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https://socratic.org/questions/58a26481b72cff453ee79d5f | English Grammar
Topics
# Question #79d5f
Mar 9, 2017
In the explanation I copied the prewriting document my English teacher gave my class. Our assignment was a play review, but I think you can still use this.
#### Explanation:
Review/Critique of a Play (or Book): Tips and Guidelines
Prewriting: Consider the following questions when reviewing a play.
“The first moments are critical. You can sit there, tense and worried, freezing the creative energies, or you can start writing something, perhaps something silly. It simply doesn’t matter what you write; it only matters that you write. In five or ten minutes the imagination will heat, the tightness will fade, and a certain spirit and rhythm will take over.”
$$ —Leonard Bernstein
What questions
• What are you reviewing? What is it about? What's the plot?
• What's the theme?
• What is the author's/director's purpose?
• What genre or classification does it fit?
• What is the tone? What is the point of view? What's the mood?
When and Where questions
• When was this done? Or when does the action take place?
• Where was this done? Or where does the action take place?
Who questions
• Who wrote it, directed it, or acted in it? What else have they done?
• Who are the main characters?
• Who's the intended audience?
How questions
• How does it convey its main point, mood, or theme? How does the audience/reader react to it?
• How well does it fulfill its purpose?
Evaluation questions
• Did I like this in general? Why?
• Did I agree with the main theme/purpose? Why or why not?
• What specifically did I like/dislike? Why?
After you have answered these questions, begin selecting and organizing the information that you'll include in your paper.
Once you've done the prewriting, you're ready to think about the requirements and structure of a review which your teacher might have given you, and decide how to divide what info into what paragraphs, etc.
Credit: You can thank my teacher Mrs. Belinda Snyman for this resource.
##### Impact of this question
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http://math.stackexchange.com/questions/168334/is-this-conjecture-on-fibonacci-sums-correct | # Is this conjecture on Fibonacci sums correct?
I have the following conjecture, need to know a proof just in case mine is wrong, or the conjecture itself is wrong.
The sum of $k$ distinct Fibonacci numbers can be written in at most $k$ ways as the sum of another $k$ distinct numbers from the sequence
Proof: Take, say 4, Fibonacci numbers with distinct values: $$144+34+3+2$$ We can see that we must maintain the distinctness and number of the Fibonacci numbers. So when we split the numbers; $$[89+55]+[13+21]+3+2$$
It is immediately apparent that if some numbers are split into smaller Fibonacci numbers, others must be merged to keep only 4 numbers. Thus, 3+2 becomes 5, and either 144 or 34 kept as-is. Thus, $$144+34+3+2=89+55+34+5=144+21+13+5$$
I know it's a rudimentary proof, and $k$ ways of writing the same sum is probably a wrong upper bound, but at least it works for now.
Please do let me know what's wrong. Thanks.
-
Use single dollar signs, e.g. $k$, for inline mathematics, and use double dollar signs, e.g. $$a^2+b^2=c^2$$, for mathematics you want to display on a separate line. – Zev Chonoles Jul 8 '12 at 19:40
We show that the conjectured upper bound of $k$ is a fair distance from the truth.
Let $W$ be a set of $3n$ distinct Fibonacci numbers, of which $n$ are lonely (no other Fibonacci number in $W$ is near them) and the remaining $2n$ are lonely couples. A lonely couple is a set of two consecutive Fibonacci numbers, with no other element of $W$ near them. Let $N$ be the sum of the Fibonacci numbers in $W$.
Then we can get another representation of $N$ as a sum of $3n$ Fibonacci numbers by selecting any $k$ lonely numbers, and representing each of them as a sum of two consecutive Fibonacci numbers, and selecting any $k$ lonely couples, and expressing each of their sums as a single Fibonacci number.
The $k$ lonely numbers can be chosen from the $n$ lonely numbers in $W$ in $\binom{n}{k}$ ways. For each choice, the $k$ lonely couples can be chosen in $\binom{n}{k}$ ways. It follows that $N$ has at least $$\sum_{k=0}^n \binom{n}{k}\binom{n}{k}$$ representations as a sum of distinct Fibonacci numbers. It is well-known that the above sum is equal to $\binom{2n}{n}$. For large $n$, this is much larger than the $3n$ that the conjecture would suggest. Indeed by using the Stirling formula, one can show that $\binom{2n}{n}$ is asymptotically equal to $\sqrt{\frac{2}{\pi}}\frac{2^{2n}}{\sqrt{2n+1}}$.
-
Cute!${}{}{}{}$ – Brian M. Scott Jul 8 '12 at 21:03
It seems that you require k=n, in which case the argument can be simplified to: Let W be the sum of 2n distinct Fibonacci numbers, at least 3 positions apart. Pick n to be split, which can be done in $2n \choose n$ ways. But a good approach. – Ross Millikan Jul 9 '12 at 3:42
As a general rule, you'll want to use Zeckendorf's theorem to find these representations; it says that any number has a unique representation as the sum of nonconsecutive Fibonacci numbers. As André has noted, your conjecture is false in general, but it is possible to find a straightforward bound on the number of possible sums.
Let's say you want to write $k$ as the sum of $n$ Fibonacci numbers, and the Zeckendorf's theorem sum contains $m<n$ terms. From any $n$-term sum you like, you'll be able to get the Zeckendorf sum by repeatedly combining terms until no remaining terms are consecutive. This implies that you can get any $n$-term sum by starting with the Zeckendorf sum and splitting up terms in it until you get $n$ of them.
Say you start with a single term $F_a$. The only way to split that is as $F_a=F_{a-1}+F_{a-2}$; the only way to split that is as $F_{a-1}+F_{a-3}+F_{a-4}$; and so on -- that is, any sum that began as a single Fibonacci number has at most one representation as the sum of $n$ distinct Fibonacci numbers for any $n$ (since at each point the indices differ by at most two, the only additional split that's possible comes from breaking up the smallest number in the sum).
So, if you start with a Zeckendorf sum that has $m$ terms, your only possible decision is how many times to split up each of those terms; once you know that, you'll have a unique sum. (It may be that your terms will "collide" and you won't get a sum of distinct Fibonacci numbers, but you'll certainly get every possible sum from some such specification, so this leads to an overcount.) To get an $n$-term sum, you need to split a total of $n-m$ times. By a stars-and-bars argument, there are at most ${n-1 \choose m-1}$ ways of doing this. So a repaired version of your conjecture would state:
If the Zeckendorf sum for $k$ contains $m$ terms, there are at most ${n-1 \choose m-1}$ ways of writing $k$ as the sum of $n$ distinct Fibonacci numbers.
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http://scitation.aip.org/content/aip/journal/jcp/126/8/10.1063/1.2437197 | • journal/journal.article
• aip/jcp
• /content/aip/journal/jcp/126/8/10.1063/1.2437197
• jcp.aip.org
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Effective method to compute Franck-Condon integrals for optical spectra of large molecules in solution
USD
10.1063/1.2437197
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Affiliations:
1 Istituto per i Processi Chimico-Fisici del CNR, Area della Ricerca del CNR Via Moruzzi 1, I-56124 Pisa, Italy
2 Dipartimento di Chimica, Università Federico II, Complesso Monte Sant Angelo, via Cintia, I-80126 Napoli, Italy and Istituto di Biostrutture e Bioimmagini del CNR, via Mezzocannone 16, I-80134 Napoli, Italy
3 Istituto per i Processi Chimico-Fisici del CNR, Area della Ricerca del CNR Via Moruzzi 1, I-56124 Pisa, Italy
4 Dipartimento di Chimica, Università Federico II, Complesso Monte Sant Angelo, via Cintia, I-80126 Napoli, Italy
a) Author to whom correspondence should be addressed. Electronic mail: f.santoro@ipcf.cnr.it
J. Chem. Phys. 126, 084509 (2007)
/content/aip/journal/jcp/126/8/10.1063/1.2437197
http://aip.metastore.ingenta.com/content/aip/journal/jcp/126/8/10.1063/1.2437197
## Figures
FIG. 1.
Schematic drawing of anthracene (a), of the anti-conformer of C153 (b), and of coumarin (c). Carbon and hydrogen atoms are depicted in green and in yellow, respectively, fluorine in violet, and nitrogen in blue.
FIG. 2.
Log plot of the number of vibrational states of the anti-C153 excited electronic state in gas phase, obtained by a direct count, together with its extrapolation at higher frequency obtained by a power-law fit.
FIG. 3.
Absorption spectrum of anthracene in gas phase at , and its convergence with respect to (, , and from lower to upper curve, respectively). The spectra have been convoluted with a Gaussian with .
FIG. 4.
Upper panel: decomposition of the absorption spectrum of the anti-isomer of C153 in gas phase, in the contributions of the different classes (increasing the maximum peak of the contribution shifts toward the blue, while its shape becomes progressively flatter). Lower panel: assignments of the main bands , where label the oscillator and its quantum number.
FIG. 5.
Absorption spectrum of the anti-isomer of C153 in gas phase at , and its convergence with respect to . Notice that the intensity of the blue wing increases with increasing accuracy, i.e., with increasing (from to from lower to upper curve). The spectra have been convoluted with a Gaussian with .
FIG. 6.
Absorption spectrum of C153 computed in gas phase (black dash-dot line), in cyclohexane (red dot line), and in DMSO according to the nonequilibrium (blue line) and equilibrium limits (gray thick line). The spectra have been convoluted with a Gaussian with .
FIG. 7.
C153 Franck-Condon factors for the imaginary transition (upper panel) and lower panel.
FIG. 8.
Phosphorescence spectra of coumarin. (a) results in gas phase (blue line with the peaks redshifted) and ethanol (black line) and results in ethanol (red dot line, for this case the stick spectrum is also plotted) convoluted with a Gaussian with . (b) Comparison of the spectrum in ethanol (red dash line) with the experimental spectrum (black solid line) in the same solvent at ; the computed spectrum has been blue shifted by .
## Tables
Table I.
Details of the computation of the anthracene spectrum at . and transitions have been computed allowing a maximum quantum number (1254 integrals) and (308 880 integrals), respectively. For the transitions to be computed have been selected so that their total number is . Numbers in parentheses report the number of oscillators actually excited after the selection, for each class of integrals .
Table II.
Details of the computation of the spectrum of C153 at . and transitions have been computed allowing a maximum quantum number (2958 integrals) and (741 744 integrals), respectively. For the transitions to be computed have been selected so that their total number is . Numbers in parentheses report the number of oscillators actually excited after the selection, for each class of integrals .
/content/aip/journal/jcp/126/8/10.1063/1.2437197
2007-02-28
2014-04-24
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### Most cited this month
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This is a required field | {"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": 0.8158084154129028, "perplexity": 3852.84345512998}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-15/segments/1398223206672.15/warc/CC-MAIN-20140423032006-00196-ip-10-147-4-33.ec2.internal.warc.gz"} |
https://www.physicsforums.com/threads/simple-geometry-proof.283544/ | # Simple Geometry Proof
1. Jan 7, 2009
### forty
Given 3 points of the triangle:
(1,2)
(4,6)
(9,10)
Determine if point (5,4) belongs to triangle (is located inside the triangle).
the only way i can think of doing this is as follows but there must be a more sound way.
so you have lines:
(1,2)->(4,6)
(4,6)->(9,10)
(1,2)->(9,10)
you need all 3 of the following to hold true for point (5,4)
y <= 4/3x + 2/3 (true)
y >= x + 1 (false)
y <= 4/5x + 14/5 (false)
any help greatly appreciated.
2. Jan 7, 2009
### symbolipoint
If by "Given 3 points" you really mean "Given 3 vertices", then your basic approach is very good. As long as you identified the correct lines, then you can set up the suitable inequalities and determine the necessary truths for the conditions.
You can easily check about the point by actually drawing the whole graph.
Last edited: Jan 7, 2009
3. Jan 7, 2009
### forty
Yes I do mean vertices. So this is pretty much the simplest way of going about it?
Thanks.
4. Jan 7, 2009
### symbolipoint
Make the graph of the inequalities; this can help you to explain the proof AND to show the proof graphically. Either the point to test is within the inequalities region or it is not within the inequalities region. | {"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": 0.8253633975982666, "perplexity": 1149.0831048534733}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-13/segments/1521257647498.68/warc/CC-MAIN-20180320150533-20180320170533-00237.warc.gz"} |
https://www.gradesaver.com/textbooks/math/algebra/elementary-algebra/chapter-2-real-numbers-2-1-rational-numbers-multiplication-and-division-problem-set-2-1-page-48/12 | ## Elementary Algebra
Published by Cengage Learning
# Chapter 2 - Real Numbers - 2.1 - Rational Numbers: Multiplication and Division - Problem Set 2.1: 12
#### Answer
$\dfrac{3}{10}$
#### Work Step by Step
Cancelling the common factor between the numerator and the denominator, the given expression, $\dfrac{-24}{-80} ,$ simplifies to \begin{array}{l}\require{cancel} \dfrac{\cancel{-8}\cdot3}{\cancel{-8}\cdot10} \\\\= \dfrac{3}{10} \end{array}
After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback. | {"extraction_info": {"found_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": 0.8872195482254028, "perplexity": 2948.5609791607344}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-22/segments/1526794866772.91/warc/CC-MAIN-20180524190036-20180524210036-00184.warc.gz"} |
https://codegolf.stackexchange.com/questions/51396/visual-long-multiplication/51456 | # Visual Long Multiplication
There is a nice way to perform long multiplication for two integers without having to do anything but counting, which occasional gets shared around the internet. You write the digits of each number as a bunch of slanted lines, with the two numbers at a 90 degree angle. Then you can simply count the intersections in the separate columns that arise. A diagram will probably clarify this. Here is an example for calculating 21 * 32:
If you google for "visual/graphical long multiplication" you'll find a lot more examples.
In this challenge, you are to generate these diagrams using ASCII art. For the same example, the output would look like this:
\ /
X /
\ / X /
\ X / X
X X / \ /
/ X X X /
/ X \ / X
/ \ X / \
X X
/ X \
/ \
It's probably easiest to figure out the construction rules for these from some examples (see below), but here some details:
• Intersecting segments are X, non-intersecting segments of the lines are / or \.
• There should be exactly one segment after the outermost intersections.
• There should be exactly one segment between intersections belonging to different digits. If there are zero-digits, these will result in consecutive / or \ segments.
• You have to support any positive input (at least up to some reasonable limit like 216 or 232), and any digits from 0 to 9. However, you may assume that there neither leading nor trailing 0s.
• You must not print extraneous leading whitespace or leading or trailing empty lines.
• You may print trailing whitespace but it must not exceed the diagram's axis-aligned bounding box.
• You may optionally print a single trailing newline.
• You may choose in which order you take the two input numbers. However, it you must support arbitrary numbers for either orientation, so you can't choose something like "The larger number is given first".
• If you're taking input as a string, you can use any non-digit separator between the two numbers.
You may write a program or function, taking input via STDIN (or closest alternative), command-line argument or function argument and outputting the result via STDOUT (or closest alternative), function return value or function (out) parameter.
This is code golf, the shortest answer (in bytes) wins.
## Examples
1*1
\ /
X
/ \
2*61
\ /
\ X /
X X /
/ X X /
/ X X /
/ X X /
/ X X
/ X \ /
/ \ X
X \
/ \
45*1
\ /
\ X
\ X \
\ X \
\ X \
X \
\ / \
\ X
\ X \
\ X \
X \
/ \
21001*209
\ /
X /
/ X
/ / \
\ / / \ /
X / X /
\ / X / X /
\ X / \ / / X /
X X \ / / / X /
/ X \ X / / / X /
/ \ \ / X / / / X /
\ X / X / / / X /
X X / X / / / X /
/ X X / X / / / X
/ X X / X / / / \
/ X X / X / /
/ X X / X /
/ X X / X
/ X X / \
/ X X
/ X \
/ \
• A function with 2 string parameters or just one single string and I have to split it in my code? – edc65 Jun 12 '15 at 12:30
• @edc65 Two strings or even two integer parameters are fine. – Martin Ender Jun 12 '15 at 12:39
# Pyth - 79 bytes
A translation of @AlexeyBurdin's answer. Can probably be golfed a lot more.
AzHmu++Gm1sH]Zd]Z,_zwK+lzlHJmm\ KK .e.eX@J+kY+-Yklz@" \/x"+byZHzjbmjk:d2_1:J1_2
Takes input as two numbers, newline separated. Explanation coming soon.
## python, 303
def f(s):
a,b=s.split('*')
a,b=map(lambda l:reduce(lambda x,y:x+[1]*int(y)+[0],l,[0]),[reversed(a),b])
n=sum(map(len,[a,b]))
l=[[' ']*n for i in xrange(n)]
for i,x in enumerate(a):
for j,y in enumerate(b):
l[i+j][j-i+len(a)]=r' \/x'[x+2*y]
return '\n'.join(''.join(x[2:-1]) for x in l[1:-2])
Verification:
print '---'
print '\n'.join('"%s"'%x for x in f('21001*209').split('\n'))
print '---'
---
" \ / "
" x / "
" / x "
" / / \ "
" \ / / \ / "
" x / x / "
" \ / x / x / "
"\ x / \ / / x / "
" x x \ / / / x / "
"/ x \ x / / / x / "
" / \ \ / x / / / x / "
" \ x / x / / / x / "
" x x / x / / / x /"
" / x x / x / / / x "
" / x x / x / / / \"
" / x x / x / / "
" / x x / x / "
" / x x / x "
" / x x / \ "
" / x x "
" / x \ "
" / \ "
---
• Just a few quick golfs: reversed is the same as [::-1], you can put the contents of the for loop into one line to save on indentation, len(a)+len(b) is shorter than sum(map(len,[a,b])), don't use xrange in golfing, the space in ) for can be removed, and since you are using python2, you can combine spaces and tabs in indentation. – Maltysen Jun 7 '15 at 17:44
• Thanks much. These gives 22 bytes. But I don't think it would be the shortest. I don't code pyth but I've seen 31-byte programs... Btw, 303 is the count when every 4-spaces is replaced by a tab actually. – Alexey Burdin Jun 7 '15 at 18:05
• Here, I was able to get 276 from simple syntactic golfing: gist.github.com/Maltysen/e8231c0a9b585e2a4941 – Maltysen Jun 7 '15 at 18:09
• Also, do you mind if I translate your program to Pyth and post it as a separate answer? – Maltysen Jun 7 '15 at 18:10
• You can set e=enumerate at the start to golf 4 chars – sagiksp Jun 8 '17 at 10:47
# Python 3, 205 bytes
L=a,b=[eval("+[0]+[1]*".join("0%s0"%x)[2:])for x in input().split()]
A,B=map(len,L)
for c in range(2,A+B-1):print((" "*abs(c-A)+" ".join(" \/X"[a[i-c]+2*b[i]]for i in range(max(0,c-A),min(c,B))))[1:A+B-2])
The expressions are quite long so I think there's a fair amount of room for improvement, but anyway...
Takes input space-separated via STDIN, e.g.
21 32
\ /
X /
\ / X /
\ X / X
X X / \ /
/ X X X /
/ X \ / X
/ \ X / \
X X
/ X \
/ \
There's a possible trailing space on some lines, but the A+B-2 ensures that all of the trailing spaces are within the bounding box.
# C#, 451 bytes
void d(string s){var S=s.Split('*');int X=S[1].Select(c=>c-47).Sum(),Y=S[0].Select(c=>c-47).Sum(),L=9*(X+Y),A=1,B=L/3,i,j;var a=Range(0,L).Select(_=>new int[L]).ToArray();foreach(var c in S[1]){for(i=48;i<c;++i){for(j=-1;j<Y;++j)a[B-j][A+j]=1;A++;B++;}A++;B++;}A=1;B=L/3;foreach(var c in S[0]){for(i=48;i<c;++i){for(j=-1;j<X;++j)a[B+j][A+j]|=2;A++;B--;}A++;B--;}Write(Join("\n",a.Select(r=>Concat(r.Select(n=>@" /\X"[n]))).Where(r=>r.Trim().Any())));}
Formatted for readability, the function in context:
using System.Linq;
using static System.Console;
using static System.Linq.Enumerable;
using static System.String;
class VisualMultiply
{
static void Main(string[] args)
{
new VisualMultiply().d("21001*209");
WriteLine();
}
void d(string s)
{
var S = s.Split('*');
int X = S[1].Select(c => c - 47).Sum(),
Y = S[0].Select(c => c - 47).Sum(),
L = 9 * (X + Y),
A = 1,
B = L / 3,
i,
j;
var a = Range(0, L).Select(_ => new int[L]).ToArray();
foreach (var c in S[1])
{
for (i = 48; i < c; ++i)
{
for (j = -1; j < Y; ++j)
a[B - j][A + j] = 1;
A++;
B++;
}
A++;
B++;
}
A = 1;
B = L / 3;
foreach (var c in S[0])
{
for (i = 48; i < c; ++i)
{
for (j = -1; j < X; ++j)
a[B + j][A + j] |= 2;
A++;
B--;
}
A++;
B--;
}
Write(Join("\n", a.Select(r => Concat(r.Select(n => @" /\X"[n]))).Where(r => r.Trim().Any())));
}
}
The bitwise OR was just for fun, but addition would work too.
# JavaScript (ES6) 271
I'm sure that there is a solution that builds the output row by row, fiddling with math and x,y coordinates (x+y==k, x-y==k ...). But I still can't nail it.
So here is a solution that simply draws the lines one by one.
Run the snippet in Firefox to test.
F=(a,b)=>( // string parameters
t=u=0,[for(v of a)t-=~v],[for(v of b)u-=~v],
r=t+u,o=[...' '.repeat(r*r-r)],
L=(x,y,n,z,m,c)=>{
for(i=0;d=n[i++];)
for(j=0;++x,y+=z,j++<d;)
for(l=m+1,p=x+y*r-1-r;l--;p+=r-z,o[p-p%r-1]='\n')
o[p]=o[p]>' '&&o[p]!=c?'X':c
},
L(u,0,a,1,u,'/'),
L(0,u,b,-1,t,'\\'),
o.join('')
)
// TEST
function test()
{
O.innerHTML= F(A.value, B.value);
}
test();
<input id=A value=21001> * <input id=B value=209> <button onclick='test()'>-></button>
<pre id=O></pre>
## VC++ (289)280
t(char*a){int i,j,k,r,c=1,e,A=0,B=0,*C,G[99],f,u;for(C=&A;c+48|(k=(c=(*(a+=c<1))---48)>0);G[2**(C=!(c+6)?&(B+=A):&(++*C))]=k**C);for(i=0;i<B*B;printf("\n%c"+!!j,32+15*((k=(c<(f=G[(c=i/B)+(j=i%B)+A+2]))*(j<f)*(f>A))+4*(r=(!!e*B>c+(e=G[A+j-c]))*(!!e*c>A-e-2)*(e<A)))+13*k*r),i++);
## Usage
#include <stdio.h>
#include <conio.h>
int t(char*);
int main(void)
{ char a[]="123*45";
t((char*)a);
getch();
return 0;
}
int
t(char*a){int i,j,k,r,c=1,e,A=0,B=0,*C,G[99],f,u;memset(G,0,396);for(C=&A;c+48|(k=(c=(*(a+=c<1))---48)>0);G[2**(C=!(c+6)?&(B+=A):&(++*C))]=k**C);for(i=0;i<B*B;printf("\n%c"+!!j,32+15*((k=(c<(f=G[(c=i/B)+(j=i%B)+A+2]))*(j<f)*(f>A))+4*(r=(!!e*B>c+(e=G[A+j-c]))*(!!e*c>A-e-2)*(e<A)))+13*k*r),i++);
//---------------------------
return 0;}
## Results
\ /
\ x /
\ x x /
x x x /
\ / x x x
\ x / x x \ /
x x / x \ x /
\ / x x / \ x x /
x / x x x x x /
/ x / x \ / x x x /
/ x / \ x / x x x
/ x x x / x x \
/ \ / x x / x \
x / x x / \
/ x / x x
/ x / x \
/ x / \
/ x
/ \
• the function iterates one single loop , and use some geometricks and ascii trifling.
• What's the ---48 for? – LegionMammal978 Jun 14 '15 at 12:56
• @LegionMammal978 sometimes i write things then i forget even why did i put it there :D anyway im busy doing something else, when i finish , ill remember for you ; (does this code go well in your compilater) ? – Abr001am Jun 14 '15 at 13:12
• @LegionMammal978 here ,array content at specific (actual) index is subtracted to 48 before it decrements , subtracting 48 in order to wait a coming nil character then decrement step by step forward in loop (or backwards as ascii pattern) – Abr001am Jun 14 '15 at 15:52
• 48 is the ascii representation of "0" – Abr001am Jun 14 '15 at 15:55
• I see now, it works like ...)-- - 48).... – LegionMammal978 Jun 20 '15 at 17:23
# Canvas, 41 bytes
（Ａ┬｛［１｝０｝┐）
⁷Ｌ├Ｘ⁷ｌＹø；｛³×？³ｙ³－╵ｘ＼╋
⁸⤢↔╶╶⁸ｎ
Try it here!
## C (329 b)
int f(char*a){int i,j,r,k,c,h,o,e=15,m=99,A=0,B=0,*C,L[m][m],G[m],*g=G;for(C=&A;(c=*a-48)+48;C=!(c+6)?&B:&(*C+=(*g++=c+1)),a++);for(i=B-1,j=0;j<(r=A+B-1);i--,j++)for(k=0,o=4*!!((*(g-=!*g))---1);k<=*(C=(h=i<0)?&B:&A);k++)L[abs(i)+k][j+k-2*k*h]+=o/(3*h+1)*e;for(i=0;i<r*r;i++)printf("\n%c"+!!(i%r),((h=L[i/r][i%r])>e*4)?120:h+32);}
## TRY IT
• It seems there are columns of spaces after every character, and the final non-intersecting segments at the bottom ends are missing. You're also using the digits in reverse order. – Martin Ender Jun 9 '15 at 15:46
• @MartinBüttner imagine someone is doing this on the moon and u watching it by telescope , that s the way you should perceive the diagram (-joking-i ll adjust that later) – Abr001am Jun 9 '15 at 16:52
# R, 294 bytes
d=do.call;r=outer;m=d(r,c(Map(function(y,w)d(c,c(lapply(y%/%10^rev(0:log10(y))%%10,function(z)c(0,rep(w,z))),0)),scan(),1:2),+))+1;p=matrix(" ",u<-sum(dim(m)),u);p[d(r,c(lapply(dim(m),seq),function(a,b)nrow(m)-a+b+u*(a+b-2)))]=c(" ","\\","/","X")[m];cat(apply(p,1,paste,collapse=""),sep="\n")
Try it online!
# Jelly, 58 bytes
ŒDṙLN‘ƊṚị“\/X ”K€
L‘0xż1xⱮ$F DÇ€Ḥ2¦+þ/µZJUṖ;J’⁶xⱮżÑṖḊẎḊ$€Y
Try it online!
### Explanation
A full program that takes the two numbers as a list of two integers and returns a string.
Helper link 1: rotate the matrix
ŒD | get the diagonals
ṙ | rotate left by
LN‘Ɗ | minus num columns +1
Ṛ | reverse order
ị“\/X ” | index into \/X
K€ | join each with spaces
Helper link 2: generate the row and column templates
L‘0x | 0 copied (num digits + 1) times
ż | interleaved with
1xⱮ$| 1 copied as specified by the digits F | flattened Main link D | convert to decimal digits Ç€ | call above link for each number Ḥ2¦ | double the second one +þ/ | outer product using + µ | start a new monadic chain ZJUṖ;J’ | reversed range counting down | the columns, followed by range counting up the rows (without duplicating 0 in the middle) ⁶xⱮ | that many spaces (to provide indents) ż | interleaved with Ñ | rotated matrix ṖḊẎḊ$€ Y | remove blank rows and columns and join with newlines | {"extraction_info": {"found_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": 0.684895396232605, "perplexity": 3760.983452051637}, "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-2020-40/segments/1600400208095.31/warc/CC-MAIN-20200922224013-20200923014013-00369.warc.gz"} |
https://hal-centralesupelec.archives-ouvertes.fr/hal-01262604 | # Mathematical and numerical analysis of low-frequency scattering from a PEC ring torus in a conductive medium
Abstract : The electric and magnetic fields scattered offa non-penetrable ring torus, being characterized as perfect conductor, embedded in a homogeneous conductive medium and illu- minated by a low-frequency magnetic dipole of arbitrary orientation and harmonic time-dependence are investigated herein. Upon definition of the complex wave number of the exterior medium k via its skin-depth, the 3-D scattering boundary value problem is handled via convenient low-frequency expansions in terms of powers of (ik ) to n, n ≥ 0 for the fields. A Maxwell-type problem is transformed into intertwined Laplace’s or Poisson’s potential-type boundary value problems with impenetrable boundary conditions. Using a toroidal coordinate system attached to the torus, they are solved as infinite series expansions for the fields in terms of toroidal eigenfunctions. In practice, what is accessible to the measurement is the scattered magnetic field. The static term (n = 0) provides most of its real (or in-phase) part and the second-order term (n = 2) consists of most of its imaginary part (quadrature), where in both cases a small contribution of the third-order term (n = 3) is being calculated. For n = 1, there exists no field, while the terms for n ≥ 4 and for such kind of applications have been proved to be of minor significance, hence they are neglected. The resulting infinite linear systems can be solved at any accuracy level through a cut-offprocess or via an analytical technique based on the method of finite continuous fraction solutions. Basics of the far-field approximation and the magnetic po- larizability tensor are also included. At implementation stage, simulations are proposed in various situations, where a full-wave, finite-element approach is discussed.
Keywords :
Type de document :
Article dans une revue
Applied Mathematical Modelling, Elsevier, 2016, 40 (13-14), pp.6477-6500. 〈10.1016/j.apm.2016.01.053〉
Domaine :
https://hal-centralesupelec.archives-ouvertes.fr/hal-01262604
Contributeur : Dominique Lesselier <>
Soumis le : mardi 26 janvier 2016 - 19:48:14
Dernière modification le : jeudi 11 janvier 2018 - 06:19:10
### Citation
Panayiotis Vafeas, Polycarpos K. Papadopoulos, Ping-Ping Ding, Dominique Lesselier. Mathematical and numerical analysis of low-frequency scattering from a PEC ring torus in a conductive medium. Applied Mathematical Modelling, Elsevier, 2016, 40 (13-14), pp.6477-6500. 〈10.1016/j.apm.2016.01.053〉. 〈hal-01262604〉
### Métriques
Consultations de la notice | {"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": 0.8137029409408569, "perplexity": 2175.7345343924417}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1518891814079.59/warc/CC-MAIN-20180222081525-20180222101525-00072.warc.gz"} |
https://docs.julialang.org/en/release-0.5/devdocs/functions/ | # Julia Functions¶
This document will explain how functions, method definitions, and method tables work.
## Method Tables¶
Every function in Julia is a generic function. A generic function is conceptually a single function, but consists of many definitions, or methods. The methods of a generic function are stored in a method table. Method tables (type MethodTable) are associated with TypeNames. A TypeName describes a family of parameterized types. For example Complex{Float32} and Complex{Float64} share the same Complex type name object.
All objects in Julia are potentially callable, because every object has a type, which in turn has a TypeName.
## Function calls¶
Given the call f(x,y), the following steps are performed: first, the method table to use is accessed as typeof(f).name.mt. Second, an argument tuple type is formed, Tuple{typeof(f), typeof(x), typeof(y)}. Note that the type of the function itself is the first element. This is because the type might have parameters, and so needs to take part in dispatch. This tuple type is looked up in the method table.
This dispatch process is performed by jl_apply_generic, which takes two arguments: a pointer to an array of the values f, x, and y, and the number of values (in this case 3).
Throughout the system, there are two kinds of APIs that handle functions and argument lists: those that accept the function and arguments separately, and those that accept a single argument structure. In the first kind of API, the “arguments” part does not contain information about the function, since that is passed separately. In the second kind of API, the function is the first element of the argument structure.
For example, the following function for performing a call accepts just an args pointer, so the first element of the args array will be the function to call:
jl_value_t *jl_apply(jl_value_t **args, uint32_t nargs)
This entry point for the same functionality accepts the function separately, so the args array does not contain the function:
jl_value_t *jl_call(jl_function_t *f, jl_value_t **args, int32_t nargs);
Given the above dispatch process, conceptually all that is needed to add a new method is (1) a tuple type, and (2) code for the body of the method. jl_method_def implements this operation. jl_first_argument_datatype is called to extract the relevant method table from what would be the type of the first argument. This is much more complicated than the corresponding procedure during dispatch, since the argument tuple type might be abstract. For example, we can define:
(::Union{Foo{Int},Foo{Int8}})(x) = 0
which works since all possible matching methods would belong to the same method table.
## Creating generic functions¶
Since every object is callable, nothing special is needed to create a generic function. Therefore jl_new_generic_function simply creates a new singleton (0 size) subtype of Function and returns its instance. A function can have a mnemonic “display name” which is used in debug info and when printing objects. For example the name of Base.sin is sin. By convention, the name of the created type is the same as the function name, with a # prepended. So typeof(sin) is Base.#sin.
## Closures¶
A closure is simply a callable object with field names corresponding to captured variables. For example, the following code:
function adder(x)
return y->x+y
end
is lowered to (roughly):
immutable ##1{T}
x::T
end
(_::##1)(y) = _.x + y
return ##1(x)
end
## Constructors¶
A constructor call is just a call to a type. The type of most types is DataType, so the method table for DataType contains most constructor definitions. One wrinkle is the fallback definition that makes all types callable via convert:
(::Type{T}){T}(args...) = convert(T, args...)::T
In this definition the function type is abstract, which is not normally supported. To make this work, all subtypes of Type (Type, TypeConstructor, Union, and DataType) currently share a method table via special arrangement.
## Builtins¶
The “builtin” functions, defined in the Core module, are:
is typeof sizeof issubtype isa typeassert throw tuple getfield setfield! fieldtype
nfields isdefined arrayref arrayset arraysize applicable invoke apply_type _apply
_expr svec
These are all singleton objects whose types are subtypes of Builtin, which is a subtype of Function. Their purpose is to expose entry points in the run time that use the “jlcall” calling convention:
jl_value_t *(jl_value_t*, jl_value_t**, uint32_t)
The method tables of builtins are empty. Instead, they have a single catch-all method cache entry (Tuple{Vararg{Any}}) whose jlcall fptr points to the correct function. This is kind of a hack but works reasonably well.
## Keyword arguments¶
Keyword arguments work by associating a special, hidden function object with each method table that has definitions with keyword arguments. This function is called the “keyword argument sorter” or “keyword sorter”, or “kwsorter”, and is stored in the kwsorter field of MethodTable objects. Every definition in the kwsorter function has the same arguments as some definition in the normal method table, except with a single Array argument prepended. This array contains alternating symbols and values that represent the passed keyword arguments. The kwsorter’s job is to move keyword arguments into their canonical positions based on name, plus evaluate and substite any needed default value expressions. The result is a normal positional argument list, which is then passed to yet another function.
The easiest way to understand the process is to look at how a keyword argument method definition is lowered. The code:
function circle(center, radius; color = black, fill::Bool = true, options...)
# draw
end
actually produces three method definitions. The first is a function that accepts all arguments (including keywords) as positional arguments, and includes the code for the method body. It has an auto-generated name:
function #circle#1(color, fill::Bool, options, circle, center, radius)
# draw
end
The second method is an ordinary definition for the original circle function, which handles the case where no keyword arguments are passed:
function circle(center, radius)
#circle#1(black, true, Any[], circle, center, radius)
end
This simply dispatches to the first method, passing along default values. Finally there is the kwsorter definition:
function (::Core.kwftype(typeof(circle)))(kw::Array, circle, center, radius)
options = Any[]
# push remaining elements of kw into options array
#circle#1(color, fill, options, circle, center, radius)
end
The front end generates code to loop over the kw array and pick out arguments in the right order, evaluating default expressions when an argument is not found.
The function Core.kwftype(t) fetches (and creates, if necessary) the field t.name.mt.kwsorter.
This design has the feature that call sites that don’t use keyword arguments require no special handling; everything works as if they were not part of the language at all. Call sites that do use keyword arguments are dispatched directly to the called function’s kwsorter. For example the call:
circle((0,0), 1.0, color = red; other...)
is lowered to:
kwfunc(circle)(Any[:color,red,other...], circle, (0,0), 1.0)
The unpacking procedure represented here as other... actually further unpacks each element of other, expecting each one to contain two values (a symbol and a value). kwfunc (also in Core) fetches the kwsorter for the called function. Notice that the original circle function is passed through, to handle closures.
## Compiler efficiency issues¶
Generating a new type for every function has potentially serious consequences for compiler resource use when combined with Julia’s “specialize on all arguments by default” design. Indeed, the initial implementation of this design suffered from much longer build and test times, higher memory use, and a system image nearly 2x larger than the baseline. In a naive implementation, the problem is bad enough to make the system nearly unusable. Several significant optimizations were needed to make the design practical.
The first issue is excessive specialization of functions for different values of function-valued arguments. Many functions simply “pass through” an argument to somewhere else, e.g. to another function or to a storage location. Such functions do not need to be specialized for every closure that might be passed in. Fortunately this case is easy to distinguish by simply considering whether a function calls one of its arguments (i.e. the argument appears in “head position” somewhere). Performance-critical higher-order functions like map certainly call their argument function and so will still be specialized as expected. This optimization is implemented by recording which arguments are called during the analyze-variables pass in the front end. When cache_method sees an argument in the Function type hierarchy passed to a slot declared as Any or Function, it pretends the slot was declared as ANY (the “don’t specialize” hint). This heuristic seems to be extremely effective in practice.
The next issue concerns the structure of method cache hash tables. Empirical studies show that the vast majority of dynamically-dispatched calls involve one or two arguments. In turn, many of these cases can be resolved by considering only the first argument. (Aside: proponents of single dispatch would not be surprised by this at all. However, this argument means “multiple dispatch is easy to optimize in practice”, and that we should therefore use it, not “we should use single dispatch”!) So the method cache uses the type of the first argument as its primary key. Note, however, that this corresponds to the second element of the tuple type for a function call (the first element being the type of the function itself). Typically, type variation in head position is extremely low — indeed, the majority of functions belong to singleton types with no parameters. However, this is not the case for constructors, where a single method table holds constructors for every type. Therefore the Type method table is special-cased to use the first tuple type element instead of the second.
The front end generates type declarations for all closures. Initially, this was implemented by generating normal type declarations. However, this produced an extremely large number of constructors, all of which were trivial (simply passing all arguments through to new). Since methods are partially ordered, inserting all of these methods is O(n^2), plus there are just too many of them to keep around. This was optimized by generating composite_type expressions directly (bypassing default constructor generation), and using new directly to create closure instances. Not the prettiest thing ever, but you do what you gotta do.
The next problem was the @test macro, which generated a 0-argument closure for each test case. This is not really necessary, since each test case is simply run once in place. Therefore I modified @test to expand to a try-catch block that records the test result (true, false, or exception raised) and calls the test suite handler on it.
However this caused a new problem. When many tests are grouped together in a single function, e.g. a single top level expression, or some other test grouping function, that function could have a very large number of exception handlers. This triggered a kind of dataflow analysis worst case, where type inference spun around for minutes enumerating possible paths through the forest of handlers. This was fixed by simply bailing out of type inference when it encounters more than some number of handlers (currently 25). Presumably no performance-critical function will have more than 25 exception handlers. If one ever does, I’m willing to raise the limit to 26.
A minor issue occurs during the bootstrap process due to storing all constructors in a single method table. In the second bootstrap step, where inference.ji is compiled using inference0.ji, constructors for inference0’s types remain in the table, so there are still references to the old inference module and inference.ji is 2x the size it should be. This was fixed in dump.c by filtering definitions from “replaced modules” out of method tables and caches before saving a system image. A “replaced module” is one that satisfies the condition m != jl_get_global(m->parent, m->name) — in other words, some newer module has taken its name and place.
Another type inference worst case was triggered by the following code from quadgk.jl:
function do_quadgk{Tw}(f, s, n, ::Type{Tw}, abstol, reltol, maxevals, nrm)
if eltype(s) <: Real # check for infinite or semi-infinite intervals
s1 = s[1]; s2 = s[end]; inf1 = isinf(s1); inf2 = isinf(s2)
if inf1 || inf2
if inf1 && inf2 # x = t/(1-t^2) coordinate transformation
return do_quadgk(t -> begin t2 = t*t; den = 1 / (1 - t2);
f(t*den) * (1+t2)*den*den; end,
map(x -> isinf(x) ? copysign(one(x), x) : 2x / (1+hypot(1,2x)), s),
n, Tw, abstol, reltol, maxevals, nrm)
end
s0,si = inf1 ? (s2,s1) : (s1,s2)
if si < 0 # x = s0 - t/(1-t)
return do_quadgk(t -> begin den = 1 / (1 - t);
f(s0 - t*den) * den*den; end,
reverse!(map(x -> 1 / (1 + 1 / (s0 - x)), s)),
n, Tw, abstol, reltol, maxevals, nrm)
else # x = s0 + t/(1-t)
return do_quadgk(t -> begin den = 1 / (1 - t);
f(s0 + t*den) * den*den; end,
map(x -> 1 / (1 + 1 / (x - s0)), s),
n, Tw, abstol, reltol, maxevals, nrm)
end
end
end
This code has a 3-way tail recursion, where each call wraps the current function argument f in a different new closure. Inference must consider 3^n (where n is the call depth) possible signatures. This blows up way too quickly, so logic was added to typeinf_uncached to immediately widen any argument that is a subtype of Function and that grows in depth down the stack. | {"extraction_info": {"found_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": 0.248191699385643, "perplexity": 2720.7822516390934}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1531676590493.28/warc/CC-MAIN-20180719031742-20180719051742-00034.warc.gz"} |
https://starcoder.org/usaco/USACO-2007-Mar-Gold-P3-Face-The-Right-Way/ | # USACO 2007 March Gold P3: Face The Right Way
Description
Farmer John has arranged his N (1 ≤ N ≤ 5,000) cows in a row and many of them are facing forward, like good cows. Some of them are facing backward, though, and he needs them all to face forward to make his life perfect.
Fortunately, FJ recently bought an automatic cow turning machine. Since he purchased the discount model, it must be irrevocably preset to turn K (1 ≤ K ≤ N) cows at once, and it can only turn cows that are all standing next to each other in line. Each time the machine is used, it reverses the facing direction of a contiguous group of K cows in the line (one cannot use it on fewer than K cows, e.g., at the either end of the line of cows). Each cow remains in the same location as before, but ends up facing the opposite direction. A cow that starts out facing forward will be turned backward by the machine and vice-versa.
Because FJ must pick a single, never-changing value of K, please help him determine the minimum value of K that minimizes the number of operations required by the machine to make all the cows face forward. Also determine M, the minimum number of machine operations required to get all the cows facing forward using that value of K.
Input
Line 1: A single integer: N Lines 2..N+1: Line i+1 contains a single character, F or B, indicating whether cow i is facing forward or backward.
Output
Line 1: Two space-separated integers: K and M
SAMPLE INPUT:
7
B
B
F
B
F
B
B
SAMPLE OUTPUT:
3 3
Hint
For K = 3, the machine must be operated three times: turn cows (1,2,3), (3,4,5), and finally (5,6,7)
Explanation of the sample:
There are 4 cows. Cows #1 and #3 must be no more than 10 units apart, cows #2 and #4 must be no more than 20 units apart, and cows #2 and #3 dislike each other and must be no fewer than 3 units apart.
The best layout, in terms of coordinates on a number line, is to put cow #1 at 0, cow #2 at 7, cow #3 at 10, and cow #4 at 27.
Solution:
• Brute force test K size.
• For each K, the i-th cow is will be forced to turn around by a backward facing cow from [i-k+1, i].
