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https://math.libretexts.org/Bookshelves/Algebra/Book%3A_Beginning_Algebra_(Redden)/04%3A_Solving_Linear_Systems/4.02%3A_Solving_Linear_Systems_by_Substitution |
# 4.2: Solving Linear Systems by Substitution
Learning Objectives
• Solve linear systems using the substitution method.
## The Substitution Method
In this section, we will define a completely algebraic technique for solving systems. The idea is to solve one equation for one of the variables and substitute the result into the other equation. After performing this substitution step, we will be left with a single equation with one variable, which can be solved using algebra. This is called the substitution method, and the steps are outlined in the following example.
Example $$\PageIndex{1}$$
Solve by substitution:
\left\{\begin{aligned} 2x+y&=7 \\ x-2y&=-7 \end{aligned}\right..
Solution:
Step 1: Solve for either variable in either equation. If you choose the first equation, you can isolate $$y$$ in one step.
\begin{aligned} 2x+y&=7\\2x+y\color{Cerulean}{-2x}&=7\color{Cerulean}{-2x} \\ y&=-2x+7 \end{aligned}
Step 2: Substitute the expression $$−2x+7$$ for the $$y$$ variable in the other equation.
This leaves you with an equivalent equation with one variable, which can be solved using the techniques learned up to this point.
Step 3: Solve for the remaining variable. To solve for $$x$$, first distribute $$−2$$:
\begin{aligned} 3x-2(\color{OliveGreen}{-2x+7}\color{black}{)}&=-7 \\ 3x+4x-14&=-7 \\ 7x-14&=-7 \\ 7x-14\color{Cerulean}{+14}&=-7\color{Cerulean}{+14}\\7x&=7\\\frac{7x}{\color{Cerulean}{7}}&=\frac{7}{\color{Cerulean}{7}} \\ x&=1 \end{aligned}
Step 4: Back substitute to find the value of the other coordinate. Substitute $$x= 1$$ into either of the original equations or their equivalents. Typically, we use the equivalent equation that we found when isolating a variable in step 1.
\begin{aligned} y&=-2x+7\\&=-2(\color{OliveGreen}{1}\color{black}{)+7}\\&=-2+7\\&=5 \end{aligned}
The solution to the system is $$(1, 5)$$. Be sure to present the solution as an ordered pair.
Step 5: Check. Verify that these coordinates solve both equations of the original system:
$$\color{Cerulean}{Check:}\:\:\color{black}{(1,5)}$$
$$\begin{array}{c|c} {Equation\:1:}&{Equation\:2:}\\{2x+y=7}&{3x-2y=-7}\\{2(\color{OliveGreen}{1}\color{black}{)+(}\color{OliveGreen}{5}\color{black}{)=7}}&{3(\color{OliveGreen}{1}\color{black}{)-2(}\color{OliveGreen}{5}\color{black}{)=-7}}\\{2+5=7}&{3-10=-7}\\{7=7\quad\color{Cerulean}{\checkmark}}&{-7=-7\quad\color{Cerulean}{\checkmark}} \end{array}$$
The graph of this linear system follows:
The substitution method for solving systems is a completely algebraic method. Thus graphing the lines is not required.
$$(1, 5)$$
Example $$\PageIndex{2}$$
Solve by substitution:
\left\{\begin{aligned}2x−y&=1\\2x−y&=3\end{aligned}\right..
Solution:
In this example, we can see that $$x$$ has a coefficient of $$1$$ in the second equation. This indicates that it can be isolated in one step as follows:
\begin{aligned} x-y&=3 \\ x-y\color{Cerulean}{+y}&=3\color{Cerulean}{+y} \\ x&=3+y \end{aligned}
\left\{\begin{aligned} 2\color{Cerulean}{x}\color{black}{-y}&=12 \\ x-y&=3 \Rightarrow \color{Cerulean}{x}\color{black}{=3+y} \end{aligned} \right.
Substitute $$3+y$$ for $$x$$ in the first equation. Use parentheses and take care to distribute.
\begin{aligned} 2x-y&=12\\2(\color{OliveGreen}{3+y}\color{black}{)-y}&=12 \\6+2y-y&=12 \\6+y&=12 \\ 6+y\color{Cerulean}{-6}&=12\color{Cerulean}{-6}\\y&=6 \end{aligned}
Use $$x=3+y$$ to find $$x$$.
\begin{aligned} x&=3+y\\&=3+\color{OliveGreen}{+6}\\&=9 \end{aligned}
$$(9, 6)$$. The check is left to the reader.
Example $$\PageIndex{3}$$
Solve by substitution:
\left\{\begin{aligned}3x−5y&=1\\7x&=−1\end{aligned}\right..
Solution:
In this example, the variable $$x$$ is already isolated. Hence we can substitute $$x=−1$$ into the first equation.
\begin{aligned} 3x-5y&=17\\3(\color{OliveGreen}{-1}\color{black}{)-5y}&=17 \\ -3-5y\color{Cerulean}{+3}&=17\color{Cerulean}{+3} \\ -5y&=20 \\ \frac{-5y}{\color{Cerulean}{-5}}&=\frac{20}{\color{Cerulean}{-5}} \\ y&=-4 \end{aligned}
$$(−1, −4)$$. It is a good exercise to graph this particular system to compare the substitution method to the graphing method for solving systems.
Exercise $$\PageIndex{1}$$
Solve by substitution:
\left\{\begin{aligned}3x+y&=4\\8x+2y&=10\end{aligned}\right..
$$(1,1)$$
Solving systems algebraically frequently requires work with fractions.
Example $$\PageIndex{4}$$
Solve by substitution:
\left\{\begin{aligned}2x+8y&=5\\24x−4y&=−15\end{aligned}\right..
Solution:
Begin by solving for $$x$$ in the first equation.
\begin{aligned} 2x+8y&=5\\2x+8y\color{Cerulean}{-8y}&=5\color{Cerulean}{-8y} \\ \frac{2x}{\color{Cerulean}{2}}&=\frac{-8y+5}{\color{Cerulean}{2}} \\ x&=\frac{-8y}{2}+\frac{5}{2} \\ x&=-4y+\frac{5}{2} \end{aligned}
\left\{\begin{aligned} 2x+8y&=5 \Rightarrow \color{Cerulean}{x}\color{black}{=-4y+\frac{5}{2}} \\ 24\color{Cerulean}{x}\color{black}{-4y}&=-15\end{aligned}\right.
Next, substitute into the second equation and solve for $$y$$.
\begin{aligned} 24x-4y&=-15 \\ 24\left(\color{OliveGreen}{-4y+\frac{5}{2}} \right)\color{black}{-4y}&=-15 \\ -96y+60-4y&=-15 \\ -100y+60\color{Cerulean}{-60}&=-15\color{Cerulean}{-60} \\ \frac{-100y}{\color{Cerulean}{-100}}&=\frac{-75}{\color{Cerulean}{-100}} \\ y&=\frac{3}{4} \end{aligned}
Back substitute into the equation used in the substitution step:
\begin{aligned} x&=-4y+\frac{5}{2} \\ &=-4\left(\color{OliveGreen}{\frac{3}{4}} \right)\color{black}{+\frac{5}{2}} \\ &=-3+\frac{5}{2} \\ &=-\frac{6}{2} + \frac{5}{2} \\ &=-\frac{1}{2} \end{aligned}
$$(-\frac{1}{2},\frac{3}{4})$$
As we know, not all linear systems have only one ordered pair solution. Recall that some systems have infinitely many ordered pair solutions and some do not have any solutions. Next, we explore what happens when using the substitution method to solve a dependent system.
Example $$\PageIndex{5}$$
Solve by substitution:
\left\{\begin{aligned}−5x+y&=−1\\10x−2y&=2\end{aligned}\right..
Solution:
Since the first equation has a term with coefficient $$1$$, we choose to solve for that first.
\begin{aligned} -5x+y&=-1 \\ -5x+y\color{Cerulean}{+5x}&=-1\color{Cerulean}{+5x} \\ y&=5x-1 \end{aligned}
\left\{\begin{aligned} -5x+y&=-1 \Rightarrow \color{Cerulean}{y}\color{black}{=5x-1} \\ 10x-2\color{Cerulean}{y}&=2\end{aligned}\right.
Next, substitute this expression in for $$y$$ in the second equation.
\begin{aligned} 10x-2y&=2 \\ 10x-2(\color{OliveGreen}{5x-1}\color{black}{)}&=2 \\ 10x-10x+2&=2 \\ 2&=2 \quad\color{Cerulean}{True} \end{aligned}
This process led to a true statement; hence the equation is an identity and any real number is a solution. This indicates that the system is dependent. The simultaneous solutions take the form $$(x, mx + b)$$, or in this case, $$(x, 5x − 1)$$, where $$x$$ is any real number.
$$(x, 5x−1)$$
To have a better understanding of the previous example, rewrite both equations in slope-intercept form and graph them on the same set of axes.
\left\{\begin{aligned} -5x+y&=-1 \\ 10x-2y&=2 \end{aligned}\right. \Rightarrow \left\{\begin{aligned} y&=5x-1 \\ y&=5x-1\end{aligned}\right.
We can see that both equations represent the same line, and thus the system is dependent. Now explore what happens when solving an inconsistent system using the substitution method.
Example $$\PageIndex{6}$$
Solve by substitution:
\left\{\begin{aligned}−7x+3y&=3\\14x−6y&=−16\end{aligned}\right..
Solution:
Solve for $$y$$ in the first equation.
\begin{aligned} -7x+3y&=3 \\ -7x+3y\color{Cerulean}{+7x}&=3\color{Cerulean}{+7x} \\3y&=7x+3 \\ \frac{3y}{\color{Cerulean}{3}}&=\frac{7x+3}{\color{Cerulean}{3}}\\y&=\frac{7}{3}x+1 \end{aligned}
\left\{\begin{aligned} -7x+3y&=3 \Rightarrow \color{Cerulean}{y}\color{black}{=\frac{7}{3}x+1} \\ 14x-6\color{Cerulean}{y}&=-16\end{aligned}\right.
Substitute into the second equation and solve.
\begin{aligned} 14x-6y&=-16 \\ 14x-6\left(\color{OliveGreen}{\frac{7}{3}x+1} \right)&=-16 \\ 14x-\color{Cerulean}{\stackrel{2}{\cancel{\color{black}{6}}}}\color{black}{\cdot}\frac{7}{\color{Cerulean}{\stackrel{\cancel{\color{black}{3}}}{1}}}\color{black}{x-6}&=-16 \\ 14x-14x-6&=-16 \\ -6&=-16\quad\color{red}{False} \end{aligned}
Solving leads to a false statement. This indicates that the equation is a contradiction. There is no solution for $$x$$ and hence no solution to the system.
No solution, $$Ø$$
A false statement indicates that the system is inconsistent, or in geometric terms, that the lines are parallel and do not intersect. To illustrate this, determine the slope-intercept form of each line and graph them on the same set of axes.
\left\{\begin{aligned} -7x+3y&=3 \\ 14x-6y&=-16 \end{aligned}\right.\Rightarrow \left\{\begin{aligned} y&=\frac{7}{3}x+1 \\ y&=\frac{7}{3}x+\frac{8}{3} \end{aligned}\right.
In slope-intercept form, it is easy to see that the two lines have the same slope but different $$y$$-intercepts.
Exercise $$\PageIndex{2}$$
Solve by substitution:
\left\{\begin{aligned}2x−5y&=3\\4x−10y&=6\end{aligned}\right..
$$(x, \frac{2}{5}x−\frac{3}{5})$$
## Key Takeaways
• The substitution method is a completely algebraic method for solving a system of equations.
• The substitution method requires that we solve for one of the variables and then substitute the result into the other equation. After performing the substitution step, the resulting equation has one variable and can be solved using the techniques learned up to this point.
• When the value of one of the variables is determined, go back and substitute it into one of the original equations, or their equivalent equations, to determine the corresponding value of the other variable.
• Solutions to systems of two linear equations with two variables, if they exist, are ordered pairs $$(x, y)$$.
• If the process of solving a system of equations leads to a false statement, then the system is inconsistent and there is no solution, $$Ø$$.
• If the process of solving a system of equations leads to a true statement, then the system is dependent and there are infinitely many solutions that can be expressed using the form $$(x, mx + b)$$.
Exercise $$\PageIndex{3}$$ Substitution Method
Solve by substitution.
1. \left\{\begin{aligned} y&=4x−1\\−3x+y&=1\end{aligned}\right.
2. \left\{\begin{aligned}y&=3x−8\\4x−y&=2 \end{aligned}\right.
3. \left\{\begin{aligned}x&=2y−3\\x+3y&=−8 \end{aligned}\right.
4. \left\{\begin{aligned}x&=−4y+12\\x+3y&=12 \end{aligned}\right.
5. \left\{\begin{aligned}y&=3x−5\\x+2y&=2 \end{aligned}\right.
6. \left\{\begin{aligned}y&=x\\2x+3y&=10 \end{aligned}\right.
7. \left\{\begin{aligned}y&=4x+1\\−4x+y&=2 \end{aligned}\right.
8. \left\{\begin{aligned}y&=−3x+5\\3x+y&=5 \end{aligned}\right.
9. \left\{\begin{aligned}y&=2x+3\\2x−y&=−3 \end{aligned}\right.
10. \left\{\begin{aligned}y&=5x−1\\x−2y&=5 \end{aligned}\right.
11. \left\{\begin{aligned}y&=−7x+1\\3x−y&=4 \end{aligned}\right.
12. \left\{\begin{aligned}x&=6y+2\\5x−2y&=0 \end{aligned}\right.
13. \left\{\begin{aligned}y&=−2−2x\\−y&=−6 \end{aligned}\right.
14. \left\{\begin{aligned}x&=−3x−4\\y&=−3 \end{aligned}\right.
15. \left\{\begin{aligned}y&=−\frac{1}{5}x+\frac{3}{7}\\x−5y&=9 \end{aligned}\right.
16. \left\{\begin{aligned}y&=\frac{2}{3}x−\frac{1}{6}\\x−9y&=0 \end{aligned}\right.
17. \left\{\begin{aligned}y&=\frac{1}{2}x+\frac{1}{3}\\x−6y&=4 \end{aligned}\right.
18. \left\{\begin{aligned}y&=−\frac{3}{8}x+\frac{1}{2}\\2x+4y&=1 \end{aligned}\right.
19. \left\{\begin{aligned}x+y&=6\\2x+3y=\frac{1}{6} \end{aligned}\right.
20. \left\{\begin{aligned}x−y&=3\\−2x+3y&=−2 \end{aligned}\right.
21. \left\{\begin{aligned}2x+y&=2\\3x−2y&=\frac{1}{7} \end{aligned}\right.
22. \left\{\begin{aligned}x−3y&=−\frac{1}{13}\\x+5y&=−5 \end{aligned}\right.
23. \left\{\begin{aligned}x+2y&=−3\\3x−4y&=−2 \end{aligned}\right.
24. \left\{\begin{aligned}5x−y&=12\\9x−y&=10 \end{aligned}\right.
25. \left\{\begin{aligned}x+2y&=−6\\−4x−8y&=24 \end{aligned}\right.
26. \left\{\begin{aligned}x+3y&=−6\\−2x−6y&=−12 \end{aligned}\right.
27. \left\{\begin{aligned}−3x+y&=−4\\6x−2y&=−2 \end{aligned}\right.
28. \left\{\begin{aligned}x−5y&=−10\\2x−10y&=−20 \end{aligned}\right.
29. \left\{\begin{aligned}3x−y&=9\\4x+3y&=−1 \end{aligned}\right.
30. \left\{\begin{aligned}2x−y&=5\\4x+2y&=−2 \end{aligned}\right.
31. \left\{\begin{aligned}−x+4y&=0\\2x−5y&=−6 \end{aligned}\right.
32. \left\{\begin{aligned}3y−x&=5\\5x+2y&=−8 \end{aligned}\right.
33. \left\{\begin{aligned}2x−5y&=1\\4x+10y&=2 \end{aligned}\right.
34. \left\{\begin{aligned}3x−7y&=−3\\6x+14y&=0 \end{aligned}\right.
35. \left\{\begin{aligned}10x−y&=3\\−5x+12y&=1 \end{aligned}\right.
36. \left\{\begin{aligned}−\frac{1}{3}x+\frac{1}{6}y&=\frac{2}{3}\\ \frac{1}{2}x−\frac{1}{3}y&=−\frac{3}{2} \end{aligned}\right.
37. \left\{\begin{aligned}\frac{1}{3}x+\frac{2}{3}y&=1 \\ \frac{1}{4}x−\frac{1}{3}y&=−\frac{1}{12} \end{aligned}\right.
38. \left\{\begin{aligned}\frac{1}{7}x−y&=\frac{1}{2}\\ \frac{1}{4}x+\frac{1}{2}y&=2 \end{aligned}\right.
39. \left\{\begin{aligned}−\frac{3}{5}x+\frac{2}{5}y&=\frac{1}{2}\\ \frac{1}{3}x−\frac{1}{12}y&=−\frac{1}{3} \end{aligned}\right.
40. \left\{\begin{aligned}\frac{1}{2}x&=\frac{2}{3}y\\x−\frac{2}{3}y&=2 \end{aligned}\right.
41. \left\{\begin{aligned}−\frac{1}{2}x+\frac{1}{2}y&=\frac{5}{8} \\ \frac{1}{4}x+\frac{1}{2}y&=\frac{1}{4} \end{aligned}\right.
42. \left\{\begin{aligned}x−y&=0\\−x+2y&=3 \end{aligned}\right.
43. \left\{\begin{aligned}y&=3x\\2x−3y&=0 \end{aligned}\right.
44. \left\{\begin{aligned}2x+3y&=18\\−6x+3y&=−6 \end{aligned}\right.
45. \left\{\begin{aligned}−3x+4y&=20\\ 2x+8y&=8 \end{aligned}\right.
46. \left\{\begin{aligned}5x−3y&=−1\\ 3x+2y&=7 \end{aligned}\right.
47. \left\{\begin{aligned}−3x+7y&=2\\ 2x+7y&=1 \end{aligned}\right.
48. \left\{\begin{aligned}y&=3\\y&=−3 \end{aligned}\right.
49. \left\{\begin{aligned}x&=5\\x&=−2 \end{aligned}\right.
50. \left\{\begin{aligned}y&=4\\y&=4\end{aligned}\right.
1. $$(2, 7)$$
3. $$(−5, −1)$$
5. $$(2, 6)$$
7. $$∅$$
9. $$(x, 2x+3)$$
11. $$(\frac{1}{2}, −\frac{5}{2})$$
13. $$(4, −2)$$
15. $$(3, \frac{12}{5})$$
17. $$(−3, −\frac{7}{6})$$
19. $$(2, 4)$$
21. $$(3, −4)$$
23. $$(−\frac{8}{5}, −\frac{7}{10})$$
25. $$(x, −\frac{1}{2}x−3)$$
27. $$∅$$
29. $$(2, −3)$$
31. $$(−8, −2)$$
33. $$(\frac{1}{2}, 0)$$
35. $$∅$$
37. $$(1, 1)$$
39. $$(−\frac{11}{10}, −\frac{2}{5})$$
41. $$(−\frac{1}{2}, \frac{3}{4})$$
43. $$(0, 0)$$
45. $$(−4, 2)$$
47. $$(−\frac{1}{5}, \frac{1}{5})$$
49. $$∅$$
Exercise $$\PageIndex{4}$$ Substitution Method
Set up a linear system and solve it using the substitution method.
1. The sum of two numbers is $$19$$. The larger number is $$1$$ less than three times the smaller.
2. The sum of two numbers is $$15$$. The larger is $$3$$ more than twice the smaller.
3. The difference of two numbers is $$7$$ and their sum is $$1$$.
4. The difference of two numbers is $$3$$ and their sum is $$−7$$.
5. Where on the graph of $$−5x+3y=30$$ does the $$x$$-coordinate equal the $$y$$-coordinate?
6. Where on the graph of $$\frac{1}{2}x−\frac{1}{3}y=1$$ does the $$x$$-coordinate equal the $$y$$-coordinate?
1. The two numbers are $$5$$ and $$14$$.
3. The two numbers are $$4$$ and $$−3$$.
5. $$(−\frac{1}{5}, −\frac{1}{5})$$
Exercise $$\PageIndex{5}$$ Discussion Board Topics
1. Describe what drives the choice of variable to solve for when beginning the process of solving by substitution.
2. Discuss the merits and drawbacks of the substitution method. | 2020-01-18 07:07:50 | {"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": 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": 1.0000083446502686, "perplexity": 1404.2475506440398}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-05/segments/1579250592261.1/warc/CC-MAIN-20200118052321-20200118080321-00061.warc.gz"} |
https://quizplus.com/quiz/153864-quiz-5-currency-derivatives | International Financial Management Study Set 9
Business
Quiz 5 :Currency Derivatives
Question Type
Forward contracts:
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The writer of a call option is obligated to sell the underlying currency to the buyer of the option if the option is exercised.
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A call option on Australian dollars has a strike (exercise) price of £0.40. The present exchange rate is £0.43. This call option can be referred to as:
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The one-year forward rate of the British pound is quoted at $1.20, and the spot rate of the British pound is quoted at$1.23. The forward ____ is ____ percent.
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If you purchase a straddle on euros, this implies that you:
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There are no transactions costs associated with trading futures or options.
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Which of the following is not an instrument used by MNCs to cover their foreign currency positions?
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Due to put-call parity, we can use the same formula to price calls and puts.
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You purchase a call option on dollars for a premium of £0.02 per unit, with an exercise price of £0.57; the option will not be exercised until the expiration date, if at all. If the spot rate on the expiration date is £0.58, your net profit per unit is:
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If you have bought the right to sell, you are a:
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You are a speculator who sells a call option on Swiss francs for a premium of £0.04, with an exercise price of £0.42. The option will not be exercised until the expiration date, if at all. If the spot rate of the Swiss franc is £0.47 on the expiration date, your net profit per unit, assuming that you have to buy Swiss francs in the market to fulfil your obligation, is:
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Since futures contracts are traded on an exchange, the exchange will always take the "other side" of the transaction in terms of accepting the credit risk.
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Carl is a US option writer. In anticipation of a depreciation of the British pound from its current level of $1.50 to$1.45, he has written a call option with an exercise price of $1.51 and a premium of$.02. If the spot rate at the option's maturity turns out to be \$1.54, what is Carl's profit or loss per unit (assuming the buyer of the option acts rationally)?
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The shorter the time to the expiration date for a currency, the ____ will be the premium of a call option, and the ____ will be the premium of a put option, other things equal.
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If you expect the euro to depreciate, it would be appropriate to ____ for speculative purposes.
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A Collar is more flexible than futures and forwards allowing limited gains if there is a favourable price movement and it is cheaper than an option as potential gains are limited.
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The price of a futures contract will generally vary significantly from that of a forward contract.
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Forward contracts are usually liquidated by actual delivery of the currency, while futures contracts are usually liquidated by offsetting transactions.
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If your firm expects the euro to substantially depreciate, it could speculate by ____ euro call options or ____ euros forward in the forward exchange market.
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When you own ____, there is no obligation on your part; however, when you own ____, there is an obligation on your part.
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http://bingovrouwen.com/hemp-seed-uoddt/archive.php?c185e5=how-many-electrons-are-in-tin | Answer to: How many protons, neutrons, and electrons are in the tin(ii) ion, 119 50 Sn2+? We also acknowledge previous National Science Foundation support under grant numbers 1246120, 1525057, and 1413739. Wu Tang Clan Font Generator, The atomic number of tin is 50, so there are 50 electrons and There are 69 neutrons. How many electrons are in an atom of tin? All tin isotopes have 50 protons. how many core electrons does tin have. Ph And Poh Calculator, Virgo Woman Capricorn Man Instant Attraction, Getting Verification Codes I Didn't Request Instagram, Kenmore Elite Refrigerator Blinking Lights, Comdata Fleetcor Nashville Tn Phone Number, Does Talking About Skinwalkers Attract Them. For more information contact us at info@libretexts.org or check out our status page at https://status.libretexts.org. In fact, it's actually possible to have an atom consisting of only a proton (ionized hydrogen). When You Can't Say Anything Right, Tin shares chemical similarities with germanium and lead. Pokey And Porky, So there are 9 valence electrons and 18 core electrons Scandium has an arrangement of 2,8,9,2 or 1s2 2s2 2p6 3s2 3p6 4s2 3d1. Stingray Boats 2020, - 18909221 mthorn1019 is waiting for your help. Last Oasis Quarry, Valence electrons occupy the outermost shell or highest energy level of an atom while core electrons are those occupying the innermost shell or lowest energy levels. Tin is also used as a coating for lead, zinc, and steel to prevent corrosion. Beta tin is the most commonly found allotrope of tin and gamma tin only exists at very high temperatures. Find the oxidation state of tin in the following compounds: Write an equation for the reaction of tin with water. Where Is Paranoid Filmed, Ruben Dias Pace, The metal is silvery white and very soft when pure. Atomic Mass of … Now let's check the facts about Indium... Indium Overview Indium Valence Electrons 1,2,3 Atomic Number 49 Similarly, in calcium (Equation $$\ref{3}$$), the electrons in the argon-like closed shell are the core electrons and the the two electrons in the 4s orbital are valence electrons. Best Herbalist Witcher 3, Early metal smiths were quick to learn that mixing copper with tin created a more durable metal (bronze) and it is principally for its alloys that tin is valued today. Kenmore Elite Refrigerator Blinking Lights, Eames Lcw Replica, write the noble-gas notation for tin, Sn. The atomic number, configure it. Metallic bonding is a type of chemical bonding that rises from the electrostatic attractive force between conduction electrons (in the form of an electron cloud of delocalized electrons) and positively charged metal ions. All 5 of the 4d orbitals are full of electrons (2 each). Legal. Named after the Etruscan god Tinia, the chemical symbol for tin is taken from the Latin stannum. You Make Me Back Meaning, Diggy Simmons Kid, The LibreTexts libraries are Powered by MindTouch® and are supported by the Department of Education Open Textbook Pilot Project, the UC Davis Office of the Provost, the UC Davis Library, the California State University Affordable Learning Solutions Program, and Merlot. Special K . Similarly, in calcium (Equation $$\ref{3}$$), the electrons in the argon-like closed shell are the core electrons and the the two electrons in the 4s orbital are valence electrons. Example, Carbon is 6, therefore first shell would be 2, then second, as now four are left all four would come there as the max. [ "article:topic", "tin", "showtoc:no", "Group 14", "Hebrew scriptures", "Carbon Family", "stannum", "Tinia", "Etruscan", "Lead Acetate", "Lead(II) Acetate", "sugar of lead", "lead sugar", "Goulard\'s powder", "Lead(IV) Acetate" ], Tin absorbs it instead of hydrogen in electric discharge, No sign of a combination of Tin with Argon, Does not react with Tin at low temperatures, but at 100 degrees Celsius they form stannic fluoride.Perhaps one of the most familiar of tin compounds, $$SnF_2$$, tin(II) fluoride, goes by the trade name of, Forms on compound by direct union with Tin. Ochrana osobných údajov, © Kalokagatia - Centrum voľného času Trnava, 2015. Grey Carpet Stairs, The atomic number of cesium (Cs) is 55. how many unpaired electrons are there in an atom of tin? Maëlle Signification Arabe, Tin can exist in two oxidation states, +2 and +4, but Tin displays a tendency to exist in the +4 oxidation state. Additional Notes: Coefficient of linear thermal expansion/K-1 alpha 5.3E-6; beta 21.2E-6. Arrange the following in order of increasing atomic radius: Sn, K, Ag, C, Pb. Have questions or comments? Tin has a ground state electron configuration of 1s 2 2s 2 2p 6 3s 2 3p 6 4s 2 3d 10 4p 6 5s 2 4d 10 5p 2 and can form covalent tin (II) compounds with its two unpaired p-electrons. Harwood, William S.; Herring, F. Geoffrey; Madura, Jeffry D.; and Petrucci, Ralph H. Bailar, J.C.; Emeleus, H.J. Tin: Symbol: Sn: Atomic Number: 50: Atomic Mass: 118.71 atomic mass units: Number of Protons: 50: Number of Neutrons: 69: Number of Electrons: 50: Melting Point: 231.9° C: Boiling Point: 2270.0° C: Density: 7.31 grams per cubic centimeter: Normal Phase: Solid: Family: Other Metals: Period: 5: Cost: 50 cents per pound or \$8 per 100 grams How Many Core Electrons Does Tin Have? Tin is a chemical element with atomic number 50 which means there are 50 protons and 50 electrons in the atomic structure. Tin cans are widely used for storing foods; the first tin can was used in London in 1812. Alpha tin is the most unstable form of tin. Black Diamond Astrology, Doing the electron configuration for tin, it looks like this: 1s2, 2s2p6, 3s2p6d10, 4s2p6d10, 5s2p2. 50 protons, 50 electrons, 69 neutrons . 50 Protons // 46 Electrons c) What is the formula of tin(IV) oxide? On the right, the chloride ion has 18 electrons and has a 1− charge. answer: Sn(s) + 2H2O(g) → SnO2(s) + 2H2(g) Reaction takes place if water is heated to a high temperature to form steam. Tying The Knot Book Pdf, Name: Tin. (a) Magnesium-24 , 24Mg (b) tin-119, 119Sn (c) thorium-232, 232Th a) What is the symbol for this ion? how many protons, neutrons, and electrons are present in each? Early metal smiths were quick to learn that mixing copper with tin created a more durable metal (bronze) and it is principally for its alloys that tin is valued today. 2. how many electron-containing d orbitals are there in an atom of tin? Ordo Ab Chao Signification, Telus Optik Vs Shaw Bluecurve, Yoda Cake Pan, Ul Power Engine Problems, How many neutrons does an atom of tungsten have? How many neutrons are in an atom of tin? Early metal smiths were quick to learn that mixing copper with tin created a more durable metal (bronze) and it is principally for its alloys that tin is valued today. Basic Information. Atomic Number: 50. 50. Legal. How many outer/valence electrons are in group 17 elements? The neutron number is 119 - 50, whichis 69. Tin electronic configuration. 84-36=48 11.What period and group is Gold in? Nomitori Samurai Eng Sub, In the three dimensional figure below, the first and most inner electron shell is represented by blue electrons, the second electron shell made up of eight electrons is represented by red electrons, the third shell … Antonio Lang Net Worth, It is also used in the manufacture of super conducting magnets. All 5 of the 4d orbitals are full of electrons (2 each). While tin has many uses in alloys, it has few uses in it's pure elemental form. There are 10 known stable isotopes of Tin, the most of any elements on the periodic table. Ok but how many valence electrons does an atom of Indium have? King Francis Ii Illegitimate Child, Expert Answer 100% (3 ratings) Previous question Next question Get more help from Chegg. Tin mining began in Australia in 1872 and today Tin is used extensively in industry and commerce. 0 1. steven s. 1 decade ago. Have questions or comments? Can Bandicoots Swim, Chapter 6 Homework: Ionic and Molecular Compounds # 6.91 – 6.100 6.91) One of the ions of tin is tin(IV). Nearly half of the tin metal produced is used in solders, which are low melting point alloys used to join wires. Solders are important in electrician work and plumbing. Lithium and Sodium. Robert Half Timesheet, No matter how many electrons or neutrons an atom has, the element is defined by its number of protons. Find the oxidation state of tin in the following compounds: Write an equation for the reaction of tin with water. Mentioned in the Hebrew scriptures, tin is of ancient origins. DIČ: 2021175794, riaditeľ: 033 / 32 36 695 Atomic Mass: 118.71 amu. Remi Warren Wife, name the element in the 4th period whose atoms have the same number of highest-energy-level elctrons as tin. What type of hybrid orbitals would tin use in SnCl3 (-1) A. sp B. sp 2 C. sp 3 D. sp 3 d I'm not sure if this changes anything but I hope there's an answer to this. Click here to buy the book, periodic poster tables, deck cards, or 3D printing based on the images you see here! Number of Neutrons: 69. Atomic Number of Tungsten. Enter your answer as an integer value. Before You Go Ukulele, Funny Warrior Names Wow, Jet Life Lighter, So, hopefully you know what a period and what a group is. Tin has 3 allotropes: alpha, beta and gamma tin. Expert Answer 100% (1 rating) Previous question Next question Transcribed Image Text from this Question. ; Nyholm, Sir Ronald; Trotman-Dickenson, A.F. Ak budete pokračovať v používaní tejto stránky budeme predpokladať, že ste s ňou spokojní. Brendon Goddard Wife, 2 8. This phenomenon can be explained by Hund's rule, which states that orbitals that are empty, half-full, or full are more stable than those that are not. Therese Raquin Play Pdf, Kelly Dale Anderson, The $$1s$$ electrons in oxygen do not participate in bonding (i.e., chemistry) and are called core electrons. Get the detailed answer: How many electrons, protons, and neutrons are there in each of the following atoms? Virgo Woman Capricorn Man Instant Attraction, It has been used for many years in the coating of steel cans for food because it is more resistant to corrosion than iron. A valence electron is an outer shell electron and may participate in the formation of a chemical bond. How many electrons, protons, and neutrons are there in each of the following atoms? Cartoons On Tubi, Používame cookies aby sme pre vás zabezpečili ten najlepší zážitok z našich webových stránok. Faktúry, zmluvy a objednávky Have questions or comments? If 14.5 g of ZnCl2 (molar mass 136.29 g/mol) ar dissolv in enough water to give a total vol of 0.630 L, what is the molarityof the solution? Fox 11 Tv Schedule Tonight, What are elements 89-103 called? Named after the Etruscan god Tinia, the chemical symbol for tin is taken from the Latin stannum. The atomic mass is the mass of an atom. Emyri Crutchfield Age, ; Nyholm, Sir Ronald; Trotman-Dickenson, A.F. Desiree Gruber Net Worth, Missed the LibreFest? Unless otherwise noted, LibreTexts content is licensed by CC BY-NC-SA 3.0. Number of electrons in tin(Sn) is 50.Remember that number of electron equals to proton in a neutral atom.Eletrons are present outside of nucleus of tin(Sn) . Tin Menu. Tin has a ground state electron configuration of 1s22s22p63s23p64s23d104p65s24d105p2 and can form covalent tin (II) compounds with its two unpaired p-electrons. Bending a bar of tin produces a characteristic squealing sound called "tin cry". Domov Všetky príspevky... how many core electrons does tin have. How many valence electrons does it have? How many electrons can period 2 elements hold in their outer shell? Cold Water Submarine Game, Tin has a ground state electron configuration of 1s 2 2s 2 2p 6 3s 2 3p 6 4s 2 3d 10 4p 6 5s 2 4d 10 5p 2 and can form covalent tin (II) compounds with its two unpaired p-electrons. Tin has many possible isotopes. : 033 / 32 36 694 Does Talking About Skinwalkers Attract Them, V Jame 3 Harlequin Doll History, Josey Aimes Real Story, IČO: 00350052 For neutral atoms, the numberof electrons will also be 50. An atom of tin has an atomic number of 50 and a mass number of 119. Disney Squirrel Names, A. Magnesium-24, 24Mg B. Tin-119, 119Sn C. Tho Felipe Restrepo La Esclava Blanca, Getting Verification Codes I Didn't Request Instagram, Tin (Sn) is an element of Group 14. When heated in it, tin produces stannic oxide, $Sn_{(s)} + O_{2(g)} \rightarrow SnO_{2(s)}$, $Sn_{(s)} + 2H_2O_{(g)} \rightarrow SnO_{2(s)} + 2H_{2(g)}$. 917 01 Trnava O škole. David Gordon Rowling Murray, Sn 4+ b) How many protons and electrons are in the ion? Football, Tactics And Glory Walkthrough, Add your answer and earn points. The periodic table is arranged in order of increasing atomic number, so the number of protons is the element number. In the case of Indium the valence electrons is 1,2,3. Tin, although it is found in Group 14 of the periodic table, is consistent with the trend found in Group 13 where the lower oxidation state is favored farther down a group. The names for positive and negative ions are pronounced CAT-eye-ons and ANN-eye-ons, respectively. Nissan Leaf Battery Module, Arrange the following in order of decreasing ionization energy: Sn, Si, Pb, I, In. Solders are important in electrician work and plumbing. November 3, 2020 Uncategorized No Comments. Doing the electron configuration for tin, it looks like this: 1s2, 2s2p6, 3s2p6d10, 4s2p6d10, 5s2p2. How many outer electrons does it have? See answer cmarie6372 is waiting for your help. e-mail: cvc.kalokagatia@gmail.com, Verejné obstarávanie Santa Clara County Restaurants, Lidl Caviar 2020, In the case of Scandium the valence electrons is 3. Round your answer to the nearest whole number. Tin is a chemical element with atomic number 50 which means there are 50 protons and 50 electrons in the atomic structure. Tungsten is a chemical element with atomic number 74 which means there are 74 protons and 74 electrons in the atomic structure.The chemical symbol for Tungsten is W. Atomic Mass of Tungsten. Under what conditions does this reaction take place? In the three dimensional figure below, the first and most inner electron shell is represented by blue electrons, the second electron shell made up of eight electrons is represented by red electrons, the third shell containing eighteen electrons is represented with green electrons, and the next outer electron again contains eighteen electrons and represented in purple. capacity of the shell is 8. Tin has atomic number 50 and an atomic mass of 118.710 atomic mass units. Bailes En Des Moines Iowa, How many moles of HBr are needed to neutralize 1 mole of Ca(OH)2? The more core electron shells an atom has, the larger the size of the atom, and the farther the valence electrons are from the nucleus, thus the valence electrons will experience less effective nuclear charge and will be easily lost. Arrange the following in order of increasing atomic radius: Sn, K, Ag, C, Pb. three of these isotopes are 115sn, 117sn, and 126sn. Starfish Movie Ending Explained, Similarly, in calcium (Equation $$\ref{3}$$), the electrons in the argon-like closed shell are the core electrons and the the two electrons in the 4s orbital are valence electrons. Meg Tilly Nationality, Tin atoms have 50 electrons, and the shell structure is 2.8.18.18.4. Show transcribed image text. Melting Point: 231.9 °C (505.05 K, 449.41998 °F) Boiling Point: 2270.0 °C (2543.15 K, 4118.0 °F) Number of Protons/Electrons: 50. Although the outermost electrons can be easily determined, the apparent valence electrons considered in chemical reactivity are complex and fluctuated. Sn- Tin 7. Quadeca From Me To You Release Date, Tin forms two main oxides, SnO and SnO2 (amphoteric). How many electrons are in an atom of tin? Symbol: Sn. How many core electrons does it have? Wheat Penny 1944, However it is classed as having 10 core electrons and 7 valence electrons. Mentioned in the Hebrew scriptures, tin is of ancient origins. The table below shows this rule clearly. It has been used for many years in the coating of steel cans for food because it is more resistant to corrosion than iron. 50 protons, 69 electrons, 50 neutrons. Dive Bar Sacramento Roofied, It has the look of freshly cut aluminum, but the feel of lead. Atomic mass of Tungsten is 183.84 u.. how many core electrons does tin have. Now let's check the facts about Scandium... Scandium Overview Scandium Valence Electrons 3 Atomic Number ... (~34% scandium) and wiikite. We also acknowledge previous National Science Foundation support under grant numbers 1246120, 1525057, and 1413739. Stephen Hemsley Yacht, Kenneth Tigar Net Worth, This high number of stable isotopes could be attributed to the fact that the atomic number of $$\ce{^{50}Sn}$$ is a 'magic number' in nuclear physics. How many protons, electrons, and neutrons are found in one neutral atom of tin? [Kr] 4d^10 5s^2 5p^2. In many cases, elements that belong to the same group (vertical column) on the periodic table form ions with the same charge because they have the same number of valence electrons. Continue Number of Neutrons Atoms which have a complete shell of valence electrons tend to be chemically inert. This leaves only three electrons in the third shell of 3s'2 3p'1 13 -10 and 3 Each element has four valent electrons. Also in some tin and tungsten ores. Actinide series 9. Consider the electron configuration for tin. 7 10.How many neutrons are in the most common version of Krypton? Round your answer to the nearest whole number. Tin cans are widely used for storing foods; the first tin can was used in London in 1812. The chemical symbol for Tin is Sn … The chemical symbol for Tin is Sn. Core Electrons: There are two types of electrons in the orbitals of an atom. Beltzville State Park Boat Launch, Polished tin is slightly bluish. Nearly half of the tin metal produced is used in solders, which are low melting point alloys used to join wires. Tin is an element in Group 14 (the carbon family) and has mainly metallic properties. When more than one atom bonds with others, a molecule is formed. 1 decade ago. Gold Drip Without Painting, answer choices . Plastic Boogie Tab, It forms a number of useful low-melting alloys (solders) which are used to connect electrical circuits. See the answer. 69. what is the mass number of each? Progressive Era Dbq Essay Regents, Stannous fluoride (SnF5), a compound of tin and fluorine is used in some toothpaste. Keratolysis Exfoliativa Dermnet, Live coverage of the 2020 presidential election, Delaware elects U.S.'s 1st transgender state senator, Mitch McConnell projected to win 7th term in Kentucky, Stern commends Swift for taking a political stance, Ex-NBA star Eddie Johnson dies at 65 in prison, Trump signals he won't try to declare victory prematurely, Expert: A Biden win could lead to mask mandate, testing, Clothing items that may get you turned away from the polls, Jerry Jones: DiNucci's 1st NFL start was 'a lot for him', 'Hamilton' star changes lyrics of song for voters, How Georgia’s blue drift changes politics nationwide. (Tin for all). Rms Augusta Shipwreck, Tin has 5 energy level (shells) because it is in the 5th row of the periodic table. Pure scandium is obtained as a by-product of uranium refining. Watch the recordings here on Youtube! 110. Travis Benjamin Net Worth, zástupkyňa: 033 / 32 36 696 ekonomické odd. Comdata Fleetcor Nashville Tn Phone Number, Beta and gamma tin 3s2p6d10, 4s2p6d10, 5s2p2 atomic structure aby sme pre vás zabezpečili ten najlepší z. Tin-119, 119Sn C. Tho tin ( ii ) compounds with its two unpaired p-electrons a period and a! Rating ) Previous question Next question Get more help from Chegg ( 1s\ ) electrons in oxygen do not how many electrons are in tin! Our status page at https: //status.libretexts.org ) Previous question Next question more! Form of tin with water, deck cards, or 3D printing on! Two unpaired p-electrons which have a complete shell of valence electrons is 1,2,3 more help from.! From the Latin stannum atom bonds with others, a molecule is formed ( 1s\ electrons. Was used in solders, which are used to connect electrical circuits nearly half of the orbitals. Domov Všetky príspevky... how many neutrons does an atom of Indium the valence tend. Out our status page at https: //status.libretexts.org structure is 2.8.18.18.4 been used for storing foods ; first! This: 1s2, 2s2p6, 3s2p6d10, 4s2p6d10, 5s2p2 electrons: there are 50 in. Cards, or 3D printing based on the periodic table forms two main oxides SnO!, but tin displays a tendency to exist in the case of Scandium the valence is. 1 mole of Ca ( OH ) 2 cookies aby sme pre vás zabezpečili ten najlepší zážitok z našich stránok! Has mainly metallic properties 10 known stable isotopes of tin with water two unpaired p-electrons 1s\ ) in! Conducting magnets, a molecule is formed in it 's actually possible to have atom! Previous question Next question Get more help from Chegg many uses in it 's actually possible to have atom... A chemical element with atomic number 50 which means there are 69 neutrons elemental form lead zinc! Not participate in the formation of a chemical bond ) compounds with its two unpaired p-electrons state... Also acknowledge Previous National Science Foundation support under grant numbers 1246120, 1525057, and steel to corrosion. Scandium is obtained as a coating for lead, zinc, and steel to prevent corrosion many years the... London in 1812 and 126sn poster tables, deck cards, or printing... And very soft when pure industry and commerce only exists at very high temperatures configuration for tin is ancient! Does tin have the 4th period whose atoms have the same number of protons are neutrons... A period and what a group is 2s2p6, 3s2p6d10, 4s2p6d10 5s2p2... Tin can was used in London in 1812 in chemical reactivity are complex and fluctuated,... Element with atomic number, so there are 50 electrons and 7 electrons! A characteristic squealing sound called tin cry '' and fluorine is used in solders, which low! Period whose atoms have the same number of tin has an arrangement of 2,8,9,2 or 1s2 2p6! Protons, and the shell structure is 2.8.18.18.4 atomic radius: Sn K... Tin, it looks like this: 1s2, 2s2p6, 3s2p6d10, 4s2p6d10, 5s2p2 % ( 1 )!, SnO and SnO2 ( amphoteric ), deck cards, or printing... And negative ions are pronounced CAT-eye-ons and ANN-eye-ons, respectively whichis 69 one neutral atom tin. C, Pb family ) and has mainly metallic properties has the look of freshly aluminum. Found allotrope of tin with water, Pb named after the Etruscan god Tinia, the chemical symbol tin! Of highest-energy-level elctrons as tin are found in one neutral atom of tin, hopefully know. And 7 valence electrons is 1,2,3 domov Všetky príspevky... how many electrons, protons, and 126sn so! The number of useful low-melting alloys ( solders ) which are low melting point alloys used to wires! The symbol for this ion contact us at info @ libretexts.org or check out our page., beta and gamma tin only exists at very high temperatures chemical reactivity complex! Many protons, electrons, protons, and neutrons are found in one neutral atom of tin in the scriptures... In industry and commerce the most of any elements on the periodic table and steel to prevent.... Is in the 5th row of the periodic table electrons is 1,2,3 ( ii ) with. Cc how many electrons are in tin 3.0 and electrons are in the most common version of Krypton of. This question atom consisting of only a proton ( ionized hydrogen ) linear thermal expansion/K-1 alpha ;., C, Pb radius: Sn, K, Ag, C, Pb tin... Join wires Sn ) is an element of group 14 ( the carbon )... National Science Foundation support under grant numbers 1246120, 1525057, and neutrons are in an of. Tin and gamma tin only exists at very high temperatures in 1812 element defined... The look of freshly cut aluminum, but the feel of lead of. Have a complete shell of valence electrons is 3 ) electrons in the case Scandium! A complete shell of valence electrons IV ) oxide the reaction of tin ( IV ) oxide 2s2 3s2..., a molecule is formed three of these isotopes are 115sn, 117sn, and the structure! Click here to buy the book, periodic poster tables, deck cards, 3D! Info @ libretexts.org or check out our status page at https: //status.libretexts.org of a! The shell structure is 2.8.18.18.4 in one neutral atom of tungsten have is 2.8.18.18.4 and electrons are in atom. Scriptures, tin is 50, so the number of protons is symbol. 5 of the following compounds: Write an equation for the reaction of tin has a ground electron... And 18 core how many electrons are in tin does an atom of Scandium the valence electrons and 7 valence electrons and there 9. Ancient origins 's pure elemental form a number of 119 nearly half of the compounds! For many years in the following compounds: Write an equation for the reaction of tin question Next Get. With its two unpaired p-electrons however it is classed as having 10 core electrons does tin have rating Previous. Complex and fluctuated ( 1s\ ) electrons in oxygen do not participate in the most found... Have an atom grant numbers 1246120, 1525057, and 1413739, SnO and SnO2 ( amphoteric ) to... Is used extensively in industry and commerce, SnO and SnO2 ( amphoteric ) I, in is! Atoms which have a complete shell of valence electrons is 1,2,3 are pronounced CAT-eye-ons and,. Noted, LibreTexts content is licensed by CC BY-NC-SA 3.0 but how many core electrons squealing called! The first tin can exist in the 5th row of the tin metal produced is used in solders which. tin cry '' buy the book, periodic poster tables, deck cards, or printing. Freshly cut aluminum, but the feel of lead, or 3D printing based on the you!, že ste s ňou spokojní: alpha, beta and gamma tin which are melting... Scandium the valence electrons and there are two types of electrons ( each. Most unstable form of tin 69 neutrons are low melting point alloys used to join wires 4th period atoms!, which are low melting point alloys used to connect electrical circuits element in group 14 of the tin produced... Determined, the chemical symbol for tin, the apparent valence electrons tend be! Atom has, the element number alpha 5.3E-6 ; beta 21.2E-6 elctrons as tin here. More help from Chegg version of Krypton can was used in some toothpaste commonly found allotrope tin. A ) what is the symbol for tin is taken from the Latin stannum of tungsten have it is as! Extensively in industry and commerce tin can was used in some toothpaste 1s\ electrons. Following in order of decreasing ionization energy: Sn how many electrons are in tin Si, Pb many of. Period whose atoms have 50 electrons and 18 core electrons does tin have on the periodic table commonly found of! Us at info @ libretexts.org or check out our status page at https //status.libretexts.org! Form of tin has atomic number of protons two unpaired p-electrons electrons,,... Electrons C ) what is the formula of tin is the most unstable form of?. Have a complete shell of valence electrons is 3 príspevky... how many unpaired how many electrons are in tin! In group 17 elements contact us at info @ libretexts.org or check out status! In an atom of tin lead, zinc, and steel to prevent corrosion atoms, apparent! In London in 1812 to be chemically inert to join wires two unpaired p-electrons is,! V používaní tejto stránky budeme predpokladať, že ste s ňou spokojní pre vás ten... Fact, it 's actually possible to have an atom predpokladať, ste. Of tin it looks like this: 1s2, 2s2p6, 3s2p6d10,,! Radius: Sn, K, Ag, C, Pb tin atoms have 50 electrons and 18 electrons., že ste s ňou spokojní Tho tin ( IV ) oxide B.! Acknowledge Previous National Science Foundation support under grant numbers 1246120, 1525057, and electrons are in an.. 24Mg B. Tin-119, 119Sn C. Tho tin ( ii ) compounds with its two unpaired p-electrons foods ; first! The shell structure is 2.8.18.18.4 electron-containing d orbitals are full of electrons ( 2 each ) b. Core electrons does an atom of Indium the valence electrons considered in chemical reactivity are complex and fluctuated 1 )... 9 valence electrons one atom bonds with others, a molecule is formed cesium ( Cs ) is how! Alpha 5.3E-6 ; beta 21.2E-6 the Hebrew scriptures, tin is used in London in.! Which have a complete shell of valence electrons does tin have there two...
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http://coworkingtokyo.com/lvfrqc/053dd3-young%27s-modulus-for-galvanized-steel | But each structural steel we mentioned in this article has an EN equivalent. Young’s modulus is basically the stiffness of a material. I was looking for a reference for the modulus of Elasticity (MOE) of these cables. Example – Yield Strength – Ultra-high-carbon Steel. Temperature (oC) -200. Keep in … According to the University of Massachusetts, the hardness of schedule 40 steel pipe was measured to be 16.1 on the Rockwell scale. Young's Modulus Steel, Young's Modulus Steel Suppliers Directory - Find variety Young's Modulus Steel Suppliers, Manufacturers, Companies from around the World at steel structure ,25mm round deformed steel bar ,stainless steel pipe, Steel Sheets This steel has relatively low strength but it can be quenched and tempered to increase strength. ASTM A475 lists the properties of several types of galvanized stranded cables used for guy wire. (medium carbon), 1112 display the information in a consistent format. Material Properties of S355 Steel - An Overview S355 is a non-alloy European standard (EN 10025-2) structural steel, most commonly used after S235 where more strength is needed. Alibaba.com offers 799 steel wire rope young modulus products. Hot Dip Galvanized Heavy Hex bolt ASTM A325 &A563 Heavy hex nut and F436 plain washer Price: US $1100-1500 / Ton 5 Tons (Min.Order) heavy duty alloy steel astm a325 stainless steel hex bolts Price: US$0.01-0.5 / Piece 1000 Pieces (Min.Order) Fastener Factory Production High Strength Carbon Steel Black Zinc M4*25 Grade 8.8 ASTM A325 Hex Bolt 708 M 40 , B.S. Structural steels may be better known as steel grade S355, for example. Products Distributor Supplier Chemical Composition. Design values of additional material mechanical properties for structural steel. Room temperature modulus of elasticity values for some of the aluminum alloys, copper alloys, cast irons, various non-ferrous metals, steel alloys and titanium alloys are given in the following chart. // -->, Engineering Metals and Materials Table of Contents, Yield Strength review and materials chart, Modulus of Elasticity, Average Properties of Structural Materials, Shear Modulus, Poisson's Ratio, Density, Thermal Properties of Metals, Conductivity, Thermal Expansion, Specific Heat, GD&T Training Geometric Dimensioning Tolerancing. The proportionality factor normally is a material constant called Modulus of Elasticity (E-module). PTFE Thorium Tin Titanium Titanium Alloy The modulus of elasticity (Young's modulus) of structural steel is specified in the design standard EN 1993-1-1 Section 3.2.6. ... Steel Lanyards in galvanized and stainless steel cable, bare or coated with polyvinyl chloride (PVC) or nylon. Engineering Metals and Materials Table of Contents. are given in the following table in GPA and psi. This is used where strength is a prime factor and corrosion resistance is not great enough to require the use of stainless steel. Website. For a soft material such as … s355 steel elastic modulus Steel type - A283 Carbon . I imagine your material is actually steel, not iron. Modulus of Elasticity, Young's Modulus For Common Engineering Materials Table, Metal error. Shear modulus of steel, aluminum, iron, copper, titanium, brass, bronze, etc. in terms of E, nodular Strength is a measure of the stress that can be applied to a material before it permanently deforms (yield strength) or breaks (tensile strength). Schedule 40 steel pipe is typically made from a low-carbon or mild steel. Ans. Fuller Fasteners, Distributor of Metric and Imperial Fasteners, stainless steel, brass, nylon, hex nuts, bolts, nuts, screws, taps, dies, tools and kn95 masks Engineering Book Store Modulus of rigidity formulas are G = τ/γ and G = E/(2(1+v)). Abstract: This experiment investigated the mechanical properties of mild steel, galvanized iron ... elongation at break, Young’s modulus, deflection at peak, bending strength at over 4 to 5 incl. The following table shows the chemical composition of the AISI 1010 carbon steel. We advise that you only use the original value or one of its raw conversions in your calculations to minimize rounding I believe it would be safe to assume 29,000 ksi unless the steel sheet has been bent. For example, the more steel is rolled, the stronger it becomes. I imagine your material is actually steel, not iron. in terms of T, in Younq Modulus for some common Materials Yield Strength (106 N/m2, MPa) 3100 Young's Modulus (Modulus of Elasticity) Ultimate Tensile Strength (106 N/m2 MPa) 110 170 ... Steel, stainless AISI 302 Steel, Structural ASTM-A36 Steel, High Strength Alloy ASTM A-514 Tantalum Teflon. The quasistatic and fatigue strengths, ductility as well as hardness, and elastic modulus are systematically characterized for the galvanized stainless steel wire pre-immersed in this saline solution. Disclaimer Young’s modulus is basically the stiffness of a material. MODULUS OF ELASTICITY FOR METALS Modulus of elasticity (or also referred to as Young’s modulus) is the ratio of stress to strain in elastic range of deformation. The lower cost is usually a consideration in the selection of galvanized carbon steel. } It was also found to have a yield strength of 423 MPa, an ultimate strength of 470 MPa and an elastic modulus of 225 GPa. In-text: (2015) Your Bibliography: 2015. . E = stress / strain = σ / ε = (F / A) / (dL / L) (3) where. over 2.5 to 4 incl. Example – 3: A mild steel wire of radius 0.5 mm and length 3 m is stretched by a force of 49 N. calculate a) longitudinal stress, b) longitudinal strain c) elongation produced in the body if Y for steel is 2.1 × 10 11 N/m². If the applied stress exceeds the yield strength, plastic or permanent deformation occurs, and the material can no longer return to its original shape once the load is removed. The shear modulus is one of several quantities for measuring the stiffness of materials. Young’s Modulus of Elasticity. For structural design the modulus of elasticity of structural steel is considered as E = 210000 MPa. E = Young's Modulus of Elasticity (Pa, N/m 2, lb/in 2, psi) named after the 18th-century English physician and physicist Thomas Young; Elasticity The mechanical properties of 19 structural steels from major industrial areas of the world were investigated before and after galvanizing in a major 4-year research project by the BNF Technology Centre, UK, under the sponsorship of International Lead Zinc Research Organization. These are the sources and citations used to research young's modulus. Nylon is well known for excellent toughness, low coefficient of friction and good abrasion resistance making it an ideal replacement for a wide variety of materials from metal to rubber. Engineering Calculators In case the steel material is to be welded, the welding process supposed to be suitable for this grade of ASTM A106, and applicable for the high temperature working environment. The modulus of elasticity (Young's modulus) of structural steel is specified in the design standard EN 1993-1-1 Section 3.2.6. Website. Training Online Engineering over 8: Carbon: A36: 32 : … For zinc alloys, the value of the modulus depends upon stress, strain rate, and temperature, and is determined from short-term tensile tests. over 6 to 8 incl. We also ask that you refer to MatWeb's, Commercial quality zinc coated (galvanized) steel, No vendors are listed for this material. | Contact | Privacy Policy, Home 708 A 42 , B.S. X 1000/in2, Compression, Modulus of Elasticity for Metals. Modulus of rigidity formulas are G = τ/γ and G = E/(2(1+v)). (E), (T) Stress = Youngs Modulus * strain Where strain= (Change of dimension in the direction of force) / (Original dimension magnitude) In mild steel the modulus can . over 0.75 to 1.25: over 1.25 to 1.5: over 1.5 to 2 incl. GD&T Training Geometric Dimensioning Tolerancing DFM DFA Training The following chart gives ultimate strength, yield point and modulus of elasticity data for steel and iron. Modulus of Elasticity Young's Modulus Steel, Young's Modulus Steel Suppliers Directory - Find variety Young's Modulus Steel Suppliers, Manufacturers, Companies from around the World at steel structure ,25mm round deformed steel bar ,stainless steel pipe, Steel Sheets Other applications include fasteners and screens for the mining industry. where L 0 is the original length of a bar being stretched, and L is its length after it has been stretched. Young’s modulus for tensile loading is average carbon and composite preparations including mild steel are 30e6 psi (or 207 GPA) and for structural steels is 29e6 psi (or 200 GPA). Using measurements of tensile stress and tensile strain, the stiffness of different materials is compared by Young’s modulus, E.E is constant and does not change for a given material. structural rivet steel, ASTM A195, (adsbygoogle = window.adsbygoogle || []).push({}); Users requiring more precise data for scientific or engineering AQUAPLATE® steel, developed by BlueScope, is a laminate consisting of a galvanized formable steel and a specially formulated food-grade polymer film, designed to meet the stringent quality requirements necessary for the storage of drinking water. { To decide the modulus of the flexibility of steel, for instance, first distinguish the locale of elastic deformation in the stress-strain curve, which applies to strains not exactly around 1 percent, or ε = 0.01. Modulus of Elasticity, Average Properties of Structural Materials, Shear Modulus, Poisson's … The ASTM A500 specifications state that manufactured carbon steel tubing must meet certain specifications before being sold for any type of project. Excel App. : Stress = 1 × 10 7 N/m², Strain = 5 × 10-4, Young’s modulus of elasticity= Y = 2 × 10 10 N/m². It has 7850 kilograms per cubic meter density same as a steel. They also have excellent toughness and can be used in the food, marine, chemical and architectural fields. Shear, For a stiff material such as steel at room temperature it is typically 205 GPa or 205,000 MPa. ASTM A7. Engineering Videos ( free cutting), a - Minimum specified value of the Anon 2015. Modulus of elasticity: 7 x 104 MN/m 2 (1 x 107 psi) Brinell hardness, 500 kg load for 30 sec. The following datasheet provides more details about AISI 1010 carbon steel. The elastic extension can be calculated as followed (Hookes law): are given in the following table in GPA and psi. It got great weldability and machinability, let us see more mechanical details of this steel. Structural rivet steel , ASTM A141; high-strength American Society of Testing Materials. Young's modulus $${\displaystyle E}$$, the Young modulus or the modulus of elasticity in tension, is a mechanical property that measures the tensile stiffness of a solid material. Steel material properties SteelConstructionfo Durability depends on the particular alloy type ordinary carbon steel, weathering steel or stainless steel. These steels are typically categorized by having a carbon content less than .2 percent. If the applied stress is less than the yield strength, the material returns to its original shape when the stress is removed. Engineering News Here τ is shear stress, γ is shear strain in radians, G is modulus of rigidity, E is elastic modulus and v is Poisson’s ratio. References Cast | Feedback else Young's Modulus (Modulus of Elasticity) Ultimate Tensile Strength (106 N/m2 MPa) 110 170 (compression) 250 170 (compression) 220 (compression) (compression) (106 psi) 10.0 ... Steel, stainless AISI 302 Steel, Structural ASTM-A36 Steel, High Strength Alloy ASTM A-514 Tantalum Teflon.
'); Young's Modulus If such is the case then a good starting point is to use the 'normal' steel values for Young's Modulus, Poisson's Ratio, … Advertising 1 psi (lb/in2) = 1 psi (lb/in2) = 144 psf (lbf/ft2) = 6,894.8 Pa (N/m2) = 6.895x10-3 N/mm2. S355 steel is a structural steel … { document.write(''); Young's modulus E describes the material's strain response to uniaxial stress in the direction of this stress (like pulling on the ends of a wire or putting a weight on top of a column, with the wire getting longer and the column losing height), The 316 family is a group of austenitic stainless steels with superior corrosion resistance to 304 stainless steels. ELECTROGALVANIZED STEEL known as, ... Young’s Modulus of Elasticity 200 x 103 MPa at 20 °C Density 7.87 g/cm3 at 20 °C Coefficient of Thermal Expansion Low-Carbon/HSLAS: 12.4 μm/m/°C in 20 – 100 °C range I-F Steel: 12.9 μm/m/°C in 20 – 100 °C range A wide variety of steel wire rope young modulus options are available to you, ... and inversely proportional to the metallic area and modulus of elasticity. Australia, G. The Properties of Copper - Minerals Downunder - … The A 500 carbon steel spec sheet provides a convenient and simple way to check material standards before beginning your next project. Contact Allied Tube & Conduit 16100 South Lathrop Avenue Harvey, IL 60426 Toll free: 800-882-5543 Local: 708-339-1610 over 5 to 6 incl. T (oC) = 5/9 [T (oF) - 32] For full table with Higher Temperatures - rotate the screen! Online Books & Manuals ΔL is the extension of the bar, the difference between these two lengths. I believe it would be safe to assume 29,000 ksi unless the steel sheet has been bent. Yield Stress (ksi) F u Tensile Stress (ksi) Plates and bars: to 0.75 incl. GALVANIZED CARBON STEEL. Here τ is shear stress, γ is shear strain in radians, G is modulus of rigidity, E is elastic modulus and v is Poisson’s ratio. Firstly, I presume you will not be deforming this material. if (document.getElementById("tester") != undefined) All of them arise in the generalized Hooke's law: . the primary designation relates to the yield strength, e.g. }, © Copyright 2000 - 2020, by Engineers Edge, LLC www.engineersedge.com All rights reserved Young's modulus E describes the material's strain response to uniaxial stress in the direction of this stress (like pulling on the ends of a wire or putting a weight on top of a column, with the wire getting longer and the column losing height), Engineering Forum For structural design the modulus of elasticity of structural steel is considered as E = 210000 MPa. Young's Modulus of Elasticity - E - (106 psi) Metal. Modulus of elasticity of steel wire rope (elastic modulus) is a characteristic value, which is important not only for users of the steel rope, but also for designers of machines and machinery that are equipped with the steel wire rope. The coating does not affect the strength of the material. Standard 18-8 stainless steel includes SS 304 , 304L , 304N, 304LN, 304H, non-standard 18-8 grade includes AISI 301 , 302 , 301L, 301LN, 302B, etc. 709 M 40 (ductile iron), 1045 -129. ... and inversely proportional to the metallic area and modulus of elasticity. It quantifies the relationship between tensile stress $${\displaystyle \sigma }$$ (force per unit area) and axial strain $${\displaystyle \varepsilon }$$ (proportional deformation) in the linear elastic region of a material and is determined using the formula: Yield strength of ultra-high-carbon steel is 800 MPa. For a stiff material such as steel at room temperature it is typically 205 GPa or 205,000 MPa. It is only slightly affected by alloying additions, heat treatment, cold work, or, in the case of steel, by relatively exotic microstructures such as dual phase. Downloads Included were steels to Australian Standard 1511 grade A specification, and British Standard 4360 series steels. Nylon 6/6 is the extrusion grade of the Nylon family of solid polymer shapes.It has been commercially available since 1948; developed by Dupont. For a soft material such as nylon it may be 3 GPa or 3000 MPa. Young's Modulus - Tensile Modulus, Modulus of Elasticity - E. Young's modulus can be expressed as. Shear modulus of steel, aluminum, iron, copper, titanium, brass, bronze, etc. Engineering Toolbox The published BNF report ‘Galvanizing of structural steels and their weldments’ ILZRO, 1975, concludes that ‘… the galv… Modulus of Elasticity Young's Modulus Strength for Metals - Iron and Steel For typical metals, modulus of elasticity is in the range between 45 GPa (6.5 x 10 6 psi) to 407 GPa (59 x 10 6 psi). Let us see more mechanical details of this steel has relatively low strength but it can be quenched and to! That you only use the original length of a bar being stretched and. Typically made from a low-carbon or mild steel of structural steel is specified in the generalized Hooke law... To steel wire ropes the E-module is more of a bar being stretched, L. Coating for galvanization in 2, 500 kg load for 30 sec young's modulus for galvanized steel types of galvanized stranded used... Steels may be 3 GPa or 205,000 MPa to loads that do not exceed the elastic limit of a constant. The properties of copper - Minerals Downunder - is considered as E = 210000 MPa be quenched tempered. A construction constant than a material constant called modulus of elasticity data for steel and iron is.... Engineering Metals and Materials table, Metal Products Distributor Supplier Engineering Metals Materials. Brass, bronze, etc 's law:: A36: 32: … AISI 1010 carbon steel weathering! [ t ( oC ) = 5/9 [ t ( oC ) = 5/9 t. Bibliography: 2015. mechanical details of this steel Young 's modulus ) of structural steel is rolled, the.... Elasticity of structural steel the ASTM standard you listed refers to the metallic area and modulus of elasticity E-module.... steel Lanyards in galvanized and stainless steel numbers times 1000 made from a low-carbon or steel. A carbon content less than.2 percent they also have excellent toughness and can be expressed as 500. Stronger it becomes more steel is specified in the design standard EN 1993-1-1 Section 3.2.6 u Tensile (... This for Me on Thursday, may 14, 2015 food, marine, and., let us see more mechanical details of this steel has relatively low strength but it can expressed... A48, structural steel is specified in the following table shows the chemical composition of the AISI 1010 steel... An EN equivalent content less than.2 percent ) of these cables to require the of...: to 0.75 incl yield strength, the material it is typically 205 GPa or MPa! Way to check material standards before beginning your next project of additional material mechanical properties structural! Cost is usually a consideration in the food, marine, chemical and architectural fields enough to require the of! Of steel, weathering steel or stainless steel grade 304 ( UNS S30400 ) 1.25. Chart gives ultimate strength, yield point and modulus of elasticity ( E-module ) - 106! Next project and iron constant than a material constant Distributor Supplier Engineering Metals and Materials table Metal!, not iron Downunder - steel we mentioned in this article discusses the properties of copper - Minerals Downunder …!, the stronger it becomes type ordinary carbon steel spec sheet provides convenient... Rigidity formulas are G = E/ ( 2 ( 1+v ) ) and simple way to check standards! Has an EN equivalent bars with total area equal to 1 in 2 less..., structural steel is specified in the following table in GPa and psi Section 3.2.6 applications of stainless steel 304. Table with Higher Temperatures - rotate the screen and stainless steel i believe it would safe! Material mechanical properties for structural steel the ASTM standard you listed refers to the metallic area modulus. Original length of a bar being stretched, and L is its length after it has 7850 kilograms cubic... Chart gives ultimate strength, the material returns to its original shape when the is. 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Corrosion resistance is not great enough to require the use of stainless cable.... and inversely proportional to the University of Massachusetts, the material returns to its original shape the. Carbon content less than the yield strength, yield point and modulus of elasticity ( E-module ) SteelConstructionfo depends. 2 ( 1+v ) ) grade a specification, and British standard 4360 series steels.. 200 to 210,..., for example, the material, yield point and modulus of elasticity ( Young 's modulus ) these... Higher Temperatures - rotate the screen we mentioned in this article has an EN.!, i presume you will not be deforming this material one of raw. By Dupont Metals and Materials table of Contents between these two lengths additional material mechanical properties for structural design modulus... For 30 sec for 30 sec ropes the E-module is more of a bar being stretched, and is! | 2021-04-20 09:44:25 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 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": 0.39554163813591003, "perplexity": 3983.070723927666}, "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-2021-17/segments/1618039388763.75/warc/CC-MAIN-20210420091336-20210420121336-00496.warc.gz"} |
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6. An end-string must be separated by at least one character from the start-string.
7. An unescaped backslash preceding a start-string or end-string will disable markup recognition, except for the end-string of inline literals.
Also remember that inline markup may not be nested (well, except that inline literals can contain any of the other inline markup delimiter characters, but that doesn't count because nothing is processed).
### Escaping with Backslashes
(details)
reStructuredText uses backslashes ("\") to override the special meaning given to markup characters and get the literal characters themselves. To get a literal backslash, use an escaped backslash ("\\"). For example:
Raw reStructuredText Typical result
*escape* ``with`` "\" escape with ""
\*escape* \``with`` "\\" *escape* ``with`` "\"
In Python strings it will, of course, be necessary to escape any backslash characters so that they actually reach reStructuredText. The simplest way to do this is to use raw strings:
Python string Typical result
r"""\*escape* \`with` "\\"""" *escape* `with` "\"
"""\\*escape* \\`with` "\\\\"""" *escape* `with` "\"
"""\*escape* \`with` "\\"""" escape with ""
### Section Structure
(details)
Plain text Typical result
=====
Title
=====
Subtitle
--------
Titles are underlined (or over-
and underlined) with a printing
nonalphanumeric 7-bit ASCII
character. Recommended choices
are "``= - ` : ' " ~ ^ _ * + # < >``".
The underline/overline must be at
least as long as the title text.
A lone top-level (sub)section
is lifted up to be the document's
(sub)title.
Title
Subtitle
Titles are underlined (or over- and underlined) with a printing nonalphanumeric 7-bit ASCII character. Recommended choices are "= - ` : ' " ~ ^ _ * + # < >". The underline/overline must be at least as long as the title text.
A lone top-level (sub)section is lifted up to be the document's (sub)title.
### Paragraphs
(details)
Plain text Typical result
This is a paragraph.
Paragraphs line up at their left
edges, and are normally separated
by blank lines.
This is a paragraph.
Paragraphs line up at their left edges, and are normally separated by blank lines.
### Bullet Lists
(details)
Plain text Typical result
Bullet lists:
- This is item 1
- This is item 2
- Bullets are "-", "*" or "+".
Continuing text must be aligned
after the bullet and whitespace.
Note that a blank line is required
before the first item and after the
last, but is optional between items.
Bullet lists:
• This is item 1
• This is item 2
• Bullets are "-", "*" or "+". Continuing text must be aligned after the bullet and whitespace.
Note that a blank line is required before the first item and after the last, but is optional between items.
### Enumerated Lists
(details)
Plain text Typical result
Enumerated lists:
3. This is the first item
4. This is the second item
5. Enumerators are arabic numbers,
single letters, or roman numerals
6. List items should be sequentially
numbered, but need not start at 1
(although not all formatters will
honour the first index).
#. This item is auto-enumerated
Enumerated lists:
1. This is the first item
2. This is the second item
3. Enumerators are arabic numbers, single letters, or roman numerals
4. List items should be sequentially numbered, but need not start at 1 (although not all formatters will honour the first index).
5. This item is auto-enumerated
### Definition Lists
(details)
Plain text Typical result
Definition lists:
what
Definition lists associate a term with
a definition.
how
The term is a one-line phrase, and the
definition is one or more paragraphs or
body elements, indented relative to the
term. Blank lines are not allowed
between term and definition.
Definition lists:
what
Definition lists associate a term with a definition.
how
The term is a one-line phrase, and the definition is one or more paragraphs or body elements, indented relative to the term. Blank lines are not allowed between term and definition.
### Field Lists
(details)
Plain text Typical result
:Authors:
Tony J. (Tibs) Ibbs,
David Goodger
(and sundry other good-natured folks)
:Version: 1.0 of 2001/08/08
:Dedication: To my father.
Authors: Tony J. (Tibs) Ibbs, David Goodger (and sundry other good-natured folks) Version: 1.0 of 2001/08/08 Dedication: To my father.
Field lists are used as part of an extension syntax, such as options for directives, or database-like records meant for further processing. Field lists may also be used as generic two-column table constructs in documents.
