to be neutral. Cartoonists’ limited use of humour when depicting the virus is a reflection on the gravity of the COVID-19 pandemic. Several of the scary cartoons contained a representation of death in the shape of the grim reaper, visualised in the context of poor communities facing a dual threat of COVID-19 together with poverty and hunger (see Figure 15 a) and children who are scared to return to school (see Figure 15 b). As mentioned before, cartoonists frequently commented on the socio-economic impact of the virus on a society that was already in crisis before COVID-19. A cartoon by Zapiro (Figure 16 ) reflects on the seemingly impossible odds that government’s economic rescue plan could succeed when faced with high levels of poverty, unemployment and inequality. One of the boulders rushing downhill and threatening to crush this plan is labelled “apartheid-style lockdown”. This refers to the heavy-handed enforcement of lockdown regulations and abuse of power by the policy and army, including humiliation of citizens for minor infringements, a high number of arrests and several fatalities that made the headlines during the initial weeks of the lockdown period. ## 11 Discussion Editorial cartoons play an important role in the public communication of science as they can communicate complex scientific information in an accessible, visual way and within a context that is relevant to the readers of that publication. Furthermore, cartoons provide a vehicle to dispel disinformation in language that resonate with audiences’ lived experience and contexts. The fact that the majority of editorial cartoons during our study period did not depict the virus as such directly, but related aspects such as its socio-economic and political impacts, suggests that science communication in this context needs to be defined more broadly to encompass not only the transmission (in visual form) of scientific facts, but also the social, economic and political dimensions of scientific events and developments, in this case the impact of a devastating pandemic on a highly unequal society. Cartoons, despite their location within journalistic discourse, are however not value-free, objective representations of reality or descriptions of scientific facts. They are, by their very nature as artistic expressions, interpretations of political, social and scientific reality. For this reason, tools such as anthropomorphism are important to consider as they provide a glimpse into the prevailing public attitudes and perceptions around a set of scientific facts, while cartoons, at the same time, help to shape public attitudes and perceptions. Given the prevalence of disinformation during the so-called COVID-19 ‘infodemic’, editorial cartoons can be read as metaphorical expressions of broader anxieties, fears and (mis)conceptions. Our analysis found that cartoonists’ depictions of the coronavirus largely evoked emotions of fear and danger. The images were rendered in exaggerated fashion (e.g. an emphasis on spikes) or striking colours (often red, signalling threat and danger) and where anthropomorphic elements were used, these often served the function of ascribing agency and intentionality to the virus — heightening not only the element of threat, but also possibly diminishing the human agency that may be used to counter it. These representations are not intended to be taken literally. Rather, they provide symbolic and metaphorical interpretations of the virus within a specific cultural, economic and political context, intended to resonate with broader journalistic discourses and historical antecedents such as the HIV/Aids pandemic. The imagery therefore not only represents the virus itself, but public attitudes, responses and emotions — primary among them, our analysis suggests, that of fear and threat. ## 12 Concluding remarks Our research shows that South African cartoonists do include science-related issues in their work and have made a notable contribution to media content since news about the novel coronavirus and associated COVID-19 pandemic surfaced and gained momentum. While their illustrations are not scientifically accurate, they are persuasive and rich in visual rhetoric and contribute to the creation of meaning around the virus. In line with earlier research on cartoons as a form of rhetoric [Medhurst and DeSousa, 1981 ] and the power of visual material [Joffe, 2008 ], it is reasonable to conclude that, during a time of crisis, editorial cartoons increase and influence public interest and debate in science-related topics. Our understanding of the role of fear in persuasion [e.g. Dillard and Anderson, 2004 ], suggests that the dominant emotional tone of fear contributes to the persuasive effect of these cartoons that would add to public concern and anxiety about the coronavirus. Therefore, as a form of social commentary that is designed to provoke, these cartoons could be excellent triggers for public dialogue about science-related issues and social impacts during a health crisis. We conclude that editorial cartoons are important for research and practice of science communication not only because they provide a way to disseminate information, but also because they are useful sources of data to gauge public sentiments and perceptions, especially during a public health pandemic. Future research could build on this initial exploratory work, to include interviews with cartoonists to gain a better understanding of how they engage with science-related topics and how they make choices when it comes to illustrating scientists and science concepts. Also, focus groups with diverse groups of newspapers readers could shed light on how people respond to science-themed editorial cartoons and what messages they take away after engaging with these cartoons. ## Acknowledgments This work is based on the research supported by the South African National Institute for the Humanities and Social Sciences. ## References Abdool Karim, S. S. 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(2016). ‘No joke: understanding public sentiment toward selling and salespeople through cartoon analysis’. Marketing Theory 16 (2), pp. 171–193. https://doi.org/10.1177/1470593115607940 . Wood, M. (2019). ‘The potential for anthropomorphism in communicating science: inspiration from Japan’. Cultures of Science 2 (1), pp. 23–34. https://doi.org/10.1177/209660831900200103 . World Health Organisation (20th January 2020). Novel Coronavirus (2019-nCoV) situation report — 1 . URL: https://www.who.int/docs/default-source/coronaviruse/situation-reports/20200121-sitrep-1-2019-ncov.pdf . ## Authors Marina Joubert is a researcher at the South African Research Chair in Science Communication & Centre for Research on Evaluation, Science and Technology, Stellenbosch University, South Africa. Her research interests focus on scientists’ role in public communication of science, online interfaces between science and society, and the use of visual tools to engage the public with science. Twitter: @marinajoubert. E-mail: marinajoubert@sun.ac.za . Herman Wasserman is a Professor of Media Studies and Director of the Centre for Film and Media Studies at the University of Cape Town, South Africa. He has published and presented widely on misinformation in Africa, including presentations to the World Health Organization. He is a Fellow of the International Communication Association and an elected member of the Academy of Science of South Africa. E-mail: herman.wasserman@uct.ac.za . ## Endnotes One of the meanings of the word ‘corona’ is ‘something suggesting a crown’ (Source: Online Merriam-Webster Dictionary; see https://www.merriam-webster.com/dictionary/corona ).	2023-03-27 16:56:53	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 3, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 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": 0.26059216260910034, "perplexity": 7018.252133248908}, "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-2023-14/segments/1679296948673.1/warc/CC-MAIN-20230327154814-20230327184814-00087.warc.gz"}
http://mathhelpforum.com/advanced-algebra/35091-linear-maps-proving-its-linear-describing-kernal.html	# Thread: Linear maps. Proving its linear, and describing kernal. 1. ## Linear maps. Proving its linear, and describing kernal. Let c be an invertible nxn matrix and consider the map T:M(subscript)n->M(subscript)n defined by T(X)=CX-XC (a) show that T is a linear map (b) Describe kerT, hence show that T is never invertible. Thanks in advance, you guys help so much. Even if something may be so simple, if someone doesnt take the time out to show you, you will never understand..Cheers 2. Hello a) Let $\lambda\in\mathbb{K},\,X,\,Y\in\mathcal{M}_n(\math bb{K})$. You have to show that $T(\lambda X+Y)=\lambda T(X)+T(Y)$ which comes by developing $T(\lambda X+Y)=C(\lambda X+Y)-(\lambda X+Y)C=\ldots$ b) Hint : $T(X)$ is called the commutator of $X$ and $C$ 3. look in page 54 of lecture notes	2016-09-25 00:55:09	{"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": 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": 0.7814561128616333, "perplexity": 1022.3124256574708}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-40/segments/1474738659680.65/warc/CC-MAIN-20160924173739-00304-ip-10-143-35-109.ec2.internal.warc.gz"}
http://physics.aps.org/synopsis-for/10.1103/PhysRevLett.108.243201	# Synopsis: Helium Ions Give Electrons the Shake-Off Singly ionized helium-6 is an ideal atom for testing the quantum mechanical response of electrons to a decaying nucleus. The recoil and sudden change in charge of an atomic nucleus emitting a beta particle can literally shake an electron off the atom. Calculations of the probability of shake-off are most accurate when the change in nuclear potential is fast and the electron is in a hydrogenlike orbit, unperturbed by interactions with other electrons, but few reactions involve parent and daughter nuclei with such an ideal structure. In Physical Review Letters, Claire Couratin of Caen University, France, and colleagues present the first measurement of electron shake-off in the beta decay of ionized helium-$6$ (${}^{6}{\text{He}}^{+}$). With a half-life of just under a second, ${}^{6}{\text{He}}^{+}$ beta decays into doubly ionized lithium-$6$ (${}^{6}{\text{Li}}^{2+}$), a daughter nucleus in which shake-off can be described with a simple quantum mechanical calculation. Calculations have predicted that two percent of the daughter lithium would shake off an electron, leaving ${}^{6}{\text{Li}}^{3+}$. Couratin et al. performed a series of experiments in which they collected and confined $20,000$ ${}^{6}{\text{He}}^{+}$ ions into a trap from a beam of ${}^{6}\text{He}$ produced at France’s Large Heavy Ion National Accelerator. The trap is outfitted with detectors that measure the coincidence of beta particles and ${}^{6}{\text{Li}}^{2+}$ and ${}^{6}{\text{Li}}^{3+}$, allowing the team to measure the probability of shake off in ${}^{6}{\text{Li}}^{2+}$ with a relative precision of about a percent. Their result is in excellent agreement with theory, which could make ${}^{6}{\text{He}}^{+}$ a textbook example for experiments to come. – Jessica Thomas ### Announcements More Announcements » ## Previous Synopsis Atomic and Molecular Physics Graphene ## Related Articles Atomic and Molecular Physics ### Viewpoint: Cool Physics with Warm Ions Ultrafast laser pulses can be used to control and characterize the quantum motion of a single trapped ion over 5 orders of magnitude in temperature. Read More » Atomic and Molecular Physics ### Synopsis: The Quantum Hall Effect Leaves Flatland Cold atoms in an optical lattice with a synthetic extra dimension could be used to see the 4D version of the quantum Hall effect. Read More » Condensed Matter Physics ### Viewpoint: Emerging Quantum Order in an Expanding Gas The spontaneous emergence of long-range quantum order, normally the preserve of low-temperature equilibrium states, has been observed in an expanding cloud of potassium atoms. Read More »	2015-11-28 00:32:08	{"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": 0.48951441049575806, "perplexity": 1569.353221112246}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-48/segments/1448398450715.63/warc/CC-MAIN-20151124205410-00047-ip-10-71-132-137.ec2.internal.warc.gz"}
https://web2.0calc.com/questions/geometry_8382	+0 # Geometry 0 55 2 +250 In triangle ABC, AB = 10, BC = 24, and AC = 26. Find the length of the shortest altitude in this triangle. I think its a right triangle, but don't know how to use that information to solve the problem. May 15, 2022 ### 2+0 Answers #1 +1750 +1 It is indeed a right triangle, and the shortest altitude will be perpendicular to the hypotenuse. The area of the triangle is $$10 \times 24 \div 2 = 120$$. Because the altitude is perpendicular to the hypotenuse, we know that $$\text{hypotenuse} \times\text {altitude} \div 2 = [\text{ABC}]$$. Think of the hypotenuse as the base, and the altitude as the height. Subsituting what we know, we have: $$26 \times \text{altitude} \div 2 = 120$$, and we can solve for the altitude. Hope this helps!!! May 15, 2022 #2 +250 +1 Thank you! I got it. Thanks again! TheEarlyMathster May 16, 2022	2022-07-05 22:09:36	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9425429105758667, "perplexity": 999.0699700200577}, "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-2022-27/segments/1656104628307.87/warc/CC-MAIN-20220705205356-20220705235356-00681.warc.gz"}
https://www.physicsforums.com/threads/ideal-gas-in-the-microcanonical-ensemble-im-puzzled.272585/	# Ideal gas in the microcanonical ensemble: I'm puzzled Hi all, this is about problem 8.2 in Huang's Statistical Mechanics. I think I've been able to solve it, but the solution raised a question about the Maxwell-Boltzmann distribution. So first I provide my solution to the problem, then discuss the apparently weird point. ## Homework Statement The problem requires to use the microcanonical formalism to derive the equations of state of the ideal quantum gas, i.e. $$N = \sum_j \frac{1}{z^{-1} e^{\beta \epsilon_p}\mp 1},\qquad \frac{PV}{kT} = \mp \sum_p \log(1\mp z e^{-\beta \epsilon_p})$$ where the upper and lower signs refer to Bose-Einstein and Fermi-Dirac statistics, respectively. ## Homework Equations I think one should use the constraints inherent in the microcanonical ensemble $$N = \sum_p n_p, \qquad E = \sum_p \ve_p n_p$$ along with the formula for the set of occupation numbers maximizing the entropy $$n_p = \frac{1}{z^{-1} e^{\beta \epsilon_p}\mp 1} \qquad ()$$ and the the formula for the entropy thereby $$S = k \sum_p \left[\frac{\beta \epsilon_p - \log z }{z^{-1} e^{\beta \epsilon_p}\mp 1}\mp \log(1\mp z e^{-\beta \epsilon_p}) \right]$$ All these results are derived in section 8.5. ## The Attempt at a Solution The first equation of state is trivially obtained by plugging () in the constraint on $$N$$. The second equation of state was a bit harder, but at some point I recalled that E should be identified with the total internal energy, and $$z = e^{\beta \mu}$$. Using this information and the constraints in the formula for the entropy one gets $$S = \frac{1}{T}(U-\mu N) \mp k \sum_p \log(1\mp z e^{-\beta \epsilon_p})$$ The second equation of state is obtained after recalling that the general form of the internal energy is $$U = TS - PV + \mu N$$. 4. The weird point <=================== So far, so good. However, it seems to me that adopting the same approach with the Maxwell-Boltzmann statistics produces a weird result. The MB entropy is $$S = k \sum_p z e^{-\beta \epsilon_p} (\beta \epsilon_p - \log z)$$ so that, if I identify the same quantities as above ( total energy and number) I get $$TS = E - \mu N$$. But, assuming that $$U = TS - PV + \mu N$$ is true, wouldn't this mean $$PV=0$$ instead of the expected $$PV = NkT$$ ? Is there something I'm overlooking? Thanks a lot for any insight F	2020-08-13 18:06:02	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 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": 0.8909204006195068, "perplexity": 394.5963713129015}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-34/segments/1596439739048.46/warc/CC-MAIN-20200813161908-20200813191908-00240.warc.gz"}
https://crazyproject.wordpress.com/2011/08/14/compute-a-quotient-module/	## Compute a quotient module Let $R$ be a principal ideal domain, let $a \in R$ be nonzero, and let $M = R/(a)$. Given a prime $p \in R$, say $a = p^nq$, where $p$ does not divide $q$. Prove that $(p^k)M/(p^{k+1})M$ is module-isomorphic to $R/(p)$ if $k < n$ and to $0$ if $k \geq n$. We begin with some lemmas. Lemma 1: Let $C \subseteq A,B$ be ideals of a ring $R$, and consider $A/C$ as an $R$-module. Then $B(A/C) = (BA)/C$. Proof: $(\subseteq)$ If $x \in B(A/C)$, then $x = \sum b_i(a_i + C) = \sum (b_ia_i + C)$ $= (\sum b_ia_i) + C$ $\in (BA)/C$. $(\supseteq)$ If $x \in (BA)/C$, then $x = (\sum b_ia_i) + C$ $= \sum (b_ia_i + C)$ $= \sum b_i(a_i+C)$. Thus $x \in B(A/C)$. $\square$ Lemma 2: Let $R$ be a principal ideal domain and let $a,b,c \in R$ be nonzero with $b\|c$. Note that $(ac) \subseteq (ab)$. Prove that $(ab)/(ac) \cong_R (b)/(c)$. Proof: Let $\psi: (b) \rightarrow (ab)/(ac)$ be given by $bx \mapsto \overline{abx}$. (This is well-defined since $R$ is a domain, and is clearly an $R$-module homomorphism.) Certainly $\psi$ is surjective. Now if $bx \in \mathsf{ker}\ \psi$, then $abx \in (ac)$, so that $bx \in (c)$. Conversely, if $bx \in (c)$, then $bx = cy$ for some $y$, and so $\overline{abx} = \overline{acy} = 0$. By the First Isomorphism Theorem, $(b)/(c) \cong_R (ab)/(ac)$. $\square$ Lemma 3: Let $R$ be a principal ideal domain and $a,b,c \in R$ such that $b\|c$. If $(a,c/b) = (1)$, then $(a)((b)/(c)) = (b)/(c)$. Proof: Say $c = bd$. Note that $ax+dy = 1$ for some $x,y \in R$, so that $abx + cy = b$. Now $b+(c) = abx + (c)$ $= a(bx+(c))$ $\in (a)((b)/(c))$, so that $(a)((b)/(c)) = (b)/(c)$. $\square$ If $k < n$, then $p^{k+1}\|a$, so that $(a) \subseteq (p^k), (p^{k+1})$. By Lemma 1, we have $(p^k)(R/(a))/(p^{k+1})(R/(a)) = ((p^k)/(a))/((p^{k+1})/(a))$ $\cong_R (p^k)/(p^{k+1})$ by the Third Isomorphism Theorem. Using Lemma 2, this is isomorphic to $(1)/(p) \cong_R R/(p)$. If $k \geq n$ with (say) $k = n+t$, then $((p^k)(R/(a)))/((p^{k+1})/(R/(a)) = ((p^t)((p^n)/(p^nq)))/((p^{t+1})((p^n)/(p^nq)))$ $= ((p^n)/(p^nq))/((p^n)/(p^nq))$ $= 0$, using Lemma 3 and the Third Isomorphism Theorem.	2017-01-19 06:38:25	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 73, "codecogs_latex": 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": 0.9990124106407166, "perplexity": 28.829668568949682}, "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-2017-04/segments/1484560280485.79/warc/CC-MAIN-20170116095120-00204-ip-10-171-10-70.ec2.internal.warc.gz"}
http://math.stackexchange.com/questions/443599/find-all-points-on-a-paraboloid-where-tangent-plane-is-parallel-to-a-given-plane	# Find All Points on a Paraboloid where Tangent Plane is Parallel to a Given Plane Find all points on the paraboloid $z=x^2+y^2$ where tangent plane is parallel to the plane $x+y+z=1$ and find equations of the corresponding tangent planes. Sketch the graph of these functions. I have its answer. I don't really understand such type of questions. And I am really willing to learn. Also I added its answer as a picture. Please teach me how to solve. - What and where is the answer you have? – DonAntonio Jul 14 '13 at 19:57 I have its solution manual. I added the answer as a picture @DonAntonio do I make a mistake? – B11b Jul 14 '13 at 19:59 Since I don't know what's your mathematical background and all that looks pretty straightforward, you must tell us what is it that you don't understand... – DonAntonio Jul 14 '13 at 20:02 Perhaps it is easier to learn several variables if you try to formulate the theorems/problems in one variable. – AD. Jul 14 '13 at 20:08 In fact, I solve such tangent plane question first time. And I could not produce any idea to solve it, thus, I looked at its solution. And in general, I dont understand. In the solution, first of all, a function is defined as $f(x,y,z)=z-x^2-y^2$ and $\nabla f(x,y,z)=-2xi-2yj+k$ is found. That's the normal direction is (-2x,-2y,1) After there, I took derivatives of $x+y+z=1$ and I got (1,1,1). And so as to find parallel points, $(1,1,1)=(-2x,-2y,1)$ thus, $x=-1/2=y$ and $z=1/2$ that is paralel points are $(-1/2,-1/2,1/2)$ right? And then, what i need to do? @DonAntonio – B11b Jul 14 '13 at 20:11 To get a normal vector to the paraboloid at a point (x,y,z), we can take the gradient $\nabla f(x,y,z)=-2xi-2yj+k$. Since we want the tangent plane at the point to be parallel to the plane $x+y+z=1$, the normal vector $\nabla f(x,y,z)=-2xi-2yj+k$ has to be parallel to the vector $i+j+k$ (since this is a normal vector to $x+y+z=1$). This means that $-2xi-2yj+k$ must be a constant multiple of $i+j+k$, so $-2xi-2yj+k=c(i+j+k)$ for some constant c. Then $-2x=c$, $-2y=c$, and $1=c$, so $x=-1/2$ and $y=-1/2$. Therefore $z=x^2+y^2=1/4+1/4=1/2$ at the point of tangency, and the tangent plane has equation $x+y+z=-1/2$ at this point. - Yes!!! Everything is clear:) the answer I want is this. Thank you so much:)) – B11b Jul 14 '13 at 20:56 Sorry, but I want to ask one thing. Why $c=1$? – B11b Jul 14 '13 at 22:01 I guess, accourding to sign of $z$ – B11b Jul 14 '13 at 22:05 You're correct; setting the coefficients of k equal gives that $c=1$. – user84413 Jul 14 '13 at 22:11 Okay, now got it. thanks :) – B11b Jul 14 '13 at 22:13 You can obtain a parametrisation of your submanifold by viewing it as a graph of a function, and the parametrisation's partial derivates give a basis of the tangent space at each point. Let the paraboloid, as a submanifold, be denoted by $S$. We have $f(x,y) = (x, y, x^{2} + y^{2})$ as our parametrisation, hence $T_{f(x,y)}S = <(1,0,2x)^{t}, (0,1,2y)^{t}>$. You now get exactly two unit-length vectors that span the orthogonal complement of $T_{f(x,y)}S$. Chose such a vector, let's call it $\nu$. Now all you have to do is find the plane you want your $T_{f(x,y)}S$ to be parallel to, and check that the line defined by $c(t) = f(x,y) + t\nu$ meets the plane orthogonally. Edit: For the last part, we use that in euclidian space, a hyperplane is parallel to another hyperplane iff there exists a line that meets both orthogonally. - Thank you for helping but you explained at too advanced level. I am sure, it is true. But I am beginner of calculus. :) – B11b Jul 14 '13 at 21:01 I am sorry, I should have taken this into account. I think the other answer is more useful to you. In this example, you can visualise it fairly easily, however. Just think of the tangent plane as a sheat of paper tangential at one point to your paraboloid. One orthogonal vector is then that one vector that goes out of this one tangential point and stands, you guessed it, in a right angle on the plane. Now if you want to find a plane that is orthogonal to that sheat of paper, you extend that orth. vector to a line and look at all the planes this lines is orthogonal to as well. That's all. – David Hornshaw Jul 14 '13 at 21:18 Not need to apologize :) I read your answer carefully:) thanks. – B11b Jul 14 '13 at 21:31	2014-09-16 01:06:15	{"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": 0.8635411858558655, "perplexity": 312.4682892871601}, "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-2014-41/segments/1410657110730.89/warc/CC-MAIN-20140914011150-00086-ip-10-196-40-205.us-west-1.compute.internal.warc.gz"}