• Maintaining a sum of all the turns made previously with a K cow window. Odd value of the sum means the last cow is flipped.
• Sweep through all the cows, for a new i-th cow, sum = sum + f[i] - f[i-K+1] | {"extraction_info": {"found_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": 0.44290366768836975, "perplexity": 1689.4924969982037}, "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-2021-25/segments/1623487653461.74/warc/CC-MAIN-20210619233720-20210620023720-00157.warc.gz"} |
https://dash.harvard.edu/browse?type=subject&value=M+81 | Now showing items 1-1 of 1
• #### A Decade of SN 1993J: Discovery of Radio Wavelength Effects in the Expansion Rate
(EDP Sciences, 2009)
We studied the growth of the shell-like radio structure of supernova SN 1993J in M 81 from September 1993 to October 2003 with very-long-baseline interferometry (VLBI) observations at the wavelengths of 3.6, 6, and 18 cm. ... | {"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": 0.8371869325637817, "perplexity": 3421.973017773915}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1579251778168.77/warc/CC-MAIN-20200128091916-20200128121916-00216.warc.gz"} |
https://ftp.aimsciences.org/article/doi/10.3934/dcds.2006.14.419 | # American Institute of Mathematical Sciences
July 2006, 14(3): 419-446. doi: 10.3934/dcds.2006.14.419
## Unstable manifolds and Hölder structures associated with noninvertible maps
1 Institute of Mathematics "Simion Stoilow" of the Romanian Academy, P.O Box 1-764, RO 014-700, Bucharest, Romania
Received January 2005 Revised June 2005 Published December 2005
We study the case of a smooth noninvertible map $f$ with Axiom A, in higher dimension. In this paper, we look first at the unstable dimension (i.e the Hausdorff dimension of the intersection between local unstable manifolds and a basic set $\Lambda$), and prove that it is given by the zero of the pressure function of the unstable potential, considered on the natural extension $\hat\Lambda$ of the basic set $\Lambda$; as a consequence, the unstable dimension is independent of the prehistory $\hat x$. Then we take a closer look at the theorem of construction for the local unstable manifolds of a perturbation $g$ of $f$, and for the conjugacy $\Phi_g$ defined on $\hat \Lambda$. If the map $g$ is holomorphic, one can prove some special estimates of the Hölder exponent of $\Phi_g$ on the liftings of the local unstable manifolds. In this way we obtain a new estimate of the speed of convergence of the unstable dimension of $g$, when $g \rightarrow f$. Afterwards we prove the real analyticity of the unstable dimension when the map $f$ depends on a real analytic parameter. In the end we show that there exist Gibbs measures on the intersections between local unstable manifolds and basic sets, and that they are in fact geometric measures; using this, the unstable dimension turns out to be equal to the upper box dimension. We notice also that in the noninvertible case, the Hausdorff dimension of basic sets does not vary continuously with respect to the perturbation $g$ of $f$. In the case of noninvertible Axiom A maps on $\mathbb P^2$, there can exist an infinite number of local unstable manifolds passing through the same point $x$ of the basic set $\Lambda$, thus there is no unstable lamination. Therefore many of the methods used in the case of diffeomorphisms break down and new phenomena and methods of proof must appear. The results in this paper answer to some questions of Urbanski ([21]) about the extension of one dimensional theory of Hausdorff dimension of fractals to the higher dimensional case. They also improve some results and estimates from [7].
Citation: Eugen Mihailescu. Unstable manifolds and Hölder structures associated with noninvertible maps. Discrete & Continuous Dynamical Systems, 2006, 14 (3) : 419-446. doi: 10.3934/dcds.2006.14.419
[1] Cleon S. Barroso. The approximate fixed point property in Hausdorff topological vector spaces and applications. Discrete & Continuous Dynamical Systems, 2009, 25 (2) : 467-479. doi: 10.3934/dcds.2009.25.467 [2] Lin Shi, Dingshi Li, Kening Lu. Limiting behavior of unstable manifolds for spdes in varying phase spaces. Discrete & Continuous Dynamical Systems - B, 2021, 26 (12) : 6311-6337. doi: 10.3934/dcdsb.2021020 [3] Dongkui Ma, Min Wu. Topological pressure and topological entropy of a semigroup of maps. Discrete & Continuous Dynamical Systems, 2011, 31 (2) : 545-557 . doi: 10.3934/dcds.2011.31.545 [4] Eugen Mihailescu. Approximations for Gibbs states of arbitrary Hölder potentials on hyperbolic folded sets. Discrete & Continuous Dynamical Systems, 2012, 32 (3) : 961-975. doi: 10.3934/dcds.2012.32.961 [5] Alexanger Arbieto, Carlos Arnoldo Morales Rojas. Topological stability from Gromov-Hausdorff viewpoint. Discrete & Continuous Dynamical Systems, 2017, 37 (7) : 3531-3544. doi: 10.3934/dcds.2017151 [6] Michihiro Hirayama, Naoya Sumi. Hyperbolic measures with transverse intersections of stable and unstable manifolds. Discrete & Continuous Dynamical Systems, 2013, 33 (4) : 1451-1476. doi: 10.3934/dcds.2013.33.1451 [7] Eugen Mihailescu, Mariusz Urbański. Holomorphic maps for which the unstable manifolds depend on prehistories. Discrete & Continuous Dynamical Systems, 2003, 9 (2) : 443-450. doi: 10.3934/dcds.2003.9.443 [8] C. M. Groothedde, J. D. Mireles James. Parameterization method for unstable manifolds of delay differential equations. Journal of Computational Dynamics, 2017, 4 (1&2) : 21-70. doi: 10.3934/jcd.2017002 [9] Guizhen Cui, Yunping Jiang, Anthony Quas. Scaling functions and Gibbs measures and Teichmüller spaces of circle endomorphisms. Discrete & Continuous Dynamical Systems, 1999, 5 (3) : 535-552. doi: 10.3934/dcds.1999.5.535 [10] Hiroki Sumi, Mariusz Urbański. Bowen parameter and Hausdorff dimension for expanding rational semigroups. Discrete & Continuous Dynamical Systems, 2012, 32 (7) : 2591-2606. doi: 10.3934/dcds.2012.32.2591 [11] Sara Munday. On Hausdorff dimension and cusp excursions for Fuchsian groups. Discrete & Continuous Dynamical Systems, 2012, 32 (7) : 2503-2520. doi: 10.3934/dcds.2012.32.2503 [12] Shmuel Friedland, Gunter Ochs. Hausdorff dimension, strong hyperbolicity and complex dynamics. Discrete & Continuous Dynamical Systems, 1998, 4 (3) : 405-430. doi: 10.3934/dcds.1998.4.405 [13] Luis Barreira and Jorg Schmeling. Invariant sets with zero measure and full Hausdorff dimension. Electronic Research Announcements, 1997, 3: 114-118. [14] Jon Chaika. Hausdorff dimension for ergodic measures of interval exchange transformations. Journal of Modern Dynamics, 2008, 2 (3) : 457-464. doi: 10.3934/jmd.2008.2.457 [15] Krzysztof Barański, Michał Wardal. On the Hausdorff dimension of the Sierpiński Julia sets. Discrete & Continuous Dynamical Systems, 2015, 35 (8) : 3293-3313. doi: 10.3934/dcds.2015.35.3293 [16] Xinsheng Wang, Weisheng Wu, Yujun Zhu. Local unstable entropy and local unstable pressure for random partially hyperbolic dynamical systems. Discrete & Continuous Dynamical Systems, 2020, 40 (1) : 81-105. doi: 10.3934/dcds.2020004 [17] De-Jun Feng, Antti Käenmäki. Equilibrium states of the pressure function for products of matrices. Discrete & Continuous Dynamical Systems, 2011, 30 (3) : 699-708. doi: 10.3934/dcds.2011.30.699 [18] Marc Rauch. Variational principles for the topological pressure of measurable potentials. Discrete & Continuous Dynamical Systems - S, 2017, 10 (2) : 367-394. doi: 10.3934/dcdss.2017018 [19] Xueting Tian. Topological pressure for the completely irregular set of birkhoff averages. Discrete & Continuous Dynamical Systems, 2017, 37 (5) : 2745-2763. doi: 10.3934/dcds.2017118 [20] M. Bulíček, Josef Málek, Dalibor Pražák. On the dimension of the attractor for a class of fluids with pressure dependent viscosities. Communications on Pure & Applied Analysis, 2005, 4 (4) : 805-822. doi: 10.3934/cpaa.2005.4.805
2020 Impact Factor: 1.392 | {"extraction_info": {"found_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": 0.8203839063644409, "perplexity": 1641.8590302089756}, "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/1642320305341.76/warc/CC-MAIN-20220128013529-20220128043529-00303.warc.gz"} |
http://mathhelpforum.com/calculus/162181-find-deltaz-deltax-deltaz-deltay.html | # Math Help - Find deltaz/deltax and deltaz/deltay?
1. ## Find deltaz/deltax and deltaz/deltay?
here is what I am trying to do!
R=ln(u^2 + v^2 + w^2)
u= (x+2y)
v=(2x-y)
w=(2xy)
find deltaz/deltax and deltaz/deltay when x=y=1
This is a chain rule case correct? So:
Dr/dx=(1/((x+2y)^2+(2x-y)^2+(2xy)^2))(2(x+2y)(1)+2(2x-y)(2)+2(2xy)(2y))
Then placing 1 in all x and y makes:
Dr/dx=(14/9)?
And another one is:
let x^2 +y^2 +z^2=3xyz
find dz/dx and dz/dy
for this do I isolate z and then find dz/dx and dz/dy?
thanks!
2. Are you trying to find $\frac{dr}{dx}$ or $\frac{\Delta r}{\Delta x}$? You say it is the latter but calculate the former.
If you are looking for $\frac{dr}{dx}$ then, yes, the chain rule is the right way to go.
for the second, don't isolate z, use implicit differentiation: $2x+ 2z z_x= 3yz+ 3xyz_x$. Solve for $z_x$. Do the same to find $z_y$. | {"extraction_info": {"found_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": 0.8773480653762817, "perplexity": 1727.967323656768}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1416931010590.31/warc/CC-MAIN-20141125155650-00171-ip-10-235-23-156.ec2.internal.warc.gz"} |
https://lessonplanet.com/lesson-plans/complex-numbers/all | # Complex Numbers Teacher Resources
Find Complex Numbers lesson plans and worksheets
Showing 1 - 200 of 300 resources
9 Items in Collection
Lesson Planet
#### Perform Arithmetic Operations with Complex Numbers: High School Math Common Core
For Teachers 9th - 12th Standards
Imagine a world where all the numbers live together harmoniously. Here you have it! Check out these resources that introduce the concept of an imaginary number, go through the operations, and model how to utilize the conjugate.
35 Items in Collection
Lesson Planet
#### Algebra: High School Common Core Math
For Teachers 9th - 12th Standards
All Algebra, all the time! Here is a compiled list of resources that address all of the standards regarding Algebra Common Core for high school. Each resource has the main standard it addresses under the notes section of the item.
31 Items in Collection
Lesson Planet
#### Number and Quantity: High School Common Core Math
For Teachers 9th - 12th Standards
This collection has a resource for each standard in the Number and Quantity selection of the CCSS. While several of the resources cover multiple standards, the focus standard is listed in the notes section of each resource for easy viewing.
Lesson Planet
#### Complex Numbers
For Teachers 10th - 12th Standards
Learners are introduced to the concept of imaginary unit and complex numbers. They are taught how to add and subtract complex numbers. Young scholars define a complex number. They comprehend at least two applications of complex numbers....
1 In 1 Collection
Lesson Planet
#### Classifying Complex Numbers
For Teachers 10th - 12th Standards
Imaginary numbers are a real thing. Scholars learn about complex numbers, real numbers, and imaginary numbers. They classify given numbers as strictly complex, strictly real, or strictly imaginary in an individual or group activity.
Lesson Planet
#### Complex Numbers: Plotting and Polar Form
For Teachers 9th - 12th Standards
Explore the concept of, and use the Ti-Nspire to, convert complex numbers into polar form. Then practice graphing complex numbers in the polar coordinate plane.
Lesson Planet
#### Powers and Roots of Complex Numbers
For Teachers 9th - 12th Standards
Explore a few powers of complex numbers numerically and decide if there is a pattern and use parametric equations to represent a complex number graphically. Use De Moivre's theorem to represent the roots of the complex number...
1 In 1 Collection
Lesson Planet
#### Complex Numbers
For Teachers 9th - 12th Standards
The class practices, on paper and/or on a TI graphing calculator the concepts of how to add, multiply, divide and subtract complex numbers using the correct property.
Lesson Planet
#### Complex Numbers in Polar Form; DeMoivre’s Theorem
For Teachers 10th - 12th Standards
The iconic links between trig functions and complex numbers are introduced in a lesson on the basic properties of complex numbers in polar form. Quickly progressing through the polarization of complex coordinates, a bulk of the worksheet...
EngageNY
#### An Appearance of Complex Numbers 2
For Teachers 11th - 12th Standards
Help the class visualize operations with complex numbers with a lesson that formally introduces complex numbers and reviews the visualization of complex numbers on the complex plane. The fifth installment of a 32-part series reviews the...
Lesson Planet
#### Complex Numbers
For Students 9th - 12th Standards
Are complex numbers and binomials similar? This stack of slides provides an introduction to complex numbers and shows how to operate with them. The worked examples show a connection between operating with binomials and operating with...
Lesson Planet
#### Trigonometric Form of Complex Numbers
For Teachers 11th - 12th Standards
This lesson is written from the perspective of a student teacher. A step by step lesson in which the class works on the trigonometric form of complex numbers. They convert between trigonometric and complex forms. They will also practice...
Lesson Planet
#### Trigonometric Form of Complex Numbers
For Students 11th - Higher Ed Standards
Represent complex numbers in two ways. Pupils use the interactive to convert polar and rectangular representations of complex numbers. The learners drag an overlay back and forth over the coordinate plane to reveal the polar coordinates...
8:58
Lesson Planet
#### Complex Numbers (Part 2)
For Students 9th - 11th
This video continues looking at dividing complex numbers by looking at the conjugate of a complex number. The instructor then uses the conjugate to rationalize the denominator of a rational expression with a complex number in the...
7:21
Lesson Planet
#### Complex Numbers (Part 1)
For Students 9th - 11th
In this video, a complex number is defined and graphed on the complex plane. Sal also shows how to add, subtract, and multiply two complex numbers. He starts showing how to divide two complex numbers, but runs out of time and continues...
10:10
Lesson Planet
#### Complex Numbers (Part 1)
For Students 9th - 11th
In this video, a complex number is defined and graphed on the complex plane. Sal also shows how to add, subtract, and multiply two complex numbers. He starts showing how to divide two complex numbers, but runs out of time and continues...
8:58
Lesson Planet
#### Complex Numbers (Part 2)
For Students 9th - 11th
This video continues looking at dividing complex numbers by looking at the conjugate of a complex number. The instructor then uses the conjugate to rationalize the denominator of a rational expression with a complex number in the...
5:05
Lesson Planet
#### How Do You Graph Complex Numbers?
For Teachers 10th - 11th
Complex numbers have two parts and can be graphed on a complex plane. After an explanation of the complex plane, this video shows three examples of graphing complex numbers.
Lesson Planet
For Students 10th - 12th Standards
In this complex numbers activity, learners find the sum of complex numbers. This four-page activity contains approximately 20 multi-step problems.
Lesson Planet
#### Complex Numbers
For Teachers 9th - 12th Standards
Students examine complex numbers. For this Algebra II lesson, students investigate two programs that involve complex numbers: the MANDELER Program and SYNDIV program.
1 In 1 Collection
EngageNY
#### Complex Numbers and Transformations
For Teachers 9th - 12th Standards
Your learners combine their knowledge of real and imaginary numbers and matrices in an activity containing thirty lessons, two assessments (mid-module and end module), and their corresponding rubrics. Centered on complex numbers and...
EngageNY
#### Distance and Complex Numbers 1
For Teachers 11th - 12th Standards
To work through the complexity of coordinate geometry pupils make the connection between the coordinate plane and the complex plane as they plot complex numbers in the 11th part of a series of 32. Making the connection between the two...
Lesson Planet
#### Can You Hear Me Now? Using Cell Phone Signals to Divide Complex Numbers
For Students 9th - 12th Standards
Without complex numbers, cell phones could not function. Scholars learn to divide complex numbers by applying them to the wavelengths of cell phone signals. They work to develop a method of division incorporating the conjugate. Then,...
EngageNY
#### Distance and Complex Numbers 2
For Teachers 11th - 12th Standards
Classmates apply midpoint concepts by leapfrogging around the complex plane. The 12th lesson in a 32 segment unit, asks pupils to apply distances and midpoints in relationship to two complex numbers. The class develops a formula to find...
EngageNY
#### Trigonometry and Complex Numbers
For Teachers 11th - 12th Standards
Complex numbers were first represented on the complex plane, now they are being represented using sine and cosine. Introduce the class to the polar form of a complex number with the 13th part of a 32-part series that defines the argument...
EngageNY
#### Complex Numbers as Vectors
For Teachers 11th - 12th Standards
Show your math class how to use vectors in adding complex numbers. Vectors represent complex numbers as opposed to points in the coordinate plane. The class uses the geometric representation to add and subtract complex numbers and...
EngageNY
#### An Appearance of Complex Numbers 1
For Teachers 11th - 12th Standards
Complex solutions are not always simple to find. In the fourth lesson of the unit, the class extends their understanding of complex numbers in order to solve and check the solutions to a rational equation presented in the first lesson....
1 In 1 Collection
Lesson Planet
#### Computations with Complex Numbers
For Teachers 9th - 12th Standards
This quick set of problems provides a brief refresher on the arithmetic of complex numbers. Learners need to multiply, add and subtract, and remember features of i when raised to a power. Included solutions are clear enough that learners...
EngageNY
#### Complex Number Division 1
For Teachers 11th - 12th Standards
Conjugating in the math classroom — and we're not talking verbs! The seventh lesson in a series of 32 introduces the class to the building blocks of complex number division. During the instruction, the class learns to find the...
Lesson Planet
#### Complex Number Properties
For Teachers 10th - 12th Standards
High schoolers experiment with complex numbers to see which properties of real numbers apply to the system of complex numbers and practice computations. The study of these properties is first explored by looking at rotational...
Lesson Planet
#### Plotting, Simplifying, and Describing Complex Numbers
For Students 10th - 12th
In this complex numbers instructional activity, students simplify, plot, iterate, and state bounded or bounded for complex numbers in nine problems. The solutions are provided.
Lesson Planet
#### Computation with Real and Complex Numbers
For Students 9th - 12th Standards
In this computation with real and complex numbers worksheet, students use addition, subtraction, multiplication and division to solve 26 problems with complex numbers to win a bingo game.
Lesson Planet
#### Properties of Complex Numbers
For Students 11th - 12th Standards
For this worksheet, students evaluate complex (signed and imaginary) numbers. In addition, they are asked to graph complex numbers as well as identify a complex number on a presented graph.
Lesson Planet
#### Complex Numbers
For Students 9th
In this complex numbers learning exercise, 9th graders solve 10 different problems that include determining the absolute value of each equation. First, they convert the number to the a+bi form. Then, students select the coefficients for...
Lesson Planet
#### Multiplying and Dividing Complex Numbers
For Teachers 8th - 11th Standards
Students solve quadratic using multiplication and division. In this algebra instructional activity, students perform operation with complex numbers. They factor quadratics using the quadratic formula.
Lesson Planet
#### Complex Numbers
For Students 9th
In this complex numbers worksheet, 9th graders solve 10 different problems that include addition and subtraction of these numbers. First, they add or subtract the coefficients of similar terms algebraically. Then, students remove the...
Lesson Planet
#### Representation of Complex Numbers
For Teachers 9th - 12th
Learners write complex numbers in standard form. They add, subtract, multiply and divide complex numbers correctly.
3:38
Lesson Planet
#### Imaginary Numbers Are Real (Part 6: The Complex Plane)
For Students 9th - 12th Standards
How do addition and subtraction work on the complex plane? A short video presentation provides a clue on how to add complex numbers geometrically. The video ends with four problems to determine the rules for multiplication on the complex...
2:57
Lesson Planet
#### Imaginary Numbers Are Real (Part 4: Bombelli's Solution)
For Students 9th - 12th Standards
Is the square root of negative one crucial to the process of finding other solutions? Using the properties of the newly discovered square root of negative one, historical mathematician Bobelli is able to solve Cardan's problem. His...
Lesson Planet
#### Complex Numbers
For Teachers 10th - 12th
Build on your class' understanding of real numbers as they begin working with complex numbers. Pupils begin with an exploration of i and the patterns in the powers of i. After developing a definition for i, they simplify complex number...
Lesson Planet
#### Complex Numbers
For Students 9th
In this complex numbers learning exercise, 9th graders solve 10 different problems related to various complex numbers. First, they multiply and divide various types of complex numbers. Then, students determine the multiplicative inverse...
Lesson Planet
#### Complex Numbers
For Students 9th
In this complex numbers instructional activity, 9th graders solve 10 different problems that include either adding or subtracting complex numbers. First, they determine the sum of the real components. Then, students determine the sum of...
Lesson Planet
#### 5-9 Skills Practice: Complex Numbers
For Students 10th - 12th
In this complex numbers activity, students simplify given radicals and complex numbers. This one-page activity contains 26 problems.
Lesson Planet
#### The Solution is Complex
For Teachers 9th - 12th Standards
Consider complex numbers, roots, and quadratic equations. Use the discriminate as a way to determine the nature of a quadratic's roots. Then discuss the similarities and differences between quadratics with two, one, or no real roots....
Lesson Planet
#### Rational Expressions and Complex Numbers
For Students 11th
In this rational expressions and complex numbers worksheet, 11th graders solve and complete 24 various types of problems that include determining logarithms and polynomials. First, they determine the remaining roots of a polynomial given...
Lesson Planet
#### Complex Numbers and Operations
For Teachers 8th - 10th
In this algebra worksheet, students add, subtract and multiply using complex numbers. They apply the correct property of i as they solve. There are ten questions with an answer key.
7:22
Lesson Planet
#### Complex Numbers - Multiplying and Dividing
For Teachers 8th - 12th
Algebra In action! Watch the step-by-step process needed to multiply and divide complex numbers. The FOIL method is used to solve two different practice problems involving multiplication and multiplying by the conjugation is used to...
2:02
Lesson Planet
#### Complex Numbers - Algebra Help
For Teachers 7th - 10th
The foil method had been used for years as a way to remember how to simplify complex numbers. This process is demonstrated step-by-step, slowly so the learner will be able to follow along as the instructor solves the problem. Intended...
2 In 2 Collections
Lesson Planet
#### Operations with Complex Numbers
For Teachers 9th - 11th Standards
This activity is a great introduction to the operations of complex numbers. Combining their knowledge of algebra and the use of a calculator, your class can discover and apply the rules for adding, subtracting, and multiplying complex...
Lesson Planet
#### As If Numbers Weren't Complex Enough Already!
For Teachers 9th - 12th Standards
The class explores the concept of complex numbers on a website to generate their own Mandelbrot sets. They will practice performing operations with complex numbers and then to get a visual understanding, graph the absolute value of a...
EngageNY
#### Complex Number Division 2
For Teachers 11th - 12th Standards
Individuals learn to divide and conquer complex numbers with a little help from moduli and conjugates. In the second activity on complex number division, the class takes a closer look at the numerator and denominator of the...
EngageNY
#### The Geometric Effect of Some Complex Arithmetic 1
For Teachers 11th - 12th Standards
Translating complex numbers is as simple as adding 1, 2, 3. In the ninth lesson plan in a 32-part series, the class takes a deeper look at the geometric effect of adding and subtracting complex numbers. The resource leads pupils into...
EngageNY
#### The Geometric Effect of Some Complex Arithmetic 2
For Teachers 11th - 12th Standards
The 10th lesson in a series of 32, continues with the geometry of arithmetic of complex numbers focusing on multiplication. Class members find the effects of multiplying a complex number by a real number, an imaginary number, and another...
EngageNY
#### Linear Transformations Review
For Teachers 11th - 12th Standards
Time for matrices and complex numbers to come together. Individuals use matrices to add and multiply complex numbers by a scalar. The instructional activity makes a strong connection between the operations and graphical transformations.
Lesson Planet
#### Two Variable Function Pump
For Students 9th - 12th Standards
Use a function to operate on two variables. Pupils look at operating with complex numbers as a function of two variables. The interactive squares the input and adds a constant to it. Learners visualize the resulting output and its...
Lesson Planet
#### Complex Numbers
For Students 10th - 12th
A straightforward approach to teaching complex numbers, this lesson addresses the concepts of complex numbers, polar coordinates, Euler's formula, De moivres Theorem, and more. It includes a practice problems set with odd answers and a...
Lesson Planet
#### Complex Numbers - Week 5
For Teachers 10th - 11th
In this complex numbers worksheet, students solve problems involving polynomials, real constants containing imaginary numbers, and find the complex number that satisfies a given equation. This two-page worksheet contains seven problems.
Lesson Planet
#### Complex Numbers
For Students 10th - 12th
In this complex numbers activity, students write numbers in standard form. They identify real, imaginary and complex numbers. Students find the absolute value and conjugate of a number. This two-page activity contains 45 problems.
Lesson Planet
For Teachers 10th - 12th Standards
In this radical worksheet, students simplify complex numbers. They find the sum and difference of complex numbers. This two-page worksheet contains 11 multiple-choice problems. Answers are given on the last page.
4:25
Lesson Planet
#### Imaginary Numbers Are Real (Part 7: Complex Multiplication)
For Students 9th - 12th Standards
Multiplying complex numbers geometrically is complicated. Find an easier way with a short video that explains the process of multiplying complex numbers on the complex plane. The connection with the process and the angles and moduli sets...
Lesson Planet
#### Complex Numbers Solutions
For Students 9th - 12th Standards
Complex doesn't have to mean harder! Learners experiment with online software to determine the quadratic equations with complex solutions. They use the quadratic formula to solve equations with both real and complex solutions.
4:42
Lesson Planet
#### Imaginary Numbers Are Real (Part 3: Cardan's Problem)
For Students 9th - 12th Standards
Were complex numbers discovered or invented? A video presentation makes the case for the discovery of square roots of negative one. In order for complex numbers to be real, then they must behave like other numbers, which they do in terms...
5:41
Lesson Planet
#### Imaginary Numbers Are Real (Part 9: Closure)
For Students 9th - 12th Standards
The last video in a series about imaginary numbers demonstrates the need for complex numbers. Math pupils learn that they need to include the square root of negative one, the building block of the complex numbers, to have a set of...
1 In 1 Collection
Lesson Planet
#### Imaginary Numbers? What Do You Mean Imaginary?
For Teachers 9th - 12th Standards
Don't worry, this resource actually exists. Scholars learn about imaginary numbers and work on problems simplifying square roots of negative numbers. As an extension, they research the history of imaginary numbers.
EngageNY
#### Complex Numbers as Solutions to Equations
For Students 10th - 12th Standards
Quadratic solutions come in all shapes and sizes, so help your classes find the right one! Learners use the quadratic formula to find solutions for quadratic equations. Solutions vary from one, two, and complex.
Lesson Planet
#### DeMoivre's Theorem and nth Roots: The nth Roots of Unity
For Students 11th - Higher Ed
The nth roots of unity all have a magnitude of one. Scholars use the unit circle and DeMoivre's Theorem to find the complex roots of one and discover that the complex numbers all lie on the unit circle and are equally spaced around it...
Lesson Planet
#### Application of Complex Numbers
For Teachers 9th - 12th
Students apply operations with complex numbers to electrical circuit problems, real-world situations, utilizing TI-83 Graphing Calculators. They perform basic operations of addition, subtraction, division and multiplication with complex...
Lesson Planet
#### Complex Numbers
For Students 9th - 12th
In this algebra worksheet, learners simplify complex numbers ranging from performing basic operations to distribution with a few combine like terms. There are 44 questions.
Lesson Planet
#### Introduction to Complex Numbers
For Students 10th - 12th Standards
In this complex number activity, learners explore the properties of imaginary numbers to find the square roots of negative numbers. Explanations and examples are given prior to the exercise. This two-page activity contains ten problems.
Lesson Planet
#### Complex Equations
For Students 12th - Higher Ed
In this complex equations instructional activity, students solve and complete 40 various types of problems. First, they solve each of the equations over the set of complex numbers shown. Then, students solve each inequality and state...
Lesson Planet
#### Complex Numbers
For Students 11th
For this algebra worksheet, 11th graders solve complex numbers using division. multiplication, addition and subtraction. There are 11 questions with an answer key.
Lesson Planet
#### Complex Numbers
For Students 10th - 11th
In this algebra worksheet, students solve complex numbers using multiplication and division properties. There are 10 questions with an answer key.
Lesson Planet
#### Complex Numbers
For Students 10th - 11th
In this algebra learning exercise, students solve complex numbers using multiplication and division properties. There are 10 questions with an answer key.
Lesson Planet
#### Complex Numbers
For Students 11th
In this algebra activity, 11th graders solve complex numbers using division. multiplication, addition and subtraction. There are 11 questions with an answer key.
8:04
Lesson Planet
#### Complex Conjugates
For Students 10th - 12th
Sal discusses the usefulness of the conjugate of the complex number is this video. First, he shows both graphically and algebraically adding a complex number and its conjugate. Then, he shows how to simplify a rational expression with...
4:07
Lesson Planet
#### How Do You Add Complex Numbers by Graphing in the Complex Plane?
For Teachers 10th - 11th
Graphs usually add an extra dimension to ones understanding of mathematical concepts and graphing complex numbers is no exception. This video shows to graph complex numbers on the complex plane and what the results of adding complex...
2:45
Lesson Planet
#### How Do You Multiply Complex Numbers Using FOIL?
For Teachers 10th - 11th
How do you multiply complex numbers? The instructor in this video uses the FOIL method of multiplying binomials to multiply two complex numbers. She finishes the problem, by using prior knowledge of the definition of the imaginary unit,...
Lesson Planet
#### Worksheet 7.5 DeMoivre's Theorem and Complex Numbers
For Students 10th - 12th
In this DeMoivre's Theorem and complex numbers worksheet, students change complex numbers to real numbers. They determine square roots of complex numbers and represent them geometrically. This two-page worksheet contains eight problems.
Lesson Planet
#### Vectors
For Teachers 10th - 12th Standards
Complex numbers bridge so many concepts as learners edge into higher-level math. Here, their polar and rectangular forms link through vector notation, and the arithmetic of vectors is born. These basic math skills translate into a...
1 In 1 Collection
Lesson Planet
#### Complex Distance
For Teachers 10th - 12th Standards
Have learners graph complex numbers to gain a visual and mathematical understanding of the distance and the midpoint between two complex numbers. This lesson is short, but to the point, and addresses an important complex number concept....
Lesson Planet
#### Steady-State Circuit Analysis & Filter Design
For Teachers 9th - Higher Ed Standards
Scholars identify how the TI-89 implements phasors to perform sinusoidal steady-state analysis. The focus is on how to enter and display complex numbers. They also show how a typical steady-state application how to use the Numeric Solver...
Lesson Planet
#### Complex Analysis: Polar Form
For Students Higher Ed
For this polar form worksheet, students write complex numbers in polar form. They draw an Argand diagram containing vectors and draw sketches representing in a coordinate plane. This two-page worksheet contains thirteen multi-step...
Lesson Planet
#### Solving Quadratic Equations with Complex Roots
For Students 8th - 9th
In this quadratic equations learning exercise, students solve 10 different equations that include complex roots. First, they solve for the indicated variable and express the roots of the equation in simplest form. Then, students...
2 In 2 Collections
Lesson Planet
For Teachers 10th - 12th Standards
Through a variety of physical and theoretical situations, learners are led through the development of some of the deepest concepts in high school mathematics. Complex numbers, the fundamental theorem of algebra and rational exponents...
Lesson Planet
#### Application of Complex Numbers
For Teachers 9th - 12th
Students apply operations with complex numbers to electrical circuit problems. They use electrical current equations and graphing calculators to solve electrical engineering problems.
Lesson Planet
#### Complex numbers in polar form
For Teachers 9th - 12th
Young scholars plot complex numbers in the polar plane. They convert complex numbers in polar form to rectangular form. Students plot coordinates in the polar plane. They plot complex numbers in the complex plane. Young scholars are...
Lesson Planet
#### Complex numbers in polar form
For Teachers 9th - 12th
Students plot complex numbers in the polar plane. They are asked to list what they believe are the five most famous numbers in mathematics. Students are explained that generally accepted that the five most famous numbers in mathematics...
Lesson Planet
#### Complex Numbers
For Students Higher Ed
In this complex numbers worksheet, students simplify 9 problems involving the addition, subtraction, multiplication, and division of complex numbers.
Lesson Planet
#### Graphing and Absolute Value of Complex Numbers
For Students 10th - 12th
In this graphing and absolute value worksheet, students graph complex numbers and find the absolute value of complex numbers. Students complete 12 problems total.
Lesson Planet
#### Sixty-Eight Solving Equations and Performing Operations With Complex Numbers
For Teachers 10th - 12th
For this complex numbers worksheet, students classify numbers, perform operations on complex numbers, and find complex solutions to equations, in sixty-eight problems.
Lesson Planet
#### Complex Numbers
For Students 9th
In this complex numbers worksheet, 9th graders solve 10 different types of problems that include complex numbers in standard form. First, they state the values of the a and b components for each complex number when the number is in a...
Lesson Planet
#### Operations with Complex Numbers
For Students 10th - 11th
In this complex numbers worksheet, students simplify thirty complex number expressions and answer two critical thinking questions. The solutions are provided.
Lesson Planet
#### Imaginary and complex Numbers
For Students 11th
In this Algebra II worksheet, 11th graders simplify expression involving imaginary and complex numbers and determine the quadratic equation that would have the given complex roots. The on page worksheet contains thirty-four problems. ...
Lesson Planet
#### Twenty Equations Involving Imaginary and Complex Numbers
For Students 10th - 12th
In this complex numbers worksheet, students solve twenty equations involving imaginary and complex numbers. Four of these problems involve two variables.
Lesson Planet
#### Math 321 Spring 98. Complex Numbers
For Students Higher Ed
In this complex numbers worksheet, students find the solutions to polynomials and write them in rectangular and exponential form. This two-page worksheet contains two problems.
Lesson Planet
#### Complex Numbers
For Students 10th - 12th
In this complex numbers worksheet, students simplify the expressions of complex numbers and use the answers to answer a riddle. Students complete 15 problems.
Lesson Planet
#### Algebra II Test covering Radicals, Complex Numbers, and Finding Roots of Quadratics
For Students 10th - 12th
In this algebra two worksheet, students solve twenty-five problems in test format. The worksheet covers radicals, complex numbers, and finding roots of quadratics.
Lesson Planet
#### Topic 5.9 and 5.10 - Complex Numbers
For Students 7th - 9th
In this complex numbers worksheet, students solve problems in which they either simplify or solve algebraic expressions. There are 15 questions on this worksheet.
EngageNY
#### A Surprising Boost from Geometry
For Students 10th - 12th Standards
Working with imaginary numbers — this is where it gets complex! After exploring the graph of complex numbers, learners simplify them using addition, subtraction, and multiplication.
EngageNY
#### Discovering the Geometric Effect of Complex Multiplication
For Teachers 11th - 12th Standards
Does complex number multiplication have the class spinning? Here's a resource that helps pupils explore and discover the geometric effect of multiplying complex numbers. In the 14th installment in the 32-part unit groups look at the unit...
EngageNY
#### Exploiting the Connection to Trigonometry 1
For Teachers 11th - 12th Standards
Class members use the powers of multiplication in the 19th installment of the 32-part unit has individuals to utilize what they know about the multiplication of complex numbers to calculate the integral powers of a complex number. Groups...
EngageNY
#### Mid-Module Assessment Task - Precalculus (module 1)
For Teachers 11th - 12th Standards
Individuals show what they know about the geometric representations of complex numbers and linearity. Seventeen questions challenge them to demonstrate their knowledge of moduli and operations with complex numbers. The assessment is the...
1 In 1 Collection
Lesson Planet
#### Complex Number Operations
For Teachers 10th - 12th Standards
What do animated videos have to do with mathematics? Using operations of complex numbers and their representations on the complex plane, high schoolers observe how mathematics could be used to move animations. The lesson provides an...
Lesson Planet
#### Name the Property
For Students 10th - 12th Standards
In this property activity, students examine given problems containing complex numbers. They identify the property used in the problem. This one-page activity contains 10 problems.
Lesson Planet
#### Multiplying Complex Numbers
For Students 10th - 11th
In this complex number worksheet, students multiply binomials containing imaginary numbers. They simplify imaginary numbers to their lowest terms. This two-page worksheet contains ten problems.
Lesson Planet
#### Worksheet 7.5 Trigonometric Form for Complex Numbers
For Students 10th - 12th
In this trigonometric form worksheet, learners represent complex numbers geometrically and express complex numbers in trigonometric form. Students solve equations containing complex numbers. This two-page worksheet contains 13 problems.
Lesson Planet
#### Complex Numbers
For Students 9th
In this complex numbers worksheet, 9th graders solve and graph 10 different problems that include various complex numbers. First, they represent each of the problems shown as complex numbers graphically. Then, students graphically add...
Lesson Planet
#### Math 312 Spring 2004: Complex Numbers
For Students 12th - Higher Ed
In this complex numbers worksheet, students complete proofs for complex numbers, sketch points which solve an equation, compute and sketch an Argand diagram. This two-page worksheet contains five multi-step problems.
Lesson Planet
#### Math 312 Spring 95 - Complex Numbers
For Students Higher Ed
In this complex number learning exercise, students explore complex numbers and sketch a set of points which solve in the equation. This one-page learning exercise contains five problems.
Lesson Planet
#### Complex Analysis: Properties of Complex Numbers
For Students Higher Ed
In this properties of complex numbers worksheet, students list and explain the properties and operations used to compute the value of expressions. This one-page worksheet contains six definition questions and three equations.
12:58
Lesson Planet
#### Complex Determinant Example
For Students 10th - 12th
Sal solves a complex determinant problem from the 2010 IIT entrance test. Knowledge of determinants, the exponential form of complex numbers, trigonometric ratios, and algebraic thinking are all utilized here.
Lesson Planet
#### Iterating the Function and Complex Numbers
For Teachers 7th - 10th
Students identify the end behavior of polynomial graphs. In this algebra lesson, students factor and solve quadratic and complex equations. They factor out negative roots and identify the real and imaginary parts of an equation.
4:38
Lesson Planet
#### Imaginary Numbers Are Real (Part 5: Numbers are Two Dimensional)
For Students 9th - 12th Standards
If the square root of negative one exists, where is it on the number line? A math video presents a geometric representation of complex numbers and the complex plane, and then compares it to the geometric representation of real numbers —...
4:40
Lesson Planet
#### Imaginary Numbers Are Real (Part 8: Math Wizardry)
For Students 9th - 12th Standards
How does the Fundamental Theorem of Algebra apply to equations with complex roots? Using recently learned concepts about the complex plane, learners determine all the complex roots of polynomials. They can find the same roots as...
Lesson Planet
#### Imaginary Numbers
For Students 9th - 12th Standards
Here is a worksheet that takes all aspects of quadratic functions and incorporates imaginary numbers into the problems. The problems range from simplifying to graphing and solving by using a variety of methods with imaginary and complex...
EngageNY
#### End-of-Module Assessment Task — Precalculus (Module 1)
For Teachers 11th - 12th Standards
A transformational assessment determines how far pupils are advancing toward mastering complex and matrix standards. The assessment checks the learners' understanding of linear transformations, complex numbers and the complex plane,...
Lesson Planet
#### Complexity
For Teachers 10th - 12th Standards
Students perform mathematical operations on complex numbers. After a lecture/demo, students utilize a worksheet imbedded in this plan to gain practice performing operations on complex numbers.
Lesson Planet
#### Working With Radicals and Complex Numbers
For Teachers 9th - 11th
Learners solve problems with radicals and complex numbers. In this algebra lesson, students add, subtract, multiply and divide radicals and complex numbers using the conjugate.
Lesson Planet
#### Preliminaries and a Review of Some Geometry and Complex Numbers
For Students 9th - 11th
In this review worksheet, students explore the rules of exponents and the Pythagorean Theorem. They examine formulas for the area of polygons. Students review the topic of complex numbers. This five-page worksheet includes extensive...
EngageNY
#### Matrix Multiplication Is Not Commutative
For Teachers 11th - 12th Standards
Should matrices be allowed to commute when they are being multiplied? Learners analyze this question to determine if the commutative property applies to matrices. They connect their exploration to transformations, vectors, and complex...
Lesson Planet
#### Complex Number Operations
For Teachers 9th - 10th
Students solve problems with complex numbers. In this algebra lesson, students use addition, subtraction, multiplication and division of complex numbers.
Lesson Planet
#### The Complex Numbers
For Teachers 9th - 10th
In this algebra worksheet, students solve 16 problems involving imaginary numbers. In the first three, students find the square root of 3 negative numbers in terms of i. Nine problems involve addition, subtraction, multiplication and...
EngageNY
#### Exploiting the Connection to Trigonometry 2
For Teachers 11th - 12th Standards
The class checks to see if the formula for finding powers of a complex number works to find the roots too. Pupils review the previous day's work and graph on the polar grid. The discussion leads the class to think about how to reverse...
EngageNY
#### Justifying the Geometric Effect of Complex Multiplication
For Teachers 11th - 12th Standards
The 14th instructional activity in the unit has the class prove the nine general cases of the geometric representation of complex number multiplication. Class members determine the modulus of the product and hypothesize the relationship...
EngageNY
#### The Geometric Effect of Multiplying by a Reciprocal
For Teachers 11th - 12th Standards
Class members perform complex operations on a plane in the 17th segment in the 32-part series. Learners first verify that multiplication by the reciprocal does the same geometrically as it does algebraically. The class then circles back...
EngageNY
#### Exploiting the Connection to Cartesian Coordinates
For Teachers 11th - 12th Standards
Multiplication in polar form is nice and neat—that is not the case for coordinate representation. Multiplication by a complex number results in a dilation and a rotation in the plane. The formulas to show the dilation and rotation are...
Lesson Planet
#### Absolute Value
For Students 11th - 12th
In this absolute value worksheet, students solve 10 different equations that include solving absolute values. First, they determine whether their equation is expressed in the a+bi form. Then, students select the coefficients for a and b....
Lesson Planet
#### Complex Numbers
For Teachers 10th - 12th
In this complex numbers worksheet, students write numbers as a multiple of i. They add and subtract imaginary numbers. Students write complex quotients in standard form. This three-page worksheet contains six problems.
Lesson Planet
#### Complex Analysis: Graphical Representations
For Students Higher Ed
For this graphical representation worksheet, students draw an Argand diagram depicting complex numbers. They draw in vectors that represent complex numbers. This three-page worksheet contains approximately ten problems.
Lesson Planet
#### Complex Analysis: Graphical Representations
For Students Higher Ed
For this graphical representation worksheet, students draw an Argand diagram depicting two complex numbers in a complex plane. They draw vectors to represent complex numbers. This two-page worksheet contains five equations to solve.
Lesson Planet
#### Quaternions
For Students 11th - 12th
For this quaternions worksheet, students solve and complete 7 different problems. First, they read and identify quaternions as expressions in a given form of ordinary real numbers. Then, students add and subtract a few problems by doing...
Lesson Planet
#### Operations of Complex Numbers and Intro to DeMoivre's Theorem
For Teachers 9th - 10th
Learners solve problems with complex numbers. In this algebra lesson, students factor complex numbers and simplify equations using DeMoivre's Theorem. They add, subtract, multiply and divide using negative roots.