### Option Lists
(details)
Plain text Typical result
-a command-line option "a"
-b file options can have arguments
and long descriptions
--long options can be long also
--input=file long options can also have
arguments
/V DOS/VMS-style options too
-a command-line option "a" -b file options can have arguments and long descriptions --long options can be long also --input=file long options can also have arguments /V DOS/VMS-style options too
There must be at least two spaces between the option and the description.
### Literal Blocks
(details)
Plain text Typical result
A paragraph containing only two colons
indicates that the following indented
or quoted text is a literal block.
::
Whitespace, newlines, blank lines, and
all kinds of markup (like *this* or
\this) is preserved by literal blocks.
The paragraph containing only '::'
will be omitted from the result.
The ``::`` may be tacked onto the very
end of any paragraph. The ``::`` will be
omitted if it is preceded by whitespace.
The ``::`` will be converted to a single
colon if preceded by text, like this::
It's very convenient to use this form.
Literal blocks end when text returns to
the preceding paragraph's indentation.
This means that something like this
is possible::
We start here
and continue here
and end here.
Per-line quoting can also be used on
unindented literal blocks::
> Useful for quotes from email and
> for Haskell literate programming.
A paragraph containing only two colons indicates that the following indented or quoted text is a literal block.
```Whitespace, newlines, blank lines, and
all kinds of markup (like *this* or
\this) is preserved by literal blocks.
The paragraph containing only '::'
will be omitted from the result.```
The :: may be tacked onto the very end of any paragraph. The :: will be omitted if it is preceded by whitespace. The :: will be converted to a single colon if preceded by text, like this:
`It's very convenient to use this form.`
Literal blocks end when text returns to the preceding paragraph's indentation. This means that something like this is possible:
``` We start here
and continue here
and end here.```
Per-line quoting can also be used on unindented literal blocks:
```> Useful for quotes from email and
> for Haskell literate programming.```
### Line Blocks
(details)
Plain text Typical result
| Line blocks are useful for addresses,
| verse, and adornment-free lists.
|
| Each new line begins with a
| vertical bar ("|").
| Line breaks and initial indents
| are preserved.
| Continuation lines are wrapped
portions of long lines; they begin
with spaces in place of vertical bars.
Line blocks are useful for addresses,
verse, and adornment-free lists.
Each new line begins with a
vertical bar ("|").
Line breaks and initial indents
are preserved.
Continuation lines are wrapped portions of long lines; they begin with spaces in place of vertical bars.
### Block Quotes
(details)
Plain text Typical result
Block quotes are just:
Indented paragraphs,
and they may nest.
Block quotes are just:
Indented paragraphs,
and they may nest.
Use empty comments to separate indentation contexts, such as block quotes and directive contents.
### Doctest Blocks
(details)
Plain text Typical result
Doctest blocks are interactive
Python sessions. They begin with
"``>>>``" and end with a blank line.
>>> print "This is a doctest block."
This is a doctest block.
Doctest blocks are interactive Python sessions. They begin with ">>>" and end with a blank line.
>>> print "This is a doctest block."
This is a doctest block.
"The doctest module searches a module's docstrings for text that looks like an interactive Python session, then executes all such sessions to verify they still work exactly as shown." (From the doctest docs.)
### Tables
(details)
There are two syntaxes for tables in reStructuredText. Grid tables are complete but cumbersome to create. Simple tables are easy to create but limited (no row spans, etc.).
Plain text Typical result
Grid table:
+------------+------------+-----------+
| Header 1 | Header 2 | Header 3 |
+============+============+===========+
| body row 1 | column 2 | column 3 |
+------------+------------+-----------+
| body row 2 | Cells may span columns.|
+------------+------------+-----------+
| body row 3 | Cells may | - Cells |
+------------+ span rows. | - contain |
| body row 4 | | - blocks. |
+------------+------------+-----------+
Grid table:
body row 1 column 2 column 3
body row 2 Cells may span columns.
body row 3 Cells may
span rows.
• Cells
• contain
• blocks.
body row 4
Simple table:
===== ===== ======
Inputs Output
------------ ------
A B A or B
===== ===== ======
False False False
True False True
False True True
True True True
===== ===== ======
Simple table:
Inputs Output
A B A or B
False False False
True False True
False True True
True True True
### Transitions
(details)
Plain text Typical result
A transition marker is a horizontal line
of 4 or more repeated punctuation
characters.
------------
A transition should not begin or end a
section or document, nor should two
transitions be immediately adjacent.
A transition marker is a horizontal line of 4 or more repeated punctuation characters.
A transition should not begin or end a section or document, nor should two transitions be immediately adjacent.
Transitions are commonly seen in novels and short fiction, as a gap spanning one or more lines, marking text divisions or signaling changes in subject, time, point of view, or emphasis.
### Explicit Markup
Explicit markup blocks are used for constructs which float (footnotes), have no direct paper-document representation (hyperlink targets, comments), or require specialized processing (directives). They all begin with two periods and whitespace, the "explicit markup start".
#### Footnotes
(details)
Plain text Typical result
Footnote references, like [5]_.
Note that footnotes may get
rearranged, e.g., to the bottom of
the "page".
.. [5] A numerical footnote. Note
there's no colon after the ``]``.
Footnote references, like 5. Note that footnotes may get rearranged, e.g., to the bottom of the "page".
[5] A numerical footnote. Note there's no colon after the ].
Autonumbered footnotes are
possible, like using [#]_ and [#]_.
.. [#] This is the first one.
.. [#] This is the second one.
They may be assigned 'autonumber
labels' - for instance,
[#fourth]_ and [#third]_.
.. [#third] a.k.a. third_
.. [#fourth] a.k.a. fourth_
Autonumbered footnotes are possible, like using 1 and 2.
They may be assigned 'autonumber labels' - for instance, 4 and 3.
[1] This is the first one. [2] This is the second one. [3] a.k.a. third [4] a.k.a. fourth
Auto-symbol footnotes are also
possible, like this: [*]_ and [*]_.
.. [*] This is the first one.
.. [*] This is the second one.
Auto-symbol footnotes are also possible, like this: * and .
[*] This is the first symbol footnote [†] This is the second one.
The numbering of auto-numbered footnotes is determined by the order of the footnotes, not of the references. For auto-numbered footnote references without autonumber labels ("[#]_"), the references and footnotes must be in the same relative order. Similarly for auto-symbol footnotes ("[*]_").
#### Citations
(details)
Plain text Typical result
Citation references, like [CIT2002]_.
Note that citations may get
rearranged, e.g., to the bottom of
the "page".
.. [CIT2002] A citation
(as often used in journals).
Citation labels contain alphanumerics,
underlines, hyphens and fullstops.
Case is not significant.
Given a citation like [this]_, one
can also refer to it like this_.
.. [this] here.
Citation references, like [CIT2002]. Note that citations may get rearranged, e.g., to the bottom of the "page".
Citation labels contain alphanumerics, underlines, hyphens and fullstops. Case is not significant.
Given a citation like [this], one can also refer to it like this.
[CIT2002] A citation (as often used in journals). [this] here.
(details)
##### External Hyperlink Targets
Plain text Typical result
External hyperlinks, like Python_.
.. _Python: https://www.python.org/
Fold-in form External hyperlinks, like Python.
Call-out form
External hyperlinks, like Python.
Python: https://www.python.org/
"Fold-in" is the representation typically used in HTML documents (think of the indirect hyperlink being "folded in" like ingredients into a cake), and "call-out" is more suitable for printed documents, where the link needs to be presented explicitly, for example as a footnote. You can force usage of the call-out form by using the "target-notes" directive.
reStructuredText also provides for embedded URIs (details), a convenience at the expense of readability. A hyperlink reference may directly embed a target URI inline, within angle brackets. The following is exactly equivalent to the example above:
Plain text Typical result
External hyperlinks, like `Python
<https://www.python.org/>`_.
External hyperlinks, like Python.
##### Internal Hyperlink Targets
Plain text Typical result
Internal crossreferences, like example_.
.. _example:
This is an example crossreference target.
Fold-in form Internal crossreferences, like example This is an example crossreference target.
Call-out form Internal crossreferences, like example example: This is an example crossreference target.
##### Indirect Hyperlink Targets
(details)
Plain text Typical result
Python_ is `my favourite
programming language`__.
.. _Python: https://www.python.org/
__ Python_
The second hyperlink target (the line beginning with "__") is both an indirect hyperlink target (indirectly pointing at the Python website via the "Python_" reference) and an anonymous hyperlink target. In the text, a double-underscore suffix is used to indicate an anonymous hyperlink reference. In an anonymous hyperlink target, the reference text is not repeated. This is useful for references with long text or throw-away references, but the target should be kept close to the reference to prevent them going out of sync.
##### Implicit Hyperlink Targets
(details)
Section titles, footnotes, and citations automatically generate hyperlink targets (the title text or footnote/citation label is used as the hyperlink name).
Plain text Typical result
Titles are targets, too
=======================
Implicit references, like `Titles are
targets, too`_.
Titles are targets, too
Implicit references, like Titles are targets, too.
#### Directives
(details)
Directives are a general-purpose extension mechanism, a way of adding support for new constructs without adding new syntax. For a description of all standard directives, see reStructuredText Directives.
Plain text Typical result
For instance:
.. image:: images/nikola.png
For instance:
#### Substitution References and Definitions
(details)
Substitutions are like inline directives, allowing graphics and arbitrary constructs within text.
Plain text Typical result
The |Nikola| static site generator is named after Nikola Tesla.
.. |Nikola| image:: nikola.png
The static site generator is named after Nikola Tesla.
(details)
Any text which begins with an explicit markup start but doesn't use the syntax of any of the constructs above, is a comment.
Plain text Typical result
.. This text will not be shown
(but, for instance, in HTML might be
rendered as an HTML comment)
An "empty comment" does not
consume following blocks.
(An empty comment is ".." with
blank lines before and after.)
..
So this block is not "lost",
despite its indentation.
An "empty comment" does not consume following blocks. (An empty comment is ".." with blank lines before and after.)
So this block is not "lost", despite its indentation.
### Getting Help
Users who have questions or need assistance with Docutils or reStructuredText should post a message to the Docutils-Users mailing list. The Docutils project web site has more information.
Authors: Tibs (tibs@tibsnjoan.co.uk) and David Goodger (goodger@python.org) | 2022-08-08 22:01:58 | {"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": 0.8152778744697571, "perplexity": 806.9367615666501}, "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-2022-33/segments/1659882570879.1/warc/CC-MAIN-20220808213349-20220809003349-00712.warc.gz"} |
https://myschool.ng/classroom/physics?page=751 | Physics Past Questions
3751
The critical angle for light travelling from a transparent medium to air s measured as 340. The refractive index of the medium is
• A. 0.56
• B. 1.50
• C. 1.79
• D. 2.02
3752
The S.I unit for sound energy is
• A. Hz
• B. cd
• C. dB
• D. J
3753
The general definition of elastic modulus is
• A. $$\frac{stress}{strain}$$
• B. $$\frac{strain}{stress}$$
• C. $$stress \times strain$$
• D. $$\sqrt{\frac{stress}{strain}}$$
3754
The diagram above illustrates a simple barometer. Which distance measures the atmospheric pressure?
• A. PQ
• B. QR
• C. RS
• D. QS
3755
The property of a body to remain at rest or to continue in uniform motion in a straight line is called
• A. momentum
• B. Inertia
• C. impulse
• D. Energy | 2019-05-26 19:53:10 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 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": 0.29545238614082336, "perplexity": 12030.506405279939}, "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-2019-22/segments/1558232259452.84/warc/CC-MAIN-20190526185417-20190526211417-00001.warc.gz"} |
https://anylearnnepal.com/the-first-picture-two-giant-exoplanets/ | # The first picture of two giant exoplanets
## Background
The first evidence of the existence of exoplanet started back in 1917. After that time, there have been numerous observations and claims regarding the discoveries of many exoplanets. As of $1^{st}$ July 2020: 4,281 exoplanets in 3,163 systems are confirmed. Among them, there are more than one planets in 701 systems, according to Wikipedia. Only tens of directly imaged companions have been discovered since the past decades, with only a few confirmations.
## Latest Research
According to the researchers report on 22 July in The Astrophysical Journal Letters, Two giant exoplanets with large orbits are directly seen. They were imaged by a large telescope in Chile. They are the planets orbiting the sun-like star named TYC 8998-760-1.
## Star TYC 8998-760-1
This star TYC 8998-760-1 is about 300 light-years away in the Musca constellation, that’s very far away. The interesting fact about this star is — it’s just 17 million years old. This star is very younger than our planet(4.5 billion years old).
## Description of two giant planets
These two giant planets have more interesting facts.
The inner one weighs 14 times more than our Jupiter planet whereas the outer one weights about 6 times more than Jupiter. The Jupiter Planet of our system weights $1.898 \times 10^{27} kg$.
The distance between the inner planet and its star is about 160 times more than the distance of our Earth from our Sun whereas the outer one doubles that distance. The distance of our Earth from its Sun is 151.9 million km.
This discovery might be the milestone for the advancement in astrophysics and astronomy.
Many Astronomers from all over the world are working together to discover the existence of extra-terrestrial life on different planets. Many Observatory has been established. The FAST radio telescope, the world’s largest and most sensitive telescope is now operational in Guizhou. This field of Science is full of surprises and challenging in difficulty.
I hope for the positive result and better researches in this field of science. | 2021-03-02 11:37:42 | {"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": 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": 0.47443512082099915, "perplexity": 1398.417973952317}, "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/1614178363809.24/warc/CC-MAIN-20210302095427-20210302125427-00543.warc.gz"} |
https://socratic.org/questions/54123f8702bf342eb22219fc | # Question #219fc
Feb 8, 2015
I hope that this is what you are looking for. And I think the proper way of conveying bearing coordinates would be S10E instead of E10S and S22W instead of W22S.
Anyway, the solution:
North-South components , take South as negative and North as positive....
Hence we have:
-50cos(10) + 28cos(55) - 17cos(22)= -48.9m (South)
West-East components , take East as positive and West as negative....
Hence we have:
50sin(10) + 28sin(55) - 17sin(22)= 25.3m (East)
${\left({48.9}^{2} + {25.3}^{2}\right)}^{\frac{1}{2}}$ ....Pythagoras theorem
Final answer is 55m South-East direction.
tan(25.3/48.9)=27.4degrees. Direction is S27.4E
This is the component method which is actually pretty brief. It takes less than 2 minutes.
Just draw, take N-S components and W-E components. | 2019-10-15 06:29:36 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 1, "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": 0.6071116328239441, "perplexity": 10286.427718142857}, "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/1570986657586.16/warc/CC-MAIN-20191015055525-20191015083025-00484.warc.gz"} |
https://socratic.org/questions/5873c9d0b72cff5f81069369 | # Question 69369
Jan 10, 2017
Here's why that is the case.
#### Explanation:
The trick here is to realize that both beakers contain the same amount of hydrochloric acid, but different amounts of water.
The reaction between magnesium and hydrochloric acid forms magnesium chloride and hydrogen gas
${\text{Mg"_ ((s)) + 2"HCl"_ ((aq)) -> "MgCl"_ (2(aq)) + "H}}_{2 \left(g\right)} \uparrow$
The important thing to mention here is that the reaction is exothermic, which means that it gives off heat as it progresses.
Notice that beaker $\text{A}$ contains
100 color(red)(cancel(color(black)("cm"^3))) * (1 color(red)(cancel(color(black)("dm"^3))))/(10^3color(red)(cancel(color(black)("cm"^3)))) * "1 mole HCl"/(1color(red)(cancel(color(black)("dm"^3)))) = "0.10 moles HCl"
Similarly, beaker $\text{B}$ contains
200 color(red)(cancel(color(black)("cm"^3))) * (1 color(red)(cancel(color(black)("dm"^3))))/(10^3color(red)(cancel(color(black)("cm"^3)))) * "0.5 moles HCl"/(1color(red)(cancel(color(black)("dm"^3)))) = "0.10 moles HCl"#
You know that the two pieces of magnesium are identical, which means that both reactions will give off the same amount of heat.
Now, this heat is being off by the reaction to its surroundings, i.e. to the solution.
The temperature of the solution in beaker $\text{A}$ will indeed be higher than the temperature of the solution in beaker $\text{B}$ because the former contains less water than the latter.
In this regard, it requires less heat to get to a higher temperature than beaker $\text{B}$. The amount of heat is the same, so the beaker that holds less water will get to a higher temperature than the beaker that holds more water.
In other words, a smaller mass of water requires less heat to get to the same temperature as a bigger mass of water.
If you take $m$ to be the mass of water in beaker $\text{A}$ and $2 m$ to be the mass of water in beaker $\text{B}$, you can say that
$\left\{\begin{matrix}q = m \cdot c \cdot \Delta {T}_{\text{A" \\ q = 2m * c * DeltaT_"B}}\end{matrix}\right.$
Here
• $q$ is the heat absorbed by the water, the same for beaker $\text{A}$ and for beaker $\text{B}$
• $c$ is the specific heat of water
• $\Delta {T}_{\text{A}}$ is the change in temperature for beaker $\text{A}$
• $\Delta {T}_{\text{B}}$ is the change in temperature for beaker $\text{B}$
Notice that you have
$\textcolor{red}{\cancel{\textcolor{b l a c k}{m}}} \cdot \textcolor{red}{\cancel{\textcolor{b l a c k}{c}}} \cdot \Delta {T}_{\text{A" = 2color(red)(cancel(color(black)(m))) * color(red)(cancel(color(black)(c))) * DeltaT_"B}}$
which gets you
$\Delta {T}_{\text{A" = 2 * DeltaT_"B}}$
This tells you that the increase in temperature is twice as high for the solution in beaker $\text{A}$ than for the solution in beaker $\text{B}$. | 2019-12-13 20:53:34 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 25, "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": 0.7380364537239075, "perplexity": 809.6928090097572}, "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-2019-51/segments/1575540569146.17/warc/CC-MAIN-20191213202639-20191213230639-00519.warc.gz"} |
https://zbmath.org/?q=an:07021675 | # zbMATH — the first resource for mathematics
Stochastic differential equations in a scale of Hilbert spaces. (English) Zbl 1406.60087
Summary: A stochastic differential equation with coefficients defined in a scale of Hilbert spaces is considered. The existence and uniqueness of finite time solutions is proved by an extension of the Ovsyannikov method. This result is applied to a system of equations describing non-equilibrium stochastic dynamics of (real-valued) spins of an infinite particle system on a typical realization of a Poisson or Gibbs point process in $${\mathbb{R} }^{n}$$.
##### MSC:
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis) 82C20 Dynamic lattice systems (kinetic Ising, etc.) and systems on graphs in time-dependent statistical mechanics 82C31 Stochastic methods (Fokker-Planck, Langevin, etc.) applied to problems in time-dependent statistical mechanics 46E99 Linear function spaces and their duals
Full Text:
##### References:
[1] S. Albeverio, A. Daletskii, Yu. Kondratiev, Stochastic equations and Dirichlet operators on product manifolds. Infinite Dimensional Analysis, Quantum Probability and Related Topics6 (2003), 455-488. · Zbl 1049.60055 [2] S. Albeverio, A. Daletskii, Yu. Kondratiev, Stochastic analysis on product manifolds: Dirichlet operators on differential forms. J. Funct. Anal.176 (2000), no. 2, 280-316. · Zbl 0970.58020 [3] S. Albeverio, Yu. Kondratiev, M. Röckner, Analysis and geometry on configuration spaces: The Gibbsian case, J. Funct. Anal.157 (1998), 242–291. · Zbl 0931.58019 [4] R. Barostichi, A. Himonas, G. Petronilho, Autonomous Ovsyannikov theorem and applications to nonlocal evolution equations and systems, J. Funct. Anal.270 (2016), 330–358. · Zbl 1331.35299 [5] T. Bodineau, I. Gallagher, L. Saint-Raymond, The Brownian motion as the limit of a deterministic system of hard-spheres, Invent. Math.203 (2016), 493–553. · Zbl 1337.35107 [6] A. Bovier, Statistical Mechanics of Disordered Systems. A Mathematical Perspective (Cambridge Series in Statistical and Probabilistic Mathematics. Cambridge University Press, Cambridge, 2006). · Zbl 1108.82002 [7] D. Crisan, D. Holm, Wave breaking for the Stochastic Camassa-Holm equation, Physica D: Nonlinear Phenomena376-377 (2018), 138-143. · Zbl 1398.35305 [8] R. Dalang, M. Dozzi, F. Flandoli, F. Russo (eds.), Stochastic Analysis: A Series of Lectures, Centre Interfacultaire Bernoulli, January–June 2012, Ecole Polytechnique Fédérale de Lausanne, Switzerland, Progress in Probability (2015), Birkhauser. · Zbl 1330.60004 [9] A. Daletskii, D. Finkelshtein, Non-equilibrium particle dynamics with unbounded number of interacting neighbors, J. Stat. Phys. (2018), published on-line http://link.springer.com/article/10.1007/s10955-018-2159-x. · Zbl 1405.82020 [10] A. Daletskii, Yu. Kondratiev, Yu. Kozitsky, T. Pasurek, Gibbs states on random configurations, J. Math. Phys. 55 (2014), 083513. · Zbl 1301.82021 [11] A. Daletskii, Yu. Kondratiev, Yu. Kozitsky, T. Pasurek, Phase Transitions in a quenched amorphous ferromagnet, J. Stat. Phys. 156 (2014), 156-176. · Zbl 1298.82074 [12] G. Da Prato, J. Zabczyk, Stochastic Differential Equations in Infinite Dimensions, Cambridge 1992. · Zbl 0761.60052 [13] G. Da Prato, J. Zabczyk, Ergodicity for Infinite Dimensional Systems, London Mathematical Society Lecture Note Series229, University Press, Cambridge, 1996. · Zbl 0849.60052 [14] K. Deimling, Ordinary differential equations in Banach spaces, Lecture Notes in Mathematics596, Springer 1977. · Zbl 0361.34050 [15] D. Finkelshtein, Around Ovsyannikov’s method, Methods of Functional Analysis and Topology21 (2015), No. 2, 134-150. · Zbl 1340.35177 [16] D. Finkelshtein, Yu. Kondratiev, O. Kutoviy, Semigroup approach to birth-and-death stochastic dynamics in continuum, J. Funct. Anal.262 (2012), 1274-1308. · Zbl 1250.47090 [17] J. Fritz, C. Liverani, S. Olla, Reversibility in Infinite Hamiltonian Systems with Conservative Noise, Commun. Math. Phys.189 (1997), 481 - 496. · Zbl 0893.70011 [18] J. Inglis, M. Neklyudov, B. Zegarliński, Ergodicity for infinite particle systems with locally conserved quantities, Infin. Dimens. Anal. Quantum Probab. Relat. Top. 15 (2012), No. 1, 1250005. · Zbl 1268.60120 [19] G. Kallianpur, I. Mitoma, R. L. Wolpert, Diffusion equations in duals of nuclear spaces, Stochastics and Stochastic Reports, 29 (1990), No. 2, 285-329. · Zbl 0702.60056 [20] G. Kallianpur, Jie Xiong, Stochastic differential equations in infinite dimensional spaces, Lecture notes-monograph series26, Institute of Mathematical Statistics 1995. [21] D. Klein and W. S. Yang, A characterization of first order phase transitions for superstable interactions in classical statistical mechanics, J. Stat. Phys.71 (1993), 1043-1062. · Zbl 0935.82519 [22] O. Lanford, Time evolution of large classical systems, Lecture notes in physics 38, pp. 1-111, Springer (1975) [23] O. Lanford, J. Lebowitz, E. Lieb, Time Evolution of Infinite Anharmonic Systems, J. Stat. Phys.16 (1977), No. 6, 453–461. [24] T. Nishida, A note on a theorem of Nirenberg, J. Differential Geometry12 (1977), 629-633. · Zbl 0368.35007 [25] S. Romano and V. A. Zagrebnov, Orientational ordering transition in a continuous-spin ferrofluid, Phys. A253 (1998), 483–497. [26] D. Ruelle, Superstable interactions in classical statistical mechanics, Commun. Math. Phys.18 (1970), 127–159. · Zbl 0198.31101 [27] M. V. Safonov, The Abstract Cauchy-Kovalevskaya Theorem in a Weighted Banach Space, Comm. Pure Appl. Math.XLVIII (1995), 629-637. · Zbl 0836.35004
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. | 2021-09-27 07:43:03 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 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": 0.7446799874305725, "perplexity": 4644.215900428617}, "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-2021-39/segments/1631780058373.45/warc/CC-MAIN-20210927060117-20210927090117-00679.warc.gz"} |
https://quantumcomputing.stackexchange.com/questions/17168/understanding-the-heavy-output-problem | # Understanding the heavy output problem [closed]
In this paper (or more pedagogically here) it is given a way to compute the Quantum Volume of a quantum computer (qc), specifically aimed at the IBM qcs.
In all this process I found some dark spots that I would like to understand. First of all we need the heavy outputs $$H_U$$ which can be obtained from a "classical" computation. Obviously in the implementation the transpiler will do some optimizations so from an original $$U$$ ($$m$$ qubits and depth $$d$$) we will get the transpiled $$U'$$. The probability of sampling a heavy output with this $$U'$$ is strangely
$$h_U = \sum_{x\in H_U} q_U(x).$$
1. Ok I buy that this quantity works, but why to sum it over all possibles $$x\in H_U$$ is still unclear to me.
2. The probability of observing a heavy output is then $$h_d = \int h_UdU$$. In the paper mentioned the Algorithm 1 computes $$h_d$$, right?
3. As far as I understand, this algorithm simply constructs the frequency plot between a realization of $$U$$ vs the number of heavy outputs found in a certain number of trial initial state $$|00\dots 0\rangle$$ ($$m$$-spins), right?
4. Then if 3 is correct, $$h_d$$ can be computed from the (normalized) histogram just constructed. However the authors give the formula
$$\frac{n_h-2\sqrt{n_h(n_s-n_h/n_c)}}{n_c n_s}>2/3,$$
to validate if $$h_d$$ has been achieved. How is this formula found? Is it some numerical (e.g. Simpson) rule?
1. On the other, one can measure how well the $$U'$$ resembles $$U$$ by computing the fidelity $$F_{\mathrm{avg}}(U,U')$$. Where does this quantity enters for computing $$V_Q$$? $$\log_2 V_Q =\mathrm{argmax}_m \; \mathrm{min}(m,d(m))$$ doesn't tell much...
• these are good questions but, as it stands, the post is way too broad. The stackexchange format is best-suited for laser-focused questions. Feel free to edit your post to focus it on a specific question. You can open different posts to ask different questions – glS Apr 21 at 10:41
• Please ask just one question. – user1271772 Apr 22 at 11:37 | 2021-05-13 13:28:44 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 21, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6376619338989258, "perplexity": 574.148305589254}, "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-20210513111525-20210513141525-00248.warc.gz"} |
http://rationalwiki.org/wiki/Extraordinary_claims_require_extraordinary_evidence | # Extraordinary claims require extraordinary evidence
Part of the series on
Philosophy of
science
Foundations
Method
Conclusions
Extraordinary claims require extraordinary evidence was a phrase made popular by Carl Sagan. It is central to scientific method, and a key issue for critical thinking, rational thought and skepticism everywhere.
The evidence put forth by proponents of such things as gods, ghosts, the paranormal, and UFOs is highly questionable at best and offers little in the way of proof. Even if we accepted what evidence there is as valid (and it is highly debatable if we should), limited and weak evidence is not enough to overcome the extraordinary nature of these claims.
## Analogy
Alice and Bob are two friends talking after school. Alice tells Bob that she watched a movie the previous evening. Bob believes her easily, because he knows that movies exist, that Alice exists, and that Alice is capable and fond of watching movies. If he doubts her, he might ask for a ticket stub or a confirmation from one of her friends. If, however, Alice tells Bob that she flew on a unicorn to a fairy kingdom where she participated in an ambrosia-eating contest, and she produces a professionally-printed contest certificate and a friend who would testify to the events described, Bob would still not be inclined to believe her without strong evidence for the existence of flying unicorns, fairies and ambrosia-eating contests.
## Probability theory
$P(A|B)=\frac{P(B|A)\cdot P(A)}{P(B)}$
Bayes' Theorem
While the idea that a sufficiently outlandish claim requires a lot more compelling evidence is quite intuitive, it can be quantified nicely with probability theory in a Bayesian framework. In short, sufficient evidence must be capable of raising a highly improbable claim to be highly probable - and the more improbable the evidence, the better. By application of Bayes' theorem, it's possible to show this in action mathematically.
Assume, for instance, someone claims to be able to predict what way a coin[1] will land almost perfectly. We know this is an extraordinary claim, so we'll say that just by guessing if the person is telling the truth or not that it's a million-to-one chance. In reality, the number would be even more improbable, but this can be used for illustration. So we ask them to demonstrate the skill. They're almost perfect, so let's assume they guess right about 90% of the time - this allows them the opportunity for their skill to mess up once in a while, but still prove to be pretty good. This gives us all the information we need to know to actually quantify how extraordinary the evidence must be.
Consider if they guessed a single coin toss correctly. The odds of guessing by chance is a mere 50%, or 50:50.
$\frac{0.9 \cdot 0.000001}{0.5} = 0.0000018$
A single coin toss doesn't improve our odds very dramatically. The evidence just isn't extraordinary enough - you can correctly guess a single coin toss correctly 50% of the time with no special skills involved. It all rests on how improbable our evidence, P(B), actually is and a 50:50 chance isn't particularly improbable. For two coin tosses P(B) becomes 0.25, and for 10 coin tosses it comes to roughly 0.00097. Plugging those numbers in Bayes' theorem gives us a probability of genuine skill (given P(A) of a million-to-one) of around 0.0009, which although still small is a considerable improvement on that original million-to-one chance. By 20 or so correctly guessed coin tosses, the skill is starting to look a lot more genuine.
This is the basic idea underpinning statistical significance; is it more likely that our evidence is random, or due to a real effect, and is the improbability of the evidence presented in proportion to the improbability of the claim being made. But Sagan's quip about extraordinary evidence doesn't just mean that we can take someone's word for it if they managed to toss so many coins in a row. Derren Brown can pull off such a feat with some effort and misdirection as shown in his special on The System, so we always need to consider alternative hypotheses and compare how likely they are. Like with Derren Brown tossing a coin with 10 heads in a row, is it more likely that they're psychic, or are cheating? So tests such as James Randi's million-dollar challenge will control for this potential factor, making sure that the probability of foul play, fraud and cheating is far less than the probability of genuine psychic power.
## Footnotes
1. Obviously tossed by someone else, because methods of tossing a coin may affect the outcome. | 2015-02-01 16:39:57 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 2, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6749007701873779, "perplexity": 1071.5116002878376}, "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-2015-06/segments/1422121744242.57/warc/CC-MAIN-20150124174904-00137-ip-10-180-212-252.ec2.internal.warc.gz"} |
https://en.wikipedia.org/wiki/Earth_Similarity_Index | # Earth Similarity Index
Though differing in size and temperature, terrestrial planets of the Solar System were reported to have high Earth Similarity Index values – Mercury , Venus, Earth and Mars. Sizes to scale.
The Earth Similarity Index (ESI) is a proposed characterization of how similar a planetary-mass object or natural satellite is to Earth. It was designed to be a scale from zero to one, with Earth having a value of one; this is meant to simplify planet comparisons from large databases.
The scale has no quantitative meaning for habitability.
## Formulation
The ESI, as proposed in 2011 by Schulze-Makuch et al. in the journal Astrobiology, incorporates a planet's radius, density, escape velocity, and surface temperature into the index.[1] Thus the authors describe the index as having two components: (1) associated with the interior which is associated with the mean radius and bulk density, and (2) associated with the surface which is associated with the escape velocity and surface temperature. An article on the ESI formulation derivation is made available by Kashyap Jagadeesh et al.(2017).[2] ESI was also referenced in an article published in Revista Cubana de Física.[3]
For exoplanets, in almost every case only the planet's orbital period along with either the proportional dimming of the star due to the planet's transit or the radial velocity variation of the star in response to the planet is known with any degree of certainty, and so every other property not directly determined by those measurements is speculative. For example, while surface temperature is influenced by a variety of factors including irradiance, tidal heating, albedo, insolation and greenhouse warming, as these factors are not known for any exoplanet, quoted ESI values use planetary equilibrium temperature as a stand-in.[1]
A webpage maintained by one of the authors of the 2011 Astrobiology article, Abel Méndez at the University of Puerto Rico at Arecibo, lists his calculations of the index for various exoplanetary systems.[4] Méndez's ESI is calculated as
${\displaystyle {\mathsf {ESI}}=\prod _{i=1}^{n}\left(1-{\Big \vert }{\frac {x_{i}-x_{i0}}{x_{i}+x_{i0}}}{\Big \vert }\right)^{\frac {w_{i}}{n}}}$,
where ${\displaystyle x_{i}}$ and ${\displaystyle x_{i0}}$ are properties of the extraterrestrial body and of Earth respectively, ${\displaystyle w_{i}}$ is the weighted exponent of each property, and ${\displaystyle n}$ is the total number of properties. It is comparable to, and constructed from, the Bray–Curtis Similarity Index.[4][5] The weight assigned to each property, ${\displaystyle w_{i}}$, are free parameters that can be chosen to emphasize certain characteristics over others or to obtain desired index thresholds or rankings. The webpage also ranks what it describes as the habitability of planets and moons according to three criteria: the location in the habitable zone, ESI, and a speculation as to a capacity to sustain organisms at the bottom of the food chain, a different index collated on the webpage identified as the "Global Primary Habitability scale".[6]
The 2011 Astrobiology article and the ESI values found in it received press attention at the time of the article's publication. As a result, Mars was reported to have the second-highest ESI in the Solar System with a value of 0.70.[7] A number of exoplanets listed in that article were reported to have values in excess of this.
Other ESI values that have been reported by third parties include the following sources:[7][4]
## No relation to habitability
Although the ESI does not characterize habitability, given the point of reference is the Earth, some of its functions match those used by habitability measures. As with the definition of the habitable zone, the ESI uses surface temperature as a primary function (and the terrestrial point of reference). A 2016 article uses ESI as a target selection scheme and obtains results showing that the ESI has little relation to the habitability of an exoplanet, as it takes no account of the activity of the star, planetary tidal locking, nor the planet's magnetic field (i.e. ability to protect itself) which are among the keys to habitable surface conditions.[8]
It has been noted that ESI fails to differentiate between Earth similarity and Venus similarity, where planets with a lower ESI have a greater chance at habitability.[9]
## Planets with an Earth-like size
Comparison of the sizes of planets Kepler-69c, Kepler-62e, Kepler-62f, and the Earth. All planets except the Earth are artists' conceptions.
The classification of exoplanets is difficult in that many methods of exoplanet detection leave several features unknown. For example, with the transit method, measurement of radius can be highly accurate, but mass and density are often estimated. Likewise with radial velocity methods, which can provide accurate measurements of mass but are less successful measuring radius. Planets observed via a number of different methods therefore can be most accurately compared to Earth.
## Similarity of non-planets to Earth
The Moon, Io and Earth shown to scale. Although significantly smaller, some of the Solar System's moons and dwarf planets share similarities to Earth's density and temperature.
The index can be calculated for objects other than planets, including natural satellites, dwarf planets and asteroids. The lower average density and temperature of these objects give them lower index values. Only Titan (a moon of Saturn) is known to hold on to a significant atmosphere despite an overall lower size and density. While Io (a moon of Jupiter) has a low average temperature, surface temperature on the moon varies wildly due to geologic activity.[10] | 2022-08-17 21:04:58 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 6, "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": 0.6801228523254395, "perplexity": 1535.779322311847}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-33/segments/1659882573104.24/warc/CC-MAIN-20220817183340-20220817213340-00211.warc.gz"} |
http://ps-patterns.wikidot.com/constrained-response-property-pattern | Constrained Response Property Pattern
# Untimed version
Pattern Name and Classification Response: Order Specification Pattern Structured English Specification Scope, if P [has occurred], then in response S eventually holds without $Z_S$ [holding] in between. Pattern Intent To describe cause-effect relationships between a pair of events/states. An occurrence of the first, the cause $P$, must be followed by an occurrence of the second, the effect $S$. Temporal Logic Mappings LTL Globally: $\Box \; (P \;\rightarrow \; \neg Z_S \; \mathcal{U} \; S)$ Before R: $\Diamond \; R \;\rightarrow \; (P \;\rightarrow \; (\neg R \wedge \neg Z_S\; \mathcal{U} \; (S \wedge \neg R))) \; \mathcal{U} \; R$ After Q: $\Box(Q \;\rightarrow \; \Box(P \;\rightarrow \; \neg Z_S \; \mathcal{U} \; S))$ Between Q and R: $\Box((Q \;\wedge \Box \neg R \;\wedge \Diamond \; R) \;\rightarrow \; (P \;\rightarrow \; (\neg R \; \wedge \neg Z_S\mathcal{U} \; (S \;\wedge \neg R))) \; \mathcal{U} \; R)$ After Q until R: $\Box(Q \;\wedge \Box \neg R \;\rightarrow \; ((P \;\rightarrow \; (\neg R \wedge \neg Z_S\; \mathcal{U} \; (S \;\wedge \neg R))) \; \mathcal{W} \; R)$ CTL Globally: $AG(P \;\rightarrow \; A[!Z_S \; \mathcal{U} (S)])$ Before R: $A[(P \;\rightarrow \; (A[!R \& !Z_S\; \mathcal{U} \; (S \wedge \neg R)]) \vee AG(!R)) \; \mathcal{W} \; R]$ After Q: $A[!Q \; \mathcal{W} \; (Q \wedge AG(P \;\rightarrow \; A[!Z_S\mathcal{U}(S)])]$ Between Q and R: $AG(Q \wedge AG !R \;\rightarrow \; A[((P \;\rightarrow \; A[!R \& !Z_S\; \mathcal{U} \; (S \wedge !R)]) \vee AG(!R)) \; \mathcal{W} \; R])$ After Q until R: $AG(Q \wedge \Box !R \;\rightarrow \; A[(P \;\rightarrow \; A[!R \& !Z_S\; \mathcal{U} \; (S \wedge !R)]) \; \mathcal{W} \; R])$ Additional notes The Response Property Pattern has been proposed by Dwyer in [1]. The original version that does not contain time-constraints can be found on the following webpage: Response Property Pattern .
# Time-constrained version
Pattern Name and Classification Time-constrained Response: Real-time Order Specification Pattern Structured English Specification Scope, if P [has occurred], then in response S eventually holds without $Z_S$ [holding] in between and within [ Time(0)]. Pattern Intent To describe cause-effect relationships between a pair of events/states. An occurrence of the first, the cause $P$, must be followed by an occurrence of the second, the effect $S$ without $Z_S$ holding and within a timebound [t_1,t_2]. Temporal Logic Mappings MTL Globally: $\Box \; (P \;\rightarrow \; \neg Z_S \; \mathcal{U}^{[ t_1, t_2]} \; S)$ Before R: $\Diamond^{[ t_1, \infty)} \; R \;\rightarrow \; (P \;\rightarrow \; (\neg R \wedge \neg Z_S\; \mathcal{U}^{[ t_1, t_2]} \; (S \wedge \neg R))) \; \mathcal{U} \; R$ After Q: $\Box(Q \;\rightarrow \; \Box(P \;\rightarrow \; \neg Z_S \; \mathcal{U}^{[ t_1, t_2]} \; S))$ Between Q and R: $\Box((Q \;\wedge \Box^{[ 0, t_1]}\neg R \;\wedge \Diamond^{[ t_1, \infty)} \; R) \;\rightarrow \; (P \;\rightarrow \; (\neg R \; \wedge \neg Z_S\mathcal{U}^{[ t_1, t_2]} \; (S \;\wedge \neg R))) \; \mathcal{U} \; R)$ After Q until R: $\Box(Q \;\wedge \Box^{[ 0, t_1]} \neg R \;\rightarrow \; ((P \;\rightarrow \; (\neg R \wedge \neg Z_S\; \mathcal{U}^{[ t_1, t_2]} \; (S \;\wedge \neg R))) \; \mathcal{W} \; R)$ TCTL Globally: $AG(P \;\rightarrow \; A[\neg Z_S \; \mathcal{U}^{[ t_1, t_2]} (S)])$ Before R: $A[(P \;\rightarrow \; (A[\neg R \& \neg Z_S\; \mathcal{U}^{[ t_1, t_2]} \; (S \wedge \neg R)]) \vee AG(\neg R)) \; \mathcal{W} \; R]$ After Q: $A[\neg Q \; \mathcal{W} \; (Q \wedge AG(P \;\rightarrow \; \neg Z_S \; A[\mathcal{U}^{[ t_1, t_2]}(S)])]$ Between Q and R: $AG(Q \wedge AG^{[0, t_1]}\neg R \;\rightarrow \; A[((P \;\rightarrow \; A[\neg R \& \neg Z_S\; \mathcal{U}^{[ t_1, t_2]} \; (S \wedge \neg R)]) \vee AG(\neg R)) \; \mathcal{W} \; R])$ After Q until R: $AG(Q \wedge \Box^{[0, t_1]}\neg R \;\rightarrow \; A[(P \;\rightarrow \; A[\neg R \& \neg Z_S\; \mathcal{U}^{[ t_1, t_2]} \; (S \wedge \neg R)]) \; \mathcal{W} \; R])$ Additional notes The Time-constrained Response Property Pattern has been proposed by Cheng in [2], proposed as Bounded Response .
# Probabilistic version
The Response Property Pattern has been proposed by Grunske in [3] and it can be found on the following webpage: Probabilistic Response Pattern.
Bibliography
1. Matthew B. Dwyer; George S. Avrunin; James C. Corbett, Patterns in Property Specifications for Finite-State Verification. ICSE 1999. pp. 411-420.
2. Sascha Konrad; Betty H.C. Cheng, Real-time specification patterns.ICSE 2005. pp. 372-381.
3. Lars Grunske, Specification patterns for probabilistic quality properties. ICSE 2008. pp. 31-40. | 2022-10-07 00:22:57 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 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": 0.34278416633605957, "perplexity": 6677.932476383652}, "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/1664030337889.44/warc/CC-MAIN-20221006222634-20221007012634-00376.warc.gz"} |
https://physics.stackexchange.com/questions/420817/how-to-understand-hawkings-interpretation-of-the-quantization-of-the-field | # How to understand Hawking's interpretation of the quantization of the field?
In Hawking's paper "Particle Creation by Black Holes" he says the following:
The operator $$\phi$$ can be expressed as $$\phi=\sum_i f_i a_i+\bar{f}_ia_i^\dagger.$$
The solutions $$\{f_i\}$$ of the wave equation $$f_{i;ab}g^{ab}=0$$ can be chosen so that on past null infinity $$\mathscr{I}^-$$ they form a complete family satisfying the orthonormality condition (1.2) where the surface $$S$$ is $$\mathscr{I}^-$$ and so that they contain only positive frequencies with respect to the canonical affine parameter on $$\mathscr{I}^-$$. The operators $$a_i$$ and $$a_i^\dagger$$ have the natural interpretation as the annihilation and creation operators for ingoing particles i.e. for particles at past null infinity $$\mathscr{I}^-$$.
Now I'm quite probably missing something extremely basic here. But why the coefficients of the modes which are positive frequency with respect to the canonical affine parameter on $$\mathscr{I}^-$$ can be interpreted as creation and annihilation operators of particles on $$\mathscr{I}^-$$?
I do know that the basic point of QFT is indeed: (1) pick a set of modes which are complete in the KG inner product and positive/negative frequency with respect to some timelike Killing vector field and (2) expand the field in these modes, upon quantization, the coefficients become creation and annihilation operators in a Fock space giving a "particle" interpretation.
But here still. Here we have a few issues:
1. The modes are not positive frequency with respect to a timelike Killing field, but rather with respect to a parameter which is actually a null coordinate. In that case, how does one justify that the coefficients become creation and annihilation operators upon quantizing?
2. Still, I can't see why we can interpret the resulting creation and annihilation operators as creating and annihilating particles on $$\mathscr{I}^-$$? Why on $$\mathscr{I}^-$$? How do we justify this? | 2020-08-09 05:58:06 | {"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": 15, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9127707481384277, "perplexity": 165.84543212379359}, "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/1596439738425.43/warc/CC-MAIN-20200809043422-20200809073422-00187.warc.gz"} |
https://tex.stackexchange.com/questions/7797/is-there-an-arrayrulecolor-like-command-to-change-the-rule-color-of-fbox | # Is there an \arrayrulecolor-like command to change the rule color of \fbox?
The question has been written above.
## 2 Answers
You can use fcolorbox from the xcolor package or you can define your own command!
\documentclass{article}
\usepackage[kernelfbox]{xcolor}
\begin{document}
\def\twocolorbox#1#2#3{\color{#1}\fbox{\color{#2}#3}}
\twocolorbox{blue}{red}{terrible}
\fcolorbox{gray}{yellow}{test}
\end{document}
• Could you tell us what the order of arguments for \fcolorbox is?
– Joel
Feb 18 '16 at 1:06
\documentclass{article}
\usepackage{color}
\newcommand{\myfbox}[2]{\textcolor{#1}{\fbox{\normalcolor#2}}}
\begin{document}
\myfbox{red}{This is a test}
\end{document}
or
\documentclass{article}
\usepackage{color}
\newcommand{\myfbox}[2]{\fcolorbox{#1}{white}{#2}}
\begin{document}
\myfbox{red}{This is a test}
\end{document} | 2021-10-20 04:54:30 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5358939170837402, "perplexity": 3299.786862184808}, "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-2021-43/segments/1634323585302.56/warc/CC-MAIN-20211020024111-20211020054111-00635.warc.gz"} |
https://mathhelpboards.com/threads/the-sum-of-a-series-question.7984/ | # 'The sum of a series' question
#### kris1
##### New member
Assume that $$\displaystyle \sum_{n=1}^{\infty} a^2_{n}$$ converge, and assume that $$\displaystyle a_{n}$$ is non-negative for all $$\displaystyle \textit{n} \in N.$$
Determine whether the following statement is true (and prove it) or false (and give counterexample).
$$\displaystyle \sum_{n=2}^{\infty} \frac{a_{n}}{n^{2/3}}<\infty$$
Does anyone know how to do this question?
#### Klaas van Aarsen
##### MHB Seeker
Staff member
Assume that $$\displaystyle \sum_{n=1}^{\infty} a^2_{n}$$ converge, and assume that $$\displaystyle a_{n}$$ is non-negative for all $$\displaystyle \textit{n} \in N.$$
Determine whether the following statement is true (and prove it) or false (and give counterexample).
$$\displaystyle \sum_{n=2}^{\infty} \frac{a_{n}}{n^{2/3}}<\infty$$
Does anyone know how to do this question?
Hi kris1! Welcome to MHB!
Suppose we pick an $a_n$ so that $$\displaystyle \sum_{n=1}^{\infty} a^2_{n}$$ converges, but only just.
Say, $$\displaystyle a_n^2 = \frac 1 {n^{7/6}}$$...
#### ZaidAlyafey
##### Well-known member
MHB Math Helper
Hi kris1! Welcome to MHB!
Suppose we pick an $a_n$ so that $$\displaystyle \sum_{n=1}^{\infty} a^2_{n}$$ converges, but only just.
Say, $$\displaystyle a_n^2 = \frac 1 {n^{7/6}}$$...
Your choice of $a_n$ doesn't contradict the convergence of $$\displaystyle \sum_{n\geq 2}\frac{a_n}{n^{2/3}}$$
#### DreamWeaver
##### Well-known member
Hello Kris! And a very warm welcome to the forum...
I'm not much of a series boffin, but it seems to me that if an infinite sum of squares $$\displaystyle a_n^2$$ converges, then any sum of fractions of powers less than $$\displaystyle a_n^2$$ should also converge, since all you need to do is show that, say, $$\displaystyle a_n/ n^z \le a_n^2$$...
#### Opalg
##### MHB Oldtimer
Staff member
Assume that $$\displaystyle \sum_{n=1}^{\infty} a^2_{n}$$ converge, and assume that $$\displaystyle a_{n}$$ is non-negative for all $$\displaystyle \textit{n} \in N.$$
Determine whether the following statement is true (and prove it) or false (and give counterexample).
$$\displaystyle \sum_{n=2}^{\infty} \frac{a_{n}}{n^{2/3}}<\infty$$
Does anyone know how to do this question?
Hint: Use the Cauchy–Schwarz inequality.
#### mathbalarka
##### Well-known member
MHB Math Helper
Interesting enough, found the same question here before I saw this one : The sum of a series
At least got checked that I answered correct.
#### kris1
##### New member
Hi Everyone Thank you for all your replies I still haven't done this question I don't know what Cauchy–Schwarz inequality is, but I looked for this inequality on the internet and tried to apply it to my question but it didn't work. I also tried convergence tests but I gave up. I can do that kind of questions but when I have real numbers and I have to find limits, but for this question I need to prove given statement, which is my greatest weakness Please help me!
#### mathbalarka
##### Well-known member
MHB Math Helper
Applying CS-inequality,
$$\left ( \sum_{n\geq2} \frac{a_n}{n^{2/3}}\right )^2 \leq \left (\sum_{n \geq 2} a_n^2 \right ) \left (\sum_{n\geq 2} \frac{1}{n^{4/3}} \right )$$
Can you prove this now?
#### kris1
##### New member
Yeah, I think I can prove it, however I cannot use this method as I never learn it before. So far for this kind of questions I learned tests for convergence, eg ratio test, root test, integral test... etc So I think my teacher wants me to solve this question using these methods. But thank you very much for your replies
#### Klaas van Aarsen
##### MHB Seeker
Staff member
Yeah, I think I can prove it, however I cannot use this method as I never learn it before. So far for this kind of questions I learned tests for convergence, eg ratio test, root test, integral test... etc So I think my teacher wants me to solve this question using these methods. But thank you very much for your replies
It looks like you really need the Cauchy-Schwarz inequality... in combination with the Direct Comparison Test.
#### Opalg
##### MHB Oldtimer
Staff member
Yeah, I think I can prove it, however I cannot use this method as I never learn it before. So far for this kind of questions I learned tests for convergence, eg ratio test, root test, integral test... etc So I think my teacher wants me to solve this question using these methods. But thank you very much for your replies
If $x$ and $y$ are positive numbers then $x^2 + y^2 - 2xy =(x-y)^2 \geqslant0$, from which $xy \leqslant \frac12(x^2+y^2).$ Apply that with $x=a_n$ and $y = n^{-2/3}$ to see that $$\displaystyle \frac{a_n}{n^{2/3}} \leqslant \frac12\Bigl(a_n^2 + \frac1{n^{4/3}}\Bigr).$$ Then $$\displaystyle \sum \frac{a_n}{n^{2/3}} \leqslant \frac12\Bigl(\sum a_n^2 + \sum \frac1{n^{4/3}}\Bigr)$$, and it follows from the comparison test that $$\displaystyle \sum \frac{a_n}{n^{2/3}}$$ converges.
#### kris1
##### New member
Ohh thank you! So for the first part you used Cauchy-Schwarz inequality, right? And can I prove it by using real numbers, eg for $$\displaystyle a_{n}$$=2, and n=8 ? | 2021-06-13 03:18:32 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8514484167098999, "perplexity": 473.83522568674556}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-25/segments/1623487598213.5/warc/CC-MAIN-20210613012009-20210613042009-00407.warc.gz"} |
http://mathoverflow.net/revisions/81967/list | 2 Put math into LaTeX
Consider the n-dimensional $n$-dimensional sphere S^n. $S^n$. I'm especially interested in the n=4 $n=4$ case. The Hilbert space L^2(S^n) $L^2(S^n)$ can be decomposed into a direct sum of eigenspaces of the Laplacian, which are finite dimensional. I'm looking for non-isometric conformal transformations
f: S^n ->
$$f: S^n \to S^n$$
s.t. for some lambda, $\lambda, \mu > 0 0$ if psi $\psi$ is an eigenvector of the Laplacian with eigenvalue alpha $\alpha < lambda \lambda$ then f(psi) $f(\psi)$ is a sum of eigenvectors with eigenvalues $< mu.\mu$.
Do such f $f$ exist? If so, is it possibly to classify them?
1
# Conformal transformations and harmonic analysis on the sphere
Consider the n-dimensional sphere S^n. I'm especially interested in the n=4 case. The Hilbert space L^2(S^n) can be decomposed into a direct sum of eigenspaces of the Laplacian, which are finite dimensional. I'm looking for non-isometric conformal transformations
f: S^n -> S^n
s.t. for some lambda, mu > 0 if psi is an eigenvector of the Laplacian with eigenvalue alpha < lambda then f(psi) is a sum of eigenvectors with eigenvalues < mu.
Do such f exist? If so, is it possibly to classify them? | 2013-05-23 08:16:48 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9443551301956177, "perplexity": 557.7243623964938}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2013-20/segments/1368703035278/warc/CC-MAIN-20130516111715-00064-ip-10-60-113-184.ec2.internal.warc.gz"} |
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Click outside the text area to trigger the callback. this: If you specify this property as a categorical array, MATLAB uses the values in the array, not the full set of categories. Answered: Rik on 22 Apr 2018 I would like to insert a filled triangle as a text box on a Matlab figure. 1) edit text box -to input text in the form of a number 2) uitable - to create matrix Based off of what the user will input in the edit text box, say '5'. This callback function can access specific information about the user’s interaction Example: {'Joseph Welford'; 'Mary Reilly'; 'Roberta Silberlicht'} If you are working with polar axes, then the box command controls the outline display when the theta-axis limits do not span 360 degrees.This table lists a subset of polar axes properties related to the outline. Find the treasures in MATLAB Central and discover how the community can help you! Create a text area. 1 answer Question. Remarks. When i run the program and write in edit1 box the value eg. Now when the user press the Proceed button, the application should open that URl in a webbrowser control and fill the form on that page containing userID & password textboxes and submit it via the login button on that web page. annotation(shapeType,dim) creates a rectangle, ellipse, or text box annotation with a particular size and location in the current figure.Specify shapeType as 'rectangle', 'ellipse', or 'textbox'.Specify dim as a four-element vector of the form [x y w h].The x and y elements determine the position and the w and h elements determine the size. > In fileparts at 35 MATLAB deletes all other message boxes with the same title. I'm doing several plots, using "hold on", with different markers and colors in a cycle. One way to do this is to use "" command. Use the add method of an mlreportgen.ppt.Presentation object to add a slide to a presentation. 1 ⋮ Vote. I wish to add a text box uicontrol object just below it to add information. I have created a plot, and now I want to place a textbox on the side of it displaying values of some variables. If you specify this property as a categorical array, MATLAB uses the values in the array, not the full set of categories. Save the following code to comments.m on your MATLAB path. text and clicks outside the text area, a label thanks the app user for the Subsequent elements in the cell array are the arguments to Active 2 years ago. Value changed callback, specified as one of these values: A cell array in which the first element is a function d. Display the calculated result in the empty editable text box 3. Each element of the cell array displays on a separate line. I am using the following code. a text area. This is the default if 'PlotStyle' is 'compact'. Y — Upper-left y-coordinate position of text box character vector. txa = uitextarea creates a text area in Notice that the text area includes a scroll bar so that the app user can 5. The [R G B] vector contains the red, green, and blue values. The syntax is also very simple; You may receive emails, depending on your. Value, specified as a character vector, cell array of character vectors, string array, it, Value of text area before app user’s most recent interaction with or (B͜͡o͜͡x͜͡e͜͡d͜͡ t͜͡e͜͡x͜͡t͜͡). object. If you do not specify a parent container, You need the amssymb package to render this symbol. 0. The video offers a short tutorial on how to add specific text to the beginning/end of all cells in Excel. By default, the units are normalized to the figure. 1. result of a callback function in matlab gui. Based on your location, we recommend that you select: . Is that right? However, the comment using 'text' would be alinged to the plotted data points. 2), including the x- and y-coordinate ranges, the number of traces, segments and nodes. 'filled' Plot boxes using a narrow filled box with lines for whiskers. Choose a web site to get translated content where available and see local events and offers. pc — picas. Note that if you are setting both the FontSize and the FontUnits properties in one function call, you must set the FontUnits property first so that the MATLAB software can correctly interpret the specified FontSize.The same applies to figure and axes units — always set the Units property before setting properties whose values you want to be interpreted in those units. drawable area of the parent container. Define the Figure and ListBox properties to represent the figure and the handle to the list box, respectively. Force the box to fit tightly around the text by setting the FitBoxToText property to 'on'. The second two elements specify the length and height of the text box. as the vector [left bottom width height]. What you can do is to check if the text has changed since the button was last pushed. 1. Other MathWorks country sites are not optimized for visits from your location. Part Description; prompt: Required. I am doing a project in which I have to make a windows application that can Take a URL in textbox from user. 11/15/2018; 2 minutes to read; o; O; k; K; S; In this article. On the first screen of my GUIDE-made GUI I want the participant to enter their name in the text-box and press the OK push button. Then I close the 'Find and Replace' dialog. If the first argument hax is an axes handle, then plot into this axis, rather than the current axes returned by gca.. input argument combinations in the previous syntaxes. Based on your location, we recommend that you select: . Accelerating the pace of engineering and science. You can query the fill table with data from text box. If a ComboBox is bound to a data source, the ComboBox inserts the value the user enters or selects into that data source. ValueChangedFcn callback updates one of the labels to Learn more about matrix, text file, logical indexes to extract data MATLAB 1. The callback executes when the user changes the text and either presses To add text to one point, specify x and y as scalars. Reload the page to see its updated state. For example, You can also select a web site from the following list: Select the China site (in Chinese or English) for best site performance. Create a text box annotation with multiline text by setting the String property to a cell array. MATLAB calls the uifigure function to create a new Figure object that serves as the parent container. If there are too many rows to display in the text area, MATLAB adds a scroll bar. If there are too many rows to display in the text area, MATLAB adds a scroll bar. Name,Value pair arguments. Example: 'BoxStyle','filled' 'Colors' — Box colors RGB triplet | character vector or string scalar of color names. The words default, factory, and remove are reserved words that do not appear in text when quoted as normal characters. child containers. in — inches. 11. Follow 32 views (last 30 days) vidyadhar k on 22 Apr 2018. Value property changes programmatically. Learn more about gui, gui table, matlab, matlab gui, text box, image processing, app designer, fill table, data ... How to Display Only Filename and FileSize in MATLAB. Default: 0.5 'MarkerEdgeColor' Marker outline color, specified as an RGB triplet, hexadecimal color code, color name, or short name for one of the color options listed in the Color name-value pair argument. Cute Ⓑ̣̣̣̣̣̣Ⓛ̣̣̣ⓞ̣̣̣̣̣̣ to put on your Instagram, Facebook, Twitter and more ! MATLAB: legend for plotyy with multiple data sets. How may I do this? By continuing to use this website, you consent to our use of cookies. Would a possible solution be to use the DOS command SubWCRev.exe (I already use this for my source and header text files) ? The properties listed here are a subset of the available properties. I have read numerous articles that all point to the same setup, but i cannot get it to work. Setting Property Units. the argument name and Value is the corresponding value. txa = uitextarea(parent) view the postal code. Valid abbreviations are: px — pixels (default) cm — centimeters. it, Distance from the inner left edge of the parent container to Web browsers do not support MATLAB commands. The parent can be a txa = uitextarea(___,Name,Value) Determine the current size of the text area. Each element of the cell array displays on a separate line. But I don't know how to assign colour for the value. You can specify several name and value or 1-D categorical array. thank you text is removed. If the app user removes the text and clicks outside the text area, the contour(Z) creates a contour plot containing the isolines of matrix Z, where Z contains height values on the x-y plane.MATLAB ® automatically selects the contour lines to display. Upper-left x-coordinate of text box, specified in the form valueUnits where Units is an abbreviation for the units. Thanks to George and Sebastian for reporting the issues. 'Lorem ipsum dolor sit amet, consectetur adipiscing elit, sed do eiusmod tempor. plots 10 stems with heights from 2 to 20 in red; Optional property/value pairs may be specified to control the appearance of the plot. I don't think MATLAB will know whether text has been pasted into the text box, or if the user has typed something in. to the outer bottom edge of the text area, Distance between the right and left outer edges of the text use of a scroll bar. This website uses cookies to improve your user experience, personalize content and ads, and analyze website traffic. Vote. [MOVED from section for answers - Jan] I wanted to have a non-default background colour which is an option for uicontrol / text but not text. the outer left edge of the text area, Distance from the inner bottom edge of the parent container 0. Example: {'Joseph Welford'; 'Mary Reilly'; 'Roberta Silberlicht'}. The following table lists the properties of the ValueChangedData object. Your text in a box. Vote. MATLAB® calls the uifigure function to create the Environment Tableau Desktop 10.4 Answer cif3 boxes are filled, call the correct user-defined function with the given inputs to calculate the missing value. Accelerating the pace of engineering and science. containers: Tab, Panel, ButtonGroup, or GridLayout. Custom Markers for Matlab plot. Use this option with any of the It does not execute if the This Unable to complete the action because of changes made to the page. The callback uses the PreviousValue property returned in the event argument to populate the text area. Once they press the button, the name should be stored in the 1st column, 2nd row of an array for the participant's data in the form of a string. Select a Web Site. 1. The annotation extends from the point (x_begin, y_begin) to (x_end, y_end).By default, the units are normalized to the figure. 2. filled semicircle in Matlab. 1. ... Statistics calculated from the data input file are displayed in the text box (lower left of the main window, shown as a portion of Fig. Width of the line or edges of filled area, in points, a positive scalar. 1. Learn more about borrar, reestablecer, salir MATLAB the uifigure function, or one of its child input. How can I do that? Matlab Edit Text Boxes - Show Hint? This user control is a List Box and there I would like to insert some text. MATLAB passes this information in a ValueChangedData object as the second argument to your callback function. With some digging you should be able to add this package to your Matlab copy, but you should be aware that in that case your code is no longer portable to another copy of Matlab, unless that one has amssymb as well. MATLAB HOMEWORK!! https://se.mathworks.com/matlabcentral/answers/385245-how-can-i-create-a-text-box-alongside-my-plot#answer_307486, https://se.mathworks.com/matlabcentral/answers/385245-how-can-i-create-a-text-box-alongside-my-plot#comment_765980, https://se.mathworks.com/matlabcentral/answers/385245-how-can-i-create-a-text-box-alongside-my-plot#comment_1201685. 1. data.txt), and next time when i run the program the function must read 513 from data.txt and put the read value from text file in edit text box. For more information about writing callbacks, see Write Callbacks in App Designer. GUI Text box. Revision History November 2000 Online Only New for MATLAB 6.0 (Release 12) June 2001 Online Only Revised for MATLAB 6.1 (Release 12.1) July 2002 Online Only Revised for MATLAB 6.6 (Release 13) a new figure window and returns the TextArea Import the PPT package so that you do not have to use long, fully qualified names for the PPT API classes. Question How to change background color for text objects in a dashboard. The column and row indices of Z are the x and y coordinates in the plane, respectively. Running info in the console gives me all the information about the sound file and stores it in the workspace to the right of MATLAB. This places a text box with horizontal offset of 50% of the Figure's width, and vertical offset of 20% of the Figure's height. I have a text box with a browse button, which when clicked opens a file selection dialog, which I'm fine with. Other MathWorks country sites are not optimized for visits from your location. You have to change background color if necessary, font size, font weight, remember tag of the edit box or keep tag as it is and finally you have to change the string of the edit box from Edit Text to ‘0’ because you have to enter number here for doing various operation. I wish to have a text box in the image with each of the following on a new line, in bold with a color (red, blue, green) If you specify text that contains only a numeric value, the value is converted using sprintf('%g',value). The first two elements specify the coordinates for the lower-left corner of the text box. How to plot a filled box? Increase the text area size so that the postal code displays without the Property inspector consists of various properties of the Edit box. In a file in your current folder, create a class named ToFigure that redirects the plugin output to a figure and displays it in a list box within the figure. When an app user types text and clicks outside the text area, the Sir , x= values of text box 1 value , y= text box 2 value , xlwrite ( Exl file , cellA , 'x value ' , ' cell B ' , 'y value '); A = A+1 , B = B+1 , then .. after i inter some value after clear text box 1 for example if i inter 1 , then command will read the values of A columns when value match inter number then values of B will appear in text box2 String expression displayed as the message in the dialog box. You clicked a link that corresponds to this MATLAB command: Run the command by entering it in the MATLAB Command Window. Based on your location, we recommend that you select: . 0. Fixed a font swapping bug and a MATLAB bug affecting the export of white lines to EPS. This tutorial video teaches about using Text Box in Matlab GUI using an Example..... Download Matlab Code Here: http://www.jcbrolabs.org/matlab-codes Ask Question Asked 5 years, 11 months ago. A good day everyone, I'd like to get some ideas on how to assign colour for a specific value on my static text box for GUI. The first column will contain student numbers. list, see TextArea Properties. Parent container, specified as a Figure object created using Save the following code to logNames.m on your MATLAB path. Change cursor to loading animation. Error: While setting the 'String' property of 'UIControl': String should be char, numeric or … Well the problem is not that I cannot put text there, I … Name1,Value1,...,NameN,ValueN. I simply want my .slx model and library files to display a text box with the SVN revision number. 0 ⋮ Vote. Now, to add fills to the ternary plot, choose either the option 'To Self' or 'To Next' from the dropdown menu next to the attribute 'Fill To' under the property 'Filled Area'. specifies TextArea properties using one or more The size of the box is 10% of Figure's height by 10% of Figure's width: To place a textboxoutsidethe plot, you can modify the position and/or dimensions of the axis. i am having a problem i want to disply a number 'e.g 1000' in edit text box without using any pushbutton or anything.... i am writing this code in the call back function of edit_text but it doesn't give me the result.tag is edit1. One point is 1/72 inch. You can also check if the text box is empty, like Luffy showed you, but I … Changing a ToolTip's cursor. Thanks to George and Sebastian for reporting the issues. annotation ('textbox', [0.5, 0.2, 0.1, 0.1], 'String', "hi") This places a text box with horizontal offset of 50% of the Figure's width, and vertical offset of 20% of the Figure's height. callback functions specified as character vectors. MathWorks is the leading developer of mathematical computing software for engineers and scientists. MathWorks is the leading developer of mathematical computing software for engineers and scientists. Follow 310 views (last 30 days) Stephan on 5 Dec 2017. I have a edit text box . I have a MATLAB program I am developing in order to do some image processing stuff and need to use a user control into a MATLAB GUI user interface I created ad-hoc. This MATLAB function opens a modal dialog box entitled Open. comma-separated pairs of Name,Value arguments. I don't know how to code in VBA but am trying to automate an if/then calculation based on cell color. ', % Check each element of text area cell array for text, Value of text area after app user’s most recent interaction with If the text does not fit into the width of the text area, MATLAB wraps the text. Specify optional Scroll to the bottom of a text area programmatically. area. Then, use the add method of the resulting mlreportgen.ppt.Slide object to add a picture to the slide.. Is there way to read powerpoint file and get data?. To display any of these words individually, precede them with a backslash, such as '\default' or '\remove'. Jiro's pick this week is textbp by Peter Mao.. Have you ever wanted to place a text on a figure (using TEXT), and end up spending time trying to figure out a nice location where it doesn't cover up the data?To be reusable for arbitrary data, you have to be clever in determining the X-Y location. When an app user types The size of the box is 10% of Figure's height by 10% of Figure's width: the plot, you can modify the position and/or dimensions of the axis. Specify a size and long text for it. Related. how can I erase data from edit text boxes in gui?. ComboBox control. If createmode is 'modal', MATLAB replaces the existing message box with the specified title that was last created or clicked on with the specified modal dialog box. N.B. where mfc, mec, ms and mew are aliases for the longer property names, markerfacecolor, markeredgecolor, markersize and markeredgewidth.. If I push the replace button MATLAB replaces only that section that is highlighted with what I put in the replace field. The Position values are relative to the Warning: The fourth output, VERSN, of FILEPARTS will be removed in a future release. Use the 'Traces' section under the 'Style' menu to change the properties specific to the traces in the plot such as trace's name, color, filled area type and its color, etc. pair arguments in any order as table describes each element in the vector. If the text does not fit into the width of the text area, MATLAB wraps the text. Matlab: How to pass a variable from an edit text box in a GUI to another m file? figure. How do I draw a text box with shadow borders in LaTex? In the box plot, a box is created from the first quartile to the third quartile, a verticle line is also there which goes through the box at the median. The problem is that not always all the plots will be created, as sometimes the vector will be null, and therefore "legend" is not a good option. If all 4 boxes are filled, then give a different message to the user. The ValueChangedData object is not available to MATLAB can properly render formatted text, such as The lower-left corner of the figure maps to (0,0), and the upper-right corner maps to (1,1). A character vector containing a valid MATLAB expression (not recommended). Create a text area and two labels. What I'd like to know would be how to make the text in the text box update to show the file path and name when I've done browsing. 14 Aug 2013: 1.81.0.0: Fixed a font swapping bug and a MATLAB bug affecting the export of white lines to EPS. creates the text area in the specified parent container. A Box Plot is also known as Whisker plot is created to display the summary of the set of data values having properties like minimum, first quartile, median, third quartile and maximum. Create a text box annotation with multiline text by setting the String property to a cell array. This MATLAB function opens a modal dialog box that lists files in the current folder. area, Distance between the top and bottom outer edges of the text How to draw a text box with shadow borders in LaTex. Add code to the "Clear All" button that will reset all the text boxes (delete all text … For example: % set the width of the axis (the third value in Position), % put the textbox at 75% of the width and. The maximum length of prompt is approximately 1024 characters, depending on the width of the characters used. Choose a web site to get translated content where available and see local events and offers. In Matlab, fill() function is responsible for creating colored filled polygons from the data indicated by X and Y with vertex color acknowledged by the Colorspec that includes various color specifications. Using GUI GUIDE what is the code to get an output from a equation/code that is in the GUI code, which is assigned to a variable, to display in a static text box. Some polar axes properties affect the appearance of the outline around the polar axes. Some values occur more often than others. In App Designer, the argument is called event. The drawable area is the area These numbers will have the form 20200001, 20200002, 20200003, ... for all the people in the list. This code creates a figure window containing two labels and TextBox in Matlab Plot. Name is inside the borders of the container and does not include the area occupied by decorations such Or, you can set it to an M-by-3 matrix of M number of RGB (red, green, and blue) character vector color values.. To specify one color for all the text boxes, set BoxColor to either a color character vector or an [R G B] vector. For example, 12345678 displays as 1.23457e+07. as a menu bar or title. retrieve particular time data from .txt file. The bare-bones syntax for this is as follows: This places a text box with horizontal offset of 50% of the Figure's width, and vertical offset of 20% of the Figure's height. If you specify this property as a categorical array, MATLAB ® uses the values in the array, not the categories. Customizing cursor in Matlab. To add text to multiple points, specify x and y as vectors with equal length. For example, a=50, colour of static text box becomes green. object properties using dot notation. handle. Yes, you can. In this case I want to take that number and create populate a matrix (uitable) off of that number to be a 5 by 5 matrix. Does not execute if the text area and offers as Name1, Value1,... for all the people the... Doing several plots, using hold on '', with different markers and colors in a to... The words default, the units displays on a separate line traces, and... Boxes using a narrow filled box with shadow borders in LaTex value, specified as the in. Of it displaying values of some variables rows between two indexes in an array where the array... Matlab/Octave to SVG converter version 10-Nov-2010, Juerg Schwizer ( converter @ bluewin.ch ) bug... In matlab filled text box article using 'text ' would be alinged to the same title remain in. Properties to represent the figure and ListBox properties to represent the figure text input when! Variable from an Edit text boxes in gui? a gui to matlab filled text box m file text ( x y. Colors RGB triplet, character vector or string scalar by default, factory, and analyze traffic! Function to create a text area size so that the text and clicks outside the text to... Event.Previousvalue returns the TextArea object an abbreviation for the value property changes programmatically have an I. The handle to a cell array are the x and y as vectors with equal length that to... The array, MATLAB ® uses the values in the array, not the categories a possible solution be use! In this article cif3 boxes are filled, call the correct user-defined function with the same title Designer! If there are too many rows to display any of these values: cell. Specified in the text does not fit into the width of the available.! Juerg Schwizer ( converter @ bluewin.ch ) multiple data sets have a text box on a separate line will the! Tutorial on how to assign value to the page as a character containing... And colors in a cycle user for the plot, factory, and the handle to slide. Correct user-defined function with the given inputs to calculate the missing value brings up 'Find. Text ( x, y, z, txt ) positions the text in MATLAB! The location of the Edit box box that lists files in the specified parameters.Existing message boxes with specified. Subsequent elements in the specified parameters.Existing message boxes with the same title nonmodal message with. '' command message box with the text area, MATLAB ® uses the values in the previous syntaxes if text. The treasures in MATLAB Central and discover how the community can help you ' is 'compact ' do n't how! A ComboBox is bound to a presentation visits from your location, we recommend that you select: missing... Designer, the comment using 'text ' would be alinged to the drawable area of the text changed... Since the button was last pushed legend for plotyy with multiple data sets app Designer a URL in textbox user! The x- and y-coordinate ranges, the number of traces, segments and.. Discover how the community can help you to the page call the correct user-defined function with the title... Vidyadhar k on 22 Apr 2018 I would like to insert some text drawable! The handle to a data source, the units are normalized to the slide quoted as normal characters Welford ;., a=50, colour of static text box with the same setup, but I can not put text matlab filled text box... As '\default ' or '\remove ' that all point to the bottom of a text area size so you! I have read numerous articles that all point to the list aliases for the input I close 'Find. Section that is highlighted with what I put in the dialog box matlab filled text box files. Erase data from Edit text boxes - Show Hint see write callbacks in app Designer the. A cycle I put in the text by setting the string property 'on. Input field when clicking a button I must save to a cell displays! White lines to EPS Designer, the thank you text is removed rows to display any of the Edit.... Put on your location, we recommend that you select: ; o ; o k! Fourth output, VERSN, of FILEPARTS will be removed in a ValueChangedData object the! Arguments in any order as Name1, Value1,... for all the people in the array, the. All the people in the text box with lines for whiskers a windows application can! Fit tightly around the polar axes an RGB triplet | character vector library files to display Only Filename FileSize! The DOS command SubWCRev.exe ( I already use this option with any of these values: cell... Namen, ValueN empty editable text box uicontrol object just below it to add slide! Text box becomes green revision number around the text area in a future release replace field by gca.slx... Vidyadhar k on 22 Apr 2018 area field of FILEPARTS will be in... Can help you of m number of color names warning: the fourth output VERSN. Am trying to automate an if/then calculation based on your ] vector contains the red,,... Save the following code to comments.m on your MATLAB path specify this property as a location for the text setting. Create the figure you select: Value1,..., NameN,.! Display in the cell array of m number of color names setup, but can. Left bottom width height ] close the 'Find and replace ' dialog between. Vidyadhar k on 22 Apr 2018 I would like to insert a filled triangle as categorical..., not the full set of categories sit amet, consectetur adipiscing elit, sed do tempor. Cells in Excel box colors, specified as one of its child.. App user removes the text box annotation with multiline text by setting the FitBoxToText property to '! | 2022-06-25 05:35:22 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3892222046852112, "perplexity": 2023.0937312315034}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-27/segments/1656103034170.1/warc/CC-MAIN-20220625034751-20220625064751-00553.warc.gz"} |
https://www.zbmath.org/?q=an%3A1249.90303 | zbMATH — the first resource for mathematics
Multicriterial graph problems with MAXMIN criterion. (Russian) Zbl 1249.90303
Summary: $$r$$-criterial problems for $$r$$-weighted graphs are considered ($$r\geq 2$$). Certain types of subgraphs are called admissible. To solve the problem means to choose a Pareto optimal admissible subgraph from the complete set of alternatives (CSA). The main result of this paper is the following. Suppose that a criterion, denoted by MAXMIN, requires maximization of the minimal weight of the first edges of an admissible subgraph and that there is an effective procedure constructing the CSA for an $$(r-1)$$-criterial problem without this MAXMIN criterion. Then the CSA for the initial $$r$$-criterial problem is created effectively.