http://math.stackexchange.com/questions/162812/calc-rate-of-change-question-i-think	# Calc Rate of Change Question I think I have an interesting calc question here but im not sure how to solve it. Can someone perhaps give me a helping hand or guide me through steps? A balloon that takes images of the earth is shot up in the sky with rockets from 0 ft off the ground is given by the height of the function s(t)= $-18t^2+120t$ . a) Find velocity after 2 and 4 seconds as it approaches space. b) When does the balloon reach full altitude? c) When does it touch back down to earth? - You're missing a few things. You write that a balloon is given by a function, but maybe you mean the height of a balloon is given by a function. You have $18^2$ where you might mean $18t^2$. A rock enters the question and then leaves with no effect - what is that about? Please edit your question into something sensible. – Gerry Myerson Jun 25 '12 at 12:16 @GerryMyerson What do you mean what would you add to this question to make sense of it? – soniccool Jun 25 '12 at 12:17 Did you read any of what I wrote, other than the last sentence? I told you about three things that don't make sense, that need your attention. Please, do something about them. – Gerry Myerson Jun 25 '12 at 12:19 Oh i see thank you so much – soniccool Jun 25 '12 at 12:20 $s(t) =-18^2 + 120t$ suggests that the balloon will never come back. On the other hand $-18t^2+120t$ makes more sense. – Saurabh Jun 25 '12 at 12:21 Well, I believe that the velocity of an object is its derivative. So, find the derivative of your initial function. $$\ s(t) = -18t^2 + 120t$$ With a simple application of the power rule, we arrive at $$\ s'(t) = -36t + 120$$ $$or~ v(t) = -36t+120$$ Now, you have a function that will give you the balloon's velocity at any time t, since the derivative is the instantaneous rate of change(aka velocity). - How would i find when the balloon reaches full altitude and when it touches back down to earth? – soniccool Jun 25 '12 at 12:32 See my comments elsewhere. – Gerry Myerson Jun 25 '12 at 12:55 The rate of change of the objects height with time is the first derivative of the function s(t) this also (intuitively) would be the vertical velocity of the balloon. When the balloon has a zero velocity it's reached the top of its "curve" - its maximum height. So if $s(t)=-18t^2+120t$ then $s'(t)=-36t+120$ now we must solve this for zero to find its maximum height or evaluate it at 2 or 4 for its velocity after 2 or 4 seconds (I'll leave that last one for you, it's trivial). $$0=-36t+120\\36t=120\\t=\frac{120}{36}=\frac{10}{3}$$ when the balloon "touches" back down to earth (more aptly it crashes) the height is zero $$s(t)=0=-18t^2+120t$$ Right away this tells us that at time 0 the balloon is already at zero height. We're more interested in later on, so we divide by $t$ (knowing it's not zero anymore) then we get. $$s(t)=-18t+120\\18t=120\\t=\frac{120}{18}=\frac{20}{3}$$ In doing physics questions it's useful to write down your knowns (quantities that are given to you) and the things you want to solve for. Looking at this find a way to rewrite the question in a more "step-by-step" way before you solve. Physics questions hone a very useful set of problem solving skills and enrich you with more than just a basic understanding of Newtonian Mechanics - they train you in a type of thinking that is ubiquitous and necessary in many fields of study. - Also, it's generally good form to mark questions as "homework" if they are. – damagedgods Jun 25 '12 at 13:08 The only thing you've left for OP to do is to remove the apostrophes from "it's curve" and "it's maximum height". – Gerry Myerson Jun 25 '12 at 13:12 @GerryMyerson Fixed, cheers. – damagedgods Jun 25 '12 at 13:14	2014-07-24 09:10:49	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 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": 0.8092524409294128, "perplexity": 561.13528434935}, "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-2014-23/segments/1405997888216.78/warc/CC-MAIN-20140722025808-00010-ip-10-33-131-23.ec2.internal.warc.gz"}
https://www.tutorialspoint.com/write-a-python-code-to-combine-two-given-series-and-convert-it-to-a-dataframe	Write a Python code to combine two given series and convert it to a dataframe Assume, you have two series and the result for combining two series into dataframe as, Id Age 0 1 12 1 2 13 2 3 12 3 4 14 4 5 15 To solve this, we can have three different approaches. Solution 1 • Define two series as series1 and series2 • Assign first series into dataframe. Store it as df df = pd.DataFrame(series1) • Create a column df[‘Age’] in dataframe and assign second series inside to df. df['Age'] = pd.DataFrame(series2) Example Let’s check the following code to get a better understanding − import pandas as pd series1 = pd.Series([1,2,3,4,5],name='Id') series2 = pd.Series([12,13,12,14,15],name='Age') df = pd.DataFrame(series1) df['Age'] = pd.DataFrame(series2) print(df) Output Id Age 0 1 12 1 2 13 2 3 12 3 4 14 4 5 15 Solution 2 • Define a two series • Apply pandas concat function inside two series and set axis as 1. It is defined below, pd.concat([series1,series2],axis=1) Example Let’s check the following code to get a better understanding − import pandas as pd series1 = pd.Series([1,2,3,4,5],name='Id') series2 = pd.Series([12,13,12,14,15],name='Age') df = pd.concat([series1,series2],axis=1) print(df) Output Id Age 0 1 12 1 2 13 2 3 12 3 4 14 4 5 15 Solution 3 • Define a two series • Assign first series into dataframe. Store it as df df = pd.DataFrame(series1) • Apply pandas join function inside series2. It is defined below, df = df.join(series2) pd.concat([series1,series2],axis=1) Example Let’s check the following code to get a better understanding − import pandas as pd series1 = pd.Series([1,2,3,4,5],name='Id') series2 = pd.Series([12,13,12,14,15],name='Age') df = pd.DataFrame(series1) df = df.join(series2) print(df) Output Id Age 0 1 12 1 2 13 2 3 12 3 4 14 4 5 15	2023-03-20 08:43:47	{"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": 0.2219766229391098, "perplexity": 2677.6862918096813}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296943471.24/warc/CC-MAIN-20230320083513-20230320113513-00719.warc.gz"}
https://math.stackexchange.com/questions/2305198/general-solution-to-linear-second-order-homogeneous-ode-question	# General solution to linear second-order homogeneous ODE question I understand that the solution to a linear second-order homogeneous ODE is in the form $y=c_1y_1+c_2y_2$ where $y_1$ and $y_2$ are solutions to the ODE. I also understand why a linear combination of two unique solutions is also a solution. I do not understand why $y=c_1y_1+c_2y_2$ will give the general solution which will take into account all particular solutions. Could anyone please clear up my misunderstanding? Thank you. • A hand-wavy explanation: It might help to think of $y''(x)=0$. The general solution only depends on two arbitrary constants, $c_1$ and $c_2$, since you can only integrate the equation twice. If you have two linearly independent solutions $u$ and $v$, then $y= c_1 u + c_2 v$ is a solution for any $c_1$ and $c_2$, so we have used up our two degrees of freedom, and this $y$ must be the general solution. – user254433 Jun 1 '17 at 7:21 ## 3 Answers A linear second-order homogeneous ODE is has the form $y''+a(x)y'+b(x)y=0$, where $a$ and $b$ are continuous functions on an intervall $I$. Let $L$ be the set of all functions in $C^2(I)$, which are solutions of this ODE. Then $L$ is a vector space and $\dim L=2$. If $\{y_1,y_2\}$ is a basis of $L$ , then each solution of the ODE has the form $c_1y_1+c_2y_2$. • So basically the span of {y1,y2} is the set $L$ which has elements that satisfy the second order differential equation? And any $y_1$ and $y_2$ will be an acceptable basis as long as they are unique because their span will be describe the same set of all solutions? Then the initial conditions will lead to one particular element in this set of possible solutions? – Space20 Jun 1 '17 at 16:43 This is part of the general theory on first-order linear homogeneous systems of ODEs. Namely, if you have a system in $\mathbb{R}^n$ of the form $x' = A(t) x$, with $A\colon I \to M_n$ continuous on some interval $I$ (here $M_n$ denotes the vector space of $n\times n$ matrices with real elements), then the set of all maximal solutions is a vector subspace of $C^1(I, \mathbb{R}^n)$ of dimension $n$. Given this result, you have only to recast your second-order homogeneous linear equation to a first-order linear system in $\mathbb{R}^2$. Indeed, if your equation is of the form $$y'' + a(t) y' + b(t) y = 0$$ you can define $x_1 = y$, $x_2 = y'$, obtaining the system $$\begin{cases} x_1' = x_2, \\ x_2' = - a(t) x_2 - b(t) x_1, \end{cases}$$ i.e. $x' = A x$ with $$A = \begin{pmatrix} 0 & 1\\ -b(t) & -a(t) \end{pmatrix}\,.$$ Let $y_0$ and $y_1$ be solutions with $$(y_0(0),y'_0(0))=(1,0)\text{ and }(y_1(0),y'_1(0))=(0,1).$$ These exist by the existence theorem. For any other solution $y$ form the function $$u(x)=y(0)y_0(x)+y'(0)y_1(x).$$ Then this function is also a solution as a linear combination of solutions and it has the same initial values as $y$ in $x=0$. By the uniqueness theorem $u=y$ everywhere. This proves that the dimension of the solution space is $2$, as $(y_0,y_1)$ is a basis.	2020-04-03 18:30:44	{"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": 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": 0.9483835101127625, "perplexity": 81.35845956198602}, "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-2020-16/segments/1585370515113.54/warc/CC-MAIN-20200403154746-20200403184746-00466.warc.gz"}
https://www.aimsciences.org/article/doi/10.3934/proc.2003.2003.288	# American Institute of Mathematical Sciences 2003, 2003(Special): 288-294. doi: 10.3934/proc.2003.2003.288 ## Semiclassical and large quantum number limits of the Schrödinger equation 1 Physik-Department, Technische Universität München, 85747 Garching, Germany Received August 2002 Revised March 2003 Published April 2003 For bound one-dimensional systems, the semiclassical limit h $\to 0$ of the Schrödinger equation generally corresponds to the limit of infinite quantum numbers, and conventional WKB quantization becomes increasingly accurate in this limit. A potential well with a sufficiently strong attractive inverse-square tail supports an infinite dipole series of bound states, but the limit of infinite quantum numbers is not the semiclassical limit in this case. Semiclassical eigenvalues derived via conventional WKB quantization tend to a constant relative error in the large-quantum-number limit when the Langer modification is used. Without the Langer modification the relative error grows exponentially in the limit of large quantum numbers. Citation: Harald Friedrich. Semiclassical and large quantum number limits of the Schrödinger equation. Conference Publications, 2003, 2003 (Special) : 288-294. doi: 10.3934/proc.2003.2003.288 [1] Ruikuan Liu, Tian Ma, Shouhong Wang, Jiayan Yang. Thermodynamical potentials of classical and quantum systems. Discrete & Continuous Dynamical Systems - B, 2019, 24 (4) : 1411-1448. doi: 10.3934/dcdsb.2018214 [2] Li Chen, Xiu-Qing Chen, Ansgar Jüngel. Semiclassical limit in a simplified quantum energy-transport model for semiconductors. Kinetic & Related Models, 2011, 4 (4) : 1049-1062. doi: 10.3934/krm.2011.4.1049 [3] Xueke Pu, Boling Guo. 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Mathematical Control & Related Fields, 2019, 9 (1) : 191-219. doi: 10.3934/mcrf.2019011 Impact Factor:	2020-02-28 11:47:58	{"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": 0.667087972164154, "perplexity": 5721.95028587307}, "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-2020-10/segments/1581875147154.70/warc/CC-MAIN-20200228104413-20200228134413-00217.warc.gz"}
https://endlessorchard.com/autocad-incl-product-key-download/	Q: Transcendental equation in radicals How can I solve this transcendental equation in radicals? $$\sqrt{2x^2-3x+4}=x$$ A: hint: Use the following identity $$\sqrt{u}=\frac{\sqrt{a^2+b^2}}{\sqrt{a^2-b^2}}$$ $$\sqrt{2x^2-3x+4}=\frac{\sqrt{2(2x-1)^2-3(2x-1)+4}}{\sqrt{(2x-1)^2-3(2x-1)+4}}$$ $$\sqrt{2x^2-3x+4}=\frac{2x-1}{\sqrt{(2x-1)^2-3(2x-1)+4}}$$ Determination of chemical composition of Lactobacillus delbrueckii ssp. bulgaricus and Streptococcus thermophilus subsp. thermophilus by ¹H and ¹³C NMR spectroscopy and multivariate analysis. Water-soluble extracts from the cell-free supernatant of two strains of Lactobacillus delbrueckii ssp. bulgaricus and Streptococcus thermophilus subsp. thermophilus were characterized by (1)H and (13)C NMR spectroscopy, to identify the polysaccharide fraction. In the (1)H NMR spectra of both the supernatants, signals attributable to alpha-D-glucose units were observed, assigned to the 1→4 linkages and to the terminal glucosyl residues. The signals arising from the D-glucopyranose residues of the alpha-1,3 glycosidic bonds were assigned. The (13)C NMR spectra of the supernatants, after the removal of the polysaccharide fraction, revealed signals attributable to carbohydrate and fatty acid components. To identify and quantify the polysaccharides and to investigate the relationships among the strains, an untargeted approach, based on the combination of chemometric tools (Principal Component Analysis, PCA, and Hierarchical Cluster Analysis, HCA), was used to explore the data. (1	2022-06-30 11:05:27	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 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": 0.46830999851226807, "perplexity": 8185.437789317382}, "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-20220630092604-20220630122604-00423.warc.gz"}
https://puzzling.stackexchange.com/questions/37980/i-am-depressed-no-one-wants-me/37989	# I am depressed… No one wants me I am depressed... No one wants me. You can take test, You can do management, You can also use the force to get the answer, Always alone, But once in a while, I have lone friend, Together with him I can achieve great things. • I want to edit the dPressed so hard I'm depressed myself because probably I shouldn't since it seems to be part of the puzzle... – Miquel Coll Jul 21 '16 at 9:20 • @MiquelColl :) go on edit it... I think it can also provide a clue.... – smriti Jul 21 '16 at 9:22 Are you Stress? I am depressed... Stress Depression, also the symbol for stress σ looks like a "d"pressed(Credit to Ankoganit) No one wants me. Sure thing You can take test, Stress test You can do management, Stress Management You can also use the force to get the answer, Edit: Stress = Force / Area (Credit to Nij) Always alone, But once in a while, I have lone friend, Together with him I can achieve great things. (hints from OP) Strain, where E = stress / strain (Young's Modulus)? • spot on... you got the answer, first four lines are correct. Figure out rest, and I will accept the answer – smriti Jul 22 '16 at 4:18 • Alex, perhaps consider synonyms for your answer in an engineering context. – Nij Jul 22 '16 at 4:39 • Isn't stress' friend adrenaline? – IdiotStyle Jul 22 '16 at 7:55 • One remark: the usual symbol for stress is $\sigma$, which looks like a d with its antenna pressed down, hence the initial clue "dPressed" (which was edited later on). It's somewhat stretch though. – Ankoganit Jul 22 '16 at 15:41 • dPressed or bFallen – Jasen Jul 24 '16 at 2:20 You might be Work I am depressed... No one wants me. Many people don't like to work. You can take test, You can do management, These are jobs at which one can work. Work = Force * Distance Force is part of the formula for work, but isn't the only factor. Always alone, But once in a while, I have lone friend, Together with him I can achieve great things. Work/Time = Power In this case, when work is no longer alone, with time as his friend, they make power, which can be used to achieve great things. • Also, there was an early typo of "dpressed", which OP said "could also provide a clue". With d = distance and pressed = pushed = applied force, one could see 'dpressed' as a clue for 'distance * force'. – kayzeroshort Jul 21 '16 at 21:32 • good explanation but not an answer – smriti Jul 22 '16 at 4:20 I think the answer is can take test can do mangement Together with him I can achieve great things earning reputation points. Move the mouse pointer to spoilers to see answer. But once in a while, I have lone friend can't be online whole day..	2019-10-17 11:08:01	{"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": 0.6085571646690369, "perplexity": 3306.831895736629}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-43/segments/1570986673538.21/warc/CC-MAIN-20191017095726-20191017123226-00427.warc.gz"}
https://blog.runtux.com/	# Q-Factor of a Coax Resonator When studying transmission line theory recently for modelling transmission lines in my antenna-optimizer project, I stumbled upon a formula of the Quality (Q) factor of a coax resonator by Frank Witt [1]: \begin{equation} \frac{2.774 F_0}{A \cdot \mathbb{VF}} \end{equation} In this formula $F_0$ is the frequency of the resonator in MHz, $A$ is the loss in dB per 100 ft, and VF is the velocity factor of the cable. The formula is for a $\frac{\lambda}{4}$ resonator. I wondered about this because, since the loss in that formula is a logarithmic quantity (dB) the computation of the Q-factor should involve exponentiation. When using the stored energy definition of the Q-factor from Wikipedia, we get: \begin{equation} 2 \pi \frac{E_s}{E_d} \end{equation} where $E_s$ is the stored energy and $E_d$ is the energy dissipated per cycle. We know that the loss factor of a cable in dB involves power loss. If the loss in dB per 100m (we're using metric units) is $a$ we have for the loss in dB: \begin{equation} \frac{a \cdot l}{100} \end{equation} where $l$ is the length im meter. For a $\frac{\lambda}{4}$ resonator we get: \begin{equation} \frac{a \cdot \mathbb{VF}\lambda}{4\cdot 100} \end{equation} To compute the fraction of the power lost (instead of the logarithm of the fraction in dB) when transmitting we get \begin{equation} 1 - 10^{-\frac{a \cdot \mathbb{VF}\lambda} {4 \cdot 100 \cdot 10}} \end{equation} Replacing \begin{equation} \lambda = \frac{c}{f_0} \end{equation} into the formula where $c$ is the speed of light and $f_0$ is the resonance frequency in Hz we get \begin{equation} 1 - 10^{-\frac{a \cdot c\cdot\mathbb{VF}} {4 \cdot 100\cdot 10\cdot f_0}} \end{equation} Going back to the Wikipedia formula which involves energies to get an energy ratio from a power ratio we would have to integrate – but since this would yield the same result for the ratio we instead do a handwaving integration here: We need to get the travelled distance straight: The Wikipedia definition involves one whole period $\lambda$, not $\frac{\lambda}{4}$. And the Q-factor is the ration of the stored power to the lost power. So we have: \begin{equation} Q = \frac{2\pi}{1 - 10^{-\frac{a \cdot c\cdot\mathbb{VF}}{1000\cdot f_0}}} \end{equation} Note that this makes the resonator $Q$ independent of the type of resonator, be it a $\frac{\lambda}{4}$ or $\frac{\lambda}{2}$ resonator. When plotting Q-factors for some shortwave frequencies (they're in MHz in the figure) against the loss in dB we see that the formula derived above is fairly close to the approximation formula from Witt [1]. When plotting Q-factor against frequency (also in the shortwave range) for certain common cable types we also see that the error is not too high, especially for higher frequencies. The relative errors can also be plotted, also for some common cable types over the whole shortwave range. We see that the error is quite high for the low frequency range and is higher for the more lossy cable types like RG174. So we see that the formula is probably some approximation and is fairly accurate for higher frequencies and low loss. Now the question was open: Where does this formula come from and what is the magic constant that obviously lumps all physical constants into a magic number? When studying transmission line theory I also stumbled over an old book on the subject which once was a university textbook [2]. On p. 222 Chipman derives an approximate formula for $Q$ with a simplifying assumption that $\alpha$ (the attenuation coefficient in nepers per meter) is small. Chipman's approximate formula is: \begin{equation} Q \approx\frac{\beta_r}{2\alpha_r} \end{equation} where $\alpha$ is the attenuation coefficient in nepers per meter and $\beta$ is the phase factor of the line in radians per meter. The subscript $r$ stands for resonance. We can write \begin{equation} \lambda=\frac{c\mathbb{VF}}{f_0} \end{equation} and \begin{equation} \beta_r=\frac{2\pi}{\lambda} \end{equation} and Witts loss $A$ per 100ft can be written (converting nepers to dB) as \begin{equation} A=\frac{20\cdot 100\alpha_r}{3.2808\cdot log_e 10} \end{equation} Where the constant 3.2808 is the conversion factor m/ft. Solving for $\alpha_r$ and replacing $\lambda$ and $\alpha_r$ into Chipman's formula we get: \begin{equation} Q \approx\frac{2\cdot 2000\pi f_0} {2 c \mathbb{VF}\cdot A \cdot 3.2808\cdot log_e 10} \approx\frac{2.774 F_0}{A \mathbb{VF}} \end{equation} Where the final $F_0$ is $f_0$ in MHz. We see that the low-$\alpha$ asumption of Chipman's (and Witt's) formula holds for higher frequencies and low loss. We've already seen that the approximation if fairly good for low-loss cables: $\alpha$ in nepers per meter is a constant factor from the loss-figure in dB (be it per 100m or per 100ft). That it gets better with higher frequencies is because the loss of a cable typically increases with the square-root of the frequency while $\lambda$ decreases inverse proportionally with frequency. So, e.g., a $\frac{\lambda}{4}$ resonator has higher loss at a lower frequency. [1] (1, 