Lesson Planet
#### Complex Analysis: Complex Numbers
For Students Higher Ed
In this complex numbers worksheet, students compute the value of given expressions and write the answer in complex number form. This one-page worksheet contains three equations.
5:16
Lesson Planet
#### Imaginary Numbers Are Real (Part 2: A Little History)
For Students 9th - 12th Standards
In some cases, a square root of a negative number must exist in order to determine the roots of a cubic equation. An educational presentation provides a specific example of a cubic with a known root to have an understanding of a square...
Lesson Planet
#### Saxon Math: Algebra 2 (Section 7)
For Teachers 9th - 12th Standards
Section seven of twelve turns the mathematical eye toward higher-level concepts. From radians in the unit circle to the complex number system, logarithms to advanced factoring methods, this lesson—just past the halfway point in the...
Lesson Planet
#### Real-World Applications to Imaginary and Complex Numbers
For Teachers All
Authenticate imaginary numbers through real-life applications in science, math, and literature.
Lesson Planet
#### Complex Numbers
For Teachers 9th - 10th
Students define sine waves as it relates to digital signal. In this algebra instructional activity, students investigate the importance of complex numbers as it relates to math and observed the distortion caused by a digital signal,...
Lesson Planet
#### Complex Number
For Students 8th - 10th
In this algebra instructional activity, students identify the vertex of a quadratic functions. They identify complex numbers. There are 6 questions.
Lesson Planet
#### Complex Analysis: Polar & Exponential Forms
For Students Higher Ed
In this polar and exponential form worksheet, students use Euler's Formula to write complex numbers in exponential form. They write numbers in rectangular form. This two-page worksheet contains seven multi-step problems.
Lesson Planet
#### Easy Worksheets: Number Sets
For Students 9th - 12th Standards
In this number sets worksheet, high schoolers solve 6 multiple choice problems. Students determine the number set that the given number belongs to such as whole, integers, rational, real, complex, etc.
Lesson Planet
#### Easy Worksheet: Properties
For Students 9th - 12th Standards
In this properties worksheet, 10 short answer problems are solved. Learners name the property illustrated such as the inverse property or associative property of multiplication.
Lesson Planet
#### Polynomials and Complex and Imaginary Numbers Review
For Students 9th - 12th
In this polynomials review worksheet, high schoolers answer 20 questions regarding polynomials, synthetic division, and complex and imaginary numbers. Students also complete a 10 question spiral review of parent graphs, systems,...
Lesson Planet
#### Test Chapter 8 Algebra II
For Students 10th - 12th
In this radical equations and expressions test, students answer 4 multiple choice and 21 short answer questions.
Lesson Planet
#### Order in the Classroom
For Teachers 1st
First graders define and identify integers, rational, irrational, real, and complex numbers. They place number cards in ascending and descending order.
Lesson Planet
#### Complex Numbers
For Students 9th - 11th
In this complex number worksheet, students simplify given equations and solve for the unknown. Students add, multiply and divide algebraic expressions. This two-page worksheet contains 23 problems.
Lesson Planet
#### Exploring Harmonic Conjugates
For Teachers 9th - 10th
High schoolers investigate harmonic conjugates using Cabri Software or the Ti Calculator to analyze harmonics. They explore different angles measurements as they move their circles around and solve problems.
EngageNY
#### Wishful Thinking—Does Linearity Hold? (Part 1)
For Teachers 11th - 12th Standards
Not all linear functions are linear transformations — show your class the difference. The first lesson plan in a unit on linear transformations and complex numbers that spans 32 segments introduces the concept of linear transformations...
5:07
Lesson Planet
#### A Brief History of Numerical Systems
For Students 8th - 12th Standards
As people and civilizations have become more complex, numbers have evolved into what they are today. Watch a video that walks viewers through the history of the development of symbols into numbers and positional notations.
Lesson Planet
#### Tens and Ones with Unifix Cubes
For Students K - 2nd
Use Unifix Cubes to make math more tangible for your young pupils! A simple activity will get learners talking and collaborating...and all about MATH! In partners, learners pick a number card (these are provided, and can be simply cut...
3:55
Lesson Planet
#### Calculating Molar Volume Using Experimental Data
For Students 9th - 12th Standards
Calculating molar volume from experimental data often means the additional challenge of complex numbers and slight errors in measurement. The 23rd video in a 30-part series offers two types of experimental data to work from and models...
5:20
Lesson Planet
#### Introduction to I and Imaginary numbers
For Students 9th - 11th
Students are always fascinated by imaginary numbers. In this video, Sal defines the imaginary unit, i, and shows when raising i to an exponent it has a cyclic nature.
Lesson Planet
#### Quiz 1: Types of Functions
For Students 9th - 12th Standards
Sometimes the best things are already done for you! Here is a six-problem quiz that has a variety of problems ranging from solving quadratic equations to interpreting a function. The piece-de-resistance is the worked out answer key in...
Lesson Planet
#### Quiz 2: Types of Functions
For Students 9th - 12th Standards
Here is a resource that provides the structure of an assessment with the convenience of a full answer key. The focus is on rational, exponential, and logarithm functions with a few questions on solving polynomials.
Lesson Planet
#### Complex Number Multiplication
For Students 10th - 12th
In this multiplication worksheet, students multiply complex numbers. This interactive one-page worksheet contains 10 problems. Answers are provided.
Lesson Planet
#### Arithmetic Complex Numbers
For Teachers 10th - 11th
Students convert quadratic functions from standard form to vertex form. In this algebra instructional activity, students solve polynomials using synthetic and long division. They derive and apply the remainder theorem and factor theorem.
Lesson Planet
#### Complex Solutions?
For Students 9th - 12th Standards
Complex numbers don't need to be so ... complex. Young mathematicians determine conditions for when quadratic equations have complex solutions. Their work should rely on the quadratic formula.
2 In 2 Collections
EngageNY
#### Polynomial, Rational, and Radical Relationships
For Students 9th - 12th Standards
This assessment pair goes way beyond simple graphing, factoring and solving polynomial equations, really forcing learners to investigate the math ideas behind the calculations. Short and to-the-point questions build on one another,...
EngageNY
#### Factoring Extended to the Complex Realm
For Students 10th - 12th Standards
A solution will work one way or another: find solutions, or use solutions to find the function. Learners use polynomial identities to factor polynomials with complex solutions. They then use solutions and the Zero Product Property to...
1 In 1 Collection
Lesson Planet
#### Unit 8 Review Packet: Polar Coordinates, Polar Graphs, and Vectors
For Teachers 10th - 12th Standards
Tying together an introductory unit on polar coordinates, graphs, and vectors is often a daunting task. So many nuanced math skills develop through these lessons that making sure an assessment hits them is difficult, to say the least....
EngageNY
#### Obstacles Resolved—A Surprising Result
For Students 10th - 12th Standards
The greater the degree, the more solutions to find! Individuals find the real solutions from a graph and use the Fundamental Theorem of Algebra to find the remaining factors.
Lesson Planet
#### Imaginary Numbers
For Teachers 11th
For this Algebra II worksheet, 11th graders explain how every real number is also a complex number. The one page worksheet contains one problem with solution.
Lesson Planet
#### Number Theory: Numbers and Geometry
For Students 9th - 12th
In this math worksheet, high schoolers explore properties of the number line, both standard and imaginary. This thorough worksheet has many problems for the students to solve, and includes an answer sheet.
7:16
Lesson Planet
#### How Do You Find Higher Powers of i?
For Teachers 10th - 11th
What is �i raised to the 45th power? This video shows you how to break up the problem into a number of �i raised to 4th power, and calculate what power is left over to calculate.
Lesson Planet
#### Complex Analysis: Rectangular Form
For Students Higher Ed
In this rectangular form instructional activity, students write numbers in rectangular form. They solve complex numbers, and find the value of a function. This two-page instructional activity contains approximately 12 multi-step problems.
Lesson Planet
#### Equations and Inequalities
For Teachers Higher Ed
Students in a college algebra class use graphs to solve inequalities. Using the coordinate graphing system, they represent the relationship between x and y intercepts. They practice solving equations with complex numbers and locate...
Lesson Planet
#### Complex Number Maze
For Students 9th - 12th Standards
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#### Complex Number Subtraction
For Students 10th - 12th
For this subtraction worksheet, students find the difference of complex numbers. This one-page worksheet contains 10 problems. Answers are provided.
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#### Complex Analysis: Polynomial Equations
For Students Higher Ed
In this polynomial equation activity, students explore real fractional powers of complex numbers. This three-page activity contains examples, explanations and approximately seven problems.
EngageNY
#### Representing Reflections with Transformations
For Teachers 11th - 12th Standards
In the 16th lesson in the series of 32 the class uses the concept of complex multiplication to build a transformation in order to reflect across a given line in the complex plane. The lesson breaks the process of reflecting across a line...
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#### Find Imaginary Solutions: Imaginary Zeros
For Students 10th - 12th Standards
The resource is the real deal. Individuals investigate the imaginary zeros of f(x) = x^2 + 1. They accomplish this task by using an interactive that shows input values x = a + bi and output values x^2 + 1 on a complex plane.
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#### Basic Complex Analysis
For Students 10th - 12th
This video gives an excellent overview of the different representations of a complex number. First, Sal reviews a pictorial representation of a complex number as an Argand diagram, then shows how to find the modulus and the argument of a...
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#### Exponential Form to Find Complex Roots
For Students 10th - 12th
Sal solves the problem x^3 = 1 for all of the real and complex roots using the exponential form of the complex number. He shows how the roots found in exponential form are the same as those in a more traditional form of a complex number...
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#### Intermediate Algebra
For Students 9th - 12th Standards
Algebra concepts are all wrapped up in one nice bow. The resource combines all the concepts typically found in Algebra I and Algebra II courses in one eBook. The topics covered begin with solving linear equations and move to linear...
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#### College Algebra
For Students 9th - Higher Ed Standards
Is there more to college algebra than this? Even though the eBook is designed for a college algebra course, there are several topics that align to Algebra II or Pre-calculus courses. Topics begin with linear equation and inequalities,...
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#### Precalculus
For Students 11th - Higher Ed Standards
Take a step beyond Algebra 2. Learners use the eBook to learn concepts from the typical Precalculus course. Content starts off with a short review of functions in general and moves on to the basic functions, finishing up with more...
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For Students 9th - 12th Standards
Looking for straightforward practice on simplifying radicals and imaginary numbers? Here are 20 problems to practice these skills and an answer key for the odd-numbered questions.
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#### Algebra and Trigonometry
For Students 10th - Higher Ed Standards
Move on into trigonometry. An informative eBook takes the content of a College Algebra course and adds more relating to trigonometry and trigonometric functions. The content organization allows pupils to build upon their learning by...
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#### Introduction to I and Imaginary numbers
For Students 9th - 11th
Students are always fascinated by imaginary numbers. In this video, Sal defines the imaginary unit, i, and shows when raising i to an exponent it has a cyclic nature.
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#### Complex Number Division
For Students 9th - 12th
In this online math activity, students practice complex number division using positive and negative integers. When complete, students submit their answers and get instant feedback regarding their accuracy.
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For Students 9th - 12th
In this online math worksheet, students practice adding positive and negative integers. When complete, students submit their answers and get instant feedback regarding their accuracy.
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#### Absolute Values
For Teachers 8th - 12th
In this absolute value worksheet, students determine the absolute value of each complex number. Students complete 10 problems.
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#### Exponents - Week 1
For Teachers 10th - 12th
In this exponent worksheet, students add, subtract, multiply and divide exponents. They solve problems containing negative exponents, fractional exponents, and polynomials. This two-page worksheet contains eight problems.
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#### The Mandelbrot Set
For Teachers 10th - 12th
Students explore the concept of Mandelbrot sets and Julia sets. In this Mandelbrot and Julia set lesson plan, students use a function integrator applet to investigate two-variable function iterations. Students use Julia set and...
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#### Imaginary Numbers
For Students 9th - 12th Standards
Scholars learn to use their imagination in math class! The tutorial explains the origin of the number i and then simplifies expressions that include imaginary numbers. The examples include i raised to different powers, giving viewers...
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#### Rationalize an Imaginary Denominator with Conjugate Method
For Students 9th - 12th Standards
Explore a procedure for rationalizing a denominator that includes imaginary terms with a video that shows how to use a conjugate when working with fractions. The narrator explains the process from start to finish with each step shown in...
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#### Reptile and Amphibian Anatomy
For Teachers 4th - 12th
Learners identify and interpret the various differences between reptiles and amphibians. Then they draw an amphibian and reptile and correctly label their body parts. Students also invent new reptiles and amphibians, sketch how they...
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#### Basic Complex Analysis
For Students 10th - 12th
This video gives an excellent overview of the different representations of a complex number. First, Sal reviews a pictorial representation of a complex number as an Argand diagram, then shows how to find the modulus and the argument of a...
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#### Exponential Form to Find Complex Roots
For Students 10th - 12th
Sal solves the problem x^3 = 1 for all of the real and complex roots using the exponential form of the complex number. He shows how the roots found in exponential form are the same as those in a more traditional form of a complex number...
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#### Irrational and Imaginary Root Theorems
For Students 9th - 11th
In this irrational and imaginary root theorem learning exercise, learners identify the number of complex zeros for a given function. They write a polynomial function of leas degree with integral coefficients. This four-page learning...
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#### Plots of Polar Coordinates: Submarine Sonar
For Students 11th - Higher Ed Standards
Find the location of enemy submarines with a sonar display that doubles as a polar coordinate system. Pupils find polar coordinates that would be the same location of plotted submarines. They then determine multiple polar coordinates...
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#### Roots, Multiplicities, and Factoring Polynomials
For Students 10th - 12th
In this polynomials worksheet, students find zeros, state multiplicities, and factor twenty-two polynomials. Students then find a polynomials that satisfies the stated conditions in eighteen problems, Finally, students factor...
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#### Radicals, Complex and Absolute Value Numbers
For Teachers 9th - 11th
Students solve problems with exponents, radicals, absolute value and complex numbers. In this algebra lesson, students use properties of exponential functions to solve equations and word problems.
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For Teachers 9th - 11th
In this algebra lesson, students solve problems with radicals and complex numbers. In this algebra lesson, students relate exponential functions to the real world as they discuss growth and decay.
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#### Solving Quadratic Equations by Completing the Square
For Students 9th - 12th
In this solving quadratic equations activity, students complete the square to tell the possible answers for 18 equations. 4 answers involve the square root of -1 (i).
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#### Mathematics B: High School Exam
For Students 11th - 12th
In this mathematics instructional activity, learners solve problems about numerous high school topics including trigonometry, algebra, and pre-calculus. This instructional activity contains, but is not limited to, radicals, inverse...
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#### Chapter 10 - Objective 3.1 Quadratic Formula
For Students 11th - 12th
In this quadratic formula instructional activity, students solve quadratic equations. They use the discriminant to determine the solution or solutions to the problem. This one-page instructional activity contains
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#### Quadratic Formula with Imaginary Numbers
For Students 8th - 10th
In this quadratic equation learning exercise, students use the quadratic formula to solve 6 fill in the blank problems that involve imaginary numbers.
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#### Final Spring Semester Review
For Students 9th - 12th
In this advanced algebra semester review worksheet, students answer 63 questions spiraling a review of topics including combinations, systems of equations, absolute value, parent graphs, conics, complex numbers, and binomial theorem.
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#### Introduction to Polar Coordinates - Concept
For Students 9th - 12th Standards
Learning polar coordinates does not require visiting the North Pole, though explaining igloos is much easier using polar coordinates. The lesson begins with a video explaining how to find coordinates on a spherical plane and how to...
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#### Polynomial Divisions
For Teachers 8th - 10th
Young scholars factor polynomials and use long division t solve problems. In this algebra lesson, students find the zeros of polynomials by synthetic and long division. They perform operation using complex numbers. | {"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": 0.8036606311798096, "perplexity": 2724.3242566429417}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1593655924908.55/warc/CC-MAIN-20200711064158-20200711094158-00561.warc.gz"} |
http://mathhelpforum.com/calculus/49366-fractional-exponents-functions.html | # Math Help - Fractional Exponents, functions
1. ## Fractional Exponents, functions
A bacteria culture starts with 500 bacteria and doubles in size every 30 minutes. Graph the population function and estimate the time for the population to reach 20,000.
So far I did 20,000/500 = 2^(x/30)
which is 40= 2^(x/30)
now how do i get rid of the fractional exponent (x/30)??
-----------------------------
Also if g(x) = 4 + x + e^x
find g^-1 (5)
2. Originally Posted by rafaeli
A bacteria culture starts with 500 bacteria and doubles in size every 30 minutes. Graph the population function and estimate the time for the population to reach 20,000.
So far I did 20,000/500 = 2^(x/30)
which is 40= 2^(x/30)
now how do i get rid of the fractional exponent (x/30)??
-----------------------------
Also if g(x) = 4 + x + e^x
find g^-1 (5)
Are you familiar with logarithms? Starting with $40=2^{\frac{x}{30}}$, now take the natural log of both sides and you get $\ln(40)=\ln{ \left( 2^{\frac{x}{30}} \right)}$
Now to get rid of that exponent, use a rule that says $\ln(a^n)=n\ln(a)$ Thus $\ln(40)=\frac{x}{30} \ln(2)$.
Are you with me so far?
3. Thank you. I got that part. Took me a while to understand it but I finally got it.
Now i want to know like how many bacteria are there after t hours? | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 4, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9869737029075623, "perplexity": 676.4388352506039}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-23/segments/1405997888972.38/warc/CC-MAIN-20140722025808-00052-ip-10-33-131-23.ec2.internal.warc.gz"} |
https://arxiv.org/abs/1302.0837 | astro-ph.HE
# Title:Binary population synthesis and SNIa rates
Abstract: Despite the significance of type Ia supernovae (SNeIa) in many fields in astrophysics, SNeIa lack a theoretical explanation. We investigate the potential contribution to the SNeIa rate from the most common progenitor channels using the binary population synthesis (BPS) code SeBa. Using SeBa, we aim constrain binary processes such as the common envelope phase and the efficiency of mass retention of white dwarf accretion. We find that the simulated rates are not sufficient to explain the observed rates. Further, we find that the mass retention efficiency of white dwarf accretion significantly influences the rates, but does not explain all the differences between simulated rates from different BPS codes.
Comments: 4 pages, 5 figures, Proceedings of the conference: "370 Years of Astronomy in Utrecht". arXiv admin note: text overlap with arXiv:1302.0495 Subjects: High Energy Astrophysical Phenomena (astro-ph.HE); Solar and Stellar Astrophysics (astro-ph.SR) Cite as: arXiv:1302.0837 [astro-ph.HE] (or arXiv:1302.0837v1 [astro-ph.HE] for this version)
## Submission history
From: Silvia Toonen [view email]
[v1] Sun, 3 Feb 2013 14:17:03 UTC (84 KB) | {"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": 0.9139888882637024, "perplexity": 6440.798821515098}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-26/segments/1560627999817.30/warc/CC-MAIN-20190625092324-20190625114324-00516.warc.gz"} |
https://readchemistry.com/2019/05/29/bond-energy-definition-illustration-solved-problems/ | # Bond energy (definition, Illustration, solved Problems)
#### Bond energy
When a bond between two atoms is formed, there is a release of energy. The same amount of energy is absorbed when the bond is broken.
The bond energy is defined as: the average amount of energy required to break all bonds of a particular type in one mole of the substance.
Thus the bond energy of H – H bond is the energy required to break all the bonds in one mole of the gas.
The bond energy is expressed in kcal mol–1 or kJ mol–1.
For example, the bond energy of H – H bond is 433 kJ mol–1or 103.58 kcal mol–1.
The bond energies of some common bonds are listed below:
#### Bond Energy is a Measure of Strength of the Bond
In other words, bond energy is the force with which the atoms are bonded together. It depends upon :
(1) Size of the atom
(2) Electronegativity
(3) Bond length
A knowledge of bond enthalpy is useful for calculating heats of reaction for gaseous reactions for which no thermal data is available and which involve substances having covalent bonds.
Suppose we desire to determine the bond energy of C–H bond in methane. For this purpose we need to know the enthalpy change for the reaction:
C(g) + 4H(g) → CH4(g)
This is obtained by combining the heat of formation of methane from C(s) + H2(g) with the heat of sublimation of carbon i.e., C(s) → C(g) and the heat of dissociation of hydrogen into atoms i.e., H2(g) → 2H(g), which have been determined by spectroscopic methods. The value so obtained is 398 kcal mol–1 (or 1663.64 kJ mol–1). This represents the bond energy of four C–H bonds. Since all the bonds in methane are identical, the bond energy of C–H bond is 398/4 = 99.5 kcal mol–1.
In a similar manner the bond energies of other types of bonds have been calculated. When a bond is broken, the bond energy is positive because heat is absorbed. It is written with a minus sign when a bond is formed and heat is evolved.
The calculation of heat of reaction with the help of bond energies is illustrated in the following examples.
#### Solved Problem
Problem (1): Given that energies for H–H, O=O and O–H bonds are 104, 118 and 111 kcal mol–1 respectively, calculate the heat of the reaction:
H2(g) + ½ O2(g) → H2O(g)
Solution:
In this reaction, two O–H bonds are formed and one H–H bond is broken. Therefore we can write for ΔH
The heat of the given reaction is – 59.0 kcal mol–1
Problem (2): Calculate the bond energy of HCl, given that H–H bond energy is 433 kJ mol–1, Cl – Cl bond energy is 242 kJ mol–1and ΔHf for HCl is – 91 kJ mol–1.
Solution:
Reference: Essentials of Physical Chemistry /Arun Bahl, B.S Bahl and G.D. Tuli / multicolour edition. | {"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": 0.8395088911056519, "perplexity": 1964.6771534037812}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1656104248623.69/warc/CC-MAIN-20220703164826-20220703194826-00666.warc.gz"} |
https://journal-me.com/en/archive/vol23-2020-iss3-paper2/ | # Determination of the Equi-stress Hole Shape for a Stringer Plate Weakened by a Surface Crack
DOI https://doi.org/10.15407/pmach2020.03.016 Journal Journal of Mechanical Engineering Publisher A. Podgorny Institute for Mechanical Engineering Problems National Academy of Science of Ukraine ISSN 0131-2928 (Print), 2411-0779 (Online) Issue Vol. 23, no. 3, 2020 (September) Pages 16-26 Cited by J. of Mech. Eng., 2020, vol. 23, no. 3, pp. 16-26
Author
Minavar V. Mir-Salim-zade, Institute of Mathematics and Mechanics of the NAS of Azerbaijan (9, Vahabzade St., Baku, AZ1141, Azerbaijan), e-mail: minavar.mirsalimzade@imm.az, ORCID: 0000-0003-4237-0352
Abstract
On the basis of the principle of equal stress, a solution is given to the inverse problem of determining the optimal shape of the hole contour for a plate weakened by a surface rectilinear crack. The plate is reinforced by a regular system of elastic stiffeners (stringers). The crack originates from the hole contour perpendicular to the riveted stringers. The plate is subjected to uniform tension at infinity along the stiffeners. The plate under consideration is assumed to be either elastic or elastic-plastic. The criterion that determines the optimal shape of the hole is the condition that there is no stress concentration on the hole surface and the requirement that the stress intensity factor in the vicinity of the crack tip be equal to zero. In the case of an elastic-plastic plate, the plastic region at the moment of nucleation should encompass the entire hole contour at once, without deep penetration. The problem posed is to determine the hole shape at which the tangential normal stress acting on the contour is constant, and the stress intensity factor in the vicinity of the crack tip is zero, as well as to determine the magnitudes of the concentrated forces that replace both the action of the stringers and the stress-strain state of the reinforced plate. The method of a small parameter, the theory of analytic functions, and the method for direct solution of singular integral equations were used. The problem posed is reduced to the problem of finding a conditional extremum. The method of Lagrange indefinite multipliers was used. The obtained solution to the inverse problem allows increasing the bearing capacity of the stringer plate.
Keywords: plate, stringers, equal strength hole, crack.
References
1. Cherepanov, G. P. (1963). Obratnaya uprugoplasticheskaya zadacha v usloviyakh ploskoy deformatsii [Inverse elastic-plastic problem under plane deformation]. Izv. AN SSSR. Mekhanika i mashinostroyeniye News of the USSR Academy of Sciences. Mechanics and mechanical engineering, no. 2. pp. 57–60 (in Russian).
2. Cherepanov, G. P. (1974). Inverse problems of the plane theory of elasticity. Journal of Applied Mathematics and Mechanics, vol. 38, iss. 6, pp. 915–931. https://doi.org/10.1016/0021-8928(75)90085-4.
3. Mirsalimov, V. M. (1974). On the optimum shape of apertures for a perforated plate subject to bending. Journal of Applied Mechanics and Technical Physics, vol. 15, pp. 842–845. https://doi.org/10.1007/BF00864606.
4. Mirsalimov, V. M. (1975). Converse problem of elasticity theory for an anisotropic medium. Journal of Applied Mechanics and Technical Physics, vol. 16, pp. 645–648. https://doi.org/10.1007/BF00858311.
5. Vigdergauz, S. B. (1976). Integral equations of the inverse problem of the theory of elasticity. Journal of Applied Mathematics and Mechanics, vol. 40, iss. 3, pp. 518–522. https://doi.org/10.1016/0021-8928(76)90046-0.
6. Vigdergauz, S. B. (1977). On a case of the inverse problem of two-dimensional theory of elasticity. Journal of Applied Mathematics and Mechanics, vol. 41, iss. 5, pp. 927–933. https://doi.org/10.1016/0021-8928(77)90176-9.
7. Mirsalimov, V. M. (1977). Inverse doubly periodic problem of thermoelasticity. Mechanics of Solids, vol. 12, iss. 4, pp. 147–154.
8. Mirsalimov, V. M. (1979). A working of uniform strength in the solid rock. Soviet Mining, vol. 15, pp 327–330. https://doi.org/10.1007/BF02499529.
9. Banichuk, N. V. (1980). Optimizatsiya form uprugikh tel [Shape optimization for elastic solids]. Moscow: Nauka, 255 p. (in Russian).
10. Ostrosablin, N. I. (1981). Equal-strength hole in a plate in an inhomogeneous stress state. Journal of Applied Mechanics and Technical Physics, vol. 22, pp. 271–277. https://doi.org/10.1007/BF00907959.
11. Bondar, V. D. (1996). A full-strength orifice under conditions of geometric nonlinearity Journal of Applied Mechanics and Technical Physics, vol. 37, pp. 898–904. https://doi.org/10.1007/BF02369270.
12. Savruk, M. P. & Kravets, V. S. (2002). Application of the method of singular integral equations to the determination of the contours of equistrong holes in plates. Materials Science. vol. 38, pp. 34–46. https://doi.org/10.1023/A:1020116613794.
13. Mir-Salim-zada, M. V. (2007). Obratnaya uprugoplasticheskaya zadacha dlya klepanoy perforirovannoy plastiny [Inverse elastoplastic problem for riveted perforated plate]. Sbornik statey “Sovremennye problemy prochnosti, plastichnosti i ustoychivosti” Collected papers “Modern problems of strength, plasticity and stability”. Tver: Tver State Technical University, pp. 238–246 (in Russian).
14. Bantsuri, R. & Mzhavanadze, Sh. (2007). The mixed problem of the theory of elasticity for a rectangle weakened by unknown equi-strong holes. Proceedings of A. Razmadze Mathematical Institute, vol. 145, pp. 23–34.
15. Mir-Salim-zada, M. V. (2007). Opredeleniye formy ravnoprochnogo otverstiya v izotropnoy srede, usilennoy regulyarnoy sistemoy stringerov [Determination of equistrong hole shape in isotropic medium, reinforced by regular system of stringers]. Materialy, tehnologii, instrumenty Materials, technologies, tools, no. 12 (4), pp. 10–14 (in Russian).
16. Vigdergauz, S. (2012). Stress-smoothing holes in an elastic plate: From the square lattice to the checkerboard. Mathematics and Mechanics of Solids, vol. 17, iss. 3, pp. 289–299. https://doi.org/10.1177/1081286511411571.
17. Сherepanov, G. P. (2015). Optimum shapes of elastic bodies: Equistrong wings of aircraft and equistrong underground tunnels. Physical Mesomechanics, vol. 18, pp. 391–401. https://doi.org/10.1134/S1029959915040116.
18. Vigdergauz, S. (2018). Simply and doubly periodic arrangements of the equi-stress holes in a perforated elastic plane: The single-layer potential approach. Mathematics and Mechanics of Solids, vol. 23, iss. 5, pp. 805–819. https://doi.org/10.1177/1081286517691807.
19. Zeng, X., Lu, A. & Wang, S. (2020). Shape optimization of two equal holes in an infinite elastic plate. Mechanics Based Design of Structures and Machines, vol. 48, iss. 2, pp. 133–145. https://doi.org/10.1080/15397734.2019.1620111.
20. Kalantarly, N. M. (2017). Ravnoprochnaya forma otverstiya dlya tormozheniya rosta treshchiny prodolnogo sdviga [Equal strength hole to inhibit longitudinal shear crack growth]. Problemy Mashinostroyeniya – Journal of Mechanical Engineering, vol. 20, no. 4, pp. 31–37 (in Russian). https://doi.org/10.15407/pmach2017.04.031.
21. Mirsalimov, V. M. (2019). Maximum strength of opening in crack-weakened rock mass. Journal of Mining Science, vol. 55, pp. 9–17. https://doi.org/10.1134/S1062739119015228.
22. Mirsalimov, V. M. (2019). Inverse problem of elasticity for a plate weakened by hole and cracks. Mathematical Problems in Engineering, vol. 2019, Article ID 4931489, 11 pages. https://doi.org/10.1155/2019/4931489.
23. Mir-Salim-zade, M. V. (2019). Minimization of the stressed state of a stringer plate with a hole and rectilinear cracks. Journal of Mechanical Engineering, vol. 22, no. 2, pp. 59–69. https://doi.org/10.15407/pmach2019.02.059.
24. Mirsalimov, V. M. (2020). Minimizing the stressed state of a plate with a hole and cracks. Engineering Optimization, vol. 52, iss. 2, pp. 288–302. https://doi.org/10.1080/0305215X.2019.1584619.
25. Mir-Salim-zada, M. V. (2020). Ravnoprochnaya forma otverstiya dlya stringernoy plastiny s treshchinami [An equi-stress hole for a stringer plate with cracks]. Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mekhanika – Tomsk State University Journal of Mathematics and Mechanics, iss. 64. pp. 121–135. https://doi.org/10.17223/19988621/64/9.
26. Ishlinsky, A. Yu. & Ivlev, D. D. (2001). Matematicheskaya teoriya plastichnosti [Mathematical theory of plasticity]. Moscow: Fizmatlit, 704 p. (in Russian).
27. Muskhelishvili, N. I. (1977). Some basic problems of mathematical theory of elasticity. Dordrecht: Springer, 732 p. https://doi.org/10.1007/978-94-017-3034-1.
28. Kalandiya, A. I. (1973). Matematicheskiye metody dvumernoy uprugosti [Mathematical methods of two-dimensional elasticity]. Moscow: Nauka, 304 p. (in Russian).
29. Panasyuk, V. V., Savruk, M. P., & Datsyshin, A. P. (1976). Raspredeleniye napryazheniy okolo treshchin v plastinakh i obolochkakh [Stress distribution around cracks in plates and shells]. Kiyev: Naukova Dumka, 443 p. (in Russian).
30. Mirsalimov, V. M. (1987). Neodnomernyye uprugoplasticheskiye zadachi [Non-one-dimensional elastoplastic problems]. Moscow: Nauka, 255 p. (in Russian).
31. Mirsalimov, V. M. (1986). Some problems of structural arrest of cracks. Soviet materials science, vol. 22, pp. 81–85. https://doi.org/10.1007/BF00720871.
Received 25 April 2020
Published 30 September 2020 | {"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": 0.8800588846206665, "perplexity": 4503.278860969502}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-04/segments/1610703530835.37/warc/CC-MAIN-20210122144404-20210122174404-00585.warc.gz"} |
https://ai.stackexchange.com/questions/2817/why-cant-i-reproduce-the-experiments-in-the-original-paper-that-introduced-the | # Why can't I reproduce the experiments in the original paper that introduced the Firefly Algorithm?
I have been trying to reproduce the experiments done in the original: Firefly Algorithm for multimodal optimization (2010) by Xin-She Yang, but so far unsuccessfully. For the moment being, I'm okay if anyone points me in the right direction.
I wrote the algorithm as specified in the paper in C++ programming language (I also downloaded several other implementations from the internet for comparison purposes) and used the very same parameters as specified in the paper (a random steep of 0.2, an initial light intensity of 1.0 and a light decay coefficient of 1.0, a population size of 40). I used the two bright update equations given and for De Jung test function (as for example) a number of dimensions of 256 in a search domain in [-5.12, 5.12] as referred to in common optimization literature and in the paper.
In the paper, the algorithm converges very quickly, as can be expected, since this is a very simple test function. However, neither my implementation nor any code I have downloaded converges with that parameters.
My final questions are:
1. Am I doing something wrong with the experimental methodology or am I using the wrong parameter settings (may be something different than the original paper)?
2. Do anyone knows where can I find a code sample of the Firefly Algorithm that I can use to reproduce the experiments of the mentioned paper?
Please, notice that there may be a lot of variations of this algorithm that can produce better results, but right now I'm only interested in reproducing the experiments of the so-called paper.
I wrote some python code to reproduce this paper's purported results. My code very efficiently optimizes simple smooth functions like bowls, but does not come close to reproducing the paper's claimed results on more complex functions, including with the parameters the authors report. I think that, since both @Jairo and I were unable to reproduce the results from the information in the paper, independently, it is likely that something is wrong with the paper.
It may be possible to reproduce the paper's claimed behaviors using a library like py_swarm, however the paper is using a Firefly Algorithm (already a rarer form of a PSO), and is using a home-brew variant of that algorithm, so my guess is that rolling your own is required, as we both did.
Additionally, I find the paper's claims fairly unlikely. For example, in section 4.1, they claim to converge on the global minimum of a function with many local minima in just 10 iterations. It seems to me like most of the time the fireflies will quickly converge on the bottom of one of the gullies in this function, and get stuck there. This is also what I observe in my replications. I suspect the authors may have cherry-picked their results from the best runs without reporting this, or have omitted some key detail from the paper.
Here is my replication code, in case someone else wants to try to reproduce this:
from math import sin, pi, exp, sqrt
from random import random
from copy import deepcopy
def michalewiz_objective(x):
result = 0
for i, x_i in enumerate(x):
result -= sin(x_i)*(sin(i*(x_i**2)/pi))**20
return -result
def bowl_objective(x):
return -sum([x_i**2 for x_i in x])
pop_size = 40
max_generations = 10
alpha = 0.2
gamma = 1
beta_0 = 1
d = 2
I = michalewiz_objective
#I = bowl_objective
def move(firefly, other_firefly):
radius = sqrt(sum([(firefly[i] - other_firefly[i])**2 for i in range(0, len(firefly))]))
for i, value in enumerate(firefly):
firefly[i] += alpha * (random() - 0.5)
# Using 4*random() to match Figure 3's apparent spread.
fireflies = [[4*random() for i in range(0, d)] for j in range(0, pop_size)]
for generation in range(0, max_generations):
new_fireflies = [deepcopy(firefly) for firefly in fireflies]
for index, firefly in enumerate(fireflies):
for other_firefly in fireflies:
if I(other_firefly) > I(firefly):
move(new_fireflies[index], other_firefly)
fireflies = new_fireflies
best = max([I(f) for f in fireflies])
mean = [sum([f[0] for f in fireflies]), sum([f[1] for f in fireflies])]
print(best)
print(mean) | {"extraction_info": {"found_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": 0.8336752653121948, "perplexity": 1017.0194638393417}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1620243988927.95/warc/CC-MAIN-20210508211857-20210509001857-00309.warc.gz"} |
http://www.science.gov/topicpages/h/hydraulic+brakes.html | #### Sample records for hydraulic brakes
1. Combined hydraulic and regenerative braking system
SciTech Connect
Mericle, G.E.; Venkataperumal, R.R.
1981-06-02
A combined hydraulic and regenerative braking system and method is disclosed for an electric vehicle. The braking system being responsive to the applied hydraulic pressure in a brake line to control the braking of the vehicle to be completely hydraulic up to a first level of brake line pressure, to be partially hydraulic at a constant braking force and partially regenerative at a linearly increasing braking force from the first level of applied brake line pressure to a higher second level of brake line pressure, to be partially hydraulic at a linearly increasing braking force and partially regenerative at a linearly decreasing braking force from the second level of applied line pressure to a third and higher level of applied line pressure, and to be completely hydraulic at a linearly increasing braking force from the third level to all higher applied levels of line pressure.
2. Combined hydraulic and regenerative braking system
DOEpatents
Venkataperumal, Rama R. (Troy, MI); Mericle, Gerald E. (Mount Clemens, MI)
1981-06-02
A combined hydraulic and regenerative braking system and method for an electric vehicle, with the braking system being responsive to the applied hydraulic pressure in a brake line to control the braking of the vehicle to be completely hydraulic up to a first level of brake line pressure, to be partially hydraulic at a constant braking force and partially regenerative at a linearly increasing braking force from the first level of applied brake line pressure to a higher second level of brake line pressure, to be partially hydraulic at a linearly increasing braking force and partially regenerative at a linearly decreasing braking force from the second level of applied line pressure to a third and higher level of applied line pressure, and to be completely hydraulic at a linearly increasing braking force from the third level to all higher applied levels of line pressure.
3. 49 CFR 570.55 - Hydraulic brake system.
Code of Federal Regulations, 2010 CFR
2010-10-01
...2010-10-01 2010-10-01 false Hydraulic brake system. 570.55 Section...Than 10,000 Pounds § 570.55 Hydraulic brake system. The following requirements apply to vehicles with hydraulic brake systems. (a) Brake...
4. 49 CFR 570.57 - Air brake system and air-over-hydraulic brake subsystem.
Code of Federal Regulations, 2010 CFR
2010-10-01
...false Air brake system and air-over-hydraulic brake subsystem. 570.57 Section...57 Air brake system and air-over-hydraulic brake subsystem. The following requirements...vehicles with air brake and air-over-hydraulic brake systems. Trailer(s)...
5. 49 CFR 570.55 - Hydraulic brake system.
Code of Federal Regulations, 2011 CFR
2011-10-01
... 49 Transportation 6 2011-10-01 2011-10-01 false Hydraulic brake system. 570.55 Section 570.55... 10,000 Pounds § 570.55 Hydraulic brake system. The following requirements apply to vehicles with hydraulic brake systems. (a) Brake system failure indicator. The hydraulic brake system failure...
6. 49 CFR 570.55 - Hydraulic brake system.
Code of Federal Regulations, 2013 CFR
2013-10-01
... 49 Transportation 6 2013-10-01 2013-10-01 false Hydraulic brake system. 570.55 Section 570.55... 10,000 Pounds § 570.55 Hydraulic brake system. The following requirements apply to vehicles with hydraulic brake systems. (a) Brake system failure indicator. The hydraulic brake system failure...
7. 49 CFR 570.55 - Hydraulic brake system.
Code of Federal Regulations, 2014 CFR
2014-10-01
... 49 Transportation 6 2014-10-01 2014-10-01 false Hydraulic brake system. 570.55 Section 570.55... 10,000 Pounds § 570.55 Hydraulic brake system. The following requirements apply to vehicles with hydraulic brake systems. (a) Brake system failure indicator. The hydraulic brake system failure...
8. 49 CFR 570.55 - Hydraulic brake system.
Code of Federal Regulations, 2012 CFR
2012-10-01
... 49 Transportation 6 2012-10-01 2012-10-01 false Hydraulic brake system. 570.55 Section 570.55... 10,000 Pounds § 570.55 Hydraulic brake system. The following requirements apply to vehicles with hydraulic brake systems. (a) Brake system failure indicator. The hydraulic brake system failure...
9. 49 CFR 570.55 - Hydraulic brake system.
Code of Federal Regulations, 2010 CFR
2010-10-01
... 49 Transportation 6 2010-10-01 2010-10-01 false Hydraulic brake system. 570.55 Section 570.55... 10,000 Pounds § 570.55 Hydraulic brake system. The following requirements apply to vehicles with hydraulic brake systems. (a) Brake system failure indicator. The hydraulic brake system failure...
10. 49 CFR 570.57 - Air brake system and air-over-hydraulic brake subsystem.
Code of Federal Regulations, 2010 CFR
2010-10-01
... 49 Transportation 6 2010-10-01 2010-10-01 false Air brake system and air-over-hydraulic brake... STANDARDS Vehicles With GVWR of More Than 10,000 Pounds § 570.57 Air brake system and air-over-hydraulic brake subsystem. The following requirements apply to vehicles with air brake and...
11. Aalborg Universitet Disturbance Control of the Hydraulic Brake in a Wind Turbine
E-print Network
Yang, Zhenyu
Aalborg Universitet Disturbance Control of the Hydraulic Brake in a Wind Turbine Jepsen, Frank Brake in a Wind Turbine. In Energy Conference and Exhibition (EnergyCon), 2010 IEEE International . (pp from vbn.aau.dk on: juli 07, 2015 #12;Disturbance Control of the Hydraulic Brake in a Wind Turbine
12. 49 CFR 571.105 - Standard No. 105; Hydraulic and electric brake systems.
Code of Federal Regulations, 2012 CFR
2012-10-01
... 49 Transportation 6 2012-10-01 2012-10-01 false Standard No. 105; Hydraulic and electric brake systems. 571.105 Section 571.105 Transportation Other Regulations Relating to Transportation (Continued) NATIONAL HIGHWAY TRAFFIC SAFETY ADMINISTRATION, DEPARTMENT OF TRANSPORTATION FEDERAL MOTOR VEHICLE SAFETY STANDARDS Federal Motor Vehicle...
13. 49 CFR 571.105 - Standard No. 105; Hydraulic and electric brake systems.
Code of Federal Regulations, 2013 CFR
2013-10-01
... word, words or abbreviation, in accordance with the requirements of Standard No. 101 (49 CFR 571.101... of brake fluid as specified in 49 CFR 571.116, e.g., “DOT 3”). The lettering shall be— (a... 49 Transportation 6 2013-10-01 2013-10-01 false Standard No. 105; Hydraulic and electric...
14. 49 CFR 571.106 - Standard No. 106; Brake hoses.
Code of Federal Regulations, 2010 CFR
2010-10-01
...trailers, and motorcycles, and to hydraulic, air, and vacuum brake hose, brake...metal tubing. S5. Requirements—hydraulic brake hose, brake hose assemblies... S5.1 Construction. (a) Each hydraulic brake hose assembly shall have...
15. Automotive Brake Systems.
ERIC Educational Resources Information Center
Marine Corps Inst., Washington, DC.
This correspondence course, orginally developed for the Marine Corps, is designed to provide mechanics with an understanding of the basic operations of automotive brake systems on military vehicles. The course contains four study units covering hydraulic brakes, air brakes, power brakes, and auxiliary brake systems. A troubleshooting guide for…
16. 49 CFR 571.105 - Standard No. 105; Hydraulic and electric brake systems.
Code of Federal Regulations, 2011 CFR
2011-10-01
... Variable proportioning brake system means a system that automatically adjusts the...vehicle static axle loading and/or dynamic weight transfer between axles...Requirements. S5.1Service brake systems. Each vehicle must be...
17. 49 CFR 571.105 - Standard No. 105; Hydraulic and electric brake systems.
Code of Federal Regulations, 2012 CFR
2012-10-01
... Variable proportioning brake system means a system that automatically adjusts the...vehicle static axle loading and/or dynamic weight transfer between axles...Requirements. S5.1Service brake systems. Each vehicle must be...
18. 49 CFR 571.105 - Standard No. 105; Hydraulic and electric brake systems.