MSC:
90C35 Programming involving graphs or networks | 2021-04-18 10:56:41 | {"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": 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": 0.7370445132255554, "perplexity": 1305.7297308329955}, "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-2021-17/segments/1618038476606.60/warc/CC-MAIN-20210418103545-20210418133545-00468.warc.gz"} |
https://stats.stackexchange.com/questions/413624/sample-size-prediction-in-multivariate-a-b-testing | # Sample size prediction in multivariate A-B testing
I need to run an A-B testing with one control group (40%) and 3 variants (20%) each.
Base line = 0.65
Target lift = 0.25
Power =0.8
Confidence = 95%
I found following R code to find minimum sample size for two variants.
power.prop.test(p1=.65,p2=.65*1.25,power=.8, alternative="one.sided", sig.level = 0.05)
How to calculate sample size needed for A-B testing considering there are 3 variants(60%) and one control group (40%)?
• It depends on what your intended test is: what will be the null hypothesis and the alternative hypothesis? It also depends on how you intend to run the experiment and how you will test the hypothesis. Please supply these details. – whuber Jun 18 '19 at 18:55
• @whuber it will be click through rate. I don't have much knowledge about stats, but the experiment is going to be like-> we will send two templates with some modification and see which one is better. – Vipul Aggarwal Jun 18 '19 at 18:58
• Your response is not helpful (for me anyhow). Here is the result from one computation. You have a single group. The current success rate is 0.65. You try a new method. If the success rate improves to .90 or better you want to detect that with probability .8 using a test with significance level .05. Then you need $n = 18$ subjects. I don't suppose that is what you want, but can you explain more clearly what you do want. // Most software for comparing two groups give results for equal sample sizes in the two groups. Through simulation one can use $\ne$ gp sizes, but that's not best design. – BruceET Jun 18 '19 at 23:48
Being somewhat conservative we can dismiss the presence of three variants B/C/D and treat each control vs variant X comparison independently. This will indeed allow us to use the functionality provided by power.prop.test. Nevertheless, to ensure that these sample size computations are relevant we will need to adjust the level of significance to correct for multiple testing. With three variants B/C/D simply doing a Bonferroni correction is probably adequate (i.e. something like : power.prop.test( ..., sig.level = 0.05/3)) . Witte et al. (2000) On the relative sample size required for multiple comparisons perform a similar approach when examining differences in normally distributed variables. Jung et al. (2005) Sample size calculation for multiple testing in microarray data analysis perform a more in-depth analysis and outline a methodology for a full simulation study if we want to try this with data particular to a specific application. | 2020-09-22 18:14:01 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 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": 0.5852662920951843, "perplexity": 790.685008929549}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-40/segments/1600400206329.28/warc/CC-MAIN-20200922161302-20200922191302-00081.warc.gz"} |
https://justinyang.me/notes/2022/03/25/a-little-bit-of-this-a-little-bit-of-that/ | # A Little Bit of This, A Little Bit of That
## 2022/03/25
I’ve had a few days to get used to Blogdown, Hugo, and Xmin now, and of course I immediately took to tinkering. This is just a short post to highlight some of the changes I’ve made and to whom I owe thanks.
## Last Things, First (Footnotes, That Is)
There is nothing inherently wrong with how Hugo Xmin handles footnotes and some might go so far as to say it is elegant. Still, based on personal preference, I have wrapped my footnotes with littlefoot.js which, for, me, has nicer footnotes which are a bit easier to deal with, especially on mobile. I also didn’t want a super lengthy front page so it was nice to hide my chatty footnotes that way.
I added this to my foot_custom.html file after seeing this post on the Hugo forums. I’m very aware that this makes the page potentially load more slowly, so I’m keeping an eye out on performance.
<link rel="stylesheet" href="https://unpkg.com/littlefoot/dist/littlefoot.css" />
<script src="https://unpkg.com/littlefoot/dist/littlefoot.js" type="application/javascript" ></script>
<script type="application/javascript"> littlefoot.default() </script>
## Better Publication Lists Through Automation
One big goal for this iteration of my personal academic webpage was to minimise the time I spend manually updating content. I was very inspired by Thomas Hackl’s work on this but I changed things up a little to suit my purpose as follows:
library(scholar)
library(tidyverse)
publications <- as_tibble(get_publications("o-MsbBYAAAAJ")) %>%
arrange(desc(year)) %>%
mutate(
author = str_replace_all(author, "([A-Z]) ([A-Z]) ", "\\1\\2 "),
author = str_replace_all(author, ", \\.\\.\\.", " et al"),
author = str_replace_all(author, "JC Yang", "**JC Yang**"),
author = str_replace_all(author, "J Yang", "**J Yang**"),
title = str_replace_all(title, ":.+", "")
) %>%
mutate(
citation = paste0(
author,
". ",
"(",
year,
").",
" ",
"[",
title,
"]",
cid,
"&btnI=1&hl=en)",
". ",
"*",
journal,
"*",
" ",
number,
"."
)
) %>%
select(citation)
publications %>% knitr::kable("html", col.names = NULL)
## Frankenstein Solutions for Peer Reviews
I also wanted to be able to share an unordered list of publications for which I have served as an invited referee. I use Publons to track these and I push from Publons to ORCID, so when I came across the rorcid package, I knew I was onto something good! I managed to make this work (probably inelegantly) with a lot of help from Clarke’s great walk through of rorcid and gorkang’s solution to the issue of errors when using rcrossref::cr_journals. 1
library(tidyverse)
library(janitor)
library(rorcid)
library(rcrossref)
library(stringi)
reviews <-
orcid_peer_reviews("0000-0003-2881-4906")[[1]]$group$peer-review-group %>%
map_dfr(pluck, "peer-review-summary") %>%
as_tibble() %>%
clean_names() %>%
select(review_group_id) %>%
distinct() %>%
mutate(issn = stri_enc_toutf8(str_replace(review_group_id, "issn:", ""))) %>%
select(issn)
get_title_from_issn <- function(issn) {
tryCatch(
issn_title[[issn]],
error = function(e) {
rcrossref::cr_journals(issn)$data$title
}
)
}
journal_names <-
reviews %>% purrr::map(~ get_title_from_issn(.x)) %>% unlist() %>% as_tibble() %>% drop_na() %>% arrange(value) %>% mutate(value = str_squish(value)) %>% pivot_wider(names_from = value)
cat(paste0("- ", names(journal_names)), sep = "\n")
## I’ll Show You Mine, You Show Me Yours
I wanted an easy way to share my presentations so users could view them on mobile devices easily. Moving forward, I’d really like to make more use of reveal.js because it’s just really nice and slick but I might rely on Beamer for more technical presentations (and anyway, I needed to a way to share PDFs of older presentations when I used a lot more PowerPoint and Stata…). So I had two things to accomplish, really.
For reveal.js, I came across taipapa’s shortcode for embedding reveal.js presentations, which I shamelessly borrowed for this page by adding the following shortcode:
<iframe src="{{.Get 0}}" width="1000" height="600" frameborder="0" allowfullscreen="allowfullscreen" allow="geolocation *; microphone *; camera *; midi *; encrypted-media *"></iframe>
For PDFs, I wanted something relatively light and which could render decently on mobile devices. I ended up settling on a solution using PDF.js which I came across from anvithks, but I didn’t want to have to keep the javascript updated, so I ended up using CDNJS for PDF.js with minor modifications to the shortcode:
<script type="text/javascript" src = 'https://cdnjs.cloudflare.com/ajax/libs/pdf.js/2.9.359/pdf.min.js'></script>
<style>
#the-canvas {
border: 1px solid black;
direction: ltr;
width: 100%;
height: auto;
display: none;
}
#paginator {
display: none;
text-align: center;
margin-bottom: 10px;
}
display: none;
justify-content: center;
align-items: center;
width: 100%;
height: 350px;
}
display: inline-block;
width: 50px;
height: 50px;
border: 3px solid #d2d0d0;;
border-top-color: #383838;
animation: spin 1s ease-in-out infinite;
-webkit-animation: spin 1s ease-in-out infinite;
}
@keyframes spin {
to { -webkit-transform: rotate(360deg); }
}
@-webkit-keyframes spin {
to { -webkit-transform: rotate(360deg); }
}
</style>
<div id="paginator">
<button id="prev">Previous</button>
<button id="next">Next</button>
<span>Page: <span id="page_num"></span> / <span id="page_count"></span></span>
</div>
<div id="embed-pdf-container">
</div>
<canvas id="the-canvas"></canvas>
</div>
<script type="text/javascript">
// If absolute URL from the remote server is provided, configure the CORS
var url = '{{ .Get "url" }}';
var hidePaginator = "{{ .Get "hidePaginator" }}" === "true";
var selectedPageNum = parseInt("{{ .Get "renderPageNum" }}") || 1;
// Loaded via <script> tag, create shortcut to access PDF.js exports.
var pdfjsLib = window['pdfjs-dist/build/pdf'];
// The workerSrc property shall be specified.
pdfjsLib.GlobalWorkerOptions.workerSrc = 'https://cdnjs.cloudflare.com/ajax/libs/pdf.js/2.9.359/pdf.worker.min.js';
// Change the Scale value for lower or higher resolution.
var pdfDoc = null,
pageNum = selectedPageNum,
pageRendering = false,
pageNumPending = null,
scale = 3,
canvas = document.getElementById('the-canvas'),
ctx = canvas.getContext('2d'),
paginator = document.getElementById("paginator"),
// Attempt to show paginator and loader if enabled
showPaginator();
/**
* Get page info from document, resize canvas accordingly, and render page.
* @param num Page number.
*/
function renderPage(num) {
pageRendering = true;
// Using promise to fetch the page
pdfDoc.getPage(num).then(function(page) {
var viewport = page.getViewport({scale: scale});
canvas.height = viewport.height;
canvas.width = viewport.width;
// Render PDF page into canvas context
var renderContext = {
canvasContext: ctx,
viewport: viewport
};
// Wait for rendering to finish
pageRendering = false;
showContent();
if (pageNumPending !== null) {
// New page rendering is pending
renderPage(pageNumPending);
pageNumPending = null;
}
});
});
// Update page counters
document.getElementById('page_num').textContent = num;
}
/**
* Hides loader and shows canvas
*/
function showContent() {
canvas.style.display = 'block';
}
/**
* If we haven't disabled the loader, show loader and hide canvas
*/
canvas.style.display = 'none';
}
/**
* If we haven't disabled the paginator, show paginator
*/
function showPaginator() {
if(hidePaginator) return
paginator.style.display = 'block';
}
/**
* If another page rendering in progress, waits until the rendering is
* finished. Otherwise, executes rendering immediately.
*/
function queueRenderPage(num) {
if (pageRendering) {
pageNumPending = num;
} else {
renderPage(num);
}
}
/**
* Displays previous page.
*/
function onPrevPage() {
if (pageNum <= 1) {
return;
}
pageNum--;
queueRenderPage(pageNum);
}
/**
* Displays next page.
*/
function onNextPage() {
if (pageNum >= pdfDoc.numPages) {
return;
}
pageNum++;
queueRenderPage(pageNum);
}
/**
*/
pdfjsLib.getDocument(url).promise.then(function(pdfDoc_) {
pdfDoc = pdfDoc_;
var numPages = pdfDoc.numPages;
document.getElementById('page_count').textContent = numPages;
// If the user passed in a number that is out of range, render the last page.
if(pageNum > numPages) {
pageNum = numPages
}
// Initial/first page rendering
renderPage(pageNum);
});
}
</script>
## Shiny, Pretty Things
Hugo-Academic makes great use of Font Awesome and Academicons, and though I’m aware that they are a bit superfluous and self-indulgent, I added this here anyway because I liked them. Again, another performance hit, so I’m keeping my eye on things, but I think it’s not too bad, right? All I had to do was added these to head_custom.html:
<link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/6.1.0/css/all.min.css" rel="stylesheet">
<link href="https://cdnjs.cloudflare.com/ajax/libs/academicons/1.9.2/css/academicons.min.css" rel="stylesheet">
## Talk Nerdy to Me
Finally, I didn’t want too much clutter on my pages, but I didn’t mind having a dialogue with people with respect to these notes and with presentations. I came across María Paula’s great guide to getting utteranc.es set up and it worked like a charm! All I had to do was added the following to my notes and presentations pages:
{{ if not .Params.disable_comments }}
<script src="https://utteranc.es/client.js"
repo="yangjustinc/yangjustinc.github.io"
issue-term="title"
label="💬"
theme="github-light"
crossorigin="anonymous"
async>
</script>
## Final Thoughts
This has been a huge learning opportunity and it’s been so much fun! I’ve learned a lot just by trying things and seeing what works and what doesn’t. 2 Of course, I would be nowhere without Yihui Xie and the great blogdown book! I hope to keep learning and making this little corner of the internet my own. Thanks for being part of my journey!
1. Fun fact, I got all caught up in the great Crossref outage on March 24, and couldn’t knit that page after making some updates! I thought I broke the API or something, but I was relieved to find out it wasn’t my fault!↩︎
2. I’m sure there are still many things that don’t work, so please, if you come across something like that, just let me know!↩︎ | 2022-05-22 21:07:35 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 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": 0.20344491302967072, "perplexity": 13856.594728952385}, "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/1652662546071.13/warc/CC-MAIN-20220522190453-20220522220453-00305.warc.gz"} |
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# If x^2+12x−k=0, is x=4?
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If x^2+12x−k=0, is x=4?
(1) (x+16) is a factor of x^2+12x−k=0, where k is a constant, and x is a variable.
(2) x≠−16
P.S: Bunuel- Need your help Sir!
[Reveal] Spoiler: OA
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Re: If x^2+12x−k=0, is x=4? [#permalink]
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If x^2+12x−k=0, is x=4?
(1) (x+16) is a factor of x^2+12x−k=0, where k is a constant, and x is a variable. This implies that we can factor out $$x+16$$ from $$x^2+12x-k=0$$, so we would have $$(x+16)*(something)=0$$. Thus x=-16 is one of the roots of the given quadratic equation.
Viete's theorem states that for the roots $$x_1$$ and $$x_2$$ of a quadratic equation $$ax^2+bx+c=0$$:
$$x_1+x_2=\frac{-b}{a}$$ AND $$x_1*x_2=\frac{c}{a}$$.
Thus according to the above $$x_1+x_2=-16+x_2=\frac{-12}{1}$$ --> $$x_2=4$$.
So, we have that x is either -16 or 4. Not sufficient.
(2) x≠−16. Clearly insufficient.
(1)+(2) Since (2) says that x is NOT -16, then x=4. Sufficient.
Answer: C.
Hope it's clear.
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Re: If x^2+12x−k=0, is x=4? [#permalink]
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05 Jul 2013, 13:01
Expert's post
Bunuel wrote:
If x^2+12x−k=0, is x=4?
(1) (x+16) is a factor of x^2+12x−k=0, where k is a constant, and x is a variable. This implies that we can factor out $$x+16$$ from $$x^2+12x-k=0$$, so we would have $$(x+16)*(something)=0$$. Thus x=-16 is one of the roots of the given quadratic equation.
Viete's theorem states that for the roots $$x_1$$ and $$x_2$$ of a quadratic equation $$ax^2+bx+c=0$$:
$$x_1+x_2=\frac{-b}{a}$$ AND $$x_1*x_2=\frac{c}{a}$$.
Thus according to the above $$x_1+x_2=-16+x_2=\frac{-12}{1}$$ --> $$x_2=4$$.
So, we have that x is either -16 or 4. Not sufficient.
(2) x≠−16. Clearly insufficient.
(1)+(2) Since (2) says that x is NOT -16, then x=4. Sufficient.
Answer: C.
Hope it's clear.
(1)+(2)=> 1 says x=-16 and 2 says x is NOT -16...So,isn't it contradicting hence Insufficient..?
I'm having confusion at this point...Please help me understand!
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Re: If x^2+12x−k=0, is x=4? [#permalink]
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05 Jul 2013, 13:04
Expert's post
debayan222 wrote:
Bunuel wrote:
If x^2+12x−k=0, is x=4?
(1) (x+16) is a factor of x^2+12x−k=0, where k is a constant, and x is a variable. This implies that we can factor out $$x+16$$ from $$x^2+12x-k=0$$, so we would have $$(x+16)*(something)=0$$. Thus x=-16 is one of the roots of the given quadratic equation.
Viete's theorem states that for the roots $$x_1$$ and $$x_2$$ of a quadratic equation $$ax^2+bx+c=0$$:
$$x_1+x_2=\frac{-b}{a}$$ AND $$x_1*x_2=\frac{c}{a}$$.
Thus according to the above $$x_1+x_2=-16+x_2=\frac{-12}{1}$$ --> $$x_2=4$$.
So, we have that x is either -16 or 4. Not sufficient.
(2) x≠−16. Clearly insufficient.
(1)+(2) Since (2) says that x is NOT -16, then x=4. Sufficient.
Answer: C.
Hope it's clear.
(1)+(2)=> 1 says x=-16 and 2 says x is NOT -16...So,isn't it contradicting hence Insufficient..?
I'm having confusion at this point...Please help me understand!
(1) says that x=-16 OR x=4. The equation is $$x^2+12x-64=0$$ (k=64) --> x=-16 OR x=4.
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Re: If x^2+12x−k=0, is x=4? [#permalink]
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05 Jul 2013, 13:13
Expert's post
Got it!
I was doing the mistake by considering the Stat.1 ONLY not focusing on the solns of the eqn in 1...!
Thanks for clarifying.
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Re: If x^2+12x−k=0, is x=4? [#permalink]
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22 Aug 2013, 08:37
Bunuel wrote:
If x^2+12x−k=0, is x=4?
(1) (x+16) is a factor of x^2+12x−k=0, where k is a constant, and x is a variable. This implies that we can factor out $$x+16$$ from $$x^2+12x-k=0$$, so we would have $$(x+16)*(something)=0$$. Thus x=-16 is one of the roots of the given quadratic equation.
Viete's theorem states that for the roots $$x_1$$ and $$x_2$$ of a quadratic equation $$ax^2+bx+c=0$$:
$$x_1+x_2=\frac{-b}{a}$$ AND $$x_1*x_2=\frac{c}{a}$$.
Thus according to the above $$x_1+x_2=-16+x_2=\frac{-12}{1}$$ --> $$x_2=4$$.
So, we have that x is either -16 or 4. Not sufficient.
(2) x≠−16. Clearly insufficient.
(1)+(2) Since (2) says that x is NOT -16, then x=4. Sufficient.
Answer: C.
Hope it's clear.
Why A is not sufficient? X cannot be -16, as in this case X+16 =0. As I know 0 cannot be a factor or the integer. Pls. explan
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Re: If x^2+12x−k=0, is x=4? [#permalink]
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22 Aug 2013, 09:46
Expert's post
Dmitriy wrote:
Bunuel wrote:
If x^2+12x−k=0, is x=4?
(1) (x+16) is a factor of x^2+12x−k=0, where k is a constant, and x is a variable. This implies that we can factor out $$x+16$$ from $$x^2+12x-k=0$$, so we would have $$(x+16)*(something)=0$$. Thus x=-16 is one of the roots of the given quadratic equation.
Viete's theorem states that for the roots $$x_1$$ and $$x_2$$ of a quadratic equation $$ax^2+bx+c=0$$:
$$x_1+x_2=\frac{-b}{a}$$ AND $$x_1*x_2=\frac{c}{a}$$.
Thus according to the above $$x_1+x_2=-16+x_2=\frac{-12}{1}$$ --> $$x_2=4$$.
So, we have that x is either -16 or 4. Not sufficient.
(2) x≠−16. Clearly insufficient.
(1)+(2) Since (2) says that x is NOT -16, then x=4. Sufficient.
Answer: C.
Hope it's clear.
Why A is not sufficient? X cannot be -16, as in this case X+16 =0. As I know 0 cannot be a factor or the integer. Pls. explan
Factor of a number and factor of an expression are two different things. For example, both (x+16) and (x-4) are factors of x^2+12x−64=0 --> (x+16)(x-4)=0.
Hope this helps.
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Re: If x^2+12x−k=0, is x=4? [#permalink]
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28 Aug 2013, 22:40
Bunuel wrote:
Dmitriy wrote:
Bunuel wrote:
If x^2+12x−k=0, is x=4?
(1) (x+16) is a factor of x^2+12x−k=0, where k is a constant, and x is a variable. This implies that we can factor out $$x+16$$ from $$x^2+12x-k=0$$, so we would have $$(x+16)*(something)=0$$. Thus x=-16 is one of the roots of the given quadratic equation.
Viete's theorem states that for the roots $$x_1$$ and $$x_2$$ of a quadratic equation $$ax^2+bx+c=0$$:
$$x_1+x_2=\frac{-b}{a}$$ AND $$x_1*x_2=\frac{c}{a}$$.
Thus according to the above $$x_1+x_2=-16+x_2=\frac{-12}{1}$$ --> $$x_2=4$$.
So, we have that x is either -16 or 4. Not sufficient.
(2) x≠−16. Clearly insufficient.
(1)+(2) Since (2) says that x is NOT -16, then x=4. Sufficient.
Answer: C.
Hope it's clear.
Why A is not sufficient? X cannot be -16, as in this case X+16 =0. As I know 0 cannot be a factor or the integer. Pls. explan
Factor of a number and factor of an expression are two different things. For example, both (x+16) and (x-4) are factors of x^2+12x−64=0 --> (x+16)(x-4)=0.
Hope this helps.
Thanks. I didnt know about factors of an expression.
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# If x^2+12x−k=0, is x=4?
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Powered by phpBB © phpBB Group and phpBB SEO Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®. | 2016-05-27 22:50:13 | {"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": 0.7899411916732788, "perplexity": 4732.487334590585}, "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-2016-22/segments/1464049277091.36/warc/CC-MAIN-20160524002117-00007-ip-10-185-217-139.ec2.internal.warc.gz"} |
https://spark.apache.org/docs/3.1.3/api/python/reference/api/pyspark.mllib.linalg.Vector.html | # Vector¶
class pyspark.mllib.linalg.Vector[source]
Methods
Convert this vector to the new mllib-local representation. Convert the vector into an numpy.ndarray
Methods Documentation
asML()[source]
Convert this vector to the new mllib-local representation. This does NOT copy the data; it copies references.
Returns:
pyspark.ml.linalg.Vector
toArray()[source]
Convert the vector into an numpy.ndarray
Returns:
numpy.ndarray | 2023-02-08 20:45:45 | {"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": 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": 0.39354243874549866, "perplexity": 7459.995563762569}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764500904.44/warc/CC-MAIN-20230208191211-20230208221211-00862.warc.gz"} |
http://sustainablemassasoit.org/journal/symmetry/special_issues/Viscous_Cosmology | Journal Browser
# Special Issue "Viscous Cosmology"
A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Physics and Symmetry".
Deadline for manuscript submissions: 30 September 2020.
## Special Issue Editors
Prof. Dr. Marek Szydłowski
Website
Guest Editor
Department of High Energy Astrophysics, Jagiellonian University, Kraków, Poland
Interests: physics; cosmology; astronomy; philosophy of physics
Prof. Dr. Iver H. Brevik
Website
Co-Guest Editor
Department of Energy and Process Engineering, Norwegian University of Science and Technology, NO-7491 Trondheim, Norway
Interests: electrodynamics in continuous media; Casimir effect; cosmology; fluid dynamics
Special Issues and Collections in MDPI journals
## Special Issue Information
Dear Colleagues,
The Standard Cosmological Model is a strong idealization of the real Universe. It is assumed that spatial Universe is homogeneous and isotropic (with the Friedmann-Robertson-Walker symmetry) in which effects of dissipation are neglected at very beginning. One of the ways to question this idealization is to include effects of dissipation in the form of bulk viscosity.
Eckart (1940) introduced viscous contributions to the stress-energy tensor in his formulation of a relativistic theory of dissipative processes. At first this approach was used to avoid the initial singularity in the FRW cosmology. Nowadays, simple models of bulk viscosity, i.a., allow to study the effect of isotropic expansion on the thermodynamic properties of fluids and offer a phenomenological description of particle creation in the presence of strong gravitational fields.
Two main directions are looked upon here for a better understanding the role of viscosity in cosmology:
1. The search for a description of bulk viscosity to have a better insight in the context of general relativity and cosmology.
2. The study of cosmological models with dissipation effects where bulk viscosity is considered as a candidate for dark energy component of unsubstantial nature.
The purpose of the present Special Issue, entitled “Viscous Cosmology”, is the presentation of new ideas, methods of description of viscosity and its role in a cosmic evolution for better understanding of nature of dissipation in general relativity and cosmology.
Prof. Dr. Marek Szydłowski
Prof. Dr. Iver H. Brevik
Guest Editors
Manuscript Submission Information
Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All papers will be peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.
Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Symmetry is an international peer-reviewed open access monthly journal published by MDPI.
Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.
## Published Papers (3 papers)
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# Research
Open AccessArticle
Viscous Matter in FRW Cosmology
Symmetry 2020, 12(8), 1269; https://doi.org/10.3390/sym12081269 - 01 Aug 2020
Abstract
We investigate the dynamics of dust matter with bulk viscosity effects. We explored the analogy dynamical problem to Chaplygin gas. Due to this analogy we give exact solutions for the FRW cosmology with viscosity coefficient parameterized by the Belinskii–Khalatnikov power law dependence with [...] Read more.
We investigate the dynamics of dust matter with bulk viscosity effects. We explored the analogy dynamical problem to Chaplygin gas. Due to this analogy we give exact solutions for the FRW cosmology with viscosity coefficient parameterized by the Belinskii–Khalatnikov power law dependence with respect to energy density. These exact solutions are given in the form of hypergeometrical functions. We proved simple theorem which illustrated as viscosity effects can solved the initial singularity problem present in standard cosmological model. Full article
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Figure 1
Open AccessArticle
Remarks on Cosmological Bulk Viscosity in Different Epochs
Symmetry 2020, 12(7), 1085; https://doi.org/10.3390/sym12071085 - 01 Jul 2020
Abstract
The intention of this paper is mainly two-fold. First, we point out a striking numerical agreement between the bulk viscosity in the lepton era calculated by Husdal (2016) and our own calculations of the present-day bulk viscosity when the functional form is $ζ$ [...] Read more.
The intention of this paper is mainly two-fold. First, we point out a striking numerical agreement between the bulk viscosity in the lepton era calculated by Husdal (2016) and our own calculations of the present-day bulk viscosity when the functional form is $ζ ∼ ρ$ . From a phenomenological point of view, we thus seem to have an ansatz for the viscosity, which bridges the infancy of the Universe (∼1 s) with the present. This can also be looked upon as a kind of symmetry between the early-time cosmology and the present-day cosmology: it is quite remarkable that the kinetic theory-based bulk viscosity in the early universe and the experimentally-based bulk viscosity in the present universe can be covered by the same simple analytical formula. Second, we consider the Kasner universe as a typical anisotropic model of Bianchi-Type I, investigating whether this geometrical model is compatible with constant viscosity coefficients in the fluid. Perhaps surprisingly, the existence of a shear viscosity turns out to be incompatible with the Kasner model. By contrast, a bulk viscosity is non-problematic in the isotropic version of the model. In the special case of a Zel’dovich (stiff) fluid, the three equal exponents in the Kasner metric are even determined by the bulk viscosity alone, independent of the value of the fluid energy density. We also give a brief comparison with some other recent approaches to viscous cosmology. Full article
We investigate the particle creation, as well as the thermodynamics phenomenon of viscous generalized cosmic Chaplygin gas as a cosmic fluid by assuming the flat FRW universe. For this purpose, we extract various parameters such as the energy density $( ρ )$ , [...] Read more.
We investigate the particle creation, as well as the thermodynamics phenomenon of viscous generalized cosmic Chaplygin gas as a cosmic fluid by assuming the flat FRW universe. For this purpose, we extract various parameters such as the energy density $( ρ )$ , Hubble parameter $( H )$ , declaration parameter $( q )$ , temperature $( T f )$ , and particle number density $( n )$ in the presence of three different models of the particle creation rate ( $Γ$ ). We discuss the validity of the generalized second law of thermodynamics and thermal equilibrium condition under three models of $Γ$ and discuss the graphical behavior of above-mentioned terms. Full article | 2020-08-05 01:40:16 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 10, "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": 0.439596951007843, "perplexity": 1507.1013014739422}, "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/1596439735906.77/warc/CC-MAIN-20200805010001-20200805040001-00012.warc.gz"} |
http://mscroggs.co.uk/puzzles/tags/numbers | mscroggs.co.uk
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# Puzzles
## Archive
Show me a Random Puzzle
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## Elastic Numbers
Throughout this puzzle, expressions like $$AB$$ will represent the digits of a number, not $$A$$ multiplied by $$B$$.
A two-digit number $$AB$$ is called elastic if:
1. $$A$$ and $$B$$ are both non-zero.
2. The numbers $$A0B$$, $$A00B$$, $$A000B$$, ... are all divisible by $$AB$$.
There are three elastic numbers. Can you find them?
## Square Pairs
Source: Maths Jam
Can you order the integers 1 to 16 so that every pair of adjacent numbers adds to a square number?
For which other numbers $$n$$ is it possible to order the integers 1 to $$n$$ in such a way?
## Factorial Pattern
$$1\times1!=2!-1$$ $$1\times1!+2\times2!=3!-1$$ $$1\times1!+2\times2!+3\times3!=4!-1$$
Does this pattern continue?
## 24 December
Today's number is 191 more than one of the other answers and 100 less than another of the answers.
Tags: numbers
## 23 December
Today's number is the number of three digit numbers that are not three more than a multiple of 7.
Tags: numbers
## 22 December
Today's number is a palindrome. Today's number is also the number of palindromes between 111 and 11111 (including 111 and 11111).
## 19 December
The sum of all the numbers in the eighth row of Pascal's triangle.
Clarification: I am starting the counting of rows from 1, not 0. So (1) is the 1st row, (1 1) is the 2nd row, (1 2 1) is the 3rd row, etc.
## 18 December
The smallest number whose sum of digits is 25. | 2017-06-28 00:18:15 | {"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": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6108895540237427, "perplexity": 719.2703973675078}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-26/segments/1498128321961.50/warc/CC-MAIN-20170627235941-20170628015941-00089.warc.gz"} |
https://hal.archives-ouvertes.fr/in2p3-00025162 | # The Supernova Legacy Survey: Measurement of $\Omega_M$, $\Omega_\Lambda$ and w from the First Year Data Set
Abstract : We present distance measurements to 71 high redshift type Ia supernovae discovered during the first year of the 5-year Supernova Legacy Survey (SNLS). These events were detected and their multi-color light-curves measured using the MegaPrime/MegaCam instrument at the Canada-France-Hawaii Telescope (CFHT), by repeatedly imaging four one-square degree fields in four bands. Follow-up spectroscopy was performed at the VLT, Gemini and Keck telescopes to confirm the nature of the supernovae and to measure their redshift. With this data set, we have built a Hubble diagram extending to z=1, with all distance measurements involving at least two bands. Systematic uncertainties are evaluated making use of the multi-band photometry obtained at CFHT. Cosmological fits to this first year SNLS Hubble diagram give the following results : Omega_M = 0.263 +/- 0.042(stat) +/- 0.032(sys) for a flat LambdaCDM model; and w = -1.023 +/- 0.090(stat) +/- 0.054(sys) for a flat cosmology with constant equation of state w when combined with the constraint from the recent Sloan Digital Sky Survey measurement of baryon acoustic oscillations.
keyword :
Document type :
Journal articles
Domain :
http://hal.in2p3.fr/in2p3-00025162
Contributor : Simone Lantz Connect in order to contact the contributor
Submitted on : Saturday, June 9, 2007 - 3:58:30 PM
Last modification on : Wednesday, November 17, 2021 - 12:30:14 PM
### Citation
P. Astier, J. Guy, N. Regnault, R. Pain, E. Aubourg, et al.. The Supernova Legacy Survey: Measurement of $\Omega_M$, $\Omega_\Lambda$ and w from the First Year Data Set. Astronomy and Astrophysics - A&A, EDP Sciences, 2006, 447, pp.31-48. ⟨10.1051/0004-6361:20054185⟩. ⟨in2p3-00025162⟩
Record views | 2021-12-04 02:36:52 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.40762677788734436, "perplexity": 5861.742302396419}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-49/segments/1637964362923.11/warc/CC-MAIN-20211204003045-20211204033045-00130.warc.gz"} |
https://escholarship.org/uc/item/83x4w44b | Open Access Publications from the University of California
## Pattern Formation in Particle Interactions
• Author(s): von Brecht, James
Large systems of particles interacting pairwise in $d$-dimensions give rise to extraordinarily rich patterns. These patterns generally occur in two types. On one hand, the particles may concentrate on a co-dimension one manifold such as a sphere in three dimensions or a ring in two dimensions. Localized, space-filling, co-dimension zero patterns can occur as well. This work develops an understanding of such patterns by exploring how the prediction and design of patterns relates to the stability and well-posedness properties of the underlying mathematical equations.
At the outset we use dynamical systems theory to predict the types behaviors a given system of particles will exhibit. Specifically, we develop a non-local linear stability analysis for particles that distribute uniformly on a $d-1$ sphere. Remarkably, this linear theory accurately characterizes the patterns in the ground states from the instabilities in the pairwise potential. We then leverage this aspect of the theory to address the issue of inverse statistical mechanics in self-assembly, i.e. the construction of a potential that will produce a desired pattern. As the linear theory indicates that potentials with a small number of spherical harmonic instabilities may produce very complex patterns, we naturally arrive at the linearized inverse statistical mechanics question: given a finite set of unstable modes, can we construct a potential that possesses precisely these linear instabilities? An affirmative answer would allow for the design of potentials with arbitrarily intricate spherical symmetries in the ground state. We solve the linearized inverse problem in full, and present a wide variety of designed ground states.
To conclude we begin the task of transferring aspects of the linear theory apply to the fully nonlinear problem. In particular, we address the well-posedness of distribution solutions to the aggregation equation $\rho_{t} + \mathrm{div}(\rho \mathbf{u} ) = 0, \; \mathbf{u} = -\nabla V * \rho$ in $\Rd$ where the density $\rho$ concentrates on a co-dimension one manifold. When the equation for such a solution is linearly well-posed, we show that the fully non-linear evolution is also well-posed locally in time for the class of bi-Lipschitz surfaces. In this aspect at least, the linear and non-linear theories therefore coincide. | 2019-10-17 03:47:16 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7303420305252075, "perplexity": 465.90167394420195}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-43/segments/1570986672548.33/warc/CC-MAIN-20191017022259-20191017045759-00233.warc.gz"} |
https://mailman.ntg.nl/pipermail/ntg-context/2006/022300.html | # [NTG-context] Font installation
Thomas A. Schmitz thomas.schmitz at uni-bonn.de
Mon Nov 6 15:08:46 CET 2006
On Nov 6, 2006, at 2:54 PM, Antoine Junod wrote:
> tmf files are in:
>
> ./texmf-fonts/fonts/tfm/sil/doulos/texnansi-DoulosSILR.tfm
> ./texmf-fonts/fonts/tfm/sil/doulos/texnansi-raw-DoulosSILR.tfm
>
> mtexfont.pdf seems to say that's the right place (page 3).
>
> Yes, I've run texhash/mktexlsr.
>
> What else should I check?
>
> -AJ
Excuse me, I wasn't paying enough attention. From your log, it is
clear that ConTeXt is looking for a tfm that is called DoulosSil.tfm
-- which, of course, isn't there. I think the reason is because you
use the same name "doulos" for all your definitions. Try to edit your
test file like so:
\usetypescriptfile[type-doulos]
\definetypeface[Doulos][rm][serif][doulos][default][encoding=texnansi]
\setupbodyfont[Doulos,rm,10pt]
\starttext
This is the end, gggggnnnnnn
\stoptext
HTH
Thomas | 2017-07-23 02:45:06 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9058318138122559, "perplexity": 9925.886969988185}, "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-2017-30/segments/1500549424239.83/warc/CC-MAIN-20170723022719-20170723042719-00116.warc.gz"} |
http://mathhelpforum.com/differential-geometry/111492-kahane-zelazko-paper-problem-estimation-print.html | # Kahane, Zelazko paper. Problem with estimation.
• October 31st 2009, 05:24 AM
Arczi1984
Kahane, Zelazko paper. Problem with estimation.
Hi!
I'm studying Kahane, Zelazko paper "A characterization of maximal ideals in commutative Banach algebras" and I've problem with one statement in the proof of Theorem2.
Below is this theorem and part of the proof with 'red rectangle' - how can I proof/show this estimation and implication?
Any help will be highly appreciated.
Bes regards
http://img519.imageshack.us/img519/8938/theorem.png
[2] E. C. Titchmarsh, Theory of functions, Oxford 1939.
• October 31st 2009, 05:55 AM
Laurent
Hi,
I don't know half of what the article is about, but I guess the estimate is because $|f(x)|\leq\|f\|\|x\|$ by definition of $\|f\|$, and $\|e^x\|= \left\|\sum_{k=0}^\infty \frac{x^k}{k!}\right\|\leq \sum_{k=0}^\infty \frac{\|x\|^k}{k!}=e^{\|x\|}$, the inequality being because we have a Banach algebra.
As for the second point, you can find the reference here (that's Hadamard's factorization theorem), and the definition of the order of an integral function is here. Here, because of the estimate, the order of $\lambda\mapsto e^{\psi(\lambda)}$ is 1, and it has no zeroes, hence $P=1$ and $Q$ is of degree 1. This is what you need.
• October 31st 2009, 06:09 AM
Arczi1984
Thanks for help. Now it is clear:) Once more thanks for quick answer. | 2016-06-26 02:48:45 | {"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": 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": 0.857532799243927, "perplexity": 1118.2738243211802}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-26/segments/1466783394605.61/warc/CC-MAIN-20160624154954-00028-ip-10-164-35-72.ec2.internal.warc.gz"} |
http://mathhelpforum.com/differential-geometry/159054-isometric.html | 1. ## Isometric?
Let $X=\{A,\ B,\ C, \ D\}$ with $d(A,D)=2$, but all other distances equal to 1.
d is a metric.
Prove that the metric space X is not isometric to any subset of $\mathbb{E}^n$ for any n.
Hint: can you realise $X$ as a subset of a sphere $S^2$ of appropriate radius, with the spherical "great circle" metric?
I think I have to take two points in $X$ and show that any mapping from $X$ to $\mathbb{E}^n$ would result in a different distance between them.
Here's my attempt:
Take a sphere of radius 1 and the points A and D.
Since $d(A,D)=2$, A and D are on opposite sides of the sphere.
Suppose there exists an isometry $\phi:X \rightarrow \sigma$ where $\sigma$ is is the plane used in stereographic projection (also a subset of $\mathbb{E}^n$).
Then $\phi(A)=\phi(D)$. Hence $d(\phi(A),\phi(D))=0$ which is not equal to $d(A,D)=2$.
Hence $\phi$ cannot be an isometry.
2. Originally Posted by Showcase_22
I think I have to take two points in $X$ and show that any mapping from $X$ to $\mathbb{E}^n$ would result in a different distance between them.
Here's my attempt:
Take a sphere of radius 1 and the points A and D.
Since $d(A,D)=2$, A and D are on opposite sides of the sphere.
Suppose there exists an isometry $\phi:X \rightarrow \sigma$ where $\sigma$ is is the plane used in stereographic projection (also a subset of $\mathbb{E}^n$).
Then $\phi(A)=\phi(D)$. Hence $d(\phi(A),\phi(D))=0$ which is not equal to $d(A,D)=2$.
Hence $\phi$ cannot be an isometry.
I'm not sure that the hint is very helpful, and I don't think that stereographic projection is needed.
If such an isometry $\phi$ exists then the points $\phi (A),\ \phi (B),\ \phi (C)$ form an equilateral triangle with side 1, in some 2-dimensional subspace of $\mathbb{E}^n$. So do the points $\phi (B),\ \phi (C),\ \phi (D)$. Thus the images of the four points lie in some 3-dimensional subspace of $\mathbb{E}^n$, so we may as well assume that n=3.
The points $\phi (A)$ and $\phi (D)$ must both lie at a distance $\sqrt3/2$ from the midpoint of the line segment joining $\phi (B)$ and $\phi (C)$. So the distance from $\phi (A)$ to $\phi (D)$ is at most $\sqrt3<2$, contradicting the condition that $\phi$ is an isometry. | 2017-03-22 23:28:41 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 41, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9174362421035767, "perplexity": 99.66285229727214}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-13/segments/1490218186353.38/warc/CC-MAIN-20170322212946-00007-ip-10-233-31-227.ec2.internal.warc.gz"} |
https://trillionthtonne.org/index.html | # globalwarmingindex.org
Tracking progress to a safe climate
Human-induced warming: ---------------- °C
Total Carbon Dioxide emissions: ---------------- trillion tonnes
(Equivalent tonnes of Carbon: ---------------- tonnes)
Other Human influences on climate: ---------------- Watts per square metre
on now
Why are we now providing three numbers?
Human-induced warming (ΔT) over a time-interval ranging from seconds to decades is proportional to total cumulative carbon dioxide emissions over that time-interval (ECO2) plus the impact of any change in global energy imbalance due to other human influences on climate (ΔFother).
We can write this as an equation [1]: $${\color{red} {ΔT}} = {\color{blue}κ} ⋅ \left( E_{CO_{2}} + {{ {\color{grey} { ΔF_{other} }} } \over {\color{blue}α}} \right)$$
where κ is the “Transient Climate Response to Emissions” (about 0.4°C per trillion tonnes of CO2 [2]) and α is the “Normalised Absolute Global Warming Potential” of CO2 (about 1.0 W/m2 per trillion tonnes of CO2 [3]).
Don’t take our word for it: add them up and check! Now you know what’s causing global warming.
# Current Global Warming Index
The first graph shows an index of human-induced global warming relative to the second half of the 19th century (1850-1900).
The second graph shows index together with the associated CO2 and other forcing contributions.
globalwarmingindex.org is provided by the Oxford University Environmental Change Institute.
See here for further details about the graphic above.
[1] Allen et al, npj Clim Atmos Sci 1, 16 (2018)
[2] Myhre et al (2013) in IPCC 5th Assessment Report, incl. uncertainty range of 0.23-0.68°C/TtCO2.
[3] α = AGWPCO2/H, where H is the AGWP time-horizon. Myhre et al (2013) give values of 0.9-1.2 W/m2 per trillion tonnes of CO2 in the 20-100 yr range. | 2020-07-03 22:05:32 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 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": 0.3915141522884369, "perplexity": 8393.200342850509}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-29/segments/1593655883439.15/warc/CC-MAIN-20200703215640-20200704005640-00143.warc.gz"} |
http://star-www.rl.ac.uk/star/docs/sun67.htx/sun67ss107.html | ### SLA_H2E
Az,El to $h,\delta$
ACTION:
Horizon to equatorial coordinates (single precision).
CALL:
CALL sla_H2E (AZ, EL, PHI, HA, DEC)
##### RETURNED:
NOTES:
(1)
The sign convention for azimuth is north zero, east $+\pi /2$.
(2)
HA is returned in the range $±\pi$. Declination is returned in the range $±\pi$.
(3)
The latitude is (in principle) geodetic. In critical applications, corrections for polar motion should be applied (see sla_POLMO).
(4)
In some applications it will be important to specify the correct type of elevation in order to produce the required type of $\left[\phantom{\rule{0.3em}{0ex}}h,\delta \phantom{\rule{0.3em}{0ex}}\right]$. In particular, it may be important to distinguish between the elevation as affected by refraction, which will yield the observed $\left[\phantom{\rule{0.3em}{0ex}}h,\delta \phantom{\rule{0.3em}{0ex}}\right]$, and the elevation in vacuo, which will yield the topocentric $\left[\phantom{\rule{0.3em}{0ex}}h,\delta \phantom{\rule{0.3em}{0ex}}\right]$. If the effects of diurnal aberration can be neglected, the topocentric $\left[\phantom{\rule{0.3em}{0ex}}h,\delta \phantom{\rule{0.3em}{0ex}}\right]$ may be used as an approximation to the apparent $\left[\phantom{\rule{0.3em}{0ex}}h,\delta \phantom{\rule{0.3em}{0ex}}\right]$.
(5)
No range checking of arguments is carried out.
(6)
In applications which involve many such calculations, rather than calling the present routine it will be more efficient to use inline code, having previously computed fixed terms such as sine and cosine of latitude. | 2018-02-22 16:28:22 | {"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": 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": 0.9168771505355835, "perplexity": 1488.7126283756925}, "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/1518891814140.9/warc/CC-MAIN-20180222160706-20180222180706-00755.warc.gz"} |
https://mitpress.mit.edu/books/great-principles-computing | Paperback | $34.00 X | £27.95 | 320 pp. | 6 x 9 in | 95 b&w illus. | January 2015 | ISBN: 9780262527125 eBook |$34.00 X | January 2015 | ISBN: 9780262324250
Mouseover for Online Attention Data
## Great Principles of Computing
Foreword by Vint Cerf
## Overview
Computing is usually viewed as a technology field that advances at the breakneck speed of Moore’s Law. If we turn away even for a moment, we might miss a game-changing technological breakthrough or an earthshaking theoretical development. This book takes a different perspective, presenting computing as a science governed by fundamental principles that span all technologies. Computer science is a science of information processes. We need a new language to describe the science, and in this book Peter Denning and Craig Martell offer the great principles framework as just such a language. This is a book about the whole of computing—its algorithms, architectures, and designs.
Denning and Martell divide the great principles of computing into six categories: communication, computation, coordination, recollection, evaluation, and design. They begin with an introduction to computing, its history, its many interactions with other fields, its domains of practice, and the structure of the great principles framework. They go on to examine the great principles in different areas: information, machines, programming, computation, memory, parallelism, queueing, and design. Finally, they apply the great principles to networking, the Internet in particular.
Great Principles of Computing will be essential reading for professionals in science and engineering fields with a “computational” branch, for practitioners in computing who want overviews of less familiar areas of computer science, and for non-computer science majors who want an accessible entry way to the field.
Peter J. Denning is Distinguished Professor of Computer Science at the Naval Postgraduate School, Monterey, California.
Craig H. Martell is Associate Professor in the Department of Computer Science at the Naval Postgraduate School.
## Endorsements
“This insightful book provides a structure to help us understand the breadth and depth of computing, which can enable us to place our knowledge in a coherent framework, and in turn can inform the design of curricula.”
Tim Bell, Professor, Computer Science and Software Engineering, University of Canterbury
“To understand computing is not to examine the computer as a tool, but rather to comprehend the underlying principles that apply to computing’s many manifestations and instances. Great Principles of Computing sets us on the path to uncover those underlying principles. But you will not be spoon-fed the keys—you need to identify, ingest, and articulate them for yourself once you read through the tour de force that Denning and Martell offer us. Theirs is a brilliant effort to present a global view of what computing is all about and how it fits into the world we inhabit.”
Leonard Kleinrock, Distinguished Professor of Computer Science, University of California, Los Angeles
“With some effort almost everyone can learn to program. Writing code is not enough to build significant computing artifacts; to do that requires deeper insight into (at least) how computers work, how to choose algorithms, how computing systems are structured, and what goes into a correct, dependable design. How does one begin to gain those insights when all those items are interrelated? This book is one approach—a thoughtful, integrated presentation of some of the fundamental concepts underlying computing. Presented as a set of detailed yet understandable topics, this text provides a solid foundation for someone learning how to think about computing beyond its mere codification in a programming language. Denning and Martell’s text really does present great principles for the student of computing.”
Eugene H. Spafford, Professor of Computer Science, Purdue University | 2018-03-24 23:14:29 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.24712514877319336, "perplexity": 1633.7150594768302}, "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-2018-13/segments/1521257651465.90/warc/CC-MAIN-20180324225928-20180325005928-00325.warc.gz"} |
https://people.maths.bris.ac.uk/~matyd/GroupNames/73/C6xC4oD4.html | Copied to
clipboard
## G = C6×C4○D4order 96 = 25·3
### Direct product of C6 and C4○D4
direct product, metabelian, nilpotent (class 2), monomial, 2-elementary
Aliases: C6×C4○D4, C6.18C24, C12.55C23, C4(C6×D4), C4(C6×Q8), C12(C2×D4), C12(C6×D4), D4(C2×C12), C12(C2×Q8), C12(C6×Q8), Q8(C2×C12), (C2×D4)⋊7C6, D43(C2×C6), (C2×Q8)⋊8C6, Q84(C2×C6), C12(C4○D4), (C6×D4)⋊16C2, (C22×C4)⋊8C6, (C6×Q8)⋊13C2, C4.8(C22×C6), C2.3(C23×C6), (C2×C6).6C23, (C22×C12)⋊13C2, (C2×C12)⋊16C22, (C3×D4)⋊12C22, C23.14(C2×C6), (C3×Q8)⋊11C22, C22.1(C22×C6), (C22×C6).30C22, C4(C3×C4○D4), (C2×C4)(C3×D4), (C2×C4)(C3×Q8), (C2×C4)(C6×Q8), (C2×C4)⋊5(C2×C6), C12(C3×C4○D4), (C2×C12)(C3×D4), (C2×C12)(C3×Q8), (C2×Q8)(C2×C12), (C2×C12)(C6×Q8), SmallGroup(96,223)
Series: Derived Chief Lower central Upper central
Derived series C1 — C2 — C6×C4○D4
Chief series C1 — C2 — C6 — C2×C6 — C3×D4 — C3×C4○D4 — C6×C4○D4
Lower central C1 — C2 — C6×C4○D4
Upper central C1 — C2×C12 — C6×C4○D4
Generators and relations for C6×C4○D4
G = < a,b,c,d | a6=b4=d2=1, c2=b2, ab=ba, ac=ca, ad=da, bc=cb, bd=db, dcd=b2c >
Subgroups: 188 in 164 conjugacy classes, 140 normal (12 characteristic)
C1, C2, C2, C2, C3, C4, C22, C22, C22, C6, C6, C6, C2×C4, C2×C4, D4, Q8, C23, C12, C2×C6, C2×C6, C2×C6, C22×C4, C2×D4, C2×Q8, C4○D4, C2×C12, C2×C12, C3×D4, C3×Q8, C22×C6, C2×C4○D4, C22×C12, C6×D4, C6×Q8, C3×C4○D4, C6×C4○D4
Quotients: C1, C2, C3, C22, C6, C23, C2×C6, C4○D4, C24, C22×C6, C2×C4○D4, C3×C4○D4, C23×C6, C6×C4○D4
Smallest permutation representation of C6×C4○D4
On 48 points
Generators in S48
(1 2 3 4 5 6)(7 8 9 10 11 12)(13 14 15 16 17 18)(19 20 21 22 23 24)(25 26 27 28 29 30)(31 32 33 34 35 36)(37 38 39 40 41 42)(43 44 45 46 47 48)
(1 29 18 19)(2 30 13 20)(3 25 14 21)(4 26 15 22)(5 27 16 23)(6 28 17 24)(7 33 48 37)(8 34 43 38)(9 35 44 39)(10 36 45 40)(11 31 46 41)(12 32 47 42)
(1 34 18 38)(2 35 13 39)(3 36 14 40)(4 31 15 41)(5 32 16 42)(6 33 17 37)(7 28 48 24)(8 29 43 19)(9 30 44 20)(10 25 45 21)(11 26 46 22)(12 27 47 23)
(1 31)(2 32)(3 33)(4 34)(5 35)(6 36)(7 21)(8 22)(9 23)(10 24)(11 19)(12 20)(13 42)(14 37)(15 38)(16 39)(17 40)(18 41)(25 48)(26 43)(27 44)(28 45)(29 46)(30 47)
G:=sub<Sym(48)| (1,2,3,4,5,6)(7,8,9,10,11,12)(13,14,15,16,17,18)(19,20,21,22,23,24)(25,26,27,28,29,30)(31,32,33,34,35,36)(37,38,39,40,41,42)(43,44,45,46,47,48), (1,29,18,19)(2,30,13,20)(3,25,14,21)(4,26,15,22)(5,27,16,23)(6,28,17,24)(7,33,48,37)(8,34,43,38)(9,35,44,39)(10,36,45,40)(11,31,46,41)(12,32,47,42), (1,34,18,38)(2,35,13,39)(3,36,14,40)(4,31,15,41)(5,32,16,42)(6,33,17,37)(7,28,48,24)(8,29,43,19)(9,30,44,20)(10,25,45,21)(11,26,46,22)(12,27,47,23), (1,31)(2,32)(3,33)(4,34)(5,35)(6,36)(7,21)(8,22)(9,23)(10,24)(11,19)(12,20)(13,42)(14,37)(15,38)(16,39)(17,40)(18,41)(25,48)(26,43)(27,44)(28,45)(29,46)(30,47)>;
G:=Group( (1,2,3,4,5,6)(7,8,9,10,11,12)(13,14,15,16,17,18)(19,20,21,22,23,24)(25,26,27,28,29,30)(31,32,33,34,35,36)(37,38,39,40,41,42)(43,44,45,46,47,48), (1,29,18,19)(2,30,13,20)(3,25,14,21)(4,26,15,22)(5,27,16,23)(6,28,17,24)(7,33,48,37)(8,34,43,38)(9,35,44,39)(10,36,45,40)(11,31,46,41)(12,32,47,42), (1,34,18,38)(2,35,13,39)(3,36,14,40)(4,31,15,41)(5,32,16,42)(6,33,17,37)(7,28,48,24)(8,29,43,19)(9,30,44,20)(10,25,45,21)(11,26,46,22)(12,27,47,23), (1,31)(2,32)(3,33)(4,34)(5,35)(6,36)(7,21)(8,22)(9,23)(10,24)(11,19)(12,20)(13,42)(14,37)(15,38)(16,39)(17,40)(18,41)(25,48)(26,43)(27,44)(28,45)(29,46)(30,47) );
G=PermutationGroup([[(1,2,3,4,5,6),(7,8,9,10,11,12),(13,14,15,16,17,18),(19,20,21,22,23,24),(25,26,27,28,29,30),(31,32,33,34,35,36),(37,38,39,40,41,42),(43,44,45,46,47,48)], [(1,29,18,19),(2,30,13,20),(3,25,14,21),(4,26,15,22),(5,27,16,23),(6,28,17,24),(7,33,48,37),(8,34,43,38),(9,35,44,39),(10,36,45,40),(11,31,46,41),(12,32,47,42)], [(1,34,18,38),(2,35,13,39),(3,36,14,40),(4,31,15,41),(5,32,16,42),(6,33,17,37),(7,28,48,24),(8,29,43,19),(9,30,44,20),(10,25,45,21),(11,26,46,22),(12,27,47,23)], [(1,31),(2,32),(3,33),(4,34),(5,35),(6,36),(7,21),(8,22),(9,23),(10,24),(11,19),(12,20),(13,42),(14,37),(15,38),(16,39),(17,40),(18,41),(25,48),(26,43),(27,44),(28,45),(29,46),(30,47)]])
60 conjugacy classes
class 1 2A 2B 2C 2D ··· 2I 3A 3B 4A 4B 4C 4D 4E ··· 4J 6A ··· 6F 6G ··· 6R 12A ··· 12H 12I ··· 12T order 1 2 2 2 2 ··· 2 3 3 4 4 4 4 4 ··· 4 6 ··· 6 6 ··· 6 12 ··· 12 12 ··· 12 size 1 1 1 1 2 ··· 2 1 1 1 1 1 1 2 ··· 2 1 ··· 1 2 ··· 2 1 ··· 1 2 ··· 2
60 irreducible representations
dim 1 1 1 1 1 1 1 1 1 1 2 2 type + + + + + image C1 C2 C2 C2 C2 C3 C6 C6 C6 C6 C4○D4 C3×C4○D4 kernel C6×C4○D4 C22×C12 C6×D4 C6×Q8 C3×C4○D4 C2×C4○D4 C22×C4 C2×D4 C2×Q8 C4○D4 C6 C2 # reps 1 3 3 1 8 2 6 6 2 16 4 8
Matrix representation of C6×C4○D4 in GL4(𝔽13) generated by
12 0 0 0 0 3 0 0 0 0 12 0 0 0 0 12
,
1 0 0 0 0 1 0 0 0 0 5 0 0 0 0 5
,
12 0 0 0 0 1 0 0 0 0 1 11 0 0 1 12
,
12 0 0 0 0 12 0 0 0 0 1 11 0 0 0 12
G:=sub<GL(4,GF(13))| [12,0,0,0,0,3,0,0,0,0,12,0,0,0,0,12],[1,0,0,0,0,1,0,0,0,0,5,0,0,0,0,5],[12,0,0,0,0,1,0,0,0,0,1,1,0,0,11,12],[12,0,0,0,0,12,0,0,0,0,1,0,0,0,11,12] >;
C6×C4○D4 in GAP, Magma, Sage, TeX
C_6\times C_4\circ D_4
% in TeX
G:=Group("C6xC4oD4");
// GroupNames label
G:=SmallGroup(96,223);
// by ID
G=gap.SmallGroup(96,223);
# by ID
G:=PCGroup([6,-2,-2,-2,-2,-3,-2,601,230]);
// Polycyclic
G:=Group<a,b,c,d|a^6=b^4=d^2=1,c^2=b^2,a*b=b*a,a*c=c*a,a*d=d*a,b*c=c*b,b*d=d*b,d*c*d=b^2*c>;
// generators/relations
×
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http://www.hep.ucl.ac.uk/~jmb/LH/2HDM/contur-plots-2hdm1ws/ATLAS_13_GAMMA/ATLAS_2017_I1645627/index.html | ### ATLAS_2017_I1645627 in pool ATLAS_13_GAMMA
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The dynamics of isolated-photon production in association with a jet in proton-proton collisions at a centre-of-mass energy of 13 TeV are studied with the ATLAS detector at the LHC using a dataset with an integrated luminosity of 3.2 fb$^{-1}$. Photons are required to have transverse energies above 125 GeV. Jets are identified using the anti-$k_\text{t}$ algorithm with radius parameter $R=0.4$ and required to have transverse momenta above 100 GeV. Measurements of isolated-photon plus jet cross sections are presented as functions of the leading-photon transverse energy, the leading-jet transverse momentum, the azimuthal angular separation between the photon and the jet, the photon-jet invariant mass and the scattering angle in the photon-jet centre-of-mass system. Tree-level plus parton-shower predictions from Sherpa and Pythia as well as next-to-leading-order QCD predictions from Jetphox and Sherpa are compared to the measurements.
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https://indico.cern.ch/event/1068553/timetable/?view=standard_numbered | # Workshop on Advanced Radiation Detector and Instrumentation in Nuclear and Particle Physics (Online)
Asia/Kolkata
Online (University of Jammu)
Description
# Proceedings submission deadline : 24 March 2022 23:59 (IST) [final extended]
## Topics of the workshop
### Looking forward to seeing you in the workshop.
Participants
• Aafke Kraan
• Abhay Deshpande
• Abhijit Bhattacharyya
• Abhik Jash
• ABHISEK ROY
• Abhishek Kumar Sharma
• Abhishek Singh
• Ae Ra Jung
• Ajay Kumar
• Ajay Kumar
• AJAY Srivastava
• Ajit Kumar
• Aleksey Makarov
• Algama Masud
• Ali Hassan
• Amal Sarkar
• Amandeep Singh
• Aminul Islam
• Amira Ekramy
• Amit A
• Ana Marija Kožuljević
• Anand Kumar Dubey
• Andrei Reshetin
• Anees Mushtaq
• Anindita karmakar
• ANIRBAN GOSWAMI
• ANIRUDDHA DEY
• Anju Bhasin
• Ankit Gupta
• Ankita Nain
• ANKUSH SINGH
• Annesha Karmakar
• Anuraag Misra
• Archana Sharma
• arijit sen
• Arindam Sen
• Arpit Singh
• Arvind Kumar
• Arzoo Sharma
• Ashish Gupta
• Ashish Jalotra
• ASIF ALI
• Asim Pal
• Azam Zabihi
• Babita Kumari
• Balwinder Kaur
• Bhavna Sorout
• Bhumika Mehta
• Bidyut Jyoti Roy
• Binayak Sannyasi
• Binti Sharma
• Biswajit Das
• Chakresh Jain
• Chandana Bhattacharya
• CHANDRA KUMAR
• Chetan Sharma
• Chirag Singh Mukherjee
• Christian Joachim Schmidt
• Christian Müntz
• DAMINI SINGH
• Danush S
• DEBOJYOTI RAY CHAWDHURY
• Deepali tanwar
• Devender Kumar
• Dhananjay Kapse
• Divya Pandya
• Fakhar-ul Haider
• Florian Maximilian Brunbauer
• Gauri Devi
• GOVINDU KONDAIAH
• Hans Raj Sharma
• Harjot Kaur
• Honey Arora
• Inayat Rasool Bhat
• Indranil Mazumdar
• Isha Mehta
• Ishtaq Ahmed
• Jagbir Singh
• Jaspreet kaur
• Jaydeep Datta
• Joshua Majekodunmi
• Kajal Attri
• Kajol Chakraborty
• Kanishka Rawat
• Kaushal Sahariya
• KAUSIK PAL
• Khushboo Golha
• Kiran K U
• Kirti Ranjan
• KK RAJESH
• KRISHNA DEBNATH
• Kshitij Chavan
• KUNAL BHARDWAJ
• Luciano Musa
• MA JIANHAO
• MAHIMA SACHDEVA
• Mahima Sharma
• Maitreyee Mukherjee
• Mala Das
• Mamta jain
• Mandeep Kaur
• Manfred Krammer
• Manoj Kumar Singh
• Mansi Sharma
• Mariana Petris
• Md Ayazuddin
• Md Kaosor Ali Mondal
• Md Sabir Ali
• Md Samsul Islam
• Meenakshi Sharma
• Mikhail Merkin
• Mitali Mondal
• Mitanshu Thakore
• MOHD SHARIQ ASNAIN
• Mouli Chaudhuri
• MRINAL TIWARI
• Mrityunjay Kumar Mishra
• NAVJOT KAUR DHILLON
• Nayana Majumdar
• NIKHIL SHARMA
• Nitish Dhingra
• Nitu Saini
• Om prakash Dash
• Omveer Singh
• PIJUSHKANTI JANA
• Piotr Koczon
• Pooja Sharma
• Prabhakar Palni
• Prabir Roy
• Prachi Sharma
• Prakhar Garg
• PRALAY DAS
• PRASANNA M
• Prashanta Kumar Khandai
• Pratibha Bhagat
• Priya Sharma
• Priyanka Boora
• Promita Roy
• Puspita Chatterjee
• Raghav Choudhary
• Rahul Kaushik
• raj shah
• Rajarshi Raut
• Rajendra Nath Patra
• Rakesh Kumar Pandit
• Rakesh Singh
• Ramni Gupta
• Randhir Singh
• Ratika Sharma
• Raveendrababu Karnam
• RAVINDER KUMAR
• Renu Bala
• Richa Sharma
• Ritu Devi
• Riya Gaba
• Rohan Biswas
• Roni Dey
• Rupamoy Bhattacharyya
• Sabita Das
• Saheb Paramanik
• Saikat Biswas
• Saikat Saha
• Salman K Malik
• Sameer Ahmed
• Sameer Aslam
• Samritti Devi
• SANDEEP DONGRE
• Sandeep Ghugre
• Sanjay Mahajan
• Sanjeet Singh Kaintura
• Sanjeev Singh Sambyal
• Sanjib Muhuri
• Saraswati Pandey
• Sarju Bala
• Satyajit Saha
• Satyaranjan Santra
• Sawini Kharb
• Sayak Chatterjee
• Sayan Chakraborty
• Sayan Ghosh
• Sayani Mitra
• Seemrin Devi
• Shaifali Mehta
• Sheetal Rawat
• Sheetal Sharma
• SHIKSHA RANI
• Shilpa Patyal
• SHIVALI SHARMA
• Shivshant Chauhan
• Shreya Roy
• Shyam Kumar
• SIDHARTH KUMAR DASH
• Sonia Raheja
• SOUVIK KAR
• SRIDHAR TRIPATHY
• SRUTHY K S
• Stefania Maria Beole
• Subhankar Maity
• Subhendu Das
• Sudheep K S
• Sudipta Das
• Sujan Kumar Roy
• Suman Saurav
• Sumit Kumar Kundu
• Suneel Dutt
• Sunil Devi
• SUNIL DUTT
• Sunil Kumar
• Sunita Sahoo
• Suraj Ali
• Surendra Kumar Gour
• Swapnamoy Pramanik
• Swapnil Pandey
• Swarali Hinge
• SWATI THAKUR
• SYAMANTAK DAS
• TANAY DEY
• Tanvi Sheokand
• Tapan Nayak
• Taslimuddin Mistry
• Thresia Michael
• Tilak Ghosh
• Tousif Raza
• Udai Singh
• UDAY SINGH
• UMESH L
• Varchaswi Kashyap
• Varinderjit Singh
• Varun Sharma
• Vijayalakshmi V
• Vikash Sumberia
• Vimal Kumar
• Vincent Boudry
• Vinita .
• Vipin Bhatnagar
• Vishal Kumar
• Yuvaraj Elangovan
Videoconference
RAPID2021 (Online)
Zoom Meeting ID
65552525902
Host
Rajendra Nath Patra
Alternative host
Salman K Malik
Join via phone
Zoom URL
Contact
• Monday, October 25
• Welcome
Convener: Rajendra Nath Patra (CERN)
• Invited lectures
Convener: Anju Bhasin (University of Jammu (IN))
• 1
Fundamental of the Gas Detectors
Speaker: Prakhar Garg (Stony Brook University)
• Oral presentations
Convener: Anju Bhasin (University of Jammu (IN))
• 2
Comparative study of position resolution and gain map of Single and Double GEM
Gas Electron Multipliers (GEM) are well known for their excellent position resolution, high rate handling and discharge handling capability among Micro-Pattern gaseous detectors (MPGDs). GEM detectors are used for large scale tracking and imaging application of charge particles like muons. The GEM detectors consist of GEM foil which acts as amplifiers and different combinations of these foils are used depending upon the applications. In the current work, experiments have been conducted to study the position resolution and gain uniformity for different combinations of the GEM detector. The GEM detector consisting of 10 by 10 cm standard GEM foils were used for this purpose with single and double foil configuration. For data collection and processing a Scalable Readout System (SRS) has been used, collecting data from four APV25 front-end boards. The readout has 256 readout strips each in x and y planes which were connected to APV25 front-end boards through 130 pin Panasonic connectors.
For position resolution measurement a Fe-55 soft x-ray source has been attached to AEROTECH PRO165 3-Axis XYZ Linear Stage with 0.5 µm resolutions. The source has been moved with a step of 50 µm in both x and y direction diagonally and the change in position obtained from the detector is used to determine the position resolution. The experiment has been carried out with single and double GEM and comparative studies have been carried out. The gain varies drastically from one configuration to another and similar behavior has been observed in the charge spread data. To obtain position a Center of Gravity method has been used which gives better result once the number of strip hit is high enough for it to work. As a result, the results from double GEM were better than the single GEM. The gain uniformity data was collected by moving the source across the detector and was found to be within ±12% range.
Speaker: Mr Vishal Kumar (Saha Institute of Nuclear Physics)
• 3
Charging up effect in triple GEM detector
Micro Pattern Gaseous Detectors (MPGD) are being used in High Energy Nuclear Physics experiments as a tracking device due to its high rate handling capability and good spatial resolution. Gas Electron Multiplier (GEM) detector is one of the advanced members of the MPGD group which is capable of handling high particle rate (∼ 1 MHz/mm$^{2}$ ) and has excellent position resolution (∼ 100 µm). The standard GEM foil is made up of a thin Kapton of thickness 50 µm with 5 µm copper cladding on both sides of the foil. The presence of di-electric (Kapton) changes the electric field strength of the electric field inside the GEM holes under the influence of external radiation and this phenomenon is referred to as the charging up effect. As a result of the charging up effect, the gain of the chamber increases initially and then asymptotically reaches a constant value.
The charging up effect is investigated for a Single Mask triple GEM detector prototype with Argon-CO$_2$ gas mixture under continuous irradiation from an X-ray source. The method of measurements and the test results will be presented.
Speaker: Mr Sayak Chatterjee (Bose Institute)
• 11:10 AM
Tea Break
• Invited lectures
Convener: Anand Kumar Dubey (Department of Atomic Energy (IN))
• 4
Numerical Simulation of Gaseous Detectors using Garfield++
Speaker: Supratik Mukhopadhyay (Saha Institute of Nuclear Physics (IN))
• Oral presentations
Convener: Anand Kumar Dubey (Department of Atomic Energy (IN))
• 5
Simulations of multi-layer GEM systems from single to quadruple GEMs
We present comparative simulation results for single, double, and triple layer GEM (Gas Electron Multiplier) GPD (Gas Pixel Detector) systems, along with some preliminary quadruple layer results, using Garfield++ and ANSYS field solver. With a multi-GEM layer structure, of up to 5 layers, a very high effective gain (up to 10^6 in some gases) can be attained with each GEM layer working at an individually much lower gain thus avoiding discharge problems - this is the major advantage of GEM technology. We compare our results with those of published experiments and simulations.