2) Frank Witt. The coaxial resonator match. In Gerald L. (Jerry) Hall, editor, The ARRL Antenna Compendium, volume 2, pages 110-118. American Radio Relay League (ARRL), 1989. [2] Robert A. Chipman. Theory and Problems of Transmission Lines. Schaums Outline. McGraw-Hill, 1968. In two older posts in this blog, one about a Second SPI chipselect for Orange-Pi Zero, one about a Hitachi HD44780 text display under Linux, I talked about trying to get changes into the Linux Kernel. In case of the Orange-Pi it was a bug-fix to the SPI-Driver of the Allwinner sun6i architecture. Thanks at this point to the author Mirko of that patch who let me submit the patch in his name. The patch is in the kernel since shortly before 5.13. Since it has been marked as a bug-fix, it was backported to various stable series of the kernel as far back as the 4.4 stable series. In case of the Hitachi display it was a documentation update that should allow people to find out how to connect such a display with the necessary device tree magic but without any software change. This patch has finally been accepted into the Linux Kernel in time for the 5.15 release. # Modding a PC Power Supply WARNING: In the following I'm going to describe how to modify a power supply. Power supplies contain high voltages – even after removing the power plug they can still have high charges in capacitors. In some countries devices with mains power may be modified only by or under supervision of certified persons. So you should know what you're doing and be authorized to modify a power supply. PC power supplies are cheap and readily available but the tend to produce the correct voltages only when the drawn current from all different voltages are within the minimum/maximum specs of the power supply. Drawing high current (but within the specs of the power supply) only from a single voltage lets this voltage drop below specification. One example is the heat-bed of my 3D-printer: It used to have a PC power supply for the heat bed. The heat bed draws about 12A but only from the 12V line. The result was a voltage of about 10V when the heat-bed was heating. Another use-case is the supply of several ARM based single-board computers (e.g. Raspberry-Pi or Orange-Pi) from a single 5V line. When using a PC-Power supply for this (without drawing current from the 12V lines) the nominal 5V voltage may drop below a value where the single-board computer works reliably. A third example is the use of a power supply for powering the radio of a ham-radio operator: These radios typically don't output full power when powered with 12V or less, they typically need 13.6-13.8V for full power operation. In all these cases a modification of the power supply that keeps the chosen voltage stable or even allows to modify the chosen voltage slightly (from 12V to 13.8V for hamradio operation) would be nice. How can we achieve that? Many PC power supplies are based on the power regulator integrated circuits TL494 or KA7500 (they are pin-compatible). If you have one of those they can usually be modified for the purposes outlined above. One schematic details of those supplies is a feedback-circuit that feeds back the 5V and the 12V voltage to the regulator IC. You can find a lot of power supply schematics on Dan's PC power supply page. Take the second of the TL494 or KA7500 based supplies, it has several resistors in parallel from pin 1 of the TL494 to ground, a 27kΩ-resistor from 12V to pin 1 and a 4.7kΩ-resistor from 5V to the same pin. We can modify the voltage regulation by changing the feedback pins. Note that every power supply usually has different resistors to ground and different feedback resistors from 5V and 12V. As an example we replace the two feedback resistors to make the power supply provide stable 5V without caring for the 12V supply. WARNING: When modifying a power supply for a stable 5V or 12V source, the other voltages will no longer be stable and may become too high for use in a PC. You should never use such a modified power supply in a PC. So the first step is to identify the two resistors in the power supply. Once found we verify that the side of the resistor not connected to pin 1 of the regulator IC has 0Ω to the correct (5V or 12V) power supply output. We unsolder both resistors. Now before computing the new resistor to be placed between 5V output and pin 1 we measure the resistance between pin 1 and ground: Because we have now unsoldered the two resistors to 12V and 5V the resistor can be measured. It is good to be sure that the measured resistance matches the computed resistance from the three resistors connected in parallel: In the example we have 100kΩ, 390kΩ, and 10kΩ in parallel which should measure as \begin{equation} \frac{1}{\frac{1}{100000}+\frac{1}{390000}+\frac{1}{10000}} = 8883.83 \end{equation} When recently modifying a power supply the resistors to ground were 470kΩ, 100kΩ, and what I thought was 8.9kΩ: I interpreted the colors of the last resistor as grey-white-black-brown-brown. When measuring the three parallel resistors I measured it as 4.61kΩ instead of the expected 8033Ω. It turns out (after viewing the resistor in sunlight) that what I had interpreted as grey was really yellow-ish. So the resistor was really a 4.9kΩ resistor and the computed resulting resistance was 4625Ω. To make the power supply regulate only for 5V we connect a new resistor from pin 1 of the regulator IC to 5V and leave the 12V feedback line unconnected. But how do we chose the new resistor? To find out we need to solve a set of equations: We know from Ohms law the relation of the voltages, resistors, and currents. We know from Kirchhoff that the current through the 12V feedback resistor and the current through the 5V feedback resistor must add up to the current through the resistors to ground. These relationships are given in this maxima spreadsheet. We compute the reference voltage V_ref at pin 1 when both, the resistor from 5V and from 12V are connected. Then we chose the new resistor to 5V so that the voltage on pin1 stays the same. For the example in Dan's second schematic we get 1800Ω for R_new. For the power supply I recently modified I've already given the resistors to ground. The resistor to 12V was 39kΩ and the resistor to 5V was 9.1kΩ. The resulting R_new for that power supply was 4865Ω which I realized by connecting a 4.7kΩ and a 150Ω resistor in series which was close enought to get a good 5V output. The computation is given as the second example in the spreadsheet. A word of caution: When modifying the 5V power regulation or modifying a power supply for higher voltages (more than 12V) you should be aware that most PC power supplies have capacitors rated for 16V in the 12V output circuit. So when drawing high currents from the power supply modified for 5V the voltage on the 12V line may become too high for these capacitors. To be on the safe side the capacitors should be changed to types rated for 25V. When modifying the 12V supply we use basically the same procedure, except that we now connect the 12V feedback resistor and leave the 5V feedback open. How to compute the resistor for the 12V feedback line is left as an exercise. I recently have provided a customer with a link to a firewall image (using the Turris MOX router with a variant of OpenWRT) hosted on my own webserver. The image included keys material for an OpenVPN connection. The image file was in a hidden directory on my projects webserver. I monitored closely if there would be any downloads besides the one I expected from my customer. I am aware providing key material via an unsecured channel is not the best security practice. And in the end I had to revoke the VPN key material in the image and provide my customer with a new key via a secure channel. Now I said I monitored the downloads. About an hour (!) after my customer downloaded the image (at 21/Mar/2021:17:35:50 to be precise), it was accessed from another IP: 77.74.177.4 - - [21/Mar/2021:18:43:51 +0100] "GET /turris-image-XXXXXXX.zip HTTP/1.1" 200 77244886 "-" "Mozilla/5.0 (Windows NT 10.0; Win64; x64) AppleWebKit/537.36 (KHTML, like Gecko) Chrome/81.0.4044.92 Safari/537.36" Looking up this IP via whois yields: > whois 77.74.177.4 % This is the RIPE Database query service. ... netname: KL-NET3 descr: Kaspersky Lab Internet country: RU ... source: RIPE organisation: ORG-KL28-RIPE org-name: Kaspersky Lab AO country: RU My customer is using Kaspersky antivirus software. So the link was probably leaked to Kaspersky via the installed software. On the one hand it may well be that the purpose of Kaspersky downloading that link is a benign service (they may scan things for viruses) but in my case it means that non-public information was leaked. On the other hand it may well be that information gleaned that way is used for other purposes, too – we do not know. # Interaction of libvirt and AppArmor I'm teaching at the University of Applied Science Burgenland in Eisenstadt (Austria). We recently had a lab (which took place in the lab in Eisenstadt but students were working from home due to Covid reasons) where the task is to set everything up for virtualisation and then live-migrate a running virtual machine to another server using libvirt (we're using the command-line with virsh). For just one group out of several – with identical initial Debian installations, migration failed with an error message. The migration command was: virsh -c qemu+ssh://root@primary/system migrate --live --unsafe \ debian-1 qemu+ssh://root@secondary/system For the lab we're using NFS because setting up a more advanced filesystem would take too much time, that's why we're using the --unsafe option. The following error message resulted (error message broken to several lines, this was all in a single line): error: internal error: Process exited prior to exec: libvirt: error : unable to set AppArmor profile 'libvirt-d22db7ca-50ca-43bd-b6da-1ccecf5a83e7' for '/usr/bin/kvm': No such file or directory It turned out that this group had managed to fill up the /var partition with logfiles but after cleanup this still did produce the same message. So the hunch here is that some files that AppArmor and/or libvirt create dynamically could not be created and that was the reason why this failed. It also turned out that some AppArmor files that were correctly installed on the first machine were missing on the second. Trying to reinstall AppArmor and related files using apt-get with the --reinstall option did not work, the missing config files in /etc/apparmor.d were not re-created. So removing the packages with the purge command (which removes all config files) and then reinstalling everything fixed the installed AppArmor files and made the migration finally work. I have no idea which files were missing. When googling for the error message above I found a debian bug-report Where one of the dynamically generated files in /etc/apparmor.d/libvirt was zero length. This, however was not the problem in our case but indicates that AppArmor isn't very good at checking errors when a filesystem is full. So there are probably other files that are dynamically generated that were the problem in our case. The following sequence of deinstall and reinstall commands fixed the problem in our case, note that just removing files as in the debian bug-report did not fix the issue in our case: dpkg --purge apparmor-utils apparmor-profiles dpkg --purge apparmor rm -rf /var/cache/apparmor apt-get install apparmor apparmor-utils apparmor-profiles dpkg --purge libvirt-daemon-system apt-get install libvirt-daemon-system systemctl restart libvirtd.service systemctl restart virtlogd.service systemctl restart virtlogd.socket I'm not sure restarting the services is really necessary but there was another issue that libvirt could not connect to the virtlog socket and this was fixed by restarting the virtlog.{service,socket}. # Dynamic DNS with the bind DNS server The popular DNS server bind allows to have a configuration that enables clients to change DNS entries remotely. Since some of the public dynamic DNS services have moved to a pay-only subscription model and since I'm running my own mail and web server at a hosting site I was searching for a way to roll my own dynamic DNS service. This already is back some years now but since the Howto I used at the time seems to be gone (at least from my google bubble) I'm documenting here how it was done. I'm running this on a Debian buster server at the time of this writing, so if you're on a different system some details may change. I'm calling the domain for the dynamic services dyn.example.com in the following. The top-level config file of bind needs to include an additional config file for the dynamic domain. In my configuration this file is named.conf.handedited. In this file you need an entry for each dynamic DNS client as follows: zone "dyn.example.com" { type master; allow-transfer {none;}; file "/etc/bind/slave/pri.dyn.example.com"; update-policy { grant h1.dyn.example.com. name h1.dyn.example.com. A TXT; grant h2.dyn.example.com. name h2.dyn.example.com. A TXT; [...] }; }; In this example the hosts h1 and h2 and possibly more may edit their own DNS entry. I'm allowing them to change their A and TXT records. You may want to add AAAA for IPv6. Then the config-file /etc/bind/slave/pri.dyn.example.com contains: dyn.example.com IN SOA ns1.example.com. admin.example.com. ( 2020080100 ; serial 120 ; refresh (2 minutes) 120 ; retry (2 minutes) 120 ; expire (2 minutes) 120 ; minimum (2 minutes) ) NS ns1.example.com. h1 A 127.0.0.1 KEY 512 3 10 ( <more gibberish lines> ); alg = RSASHA512 ; key id = <number> The values in angle brackets are comments and should be replaced by the correct values in your installation. The entries A and KEY are inserted by hand for each new host allowed to set its own IP address. The KEY is the public key created below. In my experience an A-record has to be present for it to work, I'm setting the localhost address here because the client will later rewrite this IP anyway. It's customary to have the admin email address (where the @ is replaced with a dot) in the SOA record where I've put admin.example.com.. To create a new host: • Create a new public/private key pair (preferrably the client does that and sends only the public key to the DNS admin for security reasons): dnssec-keygen -T key -a RSASHA512 -b 2048 -n HOST newhost.dyn.example.com • This creates a private and a public key. Note that on the client you need both, the public and the private key although in the command line for the dynamic DNS client you will only specify the private key! • Last time I created a new key the command did not support keys longer than 2048 bit although the hash algorithm is SHA2 with a high bit-length. • You need to freeze (and make bind write the current in-memory DB to a file) bind for your dynamic domain: rndc freeze dyn.example.com • Now you may edit the config file, you want to add a stanza for the new host and increment the serial number: $EDITOR /etc/bind/slave/pri.dyn.example.com • Then don't forget to thaw the domain: rndc unfreeze dyn.example.com • Do not forget to give the new host the necessary permissions in named.conf.handedited • You probably need to reload bind: systemctl reload bind9.service On the client side the utility we use to tell bind about a new IP address of our client is called nsupdate. You can probably find this program for many client operating systems. I'm using a simple script that detects a change of a dynamic IP address and performs a bind update in case the address changed. Since you're running your own DNS server, chances are that you also have a webserver at your disposal. The following simple script allows any client to detect its own IP-address (clients are often behind a NAT firewall and we don't want to use another public service when we just got rid of public dynamic DNS services, right?): #!/bin/sh echo Content-Type: text/plain echo "" echo$REMOTE_ADDR This script is put into a cgi-bin directory of a web server and will echo the client IP address (in text form) back to the client. I name this script ip.cgi and it is available via the URL http://example.com/cgi-bin/ip.cgi in our example, see below in the client script where you need to change that URL. My bind update script (you need to change some variables) looks as follows (note that this asumes the script above runs on the top-level domain example.com, otherwise change the URL of the cgi-bin program): #!/bin/sh ZONE=dyn.example.com DOMAIN=h1.dyn.example.com DNSKEY=/etc/nsupdate/Kh1.dyn.example.com.+010+04711.private NS="ns1.example.com" registered=$(host$DOMAIN $NS 2> /dev/null \| grep 'has address' \| tail -n1 \| cut -d' ' -f4) current=$(wget -q -O- http://example.com/cgi-bin/ip.cgi) [ -n "$current" \ -a "(" "$current" != "$registered" ")" \ ] && { nsupdate -d -v -k$DNSKEY << EOF server $NS zone$ZONE update delete $DOMAIN A update add$DOMAIN 60 A $current send EOF logger -t dyndns -p daemon.notice "Updated dyndns:$registered -> \$current" } > /dev/null 2>&1 exit 0 It should be noted again that the private key (in /etc/nsupdate/Kh1.dyn.example.com.+010+04711.private in the example above) is not enough, nsupdate also needs the public key in the same directory as the private key. # Hitachi HD44780 text display under Linux For a project I'm using a text display containing the Hitachi HD44780 chip. These displays come in different sizes, common are 2 lines with 16 characters or 4 lines with 20 characters. The latter is also sold under the name 2004a. These displays use 5V. So these days with most CPUs and microcontrollers running with 3.3V or lower, the display is often connected to an I²C bus via a GPIO extender based on the PCF8574. The GPIO extenders are usually soldered to the display connector. You can buy the display and the GPIO extender separately or packaged together. You will always have to solder the GPIO extender to the display. Now the correct way to connect the display to a 3.3V I²C-bus would be with a level-converter. But there is a hardware-hack to remove the pullup resistors on the PCF8574 breakout board (they're connected to +5V) which makes the device compatible with 3.3V installations: The minimum high logic level tolerated by the PCF8574 is given as 0.7 * VCC (which would mean 3.5V) but works in practice when driven with 3.3V. Note that the numbers of the resistors (R5/R6 in the hardware-hack link) may vary in different PCF8574 boards, I've seen R8, R9 for these resistors as well as no number at all. The resistors are 4.7 kΩ, usually labelled 472 in the SMD variant. I investigated if there is a Linux driver for these displays and discovered one in drivers/auxdisplay/hd44780.c. On first glance the driver does not support I²C via the PCF8574 I/O expander. So I wrote a driver and submitted it to the kernel. In the discussion (thanks, Geert) it turned out that there is a driver for the PCF8574 in the kernel (I had discovered so much) and that the HD44780 driver in the kernel can can be configured via appropriate device tree magic to use the I/O expander. The following device tree incantations define an overlay that configures the PCF8574 on its default I²C address 0x27 and then uses the I/O expander for configuring the I/Os for the hd44780 driver: // Note that on most boards another fragment must enable the I2C-1 Bus /dts-v1/; /plugin/; / { fragment@0 { target = <&i2c1>; __overlay__ { #size-cells = <0>; pcf8574: pcf8574@27 { compatible = "nxp,pcf8574"; reg = <0x27>; gpio-controller; #gpio-cells = <2>; }; }; }; fragment@1 { target-path = "/"; __overlay__ { hd44780 { compatible = "hit,hd44780"; display-height-chars = <2>; display-width-chars = <16>; data-gpios = <&pcf8574 4 0>, <&pcf8574 5 0>, <&pcf8574 6 0>, <&pcf8574 7 0>; enable-gpios = <&pcf8574 2 0>; rs-gpios = <&pcf8574 0 0>; rw-gpios = <&pcf8574 1 0>; backlight-gpios = <&pcf8574 3 0>; }; }; }; }; Since this is non-obvious not just to me (in my research I've discovered at least two out-of-tree Linux driver implementations of drivers for the HD44780 with the PCF8574 I/O expander) I've submitted a documentation patch to make this better documented for others searching a Linux driver. Note that the driver for this display uses escape sequences to access the various special functions of the display (e.g. turning the backlight on and off, clearing the screen or defining user-defined character bitmaps). I think those are documented only in the source-code in drivers/auxdisplay/charlcd.c. # Setting up Jitsi Meet With the ongoing Corona pandemic, video conferencing is one of the means to stay in contact. Since some offerings have dubious privacy or security status, an open source solution that you can self-host is a good thing to have. Since Snowden's revelations, anybody asuming that centralized applications are not monitored is naive in the best case. An example of an application with dubious security history is Zoom: To my knowledge they're the only 3rd party software vendor who has managed that their software was removed by the operating system vendor during a security upgrade because of their lax security. They were installing an application that allowed any malicious website to enable your camera and spy on you. But they didn't learn much from it, later they were caught uploading your user data to Facebook even if you did not have a Facebook account. With that security and privacy record one cannot advocate the use of that application. Now doing audio or videoconferencing with more than two participants usually involves unencrypted/clear voice or video at the server. Even if you connect via https and your audio and/or video stream is encrypted, it is unpacked at the server and re-encrypted to the other participants of the conference. The reason is that doing otherwise, each participant would have to send streams that are encrypted for each other participant. A simple implementation would involve that the number of streams grows quadratically with the number of participants. A more sophisticated implementation would encrypt the stream for each participant in the conference. The latter makes leaving/joining of conferences hard and is not supported by the usual secure protocols used for audio and video encryption (so keys would have to be exchanged in a separate channel). This is technically the reason why most videoconferencing applications have non-encrypted (cleartext) audio and video on the server. So it is easy for the server operator to monitor everything. Jitsi-Meet is no different: We have cleartext on the server. But the good news is that you can host the server yourself. On the Jitsi-Meet Webpage you can find instructions to point the installation paths of your Debian or Ubuntu based Linux installation to the Jitsi-Meet repository. That way you can install Jitsi-Meet with the usual apt-get install jitsi-meet. Once that is done, the resulting Jitsi-Meet installation allows anyone to create new conferences. For most installations this is not what you want. There are instructions on the Jitsi-Meet github pages to allow only moderators to create new conferences. Note that the guest-domain, guest.jitsi-meet.example.com in the example, needs not be in the DNS, it's just used internally for all non-authenticated users. With the resulting server, you can host your own video conferences. There is, however, a problem with the Firefox browser interacting badly with the Jitsi-Meet implementation. The details are documented in a Jitsi-Meet bug-tracker ticket. The effect is that audio and video becomes flakey, not just for the Firefox users, but for all participants in the conference when a single Firefox user is present. For this reason it's a good idea to not allow Firefox browsers into the conference until this issue is fixed. If you want this you can edit the file /usr/share/jitsi-meet/interface_config.js in the Jitsi-Meet installation. There are two config-items, one named OPTIMAL_BROWSERS includes firefox by default. Another named UNSUPPORTED_BROWSERS is empty by default. To exclude firefox, move the firefox entry from OPTIMAL_BROWSERS to UNSUPPORTED_BROWSERS. With this setup I have now a running conference server where I don't have to trust dubious online offerings with doubtful security and privacy practices. # No sound after upgrade to debian buster I recently upgraded my desktop to debian buster. I'm not using sound very often and only discovered after some time that sound output did not work at all. Symptoms: The tool pavucontrol just showed a dummy device. pacmd list-cards Just output: 0 card(s) available. Speaker test did run (and displayed the typical 'Front Left', 'Front Right' messages) but did not output any sounds. In alsamixer I could successfully find my intel sound card and change the settings. So the kernel seemed to know about the device. But everything else in the system refused to cooperate. When turning to a web search I found the following on askubuntu: This suggests to remove timidity-daemon. And after a fast: % sudo dpkg --purge timidity-daemon (Reading database ... 