Code of Federal Regulations, 2010 CFR
2010-10-01
... Variable proportioning brake system means a system that automatically adjusts the...vehicle static axle loading and/or dynamic weight transfer between axles...Requirements. S5.1Service brake systems. Each vehicle must be...
19. 49 CFR 571.105 - Standard No. 105; Hydraulic and electric brake systems.
Code of Federal Regulations, 2013 CFR
2013-10-01
... Variable proportioning brake system means a system that automatically adjusts the...vehicle static axle loading and/or dynamic weight transfer between axles...Requirements. S5.1Service brake systems. Each vehicle must be...
20. 49 CFR 571.105 - Standard No. 105; Hydraulic and electric brake systems.
Code of Federal Regulations, 2014 CFR
2014-10-01
... Variable proportioning brake system means a system that automatically adjusts the...vehicle static axle loading and/or dynamic weight transfer between axles...Requirements. S5.1Service brake systems. Each vehicle must be...
1. 76 FR 7623 - Parts and Accessories Necessary for Safe Operation; Brakes; Application for Exemption From...
Federal Register 2010, 2011, 2012, 2013, 2014
2011-02-10
...self-contained, permanently closed hydraulic brake system'' [Emphasis added...FMCSRs to allow the use of automatic hydraulic inertia brake systems (surge brakes...self-contained, permanently closed hydraulic brake system for trailers that...
2. 49 CFR 571.105 - Standard No. 105; Hydraulic and electric brake systems.
Code of Federal Regulations, 2014 CFR
2014-10-01
... dynamic weight transfer between axles during deceleration. Wheel lockup means 100 percent wheel slip. S5... word, words or abbreviation, in accordance with the requirements of Standard No. 101 (49 CFR 571.101... of brake fluid as specified in 49 CFR 571.116, e.g., “DOT 3”). The lettering shall be—...
3. 14 CFR 25.735 - Brakes and braking systems.
Code of Federal Regulations, 2011 CFR
2011-01-01
... (1) If any electrical, pneumatic, hydraulic, or mechanical...of each wheel, brake, and tire assembly must be determined...testing that the wheel, brake and tire assembly is capable of absorbing...of each wheel, brake, and tire assembly must be...
4. 14 CFR 25.735 - Brakes and braking systems.
Code of Federal Regulations, 2013 CFR
2013-01-01
... (1) If any electrical, pneumatic, hydraulic, or mechanical...of each wheel, brake, and tire assembly must be determined...testing that the wheel, brake and tire assembly is capable of absorbing...of each wheel, brake, and tire assembly must be...
5. 14 CFR 25.735 - Brakes and braking systems.
Code of Federal Regulations, 2012 CFR
2012-01-01
... (1) If any electrical, pneumatic, hydraulic, or mechanical...of each wheel, brake, and tire assembly must be determined...testing that the wheel, brake and tire assembly is capable of absorbing...of each wheel, brake, and tire assembly must be...
6. 14 CFR 25.735 - Brakes and braking systems.
Code of Federal Regulations, 2014 CFR
2014-01-01
... (1) If any electrical, pneumatic, hydraulic, or mechanical...of each wheel, brake, and tire assembly must be determined...testing that the wheel, brake and tire assembly is capable of absorbing...of each wheel, brake, and tire assembly must be...
7. Brakes Specialist. Teacher Edition. Automotive Service Series.
ERIC Educational Resources Information Center
Oklahoma State Dept. of Vocational and Technical Education, Stillwater. Curriculum and Instructional Materials Center.
This document contains teacher's materials for a course on becoming an automotive brakes specialist, based on the National Institute of Automotive Service Excellence task lists. The course consists of three instructional units: service brake hydraulic system and wheel bearings, service drum brakes, and service disc brakes. Depending on the…
8. Hydraulics.
ERIC Educational Resources Information Center
Decker, Robert L.; Kirby, Klane
This curriculum guide contains a course in hydraulics to train entry-level workers for automotive mechanics and other fields that utilize hydraulics. The module contains 14 instructional units that cover the following topics: (1) introduction to hydraulics; (2) fundamentals of hydraulics; (3) reservoirs; (4) lines, fittings, and couplers; (5)…
9. Diesel Technology: Brakes. Teacher Edition [and] Student Edition.
ERIC Educational Resources Information Center
Hilley, Robert; Scarberry, Terry; Kellum, Mary
This document contains teacher and student materials for a course on brakes in the diesel technology curriculum. The course consists of 12 units organized in three sections. The three units of the introductory section cover: (1) brakes; (2) wheel bearings and seals; and (3) antilock brake systems. The second section, Hydraulic Brakes, contains the…
10. Hydraulics.
ERIC Educational Resources Information Center
Engelbrecht, Nancy; And Others
These instructional materials provide an orientation to hydraulics for use at the postsecondary level. The first of 12 sections presents an introduction to hydraulics, including discussion of principles of liquids, definitions, liquid flow, the two types of hydraulic fluids, pressure gauges, and strainers and filters. The second section identifies…
11. 49 CFR 571.121 - Standard No. 121; Air brake systems.
Code of Federal Regulations, 2013 CFR
2013-10-01
... compressed air or vacuum only to assist the driver in applying muscular force to hydraulic or mechanical components. Air-over-hydraulic brake subsystem means a subsystem of the air brake system that uses compressed...-type failure, in any other brake system, of a part designed to contain compressed air or brake...
12. 78 FR 21189 - Agency Requests for Approval of a New Information Collection: Motor Vehicle Brake Fluids
Federal Register 2010, 2011, 2012, 2013, 2014
2013-04-09
...brake fluids as well as packagers of hydraulic system mineral oils. The information...requirements for motor vehicle brake fluids and hydraulic system mineral oils. Section 5.2...brake fluids as well as packagers of hydraulic system mineral oils. The...
13. Hydraulics.
ERIC Educational Resources Information Center
Decker, Robert L.
Designed for use in courses where students are expected to become proficient in the area of hydraulics, including diesel engine mechanic programs, this curriculum guide is comprised of fourteen units of instruction. Unit titles include (1) Introduction, (2) Fundamentals of Hydraulics, (3) Reservoirs, (4) Lines, Fittings, and Couplers, (5) Seals,…
14. Electric vehicle regenerative antiskid braking and traction control system
DOEpatents
Cikanek, S.R.
1995-09-12
An antiskid braking and traction control system for an electric or hybrid vehicle having a regenerative braking system operatively connected to an electric traction motor, and a separate hydraulic braking system includes one or more sensors for monitoring present vehicle parameters and a processor, responsive to the sensors, for calculating vehicle parameters defining the vehicle behavior not directly measurable by the sensors and determining if regenerative antiskid braking control, requiring hydraulic braking control, or requiring traction control are required. The processor then employs a control strategy based on the determined vehicle state and provides command signals to a motor controller to control the operation of the electric traction motor and to a brake controller to control fluid pressure applied at each vehicle wheel to provide the appropriate regenerative antiskid braking control, hydraulic braking control, and traction control. 10 figs.
15. Gravity brake
DOEpatents
Lujan, Richard E. (Santa Fe, NM)
2001-01-01
A mechanical gravity brake that prevents hoisted loads within a shaft from free-falling when a loss of hoisting force occurs. A loss of hoist lifting force may occur in a number of situations, for example if a hoist cable were to break, the brakes were to fail on a winch, or the hoist mechanism itself were to fail. Under normal hoisting conditions, the gravity brake of the invention is subject to an upward lifting force from the hoist and a downward pulling force from a suspended load. If the lifting force should suddenly cease, the loss of differential forces on the gravity brake in free-fall is translated to extend a set of brakes against the walls of the shaft to stop the free fall descent of the gravity brake and attached load.
16. Better Brakes
NASA Technical Reports Server (NTRS)
1976-01-01
Through continuing studies on high-temperature space materials useful for better brake linings, Bendix Corporation worked with Ames Research Center to develop a novel composite. This team worked to fabricate several combinations of composite materials and evaluated results. The one selected increases wear rates and lowers costs. It exhibits constant coefficient of friction at temperatures as high as 650 degrees Fahrenheit, a region where conventional brake linings fade markedly. Other suitable markets include brakes for trucks and industrial equipment such as overhead cranes and hoists. Afterwards brake linings could find successful application in passenger cars.
17. Braking system
DOEpatents
Norgren, D.U.
1982-09-23
A balanced braking system comprising a plurality of braking assemblies located about a member to be braked. Each of the braking assemblies consists of a spring biased piston of a first material fitted into a body of a different material which has a greater contraction upon cooling than the piston material. The piston is provided with a recessed head portion over which is positioned a diaphragm and forming a space therebetween to which is connected a pressurized fluid supply. The diaphragm is controlled by the fluid in the space to contact or withdraw from the member to be braked. A cooling means causes the body within which the piston is fitted to contract more than the piston, producing a tight shrink fit therebetween. The braking system is particularly applicable for selectively braking an arbor of an electron microscope which immobilizes, for example, a vertically adjustable low temperature specimen holder during observation. The system provides balanced braking forces which can be easily removed and re-established with minimal disturbance to arbor location.
18. Magnetostrictive Brake
NASA Technical Reports Server (NTRS)
Diftler, Myron A.; Hulse, Aaron
2010-01-01
A magnetostrictive brake has been designed as a more energy-efficient alternative to a magnetic fail-safe brake in a robot. (In the specific application, failsafe signifies that the brake is normally engaged; that is, power must be supplied to allow free rotation.) The magnetic failsafe brake must be supplied with about 8 W of electric power to initiate and maintain disengagement. In contrast, the magnetostrictive brake, which would have about the same dimensions and the same torque rating as those of the magnetic fail-safe brake, would demand only about 2 W of power for disengagement. The brake (see figure) would include a stationary base plate and a hub mounted on the base plate. Two solenoid assemblies would be mounted in diametrically opposed recesses in the hub. The cores of the solenoids would be made of the magnetostrictive alloy Terfenol-D or equivalent. The rotating part of the brake would be a ring-and spring- disk subassembly. By means of leaf springs not shown in the figure, this subassembly would be coupled with the shaft that the brake is meant to restrain. With no power supplied to the solenoids, a permanent magnet would pull axially on a stepped disk and on a shelf in the hub, causing the ring to be squeezed axially between the stepped disk and the hub. The friction associated with this axial squeeze would effect the braking action. Supplying electric power to the solenoids would cause the magnetostrictive cylinders to push radially inward against a set of wedges that would be in axial contact with the stepped disk. The wedges would convert the radial magnetostrictive strain to a multiplied axial displacement of the stepped disk. This axial displacement would be just large enough to lift the stepped disk, against the permanent magnetic force, out of contact with the ring. The ring would then be free to turn because it would no longer be squeezed axially between the stepped disk and the hub.
19. Electric vehicle regenerative antiskid braking and traction control system
DOEpatents
Cikanek, Susan R. (Wixom, MI)
1995-01-01
An antiskid braking and traction control system for an electric or hybrid vehicle having a regenerative braking system operatively connected to an electric traction motor, and a separate hydraulic braking system includes one or more sensors for monitoring present vehicle parameters and a processor, responsive to the sensors, for calculating vehicle parameters defining the vehicle behavior not directly measurable by the sensors and determining if regenerative antiskid braking control, requiring hydrualic braking control, or requiring traction control are required. The processor then employs a control strategy based on the determined vehicle state and provides command signals to a motor controller to control the operation of the electric traction motor and to a brake controller to control fluid pressure applied at each vehicle wheel to provide the appropriate regenerative antiskid braking control, hydraulic braking control, and traction control.
20. Compression relief engine brake
SciTech Connect
Meneely, V.A.
1987-10-06
A compression relief brake is described for four cycle internal-combustion engines, comprising: a pressurized oil supply; means for selectively pressurizing a hydraulic circuit with oil from the oil supply; a master piston and cylinder communicating with a slave piston and cylinder via the hydraulic circuit; an engine exhaust valve mechanically coupled to the engine and timed to open during the exhaust cycle of the engine the exhaust valve coupled to the slave piston. The exhaust valve is spring-based in a closed state to contact a valve seat; a sleeve frictionally and slidably disposed within a cavity defined by the slave piston which cavity communicates with the hydraulic circuit. When the hydraulic circuit is selectively pressurized and the engine is operating the sleeve entraps an incompressible volume of oil within the cavity to generate a displacement of the slave piston within the slave cylinder, whereby a first gap is maintained between the exhaust valve and its associated seat; and means for reciprocally activating the master piston for increasing the pressure within the previously pressurized hydraulic circuit during at least a portion of the expansion cycle of the engine whereby a second gap is reciprocally maintained between the exhaust valve and its associated seat.
1. Fuzzy logic electric vehicle regenerative antiskid braking and traction control system
DOEpatents
Cikanek, S.R.
1994-10-25
An regenerative antiskid braking and traction control system using fuzzy logic for an electric or hybrid vehicle having a regenerative braking system operatively connected to an electric traction motor, and a separate hydraulic braking system includes sensors for monitoring present vehicle parameters and a processor, responsive to the sensors, for calculating vehicle parameters defining the vehicle behavior not directly measurable by the sensor and determining if regenerative antiskid braking control, requiring hydraulic braking control, and requiring traction control are required. The processor then employs fuzzy logic based on the determined vehicle state and provides command signals to a motor controller to control operation of the electric traction motor and to the brake controller to control fluid pressure applied at each vehicle wheel to provide the appropriate regenerative braking control, hydraulic braking control, and traction control. 123 figs.
2. Fuzzy logic electric vehicle regenerative antiskid braking and traction control system
DOEpatents
Cikanek, Susan R. (Wixom, MI)
1994-01-01
An regenerative antiskid braking and traction control system using fuzzy logic for an electric or hybrid vehicle having a regenerative braking system operatively connected to an electric traction motor, and a separate hydraulic braking system includes sensors for monitoring present vehicle parameters and a processor, responsive to the sensors, for calculating vehicle parameters defining the vehicle behavior not directly measurable by the sensor and determining if regenerative antiskid braking control, requiring hydraulic braking control, and requiring traction control are required. The processor then employs fuzzy logic based on the determined vehicle state and provides command signals to a motor controller to control operation of the electric traction motor and to the brake controller to control fluid pressure applied at each vehicle wheel to provide the appropriate regenerative braking control, hydraulic braking control, and traction control.
3. 49 CFR 393.41 - Parking brake system.
Code of Federal Regulations, 2012 CFR
2012-10-01
...found on a public road (free of ice and snow). Hydraulic-braked vehicles which...found on a public road (free of ice and snow). An agricultural commodity trailer...found on a public road (free of ice and snow). (2) The parking brake...
4. 49 CFR 393.41 - Parking brake system.
Code of Federal Regulations, 2011 CFR
2011-10-01
...found on a public road (free of ice and snow). Hydraulic-braked vehicles which...found on a public road (free of ice and snow). An agricultural commodity trailer...found on a public road (free of ice and snow). (2) The parking brake...
5. 49 CFR 393.41 - Parking brake system.
Code of Federal Regulations, 2013 CFR
2013-10-01
...found on a public road (free of ice and snow). Hydraulic-braked vehicles which...found on a public road (free of ice and snow). An agricultural commodity trailer...found on a public road (free of ice and snow). (2) The parking brake...
6. 49 CFR 393.41 - Parking brake system.
Code of Federal Regulations, 2010 CFR
2010-10-01
...found on a public road (free of ice and snow). Hydraulic-braked vehicles which...found on a public road (free of ice and snow). An agricultural commodity trailer...found on a public road (free of ice and snow). (2) The parking brake...
7. 49 CFR 393.41 - Parking brake system.
Code of Federal Regulations, 2014 CFR
2014-10-01
...found on a public road (free of ice and snow). Hydraulic-braked vehicles which...found on a public road (free of ice and snow). An agricultural commodity trailer...found on a public road (free of ice and snow). (2) The parking brake...
8. 49 CFR 393.41 - Parking brake system.
Code of Federal Regulations, 2013 CFR
2013-10-01
... road (free of ice and snow). Hydraulic-braked vehicles which were not subject to the parking brake... any condition of loading in which it is found on a public road (free of ice and snow). An agricultural... condition of loading in which it is found on a public road (free of ice and snow). (2) The parking...
9. 49 CFR 393.41 - Parking brake system.
Code of Federal Regulations, 2014 CFR
2014-10-01
... road (free of ice and snow). Hydraulic-braked vehicles which were not subject to the parking brake... any condition of loading in which it is found on a public road (free of ice and snow). An agricultural... condition of loading in which it is found on a public road (free of ice and snow). (2) The parking...
10. 49 CFR 393.41 - Parking brake system.
Code of Federal Regulations, 2010 CFR
2010-10-01
... road (free of ice and snow). Hydraulic-braked vehicles which were not subject to the parking brake... any condition of loading in which it is found on a public road (free of ice and snow). An agricultural... condition of loading in which it is found on a public road (free of ice and snow). (2) The parking...
11. 49 CFR 393.41 - Parking brake system.
Code of Federal Regulations, 2011 CFR
2011-10-01
... road (free of ice and snow). Hydraulic-braked vehicles which were not subject to the parking brake... any condition of loading in which it is found on a public road (free of ice and snow). An agricultural... condition of loading in which it is found on a public road (free of ice and snow). (2) The parking...
12. A unique concept for automatically controlling the braking action of wheeled vehicles during minimum distance stops
NASA Technical Reports Server (NTRS)
Barthlome, D. E.
1975-01-01
Test results of a unique automatic brake control system are outlined and a comparison is made of its mode of operation to that of an existing skid control system. The purpose of the test system is to provide automatic control of braking action such that hydraulic brake pressure is maintained at a near constant, optimum value during minimum distance stops.
13. Optimal design of a disc-type MR brake for middle-sized motorcycle
Nguyen, Quoc-Hung; Jeon, Juncheol; Choi, Seung-Bok
2011-03-01
This research work focuses on optimal design of a disc-type magneto-rheological (MR) brake that can replace a conventional hydraulic brake (CHB) of middle-sized motorcycles. Firstly, a MR brake configuration is proposed considering the available space and the simplicity to replace a CHB by the proposed MR brake. An optimal design of the proposed MR brake is then performed considering the required braking torque, operating temperature, mass and size of the brake. In order to perform the optimization of the brake, the braking torque of the brake is analyzed based on Herschel-Bulkley rheological model of MR fluid. The constrain on operating temperature of the MR brake is determined by considering the steady temperature of the brake when the motorcycle is cruising and the temperature increase during a braking process. An optimization procedure based on finite element analysis integrated with an optimization tool is employed to obtain optimal geometric dimensions of the MR brake. Optimal solution of the MR brake is then presented and simulated performance of the optimized brake is shown with remarkable discussions.
14. 14 CFR 25.735 - Brakes and braking systems.
Code of Federal Regulations, 2010 CFR
2010-01-01
...design landing stop brake kinetic energy absorption requirement of each wheel, brake...wear range of the brake. The energy absorption rate derived from the airplane manufacturer's...accelerate-stop brake kinetic energy absorption requirement of each wheel,...
15. Automotive disc brake squeal
Kinkaid, N. M.; O'Reilly, O. M.; Papadopoulos, P.
2003-10-01
Disc brake squeal remains an elusive problem in the automotive industry. Since the early 20th century, many investigators have examined the problem with experimental, analytical, and computational techniques, but there is as yet no method to completely suppress disc brake squeal. This paper provides a comprehensive review and bibliography of works on disc brake squeal. In an effort to make this review accessible to a large audience, background sections on vibrations, contact and disc brake systems are also included.
16. TGV disc brake squeal
Lorang, X.; Foy-Margiocchi, F.; Nguyen, Q. S.; Gautier, P. E.
2006-06-01
The discomfort generated by the noise emission of braking systems in trains has aroused recently many studies on the mechanical modelling of brake noise in France. A theoretical and numerical discussion on the phenomenon of brake squeal is given in this paper in relation with some experimental data. This study is based upon a flutter instability analysis giving unstable modes of the brake system under the contact and Coulomb friction.
17. Roller Locking Brake
NASA Technical Reports Server (NTRS)
Vranish, John M.
1993-01-01
Roller locking brake is normally braking rotary mechanism allowing free rotation when electromagnet in mechanism energized. Well suited to robots and other machinery which automatic braking upon removal of electrical power required. More compact and reliable. Requires little electrical power to maintain free rotation and exhibits minimal buildup of heat.
18. Commercial Motor Vehicle Brake Assessment Tools
E-print Network
ability #12;Performance-Based Brake Tester · Assessment of brake efficiency BE = Equivalent performance Total Braking Force Total Vehicle Weight Total Braking Force Total Vehicle Weight #12;Related
19. 14 CFR 25.735 - Brakes and braking systems.
Code of Federal Regulations, 2010 CFR
2010-01-01
... braking systems. (a) Approval. Each assembly consisting of a wheel(s) and brake(s) must be approved. (b... operational landing stop at maximum landing weight. The design landing stop brake kinetic energy absorption requirement of each wheel, brake, and tire assembly must be determined. It must be substantiated...
20. 14 CFR 25.735 - Brakes and braking systems.
Code of Federal Regulations, 2014 CFR
2014-01-01
... braking systems. (a) Approval. Each assembly consisting of a wheel(s) and brake(s) must be approved. (b... operational landing stop at maximum landing weight. The design landing stop brake kinetic energy absorption requirement of each wheel, brake, and tire assembly must be determined. It must be substantiated...
1. 14 CFR 25.735 - Brakes and braking systems.
Code of Federal Regulations, 2011 CFR
2011-01-01
... braking systems. (a) Approval. Each assembly consisting of a wheel(s) and brake(s) must be approved. (b... operational landing stop at maximum landing weight. The design landing stop brake kinetic energy absorption requirement of each wheel, brake, and tire assembly must be determined. It must be substantiated...
2. 14 CFR 25.735 - Brakes and braking systems.
Code of Federal Regulations, 2013 CFR
2013-01-01
... braking systems. (a) Approval. Each assembly consisting of a wheel(s) and brake(s) must be approved. (b... operational landing stop at maximum landing weight. The design landing stop brake kinetic energy absorption requirement of each wheel, brake, and tire assembly must be determined. It must be substantiated...
3. Brake Fundamentals. Automotive Articulation Project.
ERIC Educational Resources Information Center
Cunningham, Larry; And Others
Designed for secondary and postsecondary auto mechanics programs, this curriculum guide contains learning exercises in seven areas: (1) brake fundamentals; (2) brake lines, fluid, and hoses; (3) drum brakes; (4) disc brake system and service; (5) master cylinder, power boost, and control valves; (6) parking brakes; and (7) trouble shooting. Each…
4. Aircraft hydraulic systems. Third edition
SciTech Connect
Neese, W.A.
1991-12-31
The first nine chapters concern hydraulic components including: tubing, hoses, fittings, seals, pumps, valves, cylinders, and motors. General hydraulic system considerations are included in chapters five and nine, while pneumatic systems are covered in chapter ten. Chapters eleven through fifteen are devoted to aircraft-specific systems such as: landing gear, flight controls, brakes, etc. The material is rounded out with excerpts from the Canadair Challenger 601 training guide to illustrate the use of hydraulic systems in a specific aircraft application.
5. WIND BRAKING OF MAGNETARS
SciTech Connect
Tong, H.; Xu, R. X.; Qiao, G. J.; Song, L. M.
2013-05-10
We explore the wind braking of magnetars considering recent observations challenging the traditional magnetar model. There is evidence for strong multipole magnetic fields in active magnetars, but the dipole field inferred from spin-down measurements may be strongly biased by particle wind. Recent observations challenging the traditional model of magnetars may be explained naturally by the wind braking scenario: (1) the supernova energies of magnetars are of normal value; (2) the non-detection in Fermi observations of magnetars; (3) the problem posed by low magnetic field soft gamma-ray repeaters; (4) the relation between magnetars and high magnetic field pulsars; and (5) a decreasing period derivative during magnetar outbursts. Transient magnetars with L{sub x}<- E-dot{sub rot} may still be magnetic dipole braking. This may explain why low luminosity magnetars are more likely to have radio emissions. A strong reduction of the dipole magnetic field is possible only when the particle wind is very collimated at the star surface. A small reduction of the dipole magnetic field may result from detailed considerations of magnetar wind luminosity. In the wind braking scenario, magnetars are neutron stars with a strong multipole field. For some sources, a strong dipole field may no longer be needed. A magnetism-powered pulsar wind nebula will be one of the consequences of wind braking. For a magnetism-powered pulsar wind nebula, we should see a correlation between the nebula luminosity and the magnetar luminosity. Under the wind braking scenario, a braking index smaller than three is expected. Future braking index measurement of a magnetar may tell us whether magnetars are wind braking or magnetic dipole braking.
6. 14 CFR 25.735 - Brakes and braking systems.
Code of Federal Regulations, 2012 CFR
2012-01-01
... 14 Aeronautics and Space 1 2012-01-01 2012-01-01 false Brakes and braking systems. 25.735 Section 25.735 Aeronautics and Space FEDERAL AVIATION ADMINISTRATION, DEPARTMENT OF TRANSPORTATION AIRCRAFT AIRWORTHINESS STANDARDS: TRANSPORT CATEGORY AIRPLANES Design and Construction Landing Gear § 25.735 Brakes and braking systems. (a) Approval....
7. Improved Electromagnetic Brake
NASA Technical Reports Server (NTRS)
Martin, Toby B.
2004-01-01
A proposed design for an electromagnetic brake would increase the reliability while reducing the number of parts and the weight, relative to a prior commercially available electromagnetic brake. The reductions of weight and the number of parts could also lead to a reduction of cost. A description of the commercial brake is prerequisite to a description of the proposed electromagnetic brake. The commercial brake (see upper part of figure) includes (1) a permanent magnet and an electromagnet coil on a stator and (2) a rotor that includes a steel contact plate mounted, with tension spring loading, on an aluminum hub. The stator is mounted securely on a stationary object, which would ordinarily be the housing of a gear drive or a motor. The rotor is mounted on the shaft of the gear drive or motor. The commercial brake nominally operates in a fail-safe (in the sense of normally braking) mode: In the absence of current in the electromagnet coil, the permanent magnet pulls the contact plate, against the spring tension, into contact with the stator. To release the brake, one excites the electromagnet with a current of the magnitude and polarity chosen to cancel the magnetic flux of the permanent magnet, thereby enabling the spring tension to pull the contact plate out of contact with the stator. The fail-safe operation of the commercial brake depends on careful mounting of the rotor in relation to the stator. The rotor/stator gap must be set with a tolerance between 10 and 15 mils (between about 0.25 and about 0.38 mm). If the gap or the contact pad is thicker than the maximum allowable value, then the permanent magnetic field will not be strong enough to pull the steel plate across the gap. (For this reason, any contact pad between the contact plate and the stator must also be correspondingly thin.) If the gap exceeds the maximum allowable value because of shaft end play, it becomes impossible to set the brake by turning off the electromagnet current. Although it may still be possible to set the brake by applying an electromagnet current to aid the permanent magnetic field instead of canceling it, this action can mask an out-of-tolerance condition in the brake and it does not restore the fail-safe function of setting the brake when current is lost.
8. Vehicle brake testing system
DOEpatents
Stevens, Samuel S. (Harriman, TN); Hodgson, Jeffrey W. (Lenoir City, TN)
2002-11-19
This invention relates to a force measuring system capable of measuring forces associated with vehicle braking and of evaluating braking performance. The disclosure concerns an invention which comprises a first row of linearly aligned plates, a force bearing surface extending beneath and beside the plates, vertically oriented links and horizontally oriented links connecting each plate to a force bearing surface, a force measuring device in each link, a transducer coupled to each force measuring device, and a computing device coupled to receive an output signal from the transducer indicative of measured force in each force measuring device. The present invention may be used for testing vehicle brake systems.
9. From Brake to Syzygy
E-print Network
Moeckel, Richard; Venturelli, Andrea
2011-01-01
In the planar three-body problem, we study solutions with zero initial velocity (brake orbits). Following such a solution until the three masses become collinear (syzygy), we obtain a continuous, flow-induced Poincar\\'e map. We study the image of the map in the set of collinear configurations and define a continuous extension to the Lagrange triple collision orbit. In addition we provide a variational characterization of some of the resulting brake-to-syzygy orbits and find simple examples of periodic brake orbits.
10. 49 CFR 393.55 - Antilock brake systems.
Code of Federal Regulations, 2014 CFR
2014-10-01
...49 CFR 571.105, S5.5). (b) ABS malfunction indicators for hydraulic braked...of this section shall be equipped with an ABS malfunction indicator system that meets...converter dollies and full trailers). (d) ABS malfunction circuits and signals for...
11. 49 CFR 393.55 - Antilock brake systems.
Code of Federal Regulations, 2011 CFR
2011-10-01
...49 CFR 571.105, S5.5). (b) ABS malfunction indicators for hydraulic braked...of this section shall be equipped with an ABS malfunction indicator system that meets...converter dollies and full trailers). (d) ABS malfunction circuits and signals for...
12. 49 CFR 393.55 - Antilock brake systems.
Code of Federal Regulations, 2010 CFR
2010-10-01
...49 CFR 571.105, S5.5). (b) ABS malfunction indicators for hydraulic braked...of this section shall be equipped with an ABS malfunction indicator system that meets...converter dollies and full trailers). (d) ABS malfunction circuits and signals for...
13. 49 CFR 393.55 - Antilock brake systems.
Code of Federal Regulations, 2012 CFR
2012-10-01
...49 CFR 571.105, S5.5). (b) ABS malfunction indicators for hydraulic braked...of this section shall be equipped with an ABS malfunction indicator system that meets...converter dollies and full trailers). (d) ABS malfunction circuits and signals for...
14. 49 CFR 393.55 - Antilock brake systems.
Code of Federal Regulations, 2013 CFR
2013-10-01
...49 CFR 571.105, S5.5). (b) ABS malfunction indicators for hydraulic braked...of this section shall be equipped with an ABS malfunction indicator system that meets...converter dollies and full trailers). (d) ABS malfunction circuits and signals for...
15. Unidirectional high gain brake stop
NASA Technical Reports Server (NTRS)
Lang, David J. (Inventor)
1987-01-01
This invention relates to a unidirectional high gain brake arrangement that includes in combination a shaft mounted for rotation within a housing. The shaft is rotatable in either direction. A brake is selectively releasably coupled to the housing and to the shaft. The brake has a first member. An intermittent motion device is respectively coupled through the first member to the housing and through a one-way clutch to the shaft. The brake also has a second member that is mechanically coupled to the first brake member and to the housing. The intermittent motion device causes the brake to be activated by movement imparted to the first brake member after a preset number of revolutions of the shaft in one direction. The brake is released by rotation of the shaft in an opposite direction whereby torque transmitted through the one-way clutch to the first brake member is removed.
16. 14 CFR 23.735 - Brakes.
Code of Federal Regulations, 2013 CFR
2013-01-01
...Brakes must be provided. The landing brake kinetic energy capacity rating of each main wheel brake assembly must not be less than the kinetic energy absorption requirements determined...following methods: (1) The brake kinetic energy absorption requirements...
17. 14 CFR 23.735 - Brakes.
Code of Federal Regulations, 2014 CFR
2014-01-01
...Brakes must be provided. The landing brake kinetic energy capacity rating of each main wheel brake assembly must not be less than the kinetic energy absorption requirements determined...following methods: (1) The brake kinetic energy absorption requirements...
18. 14 CFR 23.735 - Brakes.
Code of Federal Regulations, 2012 CFR
2012-01-01
...Brakes must be provided. The landing brake kinetic energy capacity rating of each main wheel brake assembly must not be less than the kinetic energy absorption requirements determined...following methods: (1) The brake kinetic energy absorption requirements...
19. 49 CFR 238.431 - Brake system.
Code of Federal Regulations, 2010 CFR
2010-10-01
... dynamic brake does not result in exceeding the allowable stopping distance; (2) The friction brake alone... speed for safe operation of the train using only the friction brake portion of the blended brake with...
20. 49 CFR 238.431 - Brake system.
Code of Federal Regulations, 2014 CFR
2014-10-01
... dynamic brake does not result in exceeding the allowable stopping distance; (2) The friction brake alone... speed for safe operation of the train using only the friction brake portion of the blended brake with...
1. 49 CFR 238.431 - Brake system.
Code of Federal Regulations, 2013 CFR
2013-10-01
... dynamic brake does not result in exceeding the allowable stopping distance; (2) The friction brake alone... speed for safe operation of the train using only the friction brake portion of the blended brake with...
2. The braking performance of a vehicle anti-lock brake system featuring an electro-rheological valve pressure modulator
Choi, Seung-Bok; Sung, Kum-Gil; Cho, Myung-Soo; Lee, Yang-Sub
2007-08-01
This paper presents the braking performances of a vehicle anti-lock brake system (ABS) featuring an electro-rheological (ER) valve pressure modulator. As a first step, the principal design parameters of the ER valve and hydraulic booster are appropriately determined by considering the Bingham property of the ER fluid and the braking pressure variation during the ABS operation. An ER fluid composed of chemically treated starch particles and silicone oil is used. An electrically controllable pressure modulator is then constructed and its pressure controllability is empirically evaluated. Subsequently, a quarter-car wheel slip model is established and integrated with the governing equation of the pressure modulator. A sliding mode controller for slip rate control is designed and implemented via the hardware-in-the-loop simulation (HILS). In order to demonstrate the superior braking performance of the proposed ABS, a full car model is derived and a sliding mode controller is formulated to achieve the desired yaw rate. The braking performances in terms of braking distance and step input steering are evaluated and presented in time domain through full car simulations.
3. Design of hydraulic output Stirling engine
NASA Technical Reports Server (NTRS)
Toscano, W. M.; Harvey, A. C.; Lee, K.
1983-01-01
A hydraulic output system for the RE-1000 free piston stirling engine (FPSE) was designed. The hydraulic output system can be readily integrated with the existing hot section of RE-1000 FPSE. The system has two simply supported diaphragms which separate the engine gas from the hydraulic fluid, a dynamic balance mechanism, and a novel, null center band hydraulic pump. The diaphragms are designed to endure more than 10 billion cycles, and to withstand the differential pressure load as high as 14 MPa. The projected thermodynamic performance of the hydraulic output version of RE-1000 FPSE is 1.87 kW at 29/7 percent brake efficiency.
4. Evaluation of aircraft brake materials
NASA Technical Reports Server (NTRS)
Ho, T. L.; Kennedy, F. E.; Peterson, M. B.
1977-01-01
A test program was carried out to evaluate several new high-temperature friction materials for use in aircraft disk brakes. A specially built test apparatus utilizing a disk brake and wheel half from a small jet aircraft was used. The apparatus enabled control of brake pressure, velocity and braking time. Tests were run under both constant and variable velocity conditions and covered a kinetic energy range similar to that encountered in aircraft brake service. The materials evaluation showed that two newly developed friction materials show potential for use in aircraft disk brakes. One of the materials is a nickel-based sintered composite, while the other is a molybdenum-based material. Both materials show much lower wear rates than conventional copper-based materials and are better able to withstand the high temperatures encountered during braking. Additional materials improvement is necessary, however, since both materials show a significant negative slope of the friction-velocity curve at low velocities.
5. Optimal design of disc-type magneto-rheological brake for mid-sized motorcycle: experimental evaluation
Sohn, Jung Woo; Jeon, Juncheol; Nguyen, Quoc Hung; Choi, Seung-Bok
2015-08-01
In this paper, a disc-type magneto-rheological (MR) brake is designed for a mid-sized motorcycle and its performance is experimentally evaluated. The proposed MR brake consists of an outer housing, a rotating disc immersed in MR fluid, and a copper wire coiled around a bobbin to generate a magnetic field. The structural configuration of the MR brake is first presented with consideration of the installation space for the conventional hydraulic brake of a mid-sized motorcycle. The design parameters of the proposed MR brake are optimized to satisfy design requirements such as the braking torque, total mass of the MR brake, and cruising temperature caused by the magnetic-field friction of the MR fluid. In the optimization procedure, the braking torque is calculated based on the Herschel-Bulkley rheological model, which predicts MR fluid behavior well at high shear rate. An optimization tool based on finite element analysis is used to obtain the optimized dimensions of the MR brake. After manufacturing the MR brake, mechanical performances regarding the response time, braking torque and cruising temperature are experimentally evaluated.
6. Experiments with airplane brakes
NASA Technical Reports Server (NTRS)
Michael, Franz
1931-01-01
This report begins by examining the forces on the brake shoes. For the determination of the load distribution over the shoes it was assumed that the brake linings follow Hooke's law, are neatly fitted and bedded in by wear. The assumption of Hooke's law, that is, the proportionality between compression of the lining and the absorption of force, is fulfilled to a certain extent for the loading, as becomes apparent from the load tests described further on. But there is a material discrepancy at unloading. From the load distribution we merely defined the position of the normal force resultant, while for the rest, the effect of the distribution was disregarded in the comparison of the different shoe dispositions.
7. Deployable Engine Air Brake
NASA Technical Reports Server (NTRS)
2014-01-01
On approach, next-generation aircraft are likely to have airframe noise levels that are comparable to or in excess of engine noise. ATA Engineering, Inc. (ATA) is developing a novel quiet engine air brake (EAB), a device that generates "equivalent drag" within the engine through stream thrust reduction by creating a swirling outflow in the turbofan exhaust nozzle. Two Phase II projects were conducted to mature this technology: (1) a concept development program (CDP) and (2) a system development program (SDP).
8. Tether Deployer And Brake
NASA Technical Reports Server (NTRS)
Carroll, Joseph A.; Alexander, Charles M.
1993-01-01
Design concept promises speed, control, and reliability. Scheme for deploying tether provides for fast, free, and snagless payout and fast, dependable braking. Developed for small, expendable tethers in outer space, scheme also useful in laying transoceanic cables, deploying guidance wires to torpedoes and missiles, paying out rescue lines from ship to ship via rockets, deploying antenna wires, releasing communication and power cables to sonobuoys and expendable bathythermographs, and in reeling out lines from fishing rods.
9. 49 CFR 238.231 - Brake system.
Code of Federal Regulations, 2011 CFR
2011-10-01
...until it is known that the air brake system is properly charged. (i) Passenger...1) The blending of friction and dynamic brake to obtain the correct retarding... (k) For new designs of braking systems, the design process shall...
10. 49 CFR 238.231 - Brake system.
Code of Federal Regulations, 2014 CFR
2014-10-01
...until it is known that the air brake system is properly charged. (i) Passenger...1) The blending of friction and dynamic brake to obtain the correct retarding... (k) For new designs of braking systems, the design process shall...
11. 49 CFR 238.231 - Brake system.
Code of Federal Regulations, 2010 CFR
2010-10-01
...until it is known that the air brake system is properly charged. (i) Passenger...1) The blending of friction and dynamic brake to obtain the correct retarding... (k) For new designs of braking systems, the design process shall...
12. 49 CFR 238.231 - Brake system.
Code of Federal Regulations, 2013 CFR
2013-10-01
...until it is known that the air brake system is properly charged. (i) Passenger...1) The blending of friction and dynamic brake to obtain the correct retarding... (k) For new designs of braking systems, the design process shall...
13. 49 CFR 238.231 - Brake system.
Code of Federal Regulations, 2012 CFR
2012-10-01
...until it is known that the air brake system is properly charged. (i) Passenger...1) The blending of friction and dynamic brake to obtain the correct retarding... (k) For new designs of braking systems, the design process shall...
14. Commercial Motor Vehicle Brake-Related Research
E-print Network
Commercial Motor Vehicle Brake-Related Research Commercial Motor Vehicle Roadside Technology Corridor Safety Technology Showcase October 14, 2010 Commercial Motor Vehicle Roadside Technology Corridor CMVRTC Brake Research · Evaluation of Smart Infrared Inspection System · Real-Time Dynamic Brake
15. Position control optimization of aerodynamic brake device for high-speed trains
Zuo, Jianyong; Luo, Zhuojun; Chen, Zhongkai
2014-03-01
The aerodynamic braking is a clean and non-adhesion braking, and can be used to provide extra braking force during high-speed emergency braking. The research of aerodynamic braking has attracted more and more attentions in recent years. However, most researchers in this field focus on aerodynamic effects and seldom on issues of position control of the aerodynamic braking board. The purpose of this paper is to explore position control optimization of the braking board in an aerodynamic braking prototype. The mathematical models of the hydraulic drive unit in the aerodynamic braking system are analyzed in detail, and the simulation models are established. Three control functions—constant, linear, and quadratic—are explored. Two kinds of criteria, including the position steady-state error and the acceleration of the piston rod, are used to evaluate system performance. Simulation results show that the position steady state-error is reduced from around 12-2 mm by applying a linear instead of a constant function, while the acceleration is reduced from 25.71-3.70 m/s2 with a quadratic control function. Use of the quadratic control function is shown to improve system performance. Experimental results obtained by measuring the position response of the piston rod on a test-bench also suggest a reduced position error and smooth movement of the piston rod. This implies that the acceleration is smaller when using the quadratic function, thus verifying the effectiveness of control schemes to improve to system performance. This paper proposes an effective and easily implemented control scheme that improves the position response of hydraulic cylinders during position control.
16. Automatic transmission brake assembly including an overrunning roller brake and a friction brake
SciTech Connect
Premiski, V.; Hohnel, R.; Premiski, C.
1988-10-11
This patent describes an overrunning roller brake assembly for a planetary gear unit in an automatic transmission for automobiles, the gear unit having a ring gear, a carrier and a sun gear, the carrier having planet pinions thereon engaging the sun and ring gears; a brake for anchoring a reaction member of the gear unit, at least one other member of the gear unit being adapted to receive driving torque; the brake comprising an annular inner brake race surrounding a fixed part of the transmission, an annular outer brake race connected to the reaction member and surrounding the inner race, the outer race comprising an extrusion with an outer brake drum surface adapted to be engaged by a reaction friction brake band; overrunning brake rollers between the races, a pair of support rings between the races on either side of the rollers; the support rings having a C-shaped cross section whereby the inner and outer surfaces thereof provide a bearing support for the races; retainer rings enclosed within the support rings, the retainer rings having a radial thickness approximately equal to the radial inside dimension of the C-shaped cross section of the support rings whereby radial loads are transmitted between the races through the retainer rings and support rings.
17. AUTOMOTIVE DIESEL MAINTENANCE 2. UNIT IX, AUTOMATIC TRANSMISSIONS--HYDRAULIC SYSTEM (PART I).
ERIC Educational Resources Information Center
Human Engineering Inst., Cleveland, OH.
THIS MODULE OF A 25-MODULE COURSE IS DESIGNED TO DEVELOP AN UNDERSTANDING OF THE OIL FLOW WITHIN HYDRAULIC TRANSMISSIONS USED ON DIESEL POWERED VEHICLES. TOPICS ARE GENERAL DESCRIPTION, HYDRAULIC CIRCUITS, AND BRAKE HYDRAULIC CIRCUIT AND OPERATION. THE MODULE CONSISTS OF A SELF-INSTRUCTIONAL PROGRAMED TRAINING FILM "LEARNING ABOUT THE ALLISON…
18. 49 CFR 238.231 - Brake system.
Code of Federal Regulations, 2010 CFR
2010-10-01
... by testing or previous service. (h) Hand brakes and parking brakes. (1) Except for a locomotive that... be designed so that: (1) The blending of friction and dynamic brake to obtain the correct retarding force is automatic; (2) Loss of power or failure of the dynamic brake does not result in exceeding...
19. 49 CFR 238.231 - Brake system.
Code of Federal Regulations, 2013 CFR
2013-10-01
... by testing or previous service. (h) Hand brakes and parking brakes. (1) Except for a locomotive that... be designed so that: (1) The blending of friction and dynamic brake to obtain the correct retarding force is automatic; (2) Loss of power or failure of the dynamic brake does not result in exceeding...
20. 49 CFR 238.231 - Brake system.