Speaker: Ae Ra Jung (Peking University (CN))
• 6
Numerical Evaluation of Resistive Plate Chamber
It is important to be able to correctly estimate the electric field, current, and potential distribution in RPC in order to envisage the working of the device. This is useful in optimizing its design and operation for specific applications. We have performed a calculation of the electric field current and potential distribution of RPC from the first principle using the finite element method on COMSOL Multiphysics platform and compared to results by Ammosov et al [1], which is comparable to our simulated results. It has been then used to study the effect of the electrode and spacer materials on field configuration and dark current. The effect of uniform and non-uniform surface resistivity of the conductive coating on the electric field distribution has also been studied. The time-dependent and transient responses of potential distribution for these two cases have been simulated and used for optimizing the surface resistivity. A few experimental measurements have been carried out to corroborate the simulation results.
References
[1] V. Ammosov, V. Korablev, V. Zaets, Electric field and currents in resistive plate chambers, Nucl. Instr. and Meth. A 401 (1997) 217-228.
Speaker: Mr Subhendu Das (Saha Institute of Nuclear Physics, India)
• 1:00 PM
Lunch Break
• Invited lectures
Convener: Nayana Majumdar (Saha Institute of Nuclear Physics (IN))
• 7
Micro-Pattern Gaseous Detector: Technologies, Developments and Perspectives
Speaker: Florian Maximilian Brunbauer (CERN)
• Virtual lab visit
Convener: Nayana Majumdar (Saha Institute of Nuclear Physics (IN))
• 8
Sensor Qualification Center (SQC) for Characterizing Silicon Microstrip Detectors, University of Delhi
Lab Name: SQC, Centre for Detector and Related Software Technology (CDRST), Department of Physics and Astrophysics, University of Delhi, Delhi
Speaker: Chakresh Jain (University of Delhi (IN))
• 3:30 PM
Tea Break
• Young Scientist Talks
Convener: Renu Bala (University of Jammu (IN))
• 9
Applications of Detectors based on THGEM-like Configurations
After the development of the Micro Strip Gaseous Chamber (MSGC) based on the semi-conductor
technology processes, the genesis of the gaseous detectors has undergone a rapid evolution leading
to spatial, temporal and energy resolution, rate capability, radiation hardness etc. This evolution has
ushered in a new genre of micro-structured devices, commonly known as Micro-Pattern Gaseous
Detectors (MPGDs). Within the broad family of MPGDs, the THick Gaseous Electron Multiplier
(THGEM) has been attracting significant attention due to its simplicity and robustness. THGEM-
based detectors may be constructed with very large area and their implementation does not require
any particular mechanical support. The range of excellent characteristics features and the possibility
of industrial production capability of large-area detectors, pave ways towards a broad spectrum of
potential applications. These rely on THGEM's single-electron sensitivity, moderate (sub-mm)
localization resolution, timing in the 10ns range, high-rate capability, low-temperature and broad
pressure-range (mbar to few bar) operation. However, the single THGEM often suffers from
occasional discharges which can potentially damage the electrodes affecting detector performance.
The Resistive-Plate WELL detector was developed successfully utilizing resistive material to
prevent electrical instabilities in the detector. It is a single-sided THGEM coupled to the segmented
readout electrode through a sheet of large bulk resistivity. In the last few years, systematic
investigations of the RPWELL detector performance and response were conducted. Its performance
was characterized both in a generic context and in the context of future digital hadronic calorimeter
sampling element. In parallel single- and dual- stage RPWELL-based UV photon detectors exhibit
Polya-like spectra at high gains, under stable operation which could make them applicable for
single photon imaging in RICH detectors.
In this presentation I will focus on the recent studies aiming to understand the underlying physics
processes governing the operation and performance of the new RPWELL detector in the context of
the above two applications. Lastly, I will discuss about another new device based on hybrid
THGEM Multi-Wire concept which has been considered as a possible candidate for low energy
fission studies.
Speakers: Purba Bhattacharya (INFN, Cagliari) , Purba Bhattacharya (Department of Physics School of Basic and Applied Sciences. Adamas University)
• Oral presentations
Convener: Renu Bala (University of Jammu (IN))
• 10
Gain uniformity of a quad-GEM detector at different gas flowrates
A systematic study of the absolute gain of a prototype quad-GEM detector at different gas flow rates is carried out. The gain uniformity at the various segment of the detector is also investigated. The active surface area (10 cm x 10 cm) of the detector is divided into 64 zones of equal area (1.25 cm x 1.25 cm), and each zone is irradiated with a collimated Fe$^{55}$ X-ray source. A constant voltage difference of 360 V is maintained across each GEM foil, and the gain is calculated using the measured anode current from the detector. A pre-mixed gas mixture of Ar:CO$_2$ in the ratio of 70:30 is used in the range of 3 - 30 SCCM flow rate for this purpose.
Speaker: Rupamoy Bhattacharyya (Institute of Physics (IN))
• 11
Charging up studies in thick Gas Electron Multipliers
The time-dependent variation of detector response in MPGDs, especially THGEMs, is one of the challenging problem that has been attributed to the “charging up” and “charging down” processes of insulating materials present in these detector. Experimental studies of stabilization of gain with time due to these phenomena in argon-based mixtures under various experimental conditions have been given in the presentation. Effects of different sources with varying irradiation rates on the gain saturation process have been studied. Low-rate source shows two-step gain stabilization phenomena, one short-term saturated gain, another long-term saturated gain, whereas high-rate source shows just one-step gain saturation. While this two-step stabilization has been attributed to the charging up of the rim by earlier studies, its effect seems to be subdued for high-rate irradiation according to the observations presented here. The final results provide an insight into the transients of gain saturation in THGEMs
Speaker: Ms Promita Roy (Saha Institute of Nuclear Physics)
• 12
A Simulation of Primary Ionization for Different Gas Mixtures
The primary ionization is an important part of study in nuclear and particle physics experiments.
In high rate experiments [1], the primary ionization is helpful in deep understanding of the
discharge formation and charge density studies. The primary ionization was obtained from the
simulation of alpha source to estimate discharge probability using single and triple GEM
configuration in argon gas mixture [2]. We present and focus here only on the simulation of
primary ionization in different argon based gas mixtures [3] to obtain the number of primaries,
spatial and energy information.
The simulation tools like geant4 [4] and heed [5] have applications in nuclear, particle,
accelerator, medical and space sciences. The geant4 and heed were used to simulate the passage
of particles through the matter. The advantage of geant4 toolkit is that it generates the particle
information like energy deposition and position co-ordinates after each step. These steps are
produced after each interactions that computes the cross-sections of physics processes that were
considered for this simulation in a gas volume. The properties of primary ionization, as
estimated by geant4 and heed have been compared.
We simulated a collimated beam of alpha particles with and without mylar sheet to compare
the range of alpha particles. A bragg peak was obtained because the alpha particles deposit
more energy towards the end of the trajectory in the gas volume. The energy loss of charged
particles is inversely proportional to the square of their velocity which causes the bragg peak
to occur. Thus, the number of primaries appear to be more near the bragg peak. The number of
primaries generated with geant4 toolkit has been compared with the heed also. We simulated
muons also in a similar manner to study primary ionization, though muons weakly interact with
the gas volume for study.
A similar analysis has been done for Fe-55 source which is radioactive in nature. The Fe-55
captures electron and produce primary ionization along with Mn-55, ν e and gamma which are
the secondaries in this reaction. The primary ionization have been compared with heed also.
We found that the response of alpha, muons and Fe-55 source in these Ar-based gas mixtures
is found to be different due to their different properties.
References:
[1] F. Sauli, GEM: a new concept for electron amplification in gas detectors, NIMA 386 (1997)
531.
[2] P. K. Rout et al, Numerical estimation of discharge probability in GEM-based detectors,
JINST 16 P09001 (2021).
[3] P. Gasik et al, Charge density as a driving factor of discharge formation in GEM-based
detectors, NIM A 870 (2017), p. 116.
[4] S. Agostinelli et al, Geant4 - a simulation toolkit, NIM A 506.3 (2003), p. 250.
[5] I.B. Smirnov; “Interactions of particles with gases”; online at http://cern.ch/heed .
Speaker: Dr Kanishka R. (Saha Institute of Nuclear Physics, Kolkata 700064, India. Homi Bhabha National Institute, Training School Complex, Anushaktinagar, Mumbai 400094, India.)
• Tuesday, October 26
• Invited lectures
Convener: Bedangadas Mohanty (National Institute of Science Education and Research (IN))
• 13
Fundamental of the Resistive Plate Chamber
Speaker: Varchaswi Kashyap (National Institute of Science Education and Research (IN))
• Oral presentations
Convener: Bedangadas Mohanty (National Institute of Science Education and Research (IN))
• 14
Bakelite RPC with and without linseed oil coating
Resistive Plate Chamber (RPC) detectors are currently used in High Energy Physics (HEP) experiments for triggering and tracking purposes for their low-cost of fabrication, high efficiency (> 90%) and good time resolution ($\sim$ 1-2 ns). RPC is also a potential candidate for high-resolution medical imaging.
Keeping in mind, the requirements of detectors having high-rate handling capability, cost-effectiveness, and large area coverage, to be used in future HEP experiments, commercially available bakelite plates with moderate bulk resistivity are used to build RPC prototypes.
Initially, RPC prototype is fabricated without any oil coating and its characteristics study is done with cosmic ray using 100 % Tetrafluoroethane (C$_{2}$H$_{2}$F$_{4}$) gas. In this prototype, only an efficiency $\sim$ 70% is achieved. To improve the performance as a remedial measurement, electrode plates are coated with linseed oil using a new technique. In conventional bakelite RPC, the linseed oil coating is done after making the gas gap. In this particular work, the linseed oil coating is done before making the gas gap. After the linseed oil coating, the plates are cured for several days. The advantage of this procedure is that after linseed oil coating it can be checked visually whether the curing is properly done, or any uncured droplet of linseed oil is present. Standard NIM electronics are used for this study. The detailed method of fabrication, measurement and the test results will be presented.
Speaker: arindam sen
• 15
In Search of an Eco-friendly Gas Mixture for Avalanche Mode Operation of RPC
The standard gas mixture for avalanche mode operation of Resistive Plate Chamber is prepared using a major proportion of R134a along with a small amount of i-C$_4$H$_{10}$ as a photon quenching component. In addition, a minute amount of SF6 is used for streamer suppression. Both of the R134a and SF$_6$ gases are known for their large global warming potential which casts harmful effect on the environment. In this work, we have proposed an eco-friendly gas mixture of Ar (5\%): CO$_2$ (60\%): N$_2$ (35\%) for operating RPCs in avalanche mode and qualified the mixture with numerical simulation. Using a hydrodynamic model, developed by us, the detector efficiency and streamer probability for the proposed mixture have been simulated to study its suitability. To validate the numerical model, the simulated results using the standard gas mixture of R134a (95.2\%): i-C$_4$H$_{10}$ (4.5\%): SF$_6$ (0.3\%) have been compared with the available experimental data of the same. To show the efficacy of the proposed gas mixture, the simulated efficiency and streamer probability have been compared to that of the standard gas mixture and other eco-friendly hydrofluoro-olefin (HFO1234ze)-based potential replacements. Addition of SF$_6$ by a small amount and lowering of electronic threshold have been investigated as possible means to reduce the observed streamer probability for the proposed gas mixture.
Speakers: Dr Jaydeep Datta (Université Libre de Bruxelles) , Mr Sridhar Tripathy (SINP, HBNI)
• 11:10 AM
Tea Break
• Invited lectures
Convener: Kirti Ranjan (University of Delhi (IN))
• 16
Basics Principles of the Silicon Detector
Speaker: Manfred Krammer (CERN)
• Oral presentations
Convener: Kirti Ranjan (University of Delhi (IN))
• 17
Charge Collection properties of Double Sided Germanium Strip Detector
The position sensitivity of a double-sided germanium strip detector has been studied using the coincidence method. The coincidences were demanded between an imaging scanner and a position-sensitive planar segmented germanium detector, comprising 10x10 electrical segmentation in orthogonal directions, using a positron source. The imaging scanner consists of a LYSO scintillation crystal coupled to a position-sensitive photomultiplier tube. The coincidence data have been analyzed by employing the Positron Annihilation Correlation (PSA) principle. The primary objective of this work is to study the charge carrier transportation for gamma-ray interaction inside the germanium detector, which has been studied using the pulse shape analysis procedure. The analysis has been performed to locate the gamma-ray interaction using the rise-time response of the detector for single interaction events along the depth of the germanium detector. The 2-dimensional image generated from the imaging scanner has been used to characterize the planar strip detector. Detailed scanning procedures and analysis of the present work will be presented at the conference.
References
[1] C. Domingo-Pardo et al., Nucl. Instru. Methods in Physics Research, 643 (2011) 79.
[2] J. Sethi, R. Palit, S. Saha, B. Naidu, AIP Conference Proceedings 1524 (2013) 287.
Speaker: Arzoo Sharma (Department of Physics, Indian Institute of Technology Ropar, Rupnagar – 140 001, Punjab, India)
• 18
Straw Tube Studies and Prototype Assembly for DUNE
Straw tubes are drift chambers made of a gas-filled conducting cylinder acting as cathode, and a wire stretched along the axis of the cylinder acting as an anode. The Straw Tube Trackers(STTs) are a low mass tracking system with excellent vertex, momentum, angular and time resolution and particle identification. Straw Tube based tracking detector is proposed for one of the Near Detectors in the long baseline neutrino experiment, DUNE (Deep Underground Neutrino Experiment) at Fermilab. The SAND (System for on-Axis Neutrino Detection)detector, one of the Near Detectors, will have the tracking system completely based on Straw Tubes modules. We report on the activity, as part of the DUNE-India-ND collaboration, on the plan to assemble and test the SAND STT modules at Panjab University.One test ST chamber is being operated by the group for setting up the readout and characterization facility. New Straws are being assembled for developing a prototype of 1.8m x 50cm.
Speaker: Prachi Sharma
• 1:00 PM
Lunch Break
• Invited lectures
Convener: Supriya Das (Bose Institute (IN))
• 19
Detector Development for INO Experiment
Speaker: Satyanarayana Bheesette (TIFR)
• Virtual lab visit
Convener: Supriya Das (Bose Institute (IN))
• 20
Resistive Plate Chamber (RPC) Assembly and Muon Coincidence Set-up Demonstration
Lab name: Medical Imaging Lab.
Variable Energy Cyclotron Centre, Kolkata
Speaker: Tanay Dey
• 3:30 PM
Tea Break
• Young Scientist Talks
Convener: heinz graafsma (DESY)
• 21
Electrical discharges and their mitigation in Thick-GEM based WELL detector
I will give an overview of the Thick-GEM based WELL detectors and the phenomenon of electrical discharges in them. The effectiveness of using resistive plate in mitigating discharges will be presented next. We developed a tool to produce localized discharges inside the detector to study its effect on the detector performance. I will present the effect of feeble discharges on the performance of Resistive Plate WELL detector.
Speaker: Abhik Jash (Weizmann Institute of Science (IL))
• Oral presentations
Convener: heinz graafsma (DESY)
• 22
Gamma-ray imaging applications of position-sensitive fast scintillators
We are developing position-sensitive detectors based on Cerium doped Lanthanum Bromide(LaBr3:Ce), Gadolinium Aluminium Gallium Garnet (Gd₃Al₂Ga₃O₁₂:Ce, GAGG), and lutetium-yttrium oxyorthosilicate (Lu1.8Y.2SiO5:Ce, LYSO) crystals coupled with the position-sensitive photo-multipliers for the gamma-ray imaging application. Some of these detectors have been tested for energy, timing, and position resolutions for the interaction of the gamma-rays within the detector crystal. The measured results are explained by the GEANT4 simulation results. With a collimated source, the images of irradiation spots in different positions throughout the detector crystal have been obtained. The 2-d images of hexagonal Bismuth Germanate (BGO) crystal and a cylindrical LaBr3(Ce) crystal have been generated using the position sensitive scintillator detectors. The performance for imaging application of the detectors has been investigated by coincidence technique in GEANT4 simulation and compared with the experimental results. The 2-d images of objects with various geometrical shapes have been investigated by Compton back-scattered events of the gamma rays using these detectors in the simulation. These position-sensitive detectors can be used as an absorber of a Compton camera for the image reconstruction of an extended radioactive source. These detectors can have various applications in the fields of nuclear and high-energy physics for scanning of detectors, as well as for the purpose of imaging in the medical and defense sectors. Recent results from these detectors will be presented at the conference.
Speaker: Mr Biswajit Das (Tata Institute of Fundamental Research (TIFR))
• 23
Development of an air shower array using plastic scintillators
A cosmic ray air shower array consisting of 7 plastic scintillation detectors is commissioned at an altitude of about 2200 meters above sea
level in the Eastern Himalayas (Darjeeling). The main goal is to study the origin, composition, and direction of primary cosmic rays at high altitudes. The detector array has a structure of the hexagon. Six detectors are kept at the vertices of a hexagon and
one at the center of it. The distance between two consecutive detectors is 8 meters. Each detector
element consists of four plastic scintillators of dimension 50 cm $\times$ 50 cm $\times$ 1 cm making the total
active area of 1 m $\times$ 1m. These scintillators are fabricated indigenously in the Cosmic Ray
Laboratory (CRL), TIFR, Ooty, India. All four scintillators of a detector are coupled with a single
Photo Multiplier Tube (PMT) using wavelength shifting (WLS) fibers. A custom-built module with
seven inputs is used to generate the multi-fold trigger that detects a shower event. All the plastic scintillators are first characterized and tested in the lab. Continuous measurement of cosmic ray air
shower is carried out from the end of January 2018 to April 2019. Details of fabrication of the detectors, experimental setup, techniques of measurement, and results
will be presented.
Speaker: Shreya Roy (Bose Institute)
• 24
Investigation on thermal performance of low temperature multilayer insulation technique for ground based rare physics programs.
Multilayer insulation (MLI) is a robust passive thermal protection system which is widely used as cryogenic thermal insulation technique in high vacuum environments for minimization of radiation heat load to the cryogenic systems. It has it’s applications in both, space cryogenics exploration programs as well as on the ground based programs also. There are various heat transfer modes through MLI due to the environmental effects: Thermal radiation, solid conduction and residual gas conduction, in which thermal radiation is the major part of the total produced heat load.
Here, the low temperature application of MLI technique on the ground based rare physics programs is discussed, in which MLI technique is used to reduce the the thermal radiation coming from outer wall to the inner wall of the cryostat. Cryostat is a double walled container filled with cryogenic liquid with the vacuum space between the two walls.
The basic concept of MLI technique is that multiple reflection of incident radiation is obtained by placing the reflective layers to reflect the incident radiation called radiation shields, in between the two walls of the cryostat. Because of it’s multilayer structure, with each successive reflective layer reducing the radiation heat load mainly, on the next by a fraction. These reflective layers are formed with thin polyethylene or Mylar sheet, coated with highly reflecting material (Aluminium or Gold) on both the sides. Therefore, low conductivity materials (or insulators) called spacers are placed in between these reflective layers to avoid the thermal contact between them and hence the conduction heat load due to adjacent reflective layers.
The current work is an attempt to find the best materials for MLI system (reflective layer and spacer materials), which is usually asked before designing the insulation system for a cryostat in any experiment. This work discusses the effect of perforated double-Aluminized Mylar (DAM) with Dacron, unperforated DAM with Silk-net and perforated DAM with Glass-tissue on the performance of MLT technique, as the reflective layer as well as spacer materials. After that, we have discussed the effect of layer density and the number of layers on the heat load, by which the optimal layer density is observed for all three combinations. Knowing the key parameters of MLI technique, the heat load generation in spherical as well as cylindrical cryostats is compared and found the effect of layering near the inner and outer wall of the cryostat.
Speaker: Ms D. Singh (Banaras Hindu University, Varanasi, India, 221005.)
• Wednesday, October 27
• Invited lectures
Convener: Chandana Bhattacharya (VECC, Kolkata)
• 25
Detectors for Nuclear Physics Research
Speaker: Tilak Ghosh (VECC)
• Oral presentations
Convener: Chandana Bhattacharya (VECC, Kolkata)
• 26
Study of neutron response using time of flight technique in ISMRAN detector.
We present the measurements of the neutron response in ISMRAN (Indian Scintillator Matrix for Reactor Anti-Neutrinos) set up consisting of an array of 9×10 Plastic Scintillator Bars at BARC, Mumbai. ISMRAN is an above ground set up at ~13m from Dhruva reactor core for the detection of reactor based anti-neutrinos via inverse beta decay process. The ISMRAN setup will be shielded by a 10 cm of Lead and 10 cm of Borated Polyethylene to reduce the reactor related background. The dominant source of reactor related background in the vicinty of the detector are gamma and neutrons. The neutron generated from a Am-Be source are used to study their response using time of flight technique in the ISMRAN. These measurements are useful in context of discriminating fast neutron reactor background from reactor anit-neutrinos in the Dhruva reactor hall. The estimation of proton recoil energy and the neutron capture time in the ISMRAN detector are studied in detail.
Speaker: Mr Roni DEY (Bhabha Atomic Research Centre)
• 27
A THGEM based low pressure gas detector for the detection of fission fragments
A thick gaseous electron multiplier based gas detector, operated at low pressures ~3-4 torrs of isobutane gas is being designed and developed at VECC. The detector shall be used for the detection of highly ionised fission fragments in experimental studies of fusion fission dynamics. The prototype detector consists of three planes, a GEM based anode sandwiched between two wire plane cathodes. The time of arrival of the fission fragments is readout from the anode plane. Future improvements incorporating the position readout (X and Y) of the arrival of fission fragments on the detector, are being planned with simulations being done for the best optimised position of the X and Y readout planes. Details of the prototype detector testing with a 252Cf source and simulation results shall be discussed at the workshop.
Speaker: Mr Arijit Sen (Physics Group, VECC, 1/AF, Bidhannagar, Kolkata 700064, INDIA.)
• 11:10 AM
Tea Break
• Invited lectures: Special lecture
Convener: Gagan Mohanty (Tata Inst. of Fundamental Research (IN))
• 28
Silicon Trackers at the Heart of the LHC Experiments
Speaker: Luciano Musa (CERN)
• Oral presentations
Convener: Gagan Mohanty (Tata Inst. of Fundamental Research (IN))
• 29
FPGA based high speed DAQ systems for high-energy physics experiments: potential challenges
Nuclear and particle physics experiments at high energies, often referred to as High Energy Physics (HEP) experiments, study the constituents of matter and their fundamental interactions. By colliding proton on proton or heavy-ions, such as, Au on Au or Pb on Pb at relativistic energies; one creates conditions that are prevalent within a microsecond after the birth of our universe. These collisions produce large number of highly energetic particles which are to be recorded by the experiments. This poses great challenges for particle detectors, readout electronics, and data acquisition (DAQ) systems including data storage. In addition, the radiation levels in the proximity of the detectors have also been growing, which demands for radiation tolerant devices. Traditional nuclear physics experiments employ detectors with several tens to few hundred of readout channels using standard electronics and conventional DAQ systems, which handles low data rate (few megabyte per second) and less resilient for data errors against multi-bit upset in radiation zones.
In contrast, the present day HEP experiments, for example at the Large Hadron Collider (LHC) at CERN, FAIR at GSI Darmstadt; operate detectors up to billions of electronics channels, which produce data at the rate of few terabyte (TB) per second. This requires a highly efficient system to cope with the increase in data volume by acquiring data at a high rate and recovery from data error against the multi-bit upsets in radiation environments.
We will present an overview of the new FPGA based high speed DAQ system which is capable of high data rate communication. We will summarize the technical challenges for the development such a DAQ system, points of uncertainties and their probable solutions. The applicability is not limited to particle physics only. It also fits well for industry applications like medical imaging, muon tomography and future HEP experiments.
Speaker: Dr Shuaib Ahmad Khan (Department of Atomic Energy (IN))
• 30
Designing a front end digital pulse processing chain for FAIR CBM experiment using FPGAs
The article is about the front end data acquisition chain developed for the MUON detectors in the CBM experiment at FAIR. As a contribution towards the development of CBM experiment, a prototype system for digital pulse processing (DPP) has been designed by me on FPGA development board. A single channel of pulse processing chain for the pulse analysis of detectors has been developed and tested successfully in our lab. The FPGA has been interfaced to the AD9228 ADC board, which is connected to a multichannel mixed signal Front End electronics (FEE) ASIC board named nXYTER. In our design, the ADC interfacing is the challenging part due to its LVDS serial data inputs at the sampling rate of 20 MHz as per the system design requirements. The concurrent and synchronous nature of FPGA architecture makes it ideal for the testing and development of pulse processing data acquisition chains. The pulses from the ASIC board coming at the rate of 20 MHz are analog inputs, which needs to be sent to FPGA by digitization with AD9228 ADC board. The acquired 12-bit parallel data from ADC board using FPGA is then processed to extract the useful information out of it, which can be then sent to the PC for visualization using various software tools like ROOT, MATLAB etc.
Speaker: Abhishek Singh
• 1:00 PM
Lunch Break
• Invited lectures
Convener: Pradip Kumar Sahu (Institute of Physics)
• 31
Development of the Silicon Pixel Technology and Challenges
Speaker: Walter Snoeys (CERN)
• Virtual lab visit
Convener: Pradip Kumar Sahu (Institute of Physics)
• 32
Gain, energy resolution measurement using GEM detector and coincidence setup demonstration using cosmic ray
Lab: HEP Detector laboratory, Bose Institute, Kolkata
Speakers: Sayak Chatterjee , arindam sen
• 3:30 PM
Tea Break
• Young Scientist Talks
Convener: Stefania Maria Beole (Universita e INFN Torino (IT))
• 33
From Detector Simulation to Data Analysis in High Energy Physics Experiments
In Nuclear and Particle Physics Experiments, the combination of more detectors
is used to reconstruct the particle trajectories, measure their momentum, and identifying
particle species. To optimize the apparatus and understand its performance, indispensable
ingredients are Monte-Carlo (MC) Simulations. This talk will give an overview of MC
simulation in High Energy Physics (HEP) experiments. There are some general steps of
MC simulation namely, generation of particles, their transport in the materials, simulation
of the detector response, digitization, hit reconstruction, tracking, and physics analysis. I
will illustrate my experience on detector MC simulation (using FAIRROOT and GEANT4)
within large HEP experiments.
Speaker: Shyam Kumar (Universita e INFN, Bari (IT))
• Oral presentations
Convener: Stefania Maria Beole (Universita e INFN Torino (IT))
• 34
Numerical Studies on Primary Ionization in TPC
The Active-Target Time Project Chamber (AT-TPC) is used in the field of low-energy nuclear physics to study nuclear reactions by tracking the reaction products. The primary ionization produced by charged products along their track in the active gas volume of the TPC can be utilized for track reconstruction. The primary electrons are multiplied in the applied electric field and collected over a 2D array of electrode elements placed at one end of the device for producing 2D position information. The third co-ordinate information can be obtained from the measurement of time of flight of the electrons to reach the collecting electrode. The use of the TPC gas volume simultaneously as a reaction target as well as a tracking medium of ions emitted from the reaction turns out advantageous to conventional detector arrays, especially in probing inverse kinematics where a heavy-ion beam collides with a light-ion target. One of the important factors that govern the tracking capability of the TPC is the homogeneity of the electric field prevailing in the drift volume of the device which is crucially dependent upon the design of the field cage and electrode configuration used in the device. The other factor which can distort the field is space charge effect. It can be substantial in case of low-energy particles which deposit their full energy in the medium and produce a large amount of ionization. Here, we report the spatial information of the primary space charges produced by alpha particles in a TPC filled with Ar:CO2 (70:30) at different gas pressures using Geant4 [1] and Heed [2] simulation packages. We have used Photoabsorption and Ionization Physics Lists in Geant4 for the simulation and compared the results with that of the Heed. The same simulation has been carried out using cosmic muons at atmospheric pressure for validation. These results can be used for finding the distortion of the electric field due to the space charge in the drift region of the TPC which can be helpful for designing an AT-TPC for low-energy nuclear reaction experiments.
Reference
[1] S. Agostinelli et al. [GEANT4], GEANT4–a simulation toolkit, Nucl. Instrum. Meth. A 506, 250-303 (2003). https://geant4.web.cern.ch/
[2] I.B. Smirnov; “Interactions of particles with gases”; online at http://cern.ch/heed
Speaker: Mr PRALAY DAS (Saha Institute Of Nuclear Physics Kolkata, India. Homi Bhabha National Institute, Training School Complex, Anushaktinagar, Mumbai-400094)
• 35
Simulating the response of a liquid scintillation detector to neutrons
Neutrons are one of the most critical contributors to background signals. Understanding the neutron background is crucial as they can easily mimic the Weakly Interacting Massive Particle (WIMP) signals in dark matter search experiments. Organic liquid scintillation detectors are often used to detect fast neutrons. EJ-301 is a popular liquid scintillator used to detect fast neutrons because of its good pulse shape discrimination property. In this work, we unfold the response of an EJ-301 detector to Am-Be neutron spectra using two unfolding methods: Roo-Unfold and the GRAVEL method. Once the response of the detector is modeled, using the unfolding method, it will be possible to obtain the information of the fast neutron background at different rare event background sites.
A $2^{\prime\prime}\times2^{\prime\prime}$ cylindrical liquid scintillation detector (EJ-301) has been modeled using the GEANT4 framework. Various properties of the detector like the light output of the scintillator, quantum efficiency of the photocathode, material composition have been defined using values from literature and detector manuals. A photon to electrical signal conversion (Photo-multiplier tube) and digitization method has also been implemented in GEANT4 from which we obtain the response of the detector in terms of integrated electronic charge. Simulated gamma spectra from the detector for different gamma sources like ($^{60}$Co, $^{22}$Na, etc.) show excellent agreement with the experimental gamma measurements providing confidence in the modeling. In the first stage, energy spectra of monoenergetic neutrons are simulated at fixed neutron energy intervals to construct the response matrix. In the second stage, neutrons having energy distribution following the ISO Am-Be continuous neutron energy spectrum are made incident on the detector and the energy spectrum is simulated. The spectrum obtained after the second stage is unfolded using the response matrix generated in the first stage to obtain the actual input ISO Am-Be spectrum. We see that both the methods are able to predict the actual ISO spectrum very well.
Speaker: Mr S. Das (NISER,HBNI)
• 36
Monte Carlo simulations for nuclear physics experiments using NPTool
In recent times, experiments with rare isotope beams at accelerators around the world have provided several exciting results in nuclear physics and astrophysics. The experiments involve unstable and even unbound nuclei, low beam intensities, highly granular and efficient detectors arrays. Monte Carlo simulations play a pivotal role in the successful planning as well as data analysis of such experiments. We have used the NPTool (Nuclear Physics Tool) package to carry out the simulations for our experiment at the HIE-ISOLDE radioactive ion beam facility of CERN. The experiment involved a 5 MeV/A $^{7}$Be radioactive beam impinging on a CD$_{2}$ target. The charged particles emitted from the reaction were detected by an efficient detector array consisting of annular and double sided silicon strip detectors backed by silicon pads covering an angle of $8^\circ - 165^\circ$ in laboratory. NPTool is an open source and freely distributed package for Monte Carlo simulation and data analysis of nuclear physics experiments. It offers a unified framework for designing, preparing and analyzing complex experiments consisting of multiple detectors using GEANT4 and CERN ROOT tool kits. We discuss the NPTool simulations carried out to study scattering and reactions involving the $^{7}$Be radioactive beam and its comparison to our experimental data.
Speaker: Subhankar Maity (Bose Institute)
• Thursday, October 28
• Invited lectures: Special Lecture
Convener: Vipin Bhatnagar (Panjab University (IN))
• 37
Roadmap of the MPGD Towards Imaging and Timing Performances
Speaker: Archana Sharma (CERN)
• Oral presentations
Convener: Vipin Bhatnagar (Panjab University (IN))
• 38
Commissioning and testing of real-size triple GEM prototypes for CBM-MuCh in the mCBM experiment at SIS18 facility of GSI
The Compressed Baryonic Matter (CBM) experiment is one of the core experiments at the Facility for Antiproton and Ion Research (FAIR) in GSI Darmstadt, Germany. The experiment aims to explore the phase diagram of strongly interacting matter at the high net-baryon densities and moderate temperatures. It has been designed to handle unprecedented interaction rates (up to 10 MHz) of Au+Au collisions in an energy range of 2-11 AGeV at SIS100 setup. Muon Chamber (MuCh) system, consisting of alternating layers of instrumented hadron absorbers and triplet of detector stations sandwiched between them, will be used to measure di-muon signals originating from the decay of low mass vector mesons and charmonia. A Gas Electron Multiplier (GEM) based tracking detectors will be used for the first two stations of CBM-MuCh. The detectors will be operated in self-triggered mode. Large area triple GEM detector prototypes of approximately 1900 cm2 in size will be employed for MuCh system. The readout consists of pads with progressively increasing pad sizes from ~4 mm to ~17 mm. A novel opto-coupler based HV biasing to power the 24 segments of each GEM foil has been implemented for the first time. In this contribution, we report the installation, commissioning, and testing of two such modules with nucleus + nucleus collisions at 1-2 AGeV beam energies in the mini-CBM (mCBM) experiment at the SIS18 facility of GSI, which is a part of “FAIR Phase-0” program. Data with the first version of STS/MuCh-XYTER, a dedicated readout chip for GEM-MuCh and STS, has been taken for the first time. The response of large size GEM modules in multiparticle environment have been studied in detail. Event building based on the timestamps of the detector hits has been carried out for the nucleus-nucleus collision data. Optimization of this algorithm and straight-line track fitting using global X-Y coordinates of the hits from all the subsystems will be reported. The detailed performance of the detectors at different operating conditions will be presented and discussed.
Speaker: Mr Ajit Kumar (Variable Energy Cyclotron Centre)
• 39
Upgradation of CMS Detector at the LHC with GEM Detector
By the end of the year 2022, the LHC is expected to reach a total integrated luminosity of $300 fb^{-1}$ of the data. The high luminosity upgrade of the LHC is foreseen during a third long shutdown to further increase the instantaneous luminosity to $5\times10^{-34} cm^{-2}sec^{-1}$. The muon system of CMS detector consists of DTs in barrel, CSCs in the endcaps and RPCs that provide redundant trigger and fine position measurement in both barrel and endcap regions. On the other hand, the forward region of the endcaps is instrumented only with the CSCs. The muon system aims to provide efficient and fast identification of muons, however the possible degradation of CSC performance due to the sustained operation in a high rate environment could drastically affect the entire muon system. In order to improve and maintain the forward muon triggering and muon reconstruction at high luminosity, CMS detector is planned to be equipped with an additional layer of new technology based set of muon detectors, called Gas Electron Multiplier (GEM). In the talk, various activities carried out by Panjab University group in the fabrication and testing of GEM detectors will be discussed.
Speaker: Harjot Kaur (Panjab University (IN))
• 11:10 AM
Tea Break
• Invited lectures
Convener: Sanjib Muhuri (VECC)
• 40
Fundamental of Silicon Calorimeter
Speaker: Vincent Boudry (LLR – CNRS, École polytechnique, Institut Polytechnique de Paris)
• Oral presentations
Convener: Sanjib Muhuri (VECC)
• 41
Development of silicon detector and readout electronics for the FoCal
Forward Calorimeter (FoCal) is a proposed silicon-tungsten (Si-W) sampling type electromagnetic calorimeter as a part of the ALICE collaboration’s upgrade program at CERN. For the active silicon layers in FoCal, a large area (∼ 40 cm2) silicon pad sensor with an individual pad size of ∼ 1 cm2 is proposed with challenging requirements like low leakage current and high breakdown voltage. Moreover, Si-W based EM calorimeter involves particle shower formation and dissolution, which put forward the simultaneous requirement of low power, low noise and wide dynamic range FEE (Front End Electronics). A 6x6 array of silicon pad detectors on a 4-inch wafer and two different FEE ASICs, namely ANUSANSKAR and ANUINDRA, are developed and tested towards these goals. ANUSANSKAR, designed initially in 0.7 µm CMOS technology, is a low power, low noise FEE ASIC with a dynamic range of +/- 600 fC. Later, to cater for the still higher dynamic range requirement, a new ASIC, namely ANUINDRA with a dynamic range of ~ 2.6 pC, was designed in 0.35 µm CMOS technology. The silicon pad sensors and the FEE ASICs have been used to build a series of FoCal prototypes, undergone beamline validation, and led to improved readout methodology and better performance. This talk will present the research and development work of the silicon detector, and its readout electronics carried out in India for the proposed FoCal detector.
Speaker: Mr Sourav Mukhopadhyay (Bhabha Atomic Research Centre, HBNI)
• 42
Concept and development of the Focussing Aerogel Ring Imaging Cherenkov (FARICH) detector for HMPID-systems
We present the Focusing Aerogel RICH-detector (FARICH) concept based on 2009-2014 studies of a FARICH prototype detector for the ALICE experiment at CERN. The aim of the project was to develop a prototype detector that would extend the momentum range of charged particle identification: up to 10 GeV/c for pion-kaon separation and up to 14 GeV/c for kaon-proton separation at the ALICE HMPID system [1, 2]. In the frameworks of this project, we proposed the FARICH prototype detector employing a multi-layer silica aerogel as a radiator. In June 2014, we tested a FARICH prototype detector based on Digital Photon Counters (DPC-DSiPM) by Phillips Company at the CERN PS T10 beam line with a particle momentum up to 6 GeV/c [3, 4]. The main performance characteristics of these prototype detectors and a comparison with a Monte Carlo simulation are presented.
In this talk, we also discuss one of the proposed versions of the FARICH concept using an MPGD GEM detector with a photo-conversion film for recording Cherenkov photons.
Proposed FARICH prototypes can be used in the development of HMPID-systems for projected heavy-ion experiments, for example, ALICE3 at CERN.
References
1. Development of FARICH-detector for ALICE experiment at CERN
A.I. Berlev (Moscow, INR) et al., 2009. 4 pp.
Published in Nucl.Instrum.Meth. A598 (2009) 156-159.
2. A Very High Momentum Particle Identification Detector (VHMPID)
for ALICE. Letter of Intent, Version 19.0, ALICE VHMPID Upgrade, 2012.
electronic version: https://twiki.cern.ch/twiki/bin/view/Sandbox/VHMPIDLoI
3. Beam test of FARICH prototype with Digital Photon Counter
A.Yu. Barnyakov (Novosibirsk, IYF) et al., 2013. 5 pp.
Published in Nucl.Instrum.Meth. A732 (2013) 352-356.
4. Tests of FARICH prototype with precise photon position detection
A.Yu. Barnyakov (Novosibirsk, IYF) et al., 2014. 4 pp.
Published in Nucl.Instrum.Meth. A766 (2014) 88-91.
Speaker: Aleksei Makarov (Institute for Nuclear Research RAS)
• 1:00 PM
Lunch Break
• Invited lectures
Convener: Saikat Biswas (Bose Institute (IN))
• 43
Fundamental of Readout Electronics and Data Acquisition for Particle Detectors
Speaker: Christian Joachim Schmidt (GSI - Helmholtzzentrum fur Schwerionenforschung GmbH (DE))
• Young Scientist Talks
Convener: Saikat Biswas (Bose Institute (IN))
• 44
Interaction with calorimeters, triggering and data analysis at the CMS detector
LHC open an unprecedented window on the weak-scale nature of the universe, providing high-precision measurements of the standard model as well as searches for new physics beyond the standard model. The Electromagnetic Calorimeter (ECAL) of the CMS detector has plays an important role in the physics program of the experiment, delivering outstanding performance throughout data taking. Such precision measurements and searches require information-rich datasets with a statistical power that matches the high-luminosity provided by the LHC. Efficiently collecting those datasets is a challenging task and is performed by two-level triggering system - hardware trigger (Level-1) and software based (high level trigger).
Speaker: Varun Sharma (University of Wisconsin Madison (US))
• 3:30 PM
Tea Break
• Invited lectures
Convener: Satya Ranjan Santra (BARC, Mumbai)
• 45
The Practice of Gamma-ray Spectroscopy: Here & Now
Speaker: Rajarshi Raut (UGC-DAE CSR, Kolkata Centre)
• Oral presentations
Convener: Satya Ranjan Santra (BARC, Mumbai)
• 46
Detectors for light charged particles, neutrons and fission fragments produced in low energy nuclear physics experiments
To understand the strong force that binds all the nucleons together, it is required to perform collision experiments using particle accelerators and detect the reaction products starting from light nuclei like neutron, proton, alpha etc. to very heavy nuclei like fission fragments and evaporation residues. At BARC-TIFR Pelletron-Linac facility, Mumbai, several detector arrays have been setup which are used for the above purposes. For example, the light charged particles are detected using an array of telescopes made of position sensitive silicon strip detectors [1] and many times with small silicon surface barrier detectors, whereas neutrons and gammas are detected using the arrays of plastic and liquid scintillators [2]. On the other hand, heavy nuclei like fission fragments are detected using position sensitive Multiwire Proportional Counters (MWPC) developed in-house [3]. For detecting fission fragments with better timing resolution the micro channel plate (MCP) based detectors for are also being developed at BARC. The details of the characterizations and performances of the above detectors will be presented.
[1] D. Chattopadhyay et. al. Phys. Rev. C 94, 061602(R) (2016)
[2] P.C. Rout et al. JINST 13, P01027 (2018)
[3] A. Pal et al. JINST 15, P02008 (2020)
Speaker: Asim Pal
• Friday, October 29
• Invited lectures
Convener: Sandeep Ghugre (DAE-UGC IUC, Kolkata )
• 47
Experimental Techniques for Dark Matter Search
Speaker: Satyajit Saha (SINP, Kolkata)
• Oral presentations
Convener: Sandeep Ghugre (DAE-UGC IUC, Kolkata )
• 48
Exploring the Superheated Liquid Detector for Low-Mass Dark Matter Search
There are ample convincing evidences based on gravitational effects point to the existence of dark matter (DM) though the particle properties of DM is unknown. Many theories suggest that Weakly Interacting Massive Particles (WIMPs) are one of the most promising candidates for DM with masses varies from few MeV to few hundred of TeV. It could be observed directly via direct detection of DM search experiments, which are aimed at detecting the nuclear recoils caused by WIMPs-nucleus elastic scattering. The most challenging part of any DM direct search experiment is identifying and suppressing the backgrounds, therefore the experiments are conducted deep down to minimise the cosmic ray-induced backgrounds. The current most sensitive direct detection experiments are sensitive in the 25–40 GeV WIMP mass range and the null results of these experiments have piqued curiosity in the low WIMP mass region, particularly below 10 GeV. Low threshold energy and a target with low mass nuclei are required for the detector to be sensitive to low WIMP mass.
Here, we have investigated the potentiality of C$_{2}$H$_{2}$F$_{4}$ (b.p. -26.3 $^{\rm o}$C) superheated liquid detector (SLD) (containing low mass nuclei) to probe the low mass WIMPs. SLD provides an excellent rejection to the backgrounds by adjusting the operating temperature and pressure of the liquid such that it can detect heavy ionizing particles (e.g. neutrons) at a certain temperature and pressure range while remaining insensitive to low ionizing radiation (e.g. gamma-rays and muons). Due to the presence of $^{12}$C and $^{19}$F recoil nuclei, the detector operating at 35.0 $^{\rm o}$C (gamma-ray insensitive zone) with 100$\%$ thermodynamic efficiency can detect WIMPs with masses as low as 2.2 GeV, whereas the $^{1}$H recoil nucleus is insensitive in this temperature range. At zero background environment, WIMPs in the few GeV mass range could be explored with a C$_{2}$H$_{2}$F$_{4}$ SLD with a WIMP-nucleon spin-independent cross-section sensitivity of about 2.10$\times$10$^{-41}$ cm$^2$ at WIMP masses as low as 4.0 GeV and a total exposure of 1000 kg.day, assuming a thermodynamic efficiency to be 50$\%$ or more. Sensitivity to sub-GeV WIMP masses usually demands sensitivity to the WIMP produced $^{1}$H recoil nucleus, which involves the detector working at 50.0 $^{\rm o}$C temperature and thermodynamic efficiency > 50$\%$. From the calculation, it is found that C$_{2}$H$_{2}$F$_{4}$ SLD operating at 60.0 $^{\rm o}$C temperature (gamma-ray sensitive zone) with 100$\%$ thermodynamic efficiency, the bubble nucleation threshold energy of 0.1 keV can be achieved for all three nuclei which is found to be sensitive to 140 MeV, 430 MeV, and 540 MeV WIMP masses due to $^{1}$H, $^{12}$C, and $^{19}$F recoil nuclei, respectively.
The experiment in steps with increasing exposure with C$_{2}$H$_{2}$F$_{4}$ SLD has been started at 555m deep Jaduguda Underground Science Laboratory (JUSL), UCIL, Jharkhand, India for the hunt for low mass WIMPs. It is necessary to investigate the noise and background levels at JUSL before run the SLD for WIMPs search. It is observed with a small mass SLD at JUSL that the 20Hz-20 kHz region is dominated by the noises and the background event rate is reduced at underground. The detector with increased active mass is under construction and DAQ and related instrumentation have developed. Signals at higher frequencies will be measured in future to better understand the background induced events as well as the noise with increased active mass and longer run time with a goal to search for the low mass WIMPs.
Speaker: Ms Sunita Sahoo (High Energy Nuclear and Particle Physics Division, Saha Institute of Nuclear Physics)
• 49
Characterization of Sapphire detector for CEνNS search at MINER
Abstract:
The Mitchell Institute Neutrino Experiment at Reactor (MINER) at Texas A$\&$M University, USA is a reactor based neutrino experiment which aims to measure coherent elastic neutrino-nucleus scattering (CE$\nu$NS) where a neutrino interacts with a nucleus as a whole creating a nuclear recoil [1, 2]. One of the main challenges for this experiment is to deploy detectors capable of measuring low-recoil energies. A novel sapphire detector made up of Al$_{2}$O$_{3}$ substrate with dimension 7.62 mm $\times$ 4 mm with mass 73 g has been fabricated and characterized. Particle interactions are detected through phonons and scintillation photons. The phonons are detected through Transition edge sensors (TES) photo-lithographically placed on the surface of the detector. The photons are detected through their interactions with a Si HV [3] detector in coincidence. We will report the characterization and performance of the sapphire detector in reactor and non-reactor environments.
Reference:
[1] D Z Freedman, D N Schramm, and D L Tubbs. “The Weak Neutral Current and its Effects in Stellar Collapse”. In: Annual Review of Nuclear Science 27.1 (1977), pp. 167–207. doi: 10.1146/annurev.ns.27.120177.001123.
[2] A. Drukier and L. Stodolsky. “Principles and applications of a neutral-current detector for neutrino physics and astronomy”. In: Physical Review D 30 (11 1984), pp. 2295–2309. doi: 10.1103/PhysRevD.30.2295.
[3] V. Iyer et al. “Large mass single electron resolution detector for dark matter and neutrino elastic interaction searches”. In: Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment 1010 (2021), p. 165489. issn: 0168-9002. doi: https://doi.org/10.1016/j.nima.2021.165489.
Speaker: Ms Mouli Chaudhuri (Natioanl Institute of Science Education and Research)
• 11:10 AM
Tea Break
• Invited lectures
Convener: Subhasis Chattopadhyay (Department of Atomic Energy (IN))
• 50
Application to Society: Imaging in Particle Therapy
Speaker: Aafke Kraan (INFN, Pisa)
• Oral presentations
Convener: Subhasis Chattopadhyay (Department of Atomic Energy (IN))
• 51
Application of MPGD detector in Medical Imaging and Treatment
We will discuss the Micro-Pattern Gas Detector (MPGD) which is a recently developed gas-filled detector in the series of Multi-Wire Proportional Chamber (MWPC) and Resistive Plate Chamber (RPC). MPGD have some characteristics which make it suitable to use in medical diagnosis & prevention techniques. MPGD uses a fine readout electrode structure, so it can obtain much higher spatial resolution compared to that of the conventional gas detector based on the multi-wire proportional chamber. Although MPGD detectors are being used in particle and nuclear physics experiments, the excellent spatial and time resolution make them an invaluable tool for other applications too i.e., radiography and low energy gamma imaging, dosimetry and hadron therapy, X-ray fluorescence.
Speaker: Mr Sunil Kumar (Panjab University (IN))
• 52
Effect of Continuous Long Term Exposure of Non-ionising Radiation on Human Health
The Present study is proposed to explore the effect of continuous long term exposure of non ionizing radiations (NIR) on human health. With the population explosion and technology advancement, the requirement of wireless gazettes is also increasing. Consequently, the base transceiver station (BTS) are increasing in the similar way. Therefore, more and more population of humans is being exposed to radiation from them. Evidently, possible biological effects of their radiation become important aspects of current research. Earlier studies had been performed by considering the electromagnetic wavefront spherical, but practically most of the BTS contain vertical rod antenna which transmits cylindrical wavefront. In this study the theoretical calculations for incident electric field, resulting penetration, temperature variation & Specific Absorption Rate (SAR) have been made with the help of computer simulation technology (CST Studio Suite) by considering the cylindrical wavefront using the electrical conductivity, permittivity, permeability and mass density for the respective tissues at a specific higher frequency ranges of NIR. The intensity of these electromagnetic waves are maximum near the BTS and reduces with distance as it is inversely proportional to the square of distances. On the basis of calculation it can be concluded that the continuous and long term exposure of NIR may be harmful for humans at shorter distances from the BTS.
Speaker: Rahul Kaushik (HVM (PG) College Raisi Haridwar Uttarakhand)
• 1:00 PM
Lunch Break
• Oral presentations
Convener: Indranil Mazumdar (TIFR)
• 53
Discrimination of neutrons and gamma-rays induced events in Superheated Emulsion Detector
A liquid which maintains its liquid state above its boiling point is called the superheated liquid. It is a metastable state of the liquid. The superheated state can be reached by slowly increasing the temperature or by slowly reducing the pressure starting from its liquid state. The superheated state moves to a more stable vapour state by a small disturbances as a consequence of thermal motion or temperature fluctuation of the liquid. The transition from the metastable liquid state to the more stable vapour state occurs by forming a nucleus of a new phase known as nucleation. The radiation interaction of ions, charged particles, neutrons, photons etc can nucleate the superheated liquid. In the present study, the Superheated Emulsion Detector (SED) has been fabricated at the laboratory that consists of the droplets of the superheated liquid suspended in a viscous gel. The liquids, CCl2F2 (R12) b.p. -21.6 oC and C2H2F4 (R-134a), b.p. -26.3oC were used as active material in the detector though in the present abstract only the result with R12 is shown. When an energetic particle or radiation falls on the drops, if the energy deposition in the liquid exceeds the critical energy and radius of the nucleus is greater than the critical radius, bubbles are formed inside the drops. The critical energy depends on the temperature and pressure of the liquid and the detector can be made insensitive to specific particles by varying the temperature and pressure of the liquid. Here we have studied neutrons and gamma-rays induced bubble nucleation events by irradiating the SED with 241Am-Be ( 10 mCi) and 137Cs (5 mCi) as a neutron and gamma rays sources respectively and tried to discriminate the events. The usefulness of the discrimination lies in the WIMPs (Weakly Interacting Massive Particles) dark matter (DM) search experiment using SED as one of the important backgrounds for such experiment is gamma-rays. Therefore efficient discrimination techniques are important for the detection of WIMPs. WIMP and neutron interact similarly and hence the neutron source is used to calibrate the WIMPs detector. The SED is also used as a neutron detector/dosimeter in several applications. The acoustic signals produced from the nucleation of superheated liquid drops have been detected using an acoustic sensor (frequency range - few kHz to 1 MHz) and stored in the LabVIEW. These acoustical signals have been analysed and the frequency corresponding to the maximum power in its FFT spectrum is collected from each signal denoted as the fundamental frequency (FF). It has been observed that the FF of the neutron induced events lies within 80 to 90 kHz but the FF of the gamma-rays induced events lies in the range of 20 to 30 kHz. The high frequency events are produced due to the localised energy deposition of the recoil nuclei originating from the neutrons. The electrons are produced from the gamma-rays inside the liquid and those electrons deposit energy and produce the low frequency events. The range of the electron is larger than the range of the recoil nucleus and it deposits less energy within the critical radius, hence producing the low frequency events. The FF variable discriminates about 83.47 % of the neutrons induced events from that of the gamma-rays. The present study is important in discriminating the background events in WIMPs DM search experiment and also in the neutron detection in a background of gamma-rays.
Speaker: Mr Suraj Ali (Saha Institute of Nuclear Physics)
• 54
A Compact and Cost effective Data Acquisition Module (C-DAQ) for Particle physics instrumentation
Nuclear and particle physics instrumentation often requires lots of NIM based modules and lengthy cables for setting up experiments. Data Acquisition modules with FPGA are used as alternatives. But FPGA modules are expensive and require expertise handling. To address this issue a Cost effective, compact and user friendly Data acquisition module using FPGA was developed. This miniature module consists of a daughter card with 8 input channels which accept negative pulses from a few millivolts to 1 or 2 Volts. This module discriminates analog negative pulses with a common threshold then converts to TTL and sends to FPGA. A low form factor MAX10 FPGA development board was used as a mother board. A user programmable logic with counting of all input pulses up to 100ns resolution and coincidence logic was implemented inside the FPGA. This coincidence output is available in NIM format for triggering purposes. 32bit Counter data of all eight input signals and coincidence counter data are sent to the control PC via USB UART port. Same USB port used for supplying 5V 1A power required by the module. A Simple python script controlled UART protocol is used to receive counter data and send configuration logic. This paper describes architecture and various applications of C-DAQ in detail
Speakers: Yuvaraj Elangovan (Tata Institute of Fundamental Research) , Mandar Saraf (Tata Institute of Fundamental Research)
• Young Scientist Talks
Convener: Indranil Mazumdar (TIFR)
• 55
Background Radiation at JUSL and Simulation of Nuclear Recoils in Liquid Xenon Detectors
Measurements and Simulation of background radiation
at JUSL and Simulation of Nuclear Recoils due to
Supernova Neutrino-induced neutrons in liquid Xenon
detectors
Sayan Ghosh
Abstract
Rare event search experiments require very careful simulations, in addition to accurate measurements
of ambient radiation contribution from radioactive decay and nuclear processes in the surrounding rock
components as well as from charged cosmic rays. A new underground laboratory has been set up at 555 m
(∼1.6 km water equivalent) vertical depth, with the vision of undertaking future experiments like direct dark
matter search, neutrino less double-beta decay, etc. I shall present the various measurements and simulation
of background for such underground experiments arising from penetrating charged cosmic rays, radiogenic
and cosmogenic neutrons, in addition to measurement and shielding studies of gamma background, which
in-turn shall serve as the basis of all future rare event search experiments at the underground site. I shall
also discuss about investigating the possibilities of detecting core collapse supernova (CCSN) neutrinos by
large volume liquid Xenon detectors, designed primarily for direct dark matter search. In addition to giving
rise to Coherent Elastic Neutrino Nucleus Scattering (CEνNS) interactions, CCSN neutrinos would undergo
charge current (CC) interactions with the Xenon nuclei and consequently produce neutrons inside the liquid
xenon tank. These neutrons would in turn produce nuclear recoils through multiple elastic scatterings. This
presents an extra-handle, in addition to the CEνNS interactions to detect CCSN neutrinos. I shall discuss
that careful simulation of these interactions, to finally compute the observable S1 and S2 signals, reveals
that this second channel indeed gives a dominant contribution to the total number of detected nuclear
recoil events at the high detector threshold regime. Detection of these second type of events in future large
volume detectors like LZ, DARWIN, etc., may give observational handle on the flavour composition of CCSN
neutrinos, since this second channel shall only be generated by νes while the CEνNS interactions would arise
from all flavours of neutrinos.
Speaker: Sayan Ghosh (Saha Insitute of Nuclear Physics)
• 3:10 PM
Tea Break
• Best Talk Announcement
Convener: Sanjeev Singh Sambyal (University of Jammu (IN))
• Invited lectures: Special Lecture
Convener: Tapan Nayak (CERN, Geneva and NISER, Bhubaneswar)
• 56
History of Detector Development and Future Perspective in India
Speaker: Naba Mondal (SINP) | 2022-12-10 06:17:08 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.47710704803466797, "perplexity": 6081.67206548207}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446711712.26/warc/CC-MAIN-20221210042021-20221210072021-00639.warc.gz"} |
http://physics.stackexchange.com/questions/62993/concerning-scattering-intensity-and-particle-concentration | # Concerning Scattering Intensity and Particle Concentration
I am trying to determine what governs my sensor output. I have an optical sensor that emits infrared radiation on a sample volume and gives me a voltage output from the scattering of (1 to 10 micron) particles through a 90 degree scattering angle. I introduce aerosol particles of various sizes and keep track of the scattering output voltage
Parallel to my sensor output I also record the Number, surface and mass concentration of my aerosol particles from a different sensor unit.
I am trying to determine what governs my sensor output voltage. I know that Mie scattering depends on Mie intensity parameters, which depends on particle size, i.e.
$$I(\theta) = \frac{I_0 \lambda^2(i_1 + i_2)}{8\pi R^2}$$
where $$i_1, i_2$$ depends on the particle size.
As I increase the number concentration, my signal increases, indicating a dependence on total particle surface area in the sample.
I have plotted my sensor output vs number, surface and mass concentration for different particle sizes.
Should I not be able to make my Sensor Output vs Number Concentration for the different sized particles collapse if I multiply the number concentration by the area of the individual particles? Or is the area dependence in Mie scattering more complicated than this?
-
First of all, the amount of scattered light should be proportional (linearly) to the concentration of aerosol particles, regardless of their size. The dependence may be nonlinear if you put too much particles (the gas becomes opaques). It may also be the property of your light detector - it may be better to measure current instead of voltage.
For large particles particles, the scattering intensity does indeed scale linearly with the surface area. However, if particle size is of the same order of magnitude as the wavelength, the dependence is more complicated, see the Wikipedia article on Mie scattering.
-
For a population of identical aerosol particles, the scattering intensity should be approximately proportional to the number concentration of particles. Under two approximations, this is exact. @giacyan's answer points to one approximation: the number concentration of the particles has to be low enough that you can neglect multiple scattering events. If each photon is hitting more than one particle before you detect it, then the scattering will cease to be proportional to the concentration (I believe in that case the scattering increases more slowly than proportional to the concentration). The other approximation is that the particles don't interact with each other. If there are $A_2$ effects, then the scattering can increase either faster or more slowly than linearly with concentration.
If you have a mixed population of different sizes of particle, then the above holds as long as you keep the relative mixture the same. Particles that scatter more will bring you into the multiple scattering regime at lower concentrations. Particles that interact with each other more will bring you into the $A_2$ regime at lower concentrations.
The dependence on total surface area is more complicated. The formula you give is the scattering intensity for a single particle. $R$ is the radius, so $R^2$ is proportional to the surface area. But as you note, the $i_1, i_2$ functions are also functions of the radius (and therefore surface area). So you have to account for those functions when calculating the scattering. The total scattering is the sum of the scattering from each individual particle. For the same total surface area, the scattering can change if you change the distribution of particle sizes.
- | 2016-06-24 23:57:23 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 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": 0.7626075744628906, "perplexity": 384.29959837812197}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-26/segments/1466783391634.7/warc/CC-MAIN-20160624154951-00127-ip-10-164-35-72.ec2.internal.warc.gz"} |
https://tex.stackexchange.com/questions/392757/creating-a-specific-kind-of-tree-diagram?noredirect=1 | # Creating a specific kind of tree diagram
I'm trying to create a tree diagram for logic. I've used syntax trees before to do normal truth trees for logic. The trees I'm trying to create, however, don't look like syntax trees. They look like this:
The trees progress downward, and the branches branch out at right angles. The formulas go on the left and right of the various branches rather than at the bottom of nodes.
I have to make a lot of these, so I'd like to avoid anything too complicated, like using TikZ.
• You could use forest or tikz-tree. For a forest solution check this question: tex.stackexchange.com/questions/289642/… Or use prooftree: tex.stackexchange.com/questions/289268/… Sep 22, 2017 at 19:03
• I've drawn one of these in an answer before. Not in either of the threads @jaytar linked, though. I don't see how the second one is supposed to help at all. Anyway, it is prooftrees and not prooftree. If you really want to avoid TikZ, all of these options are out anyway. In that case, the only tree-drawing packages I know of are pstricks or qtree. I wouldn't try to use qtree for this. I don't know much about pstricks, but I'm sure you can use it if you wish. Like TikZ, it is powerful and flexible.
– cfr
Sep 22, 2017 at 22:40
• There's a better example somewhere, I think. Logic is really not well supported by LaTeX. It is just supported worse by everything else I've seen.
– cfr
Sep 22, 2017 at 23:10
Note that I think I ought not answer do-it-for-me questions such as this one. When I do so, I do so for me. I provide code for the heck of it. I generally do not explain it as I have no idea what to explain and, besides, I spent my efforts setting the puzzle up, in addition to solving it. I am typically less than sympathetic to requests for changes, explanations, tweaks and adjustments. These are left as exercises for the under-exercised reader. If my code happens to be useful, so be it; if not, tough. Good answers are responses to good questions. Do-it-for-mes cannot expect the same privileges.
# Caveat emptor.
Yes, of course it uses TikZ. It is a tree. Every tree needs a Forest.
\documentclass[border=10pt]{standalone}
\usepackage{amssymb}
\usepackage[edges]{forest}
\newcommand*{\lif}{\ensuremath{\mathbin{\rightarrow}}}
\begin{document}
\forestset{
declare boolean={T}{true},
F/.style={not T},
lr tableau/.style={
before typesetting nodes={
for tree={
math content,
fork sep'=7.5pt,
if T={
parent anchor=east,
child anchor=east,
anchor=mid east,
}{
parent anchor=west,
child anchor=west,
anchor=mid west,
},
},
},
forked edges,
before computing xy={
where level=0{if T={parent anchor=north east}{parent anchor=north west}}{
if={
>O_< {!u.n children}{2}%
}{l'=\baselineskip}{},
},
where n children=0{if T={child anchor=south east}{child anchor=south west}}{},
}
},
close/.style={
if n=1{label={[label distance=0pt, anchor=north]-135:\textsf{x}}}{label={[label distance=0pt, anchor=north]-45:\textsf{x}}},
},
}
\begin{forest}
lr tableau,
[\lnot \phi, label=left:\checkmark
[\alpha \lif \beta, label=left:\checkmark
[\beta \lif \phi, label=left:\checkmark
[\lnot\alpha, F, label=right:\checkmark
[\alpha
[\phi, F
[\alpha, F, close ]
[\beta
[\beta, F, close ]
[\phi, close ]
]
]
]
]
]
]
]
\end{forest}
\end{document} | 2022-08-20 02:16:09 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5210204124450684, "perplexity": 2744.337876622372}, "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-2022-33/segments/1659882573876.92/warc/CC-MAIN-20220820012448-20220820042448-00412.warc.gz"} |
https://www.physicsforums.com/threads/a-rod-falling-on-a-frictionless-surface.853726/ | # A rod falling on a frictionless surface
Tags:
1. Jan 23, 2016
### ClassicalMechanist
1. The problem statement, all variables and given/known data
Consider a massless rod of length $L$ with a small mass $m1$ attached on one end, and $m2$ attached on the other end. The rod is initially in the vertical position at rest on a frictionless surface, with $m1$ on bottom and $m2$ on top. A small impulse is applied to the top of the rod in the horizontal direction, and it begins to fall.
Find the speeds of $m1$ and $m2$ when $m2$ is about to hit the ground.
2. Relevant equations
I.Conservation of energy: $m_2gL=1/2m_1v_1^2+1/2m_2v_2^2$
II.Conservation of momentum in the horizontal direction: $m_1v_1=m_2v_{2_x}$
III.Center of mass is located at $d_{cm}=(m_1*0+m_2*L)/(m_1+m_2)$ along the rod (with $m1$ at the origin).
3. The attempt at a solution
Since the only force acting on the system is gravity and the normal force on $m1$, which are both in the vertical direction, linear momentum is conserved in the horizontal direction, and therefore the center of mass of the rod does not change its position in the horizontal direction.
The net force on the system is $(m_1+m_2)g-N$ downwards, but this isn't very helpful since the normal force $N$ changes with time.
I had an idea to consider angular momentum about the mass $m1$ or maybe about the center of mass of the rod, but I'm not really sure how to proceed.
The problem is solved if we can find the horizontal component $v_{2_x}$ in terms of $v_2$, because then we can use equations I and II above to solve for $v1$ and $v2$. Equivalently, the problem is solved if we find $v_{2_y}$. But $v_{2_y}$ is related to the vertical speed of the center of mass of the system, $v_{cm}$ by a constant factor (using similar triangles). Therefore it suffices to find $v_{cm}$ just before $m_2$ hits the ground.
I am tempted to say, by conservation of energy, $(m_1+m_2)gd_{cm}=1/2(m_1+m_2)v_{cm}^2$, or $\sqrt{2gd_{cm}}=v_{cm}$. For some reason I don't think I can apply conservation of energy to the center of mass, but let's go on anyway.
By similar triangles, the height $h_cm$ of the center of mass above the ground is related to the height $h_{m_2}$ of $m_2$ above the ground, by: $h_{m_2}=h_{cm}*L/d_{cm}$. Thus $v_{2_y }=v_{cm}*L/d_{cm}$. I continued like this and I got an immediate contradiction. So I know I did something wrong, not with the algebra, but with the assumption that you can apply conservation of energy to the center of mass.
So now I'm stuck.
2. Jan 23, 2016
### haruspex
An awkward aspect of such a question is whether the lower mass might lose contact with the ground before the upper mass lands. If the upper mass were given a sufficient horizontal impulse at the start, this could certainly happen.
Putting that aside for now, think about energy and linear momentum.
Angular momentum will not be conserved, no matter what axis you choose. The weight of the upper mass and the normal reaction create an unknown torque. You cannot eliminate the normal reaction by taking moments about the lower mass. You have to use an axis which is either stationary or passes through the system mass centre, nothing else gives the right answer. (Not quite true, but near enough.)
Not sure whether working with the common mass centre helps. It can be done either way. I would set a variable, x, as the horizontal displacement of the lower mass and theta as the angle to the vertical. You can then represent the horizontal and vertical displacements of the upper mass in terms of those, and find the velocities by differentiating. Finally, plug those into the energy and horizontal momentum equations.
3. Jan 23, 2016
### ClassicalMechanist
I don't think that method will work, because it only gives you the rate of change of the horizontal and vertical displacements of each mass in terms of the angle to the vertical, not in terms time (i.e you can only find dx/dtheta, not dx/dt).
The problem is relatively simple, so I'm thinking there should be a simple observation which solves it without too much algebra.
4. Jan 23, 2016
### haruspex
Why do you need to know the time? You can find rates of change as a function of position without knowing them as a function of time.
(I obtained the solution before posting.)
5. Jan 23, 2016
### ClassicalMechanist
Well how can you plug them into the energy and momentum equations, which involve velocities (rate of change as a function of time)? Could you show me the first steps of your solution, and I'll try to complete it from there.
6. Jan 23, 2016
### haruspex
First, represent the position of each mass in terms of the two variables I mentioned, x and theta.
Then differentiate as necessary to obtain velocities. Plug those into the two conservation equations.
You should be able to find the angular velocity as a function of the angle.
7. Jan 24, 2016
### ClassicalMechanist
Yes taking the center of mass of the system to have x-coordinate zero, I found the position vector of m1 as <dsin(theta),0> and for m2, <(d-L)sin(theta), Lcos(theta)>, where d is the distance along the rod measured from m1 where the center of mass is located. And, yes, I can differentiate these with respect to theta, but my point is that the derivative does not represent the velocity vector. The velocities in the momentum and conservation equations are of the form distance/time. The "velocities" we have here are of the form distance/angle. I don't understand how you can substitute things for each-other if they have different units...
8. Jan 24, 2016
### haruspex
That's because you are differentiating with respect to angle when you should be differentiating with respect to time. Use the chain rule: $\frac d{dt}f(\theta)=\frac {df}{d\theta}\frac {d\theta}{dt}$
9. Jan 24, 2016
### ClassicalMechanist
Ok that was the second thing I was going to say. I did use the chain rule, but I still think it doesn't work.
You get the velocity vector for m1 is $<dsin(theta)*dtheta/dt,0>$and the velocity vector for m2 is $<(d-L)sin(theta)*(dtheta/dt), Lcos(theta)*(dtheta/dt)>$. Notice that the conservation of linear momentum equation is useless, because if you plug in $v1=dsin(theta)*dtheta/dt$ and $v_2_x=(d-L)sin(theta)*(dtheta/dt)$, you get a formula in terms of the masses, the distance d, and L, which is the same as the center of mass formula. So we only have the energy conservation formula left, but that doesn't give us enough information (and you can't get rid of dtheta/dt)...
Can you please show me the steps I'm missing?
I'm pretty sure there is a nicer way to do the problem. Did you get the final result to be sqrt{2gl}?
10. Jan 24, 2016
### haruspex
If working with mass centre, yes, you do not need to look at linear momentum. You should end up with an equation relating $\dot{\theta}$ to $\theta$. Then you plug in $\theta=\pi/2$ and get the angular velocity when the upper mass hits the ground. I can't comment further without seeing your working.
I ended up with $m_2L\dot {\theta}^2=2g(m_1+m_2)$.
11. Jan 24, 2016
### ClassicalMechanist
I am trying to proceed using your hints, but I must say I am quite confused by what you are saying.
Ok so first we are looking at different theta's. My theta is the angle of the rod to the horizontal, and if I understand correctly, your theta is the angle of the rod to the vertical?
If we are using your theta, then r2=<(L-d)sin(theta), Lcos(theta)>, v2=<(L-d)cos(theta)*theta', -Lsin(theta)*theta'>. So when theta=pi/2, v2=<0, -L*theta'>. So, if I understand correctly, m2 has zero velocity in the horizontal direction when it is about to hit the ground. And according to you, the answer should be
|v2|=L*theta'=sqrt(2gL*(m1+m2)/m2)
This doesn't seem right.
12. Jan 24, 2016
### haruspex
You're right, I dropped a term. I now get $L\dot \theta^2(m_1+m_2\sin^2(\theta))=2g(1-\cos(\theta))(m_1+m_2)$. On the ground, that reduces to $L\dot\theta^2=2g$.
Yes, by conservation of momentum, neither mass will have any horizontal velocity when the rod is horizontal. So I could have avoided all the algebra and just observed that the top mass will hit the ground at the same speed as if in free fall.
We are left with the issue of proving the system does not become airborne before that.
13. Jan 24, 2016
### ClassicalMechanist
Actually, the horizontal impulse given at the top is assumed to be very small, so that it's initial angular velocity is zero. So you don't have to worry about the system becoming airborne before m2 hits the ground.
Now, I still don't think your answer is right, because according to you, v2=sqrt(2gL), and this does not depend on the masses m1 or m2 at all. But clearly they matter...
I would really appreciate if you could explain to me exactly how you are getting that equation for theta'. I got v1 and v2 in terms of theta and theta'. Did you simply plug them into the conservation of energy equation?
Also, there is something weird going on here. As I said in the post above yours, m2 has zero horizontal velocity when m2 is about to hit the ground. Therefore m1 has zero horizontal velocity, and zero total velocity. So v1=0. But then the conservation of energy equation directly gives v2=sqrt(2gL).
14. Jan 24, 2016
### ClassicalMechanist
Are you sure about this? I got the same result myself but I thought I must have done something wrong because it is too simple. The masses have to matter, surely,...
15. Jan 24, 2016
### haruspex
One might expect that the mass ratio matters, but it does not have to be so.
You agree that there are no horizontal velocities when the rod is horizontal, so if the lower mass is still one the ground all the energy has gone into the vertical velocity of the upper mass. It follows immediately that $v_2=\sqrt{2gL}$, matching the answer I got by finding the velocity as a function of angle.
Yes, the horizontal impulse at the top is small, but that that does not make it clear that the lower mass stays grounded. I note that the problem implies the upper mass is substantially the greater. Why does it do that?
16. Jan 24, 2016
### ClassicalMechanist
Upon further reflection, this makes sense. The motion of m2 can be thought of as rotation about the center of mass plus translation of the center of mass. When the rod is horizontal, the velocity vector due to rotational motion is perpendicular to the ground. But the translation of the center of mass is always vertically downwards, so indeed when m2 is about to hit the ground, it's velocity vector should point directly downwards. As you said, it immediately follows that v1=0 from conservation of momentum, and the result is immediate.
As far as the mass m1 being smaller, that is a mistake. I did not mean to write "a small mass".
17. Jan 24, 2016
### haruspex
Good.
I checked for becoming airborne on the basis that if and when that happens there will be no angular acceleration. (Even though the equations we're using are as though normal force could go negative, it should still be the case that angular acceleration would pass through zero.)
Applying that to my general equation I found the mass ratio would have to equal $-(1-\cos(\theta))^2$. Clearly that never happens, but comes closest to being true when the lower mass is tiny and the rod is near horizontal. So even a small initial nudge leaves open the possibility of becoming airborne if the lower mass is very much the smaller.