541273 files and directories currently installed.) Removing timidity-daemon (2.14.0-8) ... Purging configuration files for timidity-daemon (2.14.0-8) ... Processing triggers for systemd (241-7~deb10u3) ... Everything started to work immediately: The still-running pavucontrol immediately recognized a new device and I could play sound as before. # In search of a general transmission line simulator Currently I'm in search of a good formula for a transmission line with almost arbitrary shape. One project is a directional coupler, another the simulation of a Log-Periodic antenna. When trying to model a two-band Log-Periodic antenna [1] originally pioneered by Günter Lindemann, DL9HCG [2] (sk), the model did not fit reality too well: The VSWR was higher than reported by people having built this antenna. The original antenna has two square booms but since NEC2 only supports round wires, the antenna was modelled with round wires. Now for re-modelling the antenna with transmission lines (NEC2 supports those), I was searching for the impedance of the two square booms acting as a transmission line. I (re-) discovered the transmission line calculator by Hartwig Harm, DH2MIC [3] via his article in the german magazine Funkamateur [4]. But his model does not (yet?) include the parameters for two square wires. Harm uses atlc2 for estimating the parameters of his model. The software atlc2 is a reimplementation of Dave Kirkby's arbitrary transmission line calculator (which is available as source code and shipped with some Linux distributions) [5] but at least for round conductors I'm getting errors of several percent when trying to model the case of one round conductor against a wall, also reported by Harm [3]. Since atlc does not support conductors in free space we need to simulate walls in a great distance when modelling conductors. So in search of a formula for this I discovered Owen Duffy's work [6] (via a re-implementation of his calculator by Serge Y. Stroobandt, ON4AA [7] who acknowledges Duffy). He also uses atlc [5] to compute the parameters of a model. When fitting the values of Duffy's calculator to Harm's model, I'm getting a K-factor of 1.65 but the first 2 values don't agree (the first value for d = 10 and D = 15, i.e., D/d = 1.5 is off by 6.4%, for D = 20 it's still 1.5%). Since Duffy states that "figures below about 100 Ω are likely to be underestimates" [6] I'm trusting Harm's model better for those low values but I haven't measured this and I'm not understanding Duffy's argument about the proximity effenct since the model of atlc is size-independent (it just uses D/d expressed via a pixel-drawing of the model). But since we can't fully trust the model of atlc, I'm fine with the accuracy. I've not yet plugged the estimated impedance of the two square booms into an antenna model – but it seems the impedance is much higher than the 50 Ω of the real antenna. [1] Michael Zwingl. Dualband Log.Periodic Antenne für 2m/70cm im Selbstbau. Technikecke, ADL 303 Ortsgruppe Mödling des ÖVSV, July 2009. Accessed 2020-02-27, in german. [2] Günter Lindemann. Duoband LPDAs. LPDA Documentation, April 2014. Accessed 2020-02-27, in german. [3] (1, 2) Hartwig Harm. A new approach to modeling short conductor wires in highfrequency circuits. Technical report, DH2MIC, June 2018. Accessed 2020-02-27. [4] Hartwig Harm. Berechnung der Induktivität kurzer Leiterstücke. Funkamateur, 67:731–733, August 2018. In german. [5] (1, 2) Dave Kirkby. Finding the characteristics of arbitrary transmission lines. QEX, pages 3–10, December 1996. [6] (1, 2) Owen Duffy. Characteristic impedance of transmission line of two square conductors in air. Web software, July 2009. Accessed 2020-02-27. [7] Serge Y. Stroobandt. Parallel square conductor transmission line calculator. Web software, 2018. Accessed 2020-02-27.	2021-10-16 11:20:40	{"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": 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": 0.45791786909103394, "perplexity": 2982.424518359947}, "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-2021-43/segments/1634323584567.81/warc/CC-MAIN-20211016105157-20211016135157-00484.warc.gz"}
https://dsp.stackexchange.com/questions/59514/questions-about-optical-flow-implementations	# Questions about Optical Flow implementations I have some doubts related to some of the optical flow implementations. 1. How to compute angular error for optical flow algorithms? I know the formula for computing, $$\theta=\arccos(\vec{v}_c\cdot\vec{v}_e)$$ I have the computed flow field $$\vec{v}_c$$. How to get the exact flow field $$\vec{v}_e$$, ie the actual movement of pixels between frames ? 1. I am trying to implement Nagel's Paper for optical flow computation based on the discussion given in here. What I don't get is how to compute the weight matrix $$W$$. $$W$$ is given as $$W=(I_x^2+I_y^2+2\delta)^{-1}\begin{pmatrix}I_y^2+\delta &-I_xI_y\\ -I_xI_y & I_x^2+\delta \end{pmatrix}$$ Assuming that the image dimensions are $$m\times n$$ the first matrix on the RHS has dimension $$m\times n$$, but the second block matrix is of dimension $$2m\times 2n$$. What am I doing wrong ?	2019-10-15 02:54:49	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 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": 9, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8136634826660156, "perplexity": 234.8164753283941}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-43/segments/1570986655735.13/warc/CC-MAIN-20191015005905-20191015033405-00002.warc.gz"}
https://datascience.stackexchange.com/questions/86326/strange-behavior-of-cnn-when-forecasting-time-series	# Strange behavior of CNN when forecasting time series I have a time series containing 5 features. I tried to use LSTM to predict the next 112 periods in the series. However, I got very bad results. So I tried to use CNN. First, it did not work properly when using a lot of data for training, and it was not possible to find the characteristics of the series. By decreasing the data, leaving only 224 data for training and 224 for validation, CNN can find the data pattern but results in overfitting (Final epoch: loss: 4.7838e-15 - val_loss: 0.0971). The strange behavior observed is that even though it results in overfitting, it manages to generalize and predict better future values than when using some kind of regularizer. Does anyone have an explanation for this? Any tips to improve predictions in this case? The code: model = Sequential()	2021-07-23 21:42:35	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.2419007569551468, "perplexity": 609.3018651829983}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-31/segments/1627046150067.51/warc/CC-MAIN-20210723210216-20210724000216-00225.warc.gz"}
https://thepanasdalampublishing.com/article/nonparametric-regression-spss-508aaf	Small Black Slug On Dog, Black Panther Suit, Penstemon Electric Blue Care, Maytag Washing Machine Manual, Mini Oven For Baking Bread, Hydrocortisone Keratosis Pilaris Reddit, 78255 Zip Code, Cape May School Of Birding, Can Mold Grow In A Cold Room, " /> # Blog Trees automatically handle categorical features. Recall that by default, cp = 0.1 and minsplit = 20. This tutorial shows how to run it and when to use it. By allowing splits of neighborhoods with fewer observations, we obtain more splits, which results in a more flexible model. Example: is 45% of all Amsterdam citizens currently single? Making strong assumptions might not work well. SPSS sign test for two related medians tests if two variables measured in one group of people have equal population medians. $Sleep Efficiency 4. Using the Gender variable allows for this to happen. This is the main idea behind many nonparametric approaches. After train-test and estimation-validation splitting the data, we look at the train data. We also specify how many neighbors to consider via the k argument. I am studying the effects of sleep on reading comprehension ability, and I have five scores...1. Above we see the resulting tree printed, however, this is difficult to read. While it is being developed, the following links to the STAT 432 course notes. More on this much later. The R Markdown source is provided as some code, mostly for creating plots, has been suppressed from the rendered document that you are currently reading. First let’s look at what happens for a fixed minsplit by variable cp. Example: Simple Linear Regression in SPSS. We also move the Rating variable to the last column with a clever dplyr trick. The Shapiro-Wilk test examines if a variable is normally distributed in a population. \mu(\boldsymbol{x}) \triangleq \mathbb{E}[Y \mid \boldsymbol{X} = \boldsymbol{x}] Multiple logistic regression often involves model selection and checking for multicollinearity. Now that we know how to use the predict() function, let’s calculate the validation RMSE for each of these models. I am conducting a logistic regression to predict the probability of an event occuring. Principles Nonparametric correlation & regression, Spearman & Kendall rank-order correlation coefficients, Assumptions Additionally, objects from ISLR are accessed. We have to do a new calculation each time we want to estimate the regression function at a different value of $$x$$! \[ Learn more about Stata's nonparametric methods features. Nonparametric regression can be used when the hypotheses about more classical regression methods, such as linear regression, cannot be verified or when we are mainly interested in only the predictive quality of the model and not its structure.. Nonparametric regression in XLSTAT. Learn about the new nonparametric series regression command. We see that as cp decreases, model flexibility increases. Why $$0$$ and $$1$$ and not $$-42$$ and $$51$$? Our goal is to find some $$f$$ such that $$f(\boldsymbol{X})$$ is close to $$Y$$. So for example, the third terminal node (with an average rating of 298) is based on splits of: In other words, individuals in this terminal node are students who are between the ages of 39 and 70. Again, you’ve been warned. This z-test compares separate sample proportions to a hypothesized population proportion. It informs us of the variable used, the cutoff value, and some summary of the resulting neighborhood. where $$\epsilon \sim \text{N}(0, \sigma^2)$$. Recall that when we used a linear model, we first need to make an assumption about the form of the regression function. Nonparametric Regression Statistical Machine Learning, Spring 2015 Ryan Tibshirani (with Larry Wasserman) 1 Introduction, and k-nearest-neighbors 1.1 Basic setup, random inputs Given a random pair (X;Y) 2Rd R, recall that the function f0(x) = E(YjX= x) is called the regression function (of Y on X). Notice that what is returned are (maximum likelihood or least squares) estimates of the unknown $$\beta$$ coefficients. Perceived Sleep Quality 5. The plots below begin to illustrate this idea. We feel this is confusing as complex is often associated with difficult. The packages used in this chapter include: • psych • mblm • quantreg • rcompanion • mgcv • lmtest The following commands will install these packages if theyare not already installed: if(!require(psych)){install.packages("psych")} if(!require(mblm)){install.packages("mblm")} if(!require(quantreg)){install.packages("quantreg")} if(!require(rcompanion)){install.pack… In contrast, “internal nodes” are neighborhoods that are created, but then further split. With step-by-step example on downloadable practice data file. Nonparametric simple regression is calledscatterplot smoothing, because the method passes a smooth curve through the points in a scatterplot of yagainst x. We see that as minsplit decreases, model flexibility increases.$. We also see that the first split is based on the $$x$$ variable, and a cutoff of $$x = -0.52$$. SPSS Friedman test compares the means of 3 or more variables measured on the same respondents. It doesn’t! The $$k$$ “nearest” neighbors are the $$k$$ data points $$(x_i, y_i)$$ that have $$x_i$$ values that are nearest to $$x$$. \], which is fit in R using the lm() function. What about testing if the percentage of COVID infected people is equal to x? Also, you might think, just don’t use the Gender variable. This is basically an interaction between Age and Student without any need to directly specify it! We will also hint at, but delay for one more chapter a detailed discussion of: This chapter is currently under construction. At each split, the variable used to split is listed together with a condition.	2021-05-08 13:12:29	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.32542186975479126, "perplexity": 1979.9650944989367}, "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/1620243988882.7/warc/CC-MAIN-20210508121446-20210508151446-00050.warc.gz"}
https://www.jobilize.com/trigonometry/course/10-1-non-right-triangles-law-of-sines-by-openstax?qcr=www.quizover.com&page=2	10.1 Non-right triangles: law of sines (Page 3/10) Page 3 / 10 Given $\text{\hspace{0.17em}}\alpha =80°,a=120,\text{\hspace{0.17em}}$ and $\text{\hspace{0.17em}}b=121,\text{\hspace{0.17em}}$ find the missing side and angles. If there is more than one possible solution, show both. Solution 1 $\begin{array}{ll}\alpha =80°\hfill & a=120\hfill \\ \beta \approx 83.2°\hfill & b=121\hfill \\ \gamma \approx 16.8°\hfill & c\approx 35.2\hfill \end{array}$ Solution 2 $\begin{array}{l}{\alpha }^{\prime }=80°\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}{a}^{\prime }=120\hfill \\ {\beta }^{\prime }\approx 96.8°\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}{b}^{\prime }=121\hfill \\ {\gamma }^{\prime }\approx 3.2°\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}{c}^{\prime }\approx 6.8\hfill \end{array}$ Solving for the unknown sides and angles of a ssa triangle In the triangle shown in [link] , solve for the unknown side and angles. Round your answers to the nearest tenth. In choosing the pair of ratios from the Law of Sines to use, look at the information given. In this case, we know the angle $\text{\hspace{0.17em}}\gamma =85°,\text{\hspace{0.17em}}$ and its corresponding side $\text{\hspace{0.17em}}c=12,\text{\hspace{0.17em}}$ and we know side $\text{\hspace{0.17em}}b=9.\text{\hspace{0.17em}}$ We will use this proportion to solve for $\text{\hspace{0.17em}}\beta .$ To find $\text{\hspace{0.17em}}\beta ,\text{\hspace{0.17em}}$ apply the inverse sine function. The inverse sine will produce a single result, but keep in mind that there may be two values for $\text{\hspace{0.17em}}\beta .\text{\hspace{0.17em}}$ It is important to verify the result, as there may be two viable solutions, only one solution (the usual case), or no solutions. $\begin{array}{l}\beta ={\mathrm{sin}}^{-1}\left(\frac{9\mathrm{sin}\left(85°\right)}{12}\right)\hfill \\ \beta \approx {\mathrm{sin}}^{-1}\left(0.7471\right)\hfill \\ \beta \approx 48.3°\hfill \end{array}$ In this case, if we subtract $\text{\hspace{0.17em}}\beta \text{\hspace{0.17em}}$ from 180°, we find that there may be a second possible solution. Thus, $\text{\hspace{0.17em}}\beta =180°-48.3°\approx 131.7°.\text{\hspace{0.17em}}$ To check the solution, subtract both angles, 131.7° and 85°, from 180°. This gives $\alpha =180°-85°-131.7°\approx -36.7°,$ which is impossible, and so $\text{\hspace{0.17em}}\beta \approx 48.3°.$ To find the remaining missing values, we calculate $\text{\hspace{0.17em}}\alpha =180°-85°-48.3°\approx 46.7°.\text{\hspace{0.17em}}$ Now, only side $\text{\hspace{0.17em}}a\text{\hspace{0.17em}}$ is needed. Use the Law of Sines to solve for $\text{\hspace{0.17em}}a\text{\hspace{0.17em}}$ by one of the proportions. The complete set of solutions for the given triangle is Given $\text{\hspace{0.17em}}\alpha =80°,a=100,\text{\hspace{0.17em}}\text{\hspace{0.17em}}b=10,\text{\hspace{0.17em}}$ find the missing side and angles. If there is more than one possible solution, show both. Round your answers to the nearest tenth. $\beta \approx 5.7°,\gamma \approx 94.3°,c\approx 101.3$ Finding the triangles that meet the given criteria Find all possible triangles if one side has length 4 opposite an angle of 50°, and a second side has length 10. Using the given information, we can solve for the angle opposite the side of length 10. See [link] . $\begin{array}{l}\text{\hspace{0.17em}}\frac{\mathrm{sin}\text{\hspace{0.17em}}\alpha }{10}=\frac{\mathrm{sin}\left(50°\right)}{4}\hfill \\ \text{\hspace{0.17em}}\text{\hspace{0.17em}}\mathrm{sin}\text{\hspace{0.17em}}\alpha =\frac{10\mathrm{sin}\left(50°\right)}{4}\hfill \\ \text{\hspace{0.17em}}\text{\hspace{0.17em}}\mathrm{sin}\text{\hspace{0.17em}}\alpha \approx 1.915\hfill \end{array}$ We can stop here without finding the value of $\text{\hspace{0.17em}}\alpha .\text{\hspace{0.17em}}$ Because the range of the sine function is $\text{\hspace{0.17em}}\left[-1,1\right],\text{\hspace{0.17em}}$ it is impossible for the sine value to be 1.915. In fact, inputting $\text{\hspace{0.17em}}{\mathrm{sin}}^{-1}\left(1.915\right)\text{\hspace{0.17em}}$ in a graphing calculator generates an ERROR DOMAIN. Therefore, no triangles can be drawn with the provided dimensions. Determine the number of triangles possible given $\text{\hspace{0.17em}}a=31,\text{\hspace{0.17em}}\text{\hspace{0.17em}}b=26,\text{\hspace{0.17em}}\text{\hspace{0.17em}}\beta =48°.\text{\hspace{0.17em}}\text{\hspace{0.17em}}$ two Finding the area of an oblique triangle using the sine function Now that we can solve a triangle for missing values, we can use some of those values and the sine function to find the area of an oblique triangle. Recall that the area formula for a triangle is given as $\text{\hspace{0.17em}}\text{Area}=\frac{1}{2}bh,\text{\hspace{0.17em}}$ where $\text{\hspace{0.17em}}b\text{\hspace{0.17em}}$ is base and $\text{\hspace{0.17em}}h\text{\hspace{0.17em}}$ is height. For oblique triangles, we must find $\text{\hspace{0.17em}}h\text{\hspace{0.17em}}$ before we can use the area formula. Observing the two triangles in [link] , one acute and one obtuse, we can drop a perpendicular to represent the height and then apply the trigonometric property $\text{\hspace{0.17em}}\mathrm{sin}\text{\hspace{0.17em}}\alpha =\frac{\text{opposite}}{\text{hypotenuse}}\text{\hspace{0.17em}}$ to write an equation for area in oblique triangles. In the acute triangle, we have $\text{\hspace{0.17em}}\mathrm{sin}\text{\hspace{0.17em}}\alpha =\frac{h}{c}\text{\hspace{0.17em}}$ or $c\mathrm{sin}\text{\hspace{0.17em}}\alpha =h.\text{\hspace{0.17em}}$ However, in the obtuse triangle, we drop the perpendicular outside the triangle and extend the base $\text{\hspace{0.17em}}b\text{\hspace{0.17em}}$ to form a right triangle. The angle used in calculation is $\text{\hspace{0.17em}}{\alpha }^{\prime },\text{\hspace{0.17em}}$ or $\text{\hspace{0.17em}}180-\alpha .$ (1+cosA)(1-cosA)=sin^2A good Neha why I'm sending you solved question Mirza Teach me abt the echelon method Khamis exact value of cos(π/3-π/4) What is differentiation? modul questions trigonometry (1+cosA)(1-cosA)=sin^2A BINCY differentiate f(t)=1/4t to the power 4 +8 I need trigonometry,polynomial ok Augustine Why is 7 on top simplify cot x / csc x 👉🌹Solve🌻 Given that: cotx/cosx =cosx/sinx/cosx =1/sinx =cosecx Ans. Vijay what is the period of cos? Patrick simplify: cot x/csc x Catherine sorry i didnt realize you were actually asking someone else to put their question on here. i thought this was where i was supposed to. Catherine some to dereve formula for bulky density kurash Solve Given that: cotx/cosx =cosx/sinx/cosx =1/sinx =cosecx Ans. Vijay if tan alpha + beta is equal to sin x + Y then prove that X square + Y square - 2 I got hyperbole 2 Beta + 1 is equal to zero questions Thamarai ok AjA sin^4+sin^2=1, prove that tan^2-tan^4+1=0 what is the formula used for this question? "Jamal wants to save \$54,000 for a down payment on a home. How much will he need to invest in an account with 8.2% APR, compounding daily, in order to reach his goal in 5 years?" i don't need help solving it I just need a memory jogger please. Kuz A = P(1 + r/n) ^rt Dale how to solve an expression when equal to zero its a very simple Kavita gave your expression then i solve Kavita Hy guys, I have a problem when it comes on solving equations and expressions, can you help me 😭😭 Thuli Tomorrow its an revision on factorising and Simplifying... Thuli ok sent the quiz kurash send Kavita Hi Masum What is the value of log-1 Masum the value of log1=0 Kavita Log(-1) Masum What is the value of i^i Masum log -1 is 1.36 kurash No Masum no I m right Kavita No sister. Masum no I m right Kavita tan20°×tan30°×tan45°×tan50°×tan60°×tan70° jaldi batao Joju Find the value of x between 0degree and 360 degree which satisfy the equation 3sinx =tanx	2019-12-09 08:02:57	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 35, "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": 0.8030575513839722, "perplexity": 690.6171300520041}, "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-2019-51/segments/1575540518337.65/warc/CC-MAIN-20191209065626-20191209093626-00553.warc.gz"}