Code of Federal Regulations, 2014 CFR
2014-10-01
... by testing or previous service. (h) Hand brakes and parking brakes. (1) Except for a locomotive that... be designed so that: (1) The blending of friction and dynamic brake to obtain the correct retarding force is automatic; (2) Loss of power or failure of the dynamic brake does not result in exceeding...
1. 49 CFR 238.231 - Brake system.
Code of Federal Regulations, 2012 CFR
2012-10-01
... by testing or previous service. (h) Hand brakes and parking brakes. (1) Except for a locomotive that... be designed so that: (1) The blending of friction and dynamic brake to obtain the correct retarding force is automatic; (2) Loss of power or failure of the dynamic brake does not result in exceeding...
2. 49 CFR 238.231 - Brake system.
Code of Federal Regulations, 2011 CFR
2011-10-01
... by testing or previous service. (h) Hand brakes and parking brakes. (1) Except for a locomotive that... be designed so that: (1) The blending of friction and dynamic brake to obtain the correct retarding force is automatic; (2) Loss of power or failure of the dynamic brake does not result in exceeding...
3. 49 CFR 238.431 - Brake system.
Code of Federal Regulations, 2013 CFR
2013-10-01
...unit. (d) The brake system shall be designed to prevent...apply to blended braking systems: (1) Loss of power or failure of the dynamic brake does not result in...electric portion of the brake system shall be displayed for...
4. 49 CFR 238.431 - Brake system.
Code of Federal Regulations, 2014 CFR
2014-10-01
...unit. (d) The brake system shall be designed to prevent...apply to blended braking systems: (1) Loss of power or failure of the dynamic brake does not result in...electric portion of the brake system shall be displayed for...
5. 49 CFR 238.431 - Brake system.
Code of Federal Regulations, 2010 CFR
2010-10-01
...unit. (d) The brake system shall be designed to prevent...apply to blended braking systems: (1) Loss of power or failure of the dynamic brake does not result in...electric portion of the brake system shall be displayed for...
6. 49 CFR 238.431 - Brake system.
Code of Federal Regulations, 2011 CFR
2011-10-01
...unit. (d) The brake system shall be designed to prevent...apply to blended braking systems: (1) Loss of power or failure of the dynamic brake does not result in...electric portion of the brake system shall be displayed for...
7. 49 CFR 238.431 - Brake system.
Code of Federal Regulations, 2012 CFR
2012-10-01
...unit. (d) The brake system shall be designed to prevent...apply to blended braking systems: (1) Loss of power or failure of the dynamic brake does not result in...electric portion of the brake system shall be displayed for...
8. Mountain Plains Learning Experience Guide: Automotive Repair. Course: Brake Systems.
ERIC Educational Resources Information Center
Schramm, C.; Osland, Walt
One of twelve individualized courses included in an automotive repair curriculum, this course covers theory, operation, and repair of drum brakes, disc brakes, and brake system components. The course is comprised of six units: (1) Fundamentals of Brake Systems, (2) Master Cylinder, (3) Drum Brakes, (4) Disc Brakes, (5) Power Brakes, and (6)…
9. Adjustable Tooling for Bending Brake
NASA Technical Reports Server (NTRS)
Ellis, J. M.
1986-01-01
Deep metal boxes and other parts easily fabricated. Adjustable tooling jig for bending brake accommodates spacing blocks and either standard male press-brake die or bar die. Holds spacer blocks, press-brake die, bar window die, or combination of three. Typical bending operations include bending of cut metal sheet into box and bending of metal strip into bracket with multiple inward 90 degree bends. By increasing free space available for bending sheet-metal parts jig makes it easier to fabricate such items as deep metal boxes or brackets with right-angle bends.
10. Regenerative braking device
DOEpatents
Hoppie, Lyle O. (Birmingham, MI)
1982-01-12
Disclosed are several embodiments of a regenerative braking device for an automotive vehicle. The device includes a plurality of rubber rollers (24, 26) mounted for rotation between an input shaft (14) connectable to the vehicle drivetrain and an output shaft (16) which is drivingly connected to the input shaft by a variable ratio transmission (20). When the transmission ratio is such that the input shaft rotates faster than the output shaft, the rubber rollers are torsionally stressed to accumulate energy, thereby slowing the vehicle. When the transmission ratio is such that the output shaft rotates faster than the input shaft, the rubber rollers are torsionally relaxed to deliver accumulated energy, thereby accelerating or driving the vehicle.
11. Brake Stops Both Rotation And Translation
NASA Technical Reports Server (NTRS)
Allred, Johnny W.; Fleck, Vincent J., Jr.
1995-01-01
Combination of braking and positioning mechanisms allows both rotation and translation before brake engaged. Designed for use in positioning model airplane in wind tunnel. Modified version used to position camera on tripod. Brake fast and convenient to use; contains single actuator energizing braking actions against both rotation and translation. Braking actuator electric, but pneumatic actuator could be used instead. Compact and lightweight, applies locking forces close to load, and presents minimal cross section to airflow.
12. Wheel brakes and their application to aircraft
NASA Technical Reports Server (NTRS)
Dowty, G H
1928-01-01
The advantages to be gained from braking have not been ignored, and in the search for a suitable method many schemes have been suggested and tried. Some of the methods discussed in this paper include: 1) increasing the height of the landing gear; 2) air brakes of various forms; 3) sprags on tail skid and axle; and 4) wheel brakes. This report focuses on the design of wheel brakes and wheel brake controls.
13. Variable ratio regenerative braking device
DOEpatents
Hoppie, Lyle O. (Birmingham, MI)
1981-12-15
Disclosed is a regenerative braking device (10) for an automotive vehicle. The device includes an energy storage assembly (12) having a plurality of rubber rollers (26, 28) mounted for rotation between an input shaft (36) and an output shaft (42), clutches (38, 46) and brakes (40, 48) associated with each shaft, and a continuously variable transmission (22) connectable to a vehicle drivetrain and to the input and output shafts by the respective clutches. The rubber rollers are torsionally stressed to accumulate energy from the vehicle when the input shaft is clutched to the transmission while the brake on the output shaft is applied, and are torsionally relaxed to deliver energy to the vehicle when the output shaft is clutched to the transmission while the brake on the input shaft is applied. The transmission ratio is varied to control the rate of energy accumulation and delivery for a given rotational speed of the vehicle drivetrain.
14. Development of aircraft brake materials
NASA Technical Reports Server (NTRS)
Ho, T.-L.; Peterson, M. B.
1976-01-01
A program has been carried out to study and develop high temperature aircraft brake materials. A survey of the requirements of brake materials was made to select materials to meet these requirements. Based upon their physical and thermal properties, a number of materials were selected and evaluated in sliding tests which simulated aircraft braking. The mating material is 17-22 AS steel. Additives were incorporated into these materials to optimize their wear or strength behavior with particular emphasis on nickel and molybdenum base materials. Optimum materials were developed which had improved wear behavior over conventional brake materials in the simulated test. The best materials were a nickel, aluminum oxide, lead tungstate composition containing graphite and a molybdenum base material containing LPA 100 (an intermetallic compound of cobalt, molybdenum and silicon).
15. 49 CFR 571.116 - Standard No. 116; Motor vehicle brake fluids.
Code of Federal Regulations, 2013 CFR
2013-10-01
... packaged lot and tested simultaneously. Hydraulic system mineral oil means a mineral-oil-based fluid... humidified under controlled conditions; 350 ml. of SAE triethylene glycol monomethyl ether, brake fluid grade... DOT 5 fluids) followed by an acetone or ether rinse. Pass a slow stream of filtered dry air...
16. 49 CFR 571.116 - Standard No. 116; Motor vehicle brake fluids.
Code of Federal Regulations, 2014 CFR
2014-10-01
... packaged lot and tested simultaneously. Hydraulic system mineral oil means a mineral-oil-based fluid... humidified under controlled conditions; 350 ml. of SAE triethylene glycol monomethyl ether, brake fluid grade... DOT 5 fluids) followed by an acetone or ether rinse. Pass a slow stream of filtered dry air...
17. 49 CFR 571.116 - Standard No. 116; Motor vehicle brake fluids.
Code of Federal Regulations, 2012 CFR
2012-10-01
... packaged lot and tested simultaneously. Hydraulic system mineral oil means a mineral-oil-based fluid... humidified under controlled conditions; 350 ml. of SAE triethylene glycol monomethyl ether, brake fluid grade... DOT 5 fluids) followed by an acetone or ether rinse. Pass a slow stream of filtered dry air...
18. 49 CFR 570.56 - Vacuum brake assist unit and vacuum brake system.
Code of Federal Regulations, 2013 CFR
2013-10-01
... 6 2013-10-01 2013-10-01 false Vacuum brake assist unit and vacuum brake system. 570.56 Section 570.56 ...GVWR of More Than 10,000 Pounds § 570.56 Vacuum brake assist unit and vacuum brake system....
19. 49 CFR 570.56 - Vacuum brake assist unit and vacuum brake system.
Code of Federal Regulations, 2012 CFR
2012-10-01
... 6 2012-10-01 2012-10-01 false Vacuum brake assist unit and vacuum brake system. 570.56 Section 570.56 ...GVWR of More Than 10,000 Pounds § 570.56 Vacuum brake assist unit and vacuum brake system....
20. 49 CFR 570.56 - Vacuum brake assist unit and vacuum brake system.
Code of Federal Regulations, 2011 CFR
2011-10-01
... 6 2011-10-01 2011-10-01 false Vacuum brake assist unit and vacuum brake system. 570.56 Section 570.56 ...GVWR of More Than 10,000 Pounds § 570.56 Vacuum brake assist unit and vacuum brake system....
1. 49 CFR 570.56 - Vacuum brake assist unit and vacuum brake system.
Code of Federal Regulations, 2014 CFR
2014-10-01
... 6 2014-10-01 2014-10-01 false Vacuum brake assist unit and vacuum brake system. 570.56 Section 570.56 ...GVWR of More Than 10,000 Pounds § 570.56 Vacuum brake assist unit and vacuum brake system....
2. 14 CFR 27.735 - Brakes.
Code of Federal Regulations, 2013 CFR
2013-01-01
... STANDARDS: NORMAL CATEGORY ROTORCRAFT Design and Construction Landing Gear § 27.735 Brakes. For rotorcraft with wheel-type landing gear, a braking device must be installed that is— (a) Controllable by the...
3. 14 CFR 27.735 - Brakes.
Code of Federal Regulations, 2012 CFR
2012-01-01
... STANDARDS: NORMAL CATEGORY ROTORCRAFT Design and Construction Landing Gear § 27.735 Brakes. For rotorcraft with wheel-type landing gear, a braking device must be installed that is— (a) Controllable by the...
4. 14 CFR 27.735 - Brakes.
Code of Federal Regulations, 2010 CFR
2010-01-01
... STANDARDS: NORMAL CATEGORY ROTORCRAFT Design and Construction Landing Gear § 27.735 Brakes. For rotorcraft with wheel-type landing gear, a braking device must be installed that is— (a) Controllable by the...
5. 14 CFR 29.735 - Brakes.
Code of Federal Regulations, 2012 CFR
2012-01-01
... STANDARDS: TRANSPORT CATEGORY ROTORCRAFT Design and Construction Landing Gear § 29.735 Brakes. For rotorcraft with wheel-type landing gear, a braking device must be installed that is— (a) Controllable by...
6. 14 CFR 29.735 - Brakes.
Code of Federal Regulations, 2013 CFR
2013-01-01
... STANDARDS: TRANSPORT CATEGORY ROTORCRAFT Design and Construction Landing Gear § 29.735 Brakes. For rotorcraft with wheel-type landing gear, a braking device must be installed that is— (a) Controllable by...
7. 14 CFR 27.735 - Brakes.
Code of Federal Regulations, 2011 CFR
2011-01-01
... STANDARDS: NORMAL CATEGORY ROTORCRAFT Design and Construction Landing Gear § 27.735 Brakes. For rotorcraft with wheel-type landing gear, a braking device must be installed that is— (a) Controllable by the...
8. 14 CFR 27.735 - Brakes.
Code of Federal Regulations, 2014 CFR
2014-01-01
... STANDARDS: NORMAL CATEGORY ROTORCRAFT Design and Construction Landing Gear § 27.735 Brakes. For rotorcraft with wheel-type landing gear, a braking device must be installed that is— (a) Controllable by the...
9. 14 CFR 29.735 - Brakes.
Code of Federal Regulations, 2011 CFR
2011-01-01
... STANDARDS: TRANSPORT CATEGORY ROTORCRAFT Design and Construction Landing Gear § 29.735 Brakes. For rotorcraft with wheel-type landing gear, a braking device must be installed that is— (a) Controllable by...
10. 14 CFR 29.735 - Brakes.
Code of Federal Regulations, 2014 CFR
2014-01-01
... STANDARDS: TRANSPORT CATEGORY ROTORCRAFT Design and Construction Landing Gear § 29.735 Brakes. For rotorcraft with wheel-type landing gear, a braking device must be installed that is— (a) Controllable by...
11. 14 CFR 29.735 - Brakes.
Code of Federal Regulations, 2010 CFR
2010-01-01
... STANDARDS: TRANSPORT CATEGORY ROTORCRAFT Design and Construction Landing Gear § 29.735 Brakes. For rotorcraft with wheel-type landing gear, a braking device must be installed that is— (a) Controllable by...
12. 30 CFR 56.14101 - Brakes.
Code of Federal Regulations, 2010 CFR
2010-07-01
... mobile equipment shall be equipped with a service brake system capable of stopping and holding the... equipped on self-propelled mobile equipment, parking brakes shall be capable of holding the equipment...
13. 30 CFR 57.14101 - Brakes.
Code of Federal Regulations, 2010 CFR
2010-07-01
... mobile equipment shall be equipped with a service brake system capable of stopping and holding the... equipped on self-propelled mobile equipment, parking brakes shall be capable of holding the equipment...
14. Minimal models for disk brake squeal
von Wagner, Utz; Hochlenert, Daniel; Hagedorn, Peter
2007-05-01
Numerous publications on the modeling of disk brake squeal can be found in the literature. Recent publications describe the onset of disk brake squeal as an instability of the trivial solution resulting from the non-conservative friction forces even for a constant friction coefficient. Therefore, a minimal model of disk brake squeal must contain at least two degrees of freedom. A literature review of minimal models shows that there is still a lack of a minimal model describing the basic behavior of disk brake squeal which can easily be associated to an automotive disk brake. Therefore, a new minimal model of a disk brake is introduced here, showing an obvious relation to the technical system. In this model, the vibration of the disk is taken into account, as it plays a dominant role in brake squeal. The model is analyzed with respect to its stability behavior, and consequences in using it in the optimization of disk brake systems are discussed.
15. Magnetic braking in convective stars
E-print Network
Hussain, G A J
2012-01-01
Magnetic braking causes the spin-down of single stars as they evolve on the main sequence. Models of magnetic braking can also explain the evolution of close binary systems, including cataclysmic variables. The well-known period gap in the orbital period distribution of cataclysmic variable systems indicates that magnetic braking must be significantly disrupted in secondaries that are fully convective. However, activity studies show that fully convective stars are some of the most active stars observed in young open clusters. There is therefore conflicting evidence about what happens to magnetic activity in fully convective stars. Results from spectro-polarimetric studies of cool stars have found that the field morphologies and field strengths are dependent on spectral type and rotation rate. While rapidly rotating stars with radiative cores show strong, complex magnetic fields, they have relatively weak dipole components. Fully convective stars that are rapidly rotating also possess strong magnetic fields, b...
16. Compact, Lightweight Servo-Controllable Brakes
NASA Technical Reports Server (NTRS)
Lovchik, Christopher S.; Townsend, William; Guertin, Jeffrey; Matsuoka, Yoky
2010-01-01
Compact, lightweight servo-controllable brakes capable of high torques are being developed for incorporation into robot joints. A brake of this type is based partly on the capstan effect of tension elements. In a brake of the type under development, a controllable intermediate state of torque is reached through on/off switching at a high frequency.
17. Bidirectional drive and brake mechanism
NASA Technical Reports Server (NTRS)
Swan, Scott A. (inventor)
1991-01-01
A space transport vehicle is disclosed as including a body which is arranged to be movably mounted on an elongated guide member disposed in outer space and driven therealong. A drive wheel is mounted on a drive shaft and arranged to be positioned in rolling engagement with the elongated guide carrying the vehicle. A brake member is arranged on the drive shaft for movement into and out of engagement with an adjacent surface of the drive wheel. An actuator is mounted on the body to be manually moved back and forth between spaced positions in an arc of movement. A ratchet-and-pawl mechanism is arranged to operate upon movements of the actuator in one direction between first and second positions for coupling the actuator to the drive wheel to incrementally rotate the wheel in one rotational direction and to operate upon movements of the actuator in the opposite direction for uncoupling the actuator from the wheel. The brake member is threadedly coupled to the drive shaft in order that the brake member will be operated only when the actuator is moved on beyond its first and second positions for shifting the brake member along the drive shaft and into frictional engagement with the adjacent surface on the drive wheel.
18. Brake blending strategy for a hybrid vehicle
DOEpatents
Boberg, Evan S. (Hazel Park, MI)
2000-12-05
A hybrid electric powertrain system is provided including a transmission for driving a pair of wheels of a vehicle and a heat engine and an electric motor/generator coupled to the transmission. A friction brake system is provided for applying a braking torque to said vehicle. A controller unit generates control signals to the electric motor/generator and the friction brake system for controllably braking the vehicle in response to a drivers brake command. The controller unit determines and amount of regenerative torque available and compares this value to a determined amount of brake torque requested for determining the control signals to the electric motor/generator and the friction brake system.
19. Eddy current braking experiment using brake disc from aluminium series of A16061 and A17075
Baharom, M. Z.; Nuawi, M. Z.; Priyandoko, G.; Harris, S. M.
2012-09-01
The electromagnetic braking using eddy current was studied, focused on two series of aluminium as the brake disc which are A16061 and A17075. This paper presents the comparison for both series in a few varied parameters related to eddy current braking such as air-gap, number of turns and brake disc thickness. Optical tachometer has been used along with PULSE analyzer to capture the speed (rpm) and time (s). The findings shows that the smaller the air-gap, the larger of electromagnet turns and the thicker disc thickness is, will generate higher braking torque to stop the rotational motion of disc brake and give great performance for eddy current braking. Thos parameters that been evaluated also addressed a potential on expanding this knowledge to develop an electromagnetic braking system to replace the conventional braking system.
20. 49 CFR 570.57 - Air brake system and air-over-hydraulic brake subsystem.
Code of Federal Regulations, 2011 CFR
2011-10-01
... the drain cocks in the service and supply reservoir on the truck or truck-tractor. Note the pressure.... Close the drain cocks, and, with the trailer(s) uncoupled, check air pressure buildup at the... sufficient to prevent slippage. Inspection procedure. With the air system charged, open the drain cocks...
1. 49 CFR 570.57 - Air brake system and air-over-hydraulic brake subsystem.
Code of Federal Regulations, 2012 CFR
2012-10-01
... the drain cocks in the service and supply reservoir on the truck or truck-tractor. Note the pressure.... Close the drain cocks, and, with the trailer(s) uncoupled, check air pressure buildup at the... sufficient to prevent slippage. Inspection procedure. With the air system charged, open the drain cocks...
2. 49 CFR 570.57 - Air brake system and air-over-hydraulic brake subsystem.
Code of Federal Regulations, 2014 CFR
2014-10-01
... the drain cocks in the service and supply reservoir on the truck or truck-tractor. Note the pressure.... Close the drain cocks, and, with the trailer(s) uncoupled, check air pressure buildup at the... sufficient to prevent slippage. Inspection procedure. With the air system charged, open the drain cocks...
3. 49 CFR 570.57 - Air brake system and air-over-hydraulic brake subsystem.
Code of Federal Regulations, 2013 CFR
2013-10-01
... the drain cocks in the service and supply reservoir on the truck or truck-tractor. Note the pressure.... Close the drain cocks, and, with the trailer(s) uncoupled, check air pressure buildup at the... sufficient to prevent slippage. Inspection procedure. With the air system charged, open the drain cocks...
4. 49 CFR 570.57 - Air brake system and air-over-hydraulic brake subsystem.
Code of Federal Regulations, 2014 CFR
2014-10-01
...Trailer(s) must be coupled to a truck or truck-tractor...3) The warning device (visual or audible...or audible warning device connected to...to fast idle and charge the system to its...or audible warning device connected to the...to fast idle and charge the system to...
5. 49 CFR 570.57 - Air brake system and air-over-hydraulic brake subsystem.
Code of Federal Regulations, 2011 CFR
2011-10-01
...Trailer(s) must be coupled to a truck or truck-tractor...3) The warning device (visual or audible...or audible warning device connected to...to fast idle and charge the system to its...or audible warning device connected to the...to fast idle and charge the system to...
6. 49 CFR 570.57 - Air brake system and air-over-hydraulic brake subsystem.
Code of Federal Regulations, 2012 CFR
2012-10-01
...Trailer(s) must be coupled to a truck or truck-tractor...3) The warning device (visual or audible...or audible warning device connected to...to fast idle and charge the system to its...or audible warning device connected to the...to fast idle and charge the system to...
7. 49 CFR 570.57 - Air brake system and air-over-hydraulic brake subsystem.
Code of Federal Regulations, 2013 CFR
2013-10-01
...Trailer(s) must be coupled to a truck or truck-tractor...3) The warning device (visual or audible...or audible warning device connected to...to fast idle and charge the system to its...or audible warning device connected to the...to fast idle and charge the system to...
8. 49 CFR 230.77 - Foundation brake gear.
Code of Federal Regulations, 2011 CFR
2011-10-01
... 49 Transportation 4 2011-10-01 2011-10-01 false Foundation brake gear. 230.77 Section 230.77... Tenders Brake and Signal Equipment § 230.77 Foundation brake gear. (a) Maintenance. Foundation brake gear.... Brake shoes must be properly applied and kept approximately in line with the tread of the wheel....
9. 49 CFR 230.77 - Foundation brake gear.
Code of Federal Regulations, 2010 CFR
2010-10-01
... 49 Transportation 4 2010-10-01 2010-10-01 false Foundation brake gear. 230.77 Section 230.77... Tenders Brake and Signal Equipment § 230.77 Foundation brake gear. (a) Maintenance. Foundation brake gear.... Brake shoes must be properly applied and kept approximately in line with the tread of the wheel....
10. 49 CFR 230.77 - Foundation brake gear.
Code of Federal Regulations, 2013 CFR
2013-10-01
... 49 Transportation 4 2013-10-01 2013-10-01 false Foundation brake gear. 230.77 Section 230.77... Tenders Brake and Signal Equipment § 230.77 Foundation brake gear. (a) Maintenance. Foundation brake gear.... Brake shoes must be properly applied and kept approximately in line with the tread of the wheel....
11. 49 CFR 230.77 - Foundation brake gear.
Code of Federal Regulations, 2012 CFR
2012-10-01
... 49 Transportation 4 2012-10-01 2012-10-01 false Foundation brake gear. 230.77 Section 230.77... Tenders Brake and Signal Equipment § 230.77 Foundation brake gear. (a) Maintenance. Foundation brake gear.... Brake shoes must be properly applied and kept approximately in line with the tread of the wheel....
12. 49 CFR 232.109 - Dynamic brake requirements.
Code of Federal Regulations, 2013 CFR
2013-10-01
...integrity test of the dynamic brake to determine...at the grids on the system; and (2) Display...train with a brake system that includes dynamic brakes shall adopt...train with a brake system that includes dynamic brakes shall...
13. 49 CFR 232.109 - Dynamic brake requirements.
Code of Federal Regulations, 2012 CFR
2012-10-01
...integrity test of the dynamic brake to determine...at the grids on the system; and (2) Display...train with a brake system that includes dynamic brakes shall adopt...train with a brake system that includes dynamic brakes shall...
14. 49 CFR 232.109 - Dynamic brake requirements.
Code of Federal Regulations, 2014 CFR
2014-10-01
...integrity test of the dynamic brake to determine...at the grids on the system; and (2) Display...train with a brake system that includes dynamic brakes shall adopt...train with a brake system that includes dynamic brakes shall...
15. 49 CFR 232.109 - Dynamic brake requirements.
Code of Federal Regulations, 2011 CFR
2011-10-01
...integrity test of the dynamic brake to determine...at the grids on the system; and (2) Display...train with a brake system that includes dynamic brakes shall adopt...train with a brake system that includes dynamic brakes shall...
16. 49 CFR 232.109 - Dynamic brake requirements.
Code of Federal Regulations, 2010 CFR
2010-10-01
...integrity test of the dynamic brake to determine...at the grids on the system; and (2) Display...train with a brake system that includes dynamic brakes shall adopt...train with a brake system that includes dynamic brakes shall...
17. Electromagnetic braking for Mars spacecraft
NASA Technical Reports Server (NTRS)
Holt, A. C.
1986-01-01
Aerobraking concepts are being studied to improve performance and cost effectiveness of propulsion systems for Mars landers and Mars interplanetary spacecraft. Access to megawatt power levels (nuclear power coupled to high-storage inductive or capacitive devices) on a manned Mars interplanetary spacecraft may make feasible electromagnetic braking and lift modulation techniques which were previously impractical. Using pulsed microwave and magnetic field technology, potential plasmadynamic braking and hydromagnetic lift modulation techniques have been identified. Entry corridor modulation to reduce loads and heating, to reduce vertical descent rates, and to expand horizontal and lateral landing ranges are possible benefits. In-depth studies are needed to identify specific design concepts for feasibility assessments. Standing wave/plasma sheath interaction techniques appear to be promising. The techniques may require some tailoring of spacecraft external structures and materials. In addition, rapid response guidance and control systems may require the use of structurally embedded sensors coupled to expert systems or to artificial intelligence systems.
18. Space shuttle wheels and brakes
NASA Technical Reports Server (NTRS)
Carsley, R. B.
1985-01-01
The Space Shuttle Orbiter wheels were subjected to a combination of tests which are different than any previously conducted in the aerospace industry. The major testing difference is the computer generated dynamic landing profiles used during the certification process which subjected the wheels and tires to simulated landing loading conditions. The orbiter brakes use a unique combination of carbon composite linings and beryllium heat sink to minimize weight. The development of a new lining retention method was necessary in order to withstand the high temperature generated during the braking roll. As with many programs, the volume into which this hardware had to fit was established early in the program, with no provisions made for growth to offset the continuously increasing predicted orbiter landing weight.
19. Dynamics of Braking Vehicles: From Coulomb Friction to Anti-Lock Braking Systems
ERIC Educational Resources Information Center
Tavares, J. M.
2009-01-01
The dynamics of braking of wheeled vehicles is studied using the Coulomb approximation for the friction between road and wheels. The dependence of the stopping distance on the mass of the vehicle, on the number of its wheels and on the intensity of the braking torque is established. It is shown that there are two regimes of braking, with and…
20. Bidirectional Drive-And-Brake Mechanism
NASA Technical Reports Server (NTRS)
Swan, Scott A.
1991-01-01
Vehicle that crawls along monorail combines features of both bicycle and railroad handcar. Bidirectional drive-and-brake mechanism includes selectable-pawl-and-ratchet overrunning clutch (drive mechanism) and mating stationary and rotating conical surfaces pressing against each other (brake mechanism). Operates similarly to bicycle drive-and-brake mechanism except limits rotation of sprocket in both directions and brakes at both limits. Conceived for use by astronaut traveling along structure in outer space, concept also applied on Earth to make very small railraod handcars or crawling vehicles for use on large structures, in pipelines under construction, or underwater.
1. 49 CFR 236.701 - Application, brake; full service.
Code of Federal Regulations, 2010 CFR
2010-10-01
... a split reduction in brake pipe pressure at a service rate until maximum brake cylinder pressure is... other than emergency which develops the maximum brake cylinder pressure, as determined by the design...
2. Landing and Braking of Airplanes
NASA Technical Reports Server (NTRS)
Breguet, Louis
1929-01-01
In the numerical examples, we have considered an airplane landing in calm air in a fixed direction after crossing the border (with its obstacles) at a height of 30 m. Its stopping point is at a distance D from the obstacle, comprising: a distance D(sub 1) in regular gliding flight; a distance D(sub 2) in levelling off; a distance D(sub 3) in taxying on the ground. The calculations enable us to make out the following table, which gives an idea of the improvements to be expected in the use of various possible methods of braking in the air and on the ground.
3. 14 CFR 25.507 - Reversed braking.
Code of Federal Regulations, 2014 CFR
2014-01-01
... 14 Aeronautics and Space 1 2014-01-01 2014-01-01 false Reversed braking. 25.507 Section 25.507 Aeronautics and Space FEDERAL AVIATION ADMINISTRATION, DEPARTMENT OF TRANSPORTATION AIRCRAFT AIRWORTHINESS STANDARDS: TRANSPORT CATEGORY AIRPLANES Structure Ground Loads § 25.507 Reversed braking. (a) The airplane must be in a three point static...
4. 14 CFR 25.507 - Reversed braking.
Code of Federal Regulations, 2011 CFR
2011-01-01
... 14 Aeronautics and Space 1 2011-01-01 2011-01-01 false Reversed braking. 25.507 Section 25.507 Aeronautics and Space FEDERAL AVIATION ADMINISTRATION, DEPARTMENT OF TRANSPORTATION AIRCRAFT AIRWORTHINESS STANDARDS: TRANSPORT CATEGORY AIRPLANES Structure Ground Loads § 25.507 Reversed braking. (a) The airplane must be in a three point static...
5. 14 CFR 25.507 - Reversed braking.
Code of Federal Regulations, 2010 CFR
2010-01-01
... 14 Aeronautics and Space 1 2010-01-01 2010-01-01 false Reversed braking. 25.507 Section 25.507 Aeronautics and Space FEDERAL AVIATION ADMINISTRATION, DEPARTMENT OF TRANSPORTATION AIRCRAFT AIRWORTHINESS STANDARDS: TRANSPORT CATEGORY AIRPLANES Structure Ground Loads § 25.507 Reversed braking. (a) The airplane must be in a three point static...
6. 14 CFR 25.507 - Reversed braking.
Code of Federal Regulations, 2012 CFR
2012-01-01
... 14 Aeronautics and Space 1 2012-01-01 2012-01-01 false Reversed braking. 25.507 Section 25.507 Aeronautics and Space FEDERAL AVIATION ADMINISTRATION, DEPARTMENT OF TRANSPORTATION AIRCRAFT AIRWORTHINESS STANDARDS: TRANSPORT CATEGORY AIRPLANES Structure Ground Loads § 25.507 Reversed braking. (a) The airplane must be in a three point static...
7. 14 CFR 25.507 - Reversed braking.
Code of Federal Regulations, 2013 CFR
2013-01-01
... 14 Aeronautics and Space 1 2013-01-01 2013-01-01 false Reversed braking. 25.507 Section 25.507 Aeronautics and Space FEDERAL AVIATION ADMINISTRATION, DEPARTMENT OF TRANSPORTATION AIRCRAFT AIRWORTHINESS STANDARDS: TRANSPORT CATEGORY AIRPLANES Structure Ground Loads § 25.507 Reversed braking. (a) The airplane must be in a three point static...
8. TMV Technology Capabilities Brake Stroke Monitor
E-print Network
TMV Technology Capabilities Brake Stroke Monitor Brake monitoring systems are proactive maintenance This technology allows for CMV operators to have knowledge of their steer, drive, and tandem axle group weights setup is required. Current Safety/Enforcement Technologies EOBR (electronic on-board recorder) On
9. 49 CFR 393.52 - Brake performance.
Code of Federal Regulations, 2011 CFR
2011-10-01
... percentage of its gross weight specified in the table in paragraph (d) of this section; (2) Decelerating to a... of the braking force at each wheel of the vehicle or vehicle combination as a percentage of gross vehicle or combination weight. (b) Upon application of its emergency brake system and with no other...
10. 14 CFR 23.735 - Brakes.
Code of Federal Regulations, 2012 CFR
2012-01-01
... 14 Aeronautics and Space 1 2012-01-01 2012-01-01 false Brakes. 23.735 Section 23.735 Aeronautics and Space FEDERAL AVIATION ADMINISTRATION, DEPARTMENT OF TRANSPORTATION AIRCRAFT AIRWORTHINESS STANDARDS: NORMAL, UTILITY, ACROBATIC, AND COMMUTER CATEGORY AIRPLANES Design and Construction Landing Gear § 23.735 Brakes. Link to an amendment...
11. 49 CFR 238.431 - Brake system.
Code of Federal Regulations, 2011 CFR
2011-10-01
... the controlling power car to wheel-slide conditions on any axle of the train. ... adhesion control system designed to automatically adjust the braking force on each wheel to prevent sliding during braking. In the event of a failure of this system to prevent wheel slide within preset...
12. 49 CFR 393.52 - Brake performance.
Code of Federal Regulations, 2012 CFR
2012-10-01
... 49 Transportation 5 2012-10-01 2012-10-01 false Brake performance. 393.52 Section 393.52 Transportation Other Regulations Relating to Transportation (Continued) FEDERAL MOTOR CARRIER SAFETY ADMINISTRATION, DEPARTMENT OF TRANSPORTATION FEDERAL MOTOR CARRIER SAFETY REGULATIONS PARTS AND ACCESSORIES NECESSARY FOR SAFE OPERATION Brakes § 393.52...
13. 49 CFR 393.52 - Brake performance.
Code of Federal Regulations, 2014 CFR
2014-10-01
... 49 Transportation 5 2014-10-01 2014-10-01 false Brake performance. 393.52 Section 393.52 Transportation Other Regulations Relating to Transportation (Continued) FEDERAL MOTOR CARRIER SAFETY ADMINISTRATION, DEPARTMENT OF TRANSPORTATION FEDERAL MOTOR CARRIER SAFETY REGULATIONS PARTS AND ACCESSORIES NECESSARY FOR SAFE OPERATION Brakes § 393.52...
14. Orbital-Transfer Vehicle With Aerodynamic Braking
NASA Technical Reports Server (NTRS)
Scott, C. D.; Nagy, K.; Roberts, B. B.; Ried, R. C.; Kroll, K.; Gamble, J.
1986-01-01
Vehicle includes airbrake for deceleration into lower orbit. Report describes vehicle for carrying payloads between low and high orbits around Earth. Vehicle uses thin, upper atmosphere for braking when returning to low orbit. Since less propellant needed than required for full retrorocket braking, vehicle carries larger payload and therefore reduces cost of space transportation.
15. 49 CFR 393.52 - Brake performance.
Code of Federal Regulations, 2013 CFR
2013-10-01
...-system application and braking distance in feet” (column 4) is a definite measure of the overall... section; and (3) Stopping from 20 miles per hour in a distance, measured from the point at which movement of the service brake pedal or control begins, that is not greater than the distance specified in...
16. 49 CFR 393.52 - Brake performance.
Code of Federal Regulations, 2010 CFR
2010-10-01
...-system application and braking distance in feet” (column 4) is a definite measure of the overall... section; and (3) Stopping from 20 miles per hour in a distance, measured from the point at which movement of the service brake pedal or control begins, that is not greater than the distance specified in...
17. Design of MR brake featuring tapered inner magnetic core
Sohn, Jung Woo; Oh, Jong-Soek; Choi, Seung-Bok
2015-04-01
In this work, a new type of MR brake featuring tapered inner magnetic core is proposed and its braking performance is numerically evaluated. In order to achieve high braking torque with restricted size and weight of MR brake system, tapered inner magnetic core is designed and expands the area that the magnetic flux is passing by MR fluid-filled gap. The mathematical braking torque model of the proposed MR brake is derived based on the field-dependent Bingham rheological model of MR fluid. Finite element analysis is carried out to identify electromagnetic characteristics of the conventional and the proposed MR brake configuration. To demonstrate the superiority of the proposed MR brake, the braking torque of the proposed MR brake is numerically evaluated and compared with that of conventional MR brake model.
18. Method and apparatus for electromagnetically braking a motor
NASA Technical Reports Server (NTRS)
Davis, Donald R. (Inventor); Radford, Nicolaus A (Inventor); Permenter, Frank Noble (Inventor); Parsons, Adam H (Inventor); Mehling, Joshua S (Inventor)
2011-01-01
An electromagnetic braking system and method is provided for selectively braking a motor using an electromagnetic brake having an electromagnet, a permanent magnet, a rotor assembly, and a brake pad. The brake assembly applies when the electromagnet is de-energized and releases when the electromagnet is energized. When applied the permanent magnet moves the brake pad into frictional engagement with a housing, and when released the electromagnet cancels the flux of the permanent magnet to allow a leaf spring to move the brake pad away from the housing. A controller has a DC/DC converter for converting a main bus voltage to a lower braking voltage based on certain parameters. The converter utilizes pulse-width modulation (PWM) to regulate the braking voltage. A calibrated gap is defined between the brake pad and permanent magnet when the brake assembly is released, and may be dynamically modified via the controller.
19. What brakes the Crab pulsar?
E-print Network
?adež, A; Barbieri, C; Calvani, M; Naletto, G; Barbieri, M; Ponikvar, D
2015-01-01
Optical observations provide convincing evidence that the optical phase of the Crab pulsar follows the radio one closely. Since optical data do not depend on dispersion measure variations, they provide a robust and independent confirmation of the radio timing solution. The aim of this paper is to find a global mathematical description of Crab pulsar's phase as a function of time for the complete set of published Jodrell Bank radio ephemerides (JBE) in the period 1988-2014. We apply the mathematical techniques developed for analyzing optical observations to the analysis of JBE. We break the whole period into a series of episodes and express the phase of the pulsar in each episode as the sum of two analytical functions. The first function is the best-fitting local braking index law, and the second function represents small residuals from this law with an amplitude of only a few turns, which rapidly relaxes to the local braking index law. From our analysis, we demonstrate that the power law index undergoes "inst...
20. 49 CFR 238.315 - Class IA brake test.
Code of Federal Regulations, 2013 CFR
2013-10-01
...of the set and release of the brakes shall be completed by walking the train to directly observe the set and release of each brake...that operating conditions pose a safety hazard to an inspector walking the brakes, brake indicators may be used to verify the...
1. 49 CFR 238.315 - Class IA brake test.
Code of Federal Regulations, 2010 CFR
2010-10-01
...of the set and release of the brakes shall be completed by walking the train to directly observe the set and release of each brake...that operating conditions pose a safety hazard to an inspector walking the brakes, brake indicators may be used to verify the...
2. 49 CFR 238.315 - Class IA brake test.
Code of Federal Regulations, 2012 CFR
2012-10-01
...of the set and release of the brakes shall be completed by walking the train to directly observe the set and release of each brake...that operating conditions pose a safety hazard to an inspector walking the brakes, brake indicators may be used to verify the...
3. 49 CFR 238.315 - Class IA brake test.
Code of Federal Regulations, 2014 CFR
2014-10-01
...of the set and release of the brakes shall be completed by walking the train to directly observe the set and release of each brake...that operating conditions pose a safety hazard to an inspector walking the brakes, brake indicators may be used to verify the...
4. 49 CFR 238.315 - Class IA brake test.
Code of Federal Regulations, 2011 CFR
2011-10-01
...of the set and release of the brakes shall be completed by walking the train to directly observe the set and release of each brake...that operating conditions pose a safety hazard to an inspector walking the brakes, brake indicators may be used to verify the...
5. Brakes. Auto Mechanics Curriculum Guide. Module 6. Instructor's Guide.
ERIC Educational Resources Information Center
Allain, Robert
This module is the sixth of nine modules in the competency-based Missouri Auto Mechanics Curriculum Guide. Eight units cover: introduction to automotive brake systems; disc and drum brake system components and how they operate; properties of brake fluid and procedures for bleeding the brake system; diagnosing and determining needed repairs on…
6. 49 CFR 238.317 - Class II brake test.
Code of Federal Regulations, 2010 CFR
2010-10-01
... 49 Transportation 4 2010-10-01 2010-10-01 false Class II brake test. 238.317 Section 238.317... Requirements for Tier I Passenger Equipment § 238.317 Class II brake test. (a) A Class II brake test shall be.... In these circumstances, a Class II brake test shall be performed prior to the train's departure...
7. 49 CFR 570.58 - Electric brake system.
Code of Federal Regulations, 2014 CFR
2014-10-01
... 49 Transportation 6 2014-10-01 2014-10-01 false Electric brake system. 570.58 Section 570.58... 10,000 Pounds § 570.58 Electric brake system. (a) Electric brake system integrity. The average brake... manufacturer's maximum current rating. In progressing from zero to maximum, the ammeter indication shall...
8. 49 CFR 570.58 - Electric brake system.
Code of Federal Regulations, 2010 CFR
2010-10-01
... 49 Transportation 6 2010-10-01 2010-10-01 false Electric brake system. 570.58 Section 570.58... 10,000 Pounds § 570.58 Electric brake system. (a) Electric brake system integrity. The average brake... manufacturer's maximum current rating. In progressing from zero to maximum, the ammeter indication shall...
9. 49 CFR 570.58 - Electric brake system.
Code of Federal Regulations, 2011 CFR
2011-10-01
... 49 Transportation 6 2011-10-01 2011-10-01 false Electric brake system. 570.58 Section 570.58... 10,000 Pounds § 570.58 Electric brake system. (a) Electric brake system integrity. The average brake... manufacturer's maximum current rating. In progressing from zero to maximum, the ammeter indication shall...
10. 49 CFR 570.58 - Electric brake system.
Code of Federal Regulations, 2012 CFR
2012-10-01
... 49 Transportation 6 2012-10-01 2012-10-01 false Electric brake system. 570.58 Section 570.58... 10,000 Pounds § 570.58 Electric brake system. (a) Electric brake system integrity. The average brake... manufacturer's maximum current rating. In progressing from zero to maximum, the ammeter indication shall...
11. 49 CFR 570.58 - Electric brake system.
Code of Federal Regulations, 2013 CFR
2013-10-01
... 49 Transportation 6 2013-10-01 2013-10-01 false Electric brake system. 570.58 Section 570.58... 10,000 Pounds § 570.58 Electric brake system. (a) Electric brake system integrity. The average brake... manufacturer's maximum current rating. In progressing from zero to maximum, the ammeter indication shall...
12. Modeling regenerative braking and storage for vehicles
SciTech Connect
Wicks, F.; Donnelly, K.
1997-12-31
The fuel savings benefits of regenerative braking and storage for vehicles are often described but not quantified. For example, the federal government and automobile manufacturers are sponsoring a Program for a New Generation of Vehicles (PGNV) with a goal of obtaining a performance of 80 mpg in a family size car. It is typically suggested that such a vehicle will be a hybrid engine and electric drive with regenerative braking. The authors note that while regenerative braking has the potential of saving fuel, it may also do more harm than good as a result of additional weight, less than ideal charge/discharge efficiency on the batteries or storage flywheels and the limited portion of the entire driving cycle when regenerative braking can be utilized. The authors also noted that if regenerative braking can have a net benefit, it would be on a heavy vehicle such as a municipal bus because of the frequent stop and go requirements for both traffic light and passengers. Thus the authors initiated a study of regenerative braking on such a vehicle. The resulting analysis presented in this paper includes data following municipal buses to define the driving cycle, modeling the bus power requirements from weight, aerodynamics and rolling resistance, and then calculating the fuel saving that could result from an ideal regenerative braking system.