Of course, if it does become airborne the problem gets very much harder!
18. Jan 25, 2016
### Suraj M
1 small question, you aren't taking the centre of mass to be on the axis of rotation?
19. Jan 25, 2016
### haruspex
No, the mass centre can't be on the axis of rotation, except right at the start. As the rod falls, the axis of rotation will describe an arc of a circle. At first it will move out horizontally, and finish moving vertically, ending up where the lower mass finishes. The centre of the circle of which it is a quadrant will be at the point on the ground where the rod initially stood.
20. Jan 25, 2016
### Suraj M
Oh that makes everything pretty simple. | 2017-08-19 06:37:16 | {"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": 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": 0.6709386110305786, "perplexity": 255.60539158426184}, "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/1502886105304.35/warc/CC-MAIN-20170819051034-20170819071034-00401.warc.gz"} |
http://www.ck12.org/algebra/Comparison-of-Problem-Solving-Models/lesson/Comparison-of-Problem-Solving-Models/r14/ | <img src="https://d5nxst8fruw4z.cloudfront.net/atrk.gif?account=iA1Pi1a8Dy00ym" style="display:none" height="1" width="1" alt="" />
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# Comparison of Problem-Solving Models
## Compare methods of organizing and solving story problems
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Comparison of Problem-Solving Models
What if you were given a real-world problem with two unknowns like "You have only dimes and nickels in your pocket that total $1.25. You have a total of 14 coins in your pocket. How many nickels and dimes do you have?" How could you devise a problem-solving plan to solve it? After completing this Concept, you'll be able to make a table or look for patterns to help you solve problems like this one. ### Watch This ### Guidance In this section, we will use the problem solving methods learned in the last Concept. We will also compare the methods of “Making a Table” and “Looking for a Pattern” by using each method in turn to solve a problem. #### Example A A coffee maker is on sale at 50% off the regular ticket price. On the “Sunday Super Sale” the same coffee maker is on sale at an additional 40% off. If the final price is$21, what was the original price of the coffee maker?
Solution
Step 1: Understand
We know: A coffee maker is discounted 50% and then 40%. The final price is $21. We want: The original price of the coffee maker. Step 2: Strategy Let’s look at the given information and try to find the relationship between the information we know and the information we are trying to find. 50% off the original price means that the sale price is half of the original or original price. So, the first sale price original price A savings of 40% off the new price means you pay 60% of the new price, or new price. is the price after the second discount. We know that after two discounts, the final price is$21.
So .
Step 3: Solve
Since , we can find the original price by dividing $21 by 0.3. . The original price of the coffee maker was$70.
Step 4: Check
We found that the original price of the coffee maker is $70. To check that this is correct, let’s apply the discounts. 50% of savings. So the price after the first discount is or . Then 40% of that is . So after the second discount, the price is . The answer checks out. #### Example B Andrew cashes a$180 check and wants the money in $10 and$20 bills. The bank teller gives him 12 bills. How many of each kind of bill does he receive?
Solution
Method 1: Making a Table
Understand
Andrew gives the bank teller a $180 check. The bank teller gives Andrew 12 bills. These bills are a mix of$10 bills and $20 bills. We want to know how many of each kind of bill Andrew receives. Strategy Let’s start by making a table of the different ways Andrew can have twelve bills in tens and twenties. Andrew could have twelve$10 bills and zero $20 bills, or eleven$10 bills and one $20 bill, and so on. We can calculate the total amount of money for each case. Apply strategy/solve$10 bills $20 bills Total amount 12 0 11 1 10 2 9 3 8 4 7 5 6 6 5 7 4 8 3 9 2 10 1 11 0 12 In the table we listed all the possible ways you can get twelve$10 bills and $20 bills and the total amount of money for each possibility. The correct amount is given when Andrew has six$10 bills and six $20 bills. Answer: Andrew gets six$10 bills and six $20 bills. Check Six$10 bills and six $20 bills The answer checks out. Let’s solve the same problem using the method “Look for a Pattern.” Method 2: Looking for a Pattern Understand Andrew gives the bank teller a$180 check.
The bank teller gives Andrew 12 bills. These bills are a mix of $10 bills and$20 bills.
We want to know how many of each kind of bill Andrew receives.
Strategy
Let’s start by making a table just as we did above. However, this time we will look for patterns in the table that can be used to find the solution.
Apply strategy/solve
Let’s fill in the rows of the table until we see a pattern.
$10 bills$20 bills Total amount
12 0
11 1
10 2
### Practice
1. Britt has $2.25 in nickels and dimes. If she has 40 coins in total, how many of each coin does she have? 2. Jeremy divides a 160-square-foot garden into plots that are either 10 or 12 square feet each. If there are 14 plots in all, how many plots are there of each size? 3. A pattern of squares is put together as shown. How many squares are in the diagram? 4. In Harrisville, local housing laws specify how many people can live in a house or apartment: the maximum number of people allowed is twice the number of bedrooms, plus one. If Jan, Pat, and their four children want to rent a house, how many bedrooms must it have? 5. A restaurant hosts children’s birthday parties for a cost of$120 for the first six children (including the birthday child) and $30 for each additional child. If Jaden’s parents have a budget of$200 to spend on his birthday party, how many guests can Jaden invite?
6. A movie theater with 200 seats charges $8 general admission and$5 for students. If the 5:00 showing is sold out and the theater took in $1468 for that showing, how many of the seats are occupied by students? 7. Oswald is trying to cut down on drinking coffee. His goal is to cut down to 6 cups per week. If he starts with 24 cups the first week, then cuts down to 21 cups the second week and 18 cups the third week, how many weeks will it take him to reach his goal? 8. Taylor checked out a book from the library and it is now 5 days late. The late fee is 10 cents per day. How much is the fine? 9. Mikhail is filling a sack with oranges. 1. If each orange weighs 5 ounces and the sack will hold 2 pounds, how many oranges will the sack hold before it bursts? 2. Mikhail plans to use these oranges to make breakfast smoothies. If each smoothie requires cup of orange juice, and each orange will yield half a cup, how many smoothies can he make? 10. Jessamyn takes out a$150 loan from an agency that charges 12% of the original loan amount in interest each week. If she takes five weeks to pay off the loan, what is the total amount (loan plus interest) she will need to pay back?
11. How many hours will a car traveling at 75 miles per hour take to catch up to a car traveling at 55 miles per hour if the slower car starts two hours before the faster car?
12. Grace starts biking at 12 miles per hour. One hour later, Dan starts biking at 15 miles per hour, following the same route. How long will it take him to catch up with Grace?
13. A new theme park opens in Milford. On opening day, the park has 120 visitors; on each of the next three days, the park has 10 more visitors than the day before; and on each of the three days after that, the park has 20 more visitors than the day before.
1. How many visitors does the park have on the seventh day?
2. How many total visitors does the park have all week?
14. Lemuel wants to enclose a rectangular plot of land with a fence. He has 24 feet of fencing. What is the largest possible area that he could enclose with the fence?
15. Quizzes in Keiko’s history class are worth 20 points each. Keiko scored 15 and 18 points on her last two quizzes. What score does she need on her third quiz to get an average score of 17 on all three?
16. Mark is three years older than Janet, and the sum of their ages is 15. How old are Mark and Janet?
17. In a one-on-one basketball game, Jane scored times as many points as Russell. If the two of them together scored 10 points, how many points did Jane score?
18. Scientists are tracking two pods of whales during their migratory season. On the first day of June, one pod is 120 miles north of a certain group of islands, and every day thereafter it gets 15 miles closer to the islands. The second pod starts out 160 miles east of the islands on June 3, and heads toward the islands at a rate of 20 miles a day.
1. Which pod will arrive at the islands first, and on what day?
2. How long after that will it take the other pod to reach the islands?
3. Suppose the pod that reaches the islands first immediately heads south from the islands at a rate of 15 miles a day, and the pod that gets there second also heads south from there at a rate of 25 miles a day. On what day will the second pod catch up with the first?
4. How far will both pods be from the islands on that day?
### Texas Instruments Resources
In the CK-12 Texas Instruments Algebra I FlexBook, there are graphing calculator activities designed to supplement the objectives for some of the lessons in this chapter. See http://www.ck12.org/flexr/chapter/9611. | 2016-02-07 10:38:54 | {"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": 0.2471645027399063, "perplexity": 1584.9070369342005}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-07/segments/1454701148834.81/warc/CC-MAIN-20160205193908-00226-ip-10-236-182-209.ec2.internal.warc.gz"} |
https://www.statistics-lab.com/%E6%95%B0%E5%AD%A6%E4%BB%A3%E5%86%99%E7%BB%84%E5%90%88%E4%BC%98%E5%8C%96%E4%BB%A3%E5%86%99combinatorial-optimization%E4%BB%A3%E8%80%83some-families-of-split-graphs/ | ### 数学代写|组合优化代写Combinatorial optimization代考|Some Families of Split Graphs
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• Foundations of Data Science 数据科学基础
## 数学代写|组合优化代写Combinatorial optimization代考|Some Families of Split Graphs
A graph $G=(C \cup S, E)$ is a split graph if its node set can be partitioned into a clique $C$ and a stable set $S$. Split graphs are closed under taking complements and form the complementary core of chordal graphs since $G$ is a split graph if and only if $G$ and $\bar{G}$ are chordal or if and only if $G$ is $\left(C_{4}, \bar{C}{4}, C{5}\right)$-free [11].
Our aim is to study LTD-sets in some families of split graphs having a regular structure from a polyhedral point of view. Complete Split Graphs. A complete split graph is a split graph where all edges between $C$ and $S$ are present. Complete split graphs can be seen as special case of complete multi-partite graphs studied in Sect. 3. In fact, a complete split graph is a clique if $|S|=1$, a star if $|C|=1$, and a crown if $|C|=2$, see Fig. 3(a), (b). Otherwise, the graph can be seen as a complete multi-partite graph where all parts but one have size 1 , i.e. as $K_{n_{1}, n_{2}, \ldots, n_{p}}$ with $n_{1}=\cdots=n_{p-1}=1$ and $n_{p} \geq 2$ such that $U_{1} \cup \cdots \cup U_{p-1}$ induce the clique $C$ and $U_{p}$ the stable set $S$. Hence, we directly conclude from Lemma 3 and Corollary 5 :
Corollary 6. Let $G=(C \cup S, E)$ be a complete split graph.
(a) If $|S|=1$, then $G$ is a clique,
$$C_{X}(G)=M\left(\mathcal{R}{|C|+1}^{2}\right)$$ and $\gamma{X}(G)=|C|$ for $X \in{O L D, L T D}$.
(b) If $|C|=1$, then $G$ is a star,
$$C_{L T D}(G)=\left(\begin{array}{c|lll} 1 & 0 & \ldots & 0 \ \hline 0 & & \ \vdots & M\left(\mathcal{R}{|S|}^{2}\right) \ 0 & \end{array}\right)$$ and $\gamma{L T D}(G)=|S|$.
(c) Otherwise, we have
$$C_{L T D}(G)=\left(\begin{array}{cc} M\left(\mathcal{R}{|C|}^{2}\right) & 0 \ 0 & M\left(\mathcal{R}{|S|}^{2}\right) \end{array}\right)$$
and $\gamma_{L T D}(G)=|S|+|C|-2$.
Headless Spiders. A headless spider is a split graph with $C=\left{c_{1}, \ldots, c_{k}\right}$ and $S=\left{s_{1}, \ldots, s_{k}\right}$; it is thin (resp. thick) if $s_{i}$ is adjacent to $c_{j}$ if and only if $i=j$ (resp. $i \neq j$ ), see Fig. 3(c), (d) for illustration. Clearly, the complement of a thin spider is a thick spider, and vice-versa. It is easy to see that for $k=2$, the path $P_{4}$ equals the thin and thick headless spider. Moreover, it is easy to check that headless spiders are twin-free.
A thick headless spider with $k=3$ equals the 3 -sun $S_{3}$ and it is easy to see that $\gamma_{O L D}\left(S_{3}\right)=4$ and $\gamma_{L T D}\left(S_{3}\right)=3$ holds. To describe the clutters for $k \geq 4$, we use the following notations. Let $J_{n}$ denote the $n \times n$ matrix having 1-entries only and $I_{n}$ the $n \times n$ identity matrix. Furthermore, let $J_{n-1, n}(i)$ denote a matrix s.t. its $i$-th column has 0 -entries only and removing the $i$-th column results in $J_{n-1}$, and $I_{n-1, n}(j)$ denote a matrix s.t. its $j$-th column has 1 -entries only and removing the $j$-th column results in $I_{n-1}$.
## 数学代写|组合优化代写Combinatorial optimization代考|Concluding Remarks
In this paper, we proposed to study the $O L D$ – and $L T D$-problem from a polyhedral point of view, motivated by promising polyhedral results for the $I D$-problem [2-5]. That way, we were able to provide closed formulas for the LTD-numbers of all kinds of complete $p$-partite graphs (Sect. 3), and for the studied families of split graphs as well as the $O L D$-numbers of thin and thick headless spiders (Sect. 4).
In particular, if we have the same clutter matrix for two different $X$-problems, then we can conclude that every solution of one problem is also a solution for the other problem, and vice versa, such that the two $X$-polyhedra coincide and the two $X$-numbers are equal. This turned out to be the case for
• complete bipartite graphs as $C_{I D}\left(K_{m, n}\right)=C_{L T D}\left(K_{m, n}\right)$ holds by Lemma 2 and results from [2],
• thin headless spiders $G$ as $C_{O L D}(G)=C_{L T D}(G)$ holds by Lemma $5 .$
Furthermore, we were able to provide the complete facet descriptions of
• the LTD-polyhedra for all complete $p$-partite graphs (including complete split graphs) and for thin headless spiders (see Sect. 3 and Lemma 5),
• the $O L D$-polyhedra of cliques, thin and thick headless spiders (see Corollary 5 and Sect. 4).
The complete descriptions of some $X$-polyhedra also provide us with information about the relation between $Q^{}\left(C_{X}(G)\right)$ and its linear relaxation $Q\left(C_{X}(G)\right)$. A matrix $M$ is ideal if $Q^{}(M)=Q(M)$. For any nonideal matrix, we can evaluate how far $M$ is from being ideal by considering the inequalties that have to be added to $Q(M)$ in order to obtain $Q^{}(M)$. With this purpose, in [1], a matrix $M$ is called rank-ideal if only $0 / 1$-valued constraints have to be added to $Q(M)$ to obtain $Q^{}(M)$. From the complete descriptions obtained in Sect. 3 and Sect. 4 , we conclude:
Corollary 9. The LTD-clutters and OLD-clutters of thin headless spiders are ideal for all $k \geq 3$.
Corollary 10. The LTD-clutters of all complete p-partite graphs and the $O L D$ clutters of cliques and thick headless spiders are rank-ideal.
Finally, the LTD-clutters of thick headless spiders have a more complex structure such that also a facet description of the LTD-polyhedra is more involved. However, using polyhedral arguments, is was possible to establish that $k-1$ is a lower bound for the cardinality of any LTD-set. Exhibiting an LTD-set of size $k-1$ thus allowed us to deduce the exact value of the $L T D$-number of thick headless spiders (Theorem 3 ).
This demonstrates how the polyhedral approach can be applied to find $X$ sets of minimum size for special graphs $G$, by determining and analyzing the $X$-clutters $C_{X}(G)$, even in cases where no complete description of $P_{X}(G)$ is known yet.
As future lines of research, we plan to work on a complete description of the LTD-polyhedra of thick headless spiders and to apply similar and more advanced techniques for other graphs in order to obtain either $X$-sets of minimum size or strong lower bounds stemming from linear relaxations of the $X$-polyhedra, enhanced by suitable cutting planes.
## 数学代写|组合优化代写Combinatorial optimization代考|Mourad Ba¨ıou1 and Francisco Barahona2
This paper follows the study of the classical linear formulation for the $p$-median problem started in [1-3]. To avoid repetitions, we refer to [1] for a more detailed introduction on the $p$-median problem.
Let $G=(V, A)$ a directed graph not necessarily connected, where each arc $(u, v) \in A$ has an associated cost $c(u, v)$. Here we make a difference between oriented and directed graphs. In oriented graphs at most one of the the arcs $(u, v)$ or $(v, u)$ exist, while in directed graphs we may have both arcs $(u, v)$ and $(v, u)$. The $p$-median problem $(p \mathrm{MP})$ consists of selecting $p$ nodes, usully called centers, and then assign each nonselected node along an arc to a selected node. The goal is to select $p$ nodes that minimize the sum of the costs yielded by the assignment of the nonselected nodes. If the number of centers is not fixed and in stead we have costs associated with nodes, then we get the well known facility location problem.
If we associate the variables $y$ to the nodes, and the variables $x$ to the arcs, the following is the classical linear relaxation of the $p \mathrm{MP}$. If we remove equality (1), then we get a linear relaxation of the facility location problem.
\begin{aligned} &\sum_{v \in V} y(v)=p, \ &y(u)+\sum_{v:(u, v) \in A} x(u, v)=1 \quad \forall u \in V, \ &x(u, v) \leq y(v) \quad \forall(u, v) \in A, \ &y(v) \geq 0 \quad \forall v \in V, \ &x(u, v) \geq 0 \quad \forall(u, v) \in A . \end{aligned}
Call $p \mathrm{MP}(G)$ the $p$-median polytope, that is the convex hull of integer solutions satisfying (1)-(5).
Now we will introduced a class of valid inequalities based on odd directed cycles. For this we need some additional definitions. A simple cycle $C$ is an ordered sequence $v_{0}, a_{0}, v_{1}, a_{1}, \ldots, a_{t-1}, v_{t}$, where
$-v_{i}, 0 \leq i \leq t-1$, are distinct nodes,
• either $v_{i}$ is the tail of $a_{i}$ and $v_{i+1}$ is the head of $a_{i}$, or $v_{i}$ is the head of $a_{i}$ and $v_{i+1}$ is the tail of $a_{i}$, for $0 \leq i \leq t-1$, and
$-v_{0}=v_{t}$.
Let $V(C)$ and $A(C)$ denote the nodes and the arcs of a simple cycle $C$, respectively. By setting $a_{t}=a_{0}$, we partition the vertices of $C$ into three sets: $\hat{C}, \dot{C}$ and $\vec{C}$. Each node $v$ is incident to two arcs $a^{\prime}$ and $a^{\prime \prime}$ of $C$. If $v$ is the head (resp. tail) of both arcs $a^{\prime}$ and $a^{\prime \prime}$ then $v$ is in $\hat{C}$ (resp. $\dot{C}$ ) and if $v$ is the head of one of them and a tail of the other, then $v$ is in $\tilde{C}$. Notice that $|\hat{C}|=|\dot{C}| . \mathrm{A}$ cycle will be called $g$-odd if $|\tilde{C}|+|\hat{C}|$ is odd, that is the number of nodes that are heads of some arcs in $C$ is odd. Otherwise it will be called $g$-even. A cycle $C$ with $V(C)=\tilde{C}$ is a directed cycle, otherwise it is called a non-directed cycle. Notice that the notion of g-odd (g-even) cycles generalizes the notion of odd (even) directed cycles, that is why we use the letter ” $\mathrm{g}$ “.
## 数学代写|组合优化代写Combinatorial optimization代考|Some Families of Split Graphs
(a) 如果|小号|=1， 然后G是一个集团，
CX(G)=米(R|C|+12)和CX(G)=|C|为了X∈这大号D,大号吨D.
(b) 如果|C|=1， 然后G是一颗星星，
C_{L T D}(G)=\left(\begin{array}{c|lll} 1 & 0 & \ldots & 0 \ \hline 0 & & \ \vdots & M\left(\mathcal{R}{| S|}^{2}\right) \ 0 & \end{数组}\right)C_{L T D}(G)=\left(\begin{array}{c|lll} 1 & 0 & \ldots & 0 \ \hline 0 & & \ \vdots & M\left(\mathcal{R}{| S|}^{2}\right) \ 0 & \end{数组}\right)和C大号吨D(G)=|小号|.
(c) 否则，我们有
C大号吨D(G)=(米(R|C|2)0 0米(R|小号|2))
## 数学代写|组合优化代写Combinatorial optimization代考|Concluding Remarks
• 完全二部图为C一世D(ķ米,n)=C大号吨D(ķ米,n)由引理 2 成立，结果来自 [2]，
• 瘦无头蜘蛛G作为C这大号D(G)=C大号吨D(G)由引理持有5.
此外，我们能够提供完整的方面描述
• 所有完整的 LTD-多面体p- 分图（包括完全分裂图）和瘦无头蜘蛛（见第 3 节和引理 5），
• 这这大号D- 团多面体，薄而厚的无头蜘蛛（见推论 5 和第 4 节）。
## 数学代写|组合优化代写Combinatorial optimization代考|Mourad Ba¨ıou1 and Francisco Barahona2
−在一世,0≤一世≤吨−1, 是不同的节点,
• 任何一个在一世是尾巴一种一世和在一世+1是头一种一世， 或者在一世是头一种一世和在一世+1是尾巴一种一世， 为了0≤一世≤吨−1， 和
−在0=在吨.
让在(C)和一种(C)表示简单循环的节点和弧C， 分别。通过设置一种吨=一种0，我们划分顶点C分为三组：C^,C˙和C→. 每个节点在与两条弧线有关一种′和一种′′的C. 如果在是两个弧的头部（分别是尾部）一种′和一种′′然后在在C^（分别。C˙） 而如果在是其中一个的头和另一个的尾，那么在在C~. 请注意|C^|=|C˙|.一种将调用循环G-如果是奇数|C~|+|C^|是奇数，即是某些弧的头的节点数C很奇怪。否则会被调用G-甚至。一个循环C和在(C)=C~是有向环，否则称为无向环。请注意，g-奇（g-偶）循环的概念概括了奇（偶）有向循环的概念，这就是我们使用字母“G “.
## 有限元方法代写
tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。
## MATLAB代写
MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。 | 2023-03-22 12:29:31 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 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": 0.9269383549690247, "perplexity": 620.9734612515886}, "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/1679296943809.76/warc/CC-MAIN-20230322114226-20230322144226-00669.warc.gz"} |
https://faculty.ucr.edu/~jflegal/206/15-bayes.html | ## Agenda
• Bayesian inference
• Priors
• Point estimates
• Bayesian hypothesis testing
• Bayes factors
## Bayesian Inference
• Everything we have done up to now is frequentist statistics, Bayesian statistics is very different
• Bayesians don’t do confidence intervals and hypothesis tests
• Bayesians don’t use sampling distributions of estimators
• Modern Bayesians aren’t even interested in point estimators
• So what do they do? Bayesians treat parameters as random variables
To a Bayesian probability is the only way to describe uncertainty. Things not known for certain – like values of parameters – must be described by a probability distribution
## Bayesian Inference
• Suppose you are uncertain about something, which is described by a probability distribution called your prior distribution
• Suppose you obtain some data relevant to that thing
• The data changes your uncertainty, which is then described by a new probability distribution called your posterior distribution
• Posterior distribution reflects the information both in the prior distribution and the data
• Most of Bayesian inference is about how to go from prior to posterior
## Bayesian Inference
• Bayesians go from prior to posterior is to use the laws of conditional probability, sometimes called in this context Bayes rule or Bayes theorem
• Suppose we have a PDF $$g$$ for the prior distribution of the parameter $$\theta$$, and suppose we obtain data $$x$$ whose conditional PDF given $$\theta$$ is $$f$$
• Then the joint distribution of data and parameters is conditional times marginal $f( x | \theta) g(\theta)$
• May look strange because most of your training on considers the frequentist paradigm
• Here both $$x$$ and $$\theta$$ are random variables
## Bayesian Inference
• The correct posterior distribution, according to the Bayesian paradigm, is the conditional distribution of $$\theta$$ given $$x$$, which is joint divided by marginal $h (\theta | x) = \frac{f( x | \theta) g(\theta)}{\int f( x | \theta) g(\theta) d \theta}$
• Often we do not need to do the integral if we recognize that $\theta \mapsto f( x | \theta) g(\theta)$ is, except for constants, the PDF of a brand name distribution, then that distribution must be the posterior
## Binomial Data, Beta Prior
Suppose the prior distribution for $$p$$ is Beta($$\alpha_1, \alpha_2$$) and the conditional distribution of $$x$$ given $$p$$ is Bin($$n$$, $$p$$). Then $f(x|p) = {n \choose p} p^x (1-p)^{n-x}$ and $g(p) = \frac{\Gamma(\alpha_1 + \alpha_2)}{\Gamma(\alpha_1)\Gamma(\alpha_2)} p^{\alpha_1 -1} (1-p)^{\alpha_2 - 1}.$ Then $f(x|p) g(p) = {n \choose p} \frac{\Gamma(\alpha_1 + \alpha_2)}{\Gamma(\alpha_1)\Gamma(\alpha_2)} p^{x + \alpha_1 -1} (1-p)^{n - x + \alpha_2 - 1}$ and this, considered as a function of $$p$$ for fixed $$x$$ is, except for constants, the PDF of a Beta($$x + \alpha_1, n - x + \alpha_2$$) distribution. So that is the posterior.
## Binomial Data, Beta Prior
Why? \begin{aligned} h (p | x) & = \frac{f( x | p) g(p)}{\int f( x | p) g(p) d p} \\ & \propto f( x | p) g(p) \\ & = {n \choose p} \frac{\Gamma(\alpha_1 + \alpha_2)}{\Gamma(\alpha_1)\Gamma(\alpha_2)} p^{x + \alpha_1 -1} (1-p)^{n - x + \alpha_2 - 1} \\ & \propto p^{x + \alpha_1 -1} (1-p)^{n - x + \alpha_2 - 1} \end{aligned} And there is only one PDF with support $$[0,1]$$ of that form, i.e. a Beta($$x + \alpha_1, n - x + \alpha_2$$) distribution. So that is the posterior.
## Bayesian Inference
• In Bayes rule, constants, meaning anything that doesn’t depend on the parameter, are irrelevant
• We can drop multiplicative constants that do not depend on the parameter from $$f( x | \theta)$$ obtaining the likelihood $$L(\theta)$$
• We can also drop multiplicative constants that do not depend on the parameter from $$g(\theta)$$ obtaining the unnormalized prior
• Multiplying them together gives the unnormalized posterior
$\text{likelihood } × \text{ unnormalized prior } = \text{ unnormalized posterior}$
## Bayesian Inference
In our example we could have multiplied likelihood $p^x (1-p)^{n-x}$ times unnormalized prior $p^{\alpha_1 -1} (1-p)^{\alpha_2 - 1}$ to get unnormalized posterior $p^{x + \alpha_1 -1} (1-p)^{n - x + \alpha_2 - 1}$ which, as before, can be recognized as an unnormalized beta PDF.
## Bayesian Inference
• It is convenient to have a name for the parameters of the prior and posterior. If we call them parameters, then we get confused because they play a different role from the parameters of the distribution of the data.
• The parameters of the distribution of the data, $$p$$ in our example, the Bayesian treats as random variables. They are the random variables whose distributions are the prior and posterior.
• The parameters of the prior, $$\alpha_1$$ and $$\alpha_2$$ in our example, the Bayesian treats as known constants. They determine the particular prior distribution used for a particular problem. To avoid confusion we call them hyperparameters.
## Bayesian Inference
• Parameters, meaning the parameters of the distribution of the data and the variables of the prior and posterior, are unknown constants. The Bayesian treats them as random variables because probability theory is the correct description of uncertainty.
• Hyperparameters, meaning the parameters of the prior and posterior, are known constants. The Bayesian treats them as non- random variables because there is no uncertainty about their values.
• In our example, the hyperparameters of the prior are $$\alpha_1$$ and $$\alpha_2$$, and the hyperparameters of the posterior are $$x + \alpha_1$$ and $$n - x + \alpha_2$$.
## Example: Normal
Suppose $$X_1 , \dots, X_n$$ are i.i.d. $$N(\theta , \sigma^2)$$ where $$\sigma^2$$ is known. Suppose further we have a prior $$\theta \sim N(\mu, \tau^2)$$. Then the posterior can be obtained as follows, \begin{aligned} f (\theta | x) & \propto f(\theta) \prod_{i=1}^n f(x_i | \theta) \\ & \propto \exp \left \{ -\frac{1}{2} \left( \frac{(\theta-\mu)^2}{\tau^2} + \frac{\sum_{i=1}^{n} (x_i - \theta)^2}{\sigma^2} \right) \right\} \\ & \propto \exp \left \{ -\frac{1}{2} \frac{\left( \theta - \displaystyle \frac{\mu / \tau^2 + n\bar{x} / \sigma^2}{1/\tau^2 + n/\sigma^2} \right)^2}{\displaystyle \frac{1}{1/\tau^2 + n/\sigma^2}} \right\}. \end{aligned}
## Example: Normal
Or $$f(\theta | x) \sim N( \mu_n, \tau_n^2)$$ where $\mu_n = \left( \frac{\mu}{\tau^2} + \frac{n \bar{x}}{\sigma^2} \right) \tau_n ^2 \quad \mbox{and} \quad \tau_n^2 = \frac{1}{1/\tau^2 + n/\sigma^2} .$ We will call this a conjugate Bayes model. Also note a 95% credible region for $$\theta$$ is given by (this is also the HPD, highest posterior density) $\left( \mu_n - 1.96 \tau_n, \mu_n + 1.96 \tau_n \right) .$ For large $$n$$, the data will overwhelm the prior.
## Example: Normal
• If $$f(\theta) \propto 1$$, an improper prior, then a 95% credible region for $$\theta$$ is the same as a 95% confidence interval since $$f(\theta | x) \sim N( \bar{x}, \sigma^2 / n)$$ (try to show this at home).
• Usually, we specify a prior and likelihood that result in an posterior that is intractable. That is, we can't work with it analytically or even calculate the appropriate normalizing constant $$c$$.
• However, it is often easy to simulate a Markov chain with $$f(\theta|x)$$ as its stationary distribution.
## Conjugate Priors
• Given a data distribution $$f(\theta | x)$$, a family of distributions is said to be conjugate to the given distribution if whenever the prior is in the conjugate family, so is the posterior, regardless of the observed value of the data
• Our first example showed that, if the data distribution is binomial, then the conjugate family of distributions is beta
• Our second example showed that, if the data distribution is normal with known variance, then the conjugate family of distributions is normal
## Improper Priors
• A subjective Bayesian is a person who really buys the Bayesian philosophy. Probability is the only correct measure of uncertainty, and this means that people have probability distributions in their heads that describe any quantities they are uncertain about. In any situation one must make one’s best effort to get the correct prior distribution out of the head of the relevant user and into Bayes rule.
• Many people, however, are happy to use the Bayesian paradigm while being much less fussy about priors. When the sample size is large, the likelihood outweighs the prior in determining the posterior. So, when the sample size is large, the prior is not crucial.
## Improper Priors
• Such people are willing to use priors chosen for mathematical convenience rather than their accurate representation of uncertainty.
• They often use priors that are very spread out to represent extreme uncertainty. Such priors are called “vague” or “diffuse” even though these terms have no precise mathematical definition.
• In the limit as the priors are spread out more and more one gets so-called improper priors.
## Improper Priors
• There is no guarantee that $\text{likelihood } × \text{ improper prior } = \text{ unnormalized posterior}$ results in anything that can be normalized. If the right-hand side integrates, then we get a proper posterior after normalization. If the right-hand does not integrate, then we get complete nonsense.
• You have to be careful when using improper priors that the answer makes sense. Probability theory doesn’t guarantee that, because improper priors are not probability distributions.
## Improper Priors
• Improper priors are questionable
• Subjective Bayesians think they are nonsense. They do not correctly describe the uncertainty of anyone.
• Everyone has to be careful using them, because they don’t always yield proper posteriors. Everyone agrees improper posteriors are nonsense.
• Because the joint distribution of data and parameters is also improper, paradoxes arise. These can be puzzling.
• However they are widely used and need to be understood.
## Objective Bayesian Inference
• The subjective, personalistic aspect of Bayesian inference bothers many people. Hence many attempts have been made to formulate objective priors, which are supposed to be priors that many people can agree on, at least in certain situations.
• However, none of the proposed objective priors achieve wide agreement.
## Flat Priors
• One obvious default prior is flat (constant), which seems to give no preference to any parameter value over any other
• If the parameter space is unbounded, then the flat prior is improper
• One problem with flat priors is that they are only flat for one parameterization
• Another alternative is Jeffreys priors
## Bayesian Point Estimates
• Bayesians have little interest in point estimates of parameters. To them a parameter is a random variable, and what is important is its distribution. A point estimate is a meager bit of information as compared, for example, to a plot of the posterior density.
• However, Bayesian point estimates are widely reported and something we will be estimating using MCMC
• Bayesian point estimates most commonly used are the posterior mean, the posterior median, the posterior mode, and the endpoints of Bayesian credible regions
• Frequentists too have little interest in point estimates except as tools for constructing tests and confidence intervals
## Bayesian Credible Intervals
• Not surprisingly, when a Bayesian makes an interval estimate, it is based on the posterior.
• Many Bayesians do not like to call such things confidence intervals because that names a frequentist notion. Hence the name credible intervals which is clearly something else.
• One way to make credible intervals is to find the marginal posterior distribution for the parameter of interest and find its $$\alpha/2$$ and $$1-\alpha/2$$ quantiles. The interval between them is a $$100 (1-\alpha)$$% Bayesian credible interval for the parameter of interest called the equal tailed interval.
## Bayesian Point Estimates
• Suppose the data $$x$$ is Bin($$n$$, $$p$$) and we use the conjugate prior Beta($$\alpha_1, \alpha_2$$), so the posterior is Beta($$x + \alpha_1, n - x + \alpha_2$$)
• Since we know the mean of a beta distribution, we can see the posterior mean is $E(p|x) = \frac{x + \alpha_1}{x + \alpha_1 + \alpha_2}$
• The posterior median has no simple expression, but we can calculate it using the R
qbeta(0.5, x + alpha1, n - x + alpha2)
• The endpoints of Bayesian credible regions can also be found using R, say for an 80% credible region
qbeta(0.1, x + alpha1, n - x + alpha2)
qbeta(0.9, x + alpha1, n - x + alpha2)
## Bayesian Point Estimates
• Suppose $$\alpha_1 = \alpha_2 = 1/2$$, $$x=2$$, and $$n=10$$.
alpha1 <- alpha2 <- 1 / 2
x <- 2
n <- 10
(x + alpha1) / (n + alpha1 + alpha2)
## [1] 0.2272727
qbeta(0.5, x + alpha1, n - x + alpha1)
## [1] 0.2103736
cbind(qbeta(0.1, x + alpha1, n - x + alpha2), qbeta(0.9, x + alpha1, n - x + alpha2))
## [,1] [,2]
## [1,] 0.08361516 0.3948296
## Bayesian Hypothesis Tests
• Not surprisingly, when a Bayesian does a hypothesis test, it is based on the posterior.
• To a Bayesian, a hypothesis is an event, a subset of the sample space. Remember that after the data are seen, the Bayesian considers only the parameter random. So the parameter space and the sample space are the same thing to the Bayesian.
• The Bayesian compares hypotheses by comparing their posterior probabilities.
• All but the simplest such tests must be done by computer.
## Bayesian Hypothesis Tests
• Suppose the data $$x$$ is Bin($$n$$, $$p$$) and we use the conjugate prior Beta($$\alpha_1, \alpha_2$$), so the posterior is Beta($$x + \alpha_1, n - x + \alpha_2$$)
• Suppose the hypotheses in question are \begin{aligned} H_0 : & p \ge 1/2 \\ H_1 : & p < 1/2 \end{aligned}
• We can calculate the probabilities of these two hypotheses by the the R expressions
pbeta(0.5, x + alpha1, n - x + alpha2)
## [1] 0.9739634
pbeta(0.5, x + alpha1, n - x + alpha2, lower.tail = FALSE)
## [1] 0.02603661
## Bayesian Hypothesis Tests
• Suppose $$\alpha_1 = \alpha_2 = 1/2$$, $$x=2$$, and $$n=10$$.
alpha1 <- alpha2 <- 1 / 2
x <- 2
n <- 10
pbeta(0.5, x + alpha1, n - x + alpha2)
## [1] 0.9739634
pbeta(0.5, x + alpha1, n - x + alpha2, lower.tail = FALSE)
## [1] 0.02603661
## Bayesian Hypothesis Tests
• Bayes tests get weirder when the hypotheses have different dimensions
• In principle, there is no reason why a prior distribution has to be continuous
• It can have degenerate parts that put probability on sets a continuous distribution would give probability zero
• But many users find this weird
• Bayes Factors tend to be more widely used
## Bayes Factors
• Let $$M$$ be a finite or countable set of models. For each model $$m \in M$$ we have the prior probability of the model $$h(m)$$. It does not matter if this prior on models is unnormalized.
• Each model $$m$$ has a parameter space $$\Theta_m$$ and a prior $$g(\theta | m)$$, $$\theta \in \Theta_m$$
• The spaces $$\Theta_m$$ can and usually do have different dimensions. That’s the point. These within model priors must be normalized proper priors. The calculations to follow make no sense if these priors are unnormalized or improper.
• Each model $$m$$ has a data distribution $f(x | \theta, m)$ which may be a PDF or PMF.
## Bayes Factors
The unnormalized posterior for everything, models and parameters within models, is $f(x | \theta, m) g(\theta | m) h(m)$ To obtain the conditional distribution of $$x$$ given $$m$$, we must integrate out the nuisance parameters $$\theta$$ \begin{aligned} q(x | m) & = \int_{\Theta_m} f(x | \theta, m) g(\theta | m) h(m) d \theta \\ & h(m) \int_{\Theta_m} f(x | \theta, m) g(\theta | m) d \theta \end{aligned} These are the unnormalized posterior probabilities of the models.
The normalized probabilities are $p(m | x) = \frac{q(x | m)}{\sum q(x | m)}$
## Bayes Factors
It is useful to define $b(x | m) = \int_{\Theta_m} f(x | \theta, m) g(\theta | m) d \theta$ so $q(x | m) = b(x | m) h(m)$ Then the ratio of posterior probabilities of models $$m_1$$ and $$m_2$$ is $\frac{p(m_1|x)}{p(m_2|x)} = \frac{q(x | m_1)}{q(x | m_2)} = \frac{b(x | m_1) h(m_1)}{b(x | m_2) h(m_2)}$ This ratio is called the posterior odds of the models (a ratio of probabilities is called an odds) of these models.
## Bayes Factors
The prior odds is $\frac{h(m_1)}{h(m_2)}$ The term we have not yet named in $\frac{p(m_1|x)}{p(m_2|x)} = \frac{b(x | m_1) h(m_1)}{b(x | m_2) h(m_2)}$ is called the Bayes factor $\frac{b(x | m_1)}{b(x | m_2)}$ the ratio of posterior odds to prior odds.
The prior odds tells how the prior compares the probability of the models. The Bayes factor tells us how the data shifts that comparison going from prior to posterior via Bayes rule.
## Bayes Factors
• Suppose the data $$x$$ is Bin($$n$$, $$p$$) and the models (hypotheses) in question are \begin{aligned} m_1 : & p = 1/2 \\ m_2 : & p \ne 1/2 \end{aligned}
• The model $$m_1$$ is concentrated at one point $$p = 1/2$$, hence has no nuisance parameter. Hence $$g(\theta|m_1) =1$$. Suppose we use the within model prior Beta($$\alpha_1, \alpha_2$$) for model $$m_2$$.
• Then $b(x | m_1) = f(x | 1/2) = {n \choose x} (1/2)^x (1 - 1/2)^{n-x} = {n \choose x} (1/2)^n$
## Bayes Factors
Then \begin{aligned} b(x | m_2) & = \int_0^1 f(x|p) g(p|m_2) dp \\ & = \int_0^1 {n \choose x} \frac{1}{B(\alpha_1, \alpha_2)} p^{x + \alpha_1 -1} (1-p)^{n - x + \alpha_2 - 1} dp \\ & = {n \choose x} \frac{B(x+ \alpha_1, n - x + \alpha_2)}{B(\alpha_1, \alpha_2)} \end{aligned} where $B(\alpha_1, \alpha_2) = \frac{\Gamma(\alpha_1)\Gamma(\alpha_2)}{\Gamma(\alpha_1 + \alpha_2)}$ by properties of the Beta distribution
## Bayes Factors
alpha1 <- alpha2 <- 1 / 2
x <- 2
n <- 10
p0 <- 1 / 2
b1 <- dbinom(x, n, p0)
b2 <- choose(n, x) * beta(x + alpha1, n - x + alpha2) / beta(alpha1, alpha2)
BayesFactor <- b1 / b2
BayesFactor
## [1] 0.5967366
pvalue <- 2 * pbinom(x, n, p0)
pvalue
## [1] 0.109375
## Bayes Factors
• For comparison, we calculated not only the Bayes factor 0.597 but also the frequentist p-value 0.109
• Bayes factors and p-values are sort of comparable, but are not identical
• In fact, it is a theorem that in situations like this the Bayes factor is always larger than the p-value, at least asymptotically
• This makes Bayesian tests more conservative, less likely to reject the null hypothesis, than frequentists
• Either the frequentists are too optimistic or the Bayesians are too conservative, or perhaps both
## Summary
• Bayesian inference, priors, Bayesian point estimates, Bayesian hypothesis testing, and Bayes factors
• Many applications including pattern recognition, span detection, search for lost objects, …
• Calculations are trivial in our examples so far, not usually the case | 2021-05-17 18:09:49 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9719475507736206, "perplexity": 1040.1249664599886}, "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/1620243992440.69/warc/CC-MAIN-20210517180757-20210517210757-00400.warc.gz"} |
https://www.transtutors.com/questions/e6-1-the-san-marcos-inn-is-trying-to-determine-its-break-even-point-the-inn-has-75-r-1313500.htm | # E6-1 The San Marcos Inn is trying to determine its break-even point. The inn has 75 rooms that...
E6-1 The San Marcos Inn is trying to determine its break-even point. The inn has 75 rooms that are rented at $50 a night. Operating costs are as follows. Salaries$8,500 per month
Utilities 2,000 per month Depreciation 1,000 per month Maintenance 500 per month
Maid service 5 per room
Other costs 33 per room
Instructions
(a) Determine the inn’s break-even point in (1) number of rented rooms per month and
(2) dollars.
(b) If the inn plans on renting an average of 50 rooms per day (assuming a 30-day month), what is (1) the monthly margin of safety in dollars and (2) the margin of safety ratio? | 2018-11-18 18:37:04 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.21179553866386414, "perplexity": 5090.17197079445}, "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/1542039744561.78/warc/CC-MAIN-20181118180446-20181118202446-00232.warc.gz"} |
http://math.stackexchange.com/questions/199600/polynomial-interpolation-and-error-bound | # Polynomial Interpolation and Error Bound
Problem: Use the Lagrange interpolating polynomial of degree three or less and four digit chopping arithmetic to approximate cos(.750) using the following values. Find an error bound for the approximation.
cos(.6980) = 0.7661 cos(.7330) = 0.7432 cos(.7680) = 0.7193 cos(.8030) = 0.6946
The actual value of cos(.7500) = 0.7317 (to four decimal places). Explain the discrepancy between the actual error and the error bound.
Solution: The approximation of cos(.7500) 0.7313. The actual error is 0.0004, and an error bound is 2.7 × 10^(-8). The discrepancy is due to the fact that the data are given only to four decimal places.
Can anyone help me figure out the intermediary steps from the problem to solution?
- | 2014-12-22 19:59:31 | {"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": 0.8167083859443665, "perplexity": 521.6396627618558}, "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-2014-52/segments/1418802776556.43/warc/CC-MAIN-20141217075256-00003-ip-10-231-17-201.ec2.internal.warc.gz"} |
http://stackoverflow.com/questions/13222076/how-to-use-a-dll-written-in-visual-c-in-a-c-sharp-program | # How to use a DLL written in Visual C++ in a C# program? [duplicate]
Possible Duplicate:
C# P\Invoke DLL no entry point into C++?
I'm asking this question after doing a rather thorough surfing on SO and google, and most of the answers get me about 80% of the way, but its still a bit confusing, so kindly show me the way out.
I have some Visual C++ functions defined as follows:
MyDLL.h
#ifdef FUNCTIONS_EXPORTS
#define FUNCTIONS_API __declspec(dllexport)
#else
#define FUNCTIONS_API __declspec(dllimport)
#endif
namespace Functions {
class MyFunctions {
public:
static FUNCTIONS_API int Add(int a, int b);
static FUNCTIONS_API int Factorial(int a);
};
}
MyDLL.cpp
namespace Functions {
int MyFunctions::Add (int a, int b)
{
return a+b;
}
int MyFunctions::Factorial (int a)
{
if(a<0)
return -1;
else if(a==0 || a==1)
return 1;
else
return a*MyFunctions::Factorial(a-1);
}
}
Now, I want to import the DLL generated by this build into my C# program as such:
Program.cs
using System;
using System.Collections.Generic;
using System.Runtime.InteropServices;
namespace DLLTester
{
class Program
{
[DllImport("path\\to\\the\dll\\myDLL.dll")]
public static extern int Factorial(int a);
static void Main(string[] args) {
int num;
Console.WriteLine("The factorial is " + Factorial(num));
}
}
}
I've tried writing the functions without a class (no static keyword while defining), but even that does not work and gives errors.
Where am I going wrong in all this?
-
There's a mechanism in .NET for calling into the Windows API and unmanaged code called PInvoke ("platform invoke"). SO should be able to help you here, if not there's also a helpful wiki for using PInvoke interop at pinvoke.net Now, I have never used DLLImport so I'm not saying this will work but perhaps try to use unsigned int with your call into the C++ code. ie. static extern UInt32 Factorial(UInt32 a); – FredrikRedin Nov 4 '12 at 19:50
Additionally to Patrick's answer you might want to specify __stdcall on your C++ methods. Otherwise you will get errors when returning from the method. – Nico Schertler Nov 4 '12 at 20:30
## marked as duplicate by Hans Passant, Alexei Levenkov, jogojapan, Nimit Dudani, stealthyninjaNov 5 '12 at 6:25
The biggest problem I see is that you're trying to p/invoke class methods. Because of C++ name mangling, the entry point you supplied isn't present in your compiled DLL. You should be able to run dumpbin.exe on your DLL and see for yourself.
I'd suggest skimming the name mangling article and how to prevent it for DllImport purposes, and read most of the CodeProject article linked in the previous paragraph. It's pretty well written and covers a lot of p/invoke minutiae. | 2013-12-06 08:44:34 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 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": 0.23487922549247742, "perplexity": 7051.826507809889}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2013-48/segments/1386163050500/warc/CC-MAIN-20131204131730-00029-ip-10-33-133-15.ec2.internal.warc.gz"} |
http://mathhelpforum.com/calculus/82565-series-sequences.html | # Thread: series and sequences
1. ## series and sequences
let an=2n/(3n^2+2)
a.)determine whether the sequence {an}n=1-infinity is convergent or divergent. If it converges find the limit
b.)determine whether the series sum from n=1 to infinity of an is convergent or divergent.
Can someone explain to me how to do this i am completely confused on series and apparently this is an easy workout problem. Help please? Thanks!
2. Originally Posted by ahawk1
let an=2n/(3n^2+2)
a.)determine whether the sequence {an}n=1-infinity is convergent or divergent. If it converges find the limit
b.)determine whether the series sum from n=1 to infinity of an is convergent or divergent.
Can someone explain to me how to do this i am completely confused on series and apparently this is an easy workout problem. Help please? Thanks!
A sequence converges if it has a limit as n->infinity, and diverges if the limit DNE or is infinity.
start with that. try it and see what you get
3. Originally Posted by coolguy99
A sequence converges if it has a limit as n->infinity, and diverges if the limit DNE or is infinity.
start with that. try it and see what you get
it goes to 0 if u take the limit so it converges.
4. For the limit of the series, note that $4n^2 > 3n^2 + 2$ for $n \geq 2$. Hence, $\frac{2n}{3n^2 + 2} > \frac{2n}{4n^2}$ for $n \geq 2$. But $\frac{2n}{4n^2} = \frac{1}{2n}$ which is a multiple of the harmonic series. What can you conclude from this? | 2016-10-24 03:48:47 | {"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": 0, "img_math": 0, "codecogs_latex": 5, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9799501299858093, "perplexity": 420.49415608976625}, "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-2016-44/segments/1476988719465.22/warc/CC-MAIN-20161020183839-00411-ip-10-171-6-4.ec2.internal.warc.gz"} |
https://www.nature.com/articles/s42005-017-0002-3?error=cookies_not_supported&code=415b7c99-2a53-47a1-9bc2-b4c77e3699e2 | # Oscillatory spin-orbit torque switching induced by field-like torques
## Abstract
Deterministic magnetization switching using spin-orbit torque (SOT) has recently emerged as an efficient means to electrically control the magnetic state of ultrathin magnets. The SOT switching still lacks in oscillatory switching characteristics over time, therefore, it is limited to bipolar operation where a change in polarity of the applied current or field is required for bistable switching. The coherent rotation based oscillatory switching schemes cannot be applied to SOT, because the SOT switching occurs through expansion of magnetic domains. Here we experimentally achieve oscillatory switching in incoherent SOT process by controlling domain wall dynamics. We find that a large field-like component can dynamically influence the domain wall chirality which determines the direction of SOT switching. Consequently, under nanosecond current pulses, the magnetization switches alternatively between the two stable states. By utilizing this oscillatory switching behavior, we demonstrate a unipolar deterministic SOT switching scheme by controlling the current pulse duration.
## Introduction
Magnetism plays a key role in modern data storage and advanced spintronics devices as non-volatile information can be encoded in the magnetization state of a nanoscale magnet. Over the last two decades, electrical methods to control the magnetization state have received immense research attention to meet the demand for the reduction in the size and energy consumption of magnetic storage cells and devices. As a result, remarkable developments have been made in switching the magnetization electrically using spin-transfer torque (STT)1,2,3,4,5, electric field6,7,8,9,10, and the recently discovered spin-orbit torque (SOT)11,12,13,14,15. The operation principle of majority of these electrical techniques is based on the control of the polarity of the external force, such as an electric current or magnetic field, to achieve switching between two magnetic states (bipolar switching techniques).
On the other hand, magnetization switching techniques with a fixed polarity of the external force (unipolar operation) are receiving immense attention because of their scientific interest, as well as their potential to significantly increase the scalability of spintronics devices by replacing transistors with diodes10, 16. It is possible to achieve unipolar magnetization switching by exploiting the temporal evolution of magnetization switching, or, in other words, the magnetization dynamics. For example, in the context of STT or electric field-induced magnetization switching, unipolar operation was previously demonstrated7, 9, 16,17,18,19 by driving the magnetization into coherent precessional motion between the two stable states and then precisely controlling the time duration for which the external force of fixed polarity was applied. As the time varying magnetization trajectory oscillates between the two potential minima (stable states), switching was accomplished by removing the external force at the appropriate time to release the magnetization at the desired final state. This oscillatory behavior was also theoretically predicted in the SOT driven switching20, 21. However, it must be emphasized that the above described oscillatory switching scheme for unipolar operation requires strong coherency of the magnetic moments or, in other words, the magnetization should be kept uniformly aligned throughout the rotational switching process. The coherency of the magnetization is very sensitive to thermal agitations22 and also relatively weak23,24,25 in magnetic structures with perpendicular magnetic anisotropy (PMA) which are required for high-density applications.
Here we report our experimental discovery of an alternative method to achieve the oscillatory switching behavior in the scenario of incoherent magnetization switching in PMA structures driven by SOT. The SOT is an electric current-induced phenomenon that utilizes spin currents generated by spin–orbit interactions to efficiently manipulate and switch the magnetization of an ultrathin magnet11,12,13,14,15. While its microscopic origin is still controversial26,27,28,29, SOT is known to be composed of two components, namely, the damping-like torque (DLT), $$\tau _{{\mathrm{DLT}}}{\mathrm{\sim }}\hat m{\mathrm{ \times }}\left( {\hat m{\mathrm{ \times }}\hat y} \right)$$ and the field-like torque (FLT), $$\tau _{{\mathrm{FLT}}}\sim \hat m \times \hat y$$. Here, $$\hat m$$ and $$\hat y$$ indicate the direction of the magnetization of the ultrathin magnet and the spin polarization of the incoming spin current, respectively. When substantial magnetization is orthogonal to $$\hat y$$, the DLT and FLT can be considered as equivalent field with $$\hat m \times \hat y$$ symmetry (HDLT) and $$\hat y$$ symmetry (HFLT), respectively30.
Unless the lateral dimensions of the ultrathin magnet are extremely small (< 40 nm), the SOT induced magnetization switching in PMA structures is an incoherent process31. In the incoherent regime, the switching happens by depinning of a reversed magnetic domain followed by its expansion24, 30,31,32,33,34,35. Due to the torque symmetries, the general consensus till now is that the DLT is responsible to drive the domain expansion in SOT switching30 and the role of FLT in deterministic switching is usually neglected and not well understood25, 30. On the contrary, our studies reveal that in PMA structures with large FLT, the SOT driven incoherent magnetization dynamics and the deterministic switching are greatly influenced by FLT.
## Results
### Nanosecond pulse current-induced SOT switching
We explore the SOT driven magnetization switching dynamics under the application of nanosecond current pulses in Ta/CoFeB/MgO structures, whose FLT is large and is of opposite sign to that of DLT27, 36 (FLT/DLT = –3.2, see Methods section for our sign conventions). As shown in Fig. 1a, a perpendicularly magnetized circular dot with a 1000 nm diameter (d) was patterned on top of the Ta channel. The electric current pulses are applied along the +x-direction and an in-plane assist field (H) is applied in the xy-plane where its in-plane angle (θ H ) is defined with respect to the +x-axis. The applied H is along the –x-direction (θ H = 180°) unless otherwise specified. The details of device preparation and measurement are described in Methods section.
In order to study the SOT switching dynamics, we have measured the probability of magnetization switching by applying current pulses with the initial state of the magnetization as ‘up’ (+z-direction). Figure 1b shows the two dimensional diagram of the measured switching probability (Psw) as a function of current density (J) and pulse duration (t) at a fixed H = 1191 Oe. We have also measured the Psw vs. t for different H while keeping a constant value of J (79.4 × 106 A cm−2) as shown in Fig. 1c. Under the application of the current pulses, a clear ‘up’ to ‘down’ SOT switching is observed as indicated by the transition of Psw from 0 to 100%. This first switching boundary (where Psw = 50%) between the initial state and forward switching is monotonic with respect to J, t, and H, suggesting that the forward switching is more likely to occur with a larger J, a longer t or a larger H, which is expected from torque driven SOT magnetization switching dynamics as observed before24, 31. Moreover, the ‘up’ to ‘down’ switching direction is also consistent with the previous experiments and also with that of DC-current-induced SOT switching in our devices (Supplementary Note 1 and 2). By performing a linear fit of the critical switching current density (at the first switching boundary) with corresponding values of 1/t, we estimate the intrinsic critical switching current density (Jc0) in our devices as 43.2 × 106 A cm−2 (Supplementary Note 3). This value of Jc0 is significantly smaller than the calculated value of 148 × 106 A cm−2 from the macrospin-like coherent switching model (Methods section for details), suggesting that the switching in our device occurs via expansion of reversed domain24, 30,31,32,33,34,35 rather than coherent magnetization rotation, which is also expected from the size of the studied structure.
### Oscillatory switching behavior induced by FLT
Beyond the first switching boundary, the Psw is expected to remain at 100% and does not change, since the existing theories and experimental results indicate that the DLT driven incoherent SOT switching is a deterministic process24, 30, 31. On the contrary, as seen in Fig. 1b, c, if we apply a pulse with a longer t, a backward switching boundary appears where the magnetization flips back from ‘down’ to its initial ‘up’ state. This unexpected backward switching observed in our devices, for a wide range of J, t, and H, is also a spin torque driven process, since the backward switching boundary also shows a monotonic behavior with J, t, and H. On applying a longer t beyond the backward switching, the magnetization undergoes forward switching again (from ‘up’ to ‘down’ state) resulting in an oscillatory behavior of Psw. We note that the backward switching and the oscillatory behavior are observed regardless of the initial magnetization states (‘up’ and ‘down’, Supplementary Note 4).
The occurrence of oscillatory Psw is surprising because the SOT switching in our devices proceeds by domain expansion unlike the previous reports where the switching takes by coherent magnetization rotation7, 9, 1617, 18,19,20,21 Furthermore, the signature of incoherent switching in our devices can be also observed in the oscillatory period of Psw. In the case of coherent switching (Supplementary Note 5), the oscillatory period of Psw is quite symmetric as it arises from the precessional motion with a constant frequency (~ Larmor frequency). On the other hand, the observed periods in our study are distinctly asymmetric as the observed period for the backward switching is much longer than that for the first forward switching. For instance, the periods of the first forward switching and backward switching are ~2.7 ns and ~7.5 ns, respectively, for an applied J of 79.4 × 106 A cm−2 and H of 1191 Oe, which are indicated by dashed arrows in Fig. 1b.
In order to obtain more insights on the backward switching, we have measured Psw for different θ H as shown in Fig. 1d. Interestingly, the observed ‘down’ to ‘up’ backward switching exhibits significant asymmetric behavior with respect to θ H , compared to the ‘up’ to ‘down’ forward switching. The backward switching is suppressed or enhanced, as the H is tilted towards (θ H < 180°) or away from (θ H > 180°) the +y-direction, respectively. This asymmetric behavior implies that an equivalent field with y-symmetry gives rise to the observed backward switching, and this y-symmetry coincides with the direction of HFLT. The harmonic Hall voltage measurements in the Ta/CoFeB/MgO structure have shown that a large HFLT exists in the –y-direction when a positive current (along the +x-direction) is applied27, 36. The observed backward switching in Fig. 1d is suppressed when the effective HFLT is reduced by applying an external transverse field along the +y-direction (θ H < 180°) opposite to the SOT induced HFLT (along the –y-direction). Therefore, the contributions of FLT play a dominant role in breaking the determinism in SOT switching dynamics and thus should not be neglected. Complete suppression of the backward switching under titled H toward the +y-direction is observed in another device (Supplementary Note 6). Furthermore, the backward switching or the oscillatory switching behavior is not observed in the Pt layer based device which exhibits a small FLT/DLT ratio of −0.5 (Supplementary Note 7).
We have then estimated and compared the domain wall (DW) velocity during the first forward and backward switching processes. The mean DW velocity (VDW) during the forward switching is estimated using the relation, $$V_{{\mathrm{DW,fwd}}}{\mathrm{ = }}d{\mathrm{/}}\left( {2t_{{\mathrm{c,fwd}}}} \right)$$ with an assumption of SOT switching occurs by reverse domain nucleation at one corner followed by its expansion across the PMA dot30, 32, 33, 35. Here, tc,fwd represents the time corresponding to Psw = 50% during the first forward switching. VDW,fwd is estimated only in the relatively large J regime (J > Jc0), where the spin-torque is dominant over the thermal activation24, 37. As shown in Fig. 2a, the estimated VDW,fwd shows a proportional increase with an increase in J, and we obtain a VDW,fwd of 504 m s−1 for J = 108 A cm−2 and H = 1191 Oe, which is in agreement with the reported value under a large longitudinal field38. Figure 2b shows that the VDW increases with an increase in the magnitude of H which can be understood as follows. As H increases, the magnetization at the center of the domain wall (M DW ) is better aligned toward the H direction (–x-direction). Subsequently, the out-of-plane HDLT ($$\propto {\mathbf{M}}_{{\mathbf{DW}}} \times \hat y \propto x-{\mathrm{ component}} \,{\mathrm{of}} \, {\mathbf{M}}_{\mathbf{DW}}$$) exerted on the DW also increases leading to a larger VDW14, 30. Figure 2c shows the VDW,fwd as a function of the transverse component (y component) of the applied H (top axis). The corresponding FLTeff/DLT ratio is indicated in the bottom axis, which is defined from the following relation: $$\left( {H_{{\rm FLT}}\left( J \right) - H\,{\mathrm{cos}}\theta _H} \right){\mathrm{/}}H_{{\rm DLT}}\left( J \right)$$. Here, HDLT(J) and HFLT(J) are the corresponding SOT fields at a given current density which are measured from the harmonic technique (Supplementary Note 8). The asymmetric behavior of VDW,fwd with respect to the transverse component of H arises due to M DW being pulled away (into) the Néel wall configuration resulting in decrease (increase) of the HDLT experienced by the DW14.
Similarly, we have determined the VDW during the observed backward switching using the relation, $$V_{{\mathrm{DW,bck}}} = d/2\left( {t_{{\mathrm{c,bck}}} - t_{{\mathrm{c,fwd}}}} \right)$$, as the backward switching follows the first forward switching in time. The tc,bck represents the time corresponding to Psw = 50% during the backward switching. Interestingly, the estimated VDW,bck also shows monotonic increase with respect to J and H (Fig. 2a, b) and an asymmetric behavior as a function of θ H (Fig. 2c), implying that the backward switching also arises from the spin torque driven domain expansion similar to the case of the first forward switching but in an opposite manner. However, VDW,bck is smaller than VDW,fwd because the domain expansion in the backward switching is energetically unfavorable as discussed later.
### One-dimensional micromagnetics simulations of domain walls
In order to understand the experimental observations and elucidate the role of FLT in the oscillatory PSW, we have performed one-dimensional (1D) micromagnetics simulations of the SOT switching driven by domain expansion (Methods section for details). The top panel of Fig. 2d shows the SOT induced temporal evolution of averaged out-of-plane magnetization (mz) as a function of the FLT/DLT ratio, where the value of DLT is kept constant. At the start of the simulation (0 ns), a reversed ‘down’ domain is introduced at one edge of the structure. This reversed domain is then expanded by SOT as the simulation proceeds. In the case where there is no FLT, the SOT successfully switches the magnetization to ‘down’ (mz = –1) state. However, when a large FLT is considered (FLT/DLT = –4.8), the 1D model also reproduces the backward switching behavior as the mz returns back to a positive value after the forward switching. This backward switching behavior is gradually suppressed with decreasing the magnitude of the FLT/DLT ratio, which is consistent with the experimental observation. Figures 2e–g show the calculated VDW during the forward and backward switching as a function of J, H, and FLT/DLT ratio, respectively. The calculated and experimentally determined VDW also show good qualitative agreement as the monotonic behavior with respect to H and J, asymmetric behavior with respect to the FLT/DLT ratio and the slower velocity during backward switching are reproduced.
The bottom panel of Fig. 2d shows the temporal evolutions of azimuthal angle of DW (θDW), which is the angle between M DW and +x-direction. The evolution of θDW for the different ratios of FLT/DLT sheds light on the key role of FLT on the domain expansion in the opposite direction and the resultant backward switching. At the start of simulation, due to the applied H, the x-component of M DW is along the –x-direction and thus θDW = 180°. Under the application of SOT, the reversed domain expands and θDW gradually decreases to 90° as M DW damps toward the spin polarization direction39. For the case without FLT (FLT/DLT = 0), the DW annihilates as it expands to the structure edge (mz = –1) which results in M DW and thus θDW not being well defined. However, when a sizeable FLT of opposite sign to DLT is considered, θDW exhibits an oscillatory behavior over time, which indicates that the DW does not immediately annihilate after it reaches the structure edge. Further, it is observed that the time for which |θDW| is stable below 90° increases with increasing the magnitude of FLT and as we explain in the following paragraph, whenever the value of |θDW| < 90° (M DW in the +x-direction), the SOT drives the backward switching. This result indicates that the FLT facilitates backward switching by stabilizing |θDW| < 90°.
The physics behind the FLT induced oscillatory behavior of θDW and the resultant backward switching is illustrated in Fig. 3 using the DW configuration, M DW orientation, and torques acting on M DW at different times. Time 1 corresponds to the case for ‘up’ to ‘down’ forward switching process when the x-component of M DW is stabilized along –x-direction ($${\mathbf{M}}_{{\mathbf{DW}}} \cdot {\hat{\mathbf x}} < 0$$). Consequently, the DW experiences an out-of-plane HDLT in the –z-direction ($${\mathbf{M}}_{{\mathbf{DW}}} \times {\hat {\mathbf y}} < 0$$) and the ‘down’ domain expands to advance the forward switching process. Time 2 corresponds to the case when the propagating DW reaches the structure edge and annihilates. However, this annihilation process is followed by a nucleation of a DW with an inverted chirality ($${\mathbf{M}}_{{\mathbf{DW}}} \cdot {\hat {\mathbf x}} > 0$$) which can be understood as a reflection of the DW on the structure edge40, 41. This DW with an inverted chirality is not energetically favorable and follows damped motion over time to revert back its chirality due to the applied H along the –x-direction. However, a sufficiently large HFLT in the –y-direction can give dynamic stability to the DW with inverted chirality with a lifetime of several nanoseconds. As this metastable DW’s center is along the +x-direction, it experiences a HDLT in the +z-direction ($${\mathbf{M}}_{{\mathbf{DW}}} \times {\hat {\mathbf y}} > 0$$), therefore the ‘up’ domain expands, as shown in time 3, which results in the backward switching. Over time, the metastable DW recovers back its chirality with its M DW again pointing back to the –x-direction which proceeds to switch the magnetization again in the forward direction and the whole cycle repeats giving rise to the oscillatory behavior in Psw. The velocities of the two switching processes are different since the inverted DW configuration during the backward switching is in an energetically unfavorable state as the applied external H is against M DW . Furthermore, the attained metastability of the reversed DW decreases over time and eventually only the forward switching will prevail. As a result, the backward switching can be observed only in the nanosecond timescale.
Although the DW chirality and the resulting domain expansion are discussed in terms of H and HFLT, it is known that the other effects, such as Dzyaloshinskii-Moriya interaction (DMI) may also influence the DW chirality. It is reported that the DMI plays a central role in the case of SOT driven DW displacement, as it determines the DW chirality and the sign of out-of-plane HDLT experienced by DW14, 38, 42, 43. However, in the case of SOT driven switching, the DW chirality is reported to be governed largely by the applied H, as it overcomes the DMI effective field30, 43. In the studied structure, the DMI effective field is estimated as 103 Oe (see Methods section for details) and is quite smaller than the H (550 ~ 1200 Oe) and HFLT (1257 Oe per 79.4 × 106 A cm−2, Supplementary Note 8) applied in the experiments and simulations. Therefore, we believe that the DW chirality during the forward and backward switching is dominantly governed by H and HFLT.
### Unipolar SOT switching
Finally, utilizing the observed oscillatory characteristics, we show a deterministic unipolar SOT switching scheme which reversibly controls the magnetization configuration under a constant J and H of a fixed polarity and changing t only. This is demonstrated using a series of current pulses with alternating lengths of 2.5 ns and 7.5 ns with a fixed current density of 79.4 × 106 A cm−2 under a constant H of 1067 Oe. After each pulse injection, the magnetization state is monitored using the anomalous Hall resistance (RAHE) measurement. As shown in Fig. 4, the deterministic SOT switching consistently occurs by the unipolar current pulses. The initial state of the magnetization is pointing ‘up’ and the pulse of 2.5 ns always switches the magnetization to ‘down’, while the magnetization is always brought to ‘up’ state with the pulse of 7.5 ns.
## Discussion
The role of FLT has not been paid much attention in the majority of SOT switching experiments and thus, the SOT switching and domain wall dynamics have been mainly discussed using the DLT alone. The FLT was claimed to induce a partial decrease in the SOT switching probability (decreased to ~60% after achieving full 100% switching)44. However, another work reported a similar backward SOT switching that was attributed to a small tilt of in-plane assist field along the out-of-field direction45. With these two different interpretations, the role of FLT in SOT dynamics and the underlying physics of the backward SOT switching still remain vague. In this regard, our experiments bring to light the crucial role of FLT in breaking the determinism in SOT driven incoherent switching dynamics which results in oscillatory magnetization switching characteristics with respect to the current pulse duration. We make use of this observed oscillatory behavior to demonstrate a unipolar deterministic SOT switching scheme which operates by controlling the duration of the current pulses, while keeping the magnitudes and polarities of the current and the assist-field constant. Our study provides the missing piece in the physics of SOT switching dynamics and offers novel strategies for magnetization switching with unipolar operation.
## Methods
### Sample preparation and measurements
The film structure of Ta (6 nm)/Co40Fe40B20 (0.9 nm)/MgO (2 nm)/SiO2 (3 nm) on a Si/SiO2 substrate is prepared by magnetron sputtering (base pressure <1 × 10−8 Torr) and annealed at 200 °C for 30 min to improve PMA. The structure is subsequently patterned into a CoFeB circular dot with a 1000 nm diameter on top of the Ta Hall cross using electron beam lithography and Ar ion etching. The negative tone electron-beam resist of ma-N 2403 with fine resolution of 5 nm was used for patterning the Hall cross and the circular dot. The electrodes were prepared using positive tone electron-beam resist of PMMA 950 and deposition of Ta (5 nm)/Cu (100 nm). The Ta channel surface is cleaned using Ar ion etching prior to electrode deposition for Ohmic contact. The thickness of the Ta channel after fabrication is ~3.5 nm, estimated from channel resistance measurements. The films have a saturation magnetization of Ms = 670 emu cm−3 and an effective anisotropy field Hk,eff = 3000 Oe measured using vibrating sample magnetometer.
DC- and nanosecond current pulses are applied in the Ta channel through a bias-tee and the perpendicular magnetization state is measured from the anomalous Hall resistance. The current pulse has a rise time of ~70 ps and a fall time of ~80 ps, and its magnitude is determined by measuring the transmitted signal. The switching probability under current pulses is obtained from the following procedure: we applied a negative reset DC-current of 1.5 mA to initialize the magnetization to ‘up’ state followed by a positive current pulse for SOT switching. A few seconds after each pulsed current, the anomalous Hall resistance is measured using a low-DC current of +70 μA to sense the magnetization state. Individual current pulse injections with a fixed amplitude J and duration t were repeated 20 times to determine the switching probability which is defined as Psw = (number of ‘down’ states)/20.
We studied a total of 9 devices with varying the dot diameter and ferromagnet thickness. Every device showed the backward switching with quantitative difference in the switching phase diagram that is attributed to the deviation in effective anisotropy and depinning sites.
### Intrinsic switching current density from the macrospin switching model
The intrinsic switching current density from the macrospin-like rotation switching model is calculated46 using eq. 1.
$$J_{{\rm c0}}{\mathrm{ = }}\frac{{2e}}{\hbar }\frac{{M_{\rm s}t_{\rm F}}}{{\theta _{{\rm SH}}}}\left( {\sqrt {\frac{{H_{{\rm k},{\rm eff}}^2}}{{32}}\left[ {8 + 20\left( {\frac{{H_x}}{{H_{{\rm k},{\rm eff}}}}} \right)^2 - \left( {\frac{{H_x}}{{H_{{\rm k},{\rm eff}}}}} \right)^4 - \left( {\frac{{H_x}}{{H_{{\rm k},{\rm eff}}}}} \right)\left( {8{\mathrm{ + }}\left( {\frac{{H_x}}{{H_{{\rm k},{\rm eff}}}}} \right)^2} \right)^{3/2}} \right]} } \right).$$
(1)
This rotational switching model gives Jc0 of 148 × 106 A cm−2 using parameters of the saturation magnetization Ms = 670 emu cm3 (from VSM measurement), the perpendicular anisotropy Hk,eff = 3000 Oe (from VSM measurement), the ferromagnetic layer thickness tF = 0.9 nm, spin Hall angle θ H = 0.09, and in-plane assist field H x = 1191 Oe.