https://cs.stackexchange.com/questions/116864/regular-expression-for-containing-010-as-a-subword/116889	# Regular expression for containing 010 as a subword I am studying for a test in computer science, and am encountering difficulties with regular expression. Here is example of a question I don't understand. I managed to solve the following question: Give a regular expression for the language of all words over $$\{a,b\}$$ which contains one of $$aa,bb$$ as a subword. My solution: $$(a ∪ b)^(aa ∪ bb)^(a ∪ b)^*.$$ I am having trouble with the following question: Give a regular expression for the language of all words over $$\{0,1\}$$ which contains $$010$$ as a subword. • L1 does not look right. All the words in L1 are such that "aa" or "bb" occurs as a substring, but not all words that satisfy the above property are in L1. – Steven Nov 8 '19 at 22:00 • cs.stackexchange.com/q/1331/755 – D.W. Nov 8 '19 at 23:48 • What do you mean by "subword"? – Yuval Filmus Nov 10 '19 at 11:27	2020-11-29 00:19:06	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 5, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3970746397972107, "perplexity": 310.00461248290577}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-50/segments/1606141195929.39/warc/CC-MAIN-20201128214643-20201129004643-00172.warc.gz"}
https://mathoverflow.net/questions/118092/order-of-products-of-elements-in-symmetric-groups/397646	# Order of products of elements in symmetric groups Let $$n \in \mathbb{N}$$. Is it true that for any $$a, b, c \in \mathbb{N}$$ satisfying $$1 < a, b, c \leq n-2$$ the symmetric group $${\rm S}_n$$ has elements of order $$a$$ and $$b$$ whose product has order $$c$$? The assertion is true at least for $$n \leq 10$$, see here. Update on Sep 2, 2015: On Aug 10, 2015 Joachim König has posted a preprint to the arXiv which gives a positive answer to the question. Assuming that this preprint is correct, this completely answers the question -- and thus also Problem 18.49 in the Kourovka Notebook. Update on Jun 18, 2014: The assertion is true at least for $$n \leq 50$$, see here (4MB text file). The list of examples in GAP-readable format can be found here. Added on Dec 11, 2013: This question will appear as Problem 18.49 in: Kourovka Notebook: Unsolved Problems in Group Theory. Editors V. D. Mazurov, E. I. Khukhro. 18th Edition, Novosibirsk 2014. Added on Nov 24, 2013: Is there really not enough known about, say, the class multiplication coefficients of $${\rm S}_n$$ to answer this question? Text of the question as of Feb 12, 2013: This question is a follow-up on Order of elements . Derek Holt's answer to that question is nice, but it seems that the degree of the permutations it gives is a lot larger than necessary. So, given natural numbers $$m, n, k > 1$$, what is the smallest $$d$$ such that the symmetric group of degree $$d$$ has elements of order $$m$$ and $$n$$ whose product has order $$k$$? - Clearly if the largest of the numbers $$m$$, $$n$$, $$k$$ is prime, then $$d$$ must be at least $$\max(m,n,k)$$, and there are some cases where $$d$$ actually must be larger. However a quick computation suggests that $$d = \max(m,n,k) + 2$$ might work always. - But does this or a similar bound hold? EDIT: Smallest-degree examples for all $$m, n, k \leq 8, m \leq n$$ can be found here. • An even stronger conjecture would be that it is the smallest $d$ such that there exist permutations $x,y,z∈\in S_d$ of orders $m,n,k$ such that ${\rm sgn}(x){\rm sgn}(y)={\rm sgn}(z)$ (where ${\rm sgn}(x)$ is $1$ and $−1$ for even and odd permutations). Can you find a counterexample to that? Jan 4 '13 at 22:53 • @Derek: I am not sure I understand your question right - depending on $m$, $n$ and $k$, the degree $d$ may of course be smaller than $\max(m,n,k)$. I performed a brief computation and found that for $d = 3, 4, 5, 6, 7, 8 and 10$ your setting permits precisely the same triples (m,n,k), while for $d = 9$, in addition (2,5,20), (2,20,5), (5,5,10), (5,5,12), (5,10,5), (5,12,5) and (5,20,2) occur (this means e.g. that there are permutations $x$, $y$ and $z$ of orders 5, 5 and 12 with sign +1 in $S_9$, but not such that $xy=z$, etc.). Jan 5 '13 at 0:28 • It looks as though my conjecture was over-optimisitic! Jan 5 '13 at 10:10 The main theorem in a paper of G. A. Miller [1] is the following: THEOREM. If $$l, m, n$$ are any three integers greater than unity, of which we call the greatest $$k$$, it is always possible to find three substitutions $$(L, M, N)$$ of $$k + 2$$ or some smaller number of elements and of orders $$l, m, n$$ respectively such that $$LM=N$$. Papers [3], [4], [5] by Brenner and Lyndon give a different proof of Miller's result, and consider the problem of finding for $$l,m,n > 1$$ the smallest $$d$$ such that $$S_d$$ contains permutations $$x,y$$ with $$(\|x\|, \|y\|, \|xy\|) = (l,m,n)$$. Other related results are e.g. in [2] and [6]. Papers [8], [9] also give a proof of the theorem by Miller. Also in [7], although it seems without assuming permutations of degree $$\leq \max(l,m,n)+2$$ in some cases. The main theorem of [10] constructs for $$l,m,n > 1$$ elements $$A,B \in PSL(2,q)$$ (for suitable $$q$$) such that $$\|A\| = l$$, $$\|B\| = m$$, and $$\|AB\| = n$$. The construction pointed out by Derek Holt here is similar but a bit shorter. Yet another construction with matrices is in [11]. References: [1] MR1505829 G. A. Miller, On the Product of Two Substitutions. Amer. J. Math. 22 (1900), no. 2, 185–190. JSTOR [2] MR1505882 G. A. Miller, Groups Defined by the Orders of Two Generators and the Order of their Product. Amer. J. Math. 24 (1902), no. 1, 96–100. JSTOR [3] MR0767585 J. L. Brenner, R. C. Lyndon, A theorem of G. A. Miller on the order of the product of two permutations. I. Jñānābha 14 (1984), 1–16. link [4] MR0809272 J. L. Brenner, R. C. Lyndon, A theorem of G. A. Miller on the order of the product of two permutations. II. The minimal degree in case a=2. Indian J. Math. 26 (1984), no. 1-3, 105–133 (1985). [5] MR0748120 J. L. Brenner, R. C. Lyndon, A theorem of G. A. Miller on the order of the product of two permutations. III. The minimal degree in case a>2. Pure Appl. Math. Sci. 20 (1984), no. 1-2, 37–51. [6] MR0743150 J. L. Brenner, R. C. Lyndon, The orbits of the product of two permutations. European J. Combin. 4 (1983), no. 4, 279–293. DOI [7] MR0053937 R. H. Fox, On Fenchel's conjecture about F-groups. Mat. Tidsskr. B 1952 (1952), 61–65. JSTOR [8] MR3508006 J. König, A note on the product of two permutations of prescribed orders. European J. Combin. 57 (2016), 50–56. DOI [9] MR3694453 J. Pan, On a conjecture about orders of products of elements in the symmetric group. J. Pure Appl. Algebra 222 (2018), no. 2, 291–296. DOI [10] MR0283093 R. D. Feuer, Torsion-free subgroups of triangle groups. Proc. Amer. Math. Soc. 30 (1971), 235–240. DOI [11] MR0207852 J. Mennicke, Eine Bemerkung über Fuchssche Gruppen. Invent. Math. 2 (1967), 301–305. DOI • Wow-- that is indeed a surprise! -- So, König's result is actually a rediscovery of a result found already 116 years before ... . Jul 16 at 9:38 • I guess the paper by Miller has been overlooked. In G. Moran, Of planar Eulerian graphs and permutations. Trans. Amer. Math. Soc. 287 (1985), no. 1, 323–341. the author comments: "Proposition 3.1 was rediscovered several times since 1900. (The author rediscovered it in 1981, in the course of establishing Theorem 1.)" Jul 17 at 3:52 The question has meanwhile been answered in the positive in: Joachim König, A note on the product of two permutations of prescribed orders. European Journal of Combinatorics 57 (2016), 50-56. The proof makes a case distinction based on the smallest $$n$$ such that there are elements of given orders $$a \leq b \leq c$$ in the symmetric group on $$n$$ points whose product is the identity: 1. $$n = c$$ is sufficient, 2. $$n = c+1$$ is needed and sufficient, and 3. $$n = c+2$$ is needed. It analyzes the various subcases, and makes use of Corollary 4.4 and Lemma 4.5 in: A.L. Edmonds, R.S. Kulkarni, R.E. Stong: Realizability of branched coverings of surfaces. Trans. Amer. Math. Soc. 282(2) (1984), 773--790. First let me paraphrase the question. Given integers $m,n,k$ each at least 2, set $d:=\max(m,n,k)+2$. Do there exist elements $a,b$ in the symmetric group $S_d$ such that $\|a\|=m$, $\|b\|=n$ and $\|ab\|=k$? It is convenient to write $c=ab$. A simple argument shows that we can assume $m\leq n\leq k$ and $d=k+2$. [The equation $b*a=bcb^{-1}$ shows we can swap $m$ and $n$ as $\|bcb^{-1}\|=k$. The equation $a^{-1}c=b$ shows we can swap $n$ and $k$ as $\|a^{-1}\|=m$. Thus we may assume $m\leq n\leq k$.] It is easy to prove the result for small cases such as $m=n=2$. With these simple ideas Stefan's table of data can be simplified, and extended. It seems that there may be results already in the literature. Can an expert help? What about the special case when $m,n,k$ are each powers of the same prime?	2021-09-23 03:56:41	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 48, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7770012617111206, "perplexity": 320.1891728737121}, "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/1631780057416.67/warc/CC-MAIN-20210923013955-20210923043955-00716.warc.gz"}
https://questions.examside.com/past-years/jee/question/the-displacement-y-of-a-wave-travelling-in-the-x-dir-2003-marks-4-dk49uspnjkhi6cd9.htm	### JEE Mains Previous Years Questions with Solutions 4.5 star star star star star 1 ### AIEEE 2003 The displacement $y$ of a wave travelling in the $x$-direction is given by $$y = {10^{ - 4}}\,\sin \left( {600t - 2x + {\pi \over 3}} \right)\,\,metres$$ where $x$ is expressed in metres and $t$ in seconds. The speed of the wave - motion, in $m{s^{ - 1}}$, is A $300$ B $600$ C $1200$ D $200$ ## Explanation $y = {10^{ - 4}}\sin \left( {600t - 2x + {\pi \over 3}} \right)$ But $y = A\sin \left( {\omega t - kx + \phi } \right)$ On comparing we get $\omega = 600;\,k = 2$ $v = {\omega \over k} = {{600} \over 2} = 300\,m{s^{ - 1}}$ 2 ### AIEEE 2003 A metal wire of linear mass density of $9.8$ $g/m$ is stretched with a tension of $10$ $kg$-$wt$ between two rigid supports $1$ metre apart. The wire passes at its middle point between the poles of a permanent magnet, and it vibrates in resonance when carrying an alternating current of frequency $n.$ The frequency $n$ of the alternating source is A $50$ $Hz$ B $100$ $Hz$ C $200$ $Hz$ D $25$ $Hz$ ## Explanation KEY CONCEPT : For a string vibrating between two rigid support, the fundamental frequency is given by $n = {1 \over {2\ell }}\sqrt {{T \over \mu }} = {1 \over {2 \times }}\sqrt {{{10 \times 9.8} \over {9.8 \times {{10}^{ - 3}}}}} = 50Hz$ As the string is vibrating in resonance to a.c of frequency $n,$ therefore both the frequencies are same. 3 ### AIEEE 2002 When temperature increases, the frequency of a tuning fork A increases B decreases C remains same D increases or decreases depending on the material ## Explanation KEY CONCEPT : The frequency of a tuning fork is given by the expression $f = {{{m^2}k} \over {4\sqrt 3 \pi {\ell ^2}}}\sqrt {{Y \over \rho }}$ As temperature increases, $\ell$ increases and therefore $f$ decreases. 4 ### AIEEE 2002 A wave $y=a$ $\sin \left( {\omega t - kx} \right)$ on a string meets with another wave producing a node at $x=0.$ Then the equation of the unknown wave is A $y = \alpha \,\sin \,\left( {\omega t + kx} \right)$ B $y = - \alpha \,\sin \,\left( {\omega t + kx} \right)$ C $y = \alpha \,\sin \,\left( {\omega t - kx} \right)$ D $y = - \alpha \,\sin \,\left( {\omega t - kx} \right)$ ## Explanation To form a node there should be superposition of this wave with the reflected wave. The reflected wave should travel in opposite direction with a phase change of $\pi$. The equation of the reflected wave will be $y = a\sin \left( {\omega t + kx + \pi } \right)$ $\Rightarrow y = - a\sin \left( {\omega t + kx} \right)$	2022-01-22 02:12:49	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 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": 0.7248263359069824, "perplexity": 1078.4893042239164}, "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/1642320303729.69/warc/CC-MAIN-20220122012907-20220122042907-00564.warc.gz"}
https://www.simscale.com/docs/validation-cases/cylinder-under-rotational-force/	# Cylinder Under Rotational Force ## Overview The aim of this test case is to validate the following functions: • centrifugal force The simulation results of SimScale were compared to the numerical results presented in [HPLA100]. The mesh used in (A) and (C) was created with the automatic-tetrahedralization-tool on the SimScale platform. The mesh used in (B) und (D) was created locally. Import validation project into workspace ## Geometry A B C D x [m] 0.0195 0.0205 0.0205 0.0195 y [m] 0 0 0 0 z [m] 0.01 0.01 0 0 To obtain the solid body the face ABCD is rotated 45° around the z-axis. Because of the symmetry of the cylinder only one quarter was modelled. ## Analysis type and Domain Tool Type : Code_Aster Analysis Type : Static Mesh and Element types : Case Mesh type Number of nodes Element type (A) quadratic tetrahedral 2893 3D isoparametric (B) quadratic hexahedral 2583 3D isoparametric (C) quadratic tetrahedral 17460 3D isoparametric (D) quadratic hexahedral 9285 3D isoparametric ## Simulation Setup Material: • isotropic: E = 200 GPa, ν $\nu$ = 0.3, ρ $\rho$ = 8000 kg/m^3 Constraints: • Face AA’BB’ and face CC’DD’ zero z-displacement • Symmetry boundary condition on face ABCD and A’B’C’D’ • Centrifugal force with a rotational speed ω $\omega$ = 1 rad/s around the z-axis applied on the whole body ## Reference Solution u(r)=(1+ν)(12ν)(1ν)Eρω2r38+Ar+Br(1) $\begin{array}{}\text{(1)}& u\left(r\right)=\frac{-\left(1+\nu \right)\left(1-2\nu \right)}{\left(1-\nu \right)E}\rho {\omega }^{2}\frac{{r}^{3}}{8}+Ar+\frac{B}{r}\end{array}$ σzz(r)=ν(1ν)ρω2r22+2νE(1+ν)(12ν)A(2) $\begin{array}{}\text{(2)}& {\sigma }_{zz}\left(r\right)=\frac{-\nu }{\left(1-\nu \right)}\rho {\omega }^{2}\frac{{r}^{2}}{2}+\frac{2\nu E}{\left(1+\nu \right)\left(1-2\nu \right)}A\end{array}$ A=(32ν)(1+ν)(12ν)4(1ν)Eρω2R2(1x2)=7.135881012(3) $\begin{array}{}\text{(3)}& A=\frac{\left(3-2\nu \right)\left(1+\nu \right)\left(1-2\nu \right)}{4\left(1-\nu \right)E}\rho {\omega }^{2}{R}^{2}\left(1-{x}^{2}\right)=7.13588\cdot {10}^{-12}\end{array}$ B=(32ν)(1+ν)8(1ν)Eρω2R4(1x2)2=3.5612581015m2(4) $\begin{array}{}\text{(4)}& B=\frac{\left(3-2\nu \right)\left(1+\nu \right)}{8\left(1-\nu \right)E}\rho {\omega }^{2}{R}^{4}\left(1-{x}^{2}{\right)}^{2}=3.561258\cdot {10}^{-15}{m}^{2}\end{array}$ x=h2R=0.001m20.02m=0.025(5) $\begin{array}{}\text{(5)}& x=\frac{h}{2R}=\frac{0.001m}{2\cdot 0.02m}=0.025\end{array}$ All stated equations used to solve the problem are derived in [HPLA100]. The parameters h $h$ and R $R$ in (5) $\text{(5)}$ are the thickness of the cross section and the radius of the middle surface of the cylinder respectively. ## Results Important The values for the comparison of the displacement ur ${u}_{r}$ and the stresses σzz ${\sigma }_{zz}$ are averaged over on edge and an area respectively Comparison of the displacement ur ${u}_{r}$ and the stresses σzz ${\sigma }_{zz}$ of the inner and the outter face obtained with SimScale and the results derived from [HPLA100]. Comparison of the displacement ur ${u}_{r}$ and the stresses σzz ${\sigma }_{zz}$ Case Quantity [HPLA100] SimScale Error (A) ur(r=0.0195m) ${u}_{r}\left(r=0.0195m\right)$ [m] 2.9424E-013 2.83491E-013 3.653% (A) ur(r=0.0205m) ${u}_{r}\left(r=0.0205m\right)$ [m] 2.8801E-013 2.8972E-013 -0.594% (A) σzz(r=0.0195m) ${\sigma }_{zz}\left(r=0.0195m\right)$ [N/m^2] 0.99488 0.992259 0.263% (A) σzz(r=0.0205m) ${\sigma }_{zz}\left(r=0.0205m\right)$ [N/m^2] 0.92631 0.929711 -0.367% (B) ur(r=0.0195m) ${u}_{r}\left(r=0.0195m\right)$ [m] 2.9424E-013 2.94195E-013 0.015% (B) ur(r=0.0205m) ${u}_{r}\left(r=0.0205m\right)$ [m] 2.8801E-013 2.87966E-013 0.015% (B) σzz(r=0.0195m) ${\sigma }_{zz}\left(r=0.0195m\right)$ [N/m^2] 0.99488 1.00893 -1.412% (B) σzz(r=0.0205m) ${\sigma }_{zz}\left(r=0.0205m\right)$ [N/m^2] 0.92631 0.914645 1.259% (C) ur(r=0.0195m) ${u}_{r}\left(r=0.0195m\right)$ [m] 2.9424E-013 2.94234E-013 0.002% (C) ur(r=0.0205m) ${u}_{r}\left(r=0.0205m\right)$ [m] 2.8801E-013 2.88003E-013 0.002% (C) σzz(r=0.0195m) ${\sigma }_{zz}\left(r=0.0195m\right)$ [N/m^2] 0.99488 0.995217 -0.034% (C) σzz(r=0.0205m) ${\sigma }_{zz}\left(r=0.0205m\right)$ [N/m^2] 0.92631 0.926616 -0.033% (D) ur(r=0.0195m) ${u}_{r}\left(r=0.0195m\right)$ [m] 2.9424E-013 2.94237E-013 0.001% (D) ur(r=0.0205m) ${u}_{r}\left(r=0.0205m\right)$ [m] 2.8801E-013 2.88007E-013 0.001% (D) σzz(r=0.0195m) ${\sigma }_{zz}\left(r=0.0195m\right)$ [N/m^2] 0.99488 0.994995 -0.012% (D) σzz(r=0.0205m) ${\sigma }_{zz}\left(r=0.0205m\right)$ [N/m^2] 0.92631 0.926415 -0.011% ## References [HPLA100] (1, 2, 3, 4) HPLA100 – Cylindre creux thermoélastique pesanten rotation uniforme	2019-05-23 22:20:39	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 33, "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": 0.4603506326675415, "perplexity": 12989.282817535679}, "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/1558232257396.96/warc/CC-MAIN-20190523204120-20190523230120-00554.warc.gz"}
https://ictp.acad.ro/category/announcements/page/4/	## (Communication) Weighted minimum gradient techniques in Current Density based Impedance Imaging by A. Tǎmǎşan We are glad to announce that Professor Alexandru Tǎmǎşan (Department of Mathematics, University of Central Florida) has positively answered to our invitation, and… ## Professor Doctor Oleg Aramă has passed away at the age of 93 With deep regret we announce that on March 6, 2018, Professor Dr. Oleg Aramă, honorary member of the Institute, has passed… ## Professor Doctor Engineer Gheorghe Farkas has passed away at the age 83 With deep regret we announce that on July 13, 2017, Professor Dr. Eng. Gheorghe Farkas, honorary member of the Institute, has passed away.… ## Mathematician and physicist Calin Vamos has passed away at the age 62 With deep regret we announce that on June 21, 2017, Mathematician and Physicist Dr. Călin Vamoş, senior researcher at the Institute, has…	2021-10-21 08:47:30	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 1, "x-ck12": 0, "texerror": 0, "math_score": 0.484064519405365, "perplexity": 6864.542203786718}, "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/1634323585382.32/warc/CC-MAIN-20211021071407-20211021101407-00408.warc.gz"}
https://trac.fact-project.org/changeset/9188	# Changeset 9188 Ignore: Timestamp: Dec 4, 2008, 1:30:45 PM (12 years ago) Message: * empty log message * Location: trunk/Documents/DrivePaper Files: 8 edited ### Legend: Unmodified r9109 %% version 1999/12/01 or later. %% %% $Id: elsarticle.cls,v 1.1 2008-08-07 14:26:10 tbretz Exp$ %% $Id: elsarticle.cls,v 1.2 2008-12-04 13:30:45 tbretz Exp$ %% \def\RCSfile{elsarticle}% r9109 ------------------------------------------------------------------------------ ------------------------------------------------------------------------------ Article (author, title, journal, year) (volume, numbe,r pages, month, note) Book (author/editor, title, publisher, year) (volume/number, series, address, edition, month, note) Conference (author, title, booktitle, year) (editor, volume/number, organization, series, pages, publisher, address, month, note) Inproceedings (author, title, booktitle, year) (editor, volume/number, organization, series, pages, publisher, address, month, note) Manual (title) (author, organization, address, edition, month, year, note) Masterthesis (author, title, school, year) (address, month, note, type) phdthesis (author, title, school, year) (address, month, note, type) unpublished (author, title, note) (month, year) misc () (author, title, howpublished, month, year, note) ------------------------------------------------------------------------------ @MISC{www:fornaxa, key = {{www-01}}, title = {\url{http://www.nrao.edu/imagegallery/}}, year=2006, note={Credit: NRAO/AUI/NSF}} @MISC{www:agnartist0, key = {{www-02}}, title = {\url{http://integral.esa.int/integ_pictures.html}}, year=2006} @MISC{www:agnartist, key = {{www-03}}, title = {\url{http://www.spacetelescope.org/images/}}, year=2006, note={Credit: ESA/NASA, the AVO Project and Paolo Padovani}} @MISC{www:compton, key = {{www-04}}, title = {\url{http://chandra.harvard.edu/resources/illustrations/xlightScatter.html}}, year=2006} @MISC{www:shower, key = {{www-05}}, title = {\url{http://www.mpi-hd.mpg.de/hfm/CosmicRay/shower.png}}, year=2006} @MISC{www:showerartist, key = {{www-06}}, title = {\url{http://abyss.uoregon.edu/~js/glossary/cosmic_rays.html}}, year=2006} @MISC{www:mars, key = {{www-07}}, title = {\url{http://magic.astro.uni-wuerzburg.de/mars/}}, year=2006} @MISC{www:google, key = {{www-08}}, title = {\url{http://earth.google.com}}, year=2006} @MISC{www:slalib, key = {{www-09}}, title = {\url{http://star-www.rl.ac.uk/star/docs/sun67.htx/sun67.html}}, year=2006} @MISC{www:root, key = {{The ROOT System Home Page}}, title = {\url{http://root.cern.ch}}, year=2008} @MISC{www:htmldoc, key = {{www-11}}, title = {\url{http://magic.astro.uni-wuerzburg.de/mars/htmldoc/}}, year=2006} @MISC{www:mysql, key = {{www-12}}, title = {\url{http://www.mysql.com}}, year=2006} @MISC{www:unified, key = {{www-13}}, title = {\url{http://chandra.harvard.edu/resources/illustrations/quasar.html}}, year=2006, note={Credit: NASA/CXC, Melissa Weiss}} @MISC{www:asdc, key = {{www-14}}, title = {\url{http://www.asdc.asi.it/blazars/}}, year=2006} @MISC{www:kva, key = {{www-15}}, title = {\url{http://tur3.tur.iac.es/}}, year=2006} @MISC{www:integral, key = {{www-16}}, title = {\url{http://altamira.asu.cas.cz/iblwg/show.php?id=131}}, year=2006} @MISC{www:ned, key = {{www-17}}, title = {\url{http://nedwww.ipac.caltech.edu/cgi-bin/nph-objsearch?objname=1es1218+304}}, year=2006} @MISC{www:gcn, key = {{GCN}}, title = {\url{http://gcn.gsfc.nasa.gov}}, year=2008} %@MISC{www:BH1m, key = {{www-02}}, title = {\url{http://www.gsfc.nasa.gov/gsfc/spacesci/pictures/blackhole/BH1m.jpg}}, year=2006} %@MISC{www:hillas, key = {{www-10}}, title = {\url{http://lpnhe-auger.in2p3.fr/slides/hillas.ps}}, year=2006} %@MISC{www:agnartist2, key = {{www-03}}, title = {\url{http://upload.wikimedia.org/wikipedia/en/4/40/Galaxies_AGN_Inner-Structure-of.jpg}}, year=2006} @BOOK{Peebles:1983, author = {Peebles, Philip~James~Edwin}, title = {Principles of Physical Cosmology}, publisher 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Conference}, volume = 5, pages = {227}, year = 2005, month = Aug, note = {astro-ph/0508274} } @INPROCEEDINGS{Cortina:2005, author = {Cortina, J. and others}, title = {Technical performance of the {MAGIC} telescope}, booktitle = {$29^{th}$ International Cosmic Ray Conference}, year = 2005, month = Aug, note = {astro-ph/0508274} } @INPROCEEDINGS{Bretz:2005mars, author = {Bretz, T.