13. Brake wear particle emissions: a review.
PubMed
Grigoratos, Theodoros; Martini, Giorgio
2015-02-01
Traffic-related sources have been recognized as a significant contributor of particulate matter particularly within major cities. Exhaust and non-exhaust traffic-related sources are estimated to contribute almost equally to traffic-related PM10 emissions. Non-exhaust particles can be generated either from non-exhaust sources such as brake, tyre, clutch and road surface wear or already exist in the form of deposited material at the roadside and become resuspended due to traffic-induced turbulence. Among non-exhaust sources, brake wear can be a significant particulate matter (PM) contributor, particularly within areas with high traffic density and braking frequency. Studies mention that in urban environments, brake wear can contribute up to 55 % by mass to total non-exhaust traffic-related PM10 emissions and up to 21 % by mass to total traffic-related PM10 emissions, while in freeways, this contribution is lower due to lower braking frequency. As exhaust emissions control become stricter, relative contributions of non-exhaust sources-and therefore brake wear-to traffic-related emissions will become more significant and will raise discussions on possible regulatory needs. The aim of the present literature review study is to present the state-of-the-art of the different aspects regarding PM resulting from brake wear and provide all the necessary information in terms of importance, physicochemical characteristics, emission factors and possible health effects. PMID:25318420
14. Statistical analysis of brake squeal noise
Oberst, S.; Lai, J. C. S.
2011-06-01
Despite substantial research efforts applied to the prediction of brake squeal noise since the early 20th century, the mechanisms behind its generation are still not fully understood. Squealing brakes are of significant concern to the automobile industry, mainly because of the costs associated with warranty claims. In order to remedy the problems inherent in designing quieter brakes and, therefore, to understand the mechanisms, a design of experiments study, using a noise dynamometer, was performed by a brake system manufacturer to determine the influence of geometrical parameters (namely, the number and location of slots) of brake pads on brake squeal noise. The experimental results were evaluated with a noise index and ranked for warm and cold brake stops. These data are analysed here using statistical descriptors based on population distributions, and a correlation analysis, to gain greater insight into the functional dependency between the time-averaged friction coefficient as the input and the peak sound pressure level data as the output quantity. The correlation analysis between the time-averaged friction coefficient and peak sound pressure data is performed by applying a semblance analysis and a joint recurrence quantification analysis. Linear measures are compared with complexity measures (nonlinear) based on statistics from the underlying joint recurrence plots. Results show that linear measures cannot be used to rank the noise performance of the four test pad configurations. On the other hand, the ranking of the noise performance of the test pad configurations based on the noise index agrees with that based on nonlinear measures: the higher the nonlinearity between the time-averaged friction coefficient and peak sound pressure, the worse the squeal. These results highlight the nonlinear character of brake squeal and indicate the potential of using nonlinear statistical analysis tools to analyse disc brake squeal.
15. Performance of an aircraft tire under cyclic braking and of a currently operational antiskid braking system
NASA Technical Reports Server (NTRS)
Tanner, J. A.
1972-01-01
An experimental investigation was conducted to study the performance of an aircraft tire under cyclic braking conditions and to study the performance of a currently operational aircraft antiskid braking system. Dry, damp, and flooded runway surface conditions were used in the investigation. The results indicated that under cyclic braking conditions the braking and cornering-force friction coefficients may be influenced by fluctuations in the vertical load, flexibility in the wheel support, and the spring coupling between the wheel and the tire-pavement interface. The cornering capability was shown to be negligible at wheel slip ratios well below a locked-wheel skid under all test surface conditions. The maximum available brake-force friction coefficient was shown to be dependent upon the runway surface condition, upon velocity, and, for wet runways, upon tire differences. Moderate reductions in vertical load and brake system pressure did not significantly affect the overall wet-runway performance of the tire.
16. Screw-released roller brake
NASA Technical Reports Server (NTRS)
Vranish, John M. (Inventor)
1999-01-01
A screw-released roller brake including an input drive assembly, an output drive assembly, a plurality of locking sprags, a mechanical tripper nut for unlocking the sprags, and a casing therefor. The sprags consist of three dimensional (3-D) sprag members having pairs of contact surface regions which engage respective pairs of contact surface regions included in angular grooves or slots formed in the casing and the output drive assembly. The sprags operate to lock the output drive assembly to the casing to prevent rotation thereof in an idle mode of operation. In a drive mode of operation, the tripper is either self actuated or motor driven and is translated linearly up and down against a spline and at the limit of its travel rotates the sprags which unlock while coupling the input drive assembly to the output drive assembly so as to impart a turning motion thereto in either a clockwise or counterclockwise direction.
17. Thermal analysis and temperature characteristics of a braking resistor for high-speed trains for changes in the braking current
Lee, Dae-Dong; Kang, Hyun-Il; Shim, Jae-Myung
2015-09-01
Electric brake systems are used in high-speed trains to brake trains by converting the kinetic energy of a railway vehicle to electric energy. The electric brake system consists of a regenerative braking system and a dynamic braking system. When the electric energy generated during the dynamic braking process is changed to heat through the braking resistor, the braking resistor can overheat; thus, failures can occur to the motor block. In this paper, a braking resistor for a high-speed train was used to perform thermal analyses and tests, and the results were analyzed. The analyzed data were used to estimate the dependence of the brake currents and the temperature rises on speed changes up to 300 km/h, at which a test could not be performed.
18. Optimal design and selection of magneto-rheological brake types based on braking torque and mass
Nguyen, Q. H.; Lang, V. T.; Choi, S. B.
2015-06-01
In developing magnetorheological brakes (MRBs), it is well known that the braking torque and the mass of the MRBs are important factors that should be considered in the product’s design. This research focuses on the optimal design of different types of MRBs, from which we identify an optimal selection of MRB types, considering braking torque and mass. In the optimization, common types of MRBs such as disc-type, drum-type, hybrid-type, and T-shape types are considered. The optimization problem is to find an optimal MRB structure that can produce the required braking torque while minimizing its mass. After a brief description of the configuration of the MRBs, the MRBs’ braking torque is derived based on the Herschel-Bulkley rheological model of the magnetorheological fluid. Then, the optimal designs of the MRBs are analyzed. The optimization objective is to minimize the mass of the brake while the braking torque is constrained to be greater than a required value. In addition, the power consumption of the MRBs is also considered as a reference parameter in the optimization. A finite element analysis integrated with an optimization tool is used to obtain optimal solutions for the MRBs. Optimal solutions of MRBs with different required braking torque values are obtained based on the proposed optimization procedure. From the results, we discuss the optimal selection of MRB types, considering braking torque and mass.
19. Parker Hybrid Hydraulic Drivetrain Demonstration
SciTech Connect
Collett, Raymond; Howland, James; Venkiteswaran, Prasad
2014-03-31
This report examines the benefits of Parker Hannifin hydraulic hybrid brake energy recovery systems used in commercial applications for vocational purposes. A detailed background on the problem statement being addressed as well as the solution set specific for parcel delivery will be provided. Objectives of the demonstration performed in high start & stop applications included opportunities in fuel usage reduction, emissions reduction, vehicle productivity, and vehicle maintenance. Completed findings during the demonstration period and parallel investigations with NREL, CALSTART, along with a literature review will be provided herein on this research area. Lastly, results identified in the study by third parties validated the savings potential in fuel reduction of on average of 19% to 52% over the baseline in terms of mpg (Lammert, 2014, p11), Parker data for parcel delivery vehicles in the field parallels this at a range of 35% - 50%, emissions reduction of 17.4% lower CO2 per mile and 30.4% lower NOx per mile (Gallo, 2014, p15), with maintenance improvement in the areas of brake and starter replacement, while leaving room for further study in the area of productivity in terms of specific metrics that can be applied and studied.
20. Hydraulic system for a ratio change transmission
DOEpatents
Kalns, Ilmars (Northville, MI)
1981-01-01
Disclosed is a drive assembly (10) for an electrically powered vehicle (12). The assembly includes a transaxle (16) having a two-speed transmission (40) and a drive axle differential (46) disposed in a unitary housing assembly (38), an oil-cooled prime mover or electric motor (14) for driving the transmission input shaft (42), an adapter assembly (24) for supporting the prime mover on the transaxle housing assembly, and a hydraulic system (172) providing pressurized oil flow for cooling and lubricating the electric motor and transaxle and for operating a clutch (84) and a brake (86) in the transmission to shift between the two-speed ratios of the transmission. The adapter assembly allows the prime mover to be supported in several positions on the transaxle housing. The brake is spring-applied and locks the transmission in its low-speed ratio should the hydraulic system fail. The hydraulic system pump is driven by an electric motor (212) independent of the prime mover and transaxle.
1. An engine air-brake integration study
E-print Network
Mulchandani, Hiten
2011-01-01
The feasibility of operating an engine air-brake (EAB) integrated with a pylon duct bifurcation in a realistic aircraft engine environment has been analyzed. The EAB uses variable exit guide vanes downstream of a high ...
2. Power-Factor Controller With Regenerative Braking
NASA Technical Reports Server (NTRS)
Nola, F. J.
1982-01-01
Modified power-factor motor-control circuit operates motor as a phase-controlled generator when load attempts to turn at higher than synchronous speed. An induction motor is required to act at times as a brake. Circuit modification allows power-factor controller to save energy in motoring mode and convert automatically to an induction-generator controller in generating, or braking, mode.
3. Method and apparatus for wind turbine braking
DOEpatents
Barbu, Corneliu (Laguna Hills, CA); Teichmann, Ralph (Nishkayuna, NY); Avagliano, Aaron (Houston, TX); Kammer, Leonardo Cesar (Niskayuna, NY); Pierce, Kirk Gee (Simpsonville, SC); Pesetsky, David Samuel (Greenville, SC); Gauchel, Peter (Muenster, DE)
2009-02-10
A method for braking a wind turbine including at least one rotor blade coupled to a rotor. The method includes selectively controlling an angle of pitch of the at least one rotor blade with respect to a wind direction based on a design parameter of a component of the wind turbine to facilitate reducing a force induced into the wind turbine component as a result of braking.
4. Brake for counter rotating bladed members
SciTech Connect
Cedoz, R.W.
1987-02-10
This patent describes a propulsion system including a gas turbine engine having an output shaft and a gear drive having a planetary gear set with a first element connected to the engine output shaft and a second element connected to a first bladed member and a third element connected to a second bladed member whereby the first and second bladed members are rotated in opposite directions by the output shaft. A brake is described comprising, a first transfer shaft supported on a stationary housing for rotation about an axis of the latter, a second transfer shaft supported on the stationary housing for rotation about the axis, gear means between one of the counter rotating bladed members and the first transfer shaft and gear means between the other of the counter rotating bladed members and the second transfer shaft. The brake also includes a selectively operable brake actuator on the housing movable between an extended position and a retracted position, and friction means between the brake actuator and each of first and second transfer shafts operative in the extended position of the brake actuator to simultaneously frictionally retard rotation of each of the first and the second transfer shafts whereby each of the counter rotating bladed members is simultaneously braked.
5. Constraining the Braking Indices of Magnetars
E-print Network
Gao, Z F; Wang, N; Yuan, J P; Peng, Q H; Du, Y J
2015-01-01
Due to the lack of long term pulsed emission in quiescence and the strong timing noise, it is impossible to directly measure the braking index $n$ of a magnetar. Based on the estimated ages of their potentially associated supernova remnants (SNRs), we estimate the values of $n$ of nine magnetars with SNRs, and find that they cluster in a range of $1\\sim$41. Six magnetars have smaller braking indices of $13$ for other three magnetars are attributed to the decay of external braking torque, which might be caused by magnetic field decay. We estimate the possible wind luminosities for the magnetars with $13$ within the updated magneto-thermal evolution models. We point out that there could be some connections between the magnetar's anti-glitch event and its braking index, and the magnitude of $n$ should be taken into account when explaining the event. Although the constrained range of the magnetars' braking indices is tentative, our method provides an effective way to constrain the magnetars' braking indices if th...
6. Automated visual inspection of brake shoe wear
Lu, Shengfang; Liu, Zhen; Nan, Guo; Zhang, Guangjun
2015-10-01
With the rapid development of high-speed railway, the automated fault inspection is necessary to ensure train's operation safety. Visual technology is paid more attention in trouble detection and maintenance. For a linear CCD camera, Image alignment is the first step in fault detection. To increase the speed of image processing, an improved scale invariant feature transform (SIFT) method is presented. The image is divided into multiple levels of different resolution. Then, we do not stop to extract the feature from the lowest resolution to the highest level until we get sufficient SIFT key points. At that level, the image is registered and aligned quickly. In the stage of inspection, we devote our efforts to finding the trouble of brake shoe, which is one of the key components in brake system on electrical multiple units train (EMU). Its pre-warning on wear limitation is very important in fault detection. In this paper, we propose an automatic inspection approach to detect the fault of brake shoe. Firstly, we use multi-resolution pyramid template matching technology to fast locate the brake shoe. Then, we employ Hough transform to detect the circles of bolts in brake region. Due to the rigid characteristic of structure, we can identify whether the brake shoe has a fault. The experiments demonstrate that the way we propose has a good performance, and can meet the need of practical applications.
7. Consideration of Materials for Aircraft Brakes
NASA Technical Reports Server (NTRS)
Peterson, M. B.; Ho, T.
1972-01-01
An exploratory investigation was conducted concerning materials and their properties for use in aircraft brakes. Primary consideration was given to the heat dissipation and the frictional behavior of materials. Used brake pads and rotors were analyzed as part of the investigation. A simple analysis was conducted in order to determine the most significant factors which affect surface temperatures. It was found that where size and weight restrictions are necessary, the specific heat of the material, and maintaining uniform contact area are the most important factors. A criterion was suggested for optimum sizing of the brake disks. Bench friction tests were run with brake materials. It was found that there is considerable friction variation due to the formation and removal of surface oxide films. Other causes of friction variations are surface softening and melting. The friction behavior at high temperature was found to be more characteristic of the steel surface rather than the copper brake material. It is concluded that improved brake materials are feasible.
8. Modeling hydraulic regenerative hybrid vehicles using AMESim and Matlab/Simulink
Lynn, Alfred; Smid, Edzko; Eshraghi, Moji; Caldwell, Niall; Woody, Dan
2005-05-01
This paper presents the overview of the simulation modeling of a hydraulic system with regenerative braking used to improve vehicle emissions and fuel economy. Two simulation software packages were used together to enhance the simulation capability for fuel economy results and development of vehicle and hybrid control strategy. AMESim, a hydraulic simulation software package modeled the complex hydraulic circuit and component hardware and was interlinked with a Matlab/Simulink model of the vehicle, engine and the control strategy required to operate the vehicle and the hydraulic hybrid system through various North American and European drive cycles.
9. Modelling and validation of magnetorheological brake responses using parametric approach
Z, Zainordin A.; A, Abdullah M.; K, Hudha
2013-12-01
Magnetorheological brake (MR Brake) is one x-by-wire systems which performs better than conventional brake systems. MR brake consists of a rotating disc that is immersed with Magnetorheological Fluid (MR Fluid) in an enclosure of an electromagnetic coil. The applied magnetic field will increase the yield strength of the MR fluid where this fluid was used to decrease the speed of the rotating shaft. The purpose of this paper is to develop a mathematical model to represent MR brake with a test rig. The MR brake model is developed based on actual torque characteristic which is coupled with motion of a test rig. Next, the experimental are performed using MR brake test rig and obtained three output responses known as angular velocity response, torque response and load displacement response. Furthermore, the MR brake was subjected to various current. Finally, the simulation results of MR brake model are then verified with experimental results.
10. Geometric optimal design of a magneto-rheological brake considering different shapes for the brake envelope
Nguyen, Q. H.; Lang, V. T.; Nguyen, N. D.; Choi, S. B.
2014-01-01
When designing a magneto-rheological brake (MRB), it is well known that the shape of the brake envelope significantly affects the performance characteristics of the brake. In this study, different shapes for the MR brake envelope, such as rectangular, polygonal or spline shape, are considered and the most suitable shape identified. MRBs with different envelope shapes are introduced followed by the derivation of the braking torque based on Bingham-plastic behavior of the magneto-rheological fluid (MRF). Optimization of the design of the MRB with different envelope shapes is then done. The optimization problem is to find the optimal value for the significant geometric dimensions of the MRB that can produce a certain required braking torque while the brake mass is minimized. A finite element analysis integrated with an optimization tool is employed to obtain optimal solutions for the MRBs. From the results, the most suitable shape for the brake envelope is identified and discussed with the reduction of mass. In addition, the results of the analysis are compared with the experimental results to verify the proposed optimal design characteristics.
11. Brake squeal reduction of vehicle disc brake system with interval parameters by uncertain optimization
Lü, Hui; Yu, Dejie
2014-12-01
An uncertain optimization method for brake squeal reduction of vehicle disc brake system with interval parameters is presented in this paper. In the proposed method, the parameters of frictional coefficient, material properties and the thicknesses of wearing components are treated as uncertain parameters, which are described as interval variables. Attention is focused on the stability analysis of a brake system in squeal, and the stability of brake system is investigated via the complex eigenvalue analysis (CEA) method. The dominant unstable mode is extracted by performing CEA based on a linear finite element (FE) model, and the negative damping ratio corresponding to the dominant unstable mode is selected as the indicator of instability. The response surface method (RSM) is applied to approximate the implicit relationship between the unstable mode and the system parameters. A reliability-based optimization model for improving the stability of the vehicle disc brake system with interval parameters is constructed based on RSM, interval analysis and reliability analysis. The Genetic Algorithm is used to get the optimal values of design parameters from the optimization model. The stability analysis and optimization of a disc brake system are carried out, and the results show that brake squeal propensity can be reduced by using stiffer back plates. The proposed approach can be used to improve the stability of the vehicle disc brake system with uncertain parameters effectively.
12. Electromagnetic brake/clutch device
NASA Technical Reports Server (NTRS)
Vranish, John M. (inventor)
1994-01-01
An electromagnetic brake/clutch device includes a drive shaft supported by at least one bearing for transmitting torque, a housing, affixed to prevent its rotation, surrounding the drive shaft, and an electromagnetically activated device within the housing to selectively prevent and allow rotation of the drive shaft. The electromagnetically activated device includes a plurality of cammed rollers to prevent counter-clockwise rotation of the drive shaft. The drive shaft includes a circumferential disk and the housing includes a reaction ring for engagement with the plurality of cammed rollers. The plurality of cammed rollers are released from engagement with the circumferential disk and the reaction ring by a plurality of tripping mechanisms within the housing. The tripping action uses the locking force to act as a release force merely by changing the boundary conditions of the roller interface angles. The tripping mechanisms include trippers for disengaging the plurality of cammed rollers and an anvil shaped portion for providing lateral movement of the trippers. The plurality of cammed rollers is preloaded to engagement with the circumferential disk and reaction ring by a spring, and is located with respect to an adjacent tripping mechanism with another spring.
13. Braking Index of Isolated Pulsars
Hamil, Oliver; Stone, Jirina; Urbanec, Martin; Urbancova, Gabriela
2015-04-01
Isolated pulsars are rotating neutron stars with accurately measured angular velocities ?, and their time derivatives which show unambiguously that the pulsars are slowing down. The exact mechanism of the spin-down is a question of debate in detail, but the commonly accepted view is that it arises through emission of magnetic dipole radiation (MDR). The energy loss by a rotating pulsar is proportional to a model dependent power of ?. This relation leads to the power law ?? = -K ?n where n is called the braking index, equal to the ratio (???)/ ??2 . The simple MDR model predicts the value of n = 3, but observations of isolated pulsars provide rather precise values of n, individually accurate to a few percent or better, in the range 1 < n < 2.8, which is consistently less than the predictions of the MDR model. In this work, we study the dynamical limits of the MDR model as a function of angular velocity. The effects of variation in the rest mass, the moment of inertia, and the dependence on a realistic Equation of State of the rotating star are considered. Furthermore, we introduce a simulated superfluid effect by which the angular momentum of the core is eliminated from the calculation.
14. Adaptive controller for regenerative and friction braking system
DOEpatents
Davis, R.I.
1990-10-16
A regenerative and friction braking system for a vehicle having one or more road wheels driven by an electric traction motor includes a driver responsive device for producing a brake demand signal having a magnitude corresponding to the level of braking force selected by the driver and friction and regenerative brakes operatively connected with the road wheels of the vehicle. A system according to this invention further includes control means for operating the friction and regenerative braking subsystems so that maximum brake torques sustainable by the road wheels of the vehicle without skidding or slipping will not be exceeded. 8 figs.
15. Adaptive controller for regenerative and friction braking system
DOEpatents
Davis, Roy I. (Ypsilanti, MI)
1990-01-01
A regenerative and friction braking system for a vehicle having one or more roadwheels driven by an electric traction motor includes a driver responsive device for producing a brake demand signal having a magnitude corresponding to the level of braking force selected by the driver and friction and regenerative brakes operatively connected with the roadwheels of the vehicle. A system according to this invention further includes control means for operating the friction and regenerative braking subsystems so that maximum brake torques sustainable by the roadwheels of the vehicle without skidding or slipping will not be exceeded.
16. Well servicing methods using a hydraulic actuated workover mast
SciTech Connect
Maroney, P.F.; Blalock, F.C.
1988-07-12
A method is described of removing a stuck object from a well by operating a hydraulically operated workover rig which has a mast with a crown and a traveling block, a first winch with a brake, a first hydraulic motor, a line connected to the winch, and tubing in a well, which comprises: (a) connecting the end of the line to the tubing; (b) providing hydraulic power fluid to drive the first motor to drive the first winch to put high stress on the tubing; (c) abruptly cutting off the hydraulic power fluid to the motor to allow the tubing to contract; (d) then operating the brake to impart a shock down the tubing; (e) repeating steps (b) and (d) above as necessary until the object becomes unstuck. A method is also described of lowering objects into a well bore using a mast having a crown block, a first drum on which a line is mounted, a first hydraulic motor for driving the first drum.
17. Hydropneumatic energy reservoir for accumulating the braking energy recovered on a vehicle
SciTech Connect
Michel, R.
1985-06-04
Hydropneumatic energy reservoir for accumulating the braking energy recovered on a vehicle by means of a hydrostatic energy recovery-restoration device, combined or not with the vehicle transmission and working between a high-pressure accumulator and a low-pressure accumulator, characterized in that it comprises several oblong cylindrical hydropneumatic accumulators connected hydraulically in parallel and placed side by side inside a single casing of small height, the space included between the said casing and the said accumulators forming the low-pressure accumulator.
18. 2. OBLIQUE VIEW OF HOIST, SHOWING CABLE DRUM, WOODEN BRAKE ...
Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey
2. OBLIQUE VIEW OF HOIST, SHOWING CABLE DRUM, WOODEN BRAKE SHOES, BRAKE HANDLE, AND REDUCTION GEARS, LOOKING SOUTHWEST - Buffalo Coal Mine, Vulcan Cable Hoist, Wishbone Hill, Southeast end, near Moose Creek, Sutton, Matanuska-Susitna Borough, AK
19. 49 CFR 570.58 - Electric brake system.
Code of Federal Regulations, 2010 CFR
2010-10-01
...2010-10-01 2010-10-01 false Electric brake system. 570.58 ...DEPARTMENT OF TRANSPORTATION VEHICLE IN USE INSPECTION STANDARDS Vehicles With GVWR of More Than 10,000 Pounds § 570.58 Electric brake system. (a)...
20. 14 CFR 27.493 - Braked roll conditions.
Code of Federal Regulations, 2013 CFR
2013-01-01
...Strength Requirements Ground Loads § 27.493 Braked roll conditions. Under braked roll conditions with the shock absorbers in their static positions— (a) The limit vertical load must be based on a load factor of at least—...
1. 14 CFR 29.493 - Braked roll conditions.
Code of Federal Regulations, 2013 CFR
2013-01-01
...Strength Requirements Ground Loads § 29.493 Braked roll conditions. Under braked roll conditions with the shock absorbers in their static positions— (a) The limit vertical load must be based on a load factor of at least—...
2. 14 CFR 27.493 - Braked roll conditions.
Code of Federal Regulations, 2014 CFR
2014-01-01
...Strength Requirements Ground Loads § 27.493 Braked roll conditions. Under braked roll conditions with the shock absorbers in their static positions— (a) The limit vertical load must be based on a load factor of at least—...
3. 14 CFR 29.493 - Braked roll conditions.
Code of Federal Regulations, 2014 CFR
2014-01-01
...Strength Requirements Ground Loads § 29.493 Braked roll conditions. Under braked roll conditions with the shock absorbers in their static positions— (a) The limit vertical load must be based on a load factor of at least—...
4. 30 CFR 57.14102 - Brakes for rail equipment.
Code of Federal Regulations, 2012 CFR
2012-07-01
...NONMETAL MINE SAFETY AND HEALTH SAFETY AND HEALTH STANDARDS-UNDERGROUND METAL AND NONMETAL MINES Machinery and Equipment Safety...14102 Brakes for rail equipment. Braking systems on railroad cars and locomotives shall be maintained in functional...
5. 30 CFR 57.14102 - Brakes for rail equipment.
Code of Federal Regulations, 2014 CFR
2014-07-01
...NONMETAL MINE SAFETY AND HEALTH SAFETY AND HEALTH STANDARDS-UNDERGROUND METAL AND NONMETAL MINES Machinery and Equipment Safety...14102 Brakes for rail equipment. Braking systems on railroad cars and locomotives shall be maintained in functional...
6. 30 CFR 57.14102 - Brakes for rail equipment.
Code of Federal Regulations, 2011 CFR
2011-07-01
...NONMETAL MINE SAFETY AND HEALTH SAFETY AND HEALTH STANDARDS-UNDERGROUND METAL AND NONMETAL MINES Machinery and Equipment Safety...14102 Brakes for rail equipment. Braking systems on railroad cars and locomotives shall be maintained in functional...
7. 30 CFR 57.14102 - Brakes for rail equipment.
Code of Federal Regulations, 2010 CFR
2010-07-01
...NONMETAL MINE SAFETY AND HEALTH SAFETY AND HEALTH STANDARDS-UNDERGROUND METAL AND NONMETAL MINES Machinery and Equipment Safety...14102 Brakes for rail equipment. Braking systems on railroad cars and locomotives shall be maintained in functional...
8. 30 CFR 57.14102 - Brakes for rail equipment.
Code of Federal Regulations, 2013 CFR
2013-07-01
...NONMETAL MINE SAFETY AND HEALTH SAFETY AND HEALTH STANDARDS-UNDERGROUND METAL AND NONMETAL MINES Machinery and Equipment Safety...14102 Brakes for rail equipment. Braking systems on railroad cars and locomotives shall be maintained in functional...
9. A pressure control scheme for air brakes in commercial vehicles
E-print Network
Bowlin, Christopher Leland
2007-04-25
This research is focused on developing a control scheme for regulating the pressure in the brake chamber of an air brake system found in most commercial vehicles like trucks, tractor-trailers and buses. Such a control ...
10. 49 CFR 232.109 - Dynamic brake requirements.
Code of Federal Regulations, 2014 CFR
2014-10-01
... 49 Transportation 4 2014-10-01 2014-10-01 false Dynamic brake requirements. 232.109 Section 232... TRAINS AND EQUIPMENT; END-OF-TRAIN DEVICES General Requirements § 232.109 Dynamic brake requirements. (a... operational status of the dynamic brakes on all locomotive units in the consist at the initial terminal for...
11. 49 CFR 232.109 - Dynamic brake requirements.
Code of Federal Regulations, 2010 CFR
2010-10-01
... 49 Transportation 4 2010-10-01 2010-10-01 false Dynamic brake requirements. 232.109 Section 232... TRAINS AND EQUIPMENT; END-OF-TRAIN DEVICES General Requirements § 232.109 Dynamic brake requirements. (a... operational status of the dynamic brakes on all locomotive units in the consist at the initial terminal for...
12. 49 CFR 232.109 - Dynamic brake requirements.
Code of Federal Regulations, 2013 CFR
2013-10-01
... 49 Transportation 4 2013-10-01 2013-10-01 false Dynamic brake requirements. 232.109 Section 232... TRAINS AND EQUIPMENT; END-OF-TRAIN DEVICES General Requirements § 232.109 Dynamic brake requirements. (a... operational status of the dynamic brakes on all locomotive units in the consist at the initial terminal for...
13. 49 CFR 232.109 - Dynamic brake requirements.
Code of Federal Regulations, 2012 CFR
2012-10-01
... 49 Transportation 4 2012-10-01 2012-10-01 false Dynamic brake requirements. 232.109 Section 232... TRAINS AND EQUIPMENT; END-OF-TRAIN DEVICES General Requirements § 232.109 Dynamic brake requirements. (a... operational status of the dynamic brakes on all locomotive units in the consist at the initial terminal for...
14. 49 CFR 229.57 - Foundation brake gear.
Code of Federal Regulations, 2013 CFR
2013-10-01
... 49 Transportation 4 2013-10-01 2013-10-01 false Foundation brake gear. 229.57 Section 229.57... Foundation brake gear. A lever, rod, brake beam, hanger, or pin may not be worn through more than 30 percent... to the wheel to prevent localized thermal stress in the edge of the rim or the flange....
15. 49 CFR 229.57 - Foundation brake gear.
Code of Federal Regulations, 2012 CFR
2012-10-01
... 49 Transportation 4 2012-10-01 2012-10-01 false Foundation brake gear. 229.57 Section 229.57... Foundation brake gear. A lever, rod, brake beam, hanger, or pin may not be worn through more than 30 percent... to the wheel to prevent localized thermal stress in the edge of the rim or the flange....
16. 49 CFR 229.57 - Foundation brake gear.
Code of Federal Regulations, 2014 CFR
2014-10-01
... 49 Transportation 4 2014-10-01 2014-10-01 false Foundation brake gear. 229.57 Section 229.57... Foundation brake gear. A lever, rod, brake beam, hanger, or pin may not be worn through more than 30 percent... to the wheel to prevent localized thermal stress in the edge of the rim or the flange....
17. 49 CFR 229.57 - Foundation brake gear.
Code of Federal Regulations, 2010 CFR
2010-10-01
... 49 Transportation 4 2010-10-01 2010-10-01 false Foundation brake gear. 229.57 Section 229.57... Foundation brake gear. A lever, rod, brake beam, hanger, or pin may not be worn through more than 30 percent... to the wheel to prevent localized thermal stress in the edge of the rim or the flange....
18. 49 CFR 229.57 - Foundation brake gear.
Code of Federal Regulations, 2011 CFR
2011-10-01
... 49 Transportation 4 2011-10-01 2011-10-01 false Foundation brake gear. 229.57 Section 229.57... Foundation brake gear. A lever, rod, brake beam, hanger, or pin may not be worn through more than 30 percent... to the wheel to prevent localized thermal stress in the edge of the rim or the flange....
19. 49 CFR 393.48 - Brakes to be operative.
Code of Federal Regulations, 2010 CFR
2010-10-01
... times be capable of operating. (b) Devices to reduce or remove front-wheel braking effort. A commercial motor vehicle may be equipped with a device to reduce the front wheel braking effort (or in the case of...-wheel braking effort) if that device meets the applicable requirements of paragraphs (b)(1) and (2)...
20. 49 CFR 393.48 - Brakes to be operative.
Code of Federal Regulations, 2013 CFR
2013-10-01
... times be capable of operating. (b) Devices to reduce or remove front-wheel braking effort. A commercial motor vehicle may be equipped with a device to reduce the front wheel braking effort (or in the case of...-wheel braking effort) if that device meets the applicable requirements of paragraphs (b)(1) and (2)...
1. 49 CFR 393.48 - Brakes to be operative.
Code of Federal Regulations, 2011 CFR
2011-10-01
... times be capable of operating. (b) Devices to reduce or remove front-wheel braking effort. A commercial motor vehicle may be equipped with a device to reduce the front wheel braking effort (or in the case of...-wheel braking effort) if that device meets the applicable requirements of paragraphs (b)(1) and (2)...
2. 30 CFR 75.1404-1 - Braking system.
Code of Federal Regulations, 2011 CFR
2011-07-01
... 30 Mineral Resources 1 2011-07-01 2011-07-01 false Braking system. 75.1404-1 Section 75.1404-1 Mineral Resources MINE SAFETY AND HEALTH ADMINISTRATION, DEPARTMENT OF LABOR COAL MINE SAFETY AND HEALTH MANDATORY SAFETY STANDARDS-UNDERGROUND COAL MINES Hoisting and Mantrips § 75.1404-1 Braking system. A locomotive equipped with a dual braking...
3. 30 CFR 75.1400-1 - Hoists; brakes, capability.
Code of Federal Regulations, 2010 CFR
2010-07-01
... 30 Mineral Resources 1 2010-07-01 2010-07-01 false Hoists; brakes, capability. 75.1400-1 Section 75.1400-1 Mineral Resources MINE SAFETY AND HEALTH ADMINISTRATION, DEPARTMENT OF LABOR COAL MINE... Hoists; brakes, capability. Brakes on hoists used to transport persons shall be capable of stopping...
4. 30 CFR 75.1404-1 - Braking system.
Code of Federal Regulations, 2010 CFR
2010-07-01
... 30 Mineral Resources 1 2010-07-01 2010-07-01 false Braking system. 75.1404-1 Section 75.1404-1 Mineral Resources MINE SAFETY AND HEALTH ADMINISTRATION, DEPARTMENT OF LABOR COAL MINE SAFETY AND HEALTH MANDATORY SAFETY STANDARDS-UNDERGROUND COAL MINES Hoisting and Mantrips § 75.1404-1 Braking system. A locomotive equipped with a dual braking...
5. 30 CFR 75.1400-1 - Hoists; brakes, capability.
Code of Federal Regulations, 2011 CFR
2011-07-01
... 30 Mineral Resources 1 2011-07-01 2011-07-01 false Hoists; brakes, capability. 75.1400-1 Section 75.1400-1 Mineral Resources MINE SAFETY AND HEALTH ADMINISTRATION, DEPARTMENT OF LABOR COAL MINE... Hoists; brakes, capability. Brakes on hoists used to transport persons shall be capable of stopping...
6. Brake Wear and Performance Test Final December 2009
E-print Network
Brake Wear and Performance Test Final Report December 2009 #12;FOREWORD This study focuses on using and quantifying associated brake component wear as a function of mileage. Additionally, ORNL was tasked. Report Date December 2009 4. Title and Subtitle Brake Wear and Performance Test Final Report 6
7. 30 CFR 75.1404 - Automatic brakes; speed reduction gear.
Code of Federal Regulations, 2012 CFR
2012-07-01
... 30 Mineral Resources 1 2012-07-01 2012-07-01 false Automatic brakes; speed reduction gear. 75.1404... Automatic brakes; speed reduction gear. Each locomotive and haulage car used in an underground coal mine... brakes, locomotives and haulage cars shall be subject to speed reduction gear, or other similar...
8. 30 CFR 75.1404 - Automatic brakes; speed reduction gear.
Code of Federal Regulations, 2011 CFR
2011-07-01
... 30 Mineral Resources 1 2011-07-01 2011-07-01 false Automatic brakes; speed reduction gear. 75.1404... Automatic brakes; speed reduction gear. Each locomotive and haulage car used in an underground coal mine... brakes, locomotives and haulage cars shall be subject to speed reduction gear, or other similar...
9. 30 CFR 75.1404 - Automatic brakes; speed reduction gear.
Code of Federal Regulations, 2010 CFR
2010-07-01
... 30 Mineral Resources 1 2010-07-01 2010-07-01 false Automatic brakes; speed reduction gear. 75.1404... Automatic brakes; speed reduction gear. Each locomotive and haulage car used in an underground coal mine... brakes, locomotives and haulage cars shall be subject to speed reduction gear, or other similar...
10. 30 CFR 75.1404 - Automatic brakes; speed reduction gear.
Code of Federal Regulations, 2013 CFR
2013-07-01
... 30 Mineral Resources 1 2013-07-01 2013-07-01 false Automatic brakes; speed reduction gear. 75.1404... Automatic brakes; speed reduction gear. Each locomotive and haulage car used in an underground coal mine... brakes, locomotives and haulage cars shall be subject to speed reduction gear, or other similar...
11. 30 CFR 75.1404 - Automatic brakes; speed reduction gear.
Code of Federal Regulations, 2014 CFR
2014-07-01
... 30 Mineral Resources 1 2014-07-01 2014-07-01 false Automatic brakes; speed reduction gear. 75.1404... Automatic brakes; speed reduction gear. Each locomotive and haulage car used in an underground coal mine... brakes, locomotives and haulage cars shall be subject to speed reduction gear, or other similar...
12. 49 CFR 570.6 - Brake power unit.
Code of Federal Regulations, 2010 CFR
2010-10-01
... 49 Transportation 6 2010-10-01 2010-10-01 false Brake power unit. 570.6 Section 570.6... Pounds or Less § 570.6 Brake power unit. (a) Vacuum hoses shall not be collapsed, abraded, broken... power assist system. This test is not applicable to vehicles equipped with full power brake system...
13. 49 CFR 570.6 - Brake power unit.
Code of Federal Regulations, 2011 CFR
2011-10-01
... 49 Transportation 6 2011-10-01 2011-10-01 false Brake power unit. 570.6 Section 570.6... Pounds or Less § 570.6 Brake power unit. (a) Vacuum hoses shall not be collapsed, abraded, broken... power assist system. This test is not applicable to vehicles equipped with full power brake system...
14. The design of aircraft brake systems, employing cooling to increase brake life
NASA Technical Reports Server (NTRS)
Scaringe, R. P.; Ho, T. L.; Peterson, M. B.
1975-01-01
A research program was initiated to determine the feasibility of using cooling to increase brake life. An air cooling scheme was proposed, constructed and tested with various designs. Straight and curved slotting of the friction material was tested. A water cooling technique, similar to the air cooling procedure, was evaluated on a curved slotted rotor. Also investigated was the possibility of using a phase-change material within the rotor to absorb heat during braking. Various phase-changing materials were tabulated and a 50%, (by weight) LiF - BeF2 mixing was chosen. It was shown that corrosion was not a problem with this mixture. A preliminary design was evaluated on an actual brake. Results showed that significant improvements in lowering the surface temperature of the brake occurred when air or water cooling was used in conjunction with curved slotted rotors.
15. From the Kinetic Energy Recovery System to the Thermo-Hydraulic Hybrid Motor Vehicle
Cristescu, Corneliu; Drumea, Petrin; Guta, Dragos; Dumitrescu, Catalin
2011-12-01
The paper presents some theoretical and experimental results obtained by the Hydraulics and Pneumatics Research Institute INOE 2000-IHP with its partners, regarding the creating of one hydraulic system able to recovering the kinetic energy of the motor vehicles, in the braking phases, and use this recovered energy in the starting and accelerating phases. Also, in the article is presented a testing stand, which was especially designed for testing the hydraulic system for recovery the kinetic energy. Through mounting of the kinetic energy recovering hydraulic system, on one motor vehicle, this vehicle became a thermo-hydraulic hybrid vehicle. Therefore, the dynamic behavior was analyzed for the whole hybrid motor vehicle, which includes the energy recovery system. The theoretical and experimental results demonstrate the possible performances of the hybrid vehicle and that the kinetic energy recovery hydraulic systems are good means to increase energy efficiency of the road motor vehicles and to decrease of the fuel consumption.
16. 14 CFR 23.735 - Brakes.
Code of Federal Regulations, 2014 CFR
2014-01-01
...=Kinetic energy per wheel (ft.-lb.); W=Design landing weight (lb.); V=Airplane speed in knots. V must be... main wheel brake assembly must not be less than the kinetic energy absorption requirements determined... design landing weight. (2) Instead of a rational analysis, the kinetic energy absorption requirements...
17. 14 CFR 23.735 - Brakes.
Code of Federal Regulations, 2011 CFR
2011-01-01
...=Kinetic energy per wheel (ft.-lb.); W=Design landing weight (lb.); V=Airplane speed in knots. V must be... main wheel brake assembly must not be less than the kinetic energy absorption requirements determined... design landing weight. (2) Instead of a rational analysis, the kinetic energy absorption requirements...
18. 14 CFR 23.735 - Brakes.
Code of Federal Regulations, 2010 CFR
2010-01-01
...=Kinetic energy per wheel (ft.-lb.); W=Design landing weight (lb.); V=Airplane speed in knots. V must be... main wheel brake assembly must not be less than the kinetic energy absorption requirements determined... design landing weight. (2) Instead of a rational analysis, the kinetic energy absorption requirements...
19. 14 CFR 23.735 - Brakes.
Code of Federal Regulations, 2013 CFR
2013-01-01
...=Kinetic energy per wheel (ft.-lb.); W=Design landing weight (lb.); V=Airplane speed in knots. V must be... main wheel brake assembly must not be less than the kinetic energy absorption requirements determined... design landing weight. (2) Instead of a rational analysis, the kinetic energy absorption requirements...
20. 30 CFR 56.14101 - Brakes.
Code of Federal Regulations, 2012 CFR
2012-07-01
... 30 Mineral Resources 1 2012-07-01 2012-07-01 false Brakes. 56.14101 Section 56.14101 Mineral Resources MINE SAFETY AND HEALTH ADMINISTRATION, DEPARTMENT OF LABOR METAL AND NONMETAL MINE SAFETY AND HEALTH SAFETY AND HEALTH STANDARDS-SURFACE METAL AND NONMETAL MINES Machinery and Equipment Safety Devices and Maintenance Requirements §...
1. 30 CFR 57.14101 - Brakes.
Code of Federal Regulations, 2012 CFR
2012-07-01
... 30 Mineral Resources 1 2012-07-01 2012-07-01 false Brakes. 57.14101 Section 57.14101 Mineral Resources MINE SAFETY AND HEALTH ADMINISTRATION, DEPARTMENT OF LABOR METAL AND NONMETAL MINE SAFETY AND HEALTH SAFETY AND HEALTH STANDARDS-UNDERGROUND METAL AND NONMETAL MINES Machinery and Equipment Safety Devices and Maintenance Requirements §...
2. Wind-Tunnel Investigations of Diving Brakes
NASA Technical Reports Server (NTRS)
Fucha, D.
1942-01-01
Unduly high diving speeds can be effectively controlled by diving brakes but their employment involves at the same time a number of disagreeable features: namely, rotation of zero lift direction, variation of diviving moment, and, the creation of a potent dead air region.
3. Use of elastomers in regenerative braking systems
The storage of potential energy as strain energy in elastomers was investigated. The evolution of the preferred stressing scheme is described, and test results on full-size elastomeric energy storage units sized for an automotive regenerative braking system application are presented. The need for elastomeric material improvements is also discussed.
4. Braking the Gas in the ? Pictoris Disk
Fernández, Rodrigo; Brandeker, Alexis; Wu, Yanqin
2006-05-01
The star ? Pictoris hosts the best studied circumstellar disk to date. Nonetheless, a long-standing puzzle has been around since the detection of metallic gas in the disk: radiation pressure from the star should blow the gas away, yet the observed motion is consistent with Keplerian rotation. In this work we search for braking mechanisms that can resolve this discrepancy. We find that all species affected by radiation force are largely ionized and dynamically coupled into a single fluid by Coulomb collisions, reducing the radiation force on species feeling the strongest acceleration. For a gas of solar composition, the effective radiation force still exceeds gravity, while a gas of enhanced carbon abundance could be self-braking. We also explore two other braking agents: collisions with dust grains and neutral gas. Grains surrounding ? Pic are photoelectrically charged to a positive electrostatic potential. If a significant fraction of the grains are carbonaceous (10% in the midplane and larger at higher altitudes), ions can be slowed down to satisfy the observed velocity constraints. For neutral gas to brake the ion fluid, we find a minimum required mass ~0.03 M?, consistent with observed upper limits on the hydrogen column density and substantially reduced relative to previous estimates. Our results favor a scenario in which metallic gas is generated by grain evaporation in the disk, perhaps during grain-grain collisions. We exclude a primordial origin for the gas but cannot rule out its production by falling evaporating bodies near the star.
5. Magnetic Braking and Protostellar Disk Formation
Mellon, Richard R.; Li, Z.