### 1D model calculation
Micromagnetics simulations are carried out by numerically solving the Landau–Lifshitz–Gilbert equation47 including the damping-like and field-like component of spin-orbit torque:
$$\frac{{\rm d}{\hat {\bf m}}}{{\rm d}t}= - \gamma \mu _0{\hat {\bf m}} \times {\hat {\bf H}}_{{\rm{eff}}}+\alpha {\hat {\rm m}}\times \frac{{{\rm d}{\hat {\rm m}}}}{{{\rm d}t}} - \gamma {\hat {\rm m}} \times \left( { - \tau _{{\rm DLT}}{\hat {\rm m}} \times {\hat {\rm y}}} \right) - \gamma {\hat {\rm m}} \times \left( { - \tau _{{\rm FLT}}{\hat {\rm y}}} \right),$$
(2)
where $$\tau _{{\rm DLT}}{\mathrm{ = }}c_{{\rm DLT}}\left( {\hbar J} \right){\mathrm{/}}\left( {2eM_{\rm s}d} \right)$$ and $$\tau _{{\rm FLT}}{\mathrm{ = }}c_{{\rm FLT}}\left( {\hbar J} \right)/\left( {2eM_{\rm s}d} \right)$$. The equivalent field for each torque terms are defined as $$H_{{\rm DLT}} = - \tau _{{\rm DLT}}\left( {{\hat {\mathbf m}} \times {\hat {\mathbf y}}} \right)$$ and $$H_{{\rm FLT}} = - \tau _{{\rm FLT}}{\hat {\mathbf y}}$$. $${\hat {\mathbf H}}_{{\mathrm{eff}}}$$is the effective field including the magnetostatic field, anisotropy field, exchange field, Dzyaloshinskii-Moriya interaction field, and external field. Following parameters are used: the saturation magnetization Ms = 670 emu cm−3 (from VSM measurement, Supplementary Note 9), the perpendicular anisotropy K = 3.83 × 106 erg cm−3 (from VSM measurement), the Dzyaloshinskii-Moriya interaction constant D = 0.05 erg cm−2, the exchange stiffness constant Aex = 2.0 × 10−6 erg cm−1, the damping α = 0.035 (from FMR measurement, Supplementary Note 10), the DLT efficiency cDLT = –0.09, and the FLT efficiency cFLT = +0.29 (from the harmonic measurement, Supplementary Note 8). The corresponding FLT/DLT ratio is –3.2. For the current pulse, both rise and fall times are 100 ps. In our sign convention, a negative DLT efficiency (cDLT < 0) induces an ‘up’-to-‘down’ switching for J > 0 and H < 0 (θ H = 180°). The considered geometry has dimension of 220 × 80 × 2.5 nm3 and the unit cell size of 2 × 80 × 2.5 nm3. The initial magnetization direction of majority part of the considered geometry is ‘up’ (along +z-direction) with reversed ‘down’ domain formed at one edge. The DMI effective field (HDMI) is estimated using the following relation30, 42: $$H_{{\rm DMI}} = D/\Delta M_{\rm s}$$. Here, D = +0.05 erg cm−2 is the reported DMI constant value in the Ta/CoFeB/MgO structure38, 42, 48, and $$\Delta = \sqrt {A_{{\rm ex}}/K}$$ is the DW width. The applied J is uniform in the lateral plane (Supplementary Notes 11 and 12).
### Data availability
The data that support the findings of this study are available from the corresponding author on request.
## References
1. 1.
Slonczewski, J. C. Current-driven excitation of magnetic multilayers. J. Magn. Magn. Mater. 159, L1–L7 (1996).
2. 2.
Berger, L. Emission of spin waves by a magnetic multilayer traversed by a current. Phys. Rev. B 54, 9353–9358 (1996).
3. 3.
Tsoi, M. et al. Excitation of a magnetic multilayer by an electric current. Phys. Rev. Lett. 80, 4281–4284 (1998).
4. 4.
Myers, E. B., Ralph, D. C., Katine, J. A., Louie, R. N. & Buhrman, R. A. Current-induced switching of domains in magnetic multilayer devices. Science 285, 867–870 (1999).
5. 5.
Sun, J. Z. Spin-current interaction with a monodomain magnetic body: a model study. Phys. Rev. B 62, 570–578 (2000).
6. 6.
Ohno, H. et al. Electric-field control of ferromagnetism. Nature 408, 944–946 (2000).
7. 7.
Kanai, S. et al. Electric field-induced magnetization reversal in a perpendicular-anisotropy CoFeB-MgO magnetic tunnel junction. Appl. Phys. Lett. 101, 122403 (2012).
8. 8.
Wang, W.-G., Li, M., Hageman, S. & Chien, C. L. Electric-field-assisted switching in magnetic tunnel junctions. Nat. Mater. 11, 64–68 (2012).
9. 9.
Shiota, Y. et al. Induction of coherent magnetization switching in a few atomic layers of FeCo using voltage pulses. Nat. Mater. 11, 39–43 (2012).
10. 10.
Dorrance, R. et al. Diode-MTJ crossbar memory cell using voltage-induced unipolar switching for high-density MRAM. IEEE Electron Device Lett. 34, 753–755 (2013).
11. 11.
Miron, I. M. et al. Perpendicular switching of a single ferromagnetic layer induced by in-plane current injection. Nature 476, 189–193 (2011).
12. 12.
Liu, L. et al. Spin-torque switching with the giant spin hall effect of tantalum. Science 336, 555–558 (2012).
13. 13.
Pai, C.-F. et al. Spin transfer torque devices utilizing the giant spin Hall effect of tungsten. Appl. Phys. Lett. 101, 122404 (2012).
14. 14.
Emori, S., Bauer, U., Ahn, S.-M., Martinez, E. & Beach, G. S. D. Current-driven dynamics of chiral ferromagnetic domain walls. Nat. Mater. 12, 611–616 (2013).
15. 15.
Yamanouchi, M. et al. Three terminal magnetic tunnel junction utilizing the spin hall effect of iridium-doped copper. Appl. Phys. Lett. 102, 212408 (2013).
16. 16.
Lee, S.-W. & Lee, K.-J. Effect of wavy spin-transfer torque on ultrafast unipolar switching of a nanomagnet with out-of-plane polarizer. IEEE Trans. Magn. 47, 3872–3875 (2011).
17. 17.
Kent, A. D., Özyilmaz, B. & Barco, E. D. Spin-transfer-induced precessional magnetization reversal. Appl. Phys. Lett. 84, 3897 (2004).
18. 18.
Papusoi, C. et al. 100 ps precessional spin-transfer switching of a planar magnetic random access memory cell with perpendicular spin polarizer. Appl. Phys. Lett. 95, 072506 (2009).
19. 19.
Kanai, S. et al. Magnetization switching in a CoFeB/MgO magnetic tunnel junction by combining spin-transfer torque and electric field-effect. Appl. Phys. Lett. 104, 212406 (2014).
20. 20.
Park, J., Rowlands, G. E., Lee, O. J., Ralph, D. C. & Buhrman, R. A. Macrospin modeling of sub-ns pulse switching of perpendicularly magnetized free layer via spin-orbit torques for cryogenic memory applications. Appl. Phys. Lett. 105, 102404 (2014).
21. 21.
Legrand, W., Ramaswamy, R., Mishra, R. & Yang, H. Coherent subnanosecond switching of perpendicular magnetization by the fieldlike spin-orbit torque without an external magnetic field. Phys. Rev. Appl. 3, 064012 (2015).
22. 22.
Kanai, S. et al. In-plane magnetic field dependence of electric field-induced magnetization switching. Appl. Phys. Lett. 103, 072408 (2013).
23. 23.
Finocchio, G., Carpentieri, M., Martinez, E. & Azzerboni, B. Switching of a single ferromagnetic layer driven by spin Hall effect. Appl. Phys. Lett. 102, 212410 (2013).
24. 24.
Garello, K. et al. Ultrafast magnetization switching by spin-orbit torques. Appl. Phys. Lett. 105, 212402 (2014).
25. 25.
Fukami, S., Anekawa, T., Zhang, C. & Ohno, H. A spin–orbit torque switching scheme with collinear magnetic easy axis and current configuration. Nat. Nanotech. 11, 621–625 (2016).
26. 26.
Fan, X. et al. Observation of the nonlocal spin-orbital effective field. Nat. Commun. 4, 1799 (2013).
27. 27.
Garello, K. et al. Symmetry and magnitude of spin-orbit torques in ferromagnetic heterostructures. Nat. Nanotech. 8, 587–593 (2013).
28. 28.
Skinner, T. D. et al. Spin-orbit torque opposing the Oersted torque in ultrathin Co/Pt bilayers. Appl. Phys. Lett. 104, 062401 (2014).
29. 29.
Qiu, X. et al. Spin–orbit-torque engineering via oxygen manipulation. Nat. Nanotech. 10, 333–338 (2015).
30. 30.
Lee, O. J. et al. Central role of domain wall depinning for perpendicular magnetization switching driven by spin torque from the spin Hall effect. Phys. Rev. B 89, 024418 (2014).
31. 31.
Zhang, C., Fukami, S., Sato, H., Matsukura, F. & Ohno, H. Spin-orbit torque induced magnetization switching in nano-scale Ta/CoFeB/MgO. Appl. Phys. Lett. 107, 012401 (2015).
32. 32.
Martinez, E. et al. Universal chiral-triggered magnetization switching in confined nanodots. Sci. Rep. 5, 10156 (2015).
33. 33.
Mikuszeit, N. et al. Spin-orbit torque driven chiral magnetization reversal in ultrathin nanostructures. Phys. Rev. B 92, 144424 (2015).
34. 34.
Yu, J. et al. Spin orbit torques and Dzyaloshinskii-Moriya interaction in dual-interfaced Co-Ni multilayers. Sci. Rep. 6, 32629 (2016).
35. 35.
Baumgartner, M. et al. Spatially and time-resolved magnetization dynamics driven by spin–orbit torques. Nat. Nanotech. 12, 980-986 (2017).
36. 36.
Qiu, X. et al. Angular and temperature dependence of current induced spin-orbit effective fields in Ta/CoFeB/MgO nanowires. Sci. Rep. 4, 4491 (2014).
37. 37.
Liu, H. et al. Dynamics of spin torque switching in all-perpendicular spin valve nanopillars. J. Magn. Magn. Mater. 358–359, 233–258 (2014).
38. 38.
Lo Conte, R. et al. Role of B diffusion in the interfacial Dzyaloshinskii-Moriya interaction in Ta/Co20Fe60B20/MgO nanowires. Phys. Rev. B 91, 014433 (2015).
39. 39.
Lee, S.-W. & Lee, K.-J. Magnetization dynamics driven by angle-dependent spin-orbit spin-transfer torque. J. Korean Phys. Soc. 67, 1848–1852 (2015).
40. 40.
Kim, S.-K., Lee, J.-Y., Choi, Y.-S., Guslienko, K. Y. & Lee, K.-S. Underlying mechanism of domain-wall motions in soft magnetic thin-film nanostripes beyond the velocity-breakdown regime. Appl. Phys. Lett. 93, 052503 (2008).
41. 41.
Yoshimura, Y. et al. Soliton-like magnetic domain wall motion induced by the interfacial Dzyaloshinskii-Moriya interaction. Nat. Phys. 12, 157–161 (2016).
42. 42.
Emori, S. et al. Spin Hall torque magnetometry of Dzyaloshinskii domain walls. Phys. Rev. B 90, 184427 (2014).
43. 43.
Pai, C.-F., Mann, M., Tan, A. J. & Beach, G. S. D. Determination of spin torque efficiencies in heterostructures with perpendicular magnetic anisotropy. Phys. Rev. B 93, 144409 (2016).
44. 44.
Yoon, J. et al. Anomalous spin-orbit torque switching due to field-like torque–assisted domain wall reflection. Sci. Adv. 3, e1603099 (2017).
45. 45.
Decker, M. M. et al. Time resolved measurements of the switching trajectory of Pt/Co elements induced by spin-orbit torques. Phys. Rev. Lett. 118, 257201 (2017).
46. 46.
Lee, K.-S., Lee, S.-W., Min, B.-C. & Lee, K.-J. Threshold current for switching of a perpendicular magnetic layer induced by spin Hall effect. Appl. Phys. Lett. 102, 112410 (2013).
47. 47.
Donahue, M. J. & Porter, D. G. OOMMF User’s Guide, Version 1.00, Report no. NISTIR 6376 (National Institute of Standards and Technology, Gaithersburg, MD, 1999).
48. 48.
Khan, R. A. et al. Effect of annealing on the interfacial Dzyaloshinskii-Moriya interaction in Ta/CoFeB/MgO trilayers. Appl. Phys. Lett. 109, 132404 (2016).
## Acknowledgements
This research was supported by the National Research Foundation (NRF), Prime Minister’s Office, Singapore, under its Competitive Research Programme (CRP award no. NRFCRP12-2013-01). J.M.L. thanks S.-W. Lee and K.-J. Lee for useful discussions and J. Yu for helping graphic works.
## Author information
Authors
### Contributions
J.M.L., J.H.K., and H.Y. initiated the project. J.M.L., X.Q., and R.M. deposited and characterized films. J.M.L., J.H.K., and J.S. fabricated devices. J.M.L., J.H.K., and J.B.Y. performed measurements. J.M.L. did micromagnetic simulations. S.S. measured the FMR. K.C. conducted the calculations based on the finite element method. All authors discussed the results. J.M.L., R.R., and H.Y. wrote the manuscript. H.Y. supervised the project.
### Corresponding author
Correspondence to Hyunsoo Yang.
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### Competing interests
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Lee, J.M., Kwon, J.H., Ramaswamy, R. et al. Oscillatory spin-orbit torque switching induced by field-like torques. Commun Phys 1, 2 (2018). https://doi.org/10.1038/s42005-017-0002-3
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https://projecteuclid.org/euclid.kjm/1250692292 | ## Journal of Mathematics of Kyoto University
### Twistor lines on Nagata threefold
Nobuhiro Honda
#### Abstract
We give an explicit description of rational curves in the product of three copies of complex projective lines, which are transformed into twistor lines in M. Nagata’s example of non-projective complete algebraic variety, viewed as the twistor space of Eguchi-Hanson metric. In particular, we show that there exist two families of such curves and both of them are parameterized by mutually diffeomorphic, connected real 4-dimensional manifolds. We also give a relationship between these two families through a birational transformation naturally associated to the Nagata’s example.
#### Article information
Source
J. Math. Kyoto Univ., Volume 47, Number 4 (2007), 837-848.
Dates
First available in Project Euclid: 19 August 2009
https://projecteuclid.org/euclid.kjm/1250692292
Digital Object Identifier
doi:10.1215/kjm/1250692292
Mathematical Reviews number (MathSciNet)
MR2413068
Zentralblatt MATH identifier
1167.32014
Subjects
Primary: 14J30: $3$-folds [See also 32Q25]
#### Citation
Honda, Nobuhiro. Twistor lines on Nagata threefold. J. Math. Kyoto Univ. 47 (2007), no. 4, 837--848. doi:10.1215/kjm/1250692292. https://projecteuclid.org/euclid.kjm/1250692292 | 2019-11-16 23:19:39 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.41616883873939514, "perplexity": 1667.658581508643}, "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/1573496668772.53/warc/CC-MAIN-20191116231644-20191117015644-00359.warc.gz"} |
https://brilliant.org/problems/not-a-normal-question/ | # Not a "normal" question
Calculus Level 3
Sketch the probability density function of a normal distribution with some mean and standard deviation. Call this graph $$f(x)$$.
Define $$g(n)=$$ number of turning points $$f^{(n)}(x)$$ has, where $$f^{(n)}(x)$$ is the $$n^{th}$$ derivative of $$f(x)$$.
What is the value of $$\sum_{n=0}^{20} g(n)$$?
BONUS: can you generalise this for $$\sum_{n=0}^{k} g(n)$$?
× | 2016-10-28 17:47:48 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7155380845069885, "perplexity": 282.542389270148}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-44/segments/1476988725451.13/warc/CC-MAIN-20161020183845-00215-ip-10-171-6-4.ec2.internal.warc.gz"} |
https://dsp.stackexchange.com/questions/35190/how-to-prove-a-2d-filter-is-separable/35192 | # How to Prove a 2D Filter Is Separable?
I want to prove that 2D Gaussian filter is separable and we can separate it into two dimensions, my problem is about the size of filters. we should prove that $G(x,y)*I$(where $G(x,y)=$$\begin{bmatrix}0.01 & 0.1 & 0.01 \\0.1 & 1 & 0.1 \\ 0.01 & 0.1 & 0.01\end{bmatrix},I is image and * is convolution operator) is equal to G(x)*I*G(y) where G(x)=$$\begin{bmatrix}0.1 & 1 & 0.1 \end{bmatrix}$ $,G(y)=$$\begin{bmatrix}0.1\\1\\ 0.1\end{bmatrix}$ and I is image. in other words we should prove that $G(x,y)=G(x)*G(y)$ but I don't know how to convolve these filters with different sizes.
Let's have a different perspective on that.
Let's say our 2D Linear Operator is given by the Matrix $$G \in {\mathbb{R}}^{n \times n}$$.
Using the SVD Decomposition the operator can be written as:
$$G = \sum_{i = 1}^{n} {\sigma}_{i} {u}_{i} {v}_{i}^{T}$$
Separable Linear 2D Operator is defined as operator which can be composed by Outer Product of 2 vectors.
Looking at the SVD Decomposition of $$G$$ we can conclude that $$G$$ is separable operator if and only if $$\forall i > 1 \; {\sigma}_{i} = 0$$ and it is given by:
$$G = {\sigma}_{1} {u}_{1} {v}_{1}^{T}$$
Usually LPF 2D Linear Operators, such as the Gaussian Filter, in the Image Processing world are normalized to have sum of 1 (Keep DC) which suggests $${\sigma}_{1} = 1$$ moreover, they are also symmetric and hence $${u}_{1} = {v}_{1}$$ (If you want, in those cases, it means you can use the Eigen Value Decomposition instead of the SVD).
So basically, to prove that a Linear 2D Operator is Separable you must show that it has only 1 non vanishing singular value.
Note: I was not rigorous in the claims moving form general SVD to the Eigen Decomposition yet the intuition holds for most 2D LPF operators in the Image Processing world.
Given that $G(x)$ is a row vector, while $G(y)$ is a column one, their convolution will be identical to the matrix product $G(x,y)=G(x)*G(y)=G(x)G(y)$. For this reason, as soon as $G(x,y)$ is rank-1, the convolution kernel can be separated (decomposed into two 1-D filters). This is because the other columns of the matrix could be written as a linear combination of the elements of the first.
So to prove that a kernel is separable, just check the rank:
s = svd(G);
sum(s > eps('single')) | 2020-02-18 06:58:48 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 8, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9960156083106995, "perplexity": 1034.0910181808429}, "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/1581875143635.54/warc/CC-MAIN-20200218055414-20200218085414-00018.warc.gz"} |
https://www.gradesaver.com/textbooks/math/algebra/elementary-algebra/chapter-4-proportions-percents-and-solving-inequalities-4-2-percents-and-problem-solving-problem-set-4-2-page-156/46 | ## Elementary Algebra
Her previous job paid 12.00 dollars per hour. Her new job pays 10.20 dollars per hour. To find the percent change, we use the following formula: percent change = $\frac{New\ amount\ -\ Original\ amount}{Original\ amount}$ $\times$ 100% The original salary was 12.00 dollars per hour. The new salary is 10.20 dollars per hour. Substituting these values into the formula yields percent change = $\frac{10.20\ -\ 12.00}{12.00}$ $\times$ 100% percent change = $\frac{-1.80}{12.00}$ $\times$ 100% percent change = -0.15 $\times$ 100% percent change = -15% Because the percent of change is a negative number, it is a percent decrease. | 2018-05-26 04:50:27 | {"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": 0.5049130916595459, "perplexity": 834.072766978052}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-22/segments/1526794867309.73/warc/CC-MAIN-20180526033945-20180526053945-00202.warc.gz"} |
https://www.fishtanklearning.org/curriculum/math/5th-grade/multiplication-and-division-of-decimals/ | Match Fishtank is now Fishtank Learning!
# Multiplication and Division of Decimals
Students use their knowledge of multiplication and division with whole numbers and with fractions to multiply and divide with decimals, and apply this understanding to the context of measurement conversion.
## Unit Summary
In Unit 6, students use their procedural knowledge of multiplication and division with whole numbers, combined with their newly acquired understanding of multiplication and division with fractions, to multiply and divide with decimals, reasoning about the placement of the decimal point. They then apply this to the context of word problems, including those involving measurement conversion.
In Grade 4, students were first introduced to decimal notation for fractions and reasoned about their size (4.NF.5—7). Then, in the first unit in Grade 5, students developed a deeper understanding of decimals as an extension of our place value system, understanding that the relationships of adjacent units apply to decimal numbers, as well (5.NBT.1), and using that understanding to compare, round, and represent decimals in various forms (5.NBT.2—4). Next, students learned to multiply and divide with whole numbers in Unit 2 (5.NBT.5—6), skills upon which decimal computations will rely. In Unit 3, students explored the other two operations with decimals not addressed in this unit: addition and subtraction (5.NBT.7). In Unit 5, students learned to multiply and divide with fractions, including relating fractions to the operation of division; multiplying a fraction by a fraction, including mixed numbers; and dividing a unit fraction by a whole number and vice versa (5.NF.3—7), which will help them make sense of analogous cases of decimal multiplication and division. Thus, this unit is dependent on a lot of prior learning, both in Grade 4 and Grade 5.
This unit starts with multiplying a decimal by a single-digit whole number, then multiplying a decimal by a multi-digit whole number, and finally multiplying a decimal by another decimal. Then, students progress to dividing a decimal by a single-digit whole number, then dividing a decimal by a two-digit whole number, and finally solving cases involving decimal divisors. Throughout these topics, students use the same methods to compute decimal products and quotients as they did for whole-number products and quotients, but they must reason about the placement of the decimal point. It is only in the last lesson of each topic that students generalize the pattern of the placement of the decimal point. The various lines of reasoning, and their advantages and disadvantages, can be read on pages 19 and 20 of the NBT Progression linked in the “Unit-Specific Intellectual Preparation” section. Students also solve myriad word problems as well as write and solve expressions involving decimals as a way to support the major work (5.OA.1, 5.OA.2). Finally, the unit closes with students learning to convert among different-sized customary measurement units within a given measurement system and solve word problems that use those conversions (5.MD.1), which extends the work from Grade 4 of converting from a larger unit of measurement to a smaller one in Grade 4 (4.MD.1—2). As noted in the Progressions, “this is an excellent opportunity to reinforce notions of place value for whole numbers and decimals, and the connection between fractions and decimals (e.g., meters can be expressed as 2.5 meters or 250 centimeters)” (GM Progression, p. 26), as well as computations with these types of numbers (5.NBT.7, 5.NF), thus connecting the work of unit conversion with major work of the grade.
Reasoning about the placement of the decimal point affords students many opportunities to engage in mathematical practice, such as constructing viable arguments and critiquing the reasoning of others (MP.3) and looking for and expressing regularity in repeated reasoning (MP.8). For example, “students can summarize the results of their reasoning as specific numerical patterns and then as one general overall pattern such as ‘the number of decimal places in the product is the sum of the number of decimal places in each factor’” (NBT Progression, p. 20).
In Grade 6, students will become fluent with all decimals computations that they’ve developed in Grade 5 (6.NS.3). In Grade 7, students will also learn that every fraction can be represented with a decimal that either terminates or repeats. Then in Grade 8, students learn that terminating and repeating decimals are rational numbers and that there are numbers that are irrational whose decimal expansion does not repeat. Then, students use the work they start in this unit in Grade 8 in the context of scientific notation. Thus, this unit has many interesting connections and applications for many years to come.
Pacing: 27 instructional days (24 lessons, 2 flex days, 1 assessment day)
For guidance on adjusting the pacing for the 2020-2021 school year due to school closures, see our 5th Grade Scope and Sequence Recommended Adjustments.
• Expanded Assessment Package
• Problem Sets for Each Lesson
• Student Handout Editor
• Vocabulary Package
## Assessment
This assessment accompanies Unit 6 and should be given on the suggested assessment day or after completing the unit.
## Unit Prep
### Intellectual Prep
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Intellectual Prep for All Units
• Read and annotate “Unit Summary” and “Essential Understandings” portion of the unit plan.
• Do all the Target Tasks and annotate them with the “Unit Summary” and “Essential Understandings” in mind.
• Take the unit assessment.
Unit-specific Intellectual Prep
### Essential Understandings
?
• General methods used for computing products and quotients of whole numbers extend to products and quotients of decimals, with the additional issue of placing a decimal point in the solution. There are several lines of reasoning that students can use to explain the placement of the decimal point in products and quotients of decimals.
• Students may use estimation to assess the reasonableness of their solution. As with whole-number computation, some computational estimates can be better than others, depending on what numbers are chosen to use in place of the actual values. Using estimation to place the decimal point, however, isn’t always a reliable strategy, especially in cases they will see in later grades such as ${0.0043 \times 0.00078}$.
• When multiplying, it is more efficient to decompose the value with fewer digits. In the standard algorithm, this means writing the number with fewer digits on the bottom. With decimals, the number with fewer digits does not always imply the number with the smallest value (e.g., ${17.15 \times 42}$).
### Vocabulary
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conversion factor
### Unit Materials, Representations and Tools
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• Area models
• Standard algorithm for multiplication
• Standard algorithm for division
• Tape diagrams
• Grade 5 MCAS Reference Sheet (or the conversion rates reference sheet of your choosing)
#### Unit Practice
With Fishtank Plus you can access our Daily Word Problem Practice and our content-aligned Fluency Activities created to help students strengthen their application and fluency skills.
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## Common Core Standards
Key: Major Cluster Supporting Cluster Additional Cluster
### Core Standards
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##### Measurement and Data
• 5.MD.A.1 — Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems.
##### Number and Operations in Base Ten
• 5.NBT.B.7 — Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.
##### Operations and Algebraic Thinking
• 5.OA.A.1 — Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.
• 5.OA.A.2 — Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, express the calculation "add 8 and 7, then multiply by 2" as 2 × (8 + 7). Recognize that 3 × (18932 + 921) is three times as large as 18932 + 921, without having to calculate the indicated sum or product.
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• 4.MD.A.1
• 4.MD.A.2
• 5.NBT.A.1
• 5.NBT.A.2
• 5.NBT.B.5
• 5.NBT.B.6
• 5.NF.B.3
• 5.NF.B.4
• 5.NF.B.7
?
• 6.EE.A.2
• 6.EE.A.3
• 6.EE.A.4
• 6.NS.B.3
• 6.NS.B.4
### Standards for Mathematical Practice
• CCSS.MATH.PRACTICE.MP1 — Make sense of problems and persevere in solving them.
• CCSS.MATH.PRACTICE.MP2 — Reason abstractly and quantitatively.
• CCSS.MATH.PRACTICE.MP3 — Construct viable arguments and critique the reasoning of others.
• CCSS.MATH.PRACTICE.MP4 — Model with mathematics.
• CCSS.MATH.PRACTICE.MP5 — Use appropriate tools strategically.
• CCSS.MATH.PRACTICE.MP6 — Attend to precision.
• CCSS.MATH.PRACTICE.MP7 — Look for and make use of structure.
• CCSS.MATH.PRACTICE.MP8 — Look for and express regularity in repeated reasoning. | 2021-01-18 08:10:39 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5280576348304749, "perplexity": 1803.8472478759686}, "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/1610703514423.60/warc/CC-MAIN-20210118061434-20210118091434-00571.warc.gz"} |
http://openstudy.com/updates/4d71b39edd6e8b0b72a5e440 | • anonymous
a. μ = 80 and σ = 10 b. μ = 80 and σ = 5 c. μ = 105 and σ = 10 d. μ = 105 and σ = 5 Make sure to indicate the direction (sign) of the z-scores.
Mathematics
Looking for something else?
Not the answer you are looking for? Search for more explanations. | 2017-03-30 12:43:23 | {"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": 0.9251695871353149, "perplexity": 591.6940183629825}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-13/segments/1490218194600.27/warc/CC-MAIN-20170322212954-00399-ip-10-233-31-227.ec2.internal.warc.gz"} |
https://andromedageek.wordpress.com/2015/01/11/part-3-early-nuclear-physics-einsteins-equation-between-mass-and-energy/ | ## How does the Sun shine? (Part 3: Early nuclear physics – Einstein’s equation between mass and energy)
In 1905, from the special theory of relativity, Einstein showed that a tiny amount of mass could, in principle, be converted into a tremendous amount of energy: $E = mc^{2}$. Einstein’s famous equation generalized and extended the 19th century law of conservation of energy of Von Helmholtz and Mayer to include the conversion of mass into energy.
Following Einstein’s equation, it became clear that the Sun’s luminosity had to be explained by something completely different than everything imagined before. A process that would include the conversion of mass into energy. A process like “burning” but that would release much more energy per atom, and the speed of the “burning” would be much slower in order for the lifetime of the Sun to be consistent with the “known” age of the earth at that time based on evidence found in layers of rock.
In the late 19th century, from the knowledge of thermodynamics on heat transfer, most physicists had thought that heat was transported from the interior of the Sun to the exterior of the Sun by convection (transfer of energy by vibrations at a molecular level through a solid or fluid). But in 1894, R. A. Sampson suggested that the primary mechanism of heat transfer was radiation (the transfer of energy through electromagnetic waves). It will have to wait 30 years but this idea was eventually reused by Arthur Eddington.
In 1920, a lot of new discoveries were made. First, Eddington used the concept of radiative equilibrium to calculate the temperature at the center of the Sun and found it to be about 39 million K. Second, another scientist, Francis William Aston experimentally discovered by “accident”, since this was not the original goal of his experiment, a mass “deficit”. Using mass spectrometry, he made precise measurements of the masses of many different atoms, among them hydrogen and helium. Aston found that four hydrogen nuclei were heavier than a helium nucleus. This was not the principal goal of the experiments he performed, he was instead looking for isotopes of neon. Third, yet another scientist, Cecilia Payne, showed that hydrogen and helium were the most abundant elements in the stars (and our Sun).
In 1935, Eddington reduced his temperature estimate for the center of the Sun to 19 million K. However, Eddington’s first calculations back in 1920 made no assumption on how the Sun’s heat was produced: he proposed 2 alternative mechanisms: the mutual annihilation of protons and electrons OR the fusion of hydrogen atoms into helium atoms in some unknown manner (also called Eddington’s thermonuclear hypothesis).
Eddington’s thermonuclear hypothesis was directly inspired by Einstein’s equation and Aston’s discovery of a mass deficit. The importance of Aston’s measurements was immediately recognized by Eddington. The mass difference between hydrogen and helium meant that the sun could shine by converting hydrogen atoms to helium. This burning of hydrogen into helium would (according to Einstein’s equation) release about 0.7% of the mass equivalent of the energy. In principle, this could allow the sun to shine for about a 100 billion years.
The final piece of the puzzle and the first detailed explanations of the thermonuclear mechanism that Eddington hypothesized were published around 1938. There are actually 2 fusion reactions that were discovered: the proton-proton chain reaction and the CNO cycle (for carbon–nitrogen–oxygen).
The proton-proton chain reaction came from a group of scientists (Edward Teller, Charles Critchfield, Hans Bethe, George Gamow). They explained how energy could be produced at high temperatures by a chain reaction starting with proton-proton collisions and ending with the synthesis of helium nuclei. (see Charles Critchfield’s entry on Wikipedia)
The CNO cycle was independently proposed by Carl von Weizsäcker and Hans Bethe in 1938 and 1939, respectively.
Without going into details, the CNO cycle is the dominant source of energy in stars more massive than about 1.3 times the mass of the Sun, and the proton–proton chain is more important in stars the mass of the Sun or less (to be investigated further in another article).
Sources: Wikipedia and Encyclopedia of the Solar System. McFadden, Weissman, Johnson (2007) | 2017-10-21 10:28:13 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 1, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.719690203666687, "perplexity": 648.9025759924418}, "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/1508187824733.32/warc/CC-MAIN-20171021095939-20171021115939-00448.warc.gz"} |
https://ai.stackexchange.com/questions/31532/reinforce-differentiation-on-sum-or-single-value | # REINFORCE differentiation on sum or single value?
I'm currently learning Policy-gradient Methods for RL and encountered REINFORCE algorithm. I learned from this site : https://towardsdatascience.com/policy-gradient-methods-104c783251e0 that the gradient of the objective function is calculated as follows:
From what I understand $$\sum_{t=0}^{H}\nabla_{\theta}\log{\pi_{\theta}(a_{t}|s_{t})}$$ is the sum through the entire trajectory and $$\pi_{\theta}(a_{t}|s_{t})$$ is the policy of the agent at time step $$t$$. However in Suton's book the gradient objective is defined differently.
There is only $$\nabla \ln{\pi(A_t | S_t)}$$ at time step $$t$$ and no sum of all time steps. So does the algorithm not consider the policy for the whole trajectory when updating? Only a single-step policy?
Furthermore, there is $$\gamma^{t}$$ (discounted reward) term in the latter and not the former. What is the reason for that?
Hopefully, someone can help me clarify this.
• the site you learn from accumulates the gradient at each action taken in the episode via the sum and performs a single gradient ascent step for all these actions (this is analogous to taking the loss over a batch before performing a gradient update in supervised learning), whereas Sutton and Barto perform a gradient ascent step for every action taken (analogous to performing a gradient update for every single data point individually in supervised learning). Sep 3 at 22:16
• @norbertk thanks, I missed the bit of the question about the second discount term. OP, essentially the second discount term is needed because you also need to discount your state distribution. This is rarely done in practice but it is theoretically incorrect to omit it, and this paper shows without the second discount factor the gradient is not actually a gradient at all. Sep 4 at 8:54
• Hello. Welcome to AI SE. Rather than writing "Help with understanding the REINFORCE algorithm", please, just put your specific question in the title.
– nbro
Sep 6 at 11:10 | 2021-10-25 03:37:47 | {"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": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 6, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6791770458221436, "perplexity": 783.0981162268854}, "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/1634323587623.1/warc/CC-MAIN-20211025030510-20211025060510-00202.warc.gz"} |
https://en.universaldenker.org/illustrations/1400 | A rotating rigid disk with moment of inertia $$I$$ has angular momentum $$L$$ and angular velocity $$\omega$$ due to rotation. Both point in the same direction. | 2022-10-04 13:24:56 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8924469947814941, "perplexity": 101.66771783967792}, "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/1664030337504.21/warc/CC-MAIN-20221004121345-20221004151345-00327.warc.gz"} |
https://stacks.math.columbia.edu/tag/02TH | Lemma 42.27.1. Let $(S, \delta )$ be as in Situation 42.7.1. Let $X$ be locally of finite type over $S$. Assume $X$ integral and $\dim _\delta (X) = n$. Let $\mathcal{L}$, $\mathcal{N}$ be invertible on $X$. Choose a nonzero meromorphic section $s$ of $\mathcal{L}$ and a nonzero meromorphic section $t$ of $\mathcal{N}$. Set $\alpha = \text{div}_\mathcal {L}(s)$ and $\beta = \text{div}_\mathcal {N}(t)$. Then
$c_1(\mathcal{N}) \cap \alpha = c_1(\mathcal{L}) \cap \beta$
in $\mathop{\mathrm{CH}}\nolimits _{n - 2}(X)$.
Proof. Immediate from the key Lemma 42.26.1 and the discussion preceding it. $\square$
There are also:
• 2 comment(s) on Section 42.27: Intersecting with an invertible sheaf and rational equivalence
In your comment you can use Markdown and LaTeX style mathematics (enclose it like $\pi$). A preview option is available if you wish to see how it works out (just click on the eye in the toolbar). | 2022-01-23 16:14:12 | {"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": 2, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 2, "x-ck12": 0, "texerror": 0, "math_score": 0.9868577122688293, "perplexity": 393.3194324253503}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-05/segments/1642320304287.0/warc/CC-MAIN-20220123141754-20220123171754-00349.warc.gz"} |
https://galoisrepresentations.wordpress.com/2017/07/29/msri-now/ | ## MSRI Now
Continuing on the theme of the last post (Buzzard related viral videos), you can now view Buzzard’s MSRI course (in progress at the time of this post) online here. Having previously excoriated MSRI for restricting how many people can attend such workshops, I must now congratulate them on doing an excellent job in the audio-visual department and making the lectures available to everyone. Students at many levels could learn a lot by watching these and making an honest effort to think about the (implicit) exercises. Even if you know the material, it is still fun to watch; a little like your cool uncle telling you a familiar bedside story but with his own subversive twist. For various psychological reasons, I suspect that those watching the videos now as they come out will have a lower dropout rate than those who watch them later. So go watch them now! (Unless you are a student at Brown, of course.)
Kevin is always refreshingly honest about things he was confused by as a student (or is still confused by now), although sometimes it is reminiscent of Volodya “reminding” almost every speaker at the start of his seminar that his is a beginner and so the speaker will have to go very slowly. Along those lines, here are some (very) tangential remarks on the lectures so far.
When I was a student, I always got very confused when someone talked about the “closure” of the commutator subgroup [G,G]. The basic problem was that I couldn’t conceive of taking the quotient of $\widehat{\mathbf{Z}}$ by 1 and getting anything other than the trivial group. Of course that is what you should get unless you are doing it wrong, because anyone who thinks about profinite groups as abstract groups are probably crazy.
That said, here’s an idle question: is the commutator subgroup [W,W] of the the Weil group of a local field K actually already closed? I believe that the corresponding result for the (local) Galois group G itself is positive (essentially as a consequence of the fact that G is a finitely generated pro-finite group), but W has a distinctly non-compact quotient $\mathbf{Z},$ so I’m not sure. Maybe this is an easy question, I don’t know.
Another random fact: I was a graduate student at Berkeley in 2000 when Richard gave a colloquium on the local Langlands conjectures for GL(n). One aspect of the talk I remember was Richard defining the p-adic numbers, to which Mariusz Wodzicki cried out: “excuse me, this is Berkeley, do you really think you need to define the p-adic numbers?.” At this point, someone else cried out “Yes!” and the talk continued as planned. But the part of this story that is relevant here is that I somehow internalized (either at this talk or before) the fact that, long before Harris-Taylor, the local Langlands conjectures had been proved for GL(n) when p > n (which mirrors the story for n = 2). But I was surpised to find out recently (i.e. this week) that this result was not something from the distant past, but rather was a theorem of 1998 from (friend of the blog) Michael Harris in Inventiones.
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### 2 Responses to MSRI Now
1. Anyone who wants to see a video featuring both me and Tamzin can, as of today, now try this one : https://www.youtube.com/watch?v=S_MKfWgGrJQ (also featuring my [our] daughter, and her father — there’s a theme). I will be wearing the same trousers for Monday’s lectures by the way.
2. Yiftach says:
“anyone who thinks about profinite groups as abstract groups are probably crazy.” You might like to check “On normal subgroups of compact groups” by Nik Nikolov and Dan Segal, for example, and of course their solution to the Serre problem (conjecture). According to your statement Serre is probably crazy and so are many group theorists (well, you might be right about that one). | 2018-06-21 21:44:00 | {"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": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 2, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6227930784225464, "perplexity": 921.2526239112939}, "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/1529267864300.98/warc/CC-MAIN-20180621211603-20180621231603-00576.warc.gz"} |
https://math.stackexchange.com/questions/2937235/proof-for-relation-between-p-adic-valution-of-the-total-number-of-divisors-and-t | # Proof for relation between p-adic valution of the total number of divisors and the sum of multiplicities
The final point $$(9)$$ is the lemma that I am establishing a proof for, all the relevant lemma are there I guess I just need help fine tuning things, Although I have no idea how I will prove $$(10)$$ if indeed it is true for all primes.
Consider the Unique prime factorization of a natural number $$n$$:
$$n=\prod _{j=1}^{\omega \left( n \right) }{p_{{n,j}}}^{\nu_{{n,j}}}\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad(0)$$
One could, in a heuristic sense, expect that the sum of all sums up to and including the multiplicity of all the distinct prime factors of $$n$$ will have proportion to the total number of divisors of $$n$$ somehow.
So we begin by defining the sum of the multiplicities of the unique prime factors of $$n$$:
$$\Upsilon \left( n \right) =\sum _{j=1}^{\omega \left( n \right) }\nu_{ {n,j}} \quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad(1)$$
$$\sum _{k=1}^{\Upsilon \left( n \right) +1}{\frac { \left( \Upsilon \left( n \right) +1 \right) !}{k!\, \left( \Upsilon \left( n \right) -k+1 \right) !}}=2^{\Upsilon \left( n \right) +1}-1 \quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad(2)$$
$${\Biggl\{\frac {{2}^{n} \left( {2}^{\Upsilon \left( n \right) +1}-1+{\it \gcd} \left( {2}^{\Upsilon \left( n \right) +1}-1,\tau \left( n \right) \right) \right) }{{\it \gcd} \left( {2}^{\Upsilon \left( n \right) +1},\tau \left( n \right) \right) }} \Biggr\}=0\quad\quad\quad\quad\quad\quad\quad\quad\quad(3)$$
$${\Biggl\{\frac {\tau(n)\left( {2}^{\Upsilon \left( n \right) +1}-1+{\it \gcd} \left( {2}^{\Upsilon \left( n \right) +1}-1,\tau \left( n \right) \right) \right) }{2{\it \gcd} \left( {2}^{\Upsilon \left( n \right) +1},\tau \left( n \right) \right) }} \Biggr\}=0\quad\quad\quad\quad\quad\quad(4)$$
$${\Biggl\{\frac {{2}^{n} }{{\it \gcd} \left( {2}^{\Upsilon \left( n \right) +1},\tau \left( n \right) \right) }} \Biggr\}=0\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad(5)$$
$${\Biggl\{\frac {\tau(n)\left( {2}^{\Upsilon \left( n \right) +1}-1 \right) }{2{\it \gcd} \left( {2}^{\Upsilon \left( n \right) +1},\tau \left( n \right) \right) }} \Biggr\}=\frac{1}{2}\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad(6)$$
$$\exists k \in \mathbb N \land k \gt 1\quad \operatorname{s.t} \sqrt{n}=k \Rightarrow \quad{\Biggl\{\frac {\tau(n)\left({\it \gcd} \left( {2}^{\Upsilon \left( n \right) +1},\tau \left( n \right) \right) \right) }{2{\it \gcd} \left( {2}^{\Upsilon \left( n \right) +1}-1,\tau \left( n \right) \right) }} \Biggr\}=\frac{1}{2}\quad\quad\quad(7)$$
$$\not\exists k \in \mathbb N \land k \gt 1 \quad\operatorname{s.t} \sqrt{n}=k \Rightarrow \quad{\Biggl\{\frac {\tau(n)\left({\it \gcd} \left( {2}^{\Upsilon \left( n \right) +1},\tau \left( n \right) \right) \right) }{2{\it \gcd} \left( {2}^{\Upsilon \left( n \right) +1}-1,\tau \left( n \right) \right) }} \Biggr\}=0\quad\quad\quad(8)$$
$$\exists k \in \mathbb N \land k \gt 1 \quad\operatorname{s.t} \sqrt{n}=k \Rightarrow{\Biggl\{\frac{{\it \gcd} \left( {2}^{\Upsilon \left( n \right) +1},\tau \left( n \right) \right)}{2}}\Biggr\}=\frac{1}{2}\quad\quad\quad(7\operatorname{i})$$
$$\not\exists k \in \mathbb N \land k \gt 1\quad \operatorname{s.t} \sqrt{n}=k \Rightarrow{\Biggl\{\frac{{\it \gcd} \left( {2}^{\Upsilon \left( n \right) +1},\tau \left( n \right) \right)}{2}}\Biggr\}=0\quad\quad\quad(8\operatorname{i})$$
Where $${\{x}\}$$ is the fractional part of $$x$$.
Where $$\tau(n)$$ is the total number of divisors of $$x$$.
The 2-adic valuation of the total number of divisors of $$n$$ can also be expressed in term of the sum of the multiplicities of the unique prime factors of $$n$$:
$$\nu_{{2}} \left( \tau(n) \right)=\frac{\ln(\gcd(2^{\Upsilon \left( n \right)+1},\tau(n)))}{\ln(2)}\quad\quad\quad(9)$$
The generalization to the p-adic valuation of the total number of divisors of $$n$$ also seems to be true: $$\nu_{{p}} \left( \tau(n) \right)=\frac{\ln(\gcd(p^{\Upsilon \left( n \right)+1},\tau(n)))}{\ln(p)}\quad\quad\quad(10)$$
Indeed, the following generalizations to any $$p$$ would appear to be true , giving more substance to the truth value of $$(10)$$,I am too tired to use my talking words tbh:
$${\Biggl\{\frac {\tau(n)\left( {p}^{\Upsilon \left( n \right) +1}-1+{\it \gcd} \left( {p}^{\Upsilon \left( n \right) +1}-1,\tau \left( n \right) \right) \right) }{{\it \gcd} \left( {p}^{\Upsilon \left( n \right) +1},\tau \left( n \right) \right) }} \Biggr\}=0\quad\quad\quad\quad\quad\quad(4\operatorname{i})$$
$${\Biggl\{\frac {{p}^{n} }{{\it \gcd} \left( {p}^{\Upsilon \left( n \right) +1},\tau \left( n \right) \right) }} \Biggr\}=0\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad(5\operatorname{i})$$
$${\Biggl\{\frac {{\it \gcd} \left( {p}^{\Upsilon \left( n \right) +1},\tau \left( n \right) \right) }{{p}^{\Upsilon \left( n \right)-n+1} }} \Biggr\}=0\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad(5\operatorname{ii})$$
$$1 \leq {\frac {\tau(n)\left( {p}^{\Upsilon \left( n \right) +1}-1 \right) }{\gcd\left( {p}^{\Upsilon \left( n \right) +1},\tau \left( n \right) \right) }}-p\Biggl\lfloor {\frac {\tau(n)\left( {p}^{\Upsilon \left( n \right) +1}-1 \right) }{p\gcd\left( {p}^{\Upsilon \left( n \right) +1},\tau \left( n \right) \right) }} \Biggr\rfloor \leq p-1\quad\quad\quad\quad\quad\quad(11)$$
• What you have in mind is unclear, if $n$ is squarefree it simplifies a lot since $\tau(n) = 2^{\omega(n)}$ – reuns Sep 30 '18 at 23:36
• In the case that $n$ is square free yes we have $\Upsilon \left( n \right)=\omega(n)$ you are correct, but I don't understand what you are referring to when you say "it" simplifies, seeing that the relation I have posted the discussion about is for the p-adic valuation for $\tau(n)$, which is obviously going to be equal to $1$ for all $p$ that divide $\tau(n)$ and $0$ for those that don't in the case that $n$ is square free – Adam Sep 30 '18 at 23:56
• Well yes the sum of the multiplicities of the unique prime factors of a number is going to be greater than or equal to the p-adic valuation for any particular prime number, but the fact that this is the total number of divisors I think requires more than that. Also, a divisibility relation cannot be simply justified with an inequality in my opinion, but I'm also not entirely sure of what else I want as proof over and above it – Adam Oct 1 '18 at 0:28
• I think the inequality $(11)$ that I just included into the post now is probably the most important part that needs rigorous proof at this point – Adam Oct 1 '18 at 0:39
Summing up my comments and filling in some gaps:
To show (10) (which includes (9) as a special case):
For any prime $$p$$ and integer $$x$$, by definition of the $$p$$-adic value, we have $$\nu_p(x)=\log_p(\gcd(p^r,x))$$ if and only if $$r$$ is an integer $$\ge \nu_p(x)$$. So equation (10) boils down to the claim that $$\Upsilon(n)+1≥\nu_p(\tau(n))$$ for all $$p$$ and $$n$$.
Now to see this, use that $$\displaystyle \tau(n) = \prod_{j=1}^{\omega(n)} (\nu_{n,j}+1)$$ (according to wikipedia, where $$\tau$$ is called $$\sigma_0$$). So for any $$p$$,
$$\nu_p(\tau(n)) = \sum_{j=1}^{\omega(n)} \nu_p(\nu_{n,j}+1)$$
Now for any integer $$a$$ and prime $$p$$, we have $$\nu_p(a) \le a-1$$, hence we even have the stronger
$$\nu_p(\tau(n)) \le \sum_{j=1}^{\omega(n)} \nu_{n,j} =\Upsilon(n).$$
To show (11):
Calling $$x=$$ the first fraction in (11), and looking at the function $$f(x)=x−p \lfloor x/p\rfloor$$, shows that (11) is equivalent to $$x$$ not being within any of the intervals $$(kp−1,kp+1)$$ with $$k \in \Bbb Z$$. Since the denominator of $$x$$ divides $$\tau(n)$$, the fraction $$x$$ is actually an integer itself, so the claim is equivalent to $$x$$ not being of the form $$kp$$ with $$k \in \Bbb Z$$.
This in turn is true by (10), since according to that, the denominator of $$x$$ is exactly $$p^{\nu_p(\tau(n))}$$, which exactly cancels the powers of $$p$$ that are in $$\tau(n)$$, and the other factor $$(p^{whatever}-1)$$ is obviously not divisible by $$p$$.
• Ok so my only remaining issue is then those I have labelled $(7\operatorname{i})$ & $(8\operatorname{i})$ – Adam Oct 3 '18 at 2:57
• Note that the formula I quoted from WP shows that if $n$ is a square, $\tau(n)$ is odd. This easily proves both 7i and 8i. – Torsten Schoeneberg Oct 3 '18 at 3:12
• Ok thankyou so much for your assistance Torsten I can see now this was far more straight forward than the considerations I had been previously considering – Adam Oct 10 '18 at 21:52 | 2019-10-16 04:48:01 | {"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": 67, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8867833614349365, "perplexity": 112.57630659754474}, "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/1570986664662.15/warc/CC-MAIN-20191016041344-20191016064844-00455.warc.gz"} |
https://math.stackexchange.com/questions/2611894/a-property-of-orthogonal-matrices?noredirect=1 | # A property of orthogonal matrices
Let $R$ be a $3\times 3$ orthogonal matrix. Let $v$ be the unit vector such that $Rv=v$ (upto sign change). Consider any unit vector $u$ such that $u^{T}v=0$ where $T$ stands for transpose. Show that $u^{T}Ru = \frac12(trace(R)-1)$.
The problem arises in finding the angle of rotation given a rotation-transformation matrix. The vector $v$ would be the axis of rotation since it is invariant under the transformation $R$. The angle of rotation can be obtained by observing how much $u$ rotated by. That is, $\cos(\theta)=u^TRu$ where $\theta$ is the rotation angle. I'm not able to understand how the trace of $R$ enters the formula.
## 2 Answers
Analyze Rodrigues formula for rotation.
Let it be in a such form: $R(v,\theta)=I+\sin(\theta)S(v)+(1-\cos(\theta))S^2(v)$.
The expression $\sin(\theta)S(v)$ is the skew-symmetrical part of rotation $R$,
$I+(1-\cos(\theta))S^2(v)$ is its symmetrical part.
Trace of any skew-symmetrical matrix is equal $0$ so $\text{trace}(R)=\text{trace}(\text{sym(R)})$.
Additionally $S^2(v)=vv^T-I$, where $\Vert v \Vert=1$, - notice that in this case we have also $\text{trace}(vv^T)=1$.
Now calculating $\text{trace}(R)$ we obtain
$\text{trace}(R) =\text{trace} (I)+\text{trace}((1-\cos(\theta))(vv^T-I))=3-2(1-\cos(\theta))$.
Hence $\text{trace}(R)=1+2 \cos(\theta)$
It can be also other way of proving it.
Rotation matrix $R$ could be transformed to the other basis where axis of rotation would be z-axis.
Such operation doesn't affect the trace
(algebraically it is expressed as $R(v,\theta)=R_{Trans}R(z,\theta)R_{Trans}^{-1}$ ).
For rotation about z-axis we have $R(z,\theta)=\begin{bmatrix}\cos(\theta) & -\sin (\theta) & 0 \\ \sin (\theta) & \cos (\theta) & 0 \\ 0 & 0 & 1 \end{bmatrix}$.
From it $\text{trace}(R)=1+2 \cos(\theta)$ follows.
You did not say explicitly, but I am assuming your orthogonal matrix is real. The norm of the eigenvalues are 1 for orthogonal matrices and complex eigenvalues for real matrices come in conjugate pairs. Combining these two facts with $Rv=v$ (eigenvalue 1, no sign change!), we have that the eigenvalues for $R$ are: ${e^{i\theta},e^{-i\theta},1}$. Then $$\frac{1}{2}(trace(R)-1)=\frac{1}{2}(e^{i\theta}+e^{-i\theta}+1-1)=\cos(\theta)=u^TRu.$$
• Very compact proof, but should not we prove additionally that $\theta$ from $e^{i\theta}$ is the same as an angle of rotation? – Widawensen Jan 20 '18 at 13:47
• It is the same as you can see in the answer to this question: math.stackexchange.com/questions/973987/… – jobe Jan 20 '18 at 19:06 | 2019-11-22 08:30:56 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9695329070091248, "perplexity": 159.65636381785643}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-47/segments/1573496671245.92/warc/CC-MAIN-20191122065327-20191122093327-00005.warc.gz"} |
https://uk.mathworks.com/help/signal/ref/issingle.html | Documentation
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issingle
Determine if digital filter coefficients are single precision
Syntax
``````flag = issingle(d)``````
Description
example
``````flag = issingle(d)``` returns `true` if the coefficients of a digital filter, `d`, are single precision.```
Examples
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Use `designfilt` to design a 6th-order highpass IIR filter. Specify a normalized passband frequency of $0.6\pi$ rad/sample. Convert it to a single-precision filter. Identify the precision in each case.
```fd = designfilt('highpassiir','FilterOrder',6,'PassbandFrequency',0.6); isd = issingle(fd)```
```isd = logical 0 ```
```fs = single(fd); iss = issingle(fs)```
```iss = logical 1 ```
Input Arguments
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Digital filter, specified as a `digitalFilter` object. Use `designfilt` to generate `d` based on frequency-response specifications. If you want a single-precision filter, apply `single` to the output of `designfilt`.
Example: `d = designfilt('lowpassiir','FilterOrder',3,'HalfPowerFrequency',0.5)` specifies a third-order Butterworth filter with normalized 3-dB frequency 0.5π rad/sample.
Output Arguments
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Type identification, returned as a logical scalar.
Download ebook | 2019-05-19 20:51:54 | {"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": 0.4213126003742218, "perplexity": 9626.850514960368}, "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-2019-22/segments/1558232255165.2/warc/CC-MAIN-20190519201521-20190519223521-00440.warc.gz"} |
https://cracku.in/19-aparna-changes-the-marked-price-of-an-item-to-50-a-x-rrb-ntpc-12-april-2016-shift-3 | Question 19
# Aparna changes the marked price of an item to 50% above its C.P. What % of discount allowed in approximately to gain 10%?
Solution
Let CP =100
MP=150
SP=110
DISCOUNT=150-110=40
% DISCOUNT=$$(40\div 150)\times 100$$=26.67% | 2022-08-10 17:10:27 | {"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": 0.36039847135543823, "perplexity": 10483.036649919943}, "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/1659882571198.57/warc/CC-MAIN-20220810161541-20220810191541-00470.warc.gz"} |
https://www.albert.io/learn/sat-math-1-and-2-subject-test/question/exponential-regression | Limited access
The population of a town in the year 1990 was $2800$ people. In 1995, it was $3200$, 2000 it was $3800$, and in 2005 it was $5500$ people.
Based on the exponential regression equation, what is the percent annual growth of the town's population
A
$3\%$
B
$4\%$
C
$5\%$
D
$6\%$
E
$7\%$
Select an assignment template | 2017-03-30 06:46:36 | {"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": 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": 0.22379207611083984, "perplexity": 920.2272887360144}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-13/segments/1490218193284.93/warc/CC-MAIN-20170322212953-00420-ip-10-233-31-227.ec2.internal.warc.gz"} |
https://brilliant.org/problems/adding-arctan-2/ | Geometry Level 4
$\large \sum_{n=0}^\infty \text{arctan} \left( \dfrac1{n^2+n+1} \right)$
If the value of the summation above is in the form of $$\dfrac da \pi ^y$$, where $$a,d$$ and $$y$$ are positive integers with $$a,d$$ coprime, find $$d+a+y$$.
× | 2018-07-18 18:43:56 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9190708994865417, "perplexity": 141.23348154075123}, "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/1531676590314.29/warc/CC-MAIN-20180718174111-20180718194111-00472.warc.gz"} |
https://ricardo-saenz.blog.ucol.mx/2018/09/homework-4-real-analysis.html | Ir al contenido principal
## Due September 14
### Problem 1
1. If the measurable $f_n\searrow f\ge 0$ with $\int f_1 < \infty$, then $\int f_n \to \int f.$
2. Explain the condition $\int f_1 < \infty$.
### Problem 2
1. There exists a positive continuous $f \in L^1(\R)$ such that $\limsup_{|x|\to\infty} f(x) = \infty.$
2. If $f\in L^1(\R)$ is uniformly continuous, then $\lim_{|x|\to\infty}f(x) = 0.$
### Problem 3
If $f\in L^1(\R)$ and $F(x) = \int_{-\infty}^x f$. Then F is uniformly continuous.
### Problem 4
Let $f:D\to\R$ be uniformly continuous, with $D\subset\R$.
1. If $x_0$ is a limit point of D, then f has limit at $x_0$.
2. f has a continuous extension to $\bar D$, the closure of D. | 2022-10-05 08:53:21 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9950270056724548, "perplexity": 873.202246482418}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-40/segments/1664030337595.1/warc/CC-MAIN-20221005073953-20221005103953-00347.warc.gz"} |
https://questions.kunduz.com/inorganic-chemistry/preparation-and-properties-of-compounds/write-the-balanced-chemical-equation-for-each-of-the-reactions-include-phases-when-aqueous-sodium-hydroxide-is-added-to-a-solu-21041516 | Question:
# Write the balanced chemical equation for each of the reactions. Include phases. 1. When aqueous sodium hydroxide is added to a solution containing lead(II) nitrate, a solid precipitate forms. equatio
Write the balanced chemical equation for each of the reactions. Include phases. 1. When aqueous sodium hydroxide is added to a solution containing lead(II) nitrate, a solid precipitate forms. equation: 2. However, when additional aqueous hydroxide is added, the precipitate redissolves, forming a soluble [Pb(OH)4]²-(aq.) complex ion. equation: | 2022-06-26 08:54:17 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9099096059799194, "perplexity": 14655.939675262254}, "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/1656103037649.11/warc/CC-MAIN-20220626071255-20220626101255-00241.warc.gz"} |
http://flr-project.org/FLasher/ | ## Overview
Projection of future population and fishery dynamics is carried out for a given set of management targets. A system of equations is solved, using Automatic Differentation (AD), for the levels of effort by fishery/fleet that will result in the required abundances, catches or fishing mortalities.
## Installation
To install this package, start R and enter:
install.packages("FLasher", repos="http://flr-project.org/R")
or directly from the github repository by using:
remotes::install_github("flr/FLasher")
WARNING: FLasher requires a 64 bit installation of R. Installation from source in R for Windows should be carried out using --no-multiarch for a 64 bit-only installation if both 32 and 64 bit R are available. | 2022-08-12 00:01:45 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 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": 0.41925567388534546, "perplexity": 3177.854641074157}, "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/1659882571536.89/warc/CC-MAIN-20220811224716-20220812014716-00484.warc.gz"} |
http://virtualphotonics.codeplex.com/discussions/453056 | This project has moved. For the latest updates, please go here.
New frequency domain button on the fluence/PhD maps - MATLAB yet?
acerussi Aug 11, 2013 at 12:16 AM Hi - thanks to the VP team for adding the magic frequency domain button to the fluence maps page. I am finding this very helpful. Question: Can this feature be replicated in the MATLAB version? I ask not only because this would be cool, but to export numerical data in the VTS web page doesnt seem to work well. you can export the image fine, but trying to read that data for plotting etc fails. Having all of this in MATLAB makes for easy analysis ... Thanks! dcuccia Coordinator Aug 11, 2013 at 12:58 AM Edited Aug 11, 2013 at 12:59 AM Sorry you're having trouble, Albert. Regarding data export in ASCII format, it looks like we added the line "% Map Values: " at the beginning of the data. Originally, you could just load this file as ascii data, with the x and z data points in the header (mainly for your reference). If you open the text file, and hit a carriage-return after "% Map Values: ", then you should have the 2D data available for matlab import: % X Values: -19.9 -19.7 -19.5 ... % Y Values: 0.1 0.3 0.5 0.7 0.9 ... % Map Values: 4.70195812655052E-05 4.9729648657582E-05 ... Then, in Matlab, you can write: x = -19.9:0.1:20; z = 0.1:0.2:19.9; temp = load('test.txt', '-ascii'); fluence = reshape(temp,[length(x)/2 length(z)])'; figure; imagesc(log(fluence)); axis equal; axis off; colormap hot; colorbar; This should let you plot something (with the default frequency domain settings) that looks like this: Regarding direct Matlab computations - you're right; it looks like FluenceOfRhoAndZAndFt not in there yet. This should be pretty straightforward - would be happy to work on this. dcuccia Coordinator Aug 11, 2013 at 1:34 AM Albert, I've just added the following to the source code, which will go out in the next release. To vts\VtsSolvers.m, add the following function, say at line 254 (after FluenceOfRhoAndZ): function r = FluenceOfRhoAndZAndFt(op, rhos, zs, fts) %% FluenceOfRhoAndZ % FluenceOfRhoAndZ(OP, RHOS, ZS) % % OP is an N x 4 matrix of optical properties % eg. OP = [[mua1, mus'1, g1, n1]; [mua2, mus'2, g2, n2]; ...]; % RHO is an 1 x M array of detector locations (in mm) % eg. RHO = [1:10]; % Z is a 1 x M array of z values (in mm) % eg. Z = linspace(0.1,19.9,100); nop = size(op,1); nrho = length(rhos); nft = length(fts); nz = length(zs); if strfind(VtsSolvers.Options.SolverType, 'SDA') fs = Vts.Factories.SolverFactory.GetForwardSolver(VtsSolvers.Options.SolverType); else fs = Vts.Modeling.ForwardSolvers.PointSourceSDAForwardSolver(); end op_net = NET.createArray('Vts.OpticalProperties', nop); for i=1:nop op_net(i) = Vts.OpticalProperties; op_net(i).Mua = op(i,1); op_net(i).Musp = op(i,2); op_net(i).G = op(i,3); op_net(i).N = op(i,4); end; % call the solver, which returns an array of (.NET) Complex structs fComplexNET = fs.FluenceOfRhoAndZAndFt(op_net,rhos,zs,fts);%,[length(fts) length(zs) length(rhos) nop]); % create a native Matlab array fReal = zeros([nft nz nrho nop]); fImag = zeros([nft nz nrho nop]); ci = 1; for i=1:nop for j=1:nrho for k=1:nz for el=1:nft fReal(el,k,j,i) = fComplexNET(ci).Real; fImag(el,k,j,i) = fComplexNET(ci).Imaginary; ci=ci+1; end end end end r = complex(fReal, fImag); end Then, in 'vts_solver_demo.m' (or in your own scripting code), here's the demo of the functionality: %% Example FluenceOfRhoAndZAndFt % Evaluate fluence as a function of rho and z using one set of optical % properties and a distributed gaussian source SDA solver type. op = [0.01 1 0.8 1.4]; rhos = linspace(0.1,19.9,100); % s-d separation, in mm zs = linspace(0.1,19.9,100); % z range in mm fts = linspace(0,1,2); % frequency range in GHz VtsSolvers.SetSolverType('DistributedPointSourceSDA'); test = VtsSolvers.FluenceOfRhoAndZAndFt(op, rhos, zs, fts); xs = [-fliplr(rhos(2:end)),rhos]; % xs = [-rhos(end:-1:2), rhos]; % f = figure; imagesc(log(test)); f = figure; imagesc(xs,zs,log([fliplr(squeeze(test(1,:,2:end))),squeeze(test(1,:,:))])); axis image title('Fluence of \rho and z and ft (ft=0GHz)'); xlabel('\rho [mm]') ylabel('z [mm]') set(f,'Name','Fluence of Rho and z and ft (ft=0GHz)'); f = figure; imagesc(xs,zs,log([fliplr(squeeze(test(2,:,2:end))),squeeze(test(2,:,:))])); axis image title('Fluence of \rho and z and ft (ft=1GHz)'); xlabel('\rho [mm]') ylabel('z [mm]') set(f,'Name','Fluence of Rho and z and ft (ft=1GHz)'); modulation = squeeze(test(2,:,:)./test(1,:,:)); figure; imagesc(xs,zs,[fliplr(modulation(:,2:end)), modulation]); axis image title('Modulation of fluence (AC/DC) of \rho and z and ft (ft=1GHz)'); xlabel('\rho [mm]') ylabel('z [mm]') set(f,'Name','Modulation of fluence (AC/DC) of Rho and z and ft (ft=1GHz)'); You should see a few images like this: ...and this: Let me know how that goes for you! acerussi Aug 11, 2013 at 5:10 PM thanks David - I think that did the trick. hopefully sometime there will be an equivalent for the time domain (to explore time gating strategies). ******************************************* Albert Cerussi, PhD Director, Diffuse Optical Spectroscopic Imaging (DOSI) Lab Beckman Laser Institute and Medical Clinic University of California, Irvine ******************************************* | 2017-08-22 18:47:03 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 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": 0.6348740458488464, "perplexity": 11071.291486557786}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-34/segments/1502886112539.18/warc/CC-MAIN-20170822181825-20170822201825-00008.warc.gz"} |
https://nrich.maths.org/2861 | ### Poly Fibs
A sequence of polynomials starts 0, 1 and each poly is given by combining the two polys in the sequence just before it. Investigate and prove results about the roots of the polys.
### Fibonacci Factors
For which values of n is the Fibonacci number fn even? Which Fibonnaci numbers are divisible by 3?
### Fixing It
A and B are two fixed points on a circle and RS is a variable diamater. What is the locus of the intersection P of AR and BS?
# Trig Rules OK
##### Age 16 to 18 Challenge Level:
Draw any two squares which meet at a common vertex $C$ and join the adjacent vertices to make two triangles $CAB$ and $CDE$.
Construct the perpendicular from $C$ to $AB$, (the altitude of the triangle). When you extend this line where does it cut $DE$?
Now bisect the line $AB$ to find the midpoint of this line $M$. Draw the median $MC$ of triangle $ABC$ and extend it to cut $DE$. What do you notice about the lines $MC$ and $DE$?
Will you get the same results about the two triangles formed if you draw squares of different sizes or at different angles to each other? Make a conjecture about the altitude of one of these triangles and prove your conjecture.
Thank you Geoff Faux for suggesting this problem. | 2019-09-18 06:00:08 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5846064686775208, "perplexity": 414.1674028285157}, "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-2019-39/segments/1568514573184.25/warc/CC-MAIN-20190918044831-20190918070831-00003.warc.gz"} |
https://nhigham.com/tag/vandermonde/ | # Conference in Honour of Walter Gautschi
Last week I had the pleasure of attending and speaking at the Conference on Scientific Computing and Approximation (March 30-31, 2018) at Purdue University, held in honour of Walter Gautschi (Professor Emeritus of Computer Science and Mathematics at Purdue University) on the occasion of his 90th birthday.
The conference was expertly organized by Alex Pothen and Jie Shen. The attendees, numbering around 70, included many of Walter’s friends and colleagues.
The speakers made many references to Walter’s research contributions, particularly in the area of orthogonal polynomials. In my talk, Matrix Functions and their Sensitivity, I emphasized Walter’s work on conditioning of Vandermonde matrices.
A Vandermonde matrix $V_n$ is an $n\times n$ matrix depending on parameters $x_1,x_2,\ldots,x_n$ that has $j$ th column $[1, x_j, \ldots, x_j^{n-1}]^T$. It is nonsingular when the $x_i$ are distinct. This is a notoriously ill conditioned class of matrices. Walter said that he first experienced the ill conditioning when he computed Gaussian quadrature formulas from moments of a weight function.
Walter has written numerous papers on Vandermonde matrices that give much insight into their conditioning. Here is a very a brief selection of Walter’s results. For more, see my chapter Numerical Conditioning in Walter’s collected works.
In a 1962 paper he showed that
$\displaystyle\|V_n^{-1}\|_{\infty} \le \max_i \prod_{j\ne i}\frac{ 1+|x_j| }{ |x_i-x_j| }.$
In 1978 he obtained
$\displaystyle\|V_n^{-1}\|_{\infty} \ge \max_i \prod_{j\ne i} \frac{ \max(1,|x_j|) }{ |x_i-x_j| },$
which differs from the upper bound by at most a factor $2^{n-1}$. A 1975 result is that for $x_i$ equispaced on $[0,1]$,
$\displaystyle\kappa(V_n)_{\infty} \sim \frac{1}{\pi} e^{-\frac{\pi}{4}} (3.1)^n.$
A 1988 paper returns to lower bounds, showing that for $x_i \ge 0$ and $n\ge 2$,
$\displaystyle\kappa(V_n)_{\infty} > 2^{n-1}.$
When some of the $x_i$ coincide a confluent Vandermonde matrix can be defined, in which columns are “repeatedly differentiated”. Walter has obtained bounds for the confluent case, too.
These results quantify the extreme ill conditioning. I should note, though, that appropriate algorithms that exploit structure can nevertheless obtain accurate solutions to Vandermonde problems, as described in Chapter 22 of Accuracy and Stability of Numerical Algorithms. | 2022-01-21 16:55:18 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 16, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7358601689338684, "perplexity": 1147.267509752708}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-05/segments/1642320303512.46/warc/CC-MAIN-20220121162107-20220121192107-00165.warc.gz"} |
https://mathoverflow.net/questions/47390/how-much-of-zfc-does-quines-new-foundations-prove/47437 | # How much of ZFC does Quine's New Foundations prove?
Main Question: Does anyone know of a reference that can tell me which axioms of ZFC Quine's New Foundations prove, disprove, and leave undecided?
Secondary Question: I've read that diagonal arguments don't go through in NF and thus can't be used to prove that the reals are uncountable. Does NF manage to prove the uncountability of the reals by some other means or does that fact (normally rendered as "$P _1(\mathbb{N}) < P(\mathbb{N})$" in order to make sense in NF) turn out to be undecidable in NF?
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Hi Amit,
Pairing (true in NF), Choice (false) and Infinity (true) are well documented. I would expect that Thomas Forster's book addresses if not outright answers most of your question; I suppose one would need to restate things like replacement appropriately to even make the question meaningful for some formulas. The book is "Set Theory with a Universal Set: Exploring an Untyped Universe" (Oxford Logic Guides), 1995, and you may enjoy reading it anyway.
Thomas is also interested in ZF, so even if the book doesn't completely answer your question, he may help guide you through the relevant literature if you email him directly.
As for the secondary question, quite a few basic ZF facts go through for NF when reformulated as you suggest (this is part of the reason why Forster, Randall Holmes, and other NF researchers, are interested in ZF, and why set theorists like Jensen and Solovay have thought about NF). One of these facts is Cantor's result. You may also be interested in Greg Kirmayer, "A refinement of Cantor’s theorem", Proceedings of the AMS 83 (4) (Dec., 1981), 774.
(Email me in a few days if this doesn't work out, and I'll go across the hall and ask Randall.)
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New Foundations also proves the Power Set Axiom. The proof is in Halperin(1944). – Carlo Von Schnitzel Nov 26 '10 at 3:12
Yes, Pairing, power-set, union follow from stratified comprehension. Extensionality is an axiom. That choice is false is due to Specker: "The axiom of choice in Quine's new foundations for mathematical logic." Proceedings of the National Academy of Sciences of the USA 39, (1953) pp. 972-975. As a corollary, Infinity holds (suitably formulated, NF does not deal with Von Neumann ordinals; in NF, ordinals and cardinals are equivalence classes). Specker mentions in his paper another (silly) corollary, namely that GCH fails (as the proof that GCH implies choice can be formalized in NF). – Andrés Caicedo Nov 26 '10 at 6:14
New Foundations is just so weird. Just weaken extensionality to allow urelemente and it no longer proves infinity or the falsity of choice. It becomes consistent with choice and relatively consistent to ZFC. What is so special about atoms with NF that makes the theory so different? The other thing that always amazed me about stratification is that it succeeds in taking care of a whole bunch of paradoxes in the same way, namely by asserting that the universe is untyped. – Carlo Von Schnitzel Nov 26 '10 at 9:52
One twist one can give to the question is to reformulate it as: which axioms of ZF(C) does NF prove to hold in the wellfounded sets?
We know the following: extensionality, pairing, sumset, power set, stratified $\Delta_0$ separation. We *don*t know if infinity can be proved to hold in the wellfounded sets and we *don*t know if every wellfounded set has a wellfounded transitive superset.
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NF does prove Cantor's theorem in the sense you indicate, $|\mathscr{P}_1(X)|<|\mathscr{P}(X)|$ for any set $X$. The usual ZF proof goes through, because definitions in that proof which need to be stratified for it to work in NF, in fact are. But if you try to prove $|X|<|\mathscr{P}(X)|$, you no longer have the right stratification, so Cantor's theorem fails in NF in this sense (which is good, as the universal set $V$ can't have a lesser cardinality than any other set).
Generally speaking, in NF one cannot prove $|X|=|\mathscr{P}_1(X)|$ because the obvious bijection $x\mapsto \{x\}$ does not have a stratified definition. One way of increasing strength of NF-style theories is to assert that more and more sets are "Cantorian" in the sense that $|X|=|\mathscr{P}_1(X)|$ (or "strongly Cantorian" in the sense that the particular bijection $x\mapsto \{x\}$ exists). This idea goes back at least to some papers of Orey (if I recall correctly), and Holmes has had a lot to say about that. Solovay proved some interesting results that link up the consistency strength of such additional axioms (on top of NFU) with large cardinal axioms for ZF. See, e.g., the paper on NFUB here.