}, title = {Standard Analysis for the {MAGIC} Telescope}, booktitle = {$29^{th}$ International Cosmic Ray Conference}, volume = 4, year = 2005, pages = 315, month = Aug, note = {astro-ph/0508274} } @INPROCEEDINGS{Gaug:2005, author = {Gaug, M. and Bartko, H. and Cortina, J. and Rico, J. and others}, title = {Calibration of the {MAGIC} telescope}, booktitle = {$29^{th}$ International Cosmic Ray Conference}, year = 2005, month = Aug, note = {astro-ph/0508274} } @INPROCEEDINGS{Riegel:2005icrc, author = {{Riegel}, B. and Bretz, T.}, title = {A systematic study of the interdependance of the {IACT} image parameters}, booktitle = {$29^{th}$ International Cosmic Ray Conference}, year = 2005, volume = 5, pages = 215, month = Aug, note = {astro-ph/0508274} } @INPROCEEDINGS{Riegel:2005icrc2, author = {{Riegel}, B. and Bretz, T. and Dorner, D. and Wagner, R.~M.}, title = {A tracking monitor for the {MAGIC} telescope}, booktitle = {$29^{th}$ International Cosmic Ray Conference}, year = 2005, volume = 5, pages = 219, month = Aug, note = {astro-ph/0508274} } @INPROCEEDINGS{Goebel:2005, author = {{Goebel}, F. and Mase, K. and Meyer, M. and Mirzoyan, R. and Shayduk, M. and Teshima, M. and others}, title = {Absolute energy scale calibration of the {MAGIC} telescope using muon images}, booktitle = {$29^{th}$ International Cosmic Ray Conference}, year = 2005, month = Aug, note = {astro-ph/0508274} } @INPROCEEDINGS{Majumdar:2005icrc, author = {{Majumdar}, P. and {Moralejo}, A. and {Bigongiari}, C. and {Blanch}, O. and {Sobczynska}, D.}, title = {{M}onte {C}arlo simulation for the {MAGIC} telescope}, booktitle = {$29^{th}$ International Cosmic Ray Conference}, year = 2005, month = Aug, note = {astro-ph/0508274} } @INPROCEEDINGS{Meyer:2005icrc, author = {{Meyer}, M. and Mannheim, K. and Bretz, T. and Dorner, D. and Riegel, B. and H\"ohne, D. and Berger, K. and others}, title = {{MAGIC} observations of high-peaked {BL} {L}ac objects}, booktitle = {$28^{th}$ International Cosmic Ray Conference}, volume = 4, pages = 335, year = 2005, month = Aug, note = {astro-ph/0508273} } @ARTICLE{Lessard:2001, author = {{Lessard}, R.~W. and {Buckley}, J.~H. and {Connaughton}, V. and {Le Bohec}, S.}, title = "{A new analysis method for reconstructing the arrival direction of TeV gamma rays using a single imaging atmospheric Cherenkov telescope}", journal = {Astroparticle Physics}, year = 2001, month = mar, volume = 15, pages = {1-18}, adsurl = {http://cdsads.u-strasbg.fr/cgi-bin/nph-bib_query?bibcode=2001APh....15....1L&db_key=AST}, adsnote = {Provided by the Smithsonian/NASA Astrophysics Data System} } @ARTICLE{Urry:1995, author = {{Urry}, C.~M. and {Padovani}, P.}, title = "{Unified Schemes for Radio-Loud Active Galactic Nuclei}", journal = {\pasp}, year = 1995, month = sep, volume = 107, pages = {803-+}, adsurl = {http://cdsads.u-strasbg.fr/cgi-bin/nph-bib_query?bibcode=1995PASP..107..803U&db_key=AST}, adsnote = {Provided by the Smithsonian/NASA Astrophysics Data System} } @ARTICLE{Urry:2000, author = {{Urry}, C.~M. and {Scarpa}, R. and {O'Dowd}, M. and {Falomo}, R. and {Pesce}, J.~E. and {Treves}, A.}, title = "{The Hubble Space Telescope Survey of BL Lacertae Objects. II. Host Galaxies}", journal = {\apj}, year = 2000, month = apr, volume = 532, pages = {816-829}, adsurl = {http://cdsads.u-strasbg.fr/cgi-bin/nph-bib_query?bibcode=2000ApJ...532..816U&db_key=AST}, adsnote = {Provided by the Smithsonian/NASA Astrophysics Data System} } @ARTICLE{Porter:1960, author = {Hill, D.~A. and Porter, N.~A}, title = "{Photography of \v{C}erenkov Light from Extensive Air Showers in the Atmosphere}", month = aug, year = 1960, journal = {\nat}, volume = 191, pages = 690, note = {Letters to Editor} } @ARTICLE{Jelley:1963, author = {{Jelley}, J.~V. and {Porter}, N.~A.}, title = "{{\v C}erenkov Radiation from the Night Sky, and its Application to {$\gamma$}-Ray Astronomy}", journal = {\qjras}, year = 1963, month = sep, volume = 4, pages = {275-+}, adsurl = {http://cdsads.u-strasbg.fr/cgi-bin/nph-bib_query?bibcode=1963QJRAS...4..275J&db_key=AST}, adsnote = {Provided by the Smithsonian/NASA Astrophysics Data System} } @ARTICLE{Padovani:1995, author = {{Padovani}, P. and {Giommi}, P.}, title = "{The connection between x-ray- and radio-selected BL Lacertae objects}", journal = {\apj}, year = 1995, month = may, volume = 444, pages = {567-581}, adsurl = {http://cdsads.u-strasbg.fr/cgi-bin/nph-bib_query?bibcode=1995ApJ...444..567P&db_key=AST}, adsnote = {Provided by the Smithsonian/NASA Astrophysics Data System} } @ARTICLE{Boella:1997, author = {{Boella}, G. and {Butler}, R.~C. and {Perola}, G.~C. and {Piro}, L. and {Scarsi}, L. and {Bleeker}, J.~A.~M.}, title = "{BeppoSAX, the wide band mission for X-ray astronomy}", journal = {\aaps}, year = 1997, month = apr, volume = 122, pages = {299-307}, adsurl = {http://cdsads.u-strasbg.fr/cgi-bin/nph-bib_query?bibcode=1997A%26AS..122..299B&db_key=AST}, adsnote = {Provided by the Smithsonian/NASA Astrophysics Data System} } @ARTICLE{Catanese:1999, author = {{Catanese}, M. and {Weekes}, T.~C.}, title = "{Very High Energy Gamma-Ray Astronomy}", journal = {\pasp}, year = 1999, month = oct, volume = 111, pages = {1193-1222}, adsurl = {http://cdsads.u-strasbg.fr/cgi-bin/nph-bib_query?bibcode=1999PASP..111.1193C&db_key=AST}, adsnote = {Provided by the Smithsonian/NASA Astrophysics Data System} } @ARTICLE{Daum:1997, author = {{Daum}, A. and others}, title = "{First results on the performance of the HEGRA IACT array}", journal = {Astroparticle Physics}, year = 1997, month = dec, volume = 8, pages = {1-2}, adsurl = {http://cdsads.u-strasbg.fr/cgi-bin/nph-bib_query?bibcode=1997APh.....8....1D&db_key=AST}, adsnote = {Provided by the Smithsonian/NASA Astrophysics Data System} } @ARTICLE{Aharonian:2004, author = {{Aharonian}, F. and others}, title = "{Observations of 54 Active Galactic Nuclei with the HEGRA system of Cherenkov telescopes}", journal = {\aap}, year = 2004, month = jul, volume = 421, pages = {529-537}, adsurl = {http://cdsads.u-strasbg.fr/cgi-bin/nph-bib_query?bibcode=2004A%26A...421..529A&db_key=AST}, adsnote = {Provided by the Smithsonian/NASA Astrophysics Data System} } @ARTICLE{Pohl:2000, author = {{Pohl}, M. and {Schlickeiser}, R.}, title = "{On the conversion of blast wave energy into radiation in active galactic nuclei and gamma-ray bursts}", journal = {\aap}, year = 2000, month = feb, volume = 354, pages = {395-410}, adsurl = {http://cdsads.u-strasbg.fr/cgi-bin/nph-bib_query?bibcode=2000A%26A...354..395P&db_key=AST}, adsnote = {Provided by the Smithsonian/NASA Astrophysics Data System} } @ARTICLE{Mannheim:1993, author = {{Mannheim}, K.}, title = "{The proton blazar}", journal = {\aap}, year = 1993, month = mar, volume = 269, pages = {67-76}, adsurl = {http://cdsads.u-strasbg.fr/cgi-bin/nph-bib_query?bibcode=1993A%26A...269...67M&db_key=AST}, adsnote = {Provided by the Smithsonian/NASA Astrophysics Data System} } # CHECK AGAIN! @INPROCEEDINGS{Sikora:2001, author = {{Sikora}, M.}, title = "{Jets in Quasars}", booktitle = {ASP Conf. Ser. 227: Blazar Demographics and Physics}, year = 2001, pages = {95-+}, adsurl = {http://cdsads.u-strasbg.fr/cgi-bin/nph-bib_query?bibcode=2001ASPC..227...95S&db_key=AST}, adsnote = {Provided by the Smithsonian/NASA Astrophysics Data System} } @ARTICLE{Sikora:1987, author = {{Sikora}, M. and {Kirk}, J.~G. and {Begelman}, M.~C. and {Schneider}, P. }, title = "{Electron injection by relativistic protons in active galactic nuclei}", journal = {\apjl}, year = 1987, month = sep, volume = 320, pages = {L81-L85}, adsurl = {http://cdsads.u-strasbg.fr/cgi-bin/nph-bib_query?bibcode=1987ApJ...320L..81S&db_key=AST}, adsnote = {Provided by the Smithsonian/NASA Astrophysics Data System} } # CHECK AGAIN @ARTICLE{Burns:1982, author = {{Burns}, M.~L. and {Lovelace}, R.~V.~E.}, title = "{Theory of electron-positron showers in double radio sources}", journal = {\apj}, year = 1982, month = nov, volume = 262, pages = {87-99}, adsurl = {http://cdsads.u-strasbg.fr/cgi-bin/nph-bib_query?bibcode=1982ApJ...262...87B&db_key=AST}, adsnote = {Provided by the Smithsonian/NASA Astrophysics Data System} } @ARTICLE{Svensson:1987, author = {{Svensson}, R.}, title = "{Non-thermal pair production in compact X-ray sources - First-order Compton cascades is soft radiation fields}", journal = {\mnras}, year = 1987, month = jul, volume = 227, pages = {403-451}, adsurl = {http://cdsads.u-strasbg.fr/cgi-bin/nph-bib_query?bibcode=1987MNRAS.227..403S&db_key=AST}, adsnote = {Provided by the Smithsonian/NASA Astrophysics Data System} } @BOOK{Berezinskii:1990, author = {{Berezinskii}, V.~S. and {Bulanov}, S.~V. and {Dogiel}, V.~A. and {Ptuskin}, V.~S.}, title = "{Astrophysics of cosmic rays}", publisher = {Amsterdam: North-Holland, 1990, edited by Ginzburg, V.L.}, year = 1990, adsurl = {http://cdsads.u-strasbg.fr/cgi-bin/nph-bib_query?bibcode=1990acr..book.....B&db_key=AST}, adsnote = {Provided by the Smithsonian/NASA Astrophysics Data System} } @ARTICLE{Mannheim:1991, author = {{Mannheim}, K. and {Biermann}, P.~L. and {Kruells}, W.~M.}, title = "{A novel mechanism for nonthermal X-ray emission}", journal = {\aap}, year = 1991, month = nov, volume = 251, pages = {723-731}, adsurl = {http://cdsads.u-strasbg.fr/cgi-bin/nph-bib_query?bibcode=1991A%26A...251..723M&db_key=AST}, adsnote = {Provided by the Smithsonian/NASA Astrophysics Data System} } @INPROCEEDINGS{Mannheim:1997, author = {{Mannheim}, K.}, title = "{AGN Models: High-Energy Emission.}", booktitle = {Very High Energy Phenomena in the Universe; Moriond Workshop}, year = 1997, pages = {17-+}, adsurl = {http://cdsads.u-strasbg.fr/cgi-bin/nph-bib_query?bibcode=1997vhep.conf...17M&db_key=AST}, adsnote = {Provided by the Smithsonian/NASA Astrophysics Data System} } @ARTICLE{Mannheim:1998, author = {{Mannheim}, K.}, title = "{Possible Production of High-Energy Gamma Rays from Proton Acceleration in the Extragalactic Radio Source Markarian 501}", journal = {Science}, year = 1998, month = jan, volume = 279, pages = {684-+}, adsurl = {http://cdsads.u-strasbg.fr/cgi-bin/nph-bib_query?bibcode=1998Sci...279..684M&db_key=AST}, adsnote = {Provided by the Smithsonian/NASA Astrophysics Data System} } @ARTICLE{Hauser:2001, author = {{Hauser}, M.~G. and {Dwek}, E.}, title = "{The Cosmic Infrared Background: Measurements and Implications}", journal = {\araa}, year = 2001, volume = 39, pages = {249-307}, adsurl = {http://cdsads.u-strasbg.fr/cgi-bin/nph-bib_query?bibcode=2001ARA%26A..39..249H&db_key=AST}, adsnote = {Provided by the Smithsonian/NASA Astrophysics Data System} } # TO BE CHECKED! @ARTICLE{Perlman:1998, author = {{Perlman}, E.~S. and {Padovani}, P. and {Giommi}, P. and {Sambruna}, R. and {Jones}, L.~R. and {Tzioumis}, A. and {Reynolds}, J.}, title = "{The Deep X-Ray Radio Blazar Survey. I. Methods and First Results}", journal = {\aj}, year = 1998, month = apr, volume = 115, pages = {1253-1294}, adsurl = {http://cdsads.u-strasbg.fr/cgi-bin/nph-bib_query?bibcode=1998AJ....115.1253P&db_key=AST}, adsnote = {Provided by the Smithsonian/NASA Astrophysics Data System} } @INPROCEEDINGS{Laurent-Muehleisen:1998, author = {{Laurent-Muehleisen}, S.~A. and {Kollgaard}, R.~I. and {Feigelson}, E.~D. }, title = "{The Rosat-Green Bank Sample of Intermediate BL Lac Objects}", booktitle = {ASP Conf. Ser. 144: IAU Colloq. 164: Radio Emission from Galactic and Extragalactic Compact Sources}, year = 1998, pages = {163-+}, adsurl = {http://cdsads.u-strasbg.fr/cgi-bin/nph-bib_query?bibcode=1998ASPC..144..163L&db_key=AST}, adsnote = {Provided by the Smithsonian/NASA Astrophysics Data System} } @ARTICLE{Caccianiga:1999, author = {{Caccianiga}, A. and {Maccacaro}, T. and {Wolter}, A. and {della Ceca}, R. and {Gioia}, I.~M.}, title = "{The REX Survey: A Search for Radio-emitting X-Ray Sources}", journal = {\apj}, year = 1999, month = mar, volume = 513, pages = {51-68}, adsurl = {http://cdsads.u-strasbg.fr/cgi-bin/nph-bib_query?bibcode=1999ApJ...513...51C&db_key=AST}, adsnote = {Provided by the Smithsonian/NASA Astrophysics Data System} } @ARTICLE{Caccianiga:2004, author = {{Caccianiga}, A. and {March{\~a}}, M.~J.~M.}, title = "{The CLASS blazar survey: testing the blazar sequence}", journal = {\mnras}, year = 2004, month = mar, volume = 348, pages = {937-954}, adsurl = {http://cdsads.u-strasbg.fr/cgi-bin/nph-bib_query?bibcode=2004MNRAS.348..937C&db_key=AST}, adsnote = {Provided by the Smithsonian/NASA Astrophysics Data System} } @ARTICLE{Kellermann:1989, author = {{Kellermann}, K.~I. and {Sramek}, R. and {Schmidt}, M. and {Shaffer}, D.~B. and {Green}, R.}, title = "{VLA observations of objects in the Palomar Bright Quasar Survey}", journal = {\aj}, year = 1989, month = oct, volume = 98, pages = {1195-1207}, adsurl = {http://cdsads.u-strasbg.fr/cgi-bin/nph-bib_query?bibcode=1989AJ.....98.1195K&db_key=AST}, adsnote = {Provided by the Smithsonian/NASA Astrophysics Data System} } @ARTICLE{Rowan:1977, author = {{Rowan-Robinson}, M.}, title = "{On the unity of activity in galaxies}", journal = {\apj}, year = 1977, month = may, volume = 213, pages = {635-647}, adsurl = {http://cdsads.u-strasbg.fr/cgi-bin/nph-bib_query?bibcode=1977ApJ...213..635R&db_key=AST}, adsnote = {Provided by the Smithsonian/NASA Astrophysics Data System} } @ARTICLE{Lawrence:1982, author = {{Lawrence}, A. and {Elvis}, M.}, title = "{Obscuration and the various kinds of Seyfert galaxies}", journal = {\apj}, year = 1982, month = may, volume = 256, pages = {410-426}, adsurl = {http://cdsads.u-strasbg.fr/cgi-bin/nph-bib_query?bibcode=1982ApJ...256..410L&db_key=AST}, adsnote = {Provided by the Smithsonian/NASA Astrophysics Data System} } @ARTICLE{Giommi:1994, author = {{Giommi}, P. and {Padovani}, P.}, title = "{Bl-Lacertae Reunification}", journal = {\mnras}, year = 1994, month = may, volume = 268, pages = {L51+}, adsurl = {http://cdsads.u-strasbg.fr/cgi-bin/nph-bib_query?bibcode=1994MNRAS.268L..51G&db_key=AST}, adsnote = {Provided by the Smithsonian/NASA Astrophysics Data System} } @ARTICLE{Antonucci:1985, author = {{Antonucci}, R.~R.~J. and {Ulvestad}, J.~S.}, title = "{Extended radio emission and the nature of blazars}", journal = {\apj}, year = 1985, month = jul, volume = 294, pages = {158-182}, adsurl = {http://cdsads.u-strasbg.fr/cgi-bin/nph-bib_query?bibcode=1985ApJ...294..158A&db_key=AST}, adsnote = {Provided by the Smithsonian/NASA Astrophysics Data System} } @ARTICLE{Fossati:1998, author = {{Fossati}, G. and {Maraschi}, L. and {Celotti}, A. and {Comastri}, A. and {Ghisellini}, G.}, title = "{A unifying view of the spectral energy distributions of blazars}", journal = {\mnras}, year = 1998, month = sep, volume = 299, pages = {433-448}, adsurl = {http://cdsads.u-strasbg.fr/cgi-bin/nph-bib_query?bibcode=1998MNRAS.299..433F&db_key=AST}, adsnote = {Provided by the Smithsonian/NASA Astrophysics Data System} } @ARTICLE{Aharonian:2000, author = {{Aharonian}, F.}, title = "{TeV gamma rays from BL Lac objects due to synchrotron radiation of extremely high energy protons}", journal = {\na}, year = 2000, month = nov, volume = 5, pages = {377-395}, adsurl = {http://cdsads.u-strasbg.fr/cgi-bin/nph-bib_query?bibcode=2000NewA....5..377A&db_key=AST}, adsnote = {Provided by the Smithsonian/NASA Astrophysics Data System} } @ARTICLE{Muecke:2003, author = {{M{\"u}cke}, A. and {Protheroe}, R.~J. and {Engel}, R. and {Rachen}, J.~P. and {Stanev}, T.}, title = "{BL Lac objects in the synchrotron proton blazar model}", journal = {Astroparticle Physics}, year = 2003, month = mar, volume = 18, pages = {593-613}, adsurl = {http://cdsads.u-strasbg.fr/cgi-bin/nph-bib_query?bibcode=2003APh....18..593M&db_key=AST}, adsnote = {Provided by the Smithsonian/NASA Astrophysics Data System} } @ARTICLE{Schlickeiser:2000, author = {{Pohl}, M. and {Schlickeiser}, R.}, title = "{On the conversion of blast wave energy into radiation in active galactic nuclei and gamma-ray bursts}", journal = {\aap}, year = 2000, month = feb, volume = 354, pages = {395-410}, adsurl = {http://cdsads.u-strasbg.fr/cgi-bin/nph-bib_query?bibcode=2000A%26A...354..395P&db_key=AST}, adsnote = {Provided by the Smithsonian/NASA Astrophysics Data System} } @ARTICLE{Lyutikov:2005, author = {{Lyutikov}, M.}, title = "{Composition of ultra-relativistic jets}", journal = {American Astronomical Society Meeting Abstracts}, year = 2005, month = may, volume = 206, pages = {-+}, adsurl = {http://cdsads.u-strasbg.fr/cgi-bin/nph-bib_query?bibcode=2005AAS...206.3008L&db_key=AST}, adsnote = {Provided by the Smithsonian/NASA Astrophysics Data System} } @ARTICLE{Sikora:2005, author = {{Sikora}, M. and {Begelman}, M.~C. and {Madejski}, G.~M. and {Lasota}, J.-P.}, title = "{Are Quasar Jets Dominated by Poynting Flux?}", journal = {\apj}, year = 2005, month = may, volume = 625, pages = {72-77}, adsurl = {http://cdsads.u-strasbg.fr/cgi-bin/nph-bib_query?bibcode=2005ApJ...625...72S&db_key=AST}, adsnote = {Provided by the Smithsonian/NASA Astrophysics Data System} } @ARTICLE{Montigny:1995, author = {{von Montigny}, C. and others}, title = "{High-Energy Gamma-Ray Emission from Active Galaxies: EGRET Observations and Their Implications}", journal = {\apj}, year = 1995, month = feb, volume = 440, pages = {525-+}, adsurl = {http://cdsads.u-strasbg.fr/cgi-bin/nph-bib_query?bibcode=1995ApJ...440..525V&db_key=AST}, adsnote = {Provided by the Smithsonian/NASA Astrophysics Data System} } @ARTICLE{Fichtel:1994, author = {{Fichtel}, C.~E. and others}, title = "{The first energetic gamma-ray experiment telescope (EGRET) source catalog}", journal = {\apjs}, year = 1994, month = oct, volume = 94, pages = {551-581}, adsurl = {http://cdsads.u-strasbg.fr/cgi-bin/nph-bib_query?bibcode=1994ApJS...94..551F&db_key=AST}, adsnote = {Provided by the Smithsonian/NASA Astrophysics Data System} } @ARTICLE{Thompson:1995, author = {{Thompson}, D.~J. and others}, title = "{The Second EGRET Catalog of High-Energy Gamma-Ray Sources}", journal = {\apjs}, year = 1995, month = dec, volume = 101, pages = {259-+}, adsurl = {http://cdsads.u-strasbg.fr/cgi-bin/nph-bib_query?bibcode=1995ApJS..101..259T&db_key=AST}, adsnote = {Provided by the Smithsonian/NASA Astrophysics Data System} } @ARTICLE{Ghisellini:1989, author = {{Ghisellini}, G. and {Maraschi}, L.}, title = "{Bulk acceleration in relativistic jets and the spectral properties of blazars}", journal = {\apj}, year = 1989, month = may, volume = 340, pages = {181-189}, adsurl = {http://cdsads.u-strasbg.fr/cgi-bin/nph-bib_query?bibcode=1989ApJ...340..181G&db_key=AST}, adsnote = {Provided by the Smithsonian/NASA Astrophysics Data System} } @ARTICLE{Weekes:1996, author = {{Weekes}, T.~C. and others}, title = "{Observations of gamma-ray sources at energies $>$300GeV.}", journal = {\aaps}, year = 1996, month = dec, volume = 120, pages = {C603+}, adsurl = {http://cdsads.u-strasbg.fr/cgi-bin/nph-bib_query?bibcode=1996A%26AS..120C.603W&db_key=AST}, adsnote = {Provided by the Smithsonian/NASA Astrophysics Data System} } @ARTICLE{Petry:1996, author = {{Petry}, D. and others}, title = "{Detection of VHE {$\gamma$}-rays from MKN 421 with the HEGRA Cherenkov Telescopes.}", journal = {\aap}, year = 1996, month = jul, volume = 311, pages = {L13-L16}, adsurl = {http://cdsads.u-strasbg.fr/cgi-bin/nph-bib_query?bibcode=1996A%26A...311L..13P&db_key=AST}, adsnote = {Provided by the Smithsonian/NASA Astrophysics Data System} } @ARTICLE{Tavecchio:1998, author = {{Tavecchio}, F. and {Maraschi}, L. and {Ghisellini}, G.}, title = "{Constraints on the Physical Parameters of TeV Blazars}", journal = {\apj}, year = 1998, month = dec, volume = 509, pages = {608-619}, adsurl = {http://cdsads.u-strasbg.fr/cgi-bin/nph-bib_query?bibcode=1998ApJ...509..608T&db_key=AST}, adsnote = {Provided by the Smithsonian/NASA Astrophysics Data System} } @ARTICLE{Bloom:1993, author = {{Bloom}, S.~D. and {Marscher}, A.~P. and {Gear}, W.~K.}, title = "{Multiwavelength Observations of Flat Radio Spectrum Quasars and Active Galaxies}", journal = {\baas}, year = 1993, month = may, volume = 25, pages = {920-+}, adsurl = {http://cdsads.u-strasbg.fr/cgi-bin/nph-bib_query?bibcode=1993AAS...182.7007B&db_key=AST}, adsnote = {Provided by the Smithsonian/NASA Astrophysics Data System} } @ARTICLE{Schmidt:1963, author = {{Schmidt}, M.}, title = "{3C 273: a star-like object with large red-shift.}", journal = {\nat}, year = 1963, volume = 197, pages = {1040-1040}, adsurl = {http://cdsads.u-strasbg.fr/cgi-bin/nph-bib_query?bibcode=1963Natur.197.1040S&db_key=AST}, adsnote = {Provided by the Smithsonian/NASA Astrophysics Data System} } @ARTICLE{Ghisellini:1994, author = {Ghisellini, G. and Maraschi, L.}, title = {Are $\gamma$-rays from {HPQ}s and {BL} {L}acs due to the same process?}, booktitle = {Proceedings of the Second Compton Symposium}, journal = {AIP Conf. 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https://planetmath.org/ProofOfHenselsLemma	# proof of Hensel’s lemma Lemma: Using the setup and terminology of the statement of Hensel’s Lemma, for $i\geq 0$, i) $\displaystyle\|f^{\prime}(\alpha_{i})\|=\|f^{\prime}(\alpha_{0})\|$ ii) $\displaystyle\left\|\frac{f(\alpha_{i})}{f^{\prime}(\alpha_{i})^{2}}\right\|\leq D% ^{2^{i}}$ iii) $\displaystyle\|\alpha_{i}-\alpha_{0}\|\leq D$ iv) $\displaystyle\alpha_{i}\in\mathcal{O}_{K}$ where $D=\left\|\frac{f(\alpha_{0})}{f^{\prime}(\alpha_{0})^{2}}\right\|$. Proof: All four statements clearly hold when $i=0$. Suppose they are true for $i$. The proof for $i+1$ essentially uses Taylor’s formula. Let $\delta=\left\|\frac{-f(\alpha_{i})}{f^{\prime}(\alpha_{i})}\right\|$. Then $f^{\prime}(\alpha_{i+1})=f^{\prime}(\alpha_{i}+\delta)=f^{\prime}(\alpha_{i})+% {\delta}u$ $f(\alpha_{i+1})=f(\alpha_{i}+\delta)=f(\alpha_{i})+f^{\prime}(\alpha_{i})% \delta+{\delta^{2}}v$ for $u,v\in\mathcal{O}_{K}$. $\|\delta\|\leq D^{2^{i}}\|f^{\prime}(\alpha_{i})\|$ by induction, and since $D<1$, it follows that $\|\delta\|<\|f^{\prime}(\alpha_{i})\|$. Since the norm is non-Archimedean, we see that $f^{\prime}(\alpha_{i+1})=f^{\prime}(\alpha_{i})$ proving i). $f(\alpha_{i})+f^{\prime}(\alpha_{i})\delta=0$ by definition of $\delta$, so $f(\alpha_{i+1})={\delta^{2}}v$ and hence $\|f(\alpha_{i+1})\|\leq\|\delta^{2}\|$. Hence $\left\|\frac{f(\alpha_{i+1})}{f^{\prime}(\alpha_{i+1})^{2}}\right\|\leq\frac{\|% \delta\|^{2}}{\|f^{\prime}(\alpha_{i+1})\|^{2}}=\frac{\|\delta\|^{2}}{\|f^{\prime}(% \alpha_{i})\|^{2}}=\left(\frac{\|\delta\|}{\|f^{\prime}(\alpha_{i})\|}\right)^{2}=% \left(\frac{\|f(\alpha_{i})\|}{\|f^{\prime}(\alpha_{i})\|^{2}}\right)^{2}\leq D^{2% ^{i+1}}$ where the last equality follows by induction. This proves ii). To prove iii), note that $\|\alpha_{i+1}-\alpha_{i}\|=\|\delta\|$ by the definitions of $\delta$ and $\alpha_{i+1}$, so $\|\alpha_{i+1}-\alpha_{i}\|\leq D^{2^{i}}\|f^{\prime}(\alpha_{i})\|=D^{2^{i}}\|f^{% \prime}(\alpha_{0}) when $i>0$ since $D^{2}. So by induction, $\|\alpha_{i+1}-\alpha_{0}\|\leq D$. Finally, to prove iv) and the proof of the lemma, $\delta\in\mathcal{O}_{K}$ since $\|\delta\|<\left\|\frac{f(\alpha_{0})}{f^{\prime}(\alpha_{0})}\right\|\leq 1$ and hence is in the valuation ring of $K$. So by induction, $\alpha_{i+1}=\alpha_{i}+\delta\in\mathcal{O}_{K}$. Proof of Hensel’s Lemma: To prove Hensel’s lemma from the above lemma, note that $\delta=\delta_{i}\to 0$ since $\|\delta\|\leq D^{2^{i}}\|f^{\prime}(\alpha_{0})\|$, so $\{\alpha_{i}\}$ converges to $\alpha\in\mathcal{O}_{K}$ since $K$ is complete. Thus $f(\alpha_{i})\to f(\alpha)$ by continuity. But $\|f(\alpha_{i})\|\leq\|\delta^{2}\|=D^{2^{i+1}}\|f^{\prime}(\alpha_{0})\|$, so $\|f(\alpha_{i})\|\to 0$, so $f(\alpha)=0$ and the proof is complete. Title proof of Hensel’s lemma ProofOfHenselsLemma 2013-03-22 15:32:16 2013-03-22 15:32:16 rm50 (10146) rm50 (10146) 5 rm50 (10146) Proof msc 13H99 msc 12J99 msc 11S99	2019-09-16 02:08:59	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 42, "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": 0.9959192276000977, "perplexity": 362.60759297061054}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-39/segments/1568514572471.35/warc/CC-MAIN-20190916015552-20190916041552-00000.warc.gz"}
http://ndl.iitkgp.ac.in/document/NHpmeVBoaHdQQTZ6a2ZMMERLSU5CdjRTN0drUHBpMHRRRkROVHgwRjdpdz0	### On the minimization of XPath queriesOn the minimization of XPath queries Access Restriction Subscribed Author Flesca, S. ♦ Furfaro, F. ♦ Masciari, E. Source ACM Digital Library Content type Text Publisher Association for Computing Machinery (ACM) File Format PDF Copyright Year ©2008 Language English Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science Subject Keyword Query containment ♦ XPath expressions ♦ Query minimization ♦ Tree pattern matching Abstract XPath expressions define navigational queries on XML data and are issued on XML documents to select sets of element nodes. Due to the wide use of XPath, which is embedded into several languages for querying and manipulating XML data, the problem of efficiently answering XPath queries has received increasing attention from the research community. As the efficiency of computing the answer of an XPath query depends on its size, replacing XPath expressions with equivalent ones having the smallest size is a crucial issue in this direction. This article investigates the minimization problem for a wide fragment of XPath (namely X $P^{[✶]}),$ where the use of the most common operators (child, descendant, wildcard and branching) is allowed with some syntactic restrictions. The examined fragment consists of expressions which have not been specifically studied in the relational setting before: neither are they mere conjunctive queries (as the combination of “//” and “*” enables an implicit form of disjunction to be expressed) nor do they coincide with disjunctive ones (as the latter are more expressive). Three main contributions are provided. The “global minimality” property is shown to hold: the minimization of a given XPath expression can be accomplished by removing pieces of the expression, without having to re-formulate it (as for “general” disjunctive queries). Then, the complexity of the minimization problem is characterized, showing that it is the same as the containment problem. Finally, specific forms of XPath expressions are identified, which can be minimized in polynomial time. ISSN 00045411 Age Range 18 to 22 years ♦ above 22 year Educational Use Research Education Level UG and PG Learning Resource Type Article Publisher Date 2008-02-01 Publisher Place New York e-ISSN 1557735X Journal Journal of the ACM (JACM) Volume Number 55 Issue Number 1 Page Count 46 Starting Page 1 Ending Page 46 #### Open content in new tab Source: ACM Digital Library	2020-07-13 07:51:49	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.1777908056974411, "perplexity": 3391.331131787004}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-29/segments/1593657143354.77/warc/CC-MAIN-20200713064946-20200713094946-00411.warc.gz"}
https://crypto.stackexchange.com/questions/33787/pycrypto-and-aes-can-i-use-a-longer-key-than-the-block-size-16byte	# PyCrypto and AES: can i use a longer key than the block size (16byte)? I see that in many scripts are used keys of 16 characters for a block of 16 byte, but can I use key of 40 (for example)? And then why in some scripts with aes module the block size is set to 32 byte if aes can handle a fixed size block of 128 bit? Is it correct? I see that in many scripts are used keys of 16 characters for a block of 16 byte, but can I use key of 40 (for example)? No, AES uses a key size of 128, 192 or 256 bits. That's 16, 24 or 32 bytes. And then why in some scripts with aes module the block size is set to 32 byte if aes can handle a fixed size block of 128 bit? Is it correct? No, that's not correct. It could however be that the module implements Rijndael instead of AES. AES is a subset of Rijndael, and Rijndael can have the block sizes 128, 160, 192, 224 and indeed 256 bits. So in that case the block size can be 256 bits. Notes: • not all implementations of Rijndael offer support for 160 and 224 bit block and key sizes (so many posts don't mention these block and key sizes); • bytes are not characters, although the name of a byte in C/C++ is traditionally called a char as for ASCII each character is represented by exactly one byte - no conversion necessary; • sometimes when characters are mentioned they actually contain hexadecimal digits; as you need two hexadecimal digits to represent one byte it may seem that 256 bits are used instead of the actual 128 bits. • thanks for the clarification, but if aes supports keys of 256 bit can i use a longer key? – HenryC Mar 18 '16 at 0:34 • @HenryC you can use a key size of 16, 24, or 32 bytes – Richie Frame Mar 18 '16 at 0:37 • Not directly. The algorithm doesn't support it but 256 is plenty anyway. You can always use a KDF such as HKDF or PBKDF2 to compress larger input into 256 bits. Sometimes a hash or HMAC is used directly as a "poor man's" KDF (SHA-256 obviously makes a lot of sense in this case). – Maarten Bodewes Mar 18 '16 at 0:39	2020-07-08 15:11:38	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.26290538907051086, "perplexity": 1413.577928580016}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-29/segments/1593655897027.14/warc/CC-MAIN-20200708124912-20200708154912-00194.warc.gz"}
http://jameswagnersurv.blogspot.com/2014/07/responsive-design-is-not-just-two-phase.html	### Responsive Design is not just Two-Phase Sampling I recently gave, along with Brady West, a short course on paradata and responsive design. We had a series of slides on what is "responsive design." I had a slide with a title similar to that of this post. I think it was "Responsive Design is not equal to Two-Phase Sampling." I sometimes have a discussion with people about using "responsive design" on their survey, but I get the sense that what they really want to know about is two-phase sampling for nonresponse. In fact, two-phase sampling, to be efficient, should have different cost structures across the phases. But the requirements for a responsive design are higher than that. Groves and Heeringa also argued that the phases should have 'complementary' design features. That is, each phase should be attractive to different kinds of sampled people. The hope is that nonresponse biases of prior phases are cancelled out by the biases of subsequent phases. Further, responsive designs can exist without two-phase sampling. Design features can be complementary, have similar costs, and not necessarily be offered to subsets of nonrespondents from the prior phase. Two-phase sampling for nonresponse was an important innovation. But I'd argue that Groves and Heeringa also came up with an important innovation which is actually different and new. 1. Regarding the first reason you give about why responsive design is not two-phase sampling: can't each phase in a two-phase (or multi-phase) sampling also be attractive to different kinds of sampled people? The way I see, two-phase sampling is just the method, but you can use different, complementary design features in each phase, so that you attract different types of respondents. In that sense to me, responsive design is not different from two-phase sampling, it's just that the former used the latter to implement it. Can you give an example of a responsive design that does not use two-phase sampling, as you suggest in the forth paragraph? 2. With regard to the first reason, my point is that the sampling isn't a design feature. Something else has to change. The original Hansen and Hurwitz article changed the mode. I find that non-samplers tend to think of two-phase sampling as somehow magic. Almost like a way to cheat on the response rate. So, emphasizing the other design change forces them to think about the possibilities. On your second question, if I had a design feature that didn't cost more, then I could at least consider switching the design without sampling. For example, if I want to offer a shortened survey to nonresponders, I don't necessarily have to subsample in order to do this. The sampling is usually related to costs... or rare resources. For instance, you might subsample in order to give the remaining sample to a subset of the "best" interviewers, however, that is defined. ### "Responsive Design" and "Adaptive Design" My dissertation was entitled "Adaptive Survey Design to Reduce Nonresponse Bias." I had been working for several years on "responsive designs" before that. As I was preparing my dissertation, I really saw "adaptive" design as a subset of responsive design. Since then, I've seen both terms used in different places. As both terms are relatively new, there is likely to be confusion about the meanings. I thought I might offer my understanding of the terms, for what it's worth. The term "responsive design" was developed by Groves and Heeringa (2006). They coined the term, so I think their definition is the one that should be used. They defined "responsive design" in the following way: 1. Preidentify a set of design features that affect cost and error tradeoffs. 2. Identify indicators for these costs and errors. Monitor these during data collection. 3. Alter the design features based on pre-identified decision rules based on the indi… ### An Experimental Adaptive Contact Strategy I'm running an experiment on contact methods in a telephone survey. I'm going to present the results of the experiment at the FCSM conference in November. Here's the basic idea. Multi-level models are fit daily with the household being a grouping factor. The models provide household-specific estimates of the probability of contact for each of four call windows. The predictor variables in this model are the geographic context variables available for an RDD sample. Let $\mathbf{X_{ij}}$ denote a $k_j \times 1$ vector of demographic variables for the $i^{th}$ person and $j^{th}$ call. The data records are calls. There may be zero, one, or multiple calls to household in each window. The outcome variable is an indicator for whether contact was achieved on the call. This contact indicator is denoted $R_{ijl}$ for the $i^{th}$ person on the $j^{th}$ call to the $l^{th}$ window. Then for each of the four call windows denoted $l$, a separate model is fit where each household is assum… ### Future of Responsive and Adaptive Design A special issue of the Journal of Official Statistics on responsive and adaptive design recently appeared. I was an associate editor for the issue and helped draft an editorial that raised issues for future research in this area. The last chapter of our book on Adaptive Survey Design also defines a set of questions that may be of issue. I think one of the more important areas of research is to identify targeted design strategies. This differs from current procedures that often sequence the same protocol across all cases. For example, everyone gets web, then those who haven't responded to web get mail. The targeted approach, on the other hand, would find a subgroup amenable to web and another amenable to mail. This is a difficult task as most design features have been explored with respect to the entire population, but we know less about subgroups. Further, we often have very little information with which to define these groups. We may not even have basic household or person chara…	2018-11-19 11:07:12	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5921518802642822, "perplexity": 1203.085854703677}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-47/segments/1542039745761.75/warc/CC-MAIN-20181119105556-20181119131556-00308.warc.gz"}
http://physics.openmetric.org/electrodynamics/em/circuits.html	# Circuits¶ ## Capacitor¶ Capacitance is defined as $C = \frac{dQ}{dV}.$ Since current is defined as $$I = \frac{dQ}{dt}$$, we derive the current and potential relation for capacitor $\begin{split}&C dV = dQ \\ \Rightarrow &C \frac{dV}{dt} = \frac{dQ}{dt} \\ \Rightarrow & C \frac{dV}{dt} = I.\end{split}$ ## Inductor¶ Inductor is defined as $L = \frac{d\Phi}{dI},$ where $$\Phi$$ is the magnetic flux of the inductor and $$I$$ is the current going through the inductor. ## Refs & Notes¶ © 2017, Lei Ma. \| Created with Sphinx and . \| \| \| \|	2018-03-18 15:39:02	{"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": 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": 0.9252871870994568, "perplexity": 1129.721223695376}, "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/1521257645824.5/warc/CC-MAIN-20180318145821-20180318165821-00158.warc.gz"}
https://hechimacocochi.com/en/blogs/news/%E7%AC%AC00%E5%9B%9E%E3%82%AE%E3%83%95%E3%83%88%E3%82%B7%E3%83%A7%E3%83%BC%E3%81%AB-%E5%87%BA%E5%B1%95%E3%81%97%E3%81%BE%E3%81%97%E3%81%9F	/ / To the 00th Gift Show Exhibited Oshisase 2020.02.26 # To the 00th Gift ShowExhibited This is where the text is included. This is where the text is included. This is where the text is included. This is where the text is included. This is where the text is included. This is where the text is included. This is where the text is included. This is where the text is included. This is where the text is included. This is where the text is included. This is where the text is included. This is where the text is included. This is where the text is included. This is where the text is included. This is where the text is included. This is where the text is included. This is where the text is included. This is where the text is included. This is where the text is included. This is where the text is included. This is where the text is included. This is where the text is included. This is where the text is included. This is where the text is included. This is where the text is included. This is where the text is included. This is where the text is included.	2021-09-21 13:56:59	{"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": 0.985598087310791, "perplexity": 179.75403582033312}, "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/1631780057225.38/warc/CC-MAIN-20210921131252-20210921161252-00351.warc.gz"}
http://openstudy.com/updates/509b2f3de4b0077374581a38	## Faman39 Group Title A bakery charges $0.10 for a cookie that is 2 inches in diameter. If the price is proportional to the area, how much do they charge for an extra large cookie that is 10 inches in diameter? Assume that each cookie is shaped of a circle.$ 0.50 $1.00$ 2.50 $12.50 one year ago one year ago • This Question is Closed 1. Faman39 Group Title @mark_o. can you able to help me with this? 2. Faman39 Group Title @campbell_st can u able to help me wit this ? 3. campbell_st Group Title ok... so what is the area of the small cookie d = 2inches so radius = 1 inch... can you find the area of a circular cookie with a radius of 1 inch..? 4. Faman39 Group Title I m not getting this prob at all, how to solve it :( dont know 5. campbell_st Group Title ok the cookie is circular \|dw:1352350196613:dw\| 6. campbell_st Group Title next you need to find the area of a cookie with diamater 10 inches of radius 5 inches... use $A = \pi r^2$ can you do that..? 7. campbell_st Group Title last step to find the cost x \|dw:1352350411354:dw\| 8. Faman39 Group Title Ok thank you :) 9. Faman39 Group Title I will try to figure out this 10. mark_o. Group Title hi the question ask for how much is the bigger area cost? for small area of dia d=2 inch = cost$0.10 put it this way on the proportion cost $x? = large A2$0.10 = small A1 setting up the proportion will be cost $x? large A2 -------- = ----------$0.10 small A1 before that what is the small area A , the large area A2 ? use area of circle either A=pi d^2/4 or pi r^2 maybe you use dia d since it is alredy given 11. mark_o. Group Title if for small area A1= pi d^2/4 A1= pi(2)^2/4 is A1= pi ? yes or no ? for large area A2=pi(10)^2/4 is A2=25 pi ? yes or no? if so plug them on your ratio cost $x? large A2 -------- = ----------$0.10 small A1 ($0.10 ) large A2 cost$ x? = x ---------- small A1 cost $x=0.10(25 pi)/pi x= 0.10 (25)=$ 2.5 is it? yes ? 12. mark_o. Group Title @ Faman39 13. Faman39 Group Title Got it thank you so so much :)	2014-07-22 13:30:31	{"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": 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": 0.9548646211624146, "perplexity": 6821.2923692287195}, "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-2014-23/segments/1405997858892.28/warc/CC-MAIN-20140722025738-00193-ip-10-33-131-23.ec2.internal.warc.gz"}
https://appsilon.github.io/rhino/articles/how-to/enable-shiny-bookmarking.html	To use Shiny bookmarking, call shiny::enableBookmarking() somewhere in your main.R: box::use( shiny, ) shiny$enableBookmarking() #' @export ui <- function(id) { ns <- shiny$NS(id) shiny$bootstrapPage( shiny$bookmarkButton(), shiny$textInput(ns("name"), "Name"), shiny$textOutput(ns("message")) ) } #' @export server <- function(id) { shiny$moduleServer(id, function(input, output, session) { output$message <- shiny$renderText(paste0("Hello ", input$name, "!")) }) } If you are using a legacy entrypoint, be sure to make your UI a function as described in the details section of shiny::enableBookmarking(). It should take request as a parameter, though it shouldn’t be used in any way in the function body. For example, with legacy_entrypoint: source in rhino.yml you might use: ui <- function(request) { bootstrapPage( bookmarkButton(), textField("text", "Text") ) }	2022-11-30 02:54:53	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 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": 0.2734180688858032, "perplexity": 8092.861651091733}, "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-2022-49/segments/1669446710719.4/warc/CC-MAIN-20221130024541-20221130054541-00093.warc.gz"}
https://www.shaalaa.com/question-bank-solutions/for-what-kinetic-energy-neutron-will-associated-de-broglie-wavelength-be-140-10-10-m-wave-nature-matter_11589	Advertisement Remove all ads # For What Kinetic Energy of a Neutron Will the Associated De Broglie Wavelength Be 1.40 × 10−10 M? - Physics For what kinetic energy of a neutron will the associated de Broglie wavelength be 1.40 × 10−10 m? Advertisement Remove all ads #### Solution De Broglie wavelength of the neutron, λ = 1.40 × 10−10 m Mass of a neutron, mn = 1.66 × 10−27 kg Planck’s constant, h = 6.6 × 10−34 Js Kinetic energy (K) and velocity (v) are related as: K = 1/2 m_nv^2 … (1) De Broglie wavelength (λ) and velocity (v) are related as: lambda = h/m_nv ...(2) Using equation (2) in equation (1), we get: K = 1/2 (m_n h^2)/(lambda^2 m_n^2) = h^2/(2lambda^2m_n) = (6.63 xx 10^(-34))^2/(2xx(1.40 xx 10^(-10))^2 xx 1.66 xx 10^(-27) ) = 6.75 xx 10^(-21) J Hence, the kinetic energy of the neutron is 6.75 × 10−21 J or 4.219 × 10−2 eV. Hence, the kinetic energy of the neutron is 6.75 × 10−21 J or 4.219 × 10−2 eV. Is there an error in this question or solution? Advertisement Remove all ads #### APPEARS IN NCERT Class 12 Physics Textbook Chapter 11 Dual Nature of Radiation and Matter Q 17.1 \| Page 408 Advertisement Remove all ads #### Video TutorialsVIEW ALL [2] Advertisement Remove all ads Share Notifications View all notifications Forgot password?	2021-03-01 23:18:44	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3734799921512604, "perplexity": 6683.523192344679}, "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-2021-10/segments/1614178363072.47/warc/CC-MAIN-20210301212939-20210302002939-00586.warc.gz"}
https://kb.osu.edu/dspace/handle/1811/19146	AIR-BROADENING COEFFICIENTS AND PRESSURE SHIFT COEFFICIENTS OF $^{12}CH_{3}D$ LINES IN THE 7.7 TO $10 \mu$m SPECTRAL REGION Please use this identifier to cite or link to this item: http://hdl.handle.net/1811/19146 Files Size Format View 1998-WF-14.jpg 148.1Kb JPEG image Title: AIR-BROADENING COEFFICIENTS AND PRESSURE SHIFT COEFFICIENTS OF $^{12}CH_{3}D$ LINES IN THE 7.7 TO $10 \mu$m SPECTRAL REGION Creators: Devi, V. Malathy; Benner, D. Chris; Smith, M. A. H.; Rinsland, C. P. Issue Date: 1998 Abstract: High quality and precise measurements of air-broadening and air-shift coefficients, relative intensities and accurate line positions have been measured for $^{12}CH_{3}D$ lines between 1000 and $1300 cm^{-1}$. The results were derived from analysis of eleven $0.005-cm^{-1}$ resolution laboratory absorption spectra recorded with the McMath-Pierce Fourier transform spectrometer at the National Solar Observatory on Kitt Peak, Arizona. The data were obtained using a high purity (99 percent) isotopic sample of $^{12}CH_{3}D$ and two absorption cells with path lengths of 25 and 150 cm. respectively. Three low-pressure spectra with $^{12}CH_{3}D$ ranging in pressures from 1 to 3 Torr and eight broadened spectra of dilute mixtures of $^{12}CH_{3}D$ in air with total pressures varying between 100 and 400 Torr were used to determine the broadening and shift coefficients. The calibration of the wavelength scale of each spectrum was performed relative to the positions of the $\nu_{2}$ band water vapor lines published by $Toth.^{a}$ A multispectrum nonlinear least-squares spectral fitting $technique^{b}$ was used. The results are compared with previous measurements and calculations. URI: http://hdl.handle.net/1811/19146 Other Identifiers: 1998-WF-14	2014-04-24 14:59:13	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6326941847801208, "perplexity": 3445.1815876200476}, "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-2014-15/segments/1398223206147.1/warc/CC-MAIN-20140423032006-00210-ip-10-147-4-33.ec2.internal.warc.gz"}