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I didn't see anyone specifically address the secondary question, so I thought I'd pipe in. In NF the natural numbers are provably Cantorian (see above for definition). Rosser's "Logic for Mathematicians" (available from Dover and a pretty nice resource) has a detailed proof on p.437. Basically, if $a \in n$ and $b \in m$ and $|a| = |\mathscr{P}_1(b)|$ then the relation pairing $n$ and $\{m\}$ turns out to be stratified and is a bijection between $\mathbb{N}$ and $\mathscr{P}_1(\mathbb{N})$. When you have such a bijection, Cantor's proof goes through in the usual fashion.
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Very sorry for the re-edit, but it did change the meaning of my answer. – Malice Vidrine Aug 13 '13 at 5:52
While I second (with highly biased motivation) the recommendation of Forster’s book, for questions like this an easier starting point than Forster’s book or Holmes’ articles might be Holmes’ book Elementary Set Theory with a Universal Set, originally volume 10 of the Cahiers du Centre de logique, with a corrected online version at http://math.boisestate.edu/~holmes/holmes/head.ps.
(This should perhaps have been a comment to the original answer, but I don’t have enough reputation points yet to post comments.)
- | 2016-02-10 08:52:27 | {"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": 0.8508123159408569, "perplexity": 585.9280553488636}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-07/segments/1454701159031.19/warc/CC-MAIN-20160205193919-00254-ip-10-236-182-209.ec2.internal.warc.gz"} |
https://terrytao.wordpress.com/tag/rescaling/ | You are currently browsing the tag archive for the ‘rescaling’ tag.
Mathematicians study a variety of different mathematical structures, but perhaps the structures that are most commonly associated with mathematics are the number systems, such as the integers ${{\bf Z}}$ or the real numbers ${{\bf R}}$. Indeed, the use of number systems is so closely identified with the practice of mathematics that one sometimes forgets that it is possible to do mathematics without explicit reference to any concept of number. For instance, the ancient Greeks were able to prove many theorems in Euclidean geometry, well before the development of Cartesian coordinates and analytic geometry in the seventeenth century, or the formal constructions or axiomatisations of the real number system that emerged in the nineteenth century (not to mention precursor concepts such as zero or negative numbers, whose very existence was highly controversial, if entertained at all, to the ancient Greeks). To do this, the Greeks used geometric operations as substitutes for the arithmetic operations that would be more familiar to modern mathematicians. For instance, concatenation of line segments or planar regions serves as a substitute for addition; the operation of forming a rectangle out of two line segments would serve as a substitute for multiplication; the concept of similarity can be used as a substitute for ratios or division; and so forth.
A similar situation exists in modern physics. Physical quantities such as length, mass, momentum, charge, and so forth are routinely measured and manipulated using the real number system ${{\bf R}}$ (or related systems, such as ${{\bf R}^3}$ if one wishes to measure a vector-valued physical quantity such as velocity). Much as analytic geometry allows one to use the laws of algebra and trigonometry to calculate and prove theorems in geometry, the identification of physical quantities with numbers allows one to express physical laws and relationships (such as Einstein’s famous mass-energy equivalence ${E=mc^2}$) as algebraic (or differential) equations, which can then be solved and otherwise manipulated through the extensive mathematical toolbox that has been developed over the centuries to deal with such equations.
However, as any student of physics is aware, most physical quantities are not represented purely by one or more numbers, but instead by a combination of a number and some sort of unit. For instance, it would be a category error to assert that the length of some object was a number such as ${10}$; instead, one has to say something like “the length of this object is ${10}$ yards”, combining both a number ${10}$ and a unit (in this case, the yard). Changing the unit leads to a change in the numerical value assigned to this physical quantity, even though no physical change to the object being measured has occurred. For instance, if one decides to use feet as the unit of length instead of yards, then the length of the object is now ${30}$ feet; if one instead uses metres, the length is now ${9.144}$ metres; and so forth. But nothing physical has changed when performing this change of units, and these lengths are considered all equal to each other:
$\displaystyle 10 \hbox{ yards } = 30 \hbox{ feet } = 9.144 \hbox{ metres}.$
It is then common to declare that while physical quantities and units are not, strictly speaking, numbers, they should be manipulated using the laws of algebra as if they were numerical quantities. For instance, if an object travels ${10}$ metres in ${5}$ seconds, then its speed should be
$\displaystyle (10 m) / (5 s) = 2 ms^{-1}$
where we use the usual abbreviations of ${m}$ and ${s}$ for metres and seconds respectively. Similarly, if the speed of light ${c}$ is ${c=299 792 458 ms^{-1}}$ and an object has mass ${10 kg}$, then Einstein’s mass-energy equivalence ${E=mc^2}$ then tells us that the energy-content of this object is
$\displaystyle (10 kg) (299 792 458 ms^{-1})^2 \approx 8.99 \times 10^{17} kg m^2 s^{-2}.$
Note that the symbols ${kg, m, s}$ are being manipulated algebraically as if they were mathematical variables such as ${x}$ and ${y}$. By collecting all these units together, we see that every physical quantity gets assigned a unit of a certain dimension: for instance, we see here that the energy ${E}$ of an object can be given the unit of ${kg m^2 s^{-2}}$ (more commonly known as a Joule), which has the dimension of ${M L^2 T^{-2}}$ where ${M, L, T}$ are the dimensions of mass, length, and time respectively.
There is however one important limitation to the ability to manipulate “dimensionful” quantities as if they were numbers: one is not supposed to add, subtract, or compare two physical quantities if they have different dimensions, although it is acceptable to multiply or divide two such quantities. For instance, if ${m}$ is a mass (having the units ${M}$) and ${v}$ is a speed (having the units ${LT^{-1}}$), then it is physically “legitimate” to form an expression such as ${\frac{1}{2} mv^2}$, but not an expression such as ${m+v}$ or ${m-v}$; in a similar spirit, statements such as ${m=v}$ or ${m\geq v}$ are physically meaningless. This combines well with the mathematical distinction between vector, scalar, and matrix quantities, which among other things prohibits one from adding together two such quantities if their vector or matrix type are different (e.g. one cannot add a scalar to a vector, or a vector to a matrix), and also places limitations on when two such quantities can be multiplied together. A related limitation, which is not always made explicit in physics texts, is that transcendental mathematical functions such as ${\sin}$ or ${\exp}$ should only be applied to arguments that are dimensionless; thus, for instance, if ${v}$ is a speed, then ${\hbox{arctanh}(v)}$ is not physically meaningful, but ${\hbox{arctanh}(v/c)}$ is (this particular quantity is known as the rapidity associated to this speed).
These limitations may seem like a weakness in the mathematical modeling of physical quantities; one may think that one could get a more “powerful” mathematical framework if one were allowed to perform dimensionally inconsistent operations, such as add together a mass and a velocity, add together a vector and a scalar, exponentiate a length, etc. Certainly there is some precedent for this in mathematics; for instance, the formalism of Clifford algebras does in fact allow one to (among other things) add vectors with scalars, and in differential geometry it is quite common to formally apply transcendental functions (such as the exponential function) to a differential form (for instance, the Liouville measure ${\frac{1}{n!} \omega^n}$ of a symplectic manifold can be usefully thought of as a component of the exponential ${\exp(\omega)}$ of the symplectic form ${\omega}$).
However, there are several reasons why it is advantageous to retain the limitation to only perform dimensionally consistent operations. One is that of error correction: one can often catch (and correct for) errors in one’s calculations by discovering a dimensional inconsistency, and tracing it back to the first step where it occurs. Also, by performing dimensional analysis, one can often identify the form of a physical law before one has fully derived it. For instance, if one postulates the existence of a mass-energy relationship involving only the mass of an object ${m}$, the energy content ${E}$, and the speed of light ${c}$, dimensional analysis is already sufficient to deduce that the relationship must be of the form ${E = \alpha mc^2}$ for some dimensionless absolute constant ${\alpha}$; the only remaining task is then to work out the constant of proportionality ${\alpha}$, which requires physical arguments beyond that provided by dimensional analysis. (This is a simple instance of a more general application of dimensional analysis known as the Buckingham ${\pi}$ theorem.)
The use of units and dimensional analysis has certainly been proven to be very effective tools in physics. But one can pose the question of whether it has a properly grounded mathematical foundation, in order to settle any lingering unease about using such tools in physics, and also in order to rigorously develop such tools for purely mathematical purposes (such as analysing identities and inequalities in such fields of mathematics as harmonic analysis or partial differential equations).
The example of Euclidean geometry mentioned previously offers one possible approach to formalising the use of dimensions. For instance, one could model the length of a line segment not by a number, but rather by the equivalence class of all line segments congruent to the original line segment (cf. the Frege-Russell definition of a number). Similarly, the area of a planar region can be modeled not by a number, but by the equivalence class of all regions that are equidecomposable with the original region (one can, if one wishes, restrict attention here to measurable sets in order to avoid Banach-Tarski-type paradoxes, though that particular paradox actually only arises in three and higher dimensions). As mentioned before, it is then geometrically natural to multiply two lengths to form an area, by taking a rectangle whose line segments have the stated lengths, and using the area of that rectangle as a product. This geometric picture works well for units such as length and volume that have a spatial geometric interpretation, but it is less clear how to apply it for more general units. For instance, it does not seem geometrically natural (or, for that matter, conceptually helpful) to envision the equation ${E=mc^2}$ as the assertion that the energy ${E}$ is the volume of a rectangular box whose height is the mass ${m}$ and whose length and width is given by the speed of light ${c}$.
But there are at least two other ways to formalise dimensionful quantities in mathematics, which I will discuss below the fold. The first is a “parametric” model in which dimensionful objects are modeled as numbers (or vectors, matrices, etc.) depending on some base dimensional parameters (such as units of length, mass, and time, or perhaps a coordinate system for space or spacetime), and transforming according to some representation of a structure group that encodes the range of these parameters; this type of “coordinate-heavy” model is often used (either implicitly or explicitly) by physicists in order to efficiently perform calculations, particularly when manipulating vector or tensor-valued quantities. The second is an “abstract” model in which dimensionful objects now live in an abstract mathematical space (e.g. an abstract vector space), in which only a subset of the operations available to general-purpose number systems such as ${{\bf R}}$ or ${{\bf R}^3}$ are available, namely those operations which are “dimensionally consistent” or invariant (or more precisely, equivariant) with respect to the action of the underlying structure group. This sort of “coordinate-free” approach tends to be the one which is preferred by pure mathematicians, particularly in the various branches of modern geometry, in part because it can lead to greater conceptual clarity, as well as results of great generality; it is also close to the more informal practice of treating mathematical manipulations that do not preserve dimensional consistency as being physically meaningless.
In this post I would like to make some technical notes on a standard reduction used in the (Euclidean, maximal) Kakeya problem, known as the two ends reduction. This reduction (which takes advantage of the approximate scale-invariance of the Kakeya problem) was introduced by Wolff, and has since been used many times, both for the Kakeya problem and in other similar problems (e.g. by Jim Wright and myself to study curved Radon-like transforms). I was asked about it recently, so I thought I would describe the trick here. As an application I give a proof of the ${d=\frac{n+1}{2}}$ case of the Kakeya maximal conjecture.
In a recent Cabinet meeting, President Obama called for a $100 million spending cut in 90 days from the various federal departments as a sign of budget discipline. While this is nominally quite a large number, it was pointed out correctly by many people that this was in fact a negligible fraction of the total federal budget; for instance, Greg Mankiw noted that the cut was comparable to a family with an annual spending of$100,000 and a deficit of $34,000 deciding on a spending cut of$3. (Of course, this is by no means the only budgetary initiative being proposed by the administration; just today, for instance, a change in the taxation law for offshore income was proposed which could potentially raise about $210 billion over the next ten years, or about$630 a year with the above scaling, though it is not clear yet how feasible or effective this change would be.)
I thought that this sort of rescaling (converting $100 million to$3) was actually a rather good way of comprehending the vast amounts of money in the federal budget: we are not so adept at distinguishing easily between $1 million,$1 billion, and $1 trillion, but we are fairly good at grasping the distinction between$0.03, $30, and$30,000. So I decided to rescale (selected items in) the federal budget, together with some related numbers for comparison, by this ratio 100 million:3, to put various figures in perspective.
This is certainly not an advanced application of mathematics by any means, but I still found the results to be instructive. The same rescaling puts the entire population of the US at about nine – the size of a (large) family – which is of course consistent with the goal of putting the federal budget roughly on the scale of a family budget (bearing in mind, of course, that the federal government is only about a fifth of the entire US economy, so one might perhaps view the government as being roughly analogous to the “heads of household” of this large family). The implied (horizontal) length rescaling of $\sqrt{100 \hbox{million}:3} \approx 5770$ is roughly comparable to the scaling used in Dubai’s “The World” (which is not a coincidence, if you think about it; the purpose of both rescalings is to map global scales to human scales). Perhaps readers may wish to contribute additional rescaled statistics of interest to those given below.
One caveat: the rescaling used here does create some noticeable distortions in other dimensional quantities. For example, if one rescales length by the implied factor of $\approx 5770$, but leaves time unrescaled (so that a fiscal year remains a fiscal year), then this will rescale all speeds by a factor of $\approx 5770$ also. For instance, the circumference of the Earth has been rescaled to a manageable-looking 6.9 kilometres (4.3 miles), but the speed of, say, a commercial airliner (typically about 900 km/hr, or 550 mi/hr) is rescaled also, to a mere 150 metres (or 160 yards) or so per hour, i.e. two or three meters or yards per minute – about the speed of a tortoise.
All amounts here are rounded to three significant figures (and in some cases, the precision may be worse than this). I am using here the FY2008 budget instead of the 2009 or 2010 one, as the data is more finalised; as such, the numbers here are slightly different from those of Mankiw. (For instance, the 2010 budget includes the expenditures for Iraq & Afghanistan, whereas in previous budgets these were appropriated separately.) I have tried to locate the most official and accurate statistics whenever possible, but corrections and better links are of course welcome.
FY 2008 budget:
• Total revenue: $75,700 • Individual income taxes:$34,400
• Social security & other payroll taxes: $27,000 • Total spending:$89,500
• Net mandatory spending: $48,000 • Medicare, Medicaid, and SCHIP:$20,500
• Social Security: $18,400 • Net interest:$7,470
• Net discretionary spending: $34,000 • Department of Defense:$14,300
• DARPA: $89 • Global War on Terror:$4,350
• Department of Education: $1,680 • Department of Energy:$729
• NASA: $519 • Net earmarks:$495
• NSF: $180 • Maths & Physical Sciences:$37.50
• Budget deficit: $13,800 • Additional appropriations (not included in regular budget) • Iraq & Afghanistan:$5,640
• Spending cuts within 90 days of Apr 20, 2009: $3 • Air force NY flyover “photo shoot”, Apr 27, 2009:$0.01
• Additional spending cuts for FY2010, proposed May 7, 2009: $510 • Projected annual revenue from proposed offshore tax code change:$630
Other figures (for comparison)
• National debt held by public 2008: $174,000 • Held by foreign/international owners 2008:$85,900
• National debt held by government agencies, 2008: $126,000 • Held by OASDI (aka (cumulative) “Social Security Surplus”):$64,500
• National GDP 2008: $427,000 • National population 2008: 9 • GDP per capita 2008:$47,000
• Land mass: 0.27 sq km (0.1 sq mi, or 68 acres)
• World GDP 2008: $1,680,000 • World population 2008: 204 • GDP per capita 2008 (PPP):$10,400
• Land mass: 4.47 sq km (1.73 sq mi)
• World’s richest (non-rescaled) person: Bill Gates (net worth $1,200, March 2009) • 2008/2009 Bailout package (TARP):$21,000 (maximum)
• Amount spent by Dec 2008: $7,410 • AIG bailout from TARP:$1,200
• AIG Federal Reserve credit line: $4,320 • AIG bonuses in 2009 Q1:$4.95
• GM & Chrysler loans: $552 • 2009/2010 Stimulus package (ARRA):$23,600
• Tax cuts (spread out over 10 years): $8,640 • State and local fiscal relief:$4,320
• Education: $3,000 • “Race to the top” education fund:$150
• Investments in scientific research: $645 • Pandemic flu preparedness:$1.50 (was initially $27, after being dropped from FY2008 and FY2009 budgets) • Additional request after A(H1N1) (“swine flu”) outbreak, Apr 28:$45
• Volcano monitoring: $0.46 (erroneously reported as$5.20)
• Salt marsh mouse preservation (aka “Pelosi’s mouse“): $0.00 (erroneously reported as$0.90)
• Market capitalization of NYSE
• May 2008 (peak): $506,000 • March 2009:$258,000
• Largest company by market cap: Exxon Mobil (approx $10,000, Apr 2009) • Value of US housing stock (2007):$545,760
• Total value of outstanding mortgages (2008): $330,000 • Total value of sub-prime mortgages outstanding (2007 est):$39,000
• Total value of mortgage-backed securities (2008): \$267,000
• Credit default swap contracts, total notional value:
• US trade balance (2007) | 2018-04-20 14:29:34 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 62, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7795867919921875, "perplexity": 596.0602626197082}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-17/segments/1524125938462.12/warc/CC-MAIN-20180420135859-20180420155859-00471.warc.gz"} |
https://www.gradesaver.com/textbooks/math/algebra/college-algebra-7th-edition/chapter-1-equations-and-graphs-section-1-6-solving-other-types-of-equations-1-6-exercises-page-139/67 | ## College Algebra 7th Edition
$x=-\frac{1}{2}$
$\displaystyle \frac{1}{x^{3}}+\frac{4}{x^{2}}+\frac{4}{x}=0$ We multiply through by $x^3$: $1+4x+4x^{2}=0$ Now we factor and solve: $(1+2x)^{2}=0$ $1+2x=0$ $2x=-1$ $x=-\frac{1}{2}$ | 2018-07-17 19:14:56 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 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": 0.9332643747329712, "perplexity": 688.7565145255722}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-30/segments/1531676589892.87/warc/CC-MAIN-20180717183929-20180717203929-00176.warc.gz"} |
https://ideas.repec.org/a/gam/jecnmx/v4y2015i1p2-d61252.html | # Interpretation and Semiparametric Efficiency in Quantile Regression under Misspecification
## Author
Listed:
• Ying-Ying Lee
() (Department of Economics, University of Oxford, Manor Road Building, Manor Road, Oxford OX1 3UQ, UK)
## Abstract
Allowing for misspecification in the linear conditional quantile function, this paper provides a new interpretation and the semiparametric efficiency bound for the quantile regression parameter β ( τ ) in Koenker and Bassett (1978). The first result on interpretation shows that under a mean-squared loss function, the probability limit of the Koenker–Bassett estimator minimizes a weighted distribution approximation error, defined as $$F_{Y}(X'\beta(\tau)|X) - \tau$$, i.e., the deviation of the conditional distribution function, evaluated at the linear quantile approximation, from the quantile level. The second result implies that the Koenker–Bassett estimator semiparametrically efficiently estimates the quantile regression parameter that produces parsimonious descriptive statistics for the conditional distribution. Therefore, quantile regression shares the attractive features of ordinary least squares: interpretability and semiparametric efficiency under misspecification.
## Suggested Citation
• Ying-Ying Lee, 2015. "Interpretation and Semiparametric Efficiency in Quantile Regression under Misspecification," Econometrics, MDPI, Open Access Journal, vol. 4(1), pages 1-14, December.
• Handle: RePEc:gam:jecnmx:v:4:y:2015:i:1:p:2-:d:61252
as
File URL: http://www.mdpi.com/2225-1146/4/1/2/pdf
File URL: http://www.mdpi.com/2225-1146/4/1/2/
## References listed on IDEAS
as
1. Komunjer, Ivana, 2005. "Quasi-maximum likelihood estimation for conditional quantiles," Journal of Econometrics, Elsevier, vol. 128(1), pages 137-164, September.
2. Newey, Whitney K. & Powell, James L., 1990. "Efficient Estimation of Linear and Type I Censored Regression Models Under Conditional Quantile Restrictions," Econometric Theory, Cambridge University Press, vol. 6(03), pages 295-317, September.
3. Arthur Lewbel, 1998. "Semiparametric Latent Variable Model Estimation with Endogenous or Mismeasured Regressors," Econometrica, Econometric Society, vol. 66(1), pages 105-122, January.
4. Roger Koenker & Samantha Leorato & Franco Peracchi, 2013. "Distributional vs. Quantile Regression," CEIS Research Paper 300, Tor Vergata University, CEIS, revised 17 Dec 2013.
5. Hahn, Jinyong, 1997. "Bayesian Bootstrap of the Quantile Regression Estimator: A Large Sample Study," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 38(4), pages 795-808, November.
6. Whang, Yoon-Jae, 2006. "Smoothed Empirical Likelihood Methods For Quantile Regression Models," Econometric Theory, Cambridge University Press, vol. 22(02), pages 173-205, April.
7. Magnac, Thierry & Maurin, Eric, 2007. "Identification and information in monotone binary models," Journal of Econometrics, Elsevier, vol. 139(1), pages 76-104, July.
8. Victor Chernozhukov & Iv·n Fern·ndez-Val & Alfred Galichon, 2010. "Quantile and Probability Curves Without Crossing," Econometrica, Econometric Society, vol. 78(3), pages 1093-1125, May.
9. Chen, Xiaohong & Pouzo, Demian, 2009. "Efficient estimation of semiparametric conditional moment models with possibly nonsmooth residuals," Journal of Econometrics, Elsevier, vol. 152(1), pages 46-60, September.
10. Newey, Whitney K, 1990. "Semiparametric Efficiency Bounds," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 5(2), pages 99-135, April-Jun.
11. Antonio F. Galvao & Kengo Kato, 2014. "Estimation and Inference for Linear Panel Data Models Under Misspecification When Both n and T are Large," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 32(2), pages 285-309, April.
12. Powell, James L., 1984. "Least absolute deviations estimation for the censored regression model," Journal of Econometrics, Elsevier, vol. 25(3), pages 303-325, July.
13. Chen, Tao & Parker, Thomas, 2014. "Semiparametric efficiency for partially linear single-index regression models," Journal of Multivariate Analysis, Elsevier, vol. 130(C), pages 376-386.
14. Xiaohong Chen & Demian Pouzo, 2012. "Estimation of Nonparametric Conditional Moment Models With Possibly Nonsmooth Generalized Residuals," Econometrica, Econometric Society, vol. 80(1), pages 277-321, January.
15. Sasaki, Yuya, 2015. "What Do Quantile Regressions Identify For General Structural Functions?," Econometric Theory, Cambridge University Press, vol. 31(05), pages 1102-1116, October.
16. Otsu, Taisuke, 2008. "Conditional empirical likelihood estimation and inference for quantile regression models," Journal of Econometrics, Elsevier, vol. 142(1), pages 508-538, January.
17. Jacho-Chávez, David T., 2009. "Efficiency Bounds For Semiparametric Estimation Of Inverse Conditional-Density-Weighted Functions," Econometric Theory, Cambridge University Press, vol. 25(03), pages 847-855, June.
18. White, Halbert, 1980. "Using Least Squares to Approximate Unknown Regression Functions," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 21(1), pages 149-170, February.
19. repec:spo:wpecon:info:hdl:2441/5rkqqmvrn4tl22s9mc4b6ga2g is not listed on IDEAS
20. Lee, Yoonseok, 2012. "Bias in dynamic panel models under time series misspecification," Journal of Econometrics, Elsevier, vol. 169(1), pages 54-60.
21. Chamberlain, Gary, 1987. "Asymptotic efficiency in estimation with conditional moment restrictions," Journal of Econometrics, Elsevier, vol. 34(3), pages 305-334, March.
22. Powell, James L., 1986. "Censored regression quantiles," Journal of Econometrics, Elsevier, vol. 32(1), pages 143-155, June.
23. Jia Chen & Degui Li & Hua Liang & Suojin Wang, 2014. "Semiparametric GEE Analysis in Partially Linear Single-Index Models for Longitudinal Data," Discussion Papers 14/26, Department of Economics, University of York.
24. Severini, Thomas A. & Tripathi, Gautam, 2001. "A simplified approach to computing efficiency bounds in semiparametric models," Journal of Econometrics, Elsevier, vol. 102(1), pages 23-66, May.
Full references (including those not matched with items on IDEAS)
### Keywords
semiparametric efficiency bounds; misspecification; conditional quantile function; conditional distribution function; best linear approximation;
### JEL classification:
• B23 - Schools of Economic Thought and Methodology - - History of Economic Thought since 1925 - - - Econometrics; Quantitative and Mathematical Studies
• C - Mathematical and Quantitative Methods
• C00 - Mathematical and Quantitative Methods - - General - - - General
• C01 - Mathematical and Quantitative Methods - - General - - - Econometrics
• C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
• C2 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables
• C3 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables
• C4 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics
• C5 - Mathematical and Quantitative Methods - - Econometric Modeling
• C8 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs
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IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers. | 2018-06-23 16:42:01 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 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": 0.6900562644004822, "perplexity": 9131.9212447695}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-26/segments/1529267865098.25/warc/CC-MAIN-20180623152108-20180623172108-00431.warc.gz"} |
https://iwaponline.com/aqua/article-abstract/56/8/533/28858/Recycling-the-wastewater-of-the-industrial-park-in?redirectedFrom=fulltext | In Taiwan, every industrial park equips a wastewater treatment plant (WWTP) to collect wastewater streaming from all the factories. These effluents, though showing high total dissolved solids (TDS) and fluctuating composition, would be a valuable water resource for industrial use after large scale purification, especially in the drought seasons. In this study, a pilot plant was installed for reclaiming the effluents from the industrial park WWTP through the membrane process. A modified spiral-wound ultrafiltration (UF) membrane with backwash function was utilized for the pretreatment of the reverse osmosis (RO) system. Evaluation results showed that the pilot plant was performing stably during the two-month operation. After the RO desalination, the quality of the reclaimed water basically met the requirement standards of intermediate-pressure boiler feedwater (150 ∼ 750 psig) of the Environmental Protection Agency, United States (USEPA). The backwashable spiral wound UF membrane provided suitable water quality for RO influent (SDI < 4) and helped reduce the cost compared to using hollow-fibre UF membrane. The total cost of recycling one-ton effluent included US$0.35 for construction and US$ 0.45 for operation/maintenance.
You do not currently have access to this content. | 2018-12-14 03:23:53 | {"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": 0.24758021533489227, "perplexity": 7974.784903128696}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-51/segments/1544376825349.51/warc/CC-MAIN-20181214022947-20181214044447-00510.warc.gz"} |
https://gre.kmf.com/question/qr/0?keyword=&page=397 | #### 题目列表
The table above shows the annual revenues of a company for seven years. Based on the information given. which of the following statements are true for the seven years?
Indicate all such statements.
When positive integers k and n are each divided by 9, the remainders are 2 and 5, respectively. If k > n, what is the remainder when k-n is divided by 9?
A group of 100 employees was ranked on a scale from 1 to 5, as shown in the table.
#### Quantity A
The average (arithmetic mean) rank of the 100 employees
3.00
#### Quantity A
The median of the first 999 positive even integers
#### Quantity B
The median of the first 999 positive odd integers
$h^{2}>1$
h
#### Quantity B
$\frac{1}{h}$
$\frac{x^{3}}{y^{6}}$=$\frac{1}{27}$
3x
#### Quantity B
$y^{2}$
When the positive integer t is divided by 5, the remainder is 3, and when t is divided by 6, the remainder is 2.
t
#### Quantity B
38
An exercise ball is made from soft elastic that has uniform thickness of 2 millimeters, and the interior of the ball is filled with air. The ball is in the shape of a sphere and has an exterior diameter of 65 centimeters. What is the radius of the interior of the ball, in millimeters?
A realtor sold two storefront properties. The realtor sold one of the properties for a profit of 25 percent of its original purchase price and the other property for a loss of 25 percent of its original purchase price. If the realtor sold each property for $210,000, by what amount did the sum of the original purchase prices of the two properties exceed$420,000?
A point p is to be selected at random inside a square whose sides have length 3. What is the probability that the circle whose center is at p and whose radius is 1/2 will not intersect the square?
Points A, B, C, and D are equally spaced on line segment AD, as shown. If $\frac{1}{3}$ of segment AB, all of segment BC, and $\frac{2}{5}$of segment CD were removed, what fraction of segment AD would remain?
The variables x and y are related by a linear equation. If y increases by 4 whenever x increases by 1, which of the following equations could represent the relationship between x and y?
Indicate all such equations.
If a and b are positive and a+2b=$\frac{16-b^{2}}{a}$, what is the value of $(a+b)^{3}$ ?
In 2014 the price of one share of a certain stock increased by 20 percent from January 1 to February 1 decreased by n percent from February 1 to March 1, and increased by 25 percent from March 1 to April 1. If the price of one share of the stock increased by 5 percent from January 1 to April I in 2014, what is the value of n?
An artist will arrange 5 identical plastic apples in wooden bowls-one made of maple, one of oak, and one of pine. How many different arrangements are possible such that each bowl will contain at least one apple?
Over the period shown, which first-class postal rate was in effect for the longest period of time?
The ratio of the first-class postal rate in effect in June 1989 to the first-class postal rate in effect in June 1979 is
The greatest percent increase in the first-class postal rate over the previous rate listed occurred in
What is the value of ($2^{236}$)($4^{-120}$)?
Of the following, which best represents the graph of the function $y=(x^{2}-x)(x-2)$?
25000 +道题目
5本备考书籍 | 2022-01-21 17:23:33 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 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": 0.39112794399261475, "perplexity": 560.9217428553886}, "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/1642320303512.46/warc/CC-MAIN-20220121162107-20220121192107-00245.warc.gz"} |
http://math.stackexchange.com/questions/159129/intersection-of-generalized-doubly-stochastic-matrix-set-and-orthogonal-matrix-s | # Intersection of Generalized doubly stochastic matrix set and Orthogonal matrix set
The definition for doubly stochastic matrix can be found here. We say a square matrix $A$ is a Generalized doubly stochastic matrix if the sum of each rows and columns of $A$ all equals 1. But A doesn't have to be non-negative.
An interesting fact(which is also easy to prove) about doubly stochastic matrix is: if $A$ is doubly stochastic and orthogonal, then $A$ is actually a permutation matrix.
So my question is: what is the intersection set for a generalized doubly stochastic matrix set and orthogonal matrix set?
More specifically, can any one give me an example of an $N \times N$ matrix $A$, which satisfy the following constraints:
• $$AA^T=I$$
• $$A*1=1$$
• $$A^T*1=1$$
• there exists at least one entry $A_{i,j}$, satisfying $A_{i,j}<0$
Thanks!
-
Sure, just take any solution to $x+y+z=x^2+y^2+z^2=1$ and form the matrix $$\left(\begin{array}{ccc} x&y&z\\y&z&x\\z&x&y\end{array}\right).$$
For instance, take $x = -\frac13$ and $y = z = \frac23$. More generally, choose the roots of the cubic $x^3 - x^2 + c$ for some small positive real $c$. | 2014-09-24 03:08:36 | {"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": 0.8805665969848633, "perplexity": 75.69862864975653}, "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-2014-41/segments/1410657141651.17/warc/CC-MAIN-20140914011221-00260-ip-10-234-18-248.ec2.internal.warc.gz"} |
https://physics.stackexchange.com/questions/589481/mathematical-definition-of-elastic-materials | # Mathematical definition of elastic materials
Physically, elastic materials are materials which return to their original state upon complete removal of applied mechanical loads under isothermal conditions.
In the book "Mechanics of Laminated Composite Plates and Shells 2nd Edition" by JN Reddy", the author defines
Materials for which the constitutive behavior is only a function of the current state of deformation are known as elastic. In the special case in which the work done by stresses during a deformation is dependent only the initial state and the current configuration, the material is called hyperelastic.
I am unable to relate the mathematical definition of elastic materials with the physical one. How is the dependence of constitutive relations on current state of deformation related to the material returning to its original state upon complete removal of loads?
It means the material has no "memory" of what previously happened to it. The deformation for any given loading is always the same (including zero deformation for zero load, as a particular case).
An inelastic material model needs some additional variables to "remember" the past history of the stress and/or strain. For example, to model plasticity you need to remember the accumulated plastic strain. To model creep or viscoelasticity you also need include the time history of the applied loads.
It is probably beneficial to list different other types of material.
This figure summarizes, the most common behaviour of the materials and their models, with wrt time (not deformation).
As other have mentioned, the idea of the purely elastic model is that at any instant its behaviour is dependent on the deformation. Most materials in the majority of structural engineering applications are considered elastic (or at least they were before the progress in FEM codes).
In reality, no material behaves as purely elastic, however, it is a very, very good approximation for a great number of calculations.
• What do the happy and unhappy faces mean? Is there some text providing the context? What is the source? – Chemomechanics Oct 26 '20 at 19:49
Here's one way in which the two definitions are not related: falling within OP's "physical definition" is not a sufficient condition for falling within OP's "mathematical definition". For example, the Kelvin/Voigt model, as illustrated in the answer by @NMech , falls within OP's "physical definition" but not within OP's "mathematical definition". I think the real answer is that different people mean subtly different things by the word "elastic", and the reader must take care.
In the case of tensile test of metals, below the yield stress for example, for a given strain there is a given stress. We can say that the stress is a function a strain $$\sigma = \sigma(\epsilon)$$.
After the yield point, plastic deformation begins, and if the sample is unloaded, it doesn't return to its original length $$L_0$$, but to a bigger length $$L_1$$.
If we compute the total strain (after unloading) as $$\frac{L_1 - L_0}{L_0}$$, it was previously (in the loading step) correspondent to a non zero stress. So, for this type of material we can not say that $$\sigma = \sigma(\epsilon)$$ anymore, it not an elastic behaviour. | 2021-05-09 08:11:07 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 5, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6847706437110901, "perplexity": 722.4629364667461}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-21/segments/1620243988961.17/warc/CC-MAIN-20210509062621-20210509092621-00417.warc.gz"} |
https://docs.mdanalysis.org/stable/documentation_pages/analysis/rdf.html | # 4.7.2.1. Radial Distribution Functions — MDAnalysis.analysis.rdf
This module contains two classes to calculate radial pair distribution functions (radial distribution functions or “RDF”). The RDF $$g_{ab}(r)$$ between types of particles $$a$$ and $$b$$ is
$g_{ab}(r) = (N_{a} N_{b})^{-1} \sum_{i=1}^{N_a} \sum_{j=1}^{N_b} \langle \delta(|\mathbf{r}_i - \mathbf{r}_j| - r) \rangle$
which is normalized so that the RDF becomes 1 for large separations in a homogenous system. The RDF effectively counts the average number of $$b$$ neighbours in a shell at distance $$r$$ around a $$a$$ particle and represents it as a density.
The radial cumulative distribution function is
$G_{ab}(r) = \int_0^r \!\!dr' 4\pi r'^2 g_{ab}(r')$
and the average number of $$b$$ particles within radius $$r$$
$N_{ab}(r) = \rho G_{ab}(r)$
(with the appropriate density $$\rho$$). The latter function can be used to compute, for instance, coordination numbers such as the number of neighbors in the first solvation shell $$N(r_1)$$ where $$r_1$$ is the position of the first minimum in $$g(r)$$.
We provide options for calculating the density of particle $$b$$ in a shell at distance $$r$$ around a $$a$$ particle, which is
$n_{ab}(r) = \rho g_{ab}(r)$
class MDAnalysis.analysis.rdf.InterRDF(g1, g2, nbins=75, range=(0.0, 15.0), norm='rdf', exclusion_block=None, **kwargs)[source]
InterRDF is a tool to calculate average radial distribution functions between two groups of atoms. Suppose we have two AtomGroups A and B. A contains atom A1, A2, and B contains B1, B2. Given A and B to InterRDF, the output will be the average of RDFs between A1 and B1, A1 and B2, A2 and B1, A2 and B2. A typical application is to calculate the RDF of solvent with itself or with another solute.
The radial distribution function is calculated by histogramming distances between all particles in g1 and g2 while taking periodic boundary conditions into account via the minimum image convention.
The exclusion_block keyword may be used to exclude a set of distances from the calculations.
Results are available in the attributes results.rdf and results.count.
Parameters
• g1 (AtomGroup) – First AtomGroup
• g2 (AtomGroup) – Second AtomGroup
• nbins (int) – Number of bins in the histogram
• range (tuple or list) – The size of the RDF
• norm (str, {'rdf', 'density', 'none'}) –
For ‘rdf’ calculate $$g_{ab}(r)$$. For ‘density’ the single particle density $$n_{ab}(r)$$ is computed. ‘none’ computes the number of particles occurences in each spherical shell.
New in version 2.3.0.
• exclusion_block (tuple) – A tuple representing the tile to exclude from the distance array.
• verbose (bool) – Show detailed progress of the calculation if set to True
results.bins
numpy.ndarray of the centers of the nbins histogram bins.
New in version 2.0.0.
Type
numpy.ndarray
bins
Alias to the results.bins attribute.
Deprecated since version 2.0.0: This attribute will be removed in 3.0.0. Use results.bins instead.
Type
numpy.ndarray
results.edges
numpy.ndarray of the nbins + 1 edges of the histogram bins.
New in version 2.0.0.
Type
numpy.ndarray
edges
Alias to the results.edges attribute.
Deprecated since version 2.0.0: This attribute will be removed in 3.0.0. Use results.edges instead.
Type
numpy.ndarray
results.rdf
numpy.ndarray of the radial distribution function values for the results.bins.
New in version 2.0.0.
Type
numpy.ndarray
rdf
Alias to the results.rdf attribute.
Deprecated since version 2.0.0: This attribute will be removed in 3.0.0. Use results.rdf instead.
Type
numpy.ndarray
results.count
numpy.ndarray representing the radial histogram, i.e., the raw counts, for all results.bins.
New in version 2.0.0.
Type
numpy.ndarray
count
Alias to the results.count attribute.
Deprecated since version 2.0.0: This attribute will be removed in 3.0.0. Use results.count instead.
Type
numpy.ndarray
Example
First create the InterRDF object, by supplying two AtomGroups then use the run() method
rdf = InterRDF(ag1, ag2)
rdf.run()
Results are available through the results.bins and results.rdf attributes:
plt.plot(rdf.results.bins, rdf.results.rdf)
The exclusion_block keyword allows the masking of pairs from within the same molecule. For example, if there are 7 of each atom in each molecule, the exclusion mask (7, 7) can be used.
New in version 0.13.0.
Changed in version 1.0.0: Support for the start, stop, and step keywords has been removed. These should instead be passed to InterRDF.run().
Changed in version 2.0.0: Store results as attributes bins, edges, rdf and count of the results attribute of AnalysisBase.
class MDAnalysis.analysis.rdf.InterRDF_s(u, ags, nbins=75, range=(0.0, 15.0), norm='rdf', density=False, **kwargs)[source]
Calculates site-specific radial distribution functions. Instead of two groups of atoms it takes as input a list of pairs of AtomGroup, [[A, B], [C, D], ...]. Given the same A and B to InterRDF_s, the output will be a list of individual RDFs between A1 and B1, A1 and B2, A2 and B1, A2 and B2 (and similarly for C and D). These site-specific radial distribution functions are typically calculated if one is interested in the solvation shells of a ligand in a binding site or the solvation of specific residues in a protein.
Parameters
• u (Universe) –
a Universe that contains atoms in ags
Deprecated since version 2.3.0: This parameter is superflous and will be removed in MDAnalysis 3.0.0.
• ags (list) – a list of pairs of AtomGroup instances
• nbins (int) – Number of bins in the histogram
• range (tuple or list) – The size of the RDF
• norm (str, {'rdf', 'density', 'none'}) –
For ‘rdf’ calculate $$g_{ab}(r)$$. For ‘density’ the single particle density $$n_{ab}(r)$$ is computed. ‘none’ computes the number of particles occurences in each spherical shell.
New in version 2.3.0.
• density (bool) –
False: calculate $$g_{ab}(r)$$; True: calculate the true single particle density $$n_{ab}(r)$$. density overwrites the norm parameter.
New in version 1.0.1: This keyword was available since 0.19.0 but was not documented. Furthermore, it had the opposite meaning. Since 1.0.1 it is officially supported as documented.
Deprecated since version 2.3.0: Instead of density=True use norm=’density’
results.bins
numpy.ndarray of the centers of the nbins histogram bins; all individual site-specific RDFs have the same bins.
New in version 2.0.0.
Type
numpy.ndarray
bins
Alias to the results.bins attribute.
Deprecated since version 2.0.0: This attribute will be removed in 3.0.0. Use results.bins instead.
Type
numpy.ndarray
results.edges
array of the nbins + 1 edges of the histogram bins; all individual site-specific RDFs have the same bins.
New in version 2.0.0.
Type
numpy.ndarray
edges
Alias to the results.edges attribute.
Deprecated since version 2.0.0: This attribute will be removed in 3.0.0. Use results.edges instead.
Type
numpy.ndarray
results.rdf
list of the site-specific radial distribution functions if norm=’rdf’ or density functions for the bins if norm=’density’. The list contains len(ags) entries. Each entry for the i-th pair [A, B] = ags[i] in ags is a numpy.ndarray with shape (len(A), len(B)), i.e., a stack of RDFs. For example, results.rdf[i][0, 2] is the RDF between atoms A[0] and B[2].
New in version 2.0.0.
Type
list
rdf
Alias to the results.rdf attribute.
Deprecated since version 2.0.0: This attribute will be removed in 3.0.0. Use results.rdf instead.
Type
list
results.count
list of the site-specific radial histograms, i.e., the raw counts, for all results.bins. The data have the same structure as results.rdf except that the arrays contain the raw counts.
New in version 2.0.0.
Type
list
count
Alias to the results.count attribute.
Deprecated since version 2.0.0: This attribute will be removed in 3.0.0. Use results.count instead.
Type
list
results.cdf
list of the site-specific cumulative counts, for all results.bins. The data have the same structure as results.rdf except that the arrays contain the cumulative counts.
This attribute only exists after get_cdf() has been run.
New in version 2.0.0.
Type
list
cdf
Alias to the results.cdf attribute.
Deprecated since version 2.0.0: This attribute will be removed in 3.0.0. Use results.cdf instead.
Type
list
Example
First create the InterRDF_s object, by supplying one Universe and one list of pairs of AtomGroups, then use the run() method:
from MDAnalysisTests.datafiles import GRO_MEMPROT, XTC_MEMPROT
u = mda.Universe(GRO_MEMPROT, XTC_MEMPROT)
s1 = u.select_atoms('name ZND and resid 289')
s2 = u.select_atoms('(name OD1 or name OD2) and resid 51 and sphzone 5.0 (resid 289)')
s3 = u.select_atoms('name ZND and (resid 291 or resid 292)')
s4 = u.select_atoms('(name OD1 or name OD2) and sphzone 5.0 (resid 291)')
ags = [[s1, s2], [s3, s4]]
rdf = InterRDF_s(u, ags)
rdf.run()
Results are available through the results.bins and results.rdf attributes:
plt.plot(rdf.results.bins, rdf.results.rdf[0][0, 0])
(Which plots the rdf between the first atom in s1 and the first atom in s2)
To generate the cumulative distribution function (cdf) in the sense of “particles within radius $$r$$”, i.e., $$N_{ab}(r)$$, use the get_cdf() method
cdf = rdf.get_cdf()
Results are available through the results.cdf attribute:
plt.plot(rdf.results.bins, rdf.results.cdf[0][0, 0])
(Which plots the cdf between the first atom in s1 and the first atom in s2)
New in version 0.19.0.
Changed in version 1.0.0: Support for the start, stop, and step keywords has been removed. These should instead be passed to InterRDF_s.run().
Changed in version 2.0.0: Store results as attributes bins, edges, rdf, count and cdf of the results attribute of AnalysisBase.
Changed in version 2.3.0: Introduce norm and exclusion_blocks attributes.
Deprecated since version 2.3.0: Instead of density=True use norm=’density’
Deprecated since version 2.3.0: The universe parameter is superflous.
get_cdf()[source]
Calculate the cumulative counts for all sites.
This is the cumulative count within a given radius, i.e., $$N_{ab}(r)$$.
The result is returned and also stored in the attribute results.cdf.
Returns
cdf – list of arrays with the same structure as results.rdf
Return type
list | 2023-02-01 06:24:33 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 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": 0.44150009751319885, "perplexity": 5361.408077596386}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764499911.86/warc/CC-MAIN-20230201045500-20230201075500-00279.warc.gz"} |
https://proofwiki.org/wiki/Category:Inverse_Secant | # Category:Inverse Secant
This category contains results about Inverse Secant.
Definitions specific to this category can be found in Definitions/Inverse Secant.
Let $z \in \C_{\ne 0}$ be a non-zero complex number.
The inverse secant of $z$ is the multifunction defined as:
$\sec^{-1} \left({z}\right) := \left\{{w \in \C: \sec \left({w}\right) = z}\right\}$
where $\sec \left({w}\right)$ is the secant of $w$.
## Subcategories
This category has the following 2 subcategories, out of 2 total.
## Pages in category "Inverse Secant"
The following 3 pages are in this category, out of 3 total. | 2020-02-23 17:02:51 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7970423102378845, "perplexity": 2258.373395623051}, "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/1581875145818.81/warc/CC-MAIN-20200223154628-20200223184628-00071.warc.gz"} |
https://codeforces.com/problemsets/acmsguru/problem/99999/531 | #### 531. Bonnie and Clyde
Time limit per test: 1.5 second(s)
Memory limit: 262144 kilobytes
input: standard
output: standard
Bonnie and Clyde are into robbing banks. This time their target is a town called Castle Rock. There are n banks located along Castle Rock's main street; each bank is described by two positive integers x i, w i, where x i represents the distance between the i-th bank and the beginning of the street and w i represents how much money the i-th bank has. The street can be represented as a straight line segment, that's why values of x i can be regarded as the banks' coordinates on some imaginary coordinate axis.
This time Bonnie and Clyde decided to split, they decided to rob two different banks at a time. As robberies aren't exactly rare in Castle Rock, Bonnie and Clyde hope that the police won't see the connection between the two robberies. To decrease the chance of their plan being discovered by the investigation, they decided that the distance between the two robbed banks should be no less than d.
Help Bonnie and Clyde find two such banks, the distance between which is no less than d and the sum of money in which is maximum.
Input
The first input line contains a pair of integers n, d (1 ≤ n ≤ 2 · 105, 1 ≤ d ≤ 108), where n is the number of banks and d is the minimum acceptable distance between the robberies. Then n lines contain descriptions of banks, one per line. Each line contains two integers x i, w i (1 ≤ x i,w i ≤ 108), x i shows how far the i-th bank is from the beginning of the street and w i shows the number of money in the bank. Positions of no two banks coincide. The banks are given in the increasing order of x i.
Output
Print two integer numbers — indicies of the required banks. The banks are numbered starting from 1 in the order in which they follow in the input data. You may print indicies in any order. If there are many solutions, print any of them. If no such pair of banks exists, print "
-1 -1
" (without quotes).
Example(s)
sample input sample output 6 3 1 1 3 5 4 8 6 4 10 3 11 2 5 3 | 2020-08-09 15:17:29 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 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": 0.17124943435192108, "perplexity": 1084.232830387607}, "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/1596439738555.33/warc/CC-MAIN-20200809132747-20200809162747-00549.warc.gz"} |
http://ficuspublishers.com/ches-cryptographic-vdc/f9e46d-product-rule-calculator | 5-a-day Workbooks. Product Cost Formula Calculator Popular problems $\frac{d}{dx}\left(x^{\frac{1}{3}}\right)$ 224 views And so now we're ready to apply the product rule. The derivative of f of x is just going to be equal to 2x by the power rule, and the derivative of g of x is just the derivative of sine of x, and we covered this when we just talked about common derivatives. Integrals / … Many of the calculator pages show work or equations that help you understand the calculations. Product rule of differentiation Calculator. The following variables and constants are reserved: e = Euler's number, the base of the exponential function (2.718281...); i = imaginary number (i ² = -1); pi, π = the ratio of a circle's circumference to its diameter (3.14159...); phi, Φ = the golden ratio (1,6180...); You can enter expressions the same way you see them in your math textbook. Any product rule with more functions can be derived in a similar fashion. Primary Study Cards. The Power Rule of Derivatives applies to find the power of more than two functions. BYJU’S online chain rule calculator tool makes the calculation faster, and it displays the derivatives and the indefinite integral in a fraction of seconds. Below is one of them. WRONG! Probability and Statistics. There's a differentiation law that allows us to calculate the derivatives of products of functions. Free radical equation calculator - solve radical equations step-by-step This website uses cookies to ensure you get the best experience. The product rule is a formula that is used to determine the derivative of a product of functions. Chain Rule Calculator is a free online tool that displays the derivative value for the given function. Derivative of sine of x is cosine of x. Sum rule of differentiation Calculator. The Product Rule is a formula developed by Leibniz used to find the derivatives of products of functions. This power rule calculator differentiates the function which a user enters in based on the calculus power rule. Sam's function $$\text{mold}(t) = t^{2} e^{t + 2}$$ involves a product of two functions of $$t$$. Calculator Soup is a free online calculator. Practice Questions; Post navigation. Foundations of Mathematics. The Calculator can find derivatives using the sum rule, the elementary power rule, the generalized power rule, the reciprocal rule (inverse function rule), the product rule, the chain rule and logarithmic derivatives. The Derivative tells us the slope of a function at any point.. The calculator defaults to rounding to the nearest integer, but settings can be changed to use other rounding modes and levels of precision. Additionally, D uses lesser-known rules to calculate the derivative … Algebra Calculator. Click here for Answers . Free online calculator that allows you to dynamically calculate the differential equation. The product rule is a formula used to find the derivatives of products of two or more functions.. Let $$u\left( x \right)$$ and $$v\left( x \right)$$ be differentiable functions. The Product Rule is defined as the product of the first function and the derivative of the second function plus the product of the derivative of the first function and the second function: Here you will find free loan, mortgage, time value of money, math, algebra, trigonometry, fractions, physics, statistics, time & date and conversions calculators. So what does the product rule say? Of course trigonometric, hyperbolic and exponential functions are also supported. This calculator finds derivative of entered function and tries to simplify the formula. The product rule tells us how to differentiate the product of two functions: (fg)’ = fg’ + gf’ Note: the little mark ’ means "Derivative of", and f and g are functions. With this section and the previous section we are now able to differentiate powers of $$x$$ as well as sums, differences, products and quotients of these kinds of functions. Geometry. Next Product Rule for Counting Textbook Answers. Estimate the product calculator is a pre-algebra tool to find the actual & estimated product of given multiplicand & multiplier by rounding off to the nearest ten, hundred & thousand. The rule of product is a guideline as to when probabilities can be multiplied to produce another meaningful probability. If ever you have to have assistance on percents or perhaps exponents, Factoring-polynomials.com is the right site to pay a visit to! Chain Rule: d d x [f (g (x))] = f … The Product Rule. The above Calculator computes a derivative of a given function with respect to a variable x using analytical differentiation. Constant rule Calculator. Factoring-polynomials.com offers great facts on zero product property calculator, trigonometric and two variables and other algebra topics. 4 • (x 3 +5) 2 = 4x 6 + 40 x 3 + 100 derivative = 24x 5 + 120 x 2. ), with steps shown. A common mistake many students make is to think that the product rule allows you to take the derivative of both terms and multiply them together. As far as accounting is concerned, the product costs of the sold products are captured in the income statement, while that of the unsold product is reflected in the inventory of finished goods. All the rounding modes the calculator is capable of are described below. Discrete Mathematics. The power rule is calculated is illustrated by the formula above. It can handle polynomial, rational, irrational, exponential, logarithmic, trigonometric, inverse trigonometric, hyperbolic and inverse hyperbolic functions. Strangely enough, it's called the Product Rule. By using this website, you agree to our Cookie Policy. GCSE Revision Cards. Type in any function derivative to get the solution, steps and graph Search for: Contact us. In calculus, the product rule is a formula used to find the derivatives of products of two or more functions.It may be stated as (⋅) ′ = ′ ⋅ + ⋅ ′or in Leibniz's notation (⋅) = ⋅ + ⋅.The rule may be extended or generalized to many other situations, including to products of multiple functions, to a rule for higher-order derivatives of a product, and to other contexts. Includes derivatives for: trig functions, inverse trig functions, hyperbolic trig functions, hyperbolic inverse trig functions, power rule, product rule, quotient rule, chain rule, sum and difference rule, derivative of logarithms, derivative of natural logarithms, derivative of e, and the derivative of a^x. Recreational Mathematics. Just supply the multiplicand & multiplier, this calculator rounds to the nearest 10, … However, there are many more functions out there in the world that are not in this form. Before using the chain rule, let's multiply this out and then take the derivative. Cramer's Rule Calculator Here you can solve systems of simultaneous linear equations using Cramer's Rule Calculator with complex numbers online for free with a very detailed solution. This app takes derivatives step-by-step, showing explanations in blue and highlighting in red the parts of the expression that have changed since the previous step. Quotient rule of differentiation Calculator. Then the product of the functions $$u\left( x \right)v\left( x \right)$$ is also differentiable and In order to master the techniques explained here it is vital that you undertake plenty of practice exercises so … Product Rule for Counting Practice Questions Click here for Questions . It is x n = nx n-1. Trigonometry Calculator. Thus we take the exponent of the base and … Specifically, the rule of product is used to find the probability of an intersection of events: An important requirement of the rule of product is that the events are independent. Find the Derivative Using Product Rule - d/dx Differentiate using the Product Rule which states that is where and . Algebra. Product Rule. You can also get a better visual and understanding of the function by using our graphing tool. This program contains notes on many types of derivatives. The derivative of with respect to is . The quotient rule states that … Calculus: Product Rule, How to use the product rule is used to find the derivative of the product of two functions, what is the product rule, How to use the Product Rule, when to use the product rule, product rule formula, with video lessons, examples and step-by-step solutions. You can use operations like addition +, subtraction -, division /, multiplication *, power ^, and common mathematical functions.Full syntax description can be found below the calculator. History and Terminology. In calculus, the quotient rule is a method of finding the derivative of a function that is the ratio of two differentiable functions. Free derivative calculator - differentiate functions with all the steps. Let f(x)=g(x)/h(x), where both g and h are differentiable and h(x)≠0. Product and Quotient Rule for differentiation with examples, solutions and exercises. And that's all you need to know to use the product rule. Product Rule. The Product Rule mc-TY-product-2009-1 A special rule, theproductrule, exists for differentiating products of two (or more) functions. Now, let's differentiate the same equation using the chain rule which states that the derivative of a composite function equals: (derivative of outside) • … Implicit multiplication (5x = 5*x) is supported. This unit illustrates this rule. Number Theory. Given the product of two functions, f(x)g(x), the derivative of the product of those two functions can be … Previous Time Calculations Textbook Exercise. Use "Function" field to enter mathematical expression with x variable. Calculus and Analysis. On the basis of the production cost per unit, the pricing of the final finished product can be determined. The Leibniz identity extends the product rule to higher-order derivatives. It is preloaded with the basic rules of differentiation including the constant rule, sum rule, product rule, quotient rule, chain rule, and power rule. The Derivative Calculator supports solving first, second...., fourth derivatives, as well as implicit differentiation and finding the zeros/roots. Chain rule of differentiation Calculator. We will repeat the formula again. The online calculator will calculate the derivative of any function using the common rules of differentiation (product rule, quotient rule, chain rule, etc. Applied Mathematics. There are a few different ways that the product rule can be represented. It uses well-known rules such as the linearity of the derivative, product rule, power rule, chain rule and so on. If this confuses you, go back to the top of the page and reread the product rule and then go through some examples in your textbook. In this form a product of functions such as the linearity of the calculator show... Questions Click here for Questions derivatives applies to find the derivatives of products of functions, 's. Developed by Leibniz used to find the power rule, theproductrule, exists for differentiating of... And inverse hyperbolic functions pay a visit to illustrated by the formula above as well as implicit differentiation and the... 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The power of more than two functions a derivative of entered function and tries to simplify the above... Sine of x function '' field to enter mathematical expression with variable., exists for differentiating products of functions the linearity of the derivative calculator supports solving first, second.... fourth... Field to enter mathematical expression with x variable and other algebra topics tool displays. Theproductrule, exists for differentiating products of functions great facts on zero product property calculator, trigonometric and variables. The rounding modes the calculator pages show work or equations that help you understand the calculations the quotient rule calculated! To simplify the formula field to enter mathematical expression with x variable to when probabilities can be multiplied produce! Our Cookie Policy offers great facts on zero product property calculator,,!, D uses lesser-known rules to calculate the derivative … this calculator derivative! Derivative using product rule mc-TY-product-2009-1 a special rule, let 's multiply this out then... Formula developed by Leibniz used to determine the derivative using product rule, but settings can be to... Is where and offers great facts on zero product property calculator, trigonometric, inverse trigonometric, hyperbolic and functions... Offers great facts on zero product property calculator, trigonometric and two variables and other algebra topics identity... Offers great facts on zero product property calculator, trigonometric and two variables and other algebra topics can also a... A guideline as to when probabilities can be multiplied to produce another meaningful probability illustrated by the formula.... And inverse hyperbolic functions, logarithmic, trigonometric, hyperbolic and exponential functions are supported... On many types of derivatives applies to find the derivatives of products of.! Mc-Ty-Product-2009-1 a special rule, chain rule and so on x using analytical differentiation offers., but settings can be represented defaults to rounding to the nearest integer, but settings can changed. The calculator is a product rule calculator as to when probabilities can be represented differential equation with x variable Cookie.! Agree to our Cookie Policy two differentiable functions by the product rule calculator above rule and so we. This out and then take the derivative, product rule, but settings be. To when probabilities can be represented integrals / … Factoring-polynomials.com offers great facts on zero property! | 2021-01-19 12:38:28 | {"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": 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": 0.7262782454490662, "perplexity": 675.2342031790918}, "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/1610703518240.40/warc/CC-MAIN-20210119103923-20210119133923-00634.warc.gz"} |
http://www.drumtom.com/q/a-wave-has-a-frequency-of-420-hz-and-a-wavelength-of-0-75-m-whats-the-velocity | # A wave has a frequency of 420 Hz and a wavelength of 0.75 m. Whats the velocity?
• A wave has a frequency of 420 Hz and a wavelength of 0.75 m. Whats the velocity?
The wave with the greatest frequency has the shortest wavelength. ... wave moves with a velocity of 350 m ... Hz and λ = 5.0 m. The frequency is given ...
Positive: 58 %
What is the wavelength of ... A certain electromagnetic wave has a wavelength of 625 nm. a.) ... Calculate the frequency (Hz) and wavelength ...
Positive: 55 %
### More resources
There are some important terms related to wave like frequency, wavelength, wave number, velocity of wave etc. ... The light has a wavelength of 400 m.
Positive: 58 %
Wavelength frequency conversion sound equation formula ... the speed of light c = 299 792 458 m/s has to be used as ... m | Light wave frequency f Hz ...
Positive: 53 %
Period and Frequency 19.1 ... A wave has a speed of 30 m/sec and a wavelength of 3 meters. ... (m/sec) Wavelength (m) Frequency (Hz) 136 236 336 436 536 636 | 2016-12-08 12:43:38 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8936944007873535, "perplexity": 1014.0539390482639}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-50/segments/1480698542588.29/warc/CC-MAIN-20161202170902-00403-ip-10-31-129-80.ec2.internal.warc.gz"} |
https://davidroodman.com/ | ## Fast and wild: new paper on my “boottest” program
Three coauthors and I just released a working paper that explains what the wild cluster bootstrap is, how to extend it to various econometric contexts, how to make it go really fast, and how to do it all with my “boottest” program for Stata. The paper is meant to be pedagogic, as most of the methodological ideas are not new. The novel ideas pertain mainly to techniques for speeding up the bootstrap, and to something called Restricted Limited-Information Maximum Likelihood estimation. The title is “Fast and Wild: Bootstrap Inference in Stata Using boottest.”
A few years ago I read the clever study by Kevin Croke that turned a short-term deworming impact study into a long-term one. Back in 2006, Harold Alderman and coauthors reported on a randomized study in Uganda of whether routinely giving children albendazole, a deworming pill, increased their weight. (Most of these children were poorly enough off that any weight gain was probably a sign of improved health.) In that study, the average lag from treatment to follow-up was 16.6 months. But randomized trials, as I like to say, are like the drop of a pebble in a pond: their ripples continue to radiate. Kevin followed up much later on the experiment by linking it to survey data from Uwezo on the ability of Ugandan children to read and do math, gathered in 2010–11. He obtained reading and math scores for some 700 children in parishes (groups of villages) that had been part of the experiment. This let him turn a study of short-term effects on weight gain into one of long-term effects on academic ability.
In a standard move, the Croke paper clusters standard errors by parish, to combat the false precision that might arise if outcomes are correlated for children within a parish for unmeasured reasons. And because there are relatively few parishes—10 in the treatment group, 12 in the control—the paper uses the “wild cluster bootstrap” to interpret the results. This method has become popular since Cameron, Gelbach, and Miller proposed it about 10 years ago.
Kevin’s paper introduced me to this method. As a part of my effort to understand it, I wrote a code fragment to apply it. I quickly saw that the available programs for wild bootstrapping in Stata, cgmreg and cgmwildboot were useful, but could be dramatically improved upon, at least in speed. And so I wrote my own program, boottest, and shared it with the community of Stata users. As programs often do, this one grew in features and complexity, largely in response to feedback from users. In standard applications, like Kevin’s, the program is so damn fast it must seem like alchemy to new users, returning instantaneously results that would once have taken long enough that you could get a cup of coffee while you waited.
The new paper offers a pedagogic introduction to wild (cluster) bootstrapping. I’m pleased and honored to have coauthored it with James MacKinnon, Morten Nielsen, and Matthew Webb. James in particular is a giant in the field; he coauthored many of the papers that led to the development of the wild cluster bootstrap (among numerous other methods), as well as a leading textbooks on econometrics.
The new paper also divulges the secrets of boottest’s speed. I think there’s a lesson here about just how much more efficiently mathematical code can sometimes be made to run when you carefully state and analyze the algorithm. And in computationally intensive techniques such as bootstraps, speed can matter.
## Revised hookworm replication
After releasing and blogging a paper in December about the GiveWell replication of Hoyt Bleakley’s study of hookworm eradication in the American South, I submitted it to the Quarterly Journal of Economics, which published the original paper in 2007. Around the first of the year, QJE rejected the paper, enclosing comments from four reviewers, including from Bleakley. The comments were very helpful in identifying errors in the replication, suggesting new things to do, and pushing me to sharpen my thinking and writing.
I just posted a new version. The story does not change. As a result, I am more sure now that the relative gains in historically hookworm-burdened parts of the South continued trends that began well before and, in the case of income, continued well after. I made two significant substantive changes, both of which strengthen my skepticism.
## Disappointment about the war on worms in the American South 100 years ago
On GiveWell.org, I just blogged a new study revisiting the evidence on whether the campaign in the 1910s to rid the South of hookworm brought major benefits. A great 2007 paper by Hoyt Bleakley suggests that it did: after eradication school attendance rose disproportionately in historically hookworm-heavy areas; and adult earnings of babies born in affected areas also later rose.
The new study revisits Bleakley’s original by reconstructing its database from primary sources, and replicating and revising the analysis. I ended up strongly questioning the original study’s conclusion. These two pairs of graphs show why. The first graph in each pair is from the original study, the second from the new version. The original graphs seem to show jumps in outcomes of interest—school attendance, earnings—but the new ones do not.
More…
## Python program to scrape your solar panel production data from Enphase website
# then downloads panel-level production data for all panels, between dates hard-coded below
# time stamps expressed in Unix epoch time
# inverter ID numbers are not serial numbers; to determine those,
# go to Devices tab on Enphase Enlighten site, hover mouse over hotlinked
# serial numbers, and examine associated links
# saves to "Panelproduction.csv"
# prints each date for which data is scraped, along with number of inverters
import requests, csv, os, getpass
from datetime import timedelta, date
from bs4 import BeautifulSoup
start_date = date(2014, 3, 1)
end_date = date(2017, 11, 14)
user_name = input('User name: ')
password = getpass.getpass('Password: ') # this is only working for me in debug mode
with open('Panelproduction.csv', 'w', newline='') as csvfile:
writer = csv.writer(csvfile)
writer.writerow(['Time','Inverter','Power'])
with requests.Session() as s:
html = s.get('https://enlighten.enphaseenergy.com')
soup = BeautifulSoup(html.text, 'html.parser')
token = soup.find('input', attrs={'name': 'authenticity_token'})['value']
for date in (end_date-timedelta(n) for n in range(int((end_date - start_date).days))):
print (date, len(data))
for inverter, inverter_data in data.items():
if inverter != 'date' and inverter != 'haiku':
for datapoint in inverter_data['POWR']:
writer.writerow([datapoint[0], inverter, datapoint[1]])
## Four points on the debate over the impact of the Mariel boatlift
There’s been more back and forth this week in the argument over whether a giant influx of Cubans into Miami in 1980 lowered wages for low-education people already living there. A seminal 1990 paper by David Card said no. A 2015 reanalysis by immigration skeptic (and Cuban immigrant) George Borjas said yes. A 2015 blog post by me and a paper by Giovanni Peri and Vasil Yasenov said I don’t think so. And now Michael Clemens and Jennifer Hunt, both of whose work appears in my immigration evidence review, have announced the discovery of what they term a flaw in the Borjas analysis. It turns out that just as the Marielitos began arriving, the Census Bureau sharply increased its coverage of black Miamians in the surveys it conducts to monitor the pulse of the U.S. economy. Since black Miamians had especially low incomes, the racial shift had the power to generate the (apparent) wage decline that Borjas highlights. Borjas retorted on Tuesday, labeling the criticism “fake news.”
So, once more, academics are arguing. And concerned observers are confused by the dueling contentions and graphs. In an attempt to clarify, I’ll make a few points.
Disclosures and disclaimers: I used to work for the Center for Global Development, where I was a colleague of Michael Clemens. Now I work for the Open Philanthropy Project, which provides general support to CGD and specific support for Michael’s work on migration. This blog post represents my personal views and does not speak for the Open Philanthropy Project.
Four points:
## Worms and more worms
I just finished the second of two posts for GiveWell on the heated academic controversy over whether it is a good idea to mass-deworm children in regions where the parasite infections are common. The first post focusses on the “internal validity” of a particularly influential study that took place along Lake Victoria, in Kenya, in the late 1990s. The second thinks through how safely we can generalize from that study to other times and places. It has a lot more graphs, including some that look pretty wormy…
## On the geometric interpretation of the determinant of a matrix
Most econometric methods are buttressed by mathematical proofs buried somewhere in academic journals that the methods converge to perfect reliability as sample size goes to infinity. Most arguments in econometrics are over how best to proceed when your data put you very far from the theoretical ideal. Prime examples are when your data are clustered (some villages get bednets and some don’t) and there are few clusters; and when instruments are weak (people offered microcredit were only slightly more likely to take it).
Mucking about in such debates recently, as they pertain to criminal justice studies I’m reviewing, I felt an urge to get back to basics, by which I mean to better understand the mathematics of methods such as LIML. That led me back to linear algebra. So I’ve been trying to develop stronger intuitions about such things as: how a square matrices can have two meanings (a set of basis vectors for a linear space, and the variances and covariances of a set of vectors); and what the determinant really is.
## Murder, I wrote
I have a new post on openphilanthropy.org suggesting that there was indeed an urban crime wave in the US in the last couple of years, but that it was mainly restricted to homicide and assault with a firearm, and may well have peaked last year.
## Murder mystery
I started studying the causes and consequences of incarceration for the Open Philanthropy Project. The subject is full of mysteries. Here’s one.
As best we can measure, the US crime rate rose from the mid-1960s to the early 1990s and then reversed:
(Following FBI definitions, this graph is of “Part I” crimes and excludes excludes drug crime, white collar crime, drunk driving offenses, traffic violations, and other minor crimes. The property crime rate is graphed against the right axis, the violent crime rate against the left.)
The strange thing is, the experts aren’t completely sure why the rise and fall. More…
In 1980, Fidel Castro suddenly allowed thousands of Cubans to leave the country—if they could find a way out. Americans, many of Cuban extraction, swooped to the rescue by bringing lots of boats to the Cuban Port of Mariel. It was called the Mariel boatlift. Some 125,000 Cubans moved to America in a matter of months and perhaps half settled in Miami.
Some 10 years later, economist David Card viewed the Mariel boatlift as a natural experiment and used it to study how immigration affects wages and employment in the receiving country. He concluded there was not much discernible impact in Miami. His paper is seminal, both for its counterintuitive finding and for its introduction of the natural-experiment approach to the study of immigration’s impacts.
Last month, George Borjas, an economist and Cuban emigré himself, revisited the data and came to opposite to conclusion from Card’s. The boatlift hurt the wages of low-education Miamians.
So I dug into the data. Borjas’s work ended up not convincing me. More on the GiveWell blog.
## Coming down to earth: What if a big geomagnetic storm does hit?
The fourth installment in my series on geomagnetic storms is now up on the GiveWell blog.
The first three posts were about the odds of a big storming hitting earth. This one shifts to the question of likely impacts. Mostly I think the evidence is reassuring. But given the stakes, I think we should not relax, and instead support more thorough research.
## On the consequences of taxing alcohol
The Open Philanthropy Project just released another big literature review of mine, this one on whether taxing alcohol save lives. I conclude that it probably does.
That’s hardly shocking. Making stuff more expensive generally leads to people to buy less. And alcohol in excess is bad for you. Perhaps the more significant finding is about the number of lives that could be saved, which is not so great next to other things that “Open Phil” might fund. E.g., we dream of financing the invention of a new research technique that leads to a cure for Alzheimer’s. The grant chasing that dream would be a longshot…but then so might be funding advocacy for raising taxes.
Coroners in the US attribute 23,000 deaths/year to alcohol-caused diseases, according to my calculation (see the report for more). The most rigorous studies I found produced a rather wide range of elasticities of death rates with respect to alcohol prices: 1–3. That means each 1% price rise reduces deaths 1–3%. And, if you do the math carefully, tax hikes sufficient to raise alcohol prices 10% would cut the alcohol death rate 9–25%, or 2,000–6,000 lives/year. This math leaves out any reduction in deaths from drunk driving, which currently amount to 10,000/year. The benefit there would presumably be of the same order of magnitude.
A few interesting things I learned and did along the way:
More…
## Geomagnetic storms: The “Big One” might only be twice as big as what’s already hit
The second post in my series on geomagnetic storms is up on GiveWell.org. It is arguably the most important and interesting in the series. It explains why I think past storms, reaching back to 1859, were probably at most twice as strong as anything our electricity-dependent societies have experienced in recent decades—and shrugged off.
Do you remember the great storms of 1982 and 2003? I didn’t notice them either. And probably you survived the Québec blackout of 1989, which was mostly over within 11 hours. Yet maybe that last doubling in storm intensity would inflict far, far more than twice as much destruction on the grid. Or maybe the grid has become much more vulnerable since 1989, even though grid operators have learned from that experience. It’s also possible I’m wrong that doubling is the worst we should fear. For all these reasons, I still think the threat deserves more attention from researchers, industry, and governments.
As I mentioned in my previous post, the strongest proponent for the view that the worst case is much worse, is John Kappenman, who has argued for a multiplier of 10 rather than 2. In the new post and the report, I trace this number in part to an obscure book of scientific scholarship written in 1925 by a Swedish telegraph engineer in French. The search involved talking to an electrical engineer in Finland, people at the Encyclopedia Britannica in Chicago (who were very helpful), and ordering said obscure book from a German book shop. Author David Stenquist describes how the storm of 1921 caused copper wires running into a telegraph office to melt—but not iron ones. He deduces that the storm-induced voltage on the line could not have been as high as 20 volts/kilometer. Yet through a scholarly game of telephone over the decades, this observation got turned on its head.
Below is a key section I scanned from the book’s yellowed pages. For more, read the post or the report.
## Geomagnetic storms: Don’t panic
My long-promised report for the Open Philanthropy Project on geomagnetic storms is posted. (Data, code, and spreadsheets are here.) The first of a series of posts based on the report just appeared on the GiveWell blog.
This has been one of the most fun projects I’ve worked on because it slices across so many disciplines, from statistics to power engineering to astrophysics. My grasp of those subjects declines in the order listed…but I think I learned enough to reach a preliminary assessment.
The risk that a major solar cataclysm could so disrupt the earth’s magnetic field as to deprive continent-scale regions of power for years looks low to me—lower than the most attention-getting voices, almost by definition, have suggested (Pete RileyJohn Kappenman). Nevertheless, a long-term, large-area blackout would do so much harm, and the risk is so poorly studied, that it absolutely deserves more attention from researchers, industry, government, and philanthropies. My preliminary risk assessment could be wrong.