http://www.oalib.com/relative/3284117	Home OALib Journal OALib PrePrints Submit Ranking News My Lib FAQ About Us Follow Us+ Title Keywords Abstract Author All Search Results: 1 - 10 of 100 matches for " " Page 1 /100 Display every page 5 10 20 Item Physics , 2015, Abstract: Based on a large Fermi blazar sample, the blazar sequence (synchrotron peak frequency $\nu_{\rm peak}$ versus synchrotron peak luminosity $L_{\rm peak}$) is revisited. It is found that there is significant anti-correlation between $\nu_{\rm peak}$ and $L_{\rm peak}$ for blazars. However, after being Doppler corrected, the anti-correlation disappears. The jet cavity power ($P_{\rm jet}$) is estimated from extended radio luminosity. So it is free of beaming effect. We find that there are significant anti-correlations between $P_{\rm jet}$ and beam-corrected $\nu_{\rm peak}^{'}$ for both blazars and radio galaxies, which supports the blazar sequence and unification of blazars and radio galaxies (an alternative relationship is the correlation between jet power and $\gamma$-ray photon index). Physics , 2012, Abstract: We have conducted a survey of Faraday rotation in a sample of 191 compact radio-loud AGNs as part of the MOJAVE (Monitoring of Jets in Active galactic nuclei with VLBA Experiments) project. The observations were carried out with the VLBA at 8.1, 8.4, 12.1 and 15.3 GHz over 12 epochs in 2006. We detect sufficiently strong linear polarization in 159 out of 211 observations to calculate the rotation measure values, resulting in a large enough sample for statistical analysis of the Faraday rotation in blazars. These Faraday rotation measures can be used to study the intrinsic magnetic field order and orientation in parsec-scale blazar jets. Our sample includes 119 sources listed in the 1FGL or 2FGL catalogs and we detect rotation measure values in 111 out of 131 maps. Of the 72 sources that are not in the gamma-ray catalogs we detect RM in 48 out of 80 maps. The median RM values of the LAT-detected sources do not differ significantly from the non-LAT-detected sources. Nine of the sources in our sample have resolved enough jets to study the transverse Faraday rotation structure, and we detect significant transverse rotation measure gradients in four sources. In two of these (3C~273 and 3C~454.3) there is additional evidence to support helical magnetic field in the parsec-scale jets. The two others (0923+392 and 2230+114) require further observations to identify the nature of the gradient. It is interesting that three of the four sources with significant rotation measure gradients are sources that have shown large gamma-ray flares. Gabriele Ghisellini Physics , 1997, Abstract: The overall spectra (SED) of blazars, from radio to gamma-ray energies, seem to obey well defined trends, with a continuity of properties between blazars of different classes. To quantify this statement we can either investigate their observed properties (see Fossati et al., this volume), or try to determine their intrinsic physical parameters by applying specific models, and trying to fit their SED. Results of the latter approach are reported here. We applied simple, one-zone, homogeneous models to all blazars strongly detected in the gamma-ray band, assuming or not the presence of seed (for the inverse Compton process) photons produced outside the active region. Our results suggest that the SEDs of blazars are ruled by the amount of radiative cooling suffered by the electrons producing most of the emission. In turn, the amount of cooling is ruled by the amount of the external photon emission, which can be identified with radiation coming from the broad line clouds. Blazar SEDs are therefore organized in a sequence: objects with no or very weak emission lines (X-ray selected BL Lacs, or HBL) are characterized by very high electron energies and a Compton luminosity of the same order of the synchrotron one. These are TeV sources. BL Lacertae objects selected in the radio band (or LBL) are characterized by smaller electron energies, more total power and more line luminosity, and by a larger ratio of the Compton to synchrotron luminosity. They are GeV sources. Increasing the total intrinsic power and the line emission luminosity, we have smaller still electron energies (more cooling) and greater still Compton to synchrotron power ratio. These are flat spectrum radio quasars, with a high energy peak located at MeV-GeV energies. Physics , 2002, Abstract: We demonstrate that the spectral differences between Flat Spectrum Radio Quasars (FSRQ) with steep gamma-ray spectra (MeV-blazars) and FSRQ with flat gamma-ray spectra (GeV-blazars) can be explained by assuming that in the MeV-blazars, the production of gamma-rays is dominated by Comptonization of infrared radiation of hot dust, whereas in the GeV-blazars -- by Comptonization of broad emission lines. Additional ingredient, required to reach satisfactory unification, is an assumption that the radiating electrons are accelerated via a two step process, in the lower energy range -- following instabilities driven by shock-reflected ions, and in the higher energy range -- via resonant scatterings off Alfven waves. Our model predicts that on average, the MeV-blazars should vary on longer time scales than GeV-blazars. Physics , 2013, DOI: 10.1088/0067-0049/208/2/15 Abstract: Blazars are the most extreme class of active galactic nuclei (AGNs). Despite a previous investigation at 102 MHz for a small sample of BL Lacs and our recent analysis of blazars detected in the Westerbork Northern Sky Survey (WENSS), a systematic study of the blazar spectral properties at frequencies below 100 MHz has been never carried out. In this paper, we present the first analysis of the radio spectral behavior of blazars based on the recent Very Large Array Low-Frequency Sky Survey (VLSS) at 74 MHz. We search for blazar counterparts in the VLSS catalog confirming that they are detected at 74 MHz. We then show that blazars present radio flat spectra {(i.e., radio spectral indices ~0.5)} when evaluated also about an order of magnitude in frequency lower than previous analyses. Finally, we discuss the implications of our findings in the context of the blazars - radio galaxies connection since the low frequency radio data provide a new diagnostic tool to verify the expectations of the unification scenario for radio-loud active galaxies. Physics , 2010, Abstract: Thanks to the wide field of view of its gamma-ray imager, the AGILE satellite obtained a long term monitoring of the brightest blazars in the sky and during the first 3 years of operation detected several blazars in a high gamma-ray state: 3C 279, 3C 454.3, PKS 1510-089, S5 0716+714, 3C 273, W Comae, and Mrk 421. Through the rapid dissemination of our alerts we were able to obtain also multi-wavelength data from many observatories such as Spitzer, Swift, RXTE, Suzaku, XMM-Newton, INTEGRAL, MAGIC, VERITAS, and ARGO as well as radio-to-optical coverage by means of the MOJAVE project, the GASP project of the WEBT and the REM Telescope. This large coverage over the whole electromagnetic spectrum gave us the opportunity to study the variability correlations between the emission at different frequencies and to build truly simultaneous spectral energy distributions of these sources from radio to gamma-rays, investigating in detail the emission mechanisms of blazars and uncovering in some cases a more complex behaviour with respect to the standard models. We present an overview of the most interesting AGILE results on these gamma-ray blazars and the relative multiwavelength data. Physics , 2002, DOI: 10.1086/342164 Abstract: Broad-band spectra of the FSRQ (flat-spectrum-radio quasars) detected in the high energy gamma-ray band imply that there may be two types of such objects: those with steep gamma-ray spectra, hereafter called MeV-blazars, and those with flat gamma-ray spectra, GeV-blazars. We demonstrate that this difference can be explained in the context of the ERC (external-radiation-Compton) model using the same electron injection function. A satisfactory unification is reachable, provided that: (a) spectra of GeV-blazars are produced by internal shocks formed at the distances where cooling of relativistic electrons in a jet is dominated by Comptonization of broad emission lines, whereas spectra of MeV-blazars are produced at the distances where cooling of relativistic electrons is dominated by Comptonization of near-IR radiation from hot dust; (b) electrons are accelerated via a two step process and their injection function takes the form of a double power-law, with the break corresponding to the threshold energy for the diffusive shock acceleration. Direct predictions of our model are that, on average, variability time scales of the MeV-blazars should be longer than variability time scales of the GeV-blazars, and that both types of the blazar phenomenon can appear in the same object. Physics , 1998, Abstract: Most models for blazars and gamma-ray bursts involve relativistic plasma outflows powered by accretion processes onto black holes. The blast wave physics developed for cosmological models of GRBs is reviewed. Two points relevant for blazar modeling are made: (1) The injection of nonthermal relativistic particles in the comoving frame is simply treated though a process of energizing the plasma as it sweeps up material from the surrounding medium. (2) The primary energy source of blazar radiation derives from the bulk kinetic energy of the outflowing plasma. Thus deceleration of the plasma blast wave must be included in blazar flaring calculations, and this process will introduce temporal and spectral effects in addition to those produced by acceleration and radiative cooling. Physics , 2009, DOI: 10.1051/0004-6361/200913740 Abstract: We investigate the dependence of gamma-ray brightness of blazars on intrinsic properties of their parsec-scale radio jets and the implication for relativistic beaming. By combining apparent jet speeds derived from high-resolution VLBA images from the MOJAVE program with millimetre-wavelength flux density monitoring data from Metsahovi Radio Observatory, we estimate the jet Doppler factors, Lorentz factors, and viewing angles for a sample of 62 blazars. We study the trends in these quantities between the sources which were detected in gamma-rays by the Fermi Large Area Telescope (LAT) during its first three months of science operations and those which were not detected. The LAT-detected blazars have on average higher Doppler factors than non-LAT-detected blazars, as has been implied indirectly in several earlier studies. We find statistically significant differences in the viewing angle distributions between gamma-ray bright and weak sources. Most interestingly, gamma-ray bright blazars have a distribution of comoving frame viewing angles that is significantly narrower than that of gamma-ray weak blazars and centred roughly perpendicular to the jet axis. The lack of gamma-ray bright blazars at large comoving frame viewing angles can be explained by relativistic beaming of gamma-rays, while the apparent lack of gamma-ray bright blazars at small comoving frame viewing angles, if confirmed with larger samples, may suggest an intrinsic anisotropy or Lorentz factor dependence of the gamma-ray emission. Physics , 2001, Abstract: In this paper we discuss the demographics of the radio blazar population: (i) what are their parent (unbeamed') sources and (ii) what magnitude and/or type of evolution have they undergone ? The discussion is based on models of radio source evolution and beaming based on a dual population' unification paradigm. These models, developed from radio blazar properties in bright samples, predict blazar demographic trends at the lower flux-density levels; samples from deep mJy-level surveys (e.g. NVSS and FIRST) may now provide direct tests of these predictions. Page 1 /100 Display every page 5 10 20 Item	2019-11-21 23:50:17	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 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": 0.6533315777778625, "perplexity": 2364.293947160393}, "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/1573496671053.31/warc/CC-MAIN-20191121231600-20191122015600-00506.warc.gz"}
http://bleacherreport.com/users/667420-rockem-boppers	## Rockem Boppers • Generating profile stats... ### Bulletin Board or to post this comment • Boone posted 1076 days ago I don't think I would agree that you are respectful. You indicated that you felt I was a moron because you didn't understand my comparison of two players. I was taking 2 players and comparing the first three seasons of each player's career, respectively. It is the same theory as comparing Michael Jordan's first 3 seasons with Lebron James first 3 seasons, or Kevin Garnett's first three seasons. Obviously we all know that those players were not drafted in the same year. However, since you do not understand that method of comparison, you referred to me as a moron. I find that very disrepectful.	2014-08-31 02:55:02	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8297429084777832, "perplexity": 2197.3472055136626}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-35/segments/1408500835872.63/warc/CC-MAIN-20140820021355-00467-ip-10-180-136-8.ec2.internal.warc.gz"}
https://codereview.stackexchange.com/questions/78175/digit-summing-function/78184	# Digit Summing Function I'm working through the common divisibility tests, and implementing them in Racket. I'm working on divisible by three, for which I thought it'd be nice to keep summing until I got to a single digit (which I can then check for divisibility by 3). My code is here, but it feels like there are rather a lot of steps, and I wonder if there's a way to make it feel a bit less imperative. (define (digits n) (cond [(zero? n) '()] [else (cons (remainder n 10) (digits (quotient n 10)))])) (define (digisum n) (apply + (digits n))) (define (repeated-digit-sum x) (let ([ds (digisum x)]) (if (< ds 10) ds (repeated-digit-sum ds)))) By the way, the fastest way to see if a number is divisible by three is to use (zero? (remainder n 3)). If you want to do the digit summing for fun, fine, but it will make your code slower. So, one way to sum the digits is to extract digits directly during the summing process, rather than building a list of digits first. (define (digisum n) (let loop ((sum 0) (n n)) (define-values (q r) (quotient/remainder n 10)) (if (zero? n) sum (loop (+ sum r) q)))) Alternatively, you can use a for comprehension for this: (define (in-digits n (base 10)) (make-do-sequence (thunk (values (curryr remainder base) (curryr quotient base) n positive? #f #f)))) (define (digisum n) (for/sum ((digit (in-digits n))) digit)) • Yep. I actually have test cases using a generalised modulo function. This is really just an exercise is learning language features. – bbcmicro Jan 21 '15 at 7:11	2020-08-04 03:25:47	{"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": 0.49799269437789917, "perplexity": 3473.4628137318346}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-34/segments/1596439735851.15/warc/CC-MAIN-20200804014340-20200804044340-00023.warc.gz"}
https://awmsltd.co.uk/blog/predicate-logic-formulas-6fe748	The precise semantic interpretation of an atomic formula and an atomic sentence will vary from theory to theory. Constants can be thought of as functions with 0-arity or which don’t take any arguments (even we drop the argument brackets). Where x ranges over a set of variables var, c ranges over nullary function symbols in F, and f ranges over those elements of F with arity n > 0. Propositional logic and its variable cousain, the predicate logic is not able to model all predicates in natural language, including that of English. The precise semantic interpretation of an atomic formula and an atomic sentence will vary from theory to theory. The predicate logic is much more complex than that of propositional logic, because of the power of this language. Note that, this works only because of the logic that fathers are unique and always defined, so ‘f’ really is a function as opposed to a mere relation. Example 21. Today we wrap up our discussion of logic by introduction quantificational logic. The other sorts in predicate logic denote truth values; expressions in predicate logic, of this kind, are formulas: Y (x, m(x)) is a formula, though x and m(x) are terms. Usually, the binary symbols are written infix rather than a prefix; thus, the term is usually written as (2 − (s(x) + y)) ∗ x. However, while a truth table always has a finite number of rows, the possible structures for a formula are always infinitely many. With the propositional rules, the rules themselves were motivated by truth-tables and considered what was needed to 'picture' the truth of the formula being extended. © Copyright 2014-2024 \| Design & Developed by Zitoc Team. Q The terms of predicated language are made up of variables, constant symbols, and functions applied to those. And in fact, this is a form of set theory with one inaccessible cardinal. The first building block of terms is constants (nullary functions) and variables. A simple form of predicate is a Boolean expression, in which case the inputs to the expression are themselves Boolean values, combined using Boolean operations. {\displaystyle P} Similarly, the notation P(x) is used to denote a sentence or statement P concerning the variable object x. The other sorts in predicate logic denote truth values; expressions in predicate logic, of this kind, are formulas: Y (x, m(x)) is a formula, though x and m(x) are terms. As a function, we keep m, S, and B as above and we write ’f’ for the function which, given an argument, returns the corresponding father. All other well-formed formulae are obtained by composing atoms with logical connectives and quantifiers. The other sorts in predicate logic denote truth values; expressions in predicate logic, of this kind, are formulas: Y (x, m(x)) is a formula, though x and m(x) are terms. Similarly, a Boolean expression with inputs predicates is itself a more complex predicate. Consider the … Logic, Page 6 Literals • A term is an object, a variable, or a function • An atomic formula (atom) is a predicate with a proper number of arguments (terms) • A literal is either an atom or the negation of an atom • No Quantifiers Well-formed Formulas (wffs) Defined recursively • Literals are wffs The discussion of Predicate logic as a formal language is to give an impression of how we code up sentences as formulas of predicate logic. First is a set of predicate symbols ‘P’, the second is a set of function symbols ‘F’ and third is a set of constant symbols ‘C’. In mathematical logic, a predicate is commonly understood to be a Boolean-valued function P: X→ {true, false}, called a predicate on X. Often we also omit brackets around quantifiers, provided that doing so introduces no ambiguities. ZITOC (Zillion Topics On Concerns) is an online concerned learning platform for those individuals who want to have basic initiative information as well as a strong grip on knowledge of their concern. The other sorts in predicate logic denote truth values; expressions in predicate logic, of this kind, are formulas: Y (x, m(x)) is a formula, though x and m(x) are terms. Predicate Logic Formulas In this chapter, we will develop the notion of formal deductive proofs for Predicate Logic. It is possible to use a similar approach for predicate logic (although, of course, there are no truth tables in predicate logic). And the notion of terms is dependent on the set F (function symbols). Suppose 0, 1,… are nullary, s is unary, and +, −, and ∗ are binary. Structures in the semantics of predicate logic are the equivalent of truth table rows in the semantics of propositional logic. A predicate logic formula involved two sorts of things. Rules for constructing Wffs We define the set of formulas over (F, P) inductively, using the already defined set of terms over F: φ ::= P(t1, t2,…,tn) \| (¬φ) \| (φ ∧ φ) \| (φ ∨ φ) \| (φ → φ) \| (∀x φ) \| (∃x φ). "Predicate (logic)" redirects here. However, while a truth table always has a finite number of rows, the possible structures for a formula are always infinitely many. Sometimes, P(x) is also called a (template in the role of) propositional function, as each choice of the placeholder x produces a proposition. For example, the formula ∀x. In predicate logic, an expression which denotes object is called term. A predicate can be a proposition if the placeholder x is defined by domain or selection. Let us start with a motivating example. Moveover, on this informative platform, individuals from everywhere could discuss and share their thoughts with others as well. Each predicate symbol and each function symbol in predicate logic must come with an arity (the number of arguments it expects). This chapter is dedicated to another type of logic, called predicate logic. https://www.tutorialspoint.com/.../discrete_mathematics_predicate_logic.htm If P ∈ P is a predicate symbol of arity n ≥ 1, and if t1, t2,…,tn are terms over F, then P(t1, t2,…,tn) is a formula. Thus, a predicate P(x) will be true or false, depending on whether x belongs to a set or not. By giving syntactic rules for the formation of predicate logic formulas, we will be more precise about it. So we may drop the set C since it is convenient to do so, and stipulate that constants are nullary functions (with 0-arity). Let us start with a motivating example. Informally, a predicate, often denoted by capital roman letters such as	2021-10-28 19:44:19	{"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": 0.8460244536399841, "perplexity": 747.8006639894975}, "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-2021-43/segments/1634323588526.57/warc/CC-MAIN-20211028193601-20211028223601-00665.warc.gz"}