I just discovered that an elite, independent scientific advisory group for the US government arrived at a similar conclusion in 2011.
It follows that the most emphatic analysts, even if they have overshot, have done a service by drawing attention to the issue. This is for me a familiar paradox.
Senior Advisor to the Open Philanthropy Project; dabbler on the side; more. | 2022-07-06 00:18:38 | {"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": 0.35075217485427856, "perplexity": 3292.8995339500643}, "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/1656104655865.86/warc/CC-MAIN-20220705235755-20220706025755-00216.warc.gz"} |
https://www.ncatlab.org/nlab/show/vertical+vector+field | nLab vertical vector field
Contents
Context
Differential geometry
synthetic differential geometry
Introductions
from point-set topology to differentiable manifolds
Differentials
V-manifolds
smooth space
Tangency
The magic algebraic facts
Theorems
Axiomatics
cohesion
tangent cohesion
differential cohesion
$\array{ && id &\dashv& id \\ && \vee && \vee \\ &\stackrel{fermionic}{}& \rightrightarrows &\dashv& \rightsquigarrow & \stackrel{bosonic}{} \\ && \bot && \bot \\ &\stackrel{bosonic}{} & \rightsquigarrow &\dashv& \mathrm{R}\!\!\mathrm{h} & \stackrel{rheonomic}{} \\ && \vee && \vee \\ &\stackrel{reduced}{} & \Re &\dashv& \Im & \stackrel{infinitesimal}{} \\ && \bot && \bot \\ &\stackrel{infinitesimal}{}& \Im &\dashv& \& & \stackrel{\text{étale}}{} \\ && \vee && \vee \\ &\stackrel{cohesive}{}& ʃ &\dashv& \flat & \stackrel{discrete}{} \\ && \bot && \bot \\ &\stackrel{discrete}{}& \flat &\dashv& \sharp & \stackrel{continuous}{} \\ && \vee && \vee \\ && \emptyset &\dashv& \ast }$
Models
Lie theory, ∞-Lie theory
differential equations, variational calculus
Chern-Weil theory, ∞-Chern-Weil theory
Cartan geometry (super, higher)
Contents
Definition
Let $\pi : P \to X$ be a bundle in the category Diff of smooth manifolds. A vector field $v \in \Gamma(T P)$ is vertical with respect to this bundle if it is in the kernel of the derivative $d \pi \colon T P \to T X$.
A differential form on $P$ is a horizontal differential form with respect to $P \to X$ it it vanishes on vertical vector fields.
Last revised on November 12, 2018 at 14:07:07. See the history of this page for a list of all contributions to it. | 2019-07-17 00:41:57 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 18, "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": 0.8688270449638367, "perplexity": 1715.5245019900644}, "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-2019-30/segments/1563195525004.24/warc/CC-MAIN-20190717001433-20190717023433-00394.warc.gz"} |
https://popflock.com/learn?s=Orders_of_magnitude_(time) | Orders of Magnitude (time)
Get Orders of Magnitude Time essential facts below. View Videos or join the Orders of Magnitude Time discussion. Add Orders of Magnitude Time to your PopFlock.com topic list for future reference or share this resource on social media.
Orders of Magnitude Time
An order of magnitude of time is usually a decimal prefix or decimal order-of-magnitude quantity together with a base unit of time, like a microsecond or a million years. In some cases, the order of magnitude may be implied (usually 1), like a "second" or "year". In other cases, the quantity name implies the base unit, like "century". In most cases, the base unit is seconds or years.
Prefixes are not usually used with a base unit of years. Therefore, it is said "a million years" instead of "a mega year". Clock time and calendar time have duodecimal or sexagesimal orders of magnitude rather than decimal, e.g., a year is 12 months, and a minute is 60 seconds.
The smallest meaningful increment of time is the Planck time-the time light takes to traverse the Planck distance, many decimal orders of magnitude smaller than a second.
The largest realized amount of time, based on known scientific data, is the age of the universe, about 13.8 billion years--the time since the Big Bang as measured in the cosmic microwave background rest frame. Those amounts of time together span 60 decimal orders of magnitude. Metric prefixes are defined spanning 10-24 to 1024, 48 decimal orders of magnitude which may be used in conjunction with the metric base unit of second.
Metric units of time larger than the second are most commonly seen only in a few scientific contexts such as observational astronomy and materials science, although this depends on the author. For everyday use and most other scientific contexts, the common units of minutes, hours (3,600 s or 3.6 ks), days (86,400 s), weeks, months, and years (of which there are a number of variations) are commonly used. Weeks, months, and years are significantly variable units whose length depend on the choice of calendar and are often not regular even with a calendar, e.g. leap years versus regular years in the Gregorian calendar. This makes them problematic for use against a linear and regular time scale such as that defined by the SI, since it is not clear which version is being used.
Because of this, the table below does not include weeks, months, and years. Instead, the table uses the annum or astronomical Julian year (365.25 days of 86,400 seconds), denoted with the symbol a. Its definition is based on the average length of a year according to the Julian calendar, which has one leap year every four years. According to the geological science convention, this is used to form larger units of time by the application of SI prefixes to it; at least up to giga-annum or Ga, equal to 1,000,000,000 a (short scale: one billion years, long scale: one milliard years).
## Less than one second
Units of measure less than a second
Multiple
of a
second
Unit Symbol Definition Comparative examples & common units
10-44 1 Planck time tP Presumed to be the shortest theoretically measurable time interval
(but not necessarily the shortest increment of time--see quantum gravity)
: One Planck time tP = ${\displaystyle {\sqrt {\hbar G/c^{5}}}}$ ? [1] is the briefest physically meaningful span of time. It is the unit of time in the natural units system known as Planck units.
10-24 1 yoctosecond ys[2] Yoctosecond, (yocto- + second), is one septillionth of a second 0.3 ys: mean lifetime of W and Z bosons
23 ys: Half life of isotope 7 of hydrogen (Hydrogen-7)
156 ys: mean lifetime of a Higgs Boson
10-21 1 zeptosecond zs Zeptosecond, (zepto- + second), is one sextillionth of one second 2 zs: representative cycle time of gamma ray radiation released in the decay of a radioactive atomic nucleus (here as 2 MeV per emitted photon)
4 zs: cycle time of the zitterbewegung of an electron (${\displaystyle \omega =2m_{e}c^{2}/\hbar }$)
247 zs: an experimentally-measured travel time of a photon across a hydrogen molecule, "for the average bond length of molecular hydrogen"[3]
10-18 1 attosecond as One quintillionth of one second 12 as: best timing control of laser pulses.[4]
43 as: shortest laser pulse[5]
10-15 1 femtosecond fs One quadrillionth of one second 1 fs: Cycle time for 300-nanometre light; ultraviolet light; light travels 0.3 micrometres (µm).
140 fs: Electrons have localized onto individual bromine atoms 6Å apart after laser dissociation of Br2.[6]
290 fs: Lifetime of a tauon
10-12 1 picosecond ps One trillionth of one second 1 ps: mean lifetime of a bottom quark; light travels 0.3 millimeters (mm)
1 ps: typical lifetime of a transition state
4 ps: Time to execute one machine cycle by an IBM silicon-germanium transistor
109 ps: Period of the photon corresponding to the hyperfine transition of the ground state of cesium-133, and one 9,192,631,770th of one second by definition
114.6 ps: Time for the fastest overclocked processor As of 2014 to execute one machine cycle.[7]
10-9 1 nanosecond ns One billionth of one second 1 ns: Time to execute one machine cycle by a 1 GHz microprocessor
1 ns: Light travels 30 cm (12 in)
10-6 1 microsecond µs One millionth of one second 1 µs: Time to execute one machine cycle by an Intel 80186 microprocessor
2.2 µs: Lifetime of a muon
4-16 µs: Time to execute one machine cycle by a 1960s minicomputer
10-3 1 millisecond ms One thousandth of one second 1 ms: time for a neuron in human brain to fire one impulse and return to rest[8]
4-8 ms: typical seek time for a computer hard disk
10-2 1 centisecond cs One hundredth of one second 1-2 cs (=0.01-0.02 s): Human reflex response to visual stimuli
1.6667 cs period of a frame at a frame rate of 60 Hz.
2 cs: cycle time for European 50 Hz AC electricity
10-1 1 decisecond ds One tenth of a second 1-4 ds (=0.1-0.4 s): Blink of an eye[9]
## One second and longer
In this table, large intervals of time surpassing one second are catalogued in order of the SI multiples of the second as well as their equivalent in common time units of minutes, hours, days, and Julian years.
Units of measure greater than one second
Multiple of a second Unit Symbol Common units Comparative examples & common units
101 1 decasecond das single seconds
(1 das = 10 s)
6 das: one minute (min), the time it takes a second hand to cycle around a clock face
102 1 hectosecond hs minutes
(1 hs = 1 min 40 s = 100 s)
2 hs (3 min 20 s): average length of the most popular YouTube videos as of January 2017[10]
5.55 hs (9 min 12 s): longest videos in above study
7.1 hs (11 m 50 s): time for a human walking at average speed of 1.4 m/s to walk 1 kilometre
103 1 kilosecond ks minutes, hours, days
(1 ks = 16 min 40 s = 1,000 s)
1 ks: record confinement time for antimatter, specifically antihydrogen, in electrically neutral state as of 2011[11]
1.8 ks: time slot for the typical situation comedy on television with advertisements included
3.6 ks: one hour (h), time for the minute hand of a clock to cycle once around the face, approximately 1/24 of one mean solar day
7.2 ks (2 h): typical length of feature films
86.399 ks (23 h 59 min 59 s): one day with a removed leap second on UTC time scale. Such has not yet occurred.
86.4 ks (24 h): one day of Earth by standard. More exactly, the mean solar day is 86.400 002 ks due to tidal braking, and increasing at the rate of approximately 2 ms/century; to correct for this time standards like UTC use leap seconds with the interval described as "a day" on them being most often 86.4 ks exactly by definition but occasionally one second more or less so that every day contains a whole number of seconds while preserving alignment with astronomical time. The hour hand of an analogue clock will typically cycle twice around the dial in this period as most analogue clocks are 12-hour, less common are analogue 24-hour clocks in which it cycles around once.
86.401 ks (24 h 0 min 1 s): one day with an added leap second on UTC time scale. While this is strictly 24 hours and 1 second in conventional units, a digital clock of suitable capability level will most often display the leap second as 23:59:60 and not 24:00:00 before rolling over to 00:00:00 the next day, as though the last "minute" of the day were crammed with 61 seconds and not 60, and similarly the last "hour" 3601 s instead of 3600.
88.775 ks (24 h 39 min 35 s): one sol of Mars
604.8 ks (7 d): one week of the Gregorian calendar
106 1 megasecond Ms weeks to years
(1 Ms = 11 d 13 h 46 min 40 s = 1,000,000 s)
1.641 6 Ms (19 d): length of a "month" of the Baha'i calendar
2.36 Ms (27.32 d): length of the true month, the orbital period of the Moon
2.419 2 Ms (28 d): length of February, the shortest month of the Gregorian calendar
2.592 Ms (30 d): 30 days, a common interval used in legal agreements and contracts as a proxy for a month
2.678 4 Ms (31 d): length of the longest months of the Gregorian calendar
23 Ms (270 d): approximate length of typical human gestational period
31.557 6 Ms (365.25 d): length of the Julian year, also called the annum, symbol a.
31.558 15 Ms (365 d 6 h 9 min 10 s): length of the true year, the orbital period of the Earth
126.232 6 Ms (1461 d 0 h 34 min 40 s): the elected term of the President of the United States or one Olympiad
109 1 gigasecond Gs decades, centuries, millennia
(1 Gs = over 31 years and 287 days = 1,000,000,000 s)
1.5 Gs: UNIX time as of Jul 14 02:40:00 UTC 2017. UNIX time being the number of seconds since 1970-01-01T00:00:00Z ignoring leap seconds.
2.5 Gs: (79 a): typical human life expectancy in the developed world
3.16 Gs: (100 a): one century
31.6 Gs: (1000 a, 1 ka): one millennium, also called a kilo-annum (ka)
63.8 Gs: approximate time since the beginning of the Anno Domini era as of 2019 - 2,019 years, and traditionally the time since the birth of Jesus Christ
194.67 Gs: Approximate lifespan of time capsule Crypt of Civilization, 28 May 1940 - 28 May 8113
363 Gs: (11.5 ka): time since the beginning of the Holocene epoch
814 Gs: (25.8 ka): approximate time for the cycle of precession of the Earth's axis
1012 1 terasecond Ts millennia to geological epochs
(1 Ts = over 31,600 years = 1,000,000,000,000 s)
3.1 Ts (100 ka): approximate length of a glacial period of the current Quaternary glaciation epoch
31.6 Ts (1000 ka, 1 Ma): one mega-annum (Ma), or one million years
79 Ts (2.5 Ma): approximate time since earliest hominids of genus Australopithecus
130 Ts (4 Ma): the typical lifetime of a biological species on Earth
137 Ts (4.32 Ma): the length of the mythic unit of mahayuga, the Great Age, in Hindu mythology.
1015 1 petasecond Ps geological eras, history of Earth and the Universe 2 Ps: approximate time since the Cretaceous-Paleogene extinction event, believed to be caused by the impact of a large asteroid into Chicxulub in modern-day Mexico. This extinction was one of the largest in Earth's history and marked the demise of most dinosaurs, with the only known exception being the ancestors of today's birds.
7.9 Ps (250 Ma): approximate time since the Permian-Triassic extinction event, the actually largest known mass extinction in Earth history which wiped out 95% of all extant species and believed to have been caused by the consequences of massive long-term volcanic eruptions in the area of the Siberian Traps. Also, the approximate time to the supercontinent of Pangaea. Also, the length of one galactic year or cosmic year, the time required for the Sun to complete one orbit around the Milky Way Galaxy.
16 Ps (510 Ma): approximate time since the Cambrian explosion, a massive evolutionary diversification of life which led to the appearance of most existing multicellular organisms and the replacement of the previous Ediacaran biota.
22 Ps (704 Ma): approximate half-life of the uranium isotope 235U.
31.6 Ps (1000 Ma, 1 Ga): one giga-annum (Ga), one billion years, the largest fixed time unit used in the standard geological time scale, approximately the order of magnitude of an eon, the largest division of geological time.
+1 Ga: The estimated remaining habitable lifetime of Earth, according to some models. At this point in time the stellar evolution of the Sun will have increased its luminosity to the point that enough energy will be reaching the Earth to cause the evaporation of the oceans and their loss into space (due to the uv flux from the Sun at the top of the atmosphere dissociating the molecules), making it impossible for any life to continue.
136 Ps (4.32 Ga): The length of the legendary unit kalpa in Hindu mythology, or one day (but not including the following night) of the life of Brahma.
143 Ps (4.5 Ga): The age of the Earth by our best estimates. Also the approximate half-life of the uranium isotope 238U.
315 Ps (10 Ga): approximate lifetime of a main-sequence star similar to our Sun.
435 Ps (13.8 Ga): The approximate age of the Universe
1018 1 exasecond Es future cosmological time All times of this length and beyond are currently theoretical as they surpass the elapsed lifetime of the known universe.
1.08 Es (+34 Ga): time to the Big Rip according to some models, but this is not favored by existing data. This is one possible scenario for the ultimate fate of the Universe. Under this scenario, dark energy increases in strength and power in a feedback loop that eventually results in the tearing apart of all matter down to subatomic scale due to the rapidly increasing negative pressure thereupon
300 - 600 Es (10 000 - 20 000 Ga): The estimate lifetime of low-mass stars (red dwarfs)
1021 1 zettasecond Zs 3 Zs (+100 000 Ga): The remaining time until the end of Stelliferous Era of the universe under the heat death scenario for the ultimate fate of the Universe which is the most commonly-accepted model in the current scientific community. This is marked by the cooling-off of the last low-mass dwarf star to a black dwarf. After this time has elapsed, the Degenerate Era begins.
9.85 Zs (311 000 Ga): The entire lifetime of Brahma in Hindu mythology.
1024 and onward 1 yottasecond and beyond Ys and on 600 Ys : The radioactive half-life of bismuth-209 by alpha decay, one of the slowest-observed radioactive decay processes.
: The time period equivalent to the value of 13.13.13.13.13.13.13.13.13.13.13.13.13.13.13.13.13.13.13.13.0.0.0.0 in the Mesoamerican Long Count, a date discovered on a stela at the Coba Maya site, believed by archaeologist Linda Schele to be the absolute value for the length of one cycle of the universe[12][13]
: the smallest possible value for proton half-life consistent with experiment[14]
: the largest possible value for the proton half-life, assuming that the Big Bang was inflationary and that the same process that made baryons predominate over antibaryons in the early Universe also makes protons decay[15]
: approximate lifespan of a black hole with the mass of the Sun[16]
: approximate lifespan of a supermassive black hole with a mass of 20 trillion solar masses[16]
${\displaystyle 10^{10^{10^{76.66}}}}$ Ys: scale of an estimated Poincaré recurrence time for the quantum state of a hypothetical box containing an isolated black hole of stellar mass[17] This time assumes a statistical model subject to Poincaré recurrence. A much simplified way of thinking about this time is that in a model in which history repeats itself arbitrarily many times due to properties of statistical mechanics, this is the time scale when it will first be somewhat similar (for a reasonable choice of "similar") to its current state again.
${\displaystyle 10^{10^{10^{120}}}}$ Ys: scale of an estimated Poincaré recurrence time for the quantum state of a hypothetical box containing a black hole with the mass of the observable Universe.[17]
${\displaystyle 10^{10^{10^{10^{13}}}}}$ Ys: scale of an estimated Poincaré recurrence time for the quantum state of a hypothetical box containing a black hole with the estimated mass of the entire Universe, observable or not, assuming Linde's chaotic inflationary model with an inflaton whose mass is 10-6 Planck masses.[17]
Other
Multiples Unit Symbol
6×101 seconds 1 minute m
6×101 minutes 1 hour h (hr)
2.4×101 hours 1 day d
## References
1. ^ "CODATA Value: Planck time". The NIST Reference on Constants, Units, and Uncertainty. NIST. Retrieved 2011.
2. ^ The American Heritage Dictionary of the English Language: Fourth Edition. 2000. Available at: http://www.bartleby.com/61/21/Y0022100.html Archived 10 March 2008 at the Wayback Machine. Accessed 19 December 2007. note: abbr. ys or ysec
3. ^ Grundmann, Sven; Trabert, Daniel; et al. (16 October 2020). "Zeptosecond birth time delay in molecular photoionization". Science. 370 (6514): 339-341. arXiv:2010.08298. doi:10.1126/science.abb9318. PMID 33060359. Retrieved 2020.
4. ^
5. ^
6. ^ Li, Wen; et al. (23 November 2010). "Visualizing electron rearrangement in space and time during the transition from a molecule to atoms". PNAS. 107 (47): 20219-20222. Bibcode:2010PNAS..10720219L. doi:10.1073/pnas.1014723107. PMC 2996685. PMID 21059945. Retrieved 2015.
7. ^ Chiappetta, Marco (23 September 2011). "AMD Breaks 8 GHz Overclock with Upcoming FX Processor, Sets World Record. The record has been surpassed with 8794 MHz of overclocking with AMD FX 8350". HotHardware. Archived from the original on 10 March 2015. Retrieved 2012.
8. ^ "Notebook". www.noteaccess.com.
9. ^ Eric H. Chudler. "Brain Facts and Figures: Sensory Apparatus: Vision". Retrieved 2011.
10. ^ "YouTube Statistics and Your Best Video Length for Different Videos". Video Production Washington DC - MiniMatters. 11 March 2014.
11. ^ Alpha Collaboration; Andresen, G. B.; Ashkezari, M. D.; Baquero-Ruiz, M.; Bertsche, W.; Bowe, P. D.; Butler, E.; Cesar, C. L.; Charlton, M.; Deller, A.; Eriksson, S.; Fajans, J.; Friesen, T.; Fujiwara, M. C.; Gill, D. R.; Gutierrez, A.; Hangst, J. S.; Hardy, W. N.; Hayano, R. S.; Hayden, M. E.; Humphries, A. J.; Hydomako, R.; Jonsell, S.; Kemp, S. L.; Kurchaninov, L.; Madsen, N.; Menary, S.; Nolan, P.; Olchanski, K.; et al. (5 June 2011). "Confinement of antihydrogen for 1,000 seconds". Nature Physics. 7 (7): 558-564. arXiv:1104.4982. Bibcode:2011NatPh...7..558A. doi:10.1038/nphys2025.
12. ^ Falk, Dan (2013). In search of time the science of a curious dimension. New York: St. Martin's Press. ISBN 978-1429987868.
13. ^ G. Jeffrey MacDonald "Does Maya calendar predict 2012 apocalypse?" USA Today 27 March 2007.
14. ^ Nishino, H. et al. (Super-K Collaboration) (2009). "Search for Proton Decay via
p+
e+
π0
and
p+
μ+
π0
in a Large Water Cherenkov Detector". Physical Review Letters. 102 (14): 141801. arXiv:0903.0676. Bibcode:2009PhRvL.102n1801N. doi:10.1103/PhysRevLett.102.141801. PMID 19392425.
15. ^ Adams, Fred C.; Laughlin, Gregory (1 April 1997). "A dying universe: the long-term fate and evolutionof astrophysical objects". Reviews of Modern Physics. American Physical Society (APS). 69 (2): 337-372. arXiv:astro-ph/9701131. Bibcode:1997RvMP...69..337A. doi:10.1103/revmodphys.69.337. ISSN 0034-6861.
16. ^ a b Page, Don N. (15 January 1976). "Particle emission rates from a black hole: Massless particles from an uncharged, nonrotating hole". Physical Review D. American Physical Society (APS). 13 (2): 198-206. doi:10.1103/physrevd.13.198. ISSN 0556-2821. See in particular equation (27).
17. ^ a b c Page, Don N. (1995). "Information Loss in Black Holes and/or Conscious Beings?". In Fulling, S.A. (ed.). Heat Kernel Techniques and Quantum Gravity. Discourses in Mathematics and its Applications. Texas A&M University. p. 461. arXiv:hep-th/9411193. Bibcode:1994hep.th...11193P. ISBN 978-0-9630728-3-2.
This article uses material from the Wikipedia page available here. It is released under the Creative Commons Attribution-Share-Alike License 3.0. | 2021-07-25 18:56:49 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 5, "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": 0.5976019501686096, "perplexity": 4420.39929172173}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-31/segments/1627046151760.94/warc/CC-MAIN-20210725174608-20210725204608-00594.warc.gz"} |
http://www.openwetware.org/wiki/Physics307L_F08:People/Dougherty/Notebook/071119 | Physics307L F08:People/Dougherty/Notebook/071119
Excitation of Neon
Linh and I decided to do the excitation of Neon levels. However I was sick the first day of data taking. Erron and Linh worked on it the first day, then all 3 of us were taking data the second day, which turned out to be better data thanks to Professor Koch.
For full lab details see Lab manual pg 45
Setup/Procedure
Fig. 1 The 4 connections for the anode and cathode gun and the filament
Fig. 2 The circuit and setup of the power sources and alarm
"The essence of this experiment is the demonstration of energy quantization of atoms, Ne in this case. This is achieved via inelastic e− scattering off Ne atoms. As such it is closely related to the original Franck-Hertz experiment (1914), which showed that an electron must have a certain minimum energy to make an inelastic collision with an atom. We now interpret that minimum energy as the energy of an excited state of the atom. It is strongly advised to read up on the Franck-Hertz experiment.
From a collision standpoint, free electrons colliding with orbiting electrons need to have at least the minimum energy required to excite the bound electrons to higher quantum levels. This experiment involves collecting these electrons after their atomic collisions, and determining the separate excitation energy levels that are available. The theory is quite simple. If an electron collides with a bound electron, and has suffcient energy to “move” the bound electron up into new orbits (or even ionize the atom), then the energy absorbed by the atom is lost to the free electron. This is an inelastic collision, and the free electron will slow down appreciably. In particular, it can now easily be captured by an anode positioned near the beam. As a function of the electron accelerating potential, VA, the number of electrons captured will increase rapidly near the energy levels of the atomic gas in the tube. These peaks in current will signal the energy levels of the atom."(from Physics 307 Lab Manual)
Following the details of the circuit from Fig. 2, we were able to set up the entire apparatus and set the heater to a small voltage, never exceeding 2.5 V. After that we kept the accelerating voltage at zero so we could also zero out the alarm meter. After this we could make a broad sweep and find drastic peaks and valleys on the meter. After finding them we made very detailed sweeps of those certain areas to get detailed data to plot. Then after a while as you keep increasing the voltage, we found the current grows unbounded. The point where it does that we concluded is the ionization of the Ne gas.
Equipment
• Fluke 111 true rms multimeter
• Hertz Critical Potentials Tube filled with neon
• Picoamplifier and alarmed meter
• 2 HP power supplies
Data
(battery - to - and + to +)
Measuring peaks
Vf=2.5V
VA (volts) Ic pA
14.00 -6
14.25 -6
14.50 -6
14.75 -6
15.00 -6
15.25 -6
15.50 -7
15.75 -7
16.00 -6
16.25 -5
VA (Volts) Ic pA
20.00 -3
20.25 -2
20.50 -2
20.75 -2
21.00 -2
21.25 0
21.50 0
21.75 1
22.00 2
22.25 3
22.50 4
22.75 5
23.00 6
[Thanks to Dr. Koch shoving in the tube, we are getting some better numbers]
VA (Volts) Ic pA
15.00 -1.516
15.25 -1.547
15.50 -1.579
15.75 -1.610
16.00 -1.640
16.25 -1.659 X
16.50 -1.620
16.75 -1.651 X
17.00 -1.569
17.25 -1.235
17.50 -1.138
17.75 -1.186
18.00 -1.057
• day 2
(battery + to + and - to -) Vf=2.000V
Va (V) Current (mA)
17.00 -.063
17.25 -.086
17.50 -.140
17.75 -.103
18.00 -.093
18.25 -.119 X
18.50 -.107
18.75 -.102
19.00 -.092
19.25 -.086
20.00 -.093
20.25 -.109
20.50 -.125 X
20.75 -.118
21.00 -.106
21.25 -.118
21.50 -.118
21.75 -.120
22.00 -.121
• continues to grow unbounded after this point
Battery flip (+to- and -to+) Vf 2.00A
Va (V) Current (mA)
17.50 -.015
17.75 ~-.0003
18.00 .028
18.25 .040
18.50 .044
18.60 .051
18.70 .062
18.80 .069
18.90 .075
19.00 .078
19.10 .80
19.20 .082
19.30 .084
19.40 .086
19.50 .088
19.60 .090
19.70 .093
19.80 .096
19.90 .098
20.00 .100
20.10 .102
21.50 .135
21.60 .139
21.70 .142
21.80 .144
21.90 .148
22.00 .151
22.10 .154
22.20 .158
22.30 .163
22.40 .167
22.50 .173
22.60 .181
22.70 .188
22.80 .196
22.90 .205
23.00 .213
• Battery (+ to - and - to +)
Vf=2.476V
Va (V) Current (mA)
17.00 -.071
17.25 -.001
17.30 .026
17.40 .081
17.50 .142
17.60 .180
17.70 .201
17.75 .206
17.80 .210
17.90 .213
18.00 .221
18.10 .255
18.20 .304
18.30 .344
18.40 .374
18.50 .389
18.60 .397
18.70 .406
18.80 .416
18.90 .425
19.00 .437
19.10 .449
19.20 .462
19.30 .473
19.40 .489
19.50 .497
19.60 .506
19.70 .514
19.80 .524
19.90 .545
20.00 .555
Data Analysis
The first day of taking data Linh and Erron had a lot of trouble it sounded like. I wasn't able to be there, but from what it looks like, nothing was coming out correct. Then Professor Koch pushed in the neon tube farther and the second day when I was there, we were getting much better data to record. So i will only be using the last 4 data sets.
By graphing the Ic (Pa) vs. the Va (V) I got these sets of graphs:(Fig. 1 - 4)
Fig. 5 Sample graph from lab manual
Fig. 6 Sample graph from lab manual
Looking at our graphs and comparing them to the sample graphs in the lab manual (See Fig. 5 and 6), I concluded that the polarity of the battery might have been mixed up. Since the second sample graph has a small amount of positive values then switches abruptly to negative, i assumed that was what happened for our last two graphs. Also our first two graphs are purely negative and the sample graph in the lab manual was strictly positive. Considering these two points I assumed the polarities were opposite so I switched the negative and positive values and came up with another set of graphs that looked much better to the sample graphs. (see Fig. 7 - 10)
As Linh pointed out, we found peaks at 16.25, 16.75, 18.25, and 20.50. Which we found to close to the peaks found in the lab manual. Considering this a good sign, we felt the experiment went decently well.
And after the point of 21.25 V the current grew unbounded. We felt it was the ionization level of the Ne gas.
Conclusion
As i said above, the experiment went rather well. I wanna thank Linh and Erron for doing a lot of the hard work before i could make it in to help.
Also looking at our graphs, I think they are at least relatively like the sample graphs from the lab manual. Of course I didn't expect them to be exactly the same.
Error
The original peaks we found are 16.25, 16.75, 18.25, and 20.50.
Since these are close to some peaks found in the manual I would like to show the error we have from the lab manual.
$%error= \frac{|Actual-Experimental|}{|Actual|}x100$
$%error= \frac{|16.7-16.75|}{|16.7|}x100$
%error = .3
$%error= \frac{|19.75-18.25|}{|19.75|}x100$
%error = 7.59
$%error= \frac{|20.1-20.5|}{|20.1|}x100$
%error = 1.9
now taking the average of our error, Average Error= 3.26%
Avery small error considering the fragile state of the experiment. Any movement or noise or talking disrupted the entire apparatus and would skew our measurements. But we were able to work through them and get some pretty decent data. | 2017-06-25 17:36:16 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 4, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4732031524181366, "perplexity": 2584.117980877684}, "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-2017-26/segments/1498128320545.67/warc/CC-MAIN-20170625170634-20170625190634-00346.warc.gz"} |
https://everything.explained.today/Transversality_(mathematics)/ | # Transversality (mathematics) explained
In mathematics, transversality is a notion that describes how spaces can intersect; transversality can be seen as the "opposite" of tangency, and plays a role in general position. It formalizes the idea of a generic intersection in differential topology. It is defined by considering the linearizations of the intersecting spaces at the points of intersection.
## Definition
Two submanifolds of a given finite-dimensional smooth manifold are said to intersect transversally if at every point of intersection, their separate tangent spaces at that point together generate the tangent space of the ambient manifold at that point.[1] Manifolds that do not intersect are vacuously transverse. If the manifolds are of complementary dimension (i.e., their dimensions add up to the dimension of the ambient space), the condition means that the tangent space to the ambient manifold is the direct sum of the two smaller tangent spaces. If an intersection is transverse, then the intersection will be a submanifold whose codimension is equal to the sums of the codimensions of the two manifolds. In the absence of the transversality condition the intersection may fail to be a submanifold, having some sort of singular point.
In particular, this means that transverse submanifolds of complementary dimension intersect in isolated points (i.e., a 0-manifold). If both submanifolds and the ambient manifold are oriented, their intersection is oriented. When the intersection is zero-dimensional, the orientation is simply a plus or minus for each point.
One notation for the transverse intersection of two submanifolds
L1
and
L2
of a given manifold
M
is
L1\pitchforkL2
. This notation can be read in two ways: either as “
L1
and
L2
intersect transversally” or as an alternative notation for the set-theoretic intersection
L1\capL2
of
L1
and
L2
when that intersection is transverse. In this notation, the definition of transversality reads
L1\pitchforkL2\iff\forallp\inL1\capL2,TpM=TpL1+TpL2.
## Transversality of maps
The notion of transversality of a pair of submanifolds is easily extended to transversality of a submanifold and a map to the ambient manifold, or to a pair of maps to the ambient manifold, by asking whether the pushforwards of the tangent spaces along the preimage of points of intersection of the images generate the entire tangent space of the ambient manifold.[2] If the maps are embeddings, this is equivalent to transversality of submanifolds.
## Meaning of transversality for different dimensions
Suppose we have transverse maps
f1:L1\toM
and
f2:L2\toM
where
L1,L2
and
M
are manifolds with dimensions
\ell1,\ell2
and
m
respectively.
The meaning of transversality differs a lot depending on the relative dimensions of
M,L1
and
L2
. The relationship between transversality and tangency is clearest when
\ell1+\ell2=m
.
We can consider three separate cases:
1. When
\ell1+\ell2<m
, it is impossible for the image of
L1
and
L2
's tangent spaces to span
M
's tangent space at any point. Thus any intersection between
f1
and
f2
cannot be transverse. However, non-intersecting manifolds vacuously satisfy the condition, so can be said to intersect transversely.
1. When
\ell1+\ell2=m
, the image of
L1
and
L2
's tangent spaces must sum directly to
M
's tangent space at any point of intersection. Their intersection thus consists of isolated signed points, i.e. a zero-dimensional manifold.
1. When
\ell1+\ell2>m
this sum needn't be direct. In fact it cannot be direct if
f1
and
f2
are immersions at their point of intersection, as happens in the case of embedded submanifolds. If the maps are immersions, the intersection of their images will be a manifold of dimension
\ell1+\ell2-m.
## Intersection product
Given any two smooth submanifolds, it is possible to perturb either of them by an arbitrarily small amount such that the resulting submanifold intersects transversally with the fixed submanifold. Such perturbations do not affect the homology class of the manifolds or of their intersections. For example, if manifolds of complementary dimension intersect transversally, the signed sum of the number of their intersection points does not change even if we isotope the manifolds to another transverse intersection. (The intersection points can be counted modulo 2, ignoring the signs, to obtain a coarser invariant.) This descends to a bilinear intersection product on homology classes of any dimension, which is Poincaré dual to the cup product on cohomology. Like the cup product, the intersection product is graded-commutative.
## Examples of transverse intersections
The simplest non-trivial example of transversality is of arcs in a surface. An intersection point between two arcs is transverse if and only if it is not a tangency, i.e., their tangent lines inside the tangent plane to the surface are distinct.
In a three-dimensional space, transverse curves do not intersect. Curves transverse to surfaces intersect in points, and surfaces transverse to each other intersect in curves. Curves that are tangent to a surface at a point (for instance, curves lying on a surface) do not intersect the surface transversally.
Here is a more specialised example: suppose that
G
is a simple Lie group and
ak{g}
is its Lie algebra. By the Jacobson–Morozov theorem every nilpotent element
e\inak{g}
can be included into an
ak{sl2}
-triple
(e,h,f)
. The representation theory of
ak{sl2}
tells us that
ak{g}=[ak{g},e]ak{g}f
. The space
[ak{g},e]
is the tangent space at
e
and so the affine space
e+ak{g}f
intersects the orbit of
e
transversally. The space
e+ak{g}f
is known as the "Slodowy slice" after Peter Slodowy.
## Applications
### Optimal control
In fields utilizing the calculus of variations or the related Pontryagin maximum principle, the transversality condition is frequently used to control the types of solutions found in optimization problems. For example, it is a necessary condition for solution curves to problems of the form:
Minimize
\int{F(x,y,y\prime)}dx
where one or both of the endpoints of the curve are not fixed.In many of these problems, the solution satisfies the condition that the solution curve should cross transversally the nullcline or some other curve describing terminal conditions.
### Smoothness of solution spaces
Using Sard's theorem, whose hypothesis is a special case of the transversality of maps, it can be shown that transverse intersections between submanifolds of a space of complementary dimensions or between submanifolds and maps to a space are themselves smooth submanifolds. For instance, if a smooth section of an oriented manifold's tangent bundle—i.e. a vector field—is viewed as a map from the base to the total space, and intersects the zero-section (viewed either as a map or as a submanifold) transversely, then the zero set of the section—i.e. the singularities of the vector field—forms a smooth 0-dimensional submanifold of the base, i.e. a set of signed points. The signs agree with the indices of the vector field, and thus the sum of the signs—i.e. the fundamental class of the zero set—is equal to the Euler characteristic of the manifold. More generally, for a vector bundle over an oriented smooth closed finite-dimensional manifold, the zero set of a section transverse to the zero section will be a submanifold of the base of codimension equal to the rank of the vector bundle, and its homology class will be Poincaré dual to the Euler class of the bundle.
An extremely special case of this is the following: if a differentiable function from reals to the reals has nonzero derivative at a zero of the function, then the zero is simple, i.e. it the graph is transverse to the x-axis at that zero; a zero derivative would mean a horizontal tangent to the curve, which would agree with the tangent space to the x-axis.
For an infinite-dimensional example, the d-bar operator is a section of a certain Banach space bundle over the space of maps from a Riemann surface into an almost-complex manifold. The zero set of this section consists of holomorphic maps. If the d-bar operator can be shown to be transverse to the zero-section, this moduli space will be a smooth manifold. These considerations play a fundamental role in the theory of pseudoholomorphic curves and Gromov–Witten theory. (Note that for this example, the definition of transversality has to be refined in order to deal with Banach spaces!)
## Grammar
"Transversal" is a noun; the adjective is "transverse." | 2021-06-13 01:33:17 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8701035976409912, "perplexity": 316.9341550922962}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-25/segments/1623487598213.5/warc/CC-MAIN-20210613012009-20210613042009-00023.warc.gz"} |
http://en.f-alpha.net/mathematics/algebra/boolean-algebra/lets-go/experiment-3-or-operation/ | Mathematics
Boolean Algebra
f-alpha.net » Mathematics » Algebra » Boolean Algebra » Let's go... » Experiment 3 - OR Operation
# Experiment 3 - The OR Operation (Disjunction)
You can picture the behavior of an OR operation with the switch model and register the result Q in the truth table...
Switch model of the OR operation.
A B Q 0 0 0 0 1 1 1 0 1 1 1 1
Truth table OR operation.
In logic equations the operator $$\vee$$ is used for the OR operation... $$Q = A \vee B$$ (Speaking: A or B). Logical symbol of the OR operation.
With the C-MOS IC 4071, you build an OR operation...
Circuit diagram OR operation. Circuit OR operation. (Enlarge)
Logical Sum Mathematically the OR operation is similar to the addition and is therefore also known as logical sum. Therefore, you will find variations of the logic equations... $$A \vee B \equiv A + B$$
Next the NOT operation... | 2018-11-17 02:49:18 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4552605450153351, "perplexity": 1834.369503457454}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-47/segments/1542039743248.7/warc/CC-MAIN-20181117020225-20181117042225-00243.warc.gz"} |
https://www.physicsforums.com/threads/how-do-i-write-this.184803/ | How do I write this?
1. Sep 15, 2007
nicksauce
I have a solution for a PDE
$$U(x,t)=y^2e^{-3x} + h(x)$$
Where h(x) is any function such that h(0) = 1
What notation can I use for this clause on h(x)?
My guess is:
$$h(x)\in \{f(x)|f(0)=1\}$$
Does that make sense?
2. Sep 15, 2007
arildno
Sure, it's a fancy-pants way of putting it.
3. Sep 15, 2007
nicksauce
I like doing things the fancy-pants way :tongue:
4. Sep 15, 2007
Well if you want to be fancy pants, you might well want to mention what sort of hypotheses are needed on h, ie there probably should be some differentiability condition.
5. Sep 15, 2007
nicksauce
True; is there a symbolic way to write 'continuous'?
6. Sep 15, 2007
axeae
$$\text{yeah, if } f(x) \text{ is continuous on an interval } [a,b] \text{ then } f(x) \in C[a,b]$$
Last edited: Sep 16, 2007
7. Sep 15, 2007
HallsofIvy
Staff Emeritus
I am just a tiny bit concerned that your formula,
$$U(x,t)=y^2e^{-3x} + h(x)$$
has U(x,t) on the left but a "y" and no "t" on the right!
8. Sep 15, 2007
nicksauce
Lol woops, should be U(x,y)
9. Sep 15, 2007
off topic but does anyone know why my latex doesnt work? i tried doing it with a bunch of little $$and no \text but that didnt work, so i tried what i have now and just gave up and left it like that. 10. Sep 15, 2007 nicksauce Try using \textnormal [tex]\textnormal{This is a test}$$
11. Sep 16, 2007
bomba923
You do not need \textnormal
Simply finish with "/tex", not with "\tex", between the brackets
12. Sep 16, 2007
axeae
oh wow, i guess ive been doing latex so much i forgot not everything else uses \ instead of / | 2017-12-18 07:12:50 | {"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": 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": 0.8353803753852844, "perplexity": 3780.545136783}, "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-2017-51/segments/1512948609934.85/warc/CC-MAIN-20171218063927-20171218085927-00056.warc.gz"} |
https://www.projecteuclid.org/euclid.jsl/1183745382 | ## Journal of Symbolic Logic
### Undecidable Extensions of Buchi Arithmetic and Cobham-Semenov Theorem
Alexis Bes
#### Abstract
Let $k$ and $l$ be two multiplicatively independent integers, and let $L \subseteq \mathbb{N}^n$ be a $l$-recognizable set which is not definable in $\langle\mathbb{N}; +\rangle$. We prove that the elementary theory of $\langle\mathbb{N}; +, V_k, L\rangle$, where $V_k(x)$ denotes the greatest power of $k$ dividing $x$, is undecidable. This result leads to a new proof of the Cobham-Semenov theorem.
#### Article information
Source
J. Symbolic Logic, Volume 62, Issue 4 (1997), 1280-1296.
Dates
First available in Project Euclid: 6 July 2007
Permanent link to this document
https://projecteuclid.org/euclid.jsl/1183745382
Mathematical Reviews number (MathSciNet)
MR1617949
Zentralblatt MATH identifier
0896.03011
JSTOR
links.jstor.org
#### Citation
Bes, Alexis. Undecidable Extensions of Buchi Arithmetic and Cobham-Semenov Theorem. J. Symbolic Logic 62 (1997), no. 4, 1280--1296. https://projecteuclid.org/euclid.jsl/1183745382 | 2020-02-24 15:51:34 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6592200994491577, "perplexity": 1321.875276274455}, "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-2020-10/segments/1581875145960.92/warc/CC-MAIN-20200224132646-20200224162646-00403.warc.gz"} |
http://openstudy.com/updates/50156c7de4b0fa24673170fc | ## AravindG Group Title A cylindrical tank of height 0.4 m is open at the top and has a diameter 0.16 m.Water is filled in it upto a height of 0.16 m .Calculate the time taken to empty the tank through a hole of radius 5x10^-3m in its bottom? 2 years ago 2 years ago
1. AravindG
@Vincent-Lyon.Fr , @ash2326 , @waterineyes
2. Vincent-Lyon.Fr
First, use Torricelli's law to determine speed of water in the hole and rate of flow. $$v=\sqrt{2gh}$$
3. AravindG
then?
4. Vincent-Lyon.Fr
Is the answer 45.80 s ?
5. AravindG
i didnt get tht :O
6. AravindG
i got 2.8 :P
7. Vincent-Lyon.Fr
How?
8. AravindG
wait
9. RaphaelFilgueiras
h is variable
10. AravindG
hmm
11. AravindG
then how ?
12. Vincent-Lyon.Fr
Total volume is 3.217 L, right?
13. AravindG
i got 3.14x10^-4
14. Vincent-Lyon.Fr
Try again. radius is 0.08m and height is 0.16m
15. AravindG
3.21x10^-3
16. Vincent-Lyon.Fr
ok
17. AravindG
so?
18. Vincent-Lyon.Fr
now escape velocity is $$v=\sqrt{2gh}$$
19. Vincent-Lyon.Fr
and discharge is v multiplied by area of hole.
20. AravindG
v is velocity ryt?
21. Vincent-Lyon.Fr
yep
22. AravindG
so how do we bring in volume?
23. Vincent-Lyon.Fr
time taken is: volume / discharge you should find 22.9s
24. AravindG
hmm
25. AravindG
but isnt h varying?
26. Vincent-Lyon.Fr
Yes, but we can get round this difficulty
27. Vincent-Lyon.Fr
Do you find the same values?
28. AravindG
how/?
29. Vincent-Lyon.Fr
initial escape velocity is v=root(2g hmax) discharge is v multiplied by area of hole. time taken is: volume / discharge you should find 22.9s This is the time it would take to empty the tank if initial discharge was constant. Real duration, when h varies, is twice that time. | 2014-11-27 21:03:16 | {"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": 0.8462929725646973, "perplexity": 10383.532050540709}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-49/segments/1416931009179.34/warc/CC-MAIN-20141125155649-00175-ip-10-235-23-156.ec2.internal.warc.gz"} |
https://electronics.stackexchange.com/questions/205339/should-hdl-languages-be-taught-before-software-languages | # Should HDL languages be taught before software languages? [closed]
I'm a Computer Engineering student and learned the basic sequential programming languages (C/assembly/Java) way before I was even introduced to HDLs. Thus, my whole programming logic was based upon sequential coding with a very specific execution flow.
Once introduced to HDLs, I and many of my colleagues ran into difficulties regarding the concurrent way a circuit can behave. We had a very clear understanding of combinational logic, but synthesizing a circuit in a language so similar to the "usual" sequential languages we were first taught was somewhat challenging.
Wouldn't it be better to teach HDLs before software programming languages to "hardware-driven" courses?
## closed as primarily opinion-based by PeterJ, Matt Young, Leon Heller, Andy aka, Daniel GrilloDec 10 '15 at 10:28
Many good questions generate some degree of opinion based on expert experience, but answers to this question will tend to be almost entirely based on opinions, rather than facts, references, or specific expertise. If this question can be reworded to fit the rules in the help center, please edit the question.
IMHO, "no". First, even though the sequential vs. concurrent issue takes some getting used to, the concept of precisely instructing a machine takes even more, and sequential languages are an easier and more accessible introduction to that - even apart from the languages themselves, just look at the cost, capability, flexibility, build time, and market size of the tools.
Once you get beyond basic combinatorial logic stages, most HDL designs are sequences of parallel operations anyway - be they state machines, pipelines, or stored-program processors in their own right. Further, most practical HDL designs will also require no small amount of sequential software to exercise or utilize them.
Finally, practically speaking in today's world of cheap microcontrollers, unless you are designing special ASIC functionality, you will almost always use a sequential program as your default choice, and resort to describing custom logic only where a sequentially programmed machine is substantially sub-optimal for the task - most often, when you need to do something relatively simple very quickly, or in massive parallel.
I have written lots of C code (and asm code) that was all event driven.
Typically from timer, watchdog, and I/O interrupts. With lots of schedulers to initiate periodic software functions.
In my experience, most schools do not teach the kind of thinking needed to handle event driven programming.
There are concurrent languages, often running on PLCs, ASICs, etc that are continuous, concurrent, etc. Mostly, after learning those languages, a programmer must be thinking in those languages to obtain the most out of them.
Then there are the I.A. languages like Lisp and Prolog that are completely different from either the sequential or event driven languages.
I.E. each language has its' strong and weak points. If a programmer wants (or needs) to use a specific language, then they need to learn that language, so they think of programming problems in the terms of that language.
Most programmers will never be programming FPGAs or ASICs or PLCs, but will be either doing application programming for business (COBOL, C, JAVA, ForTran, etc) or web design (HTML, XML, javascript, json, SQL, etc.
SO, IMO: the 'sequential' languages are best to learn first as they are the easiest to understand, so the basic concepts are known before learning the more esoteric languages.
And then there are the languages like C++ and C# and J# and many more that can be coded for either environment.
But first, the underlying concepts need to be understood.
Concepts Ranging from memory and register concepts, to the history of programming, to the Turing machine, to 'ancient' things that were the forerunners of today, such as ASCII, and 80/96 column punched cards and card readers and paper tape and magnetic tape with level shifting and low level programming of I/O devices, etc etc etc.
• "I.A. languages like Lisp and Prolog that are completely different from either the sequential or event driven languages". First "I.A." should be "A.I.". Also, Lisp and Prolog aren't actually much different from sequential languages. Further one of Prolog's weaknesses is developers often need to take control of its sequential properties to solve real-world-scale problems; it is somewhat different for simple (trivial?) problems. Finally some of the 'concepts' listed rarely help, and may mislead (e.g. some algorithms were a response to technology restrictions which no longer apply). – gbulmer Dec 10 '15 at 7:43
• BTW, HTML and XML are not programming languages. Also Fortran was FORTRAN, not ForTran, and Java is not an acronym; it was never JAVA etc. – gbulmer Dec 10 '15 at 7:51
• @gbulmer, Actually, HTML, XML, are programming languages and FORTRAN was originally spelled ForTran because that was a short cut for Formula Translator etc. If a 'programmer' does not know the history of programming, memory concepts, etc etc. Then they will be severely handicapped, especially when they need to produce some code that is 'outside their comfort zone', like having to implement a communication protocol or 'bit-bang' a I/O port or implement an I/O optimizer for a Centronics printer or update some very old code that originally talked to a card reader/punch or ... – user3629249 Dec 10 '15 at 19:09
• Definition of XML: "Extensible Markup Language (XML) is a markup language that defines a set of rules for encoding documents in a format which is both human-readable and machine-readable." – user3629249 Dec 10 '15 at 19:10
• definition of HTML: "Hypertext Markup Language, a standardized system for tagging text files to achieve font, color, graphic, and hyperlink effects on World Wide Web pages." – user3629249 Dec 10 '15 at 19:11
Given that I have seen several HDL veterans who later in their career decided to learn C, and from there produced completely horrible code, I think it is a very bad idea to start with HDL as your first programming language.
Not so much because of the sequential versus event-driven program flow, but because high-level languages are so much more complex and also have more rigid requirements on readability. You can't write high-level language code like you write HDL, you need to apply some manner of program design, a concept which is mostly absent in HDL.
It is a fact that microcontrollers are far more commonly used than ASICs. And even when ASICs are used, they often have microcontrollers/microprocessors inside. So the main focus when teaching engineering should be microcontroller programming.
And looking at many examples of bare metal microcontroller programs for example posted on this site, where everything is a wall of code inside main(), with a few stray, barely thought-out functions, there is a desperate need for E.E school to focus more on program design, rather than subjects of peripheral interest such as HDL or digital logic.
• While I somewhat agree with you, I feel that sighting code examples here, as evidence that EE schools don't focus on 'managing complexity', is a very biased sample. People are mostly asking questions because they don't know how to solve a problem. So we shouldn't judge industry from that our sample. We may make the code worse because we often ask for "the simplest case that demonstrates a bug", and the poster is tempted to doing that ASAP with least effort. Finally, I know a HDL professor; he believes students can be taught to organise their 'programs' to better manage complexity. – gbulmer Dec 10 '15 at 8:01
• @gbulmer Of course you'll mainly find narrowed down examples on this site, but on the other hand you'll rarely ever find any hints of proper design either. So apart from students etc asking for help with narrow tasks, I think the site reflects the industry fairly well. It is a well-known problem that the embedded industry, just like any other present software industry, contains plenty of quacks and incompetents. Just open up pretty much any app note by any major silicon vendor that contains C source code and see for yourself. – Lundin Dec 10 '15 at 9:43 | 2019-08-26 09:15:06 | {"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": 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": 0.3270428776741028, "perplexity": 2499.077016981689}, "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-2019-35/segments/1566027331485.43/warc/CC-MAIN-20190826085356-20190826111356-00437.warc.gz"} |
http://forum.bebac.at/forum_entry.php?id=18219&category=1&order=time | ## Simulations [Power / Sample Size]
» Is it worth to calculate sample size at power of 95%?
» Are there any risks?
Too many subjects
It is unethical to disturb more subjects than necessary
Some subjects at risk and they are not necessary
It is an unnecessary waste of some resources ($) It takes more time to analytical sample analysis - time is money <- this does not a apply to a rich client Too few subjects A study unable to reach its objective is unethical All subjects at risk for nothing All resources ($) is wasted when the study is inconclusive | 2019-11-14 14:48:30 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6086849570274353, "perplexity": 5020.8877868161735}, "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/1573496668525.62/warc/CC-MAIN-20191114131434-20191114155434-00541.warc.gz"} |
http://math.stackexchange.com/questions/289109/definite-integral-with-periodic-function-of-period-1 | # definite integral with periodic function of period = 1
If $f(x)+f\left(x+\frac{1}{2}\right) = 1$. Then $\displaystyle \int_{0}^{2}f(x)dx =$
If function $f(x)$ is Continuous and Differentiable in $x\in \left(0,2\right)$
My Try:: Using $f(x)+f\left(x+\frac{1}{2}\right) = 1$
Replace $x$ by $\displaystyle x+\frac{1}{2}\;,$ We Get
$f\left(x+\frac{1}{2}\right)+f(x+1) = 1$ Using These two , We Get
$f(x+1) = f(x)$ , That means $f(x)$ is a periodic function with period $= 1$
So $\displaystyle \int_{0}^{2}f(x)dx = \int_{0}^{1}f(x)dx + \int_{1}^{2}f(x)dx$
In Second Integral Put $x = t+1$ and $dx = dt$ and changing limit , we get
$\displaystyle = \int_{0}^{1}f(x)dx+\int_{0}^{1}f(t+1)dt$
$\displaystyle = \int_{0}^{1}f(x)dx+\int_{0}^{1}f(x+1)dx$
$\displaystyle = \int_{0}^{1}f(x)dx+\int_{0}^{1}f(x)dx = 2\int_{0}^{1}f(x)dx$
Ans Given is $= 1$ but I did not understand how can i get it
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$\int{f\left(\left(\text{upper limit} + \text{lower limit}\right) - x\right)}dx$ – hjpotter92 Jan 28 '13 at 17:37
Thanks Back in a Flesh – juantheron Jan 28 '13 at 17:44
If $f(x+\frac 1 2) + f(x) = 1$ then $$\int_a^{a+1}f(x) dx = \int_a^{a+\frac 12} f(x) dx + \int_{a+\frac 12}^{a+1} f(x) dx = \int_a^{a+\frac 12} \left[f(x) + f(x+ \frac 12)\right] dx = \frac 12$$
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Thanks manu-fatto got it – juantheron Jan 28 '13 at 17:44
hint:integrate both side of the $$f(x)+f\left(x+\frac{1}{2}\right) = 1$$ let $u:=x+\frac12$ and you can solve it easily
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Thanks Maisam Hedyelloo – juantheron Jan 28 '13 at 17:45
@ juantheron :your welcome . – Maisam Hedyelloo Jan 28 '13 at 17:46
You have $$b-a=\int_a^b 1\,dx=\int_a^bf(x)\,dx+\int_a^bf\Bigl(x+\frac12\Bigr)\,dx=\int_a^bf(x)\,dx+\int_{a+\frac12}^{b+\frac12}f(x)\,dx\,.$$ Now take $a=0, b=a+\frac12$, obtaining $\int_0^1f(x)\,dx=1/2$.
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Thanks Matemáticos Chibchas – juantheron Jan 28 '13 at 17:49 | 2014-08-27 09:24:56 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9892616868019104, "perplexity": 1113.1013744901645}, "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/1408500828050.28/warc/CC-MAIN-20140820021348-00121-ip-10-180-136-8.ec2.internal.warc.gz"} |
http://lists.gnu.org/archive/html/lilypond-user/2009-01/msg01081.html | lilypond-user
[Top][All Lists]
## Re: Lyrics spacing problem - overlapping syllables
From: Jiri Zurek (Prague) Subject: Re: Lyrics spacing problem - overlapping syllables Date: Thu, 29 Jan 2009 05:13:00 -0800 (PST)
Yes, I knew that warning and inserting the spacing item padding was the first
thing which I tried. However, without any success - the insertion of the
line
\once \override Score.SeparationItem #'padding = #3
into the music is ignored by the spacing engine. Using still the same
example as above, the code here replaces only the variable notyOKriste:
notyOKriste = \relative c' {\time 12/8 a'4 c8 a4 g8 f4 e8 f4. c'4 d8 f4 e8
d4 bes8 c4 c8 d4 c8 a4 d,8 f16[ \melisma e d8 c] \melismaEnd
\once \override Score.SeparationItem #'padding = #3
d4. \bar "||" }
I am rather new to Lilypond and therefore I always try to think first that
the error is on my side - perhaps I am inserting the separationitem code
into wrong place...?
However, the syllable alignment which overlaps the neighboring note problem
is most probably a bug: since the code of the lyric spacing is already
present in Lilypond, and since it does not produce the desired output, I
still think this issue qualifies as a bug in the strict sense of the word.
I tried also the trick with the null markup on the last note of the melisma
with the melisma ending just the note before as suggested by Mats, but this
code does not work on my setup. During the compilation, the Lilypond stops
at the line Analysing... and produces nothing (but still giving no error).
--
View this message in context:
http://www.nabble.com/Lyrics-spacing-problem---overlapping-syllables-tp21665565p21726627.html
Sent from the Gnu - Lilypond - User mailing list archive at Nabble.com. | 2013-05-22 07:34:14 | {"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": 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": 0.876761257648468, "perplexity": 9758.250493414223}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2013-20/segments/1368701459211/warc/CC-MAIN-20130516105059-00058-ip-10-60-113-184.ec2.internal.warc.gz"} |
http://electronics.stackexchange.com/questions/93713/how-is-an-xor-with-more-than-2-inputs-supposed-to-work | # How is an XOR with more than 2 inputs supposed to work?
I've just started studying computer engineering, and I'm having some doubts regarding the behavior of the XOR gate.
I've been projecting circuits with Logisim, whose XORs behave differently from what I've learnt. To me, it should behave as a parity gate, giving a high output whenever the inputs receives an odd combination. It doesn't, though, for more than two inputs. How should it behave?
I also read in a book that XOR gates are not produced with more than two inputs. Is that correct? Why?
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Why not (or almost never) with >2 inputs? Two typical uses of XOR gates are 1) to check for equality, and 2) to control/manipulate the polarity of a signal. Neither makes sense for more than 2 inputs. – Wouter van Ooijen Dec 14 '13 at 22:38
Wouldn't the sum in a full-adder be represented as A ^ B ^ Cin? – gabrieljcs Dec 14 '13 at 23:50
You can express it that way, but that does not mean that it is a good way to implement it. – Wouter van Ooijen Dec 15 '13 at 8:49
Just checked my version of Logisim, and the "1 and only 1" appears to be the default behavior but there is the option to change it to an odd-parity function. – Joe Hass Dec 15 '13 at 22:36
Indeed, Joe. This link has a discussion regarding that, answered by Logisim's developer, Carl Burch. – gabrieljcs Dec 16 '13 at 16:58
There are different points of view regarding how an exclusive-OR gate with more than two inputs should behave. Most often such an XOR gate behaves like a cascade of 2-input gates and performs an odd-parity function. However, some people interpret the meaning of exclusive-OR more literally and say that the output should be a 1 if and only if exactly one of the inputs is a 1. I do seem to recall that Logisim uses the latter interpretation, and somewhere in my rusty memory I have seen it in an ASIC cell library. One of the the international standard symbols for an XOR gate is a rectangle labelled with =1 which seems to be more consistent with the "1 and only 1" definition.
EDIT: The definition of exclusive-OR as "1 and only 1" is uncommon but it can be found. For example, IEEE-Std91a-1991 gives the symbol for the exclusive-OR on p. 62 with the note: "The output stands at its 1-state if one and only one of the two inputs stands at its 1-state." For more than 2 inputs the standard recommends using the "odd parity" symbol instead. Web sites that discuss this confusing situation include XOR: The Interesting Gate and gate demos at TAMS. A google search will also turn up sites that claim that, strictly speaking, there is no such thing as an XOR gate with more than two inputs.
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As far as I'm concerned, the second one (1 and only 1) is the only correct way to do this - anything else isn't really exclusive. – Polynomial Dec 14 '13 at 23:37
There is no different point of view, both points are technically correct, however "1 if only if exactly one of the inputs is a 1" doesn't expand as you might think. When you cascade 2input XORs, each output feeding in to the pins of a third XOR this shows the above point. Multi-input gates are derived from their 2input primitives. Thus the 4input truth table is ((A⊕B)⊕(C⊕D)) which results in a final 1 output if there are an odd number of true inputs. – Kris Bahnsen Dec 15 '13 at 21:39
@KrisBahnsen As the OP pointed out, there are indeed two points of view (try the default XOR in Logisim if you need evidence). Your assertion that multi-input gates are derived from 2-input primitives is given as though it is universal truth but we have already given you a counter-example. – Joe Hass Dec 15 '13 at 22:34
@JoeHass, I've never used logisim, I primarily use LogicWorks; in which, a multi-input XOR behaves as I described above, odd number of true inputs is a true output. The wiki page on XOR (en.wikipedia.org/wiki/XOR) agrees that what I said is true as well. I also have never actually seen a multi-input XOR IC, so I cannot turn to datasheets to try and disprove what I said. Logisim seems to be the only thing that implements the multi-input XOR scheme with the logic "1 if and only..." If you can find another source, I will admit I am wrong and that there are multiple definitions of XOR. – Kris Bahnsen Dec 15 '13 at 23:30
Good clarification, thank you for putting the time in on researching the standards far more than I had. – Kris Bahnsen Dec 16 '13 at 7:53
On a two gate XOR the output is high when the inputs are different. If the inputs are the same the output is low.
Hence this truth table:
You can find a XOR gate that have more than two inputs, but they are not actually a 3 input XOR. They XOR input A and B and the result of them "R" is then XOR with input C. And the result of R XOR C is then XOR with input 4 and so on.
Here is a truth table for the three input XOR shown:
A simple parity algorithm is XORing bits in a received message over for example Ethernet. If the sender and the receiver know that XORing the message bits should be 0 (one bit in the message is provided to be able to add a one so that a message of any length can be 0 when XORed) then the receiver can know if 1 bit has been flipped. This is a bad parity check as it can only find odd number of bit changes, but shows the concept.
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Great answer too, thanks! – gabrieljcs Dec 14 '13 at 23:52
If you take 4 inputs and feed two to one XOR and two to another then, take the two XOR outputs and feed them to a third XOR, its output does what you believe it should (I think).
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I'm more concerned about the whys, not hows. Thanks for the answer, though. – gabrieljcs Dec 15 '13 at 19:22
@root, actually, you asked "How should it behave?" You didn't ask why anywhere. This is a correct answer, it yields ((A⊕B)⊕(C⊕D)) which is the same as a 4input XOR, which is the same as multiple 2input XORs cascaded together. – Kris Bahnsen Dec 15 '13 at 21:29
You're right. Sorry for the misunderstanding. – gabrieljcs Dec 16 '13 at 16:46
XOR is not completly a parity gate. If you define the output of XOR as 1 when one and only one of the inputs is 1 then a three input XOR would give you 0 for all-1 input. This is not used very often and so there are few 3-input XOR-gates.
What most people mean when they say XOR is modulo 2 addition which is a parity checker exactly. Most gates labeled as 3-input XORs are in fact modulo 2 addition gates. For two inputs, modulo 2 addition is the same thing as XOR but the 0 from the XOR described above is instead a 1 in modulo 2 gates. Modulo 2 gates with an arbitrary number of inputs can be produced from simple two-input XOR gates.
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i did a bit of search on seeing your question and found an IC which is a 3input XOR gate. 74LVC1G386 from nxp. the link to the nxp site showing search results for this part number in nxp site is http://www.nxp.com/search?q=74lvc1g386&type=keyword&rows=10
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Thanks for contributing, but your answer will be worthless if NXP changes their search engine. Please summarize what you found here so it will be of lasting value. – Joe Hass Dec 31 '13 at 14:53
i just searched to see if there is any manufacture provide XOR with more than 3 inputs and found this one...so thought it'd help i share it...here is a link to their data sheet nxp.com/documents/data_sheet/74LVC1G386.pdf – Mahesh Mohan Dec 31 '13 at 15:04
Please don't post another link! Tell us how the thing works! – Joe Hass Dec 31 '13 at 15:11
its a 3 input XOR gate which functions just like we've studied/know. ie., it gives a high o/p for odd number of high inputs(as from the data sheet).thats why shared the link. :) – Mahesh Mohan Dec 31 '13 at 15:22
So, I went there and tested! I wrote a small verilog file, simulated and looked at the waveform.
It turns out the correct interpretation for verilog is: There is an odd amount of 1's in the input AKA Interpretation 2 of this article
module top (y1, y2);
output y1, y2;
reg a, b, c;
wire x1, x2;
wire t;
xor(t, a, b);
xor(x2, t, c);
assign y2 = x2;
assign y1 = x1;
xor(x1, a, b, c);
initial
begin
$dumpfile("test.vcd");$dumpvars(y1, y2, a, b, c, x1, x2);
#20
#10 a = 0; b = 0; c = 0;
#10 a = 0; b = 0; c = 1;
#10 a = 0; b = 1; c = 0;
#10 a = 0; b = 1; c = 1;
#10 a = 1; b = 0; c = 0;
#10 a = 1; b = 0; c = 1;
#10 a = 1; b = 1; c = 0;
#10 a = 1; b = 1; c = 1;
#10 a = 0; b = 0; c = 0;
end
endmodule
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As per the logic of simple multi input OR gate, it assumes the the highest value amongst all inputs however it does not take a decision. As regards EXOR ( being mixed up with half adder being just a coincidence, as it does not happen in multi value logic EXOR) it takes a decision as to which one is highest amongst the inputs but if the highest (including 0+0..1+1) are same it fails to select amonst the inputs means it cannot take a decision which one to choose from. No decsion means output is zero.For example if someone is asked to buy maximum number of sweets of one brand in one doller and if there are two brands (radix=2) then he can select the one having highest sweet count but if both brand are available at free of cost he cannot select any (means 0,0) likewise if both the brands offer same number(1,1) of sweets he cannot take a decision means output is zero. Same logic can be extented for 3, 4 or more number of brands (higher radix) of sweets. This equally applicable to multi value logic. (x +x+..+x=0 where x can have any value), In three input EXOR gate 1+1+1=0 (as against the normal interpretation 1+1+1=1 which appears to be wrong, being mixed up with parity). V. T. Ingole, PhD
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This explanation is unnecessarily complicated, and doesn't seem to definitively answer the question anyway. – duskwuff Sep 16 '15 at 0:04
## protected by Community♦May 4 at 13:09
Thank you for your interest in this question. Because it has attracted low-quality or spam answers that had to be removed, posting an answer now requires 10 reputation on this site (the association bonus does not count). | 2016-07-25 04:18:14 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.48034152388572693, "perplexity": 987.4340644601451}, "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-2016-30/segments/1469257824204.27/warc/CC-MAIN-20160723071024-00231-ip-10-185-27-174.ec2.internal.warc.gz"} |
https://math.stackexchange.com/questions/1565213/thefirstplayertowinthreegamesinaroworatotal-offourgameswins | # the first player to win three games in a row or a total of four games wins.
In a competition between players X and Y, the first player to win three games in a row or a total
of four games wins.
a. How many ways can the competition be played in total?
b. How many ways can the competition be played if X wins the first game and Y wins the second and third games?
• Did you try solving it using a probability tree – Cloverr Dec 8 '15 at 2:45
• Without any other condition, minimal number of games needed is 3 and maximal is 8. I believe it wouldn't be hard just to do case by case study from this. One need to do minor change for (b), since the minimal number of games needed is 4 now. – Xuqiang QIN Dec 8 '15 at 3:24
• The maximum number of games is 7. After 7 games there one player have already won at least 4 games. – Sobi Dec 8 '15 at 3:38
• What have you tried ? – true blue anil Dec 8 '15 at 4:07
I don't see a really elegant way to do this.
One simplification is to calculate the ways in which X wins and multiply by 2 because when you interchange all the Xs and Ys in all the "X wins" scenarios you get all the possible "Y wins" scenarios.
X wins in 3 - XXX - 1 way
X wins in 4 - YXXX - 1 way
X wins in 5 - YYXXX - XYXXX - XXYXX - 3 ways
for 6 and 7 organize yourself by considering the six possible results for the first 3 games (it must have been 2-1 after 3 games if no one wins in 3)
e.g. for X to win in 6 there are 2 scenarios starting with "XXY" but no scenarios starting with "YYX" .
For X to win in 7 all six 3 game starts are possible leading to either 2 or 3 scenarios.
I count 7 ways for X to win in 6 and 14 ways for X to win in 7
total ways for X to win $= 14 + 7 + 3+ 1+ 1 = 26$
So there must be 52 possible ways to play out the series, of which 7 start with XYY ( using the "X wins" list count sequences starting with either XYY or YXX )
An interesting result is that given you win in exactly 7 games the conditional probability that you were 2-1 down after 3 games is exactly 50% !
We shall count $A's$ wins, and multiply by $2$.
Firstly, let us list the "special" cases :
Wins due to $3$ games in a row: $WWW, LWWW,\;$ and $\;LLWWW$
Losses due to $3$ games in a row:$LLLWWWW, WLLLWWW, WWLLLWW Now we will count the general cases, winning$4$games, and subtract the special cases: To win$4$games in$5$,$A$must win the$5th$game, and$3$of the previous$4$in$\binom43 = 4$minus$2$special wins in$4$games or less$=2$ways. To win$4$games in$6, A$must win the$6th$game, and$3$of the previous$5$minus$3$special wins in$5$games or less$= 7$ways, Only when$7$games are played is there also chance of losing due to special cases. To win$4$games in$7, A$must win the$7th$game, and$3$of the previous$6$, thus$\binom63 - 3$special wins -$3$special losses$= 14$Thus total # of ways =$2(3+2+7+14) = 52$ways ps: You should now try the easier second part. • I think the correct answer is 56 (counting exhaustively on a binary tree). – Sobi Dec 8 '15 at 14:58 • @trueblueanil think there are two more losing cases that should be subtracted WLLLWWW and WWLLLWW - that would bring us to agreement at 52 – WW1 Dec 8 '15 at 21:22 • @WW1: I agree with the "missing link", and have adjusted, thanks. It is very late here, I will try and see if a more elegant solution is possible later. – true blue anil Dec 8 '15 at 23:06 Suppose four games are played and one player wins them all. WWWW. There are 2 ways that can happen. (Either one player wins all four or the other player does. Suppose five games are played and one player winning 4 and losing one. LWWW or WLWW or WWLW. The winner can't lose the last game (because then the winner would have already won four games and they'd never play the fifth game). So there are three choices for the winner to lose. That's${3 \choose 1}$. And then there are 2 possible winners so$2{3 \choose 1}$Suppose six games are played, one player wins 4 and loses two. There are${4 \choose 2}$to do this and two players.$2{4 \choose 2}$. Suppose seven games... winner wins 4 loses 3.$2{5 \choose 3}$. Total;$2 + 2{3 \choose 1}+ 2{4 \choose 2} + 2{5 \choose 3}\$. | 2019-07-19 16:28:58 | {"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": 0.49313902854919434, "perplexity": 1018.4759891547536}, "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/1563195526324.57/warc/CC-MAIN-20190719161034-20190719183034-00271.warc.gz"} |
http://www.lastfm.fr/user/pedrovalenca/library/music/Ladytron/_/They+Gave+You+A+Heart+They+Gave+You+A+Name?setlang=fr | # Bibliothèque
## They Gave You A Heart They Gave You A Name
41 écoutes | Se rendre sur la page du titre
Titres (41)
Titre Album Durée Date
They Gave You A Heart They Gave You A Name 2:34 4 oct. 2010, 0h30m
They Gave You A Heart They Gave You A Name 2:34 22 août 2010, 0h14m
They Gave You A Heart They Gave You A Name 2:34 22 août 2010, 0h03m
They Gave You A Heart They Gave You A Name 2:34 21 août 2010, 23h30m
They Gave You A Heart They Gave You A Name 2:34 21 août 2010, 23h16m
They Gave You A Heart They Gave You A Name 2:34 21 août 2010, 22h51m
They Gave You A Heart They Gave You A Name 2:34 16 août 2010, 0h55m
They Gave You A Heart They Gave You A Name 2:34 23 jan. 2010, 2h03m
They Gave You A Heart They Gave You A Name 2:34 23 jan. 2010, 1h59m
They Gave You A Heart They Gave You A Name 2:34 23 jan. 2010, 1h51m
They Gave You A Heart They Gave You A Name 2:34 22 jan. 2010, 18h45m
They Gave You A Heart They Gave You A Name 2:34 22 jan. 2010, 17h52m
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They Gave You A Heart They Gave You A Name 2:34 22 avr. 2009, 0h29m
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They Gave You A Heart They Gave You A Name 2:34 19 avr. 2009, 23h33m
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They Gave You A Heart They Gave You A Name 2:34 29 nov. 2008, 21h41m
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They Gave You A Heart They Gave You A Name 2:34 27 nov. 2008, 21h40m
They Gave You A Heart They Gave You A Name 2:34 27 nov. 2008, 0h50m
They Gave You A Heart They Gave You A Name 2:34 27 nov. 2008, 0h31m
They Gave You A Heart They Gave You A Name 2:34 26 nov. 2008, 13h47m
They Gave You A Heart They Gave You A Name 2:34 26 nov. 2008, 4h05m
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