2009-01-01
It is established that the formation of rotationally supported disks during the main accretion phase of star formation is suppressed by a moderately strong magnetic field in the ideal MHD limit. Non-ideal MHD effects are expected to weaken the magnetic braking, perhaps allowing the disk to reappear. I concentrate on one such effect, ambipolar diffusion, which enables the field lines to slip relative to the bulk neutral matter. I will report the results of a set of 2D (axisymmetric) simulations of the collapse of rotating, singluar isothermal cores with different degrees of magnetization and cosmic ray ionization. I demonstrate that the slippage does not sufficiently weaken the braking to allow rotationally supported disks to form for realistic levels of cloud magnetization and cosmic rayionization rate; in some cases, the magnetic braking is even enhanced. Only in dense cores with both exceptionally weak fields and unreasonably low ionization rate do such disks start to form in our simulations. I conclude that additional processes, such as Ohmic dissipation or Hall effect, are needed to enable disk formation. Alternatively, the disk may form at late times when the massive envelope that anchors the magnetic brake is dissipated, perhaps by a protostellar wind. This research was supported in part by grants from NSF and NASA.
6. Experimental investigation of an accelerometer controlled automatic braking system
NASA Technical Reports Server (NTRS)
Dreher, R. C.; Sleeper, R. K.; Nayadley, J. R., Sr.
1972-01-01
An investigation was made to determine the feasibility of an automatic braking system for arresting the motion of an airplane by sensing and controlling braked wheel decelerations. The system was tested on a rotating drum dynamometer by using an automotive tire, wheel, and disk-brake assembly under conditions which included two tire loadings, wet and dry surfaces, and a range of ground speeds up to 70 knots. The controlling parameters were the rates at which brake pressure was applied and released and the Command Deceleration Level which governed the wheel deceleration by controlling the brake operation. Limited tests were also made with the automatic braking system installed on a ground vehicle in an effort to provide a more realistic proof of its feasibility. The results of this investigation indicate that a braking system which utilizes wheel decelerations as the control variable to restrict tire slip is feasible and capable of adapting to rapidly changing surface conditions.
7. Pedestrian injury mitigation by autonomous braking.
PubMed
Rosén, Erik; Källhammer, Jan-Erik; Eriksson, Dick; Nentwich, Matthias; Fredriksson, Rikard; Smith, Kip
2010-11-01
The objective of this study was to calculate the potential effectiveness of a pedestrian injury mitigation system that autonomously brakes the car prior to impact. The effectiveness was measured by the reduction of fatally and severely injured pedestrians. The database from the German In-Depth Accident Study (GIDAS) was queried for pedestrians hit by the front of cars from 1999 to 2007. Case by case information on vehicle and pedestrian velocities and trajectories were analysed to estimate the field of view needed for a vehicle-based sensor to detect the pedestrians one second prior to the crash. The pre-impact braking system was assumed to activate the brakes one second prior to crash and to provide a braking deceleration up to the limit of the road surface conditions, but never to exceed 0.6 g. New impact speeds were then calculated for pedestrians that would have been detected by the sensor. These calculations assumed that all pedestrians who were within a given field of view but not obstructed by surrounding objects would be detected. The changes in fatality and severe injury risks were quantified using risk curves derived by logistic regression of the accident data. Summing the risks for all pedestrians, relationships between mitigation effectiveness, sensor field of view, braking initiation time, and deceleration were established. The study documents that the effectiveness at reducing fatally (severely) injured pedestrians in frontal collisions with cars reached 40% (27%) at a field of view of 40 degrees. Increasing the field of view further led to only marginal improvements in effectiveness. PMID:20728647
8. Debiasing overoptimistic beliefs about braking capacity.
PubMed
Svenson, Ola; Eriksson, Gabriella; Mertz, C K
2013-09-01
We investigated, using questionnaires, different strategies for removing drivers' overoptimism (Svenson et al., 2012a) about how fast their speed could be decreased when they were speeding compared with braking at the speed limit speed. Three different learning groups and a control group made collision speed judgments. The first learning group had the distance a car travels during a driver's reaction time for each problem. The second group had this information and also feedback after each judgment (correct speed). The third group judged collision speed but also braking distance and received correct facts after each problem. The control group had no information at all about reaction time and the distance traveled during that time. The results suggested the following rank order from poor to improved performance: control, group 1, group 3 and group 2 indicating that information about distance driven during a driver's reaction time improved collision speed judgments and that adding stopping distance information did not add to this improvement. PMID:23743252
9. Wind turbine trailing edge aerodynamic brakes
SciTech Connect
Migliore, P G; Miller, L S; Quandt, G A
1995-04-01
Five trailing-edge devices were investigated to determine their potential as wind-turbine aerodynamic brakes, and for power modulation and load alleviation. Several promising configurations were identified. A new device, called the spoiler-flap, appears to be the best alternative. It is a simple device that is effective at all angles of attack. It is not structurally intrusive, and it has the potential for small actuating loads. It is shown that simultaneous achievement of a low lift/drag ratio and high drag is the determinant of device effectiveness, and that these attributes must persist up to an angle of attack of 45{degree}. It is also argued that aerodynamic brakes must be designed for a wind speed of at least 45 m/s (100 mph).
10. Hibernation Revived by Weak Magnetic Braking
E-print Network
Rebecca G. Martin; Christopher A. Tout
2006-09-07
Cataclysmic variables undergo periodic nova explosions during which a finite mass of material is expelled on a short timescale. The system widens and, as a result, the mass-transfer rate drops. This state of hibernation may account for the variety of cataclysmic variable types observed in systems of similar mass and period. In the light of recent changes to the theory of nova ignition and magnetic braking we investigate whether hibernation remains a viable mechanism for creating cataclysmic variable diversity. We model the ratio of time spent as dwarf novae (DNe) to nova-like systems (NLs). Above a critical mass-transfer rate the system is NL and below it a DN. The dominant loss of angular momentum is by magnetic braking but the rate is uncertain. It is also uncertain what fraction of the mass accreted is expelled during the novae. We compare the models of the ratios against the period of the system for different magnetic braking rates and different ejected masses with the ratio of the number of observed NLs to DNe. We deduce that a rate of angular momentum loss a factor of ten smaller than that traditionally assumed is necessary if hibernation is to account for the observed ratios.
11. Hibernation Revived by Weak Magnetic Braking
E-print Network
Martin, R G; Martin, Rebecca G.; Tout, Christopher A.
2005-01-01
Cataclysmic variables undergo periodic nova explosions during which a finite mass of material is expelled on a short timescale. The system widens and, as a result, the mass-transfer rate drops. This state of hibernation may account for the variety of cataclysmic variable types observed in systems of similar mass and period. In the light of recent changes to the theory of nova ignition and magnetic braking we investigate whether hibernation remains a viable mechanism for creating cataclysmic variable diversity. We model the ratio of time spent as dwarf novae (DNe) to nova-like systems (NLs). Above a critical mass-transfer rate the system is NL and below it a DN. The dominant loss of angular momentum is by magnetic braking but the rate is uncertain. It is also uncertain what fraction of the mass accreted is expelled during the novae. We compare the models of the ratios against the period of the system for different magnetic braking rates and different ejected masses with the ratio of the number of observed NLs ...
12. Asbestos in brakes: exposure and risk of disease.
PubMed
Lemen, Richard A
2004-03-01
Asbestos has been incorporated into friction products since the early 1900s. Epidemiological studies have been equivocal in their analysis of the incidence of disease among mechanics servicing brakes. Decomposition of asbestos occurs during the normal usage of the brake due to thermal decomposition into forsterite, although not all asbestos is so converted. Short fibers, below 5 microm in length, are also found in brake products. Several facts are discussed including the toxicity of the remaining asbestos fibers, short asbestos fibers, and the health implications of exposure to forsterite. Control methodologies, when used appropriately, have reduced exposure to asbestos during brake servicing, but have not been able to entirely eliminate exposure to asbestos, thus bring into question the controlled use of asbestos for friction product such as brakes. Even the so called "controlled" use of asbestos containing brakes poses a health risk to workers, users, and their families. PMID:14991849
13. A proposal for dynamic calibration of brake tester
Ferreira, Paulo L. S.; Couto, Paulo R. G.; Cabral, Luiz C.; Reis, Ronaldo G.; Zillner, Marcos
2015-10-01
In Brazil there are about 400 security inspection lines carrier operating in Inspection Bodies accredited by Cgcre Inmetro [1]. The equipment in this proposal is a Brake Tester that measure vehicle braking forces and it is a component of an inspection line. This paper proposes a dynamic Brake Tester calibration using a reference torque transducer. This article can also be the basis for future discussions of the revised standard manufacturing of vehicle inspection line according to ABNT NBR 14040 [2].
14. Evaluation of materials and design modifications for aircraft brakes
NASA Technical Reports Server (NTRS)
Ho, T. L.; Kennedy, F. E.; Peterson, M. B.
1975-01-01
A test program is described which was carried out to evaluate several proposed design modifications and several high-temperature friction materials for use in aircraft disk brakes. The evaluation program was carried out on a specially built test apparatus utilizing a disk brake and wheel half from a small het aircraft. The apparatus enabled control of brake pressure, velocity, and braking time. Tests were run under both constant and variable velocity conditions and covered a kinetic energy range similar to that encountered in aircraft brake service. The results of the design evaluation program showed that some improvement in brake performance can be realized by making design changes in the components of the brake containing friction material. The materials evaluation showed that two friction materials show potential for use in aircraft disk brakes. One of the materials is a nickel-based sintered composite, while the other is a molybdenum-based material. Both materials show much lower wear rates than conventional copper-based materials and are better able to withstand the high temperatures encountered during braking. Additional materials improvement is necessary since both materials show a significant negative slope of the friction-velocity curve at low velocities.
15. Optimal design of a novel configuration of MR brake with coils placed on the side housings
Nguyen, Quoc Hung; Nguyen, Ngoc Diep; Choi, Seung-Bok
2014-03-01
It is well known that in design of traditional magneto-rheological brake (MRB), coils are placed on the cylindrical housing of the brake. In this study, a new configuration of MR brake with coils placed on the side housings of the brake is proposed and analyzed. After briefly explaining the operating principle of the proposed configuration, the braking torque of the MR brake is analyze based on Bingham-plastic rheological model of MR fluid. The optimization of the proposed and conventional MR brakes is then performed considering maximum braking torque and mass of the brake. Based on the optimal results, a comparison between the proposed MR brakes and the conventional ones is undertaken. In addition, experimental test of the MR brakes is conducted and the results are presented in order to validate the performance characteristics of the proposed MR brake.
16. 49 CFR 232.503 - Process to introduce new brake system technology.
Code of Federal Regulations, 2012 CFR
2012-10-01
...Process to introduce new brake system technology. 232.503 Section 232.503... Introduction of New Brake System Technology § 232.503 Process to introduce new brake system technology. (a) Pursuant to the...
17. 49 CFR 232.503 - Process to introduce new brake system technology.
Code of Federal Regulations, 2014 CFR
2014-10-01
...Process to introduce new brake system technology. 232.503 Section 232.503... Introduction of New Brake System Technology § 232.503 Process to introduce new brake system technology. (a) Pursuant to the...
18. 49 CFR 232.503 - Process to introduce new brake system technology.
Code of Federal Regulations, 2013 CFR
2013-10-01
...Process to introduce new brake system technology. 232.503 Section 232.503... Introduction of New Brake System Technology § 232.503 Process to introduce new brake system technology. (a) Pursuant to the...
19. 49 CFR 232.503 - Process to introduce new brake system technology.
Code of Federal Regulations, 2011 CFR
2011-10-01
...Process to introduce new brake system technology. 232.503 Section 232.503... Introduction of New Brake System Technology § 232.503 Process to introduce new brake system technology. (a) Pursuant to the...
20. 49 CFR 232.503 - Process to introduce new brake system technology.
Code of Federal Regulations, 2010 CFR
2010-10-01
...Process to introduce new brake system technology. 232.503 Section 232.503... Introduction of New Brake System Technology § 232.503 Process to introduce new brake system technology. (a) Pursuant to the...
1. 49 CFR 236.554 - Rate of pressure reduction; equalizing reservoir or brake pipe.
Code of Federal Regulations, 2010 CFR
2010-10-01
...pressure reduction; equalizing reservoir or brake pipe. 236.554 Section 236.554 Transportation...pressure reduction; equalizing reservoir or brake pipe. The equalizing-reservoir pressure or brake-pipe pressure reduction during an automatic...
2. 49 CFR 236.554 - Rate of pressure reduction; equalizing reservoir or brake pipe.
Code of Federal Regulations, 2011 CFR
2011-10-01
...pressure reduction; equalizing reservoir or brake pipe. 236.554 Section 236.554 Transportation...pressure reduction; equalizing reservoir or brake pipe. The equalizing-reservoir pressure or brake-pipe pressure reduction during an automatic...
3. 49 CFR 236.554 - Rate of pressure reduction; equalizing reservoir or brake pipe.
Code of Federal Regulations, 2014 CFR
2014-10-01
... Rate of pressure reduction; equalizing reservoir or brake pipe. 236.554 Section 236... Rate of pressure reduction; equalizing reservoir or brake pipe. The equalizing-reservoir pressure or brake-pipe pressure...
4. 49 CFR 236.554 - Rate of pressure reduction; equalizing reservoir or brake pipe.
Code of Federal Regulations, 2013 CFR
2013-10-01
... Rate of pressure reduction; equalizing reservoir or brake pipe. 236.554 Section 236... Rate of pressure reduction; equalizing reservoir or brake pipe. The equalizing-reservoir pressure or brake-pipe pressure...
5. 49 CFR 236.554 - Rate of pressure reduction; equalizing reservoir or brake pipe.
Code of Federal Regulations, 2012 CFR
2012-10-01
... Rate of pressure reduction; equalizing reservoir or brake pipe. 236.554 Section 236... Rate of pressure reduction; equalizing reservoir or brake pipe. The equalizing-reservoir pressure or brake-pipe pressure...
6. Measurement and control of brake pedal feel quality in automobile manufacturing
E-print Network
Cerilles, Jeffrey T. (Jeffrey Thomas)
2005-01-01
Customer perception of brake pedal feel quality, as related to the perception of the brake pedal feeling soft or mushy, depends on both the customer's subjective judgment of quality and the actual build quality of the brake ...
7. 49 CFR 571.135 - Standard No. 135; Light vehicle brake systems.
Code of Federal Regulations, 2011 CFR
2011-10-01
...load changes and/or dynamic weight transfer, or...S5.1. Service brake system. Each vehicle shall...variable brake proportioning system, this determination...variable brake proportioning system, dynamic tests are run...
8. 49 CFR 571.135 - Standard No. 135; Light vehicle brake systems.
Code of Federal Regulations, 2013 CFR
2013-10-01
...load changes and/or dynamic weight transfer, or...S5.1. Service brake system. Each vehicle shall...variable brake proportioning system, this determination...variable brake proportioning system, dynamic tests are run...
9. 49 CFR 571.135 - Standard No. 135; Light vehicle brake systems.
Code of Federal Regulations, 2012 CFR
2012-10-01
...load changes and/or dynamic weight transfer, or...S5.1. Service brake system. Each vehicle shall...variable brake proportioning system, this determination...variable brake proportioning system, dynamic tests are run...
10. 49 CFR 571.135 - Standard No. 135; Light vehicle brake systems.
Code of Federal Regulations, 2010 CFR
2010-10-01
...load changes and/or dynamic weight transfer, or...S5.1. Service brake system. Each vehicle shall...variable brake proportioning system, this determination...variable brake proportioning system, dynamic tests are run...
11. 49 CFR 571.135 - Standard No. 135; Light vehicle brake systems.
Code of Federal Regulations, 2014 CFR
2014-10-01
...load changes and/or dynamic weight transfer, or...S5.1. Service brake system. Each vehicle shall...variable brake proportioning system, this determination...variable brake proportioning system, dynamic tests are run...
12. 49 CFR 570.56 - Vacuum brake assist unit and vacuum brake system.
Code of Federal Regulations, 2010 CFR
2010-10-01
...If the vehicle has a low-vacuum indicator, the indicator activation level shall not be less than 8 inches of mercury. (1...the brake application and check for low-vacuum indicator activation. (ii) For a combination vehicle equipped with...
13. 49 CFR 229.57 - Foundation brake gear.
Code of Federal Regulations, 2010 CFR
2010-10-01
...System § 229.57 Foundation brake gear. A lever, rod, brake beam, hanger, or pin may not be worn through more than 30 percent of its cross-sectional area, cracked, broken, or missing. All pins shall be secured in place with...
14. 49 CFR 229.57 - Foundation brake gear.
Code of Federal Regulations, 2011 CFR
2011-10-01
...System § 229.57 Foundation brake gear. A lever, rod, brake beam, hanger, or pin may not be worn through more than 30 percent of its cross-sectional area, cracked, broken, or missing. All pins shall be secured in place with...
15. Why Brake-By-Wire (BBW) ? Advantages of BBW
E-print Network
Yao, Bin
at wheel] #12;Sectional Drawing of the Electromechanically Actuated Disk Brake From ITT Brake Pads Caliper Central Bearing Planetary Gear Bearing Planetary Gear Stator Rotor Bearing Motor Revolver Revolver Bearing Force Sensor Cap Nut (Carrier) Spindle Planetary Rollers Internal Gear Sun Gear Pressure Pin Holder
16. 49 CFR 238.313 - Class I brake test.
Code of Federal Regulations, 2010 CFR
2010-10-01
...apply and remain applied on each car in the train until a release of...brakes has been initiated on each car in response to train line electric, pneumatic, or other signals...verification that each side of each car's brake system responds...
17. 49 CFR 238.313 - Class I brake test.
Code of Federal Regulations, 2011 CFR
2011-10-01
...apply and remain applied on each car in the train until a release of...brakes has been initiated on each car in response to train line electric, pneumatic, or other signals...verification that each side of each car's brake system responds...
18. 14 CFR 25.493 - Braked roll conditions.
Code of Federal Regulations, 2012 CFR
2012-01-01
... 14 Aeronautics and Space 1 2012-01-01 2012-01-01 false Braked roll conditions. 25.493 Section 25.493 Aeronautics and Space FEDERAL AVIATION ADMINISTRATION, DEPARTMENT OF TRANSPORTATION AIRCRAFT AIRWORTHINESS STANDARDS: TRANSPORT CATEGORY AIRPLANES Structure Ground Loads § 25.493 Braked roll conditions. (a) An airplane with a tail wheel is...
19. Multidisciplinary design optimization of an automotive magnetorheological brake design
E-print Network
Park, Edward
such as the MR fluid selection, magnetic circuit design, torque requirements, weight constraints, dimensions on each wheel and the brake pedal with electrical components. There are many advantages of using a pure, we propose a MR actuator design for the brake in each wheel. The actuator consists of a rotating disk
20. A diagnostic system for air brakes in commercial vehicles
E-print Network
Coimbatore Subramanian, Shankar Ram
2007-09-17
to maintenance and hence they require frequent inspections. Current inspection techniques require an inspector to go underneath a vehicle to check the brake system for possible faults, such as leaks, worn brake pads, out-of-adjustment of push rods, etc...
1. 49 CFR 238.313 - Class I brake test.
Code of Federal Regulations, 2013 CFR
2013-10-01
...apply and remain applied on each car in the train until a release of...brakes has been initiated on each car in response to train line electric, pneumatic, or other signals...verification that each side of each car's brake system responds...
2. 49 CFR 238.313 - Class I brake test.
Code of Federal Regulations, 2012 CFR
2012-10-01
...apply and remain applied on each car in the train until a release of...brakes has been initiated on each car in response to train line electric, pneumatic, or other signals...verification that each side of each car's brake system responds...
3. Braking system for use with an arbor of a microscope
DOEpatents
Norgren, Duane U. (Orinda, CA)
1984-01-01
A balanced braking system comprising a plurality of braking assemblies located about a member to be braked. Each of the braking assemblies consists of a spring biased piston of a first material fitted into a body of a different material which has a greater contraction upon cooling than the piston material. The piston is provided with a recessed head portion over which is positioned a diaphragm and forming a space therebetween to which is connected a pressurized fluid supply. The diaphragm is controlled by the fluid in the space to contact or withdraw from the member to be braked. A cooling device causes the body within which the piston is fitted to contract more than the piston, producing a tight shrink fit therebetween. The braking system is particularly applicable for selectively braking an arbor of an electron microscope which immobilizes, for example, a vertically adjustable low temperature specimen holder during observation. The system provides balanced braking forces which can be easily removed and re-established with minimal disturbance to arbor location.
4. 49 CFR 570.5 - Service brake system.
Code of Federal Regulations, 2012 CFR
2012-10-01
... 49 Transportation 6 2012-10-01 2012-10-01 false Service brake system. 570.5 Section 570.5 Transportation Other Regulations Relating to Transportation (Continued) NATIONAL HIGHWAY TRAFFIC SAFETY ADMINISTRATION, DEPARTMENT OF TRANSPORTATION VEHICLE IN USE INSPECTION STANDARDS Vehicles With GVWR of 10,000 Pounds or Less § 570.5 Service brake...
5. 49 CFR 570.5 - Service brake system.
Code of Federal Regulations, 2013 CFR
2013-10-01
... CFR 571.105, on every new passenger car manufactured on or after January 1, 1968, and on other types...-second of an inch over the rivet heads, or the brake shoe on bonded linings or pads. Brake linings and... attached to shoe plates. (1) Inspection procedure. Examine visually for conditions indicated, and...
6. Method and apparatus for braking a derrick winch
SciTech Connect
Falcon, J.F.
1989-09-12
This patent describes an apparatus for braking a derrick winch with a winch brake. It comprises: a control lever remotely located from the winch; a servo-control circuit connecting the lever and brake for actuating the brake in response to movement of the lever, and including: a torque motor having a shaft mechanically coupled to the control lever; a brake activating device for actuating the winch brake; a first position transducer for sensing the position of the control lever; a second position transducer for sensing the position of the winch brake; a first force transducer for measuring the force applied to the winch brake; a first comparator; a second comparator. The first comparator being connected to receive signals from the first and second position transducers and to deliver an error signal to the torque motor and to the second comparator. The second comparator being connected to receive signals from the first comparator and from the first force transducer and to deliver an error signal to the actuating device.
7. Design optimization of a magnetorheological brake in powered knee orthosis
Ma, Hao; Liao, Wei-Hsin
2015-04-01
Magneto-rheological (MR) fluids have been utilized in devices like orthoses and prostheses to generate controllable braking torque. In this paper, a flat shape rotary MR brake is designed for powered knee orthosis to provide adjustable resistance. Multiple disk structure with interior inner coil is adopted in the MR brake configuration. In order to increase the maximal magnetic flux, a novel internal structure design with smooth transition surface is proposed. Based on this design, a parameterized model of the MR brake is built for geometrical optimization. Multiple factors are considered in the optimization objective: braking torque, weight, and, particularly, average power consumption. The optimization is then performed with Finite Element Analysis (FEA), and the optimal design is obtained among the Pareto-optimal set considering the trade-offs in design objectives.
8. Analysis of heat conduction in a disk brake system
Talati, Faramarz; Jalalifar, Salman
2009-06-01
In this paper, the governing heat equations for the disk and the pad are extracted in the form of transient heat equations with heat generation that is dependant to time and space. In the derivation of the heat equations, parameters such as the duration of braking, vehicle velocity, geometries and the dimensions of the brake components, materials of the disk brake rotor and the pad and contact pressure distribution have been taken into account. The problem is solved analytically using Green’s function approach. It is concluded that the heat generated due to friction between the disk and the pad should be ideally dissipated to the environment to avoid decreasing the friction coefficient between the disk and the pad and to avoid the temperature rise of various brake components and brake fluid vaporization due to excessive heating.
9. A 6-DOF vibration isolation system for hydraulic hybrid vehicles
Nguyen, The; Elahinia, Mohammad; Olson, Walter W.; Fontaine, Paul
2006-03-01
This paper presents the results of vibration isolation analysis for the pump/motor component of hydraulic hybrid vehicles (HHVs). The HHVs are designed to combine gasoline/diesel engine and hydraulic power in order to improve the fuel efficiency and reduce the pollution. Electric hybrid technology is being applied to passenger cars with small and medium engines to improve the fuel economy. However, for heavy duty vehicles such as large SUVs, trucks, and buses, which require more power, the hydraulic hybridization is a more efficient choice. In function, the hydraulic hybrid subsystem improves the fuel efficiency of the vehicle by recovering some of the energy that is otherwise wasted in friction brakes. Since the operation of the main component of HHVs involves with rotating parts and moving fluid, noise and vibration are an issue that affects both passengers (ride comfort) as well as surrounding people (drive-by noise). This study looks into the possibility of reducing the transmitted noise and vibration from the hydraulic subsystem to the vehicle's chassis by using magnetorheological (MR) fluid mounts. To this end, the hydraulic subsystem is modeled as a six degree of freedom (6-DOF) rigid body. A 6-DOF isolation system, consisting of five mounts connected to the pump/motor at five different locations, is modeled and simulated. The mounts are designed by combining regular elastomer components with MR fluids. In the simulation, the real loading and working conditions of the hydraulic subsystem are considered and the effects of both shock and vibration are analyzed. The transmissibility of the isolation system is monitored in a wide range of frequencies. The geometry of the isolation system is considered in order to sustain the weight of the hydraulic system without affecting the design of the chassis and the effectiveness of the vibration isolating ability. The simulation results shows reduction in the transmitted vibration force for different working cycles of the regenerative system.
10. Engineering report. Part 3: NASA lightweight wheel and brake sub-system. Lightweight brake development. [for application to space shuttle
NASA Technical Reports Server (NTRS)
Bok, L. D.
1973-01-01
The development of light weight wheel and brake systems designed to meet the space shuttle type requirements was investigated. The study includes the use of carbon graphite composite and beryllium as heat sink materials and the compatibility of these heat sink materials with the other structural components of the wheel and brake.
11. Protobinary Evolution Driven By Magnetic Braking
Zhao, Bo; Li, Zhi-Yun
2013-07-01
The majority of stars are in multiple systems, especially binaries. Such objects form in dense cores of molecular clouds that are observed to be strongly magnetized. Most previous studies of binary formation have either ignored magnetic fields or focused on the initial core fragmentation into binary seeds. Here I focus on the effects of the magnetic field on the orbital evolution of the protobinary during the main accretion phase, after a pair of stellar seeds have formed. By simulating a 'seed' binary system with the sink particle treatment, we show that magnetic field plays a crucial role in removing the gas angular momentum and shrinking the binary separation. Through magnetic braking, strong magnetic field is very effective in suppressing the formation of circumstellar disks and circumbinary disk along with its spiral arm structures. The magnetic field can also be responsible for the population of the low mass-ratio binaries in the observed distribution. The magnetically-braked material will have equal chance of being accreted onto either binary seed, instead of the preferential accretion onto the secondary when magnetic field is absent. Furthermore, large field mis-alignment helps to produce rotationally-supported circumbinary disks even for relatively strong magnetic fields, by weakening the magnetically-dominated structure close to the binary. Hence to explain the observed properties of binaries, the magnetic effects deserve more careful considerations in the larger context of binary formation in future studies.
12. PROTOBINARY EVOLUTION DRIVEN BY MAGNETIC BRAKING
Zhao, Bo; Li, Z.; Kratter, K. M.
2014-01-01
The majority of stars are in multiple systems, especially binaries. Such objects form in dense cores of molecular clouds that are observed to be strongly magnetized. Most previous studies of binary formation have either ignored magnetic fields or focused on the initial core fragmentation into binary seeds. Here I focus on the effects of the magnetic field on the orbital evolution of the protobinary during the main accretion phase, after a pair of stellar seeds have formed. By simulating a 'seed' binary system with the sink particle treatment, we show that magnetic field plays a crucial role in removing the gas angular momentum and shrinking the binary separation. Through magnetic braking, strong magnetic field is very effective in suppressing the formation of circumstellar disks and circumbinary disk along with its spiral arm structures. The magnetic field can also be responsible for the population of the low mass-ratio binaries in the observed distribution. The magnetically-braked material will have equal chance of being accreted onto either binary seed, instead of the preferential accretion onto the secondary when magnetic field is absent. Furthermore, large field mis-alignment helps to produce rotationally-supported circumbinary disks even for relatively strong magnetic fields, by weakening the magnetically-dominated structure close to the binary. Hence to explain the observed properties of binaries, the magnetic effects deserve more careful considerations in the larger context of binary formation in future studies.
13. 76 FR 34801 - Petition for Modification of Single Car Air Brake Test Procedures
Federal Register 2010, 2011, 2012, 2013, 2014
2011-06-14
... Federal Railroad Administration Petition for Modification of Single Car Air Brake Test Procedures In... air brake test procedures as prescribed in 49 CFR 232.305(a). FRA assigned the request Docket Number... straight air brake employed on PATH cars. The single car air brake test described in Association...
14. 49 CFR 571.122 - Standard No. 122; Motorcycle brake systems.
Code of Federal Regulations, 2013 CFR
2013-10-01
... the recommended type of brake fluid as specified in accordance with 49 CFR 571.116, e.g., “DOT 3... CFR 571.101). S5.2Durability. S5.2.1Compensation for wear. Wear of the brakes shall be compensated for... brake fluid. S5.3Measurement of dynamic performance. There are two ways in which brake...
15. 49 CFR 571.122 - Standard No. 122; Motorcycle brake systems.
Code of Federal Regulations, 2014 CFR
2014-10-01
... the recommended type of brake fluid as specified in accordance with 49 CFR 571.116, e.g., “DOT 3... CFR 571.101). S5.2Durability. S5.2.1Compensation for wear. Wear of the brakes shall be compensated for... brake fluid. S5.3Measurement of dynamic performance. There are two ways in which brake...
16. 49 CFR 238.15 - Movement of passenger equipment with power brake defects.
Code of Federal Regulations, 2010 CFR
2010-10-01
...the time that a Class I or IA brake test...the railroad's air brake or power...en route after a Class I or IA brake test... (C) Piston travel that is in excess of the Class I brake test limits...the train at the first location...
17. 49 CFR 232.103 - General requirements for all train brake systems.
Code of Federal Regulations, 2011 CFR
2011-10-01
...shall have its air brakes in effective...609. The air brakes on a...if the piston travel exceeds: ...for the car at Class I brake tests...different from Class I brake test...service for the first time on or...either the piston travel, an accurate...less than the air compressor...
18. 49 CFR 238.15 - Movement of passenger equipment with power brake defects.
Code of Federal Regulations, 2011 CFR
2011-10-01
...the time that a Class I or IA brake test...the railroad's air brake or power...en route after a Class I or IA brake test... (C) Piston travel that is in excess of the Class I brake test limits...the train at the first location...
19. The application of hydraulics in the 2,000 kW wind turbine generator
NASA Technical Reports Server (NTRS)
Onufreiczuk, S.
1978-01-01
A 2000 kW turbine generator using hydraulic power in two of its control systems is being built under the management of NASA Lewis Research Center. The hydraulic systems providing the control torques and forces for the yaw and blade pitch control systems are discussed. The yaw-drive-system hydraulic supply provides the power for positioning the nacelle so that the rotary axis is kept in line with the direction of the prevailing wind, as well as pressure to the yaw and high speed shaft brakes. The pitch-change-mechanism hydraulic system provides the actuation to the pitch change mechanism and permits feathering of the blades during an emergency situation. It operates in conjunction with the overall windmill computer system, with the feather control permitting slewing control flow to pass from the servo valve to the actuators without restriction.
20. Hydraulic fracture design optimization
SciTech Connect
1992-01-01
This research and development investigation, sponsored by US DOE and the oil and gas industry, extends previously developed hydraulic fracture geometry models and applied energy related characteristic time concepts towards the optimal design and control of hydraulic fracture geometries. The primary objective of this program is to develop rational criteria, by examining the associated energy rate components during the hydraulic fracture evolution, for the formulation of stimulation treatment design along with real-time fracture configuration interpretation and control.
1. Hydraulic fracture design optimization
SciTech Connect
1992-06-01
This research and development investigation, sponsored by US DOE and the oil and gas industry, extends previously developed hydraulic fracture geometry models and applied energy related characteristic time concepts towards the optimal design and control of hydraulic fracture geometries. The primary objective of this program is to develop rational criteria, by examining the associated energy rate components during the hydraulic fracture evolution, for the formulation of stimulation treatment design along with real-time fracture configuration interpretation and control.
2. Behavior of aircraft antiskid braking systems on dry and wet runway surfaces: Hydromechanically controlled system
NASA Technical Reports Server (NTRS)
Tanner, J. A.; Stubbs, S. M.; Smith, E. G.
1981-01-01
The investigation utilized one main gear wheel, brake, and tire assembly of a McDonnell Douglas DC-9 series 10 airplane. The landing-gear strut was replaced by a dynamometer. During maximum braking, average braking behavior indexes based upon brake pressure, brake torque, and drag-force friction coefficient developed by the antiskid system were generally higher on dry surfaces than on wet surfaces. The three braking behavior indexes gave similar results but should not be used interchangeably as a measure of the braking of this antiskid sytem. During the transition from a dry to a flooded surface under heavy braking, the wheel entered into a deep skid but the antiskid system reacted quickly by reducing brake pressure and performed normally during the remainder of the run on the flooded surface. The brake-pressure recovery following transition from a flooded to a dry surface was shown to be a function of the antiskid modulating orifice.
3. Brake lock mechanism for the two axis pointing system
NASA Technical Reports Server (NTRS)
Posey, Alan; Clark, Mike; Mignosa, Larry
1991-01-01
Six months prior to shipment of the Broadband X-ray Telescope to the Kennedy Space Center for flight aboard the Space Shuttle Columbia, a major system failure occurred. During modal survey testing of the telescope's gimbal pointing system, the roll axis brake unexpectedly released. Low level vibration and static preloads present during the modal survey were within the expected flight environment. Brake release during shuttle liftoff or ascent was an unacceptable risk to mission success; thus, a Brake Lock Mechanism (BLM) was developed.
4. Residual stresses in a cast iron automotive brake disc rotor
Ripley, Maurice I.; Kirstein, Oliver
2006-11-01
Runout, and consequent juddering and pulsation through the brake pedal, is a multi-million dollar per year warranty problem for car manufacturers. There is some suspicion that the runout can be caused by relaxation of residual casting stresses when the disc is overheated during severe-braking episodes. We report here neutron-diffraction measurements of the levels and distribution of residual strains in a used cast iron brake disc rotor. The difficulties of measuring stresses in grey cast iron are outlined and three-dimensional residual-strain distributions are presented and their possible effects discussed.
5. Braking formula for electrons of relativistic speed
Bethe, H.; Bartschat, Klaus
2014-12-01
The current translation is by Klaus Bartschat, Department of Physics and Astronomy, Drake University, Des Moines, Iowa 50311, USA. An attempt has been made to preserve Bethe's writing style as much as possible, including his use of "Volt" instead of "electron volt". Even though the term "stopping power" is quite common in present scientific English, we generally use "braking [capability]" rather than "stopping [power]", in order to emphasize the act [and ability] of slowing down the particle rather than the ultimate result of bringing it to a complete halt. Also, a few typographical errors were kept in the English translation to ensure the translation replicates the original paper. Please, see Section 3 of the annotation to Bethe's article [Fontes, C.J., Bostock, C.J. and Bartschat, K. 2014. Eur. Phys. J. H, 39: 517-536] for a list. The references were converted to EPJH style, and the footnotes are numbered consecutively.
6. A Pulsar Eases Off the Brakes
Kohler, Susanna
2015-10-01
7. Tribomaterial factors in space mechanism brake performance
NASA Technical Reports Server (NTRS)
Hawthorne, H. M.
1990-01-01
The asbestos/phenolic pads of Shuttle Remote Manipulator System (SRMS) brakes are unsuitable for use in long life space mechanisms because their friction decreases on extended sliding in high vacuum. Dehydration of the material and accumulation of wear debris in the conforming interface of this tribosystem induces the permanent friction changes. Other polymer and some ceramic based materials exhibit similar frictional torque behavior due to the development of minimal contact patches by the interfacial debris. In contrast, high friction occurs when other ceramics form many small contacts throughout fine debris beds. Generating this latter interfacial structure during run-in ensures that the in-vacuo friction remains stable thereafter. Such materials with low wear rates are potential candidates for friction elements in SSRMS and similar mechanisms.
8. A Pulsar Eases Off the Brakes
Kohler, Susanna
2016-01-01
9. Airbus A320 Braking as Predicate-Action Peter B. Ladkin
E-print Network
to interest us and others in the design of the A320 braking system [FI.93a, FI.93b, FI.93c]. This paper]. The Braking System Design of the A320. The braking system design of the A320 is described in the A320 Flight). The brakes and anti-skid system are described in [FCOM, 1.32.30: Landing Gear: Brakes and Anti
10. Thermally Actuated Hydraulic Pumps
NASA Technical Reports Server (NTRS)
Jones, Jack; Ross, Ronald; Chao, Yi
2008-01-01
Thermally actuated hydraulic pumps have been proposed for diverse applications in which direct electrical or mechanical actuation is undesirable and the relative slowness of thermal actuation can be tolerated. The proposed pumps would not contain any sliding (wearing) parts in their compressors and, hence, could have long operational lifetimes. The basic principle of a pump according to the proposal is to utilize the thermal expansion and contraction of a wax or other phase-change material in contact with a hydraulic fluid in a rigid chamber. Heating the chamber and its contents from below to above the melting temperature of the phase-change material would cause the material to expand significantly, thus causing a substantial increase in hydraulic pressure and/or a substantial displacement of hydraulic fluid out of the chamber. Similarly, cooling the chamber and its contents from above to below the melting temperature of the phase-change material would cause the material to contract significantly, thus causing a substantial decrease in hydraulic pressure and/or a substantial displacement of hydraulic fluid into the chamber. The displacement of the hydraulic fluid could be used to drive a piston. The figure illustrates a simple example of a hydraulic jack driven by a thermally actuated hydraulic pump. The pump chamber would be a cylinder containing encapsulated wax pellets and containing radial fins to facilitate transfer of heat to and from the wax. The plastic encapsulation would serve as an oil/wax barrier and the remaining interior space could be filled with hydraulic oil. A filter would retain the encapsulated wax particles in the pump chamber while allowing the hydraulic oil to flow into and out of the chamber. In one important class of potential applications, thermally actuated hydraulic pumps, exploiting vertical ocean temperature gradients for heating and cooling as needed, would be used to vary hydraulic pressures to control buoyancy in undersea research vessels. Heretofore, electrically actuated hydraulic pumps have been used for this purpose. By eliminating the demand for electrical energy for pumping, the use of the thermally actuated hydraulic pumps could prolong the intervals between battery charges, thus making it possible to greatly increase the durations of undersea exploratory missions.
11. Geomechanics of hydraulic fracturing microseismicity
E-print Network
Ze'ev, Reches
Geomechanics of hydraulic fracturing microseismicity: Part 1. Shear, hybrid, and tensile events of hydraulic- fracturing-induced microseismicity. Microseismic events are commonly used to discern stimulation patterns and hydraulic fracture evolution; however, techniques beyond fracture mapping are required
12. Geomechanics of hydraulic fracturing microseismicity
E-print Network
Ze'ev, Reches
Geomechanics of hydraulic fracturing microseismicity: Part 2. Stress state determination Seth Busetti and Ze'ev Reches ABSTRACT We investigate the hydraulic fracturing process by analysis, stress shadowing adjacent to large parent hydraulic fractures, and crack tip stress perturbations. Data
13. Regenerative braking on bicycles to power LED safety flashers
E-print Network
Collier, Ian M
2005-01-01
This work develops a method for capturing some of the kinetic energy ordinarily lost during braking on bicycles to power LED safety flashers. The system is designed to eliminate: (a) battery changing in popular LED flashers, ...
14. Evaluation strategy of regenerative braking energy for supercapacitor vehicle.
PubMed
Zou, Zhongyue; Cao, Junyi; Cao, Binggang; Chen, Wen
2015-03-01
In order to improve the efficiency of energy conversion and increase the driving range of electric vehicles, the regenerative energy captured during braking process is stored in the energy storage devices and then will be re-used. Due to the high power density of supercapacitors, they are employed to withstand high current in the short time and essentially capture more regenerative energy. The measuring methods for regenerative energy should be investigated to estimate the energy conversion efficiency and performance of electric vehicles. Based on the analysis of the regenerative braking energy system of a supercapacitor vehicle, an evaluation system for energy recovery in the braking process is established using USB portable data-acquisition devices. Experiments under various braking conditions are carried out. The results verify the higher efficiency of energy regeneration system using supercapacitors and the effectiveness of the proposed measurement method. It is also demonstrated that the maximum regenerative energy conversion efficiency can reach to 88%. PMID:25311161
15. View of main hoist wire rope drum and brakes, open ...
Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey
View of main hoist wire rope drum and brakes, open contact boards are in view at the far right wall - Puget Sound Naval Shipyard, Portal Gantry Crane No. 42, Pier 5, Farragut Avenue, Bremerton, Kitsap County, WA
16. 14 CFR 23.493 - Braked roll conditions.
Code of Federal Regulations, 2010 CFR
2010-01-01
...479 for level landings. (c) A drag reaction equal to the vertical reaction at the wheel multiplied by a coefficient of friction...wheel with brakes, except that the drag reaction need not exceed the...
17. 11. STOVE NUT USED IN THE MILL WHEN THE BRAKE ...
Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey
11. STOVE NUT USED IN THE MILL WHEN THE BRAKE WHEEL DROVE ONE PAIR OF MILLSTONES DIRECTLY; FOUND ON THE FIRST FLOOR OF THE WINDMILL AT WATERMILL - Windmill at Water Mill, Montauk Highway & Halsey Lane, Water Mill, Suffolk County, NY
18. 49 CFR 232.305 - Single car air brake tests.
Code of Federal Regulations, 2010 CFR
2010-10-01
...removed, repaired, or replaced: (i) Brake reservoir; (ii) Control valve mounting gasket; (iii) Pipe bracket stud; (iv) Service portion; (v) Emergency portion; or (vi) Pipe bracket. (5) A car is found with one or more...
19. 49 CFR 232.305 - Single car air brake tests.
Code of Federal Regulations, 2011 CFR
2011-10-01
...removed, repaired, or replaced: (i) Brake reservoir; (ii) Control valve mounting gasket; (iii) Pipe bracket stud; (iv) Service portion; (v) Emergency portion; or (vi) Pipe bracket. (5) A car is found with one or more...
20. 49 CFR 232.305 - Single car air brake tests.
Code of Federal Regulations, 2014 CFR
2014-10-01
...removed, repaired, or replaced: (i) Brake reservoir; (ii) Control valve mounting gasket; (iii) Pipe bracket stud; (iv) Service portion; (v) Emergency portion; or (vi) Pipe bracket. (5) A car is found with one or more...
1. 49 CFR 232.305 - Single car air brake tests.
Code of Federal Regulations, 2012 CFR
2012-10-01
...removed, repaired, or replaced: (i) Brake reservoir; (ii) Control valve mounting gasket; (iii) Pipe bracket stud; (iv) Service portion; (v) Emergency portion; or (vi) Pipe bracket. (5) A car is found with one or more...
2. 49 CFR 232.305 - Single car air brake tests.
Code of Federal Regulations, 2013 CFR
2013-10-01
...removed, repaired, or replaced: (i) Brake reservoir; (ii) Control valve mounting gasket; (iii) Pipe bracket stud; (iv) Service portion; (v) Emergency portion; or (vi) Pipe bracket. (5) A car is found with one or more...
3. 27. UPPER STATION, LOWER FLOOR, BULL WHEEL, BRAKE AIR CYLINDER. ...
Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey
27. UPPER STATION, LOWER FLOOR, BULL WHEEL, BRAKE AIR CYLINDER. - Monongahela Incline Plane, Connecting North side of Grandview Avenue at Wyoming Street with West Carson Street near Smithfield Street, Pittsburgh, Allegheny County, PA
4. 28. UPPER STATION, LOWER FLOOR, BULL WHEEL ROOM, SAFETY BRAKE ...
Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey
28. UPPER STATION, LOWER FLOOR, BULL WHEEL ROOM, SAFETY BRAKE ADJUSTING MACHINERY. - Monongahela Incline Plane, Connecting North side of Grandview Avenue at Wyoming Street with West Carson Street near Smithfield Street, Pittsburgh, Allegheny County, PA
5. 49 CFR 570.59 - Service brake system.
Code of Federal Regulations, 2012 CFR
2012-10-01
...the surface at the thinnest point on the lining or pad. (d) Structural and mechanical parts. Backing plates, brake spiders and caliper assemblies shall not be deformed or cracked. System parts shall not be broken, misaligned, missing,...
6. 49 CFR 570.59 - Service brake system.
Code of Federal Regulations, 2011 CFR
2011-10-01
...the surface at the thinnest point on the lining or pad. (d) Structural and mechanical parts. Backing plates, brake spiders and caliper assemblies shall not be deformed or cracked. System parts shall not be broken, misaligned, missing,...
7. 49 CFR 570.59 - Service brake system.
Code of Federal Regulations, 2013 CFR
2013-10-01
...the surface at the thinnest point on the lining or pad. (d) Structural and mechanical parts. Backing plates, brake spiders and caliper assemblies shall not be deformed or cracked. System parts shall not be broken, misaligned, missing,...
8. 49 CFR 570.59 - Service brake system.
Code of Federal Regulations, 2014 CFR
2014-10-01
...the surface at the thinnest point on the lining or pad. (d) Structural and mechanical parts. Backing plates, brake spiders and caliper assemblies shall not be deformed or cracked. System parts shall not be broken, misaligned, missing,...
9. 49 CFR 230.77 - Foundation brake gear.
Code of Federal Regulations, 2014 CFR
2014-10-01
..., DEPARTMENT OF TRANSPORTATION STEAM LOCOMOTIVE INSPECTION AND MAINTENANCE STANDARDS Steam Locomotives and...) Distance above the rails. No part of the foundation brake gear of the steam locomotive or tender shall...
10. 49 CFR 570.59 - Service brake system.
Code of Federal Regulations, 2011 CFR
2011-10-01
...) Friction materials. On each brake, the thickness of the lining or pad shall not be less than one thirty... cracks that do not impair attachment. The wire in wire-backed lining shall not be visible on the...
11. 49 CFR 570.59 - Service brake system.
Code of Federal Regulations, 2014 CFR
2014-10-01
...) Friction materials. On each brake, the thickness of the lining or pad shall not be less than one thirty... cracks that do not impair attachment. The wire in wire-backed lining shall not be visible on the...
12. 49 CFR 570.59 - Service brake system.
Code of Federal Regulations, 2012 CFR
2012-10-01
...) Friction materials. On each brake, the thickness of the lining or pad shall not be less than one thirty... cracks that do not impair attachment. The wire in wire-backed lining shall not be visible on the...
13. 49 CFR 570.5 - Service brake system.
Code of Federal Regulations, 2011 CFR
2011-10-01
... CFR 571.105, on every new passenger car manufactured on or after January 1, 1968, and on other types...) Friction materials. On each brake the thickness of the lining or pad shall not be less than one...
14. Stability analysis and \\mu-synthesis control of brake systems
E-print Network
Lignon, Sylvain; Jezequel, Louis
2008-01-01
The concept of friction-induced brake vibrations, commonly known as judder, is investigated. Judder vibration is based on the class of geometrically induced or kinematic constraint instability. After presenting the modal coupling mechanism and the associated dynamic model, a stability analysis as well as a sensitivity analysis have been conducted in order to identify physical parameters for a brake design avoiding friction-induced judder instability. Next, in order to reduce the size of the instability regions in relation to possible system parameter combinations, robust stability via \\mu-synthesis is applied. By comparing the unstable regions between the initial and controlled brake system, some general indications emerge and it appears that robust stability via \\mu-synthesis has some effect on the instability of the brake system.
15. 49 CFR 393.48 - Brakes to be operative.
Code of Federal Regulations, 2010 CFR
2010-10-01
...reduce or remove front-wheel braking effort may only be used on buses, trucks, and truck tractors manufactured before March 1...house moving dollies, specialized trailers and dollies used to transport industrial furnaces, reactors, and similar motor...
16. 49 CFR 238.313 - Class I brake test.
Code of Federal Regulations, 2014 CFR
2014-10-01
...the train properly apply; (13) Each brake disc is free of any crack in accordance with the manufacturer's specifications or, if no specifications exist, free of any crack to the extent that the design permits; (14) If the...
17. Metals associated with stormwater-relevant brake and tire samples
PubMed Central
McKenzie, Erica R.; Money, Jon E.; Green, Peter G.; Young, Thomas M.
2009-01-01
Properly apportioning the loads of metals in highway stormwater runoff to the appropriate sources requires accurate data on source composition, especially regarding constituents that help to distinguish among sources. Representative tire and brake samples were collected from privately owned vehicles and aqueous extracts were analyzed for twenty-eight elements. Correlation principal components analysis (PCA) revealed that tires were most influenced by Zn, Pb, and Cu, while brakes were best characterized by Na and Fe followed by Ba, Cu, Mg, Mn, and K; the latter three may be due to roadside soil contributions. Notably elevated Cd contributions were found in several brake samples. A targeted Cd-plated brake rotor was sampled, producing results consistent with the elevated levels found in the larger sample population. This enriched source of Cd is of particular concern due to high toxicity of Cd in aquatic ecosystems. PMID:19709720
18. 4. FLOOR 3; GENERAL VIEW LOOKING NORTH SHOWS WALLOWER, BRAKE ...
Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey
4. FLOOR 3; GENERAL VIEW LOOKING NORTH SHOWS WALLOWER, BRAKE LEVER, CASE FOR SCREENER, TOP OF GRAIN ELEVATOR, LAYSHAFT WHICH POWERS THE SCREENER AND ELEVATOR - Hayground Windmill, Windmill Lane, East Hampton, Suffolk County, NY
19. Downhole hydraulic seismic generator
DOEpatents
Gregory, Danny L. (Corrales, NM); Hardee, Harry C. (Albuquerque, NM); Smallwood, David O. (Albuquerque, NM)
1992-01-01
A downhole hydraulic seismic generator system for transmitting energy wave vibrations into earth strata surrounding a borehole. The system contains an elongated, unitary housing operably connected to a well head aboveground by support and electrical cabling, and contains clamping apparatus for selectively clamping the housing to the walls of the borehole. The system further comprises a hydraulic oscillator containing a double-actuating piston whose movement is controlled by an electro-servovalve regulating a high pressure hydraulic fluid flow into and out of upper and lower chambers surrounding the piston. The spent hydraulic fluid from the hydraulic oscillator is stored and pumped back into the system to provide high pressure fluid for conducting another run at the same, or a different location within the borehole.
20. 6. North wall and east end of air brake shop ...
Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey
6. North wall and east end of air brake shop section of roundhouse at center. East end of boiler shop section of roundhouse to the right of air brake shop. East end of blacksmith shop section of roundhouse at far right. View to southeast. - Duluth & Iron Range Rail Road Company Shops, Roundhouse, Southwest of downtown Two Harbors, northwest of Agate Bay, Two Harbors, Lake County, MN
1. 16 CFR 1512.5 - Requirements for braking system.
Code of Federal Regulations, 2010 CFR
2010-01-01
.... Bicycles shall be equipped with front- and rear-wheel brakes or rear-wheel brakes only. (b) Handbrakes...)(2), and shall be rocked back and forth with the weight of a 68.1 kg (150 lb) rider on the seat with... of at least 68.1 kg (150 lb) weight in accordance with the performance test, § 1512.18(d)(2) (v)...
2. Investigation of aerodynamic braking devices for wind turbine applications
SciTech Connect
Griffin, D.A.
1997-04-01
This report documents the selection and preliminary design of a new aerodynamic braking system for use on the stall-regulated AWT-26/27 wind turbines. The goal was to identify and design a configuration that offered improvements over the existing tip brake used by Advanced Wind Turbines, Inc. (AWT). Although the design objectives and approach of this report are specific to aerodynamic braking of AWT-26/27 turbines, many of the issues addressed in this work are applicable to a wider class of turbines. The performance trends and design choices presented in this report should be of general use to wind turbine designers who are considering alternative aerodynamic braking methods. A literature search was combined with preliminary work on device sizing, loads and mechanical design. Candidate configurations were assessed on their potential for benefits in the areas of cost, weight, aerodynamic noise, reliability and performance under icing conditions. As a result, two configurations were identified for further study: the {open_quotes}spoiler-flap{close_quotes} and the {open_quotes}flip-tip.{close_quotes} Wind tunnel experiments were conducted at Wichita State University to evaluate the performance of the candidate aerodynamic brakes on an airfoil section representative of the AWT-26/27 blades. The wind tunnel data were used to predict the braking effectiveness and deployment characteristics of the candidate devices for a wide range of design parameters. The evaluation was iterative, with mechanical design and structural analysis being conducted in parallel with the braking performance studies. The preliminary estimate of the spoiler-flap system cost was \$150 less than the production AWT-26/27 tip vanes. This represents a reduction of approximately 5 % in the cost of the aerodynamic braking system. In view of the preliminary nature of the design, it would be prudent to plan for contingencies in both cost and weight.
3. Will the tachyonic universe survive the big brake?
Keresztes, Zoltán; Gergely, László Á.; Kamenshchik, Alexander Yu.; Gorini, Vittorio; Polarski, David
2010-12-01
We investigate a Friedmann universe filled with a tachyon scalar field, which behaved as dustlike matter in the past, while it is able to accelerate the expansion rate of the Universe at late times. The comparison with type Ia supernovae (SNIa) data allows for evolutions driving the Universe into a Big Brake. Some of the evolutions leading to a Big Brake exhibit a large variation of the equation of state parameter at low redshifts, which is potentially observable with future data, though hardly detectable with present SNIa data. The soft Big Brake singularity occurs at finite values of the scale factor, vanishing energy density and Hubble parameter, but diverging deceleration and infinite pressure. We show that the geodesics can be continued through the Big Brake and that our model universe will recollapse eventually in a Big Crunch. Although the time to the Big Brake strongly depends on the present values of the tachyonic field and of its time derivative, the time from the Big Brake to the Big Crunch represents a kind of invariant time scale for all field parameters allowed by SNIa.
4. Braking and cornering studies on an air cushion landing system
NASA Technical Reports Server (NTRS)
Daugherty, R. H.
1983-01-01
An experimental investigation was conducted to evaluate several concepts for braking and steering a vehicle equipped with an air cushion landing system (ACLS). The investigation made use of a modified airboat equipped with an ACLS. Braking concepts were characterized by the average deceleration of the vehicle. Reduced lobe flow and cavity venting braking concepts were evaluated in this program. The cavity venting braking concept demonstrated the best performance, producing decelerations on the test vehicle on the same order as moderate braking with conventional wheel brakes. Steering concepts were evaluated by recording the path taken while attempting to follow a prescribed maneuver. The steering concepts evaluated included using rudders only, using differential lobe flow, and using rudders combined with a lightly loaded, nonsteering center wheel. The latter concept proved to be the most accurate means of steering the vehicle on the ACLS, producing translational deviations two to three times higher than those from conventional nose-gear steering. However, this concept was still felt to provide reasonably precise steering control for the ACLS-equipped vehicle.
5. Infrared characterization of thermal gradients on disc brakes
Panier, Stephane; Dufrenoy, Philippe; Bremond, Pierre
2003-04-01
The heat generated in frictional organs like brakes and clutches induces thermal distortions which may lead to localized contact areas and hot spots developments. Hot spots are high thermal gradients on the rubbing surface. They count among the most dangerous phenomena in frictional organs leading to damage, early failure and unacceptable braking performances such as brake fade or undesirable low frequency vibrations called hot judder. In this paper, an experimental study of hot spots occurrence in railway disc brakes is reported on. The aim of this study was to better classify and to explain the thermal gradients appearance on the surface of the disc. Thermograph measurements with an infrared camera have been carried out on the rubbing surface of brake discs on a full-scale test bench. The infrared system was set to take temperature readings in snap shot mode precisely synchronized with the rotation of the disc. Very short integration time allows reducing drastically haziness of thermal images. Based on thermographs, a classification of hot-spots observed in disc brakes is proposed. A detailed investigation of the most damaging thermal gradients, called macroscopic hot spots (MHS) is given. From these experimental researches, a scenario of hot spots occurrence is suggested step by step. Thanks to infrared measurements at high frequency with high resolution, observations give new highlights on the conditions of hot spots appearance. Comparison of the experimental observations with the theoretical approaches is finally discussed.
6. Hall drift and the braking indices of young pulsars
Gourgouliatos, K. N.; Cumming, A.
2015-01-01
Braking index measurements of young radio pulsars are all smaller than the value expected for spin-down by magnetic dipole braking. We investigate magnetic field evolution in the neutron star crust due to Hall drift as an explanation for observed braking indices. Using numerical simulations and a semi-analytic model, we show that an ?1014 G quadrupolar toroidal field in the neutron star crust at birth leads to growth of the dipole moment at a rate large enough to agree with measured braking indices. A key factor is the density at which the crust yields to magnetic stresses that build up during the evolution, which sets a characteristic minimum Hall time-scale. The observed braking indices of pulsars with inferred dipole fields of ? 1013 G can be explained in this picture, although with a significant octupole component needed in some cases. For the stronger field pulsars, those with Bd ? 1013 G, we find that the magnetic stresses in the crust exceed the maximum shear stress before the pulsar reaches its current age, likely quenching the Hall effect. This may have implications for the magnetar activity seen in the high magnetic field radio pulsar PSR J1846-0258. Observations of braking indices may therefore be a new piece of evidence that neutron stars contain subsurface toroidal fields that are significantly stronger than the dipole field, and may indicate that the Hall effect is important in a wider range of neutron stars than previously thought.
7. Development of aircraft brake materials. [evaluation of metal and ceramic materials in sliding tests simulation of aircraft braking
NASA Technical Reports Server (NTRS)
Ho, T. L.; Peterson, M. B.
1974-01-01
The requirements of brake materials were outlined and a survey made to select materials to meet the needs of high temperature brakes. A number of metals and ceramic materials were selected and evaluated in sliding tests which simulated aircraft braking. Nickel, molybdenum tungsten, Zr02, high temperature cements and carbons were tested. Additives were then incorporated into these materials to optimize their wear or strength behavior with particular emphasis on nickel and molybdenum base materials and a high temperature potassium silicate cement. Optimum materials were developed which improved wear behavior over conventional brake materials in the simulated test. The best materials are a nickel, aluminum oxide, lead tungstate composition containing graphite or molybdenum disulphite; a molybdenum base material containing LPA100 (an intermetallic compound of cobalt, molybdenum, and silicon); and a carbon material (P5).
8. Wear Modalities and Mechanisms of the Mining Non-asbestos Composite Brake Material
Bao, Jiusheng; Yin, Yan; Zhu, Zhencai; Tong, Minming; Lu, Yuhao; Peng, Yuxing
2013-08-01
The mining brake material is generally made of composite materials and its wear has important influences on the braking performance of disc brakes. In order to improve the braking reliability of mine hoisters, this paper did some tribological investigations on the mining brake material to reveal its wear modalities and mechanisms. The mining non-asbestos brake shoe and 16Mn steel were selected as braking pairs and tested on a pad-on-disc friction tester. And a SEM was used to observe the worn surface of the brake shoe. It is shown that the non-asbestos brake material has mainly five wear modalities: adhesive wear, abrasive wear, cutting wear, fatigue wear and high heat wear. At the front period of a single braking the wear modality is mainly composed of some light mechanical wear such as abrasive, cutting and point adhesive. With the temperature rising at the back period it transforms to some heavy mechanical wear such as piece adhesive and fatigue. While in several repeated brakings once the surface temperature rises beyond the thermal-decomposition point of the bonding material, the strong destructive high heat wear takes leading roles on the surface. And a phenomenon called friction catastrophe (FC) occurs easily, which as a result causes a braking failure. It is considered that the friction heat has important influences on the wear modalities of the brake material. And the reduction of friction heat must be an effective technical method for decreasing wear and avoiding braking failures.
9. Thermal measurement of brake pad lining surfaces during the braking process
Pi?tkowski, Tadeusz; Polakowski, Henryk; Kastek, Mariusz; Baranowski, Pawel; Damaziak, Krzysztof; Ma?achowski, Jerzy; Mazurkiewicz, ?ukasz
2012-06-01
This paper presents the test campaign concept and definition and the analysis of the recorded measurements. One of the most important systems in cars and trucks are brakes. The braking temperature on a lining surface can rise above 500°C. This shows how linings requirements are so strict and, what is more, continuously rising. Besides experimental tests, very supportive method for investigating processes which occur on the brake pad linings are numerical analyses. Experimental tests were conducted on the test machine called IL-68. The main component of IL-68 is so called frictional unit, which consists of: rotational head, which convey a shaft torque and where counter samples are placed and translational head, where samples of coatings are placed and pressed against counter samples. Due to the high rotational speeds and thus the rapid changes in temperature field, the infrared camera was used for testing. The paper presents results of analysis registered thermograms during the tests with different conditions. Furthermore, based on this testing machine, the numerical model was developed. In order to avoid resource demanding analyses only the frictional unit (described above) was taken into consideration. Firstly the geometrical model was performed thanks to CAD techniques, which in the next stage was a base for developing the finite element model. Material properties and boundary conditions exactly correspond to experimental tests. Computations were performed using a dynamic LS-Dyna code where heat generation was estimated assuming full (100%) conversion of mechanical work done by friction forces. Paper presents the results of dynamic thermomechanical analysis too and these results were compared with laboratory tests.
10. 49 CFR 571.105 - Standard No. 105; Hydraulic and electric brake systems.
Code of Federal Regulations, 2010 CFR
2010-10-01
... compensate for vehicle static axle loading and/or dynamic weight transfer between axles during deceleration... accordance with American Society for Testing and Materials (ASTM) Method E-274-70 (as revised July, 1974) at... word, words or abbreviation, in accordance with the requirements of Standard No. 101 (49 CFR...
11. 49 CFR 571.105 - Standard No. 105; Hydraulic and electric brake systems.
Code of Federal Regulations, 2011 CFR
2011-10-01
... compensate for vehicle static axle loading and/or dynamic weight transfer between axles during deceleration... accordance with American Society for Testing and Materials (ASTM) Method E-274-70 (as revised July, 1974) at... word, words or abbreviation, in accordance with the requirements of Standard No. 101 (49 CFR...
12. Intelligently Controllable Walker with Magnetorheological Fluid Brake
Kikuchi, Takehito; Tanida, Sosuke; Tanaka, Toshimasa; Kobayashi, Keigo; Mitobe, Kazuhisa
Caster walkers are supporting frames with casters and wheels. These tools are regularly utilized as life support tools or walking rehabilitation tools in hospitals, nursing homes and individual residences. Users of the walkers can easily move it thanks to its wheels and casters. However falling accidents often happen when it moves without users. The falling accident is very serious problem and one of leading causes of secondary injuries. In the other case, it is hard to move to desired directions if users have imbalance in their motor functions or sensory functions, e.g., hemiplegic patients. To improve safeness and operability of the walkers, we installed compact MR fluid brakes on the wheels and controlled walking speed and direction of the walker. We named this intelligently controllable walker, “i-Walker” and discussed on the control methods and experimental results in this paper. Preliminary trials for direction control of the first-generation of the i-Walker (i-Walker1) are presented. On the basis of the results, we improved the control method and hardware of the i-Walker1, and developed the second-generation (i-Walker2). System description and experimental results of the i-Walker2 are also described. The i-Walker2 has better operability and lower energy consumption than that of the i-Walker1. The line-tracing controller of the i-Walker2 well controls human motions during walking experiments on the target straight line.
13. Hydraulic Fracturing Sand
USGS Multimedia Gallery
Fine-grained silica sand is mixed with chemicals and water before being pumped into rock formations to prevent the newly created artificial fractures from closing after hydraulic fracturing is completed....
14. Hydraulic hoisting and backfilling
Sauermann, H. B.
In a country such as South Africa, with its large deep level mining industry, improvements in mining and hoisting techniques could result in substantial savings. Hoisting techniques, for example, may be improved by the introduction of hydraulic hoisting. The following are some of the advantages of hydraulic hoisting as against conventional skip hoisting: (1) smaller shafts are required because the pipes to hoist the same quantity of ore hydraulically require less space in the shaft than does skip hoisting equipment; (2) the hoisting capacity of a mine can easily be increased without the necessity of sinking new shafts. Large savings in capital costs can thus be made; (3) fully automatic control is possible with hydraulic hoisting and therefore less manpower is required; and (4) health and safety conditions will be improved.
15. Portable Hydraulic Powerpack
NASA Technical Reports Server (NTRS)
Anderson, L. A.; Henry, R. L.; Fedor, O. H.; Owens, L. J.
1986-01-01
Rechargeable hydraulic powerpack functions as lightweight, compact source of mechanical energy. Self-contained hydraulic powerpack derives energy from solid chemical charge. Combustion of charge initiated by small hammer, and revolving feeder replaces charges expended. Combustion gases cool during expansion in turbine and not too hot for release to atmosphere. Unit has applications driving wheelchairs and operating drills, winches, and other equipment in remote areas. Also replaces electric motors and internal-combustion engines as source of power in explosive atmospheres.
Nguyen, The; Munguia, Vicente; Calderon, Jose
2014-04-01
Current knee designs for prosthetic legs rely on electric motors for both moving and stationary states. The electric motors draw an especially high level of current to sustain a fixed position. The advantage of using magnetorheological (MR) fluid is that it requires less current and can have a variable braking torque. Besides, the proposed prosthetic leg is actuated by NiTinol wire, a popular shape memory alloy (SMA). The incorporation of NiTinol gives the leg more realistic weight distribution with appropriate arrangement of the batteries and wires. The prosthesis in this research was designed with MR brake as stopping component and SMA wire network as actuating component at the knee. The MR brake was designed with novel non-circular shape for the rotor that improved the braking torque while minimizing the power consumption. The design also helped simplify the control of braking process. The SMA wire network was design so that the knee motion was actively rotated in both directions. The SMA wires were arranged and played very similar role as the leg's muscles. The study started with the overall solid design of the knee including both MR and SMA parts. Theoretical models were derived and programmed in Simulink for both components. The simulation was capable of predicting the power required for moving the leg or hold it in a fixed position for a certain amount of time. Subsequently, the design was prototyped and tested to validate the theoretical prediction. The theoretical models were updated accordingly to correlate with the experimental data.
17. Thermophysical Properties of Automotive Metallic Brake Disk Materials
Kim, S. W.; Park, K.; Lee, S. H.; Kang, K. H.; Lim, K. T.
2008-12-01
The temperature distribution, the thermal deformation, and the thermal stress of automotive brake disks have quite close relations with car safety; therefore, much research in this field has been performed. However, successful and satisfactory results have not been obtained because the temperature-dependent thermophysical properties of brake disk materials are not sufficiently known. In this study, the thermophysical properties (thermal diffusivity, the specific heat, and the coefficient of thermal expansion) of three kinds of iron alloy series brake disk materials, FC250, FC170, and FCD50, and two kinds of aluminum alloy series brake disk materials, Al MMC and A356, were measured in the temperature range from room temperature to 500 °C, and the thermal conductivity was calculated using the measured thermal diffusivity, specific heat capacity, and density. As expected, the results show that the two series have significant differences in respect of the thermophysical properties, and to reduce the thermal deformation of the brake disk, the aluminum alloys with a high thermal conductivity and the iron alloys with low thermal expansion are recommended.
18. Arsenic species and leachability in the fronds of the hyperaccumulator Chinese brake (Pteris vittata L.)
E-print Network
Ma, Lena
Arsenic species and leachability in the fronds of the hyperaccumulator Chinese brake (Pteris June 2002; accepted 9 December 2002 Capsule'': Arsenic was predominantly present as inorganic arsenite in the fronds of the hyperaccumulator Chinese brake. Abstract Arsenic speciation is important
19. Brake Defect Causa on and Abatement Study (BDCAS) The Federal Motor Carrier Safety
E-print Network
whose brake force is less than 43.5 percent of its gross vehicle weight is not allowed to return to its capability of a vehicle through measurement of the brake force developed as a function of weight. Any vehicle
20. 77 FR 46633 - Parts and Accessories Necessary for Safe Operation: Brakes; Adjustment Limits
Federal Register 2010, 2011, 2012, 2013, 2014
2012-08-06
...for Safe Operation: Brakes; Adjustment Limits AGENCY: Federal Motor Carrier Safety...requirements regarding brake readjustment limits in the Federal Motor Carrier Safety Regulations...This rule amends the readjustment limits, clarifies their application, and...
1. 76 FR 54721 - Parts and Accessories Necessary for Safe Operation: Brakes; Adjustment Limits
Federal Register 2010, 2011, 2012, 2013, 2014
2011-09-02
...for Safe Operation: Brakes; Adjustment Limits AGENCY: Federal Motor Carrier Safety...rotochamber brake actuator readjustment limits in the Federal Motor Carrier Safety Regulations...NPRM) is to amend the readjustment limits, clarify their application, and...
2. Regenerative braking device with rotationally mounted energy storage means
DOEpatents
Hoppie, Lyle O. (Birmingham, MI)
1982-03-16
A regenerative braking device for an automotive vehicle includes an energy storage assembly (12) having a plurality of rubber rollers (26, 28) mounted for rotation between an input shaft (30) and an output shaft (32), clutches (50, 56) and brakes (52, 58) associated with each shaft, and a continuously variable transmission (22) connectable to a vehicle drivetrain and to the input and output shafts by the respective clutches. In a second embodiment the clutches and brakes are dispensed with and the variable ratio transmission is connected directly across the input and output shafts. In both embodiments the rubber rollers are torsionally stressed to accumulate energy from the vehicle when the input shaft rotates faster or relative to the output shaft and are torsionally relaxed to deliver energy to the vehicle when the output shaft rotates faster or relative to the input shaft.
3. Surrogate models for efficient stability analysis of brake systems
Nechak, Lyes; Gillot, Frédéric; Besset, Sébastien; Sinou, Jean-Jacques
2015-07-01
This study assesses capacities of the global sensitivity analysis combined together with the kriging formalism to be useful in the robust stability analysis of brake systems, which is too costly when performed with the classical complex eigenvalues analysis (CEA) based on finite element models (FEMs). By considering a simplified brake system, the global sensitivity analysis is first shown very helpful for understanding the effects of design parameters on the brake system's stability. This is allowed by the so-called Sobol indices which discriminate design parameters with respect to their influence on the stability. Consequently, only uncertainty of influent parameters is taken into account in the following step, namely, the surrogate modelling based on kriging. The latter is then demonstrated to be an interesting alternative to FEMs since it allowed, with a lower cost, an accurate estimation of the system's proportions of instability corresponding to the influent parameters.
4. Thermal Modeling of Disc Brake Rotor in Frictional Contact
Ali, Belhocine; Ghazaly, Nouby Mahdi
2013-01-01
Safety aspect in automotive engineering has been considered as a number one priority in development of new vehicle. Each single system has been studied and developed in order to meet safety requirement. Instead of having air bag, good suspension systems, good handling and safe cornering, there is one most critical system in the vehicle which is brake systems. The objective of this work is to investigate and analyze the temperature distribution of rotor disc during braking operation using ANSYS Multiphysics. The work uses the finite element analysis techniques to predict the temperature distribution on the full and ventilated brake disc and to identify the critical temperature of the rotor. The analysis also gives us, the heat flux distribution for the two discs.
5. Periodic brake orbits in the planar isosceles three-body problem
Chen, Nai-Chia
2013-10-01
A brake orbit is an orbit that starts with zero initial velocity. The purpose of this paper is to find periodic brake orbits in the isosceles three-body problem. We use various shooting arguments; we follow a curve of brake initial conditions under the flow until it reaches a suitable surface, and show that the image curve includes a point that corresponds to a periodic orbit. As a result, we prove the existence of six types of periodic brake orbits.
6. Evaluation of Corrosion Failure in Tractor-Trailer Brake System
SciTech Connect
Wilson, DF
2002-10-22
As reported to ORNL, concomitant with the introduction of different deicing and anti-icing compounds, there was an increase in the brake failure rate of tractor-trailer trucks. A forensic evaluation of a failed brake system was performed. Optical and scanning electron microscopic evaluation showed corrosion to be mostly confined to the brake table/lining interface. The corrosion is non-uniform as is to be expected for plain carbon steel in chloride environments. This initial analysis found no evidence for the chlorides of calcium and magnesium, which are the newly introduced deicing and antiicing compounds and are less soluble in water than the identified chlorides of sodium and potassium, in the scale. The result could be as a result of non-exposure of the examined brake table to calcium and magnesium chloride. The mechanisms for the increased failure rate are postulated as being an increased rate of corrosion due to positive shifts in the corrosion potential, and an increased amount of corrosion due to an increased ''time of wetness'' that results from the presence of hygroscopic salts. Laboratory scale evaluation of the corrosion of plain carbon steel in simulated deicing and anti-icing solutions need to be performed to determine corrosion rates and morphological development of corrosion product, to compare laboratory data to in-service data, and to rank economically feasible replacement materials for low carbon steel. In addition, the mechanical behavior of the lining attached to the brake shoe table needs to be assessed. It is opined that an appropriate adjustment of materials could easily allow for a doubling of a brake table/lining lifetime. Suggestions for additional work, to clarify the mechanisms of rust jacking and to develop possible solutions, are described.
7. 49 CFR 232.503 - Process to introduce new brake system technology.
Code of Federal Regulations, 2014 CFR
2014-10-01
... 49 Transportation 4 2014-10-01 2014-10-01 false Process to introduce new brake system technology... Technology § 232.503 Process to introduce new brake system technology. (a) Pursuant to the procedures... brake system technology, prior to implementing the plan. (b) Each railroad shall complete a...
8. 49 CFR 232.503 - Process to introduce new brake system technology.
Code of Federal Regulations, 2012 CFR
2012-10-01
... 49 Transportation 4 2012-10-01 2012-10-01 false Process to introduce new brake system technology... Technology § 232.503 Process to introduce new brake system technology. (a) Pursuant to the procedures... brake system technology, prior to implementing the plan. (b) Each railroad shall complete a...
9. 49 CFR 232.503 - Process to introduce new brake system technology.
Code of Federal Regulations, 2013 CFR
2013-10-01
... 49 Transportation 4 2013-10-01 2013-10-01 false Process to introduce new brake system technology... Technology § 232.503 Process to introduce new brake system technology. (a) Pursuant to the procedures... brake system technology, prior to implementing the plan. (b) Each railroad shall complete a...
10. Hierarchical Control Strategy for the Cooperative Braking System of Electric Vehicle.
PubMed
Peng, Jiankun; He, Hongwen; Liu, Wei; Guo, Hongqiang
2015-01-01
This paper provides a hierarchical control strategy for cooperative braking system of an electric vehicle with separated driven axles. Two layers are defined: the top layer is used to optimize the braking stability based on two sliding mode control strategies, namely, the interaxle control mode and signal-axle control strategies; the interaxle control strategy generates the ideal braking force distribution in general braking condition, and the single-axle control strategy can ensure braking safety in emergency braking condition; the bottom layer is used to maximize the regenerative braking energy recovery efficiency with a reallocated braking torque strategy; the reallocated braking torque strategy can recovery braking energy as much as possible in the premise of meeting battery charging power. The simulation results show that the proposed hierarchical control strategy is reasonable and can adapt to different typical road surfaces and load cases; the vehicle braking stability and safety can be guaranteed; furthermore, the regenerative braking energy recovery efficiency can be improved. PMID:26236772
11. 49 CFR 232.503 - Process to introduce new brake system technology.
Code of Federal Regulations, 2011 CFR
2011-10-01
... 49 Transportation 4 2011-10-01 2011-10-01 false Process to introduce new brake system technology... Technology § 232.503 Process to introduce new brake system technology. (a) Pursuant to the procedures... brake system technology, prior to implementing the plan. (b) Each railroad shall complete a...
12. Correcting Students' Misconceptions about Automobile Braking Distances and Video Analysis Using Interactive Program Tracker
ERIC Educational Resources Information Center
Hockicko, Peter; Trpišová, Beáta; Ondruš, Ján
2014-01-01
The present paper informs about an analysis of students' conceptions about car braking distances and also presents one of the novel methods of learning: an interactive computer program Tracker that we used to analyse the process of braking of a car. The analysis of the students' conceptions about car braking distances consisted in…
13. The Chinese brake fern (Pteris vittata L.), native to China, is widely naturalized in
E-print Network
Ma, Lena
The Chinese brake fern (Pteris vittata L.), native to China, is widely naturalized in many areas and anatomical aspects of Chinese brake fern (Pteris vittata; Pteridaceae) Bhaskar Bondada1, Cong Tu, and Lena Ma-0290, U.S.A.; e-mail: lqma@ifas.ufl.edu). Sur- face structure and anatomical aspects of Chinese brake fern
14. Thiol synthesis and arsenic hyperaccumulation in Pteris vittata (Chinese brake fern)
E-print Network
Ma, Lena
Thiol synthesis and arsenic hyperaccumulation in Pteris vittata (Chinese brake fern) Weihua Zhanga in arsenic detoxification. Abstract Pteris vittata (Chinese brake fern) has potential for phytoremediation to be a supplement. Ó 2004 Elsevier Ltd. All rights reserved. Keywords: Pteris vittata; Chinese brake fern; Thiols
15. Auto Mechanics I. Learning Activity Packets (LAPs). Section E--Brakes.
ERIC Educational Resources Information Center
Oklahoma State Board of Vocational and Technical Education, Stillwater. Curriculum and Instructional Materials Center.
This document contains two learning activity packets (LAPs) that outline the study activities for the "brakes" instructional area for an Auto Mechanics I course. The two LAPs cover the following topics: brake systems and power disc brakes. Each LAP contains a cover sheet that describes its purpose, an introduction, and the tasks included in the…
16. 75 FR 51521 - Federal Motor Vehicle Safety Standards; Air Brake Systems; Technical Report on the Effectiveness...
Federal Register 2010, 2011, 2012, 2013, 2014
2010-08-20
...report's title is: The Effectiveness of ABS [Antilock Braking Systems] in Heavy Truck...121) mandates antilock braking systems (ABS) on all new air-braked vehicles with a GVWR of 10,000 pounds or greater. ABS is required on tractors manufactured...
17. 49 CFR 571.122 - Standard No. 122; Motorcycle brake systems.
Code of Federal Regulations, 2012 CFR
2012-10-01
...compensated for by means of a system of automatic or manual... S5.3Measurement of dynamic performance. There are two ways in which brake system performance is measured...surface is used for all dynamic brake tests excluding...1.4Parking brake system tests. The...
18. 49 CFR 571.122 - Standard No. 122; Motorcycle brake systems.
Code of Federal Regulations, 2014 CFR
2014-10-01
...compensated for by means of a system of automatic or manual... S5.3Measurement of dynamic performance. There are two ways in which brake system performance is measured...surface is used for all dynamic brake tests excluding...1.4Parking brake system tests. The...
19. 49 CFR 571.122 - Standard No. 122; Motorcycle brake systems.
Code of Federal Regulations, 2013 CFR
2013-10-01
...compensated for by means of a system of automatic or manual... S5.3Measurement of dynamic performance. There are two ways in which brake system performance is measured...surface is used for all dynamic brake tests excluding...1.4Parking brake system tests. The...
20. 77 FR 39561 - Advanced Braking Technologies That Rely on Forward-Looking Sensors; Request for Comments
Federal Register 2010, 2011, 2012, 2013, 2014
2012-07-03
...NHTSA-2012-0057] Advanced Braking Technologies That Rely on Forward-Looking...studying advanced braking technologies that rely on forward-looking...will activate brake assist technologies in some vehicles and not...camera, LIDAR, and/or infrared sensors to assess the...
1. 49 CFR 232.309 - Equipment and devices used to perform single car air brake tests.
Code of Federal Regulations, 2013 CFR
2013-10-01
...Equipment and devices used to perform single car air brake tests. 232.309 Section...Equipment and devices used to perform single car air brake tests. (a) Equipment and devices used to perform single car air brake tests shall be tested for...
2. 49 CFR 232.309 - Equipment and devices used to perform single car air brake tests.
Code of Federal Regulations, 2014 CFR
2014-10-01
...Equipment and devices used to perform single car air brake tests. 232.309 Section...Equipment and devices used to perform single car air brake tests. (a) Equipment and devices used to perform single car air brake tests shall be tested for...
3. 49 CFR 232.309 - Equipment and devices used to perform single car air brake tests.
Code of Federal Regulations, 2010 CFR
2010-10-01
...Equipment and devices used to perform single car air brake tests. 232.309 Section...Equipment and devices used to perform single car air brake tests. (a) Equipment and devices used to perform single car air brake tests shall be tested for...
4. 49 CFR 232.309 - Equipment and devices used to perform single car air brake tests.
Code of Federal Regulations, 2012 CFR
2012-10-01
...Equipment and devices used to perform single car air brake tests. 232.309 Section...Equipment and devices used to perform single car air brake tests. (a) Equipment and devices used to perform single car air brake tests shall be tested for...
5. 49 CFR 232.309 - Equipment and devices used to perform single car air brake tests.
Code of Federal Regulations, 2011 CFR
2011-10-01
...Equipment and devices used to perform single car air brake tests. 232.309 Section...Equipment and devices used to perform single car air brake tests. (a) Equipment and devices used to perform single car air brake tests shall be tested for...
6. Hierarchical Control Strategy for the Cooperative Braking System of Electric Vehicle
PubMed Central
Peng, Jiankun; He, Hongwen; Liu, Wei; Guo, Hongqiang
2015-01-01
This paper provides a hierarchical control strategy for cooperative braking system of an electric vehicle with separated driven axles. Two layers are defined: the top layer is used to optimize the braking stability based on two sliding mode control strategies, namely, the interaxle control mode and signal-axle control strategies; the interaxle control strategy generates the ideal braking force distribution in general braking condition, and the single-axle control strategy can ensure braking safety in emergency braking condition; the bottom layer is used to maximize the regenerative braking energy recovery efficiency with a reallocated braking torque strategy; the reallocated braking torque strategy can recovery braking energy as much as possible in the premise of meeting battery charging power. The simulation results show that the proposed hierarchical control strategy is reasonable and can adapt to different typical road surfaces and load cases; the vehicle braking stability and safety can be guaranteed; furthermore, the regenerative braking energy recovery efficiency can be improved. PMID:26236772
7. 49 CFR 393.47 - Brake actuators, slack adjusters, linings/pads and drums/rotors.
Code of Federal Regulations, 2010 CFR
2010-10-01
... of the rated strokes listed in SAE J1817—Long Stroke Air Brake Actuator Marking, July 2001 (See § 393... percent of the rated stroke marked on the brake chamber by the chamber manufacturer, or the readjustment... long stroke clamp type brake actuators must be less than 51 mm (2 inches) or 80 percent of the...
8. 49 CFR 232.503 - Process to introduce new brake system technology.
Code of Federal Regulations, 2010 CFR
2010-10-01
... 49 Transportation 4 2010-10-01 2010-10-01 false Process to introduce new brake system technology... Technology § 232.503 Process to introduce new brake system technology. (a) Pursuant to the procedures... brake system technology, prior to implementing the plan. (b) Each railroad shall complete a...
9. 49 CFR 571.122 - Standard No. 122; Motorcycle brake systems.
Code of Federal Regulations, 2010 CFR
2010-10-01
...that the lining thickness of drum brake shoes may be visually inspected...removing the drums, and so that disc brake friction lining thickness may...the most heavily loaded shoe or disc pad, one per brake, as shown in Figure 1....
10. 49 CFR 232.307 - Modification of the single car air brake test procedures.
Code of Federal Regulations, 2012 CFR
2012-10-01
... 49 Transportation 4 2012-10-01 2012-10-01 false Modification of the single car air brake test... Requirements § 232.307 Modification of the single car air brake test procedures. (a) Request. The AAR or other authorized representative of the railroad industry may seek modification of the single car air brake...
11. 49 CFR 232.307 - Modification of the single car air brake test procedures.
Code of Federal Regulations, 2011 CFR
2011-10-01
... 49 Transportation 4 2011-10-01 2011-10-01 false Modification of the single car air brake test... Requirements § 232.307 Modification of the single car air brake test procedures. (a) Request. The AAR or other authorized representative of the railroad industry may seek modification of the single car air brake...
12. 49 CFR 232.307 - Modification of the single car air brake test procedures.
Code of Federal Regulations, 2014 CFR
2014-10-01
... 49 Transportation 4 2014-10-01 2014-10-01 false Modification of the single car air brake test... Requirements § 232.307 Modification of the single car air brake test procedures. (a) Request. The AAR or other authorized representative of the railroad industry may seek modification of the single car air brake...
13. 49 CFR 571.116 - Standard No. 116; Motor vehicle brake fluids.
Code of Federal Regulations, 2012 CFR
2012-10-01
... discernible without magnification; (c) The water-wet brake fluid at the end of the test shall show no jelling... walls or the surface of the metal strips; (e) At the end of the test, sedimentation of the water-wet brake fluid shall not exceed 0.10 percent by volume; (f) The pH value of water-wet brake fluid,...
14. 49 CFR 571.116 - Standard No. 116; Motor vehicle brake fluids.
Code of Federal Regulations, 2010 CFR
2010-10-01
... discernible without magnification; (c) The water-wet brake fluid at the end of the test shall show no jelling... walls or the surface of the metal strips; (e) At the end of the test, sedimentation of the water-wet brake fluid shall not exceed 0.10 percent by volume; (f) The pH value of water-wet brake fluid,...
15. 49 CFR 571.116 - Standard No. 116; Motor vehicle brake fluids.
Code of Federal Regulations, 2013 CFR
2013-10-01
... discernible without magnification; (c) The water-wet brake fluid at the end of the test shall show no jelling... walls or the surface of the metal strips; (e) At the end of the test, sedimentation of the water-wet brake fluid shall not exceed 0.10 percent by volume; (f) The pH value of water-wet brake fluid,...
16. 49 CFR 571.116 - Standard No. 116; Motor vehicle brake fluids.
Code of Federal Regulations, 2014 CFR
2014-10-01
... discernible without magnification; (c) The water-wet brake fluid at the end of the test shall show no jelling... walls or the surface of the metal strips; (e) At the end of the test, sedimentation of the water-wet brake fluid shall not exceed 0.10 percent by volume; (f) The pH value of water-wet brake fluid,...
17. 49 CFR 571.116 - Standard No. 116; Motor vehicle brake fluids.
Code of Federal Regulations, 2011 CFR
2011-10-01
... discernible without magnification; (c) The water-wet brake fluid at the end of the test shall show no jelling... walls or the surface of the metal strips; (e) At the end of the test, sedimentation of the water-wet brake fluid shall not exceed 0.10 percent by volume; (f) The pH value of water-wet brake fluid,...
18. Transient analysis of thermoelastic contact problem of disk brakes
Belhocine, Ali; Bouchetara, Mostefa
2013-06-01
The main purpose of this study is to analyze the thermomechanical behavior of the dry contact between the brake disk and pads during the braking phase. The simulation strategy is based on computer code ANSYS11. The modeling of transient temperature in the disk is actually used to identify the factor of geometric design of the disk to install the ventilation system in vehicles. The thermal-structural analysis is then used with coupling to determine the deformation established and the Von Mises stresses in the disk, the contact pressure distribution in pads. The results are satisfactory compared to those found in the literature.
19. Thermal-mechanical coupled analysis of a brake disk rotor
Belhocine, Ali; Bouchetara, Mostefa
2013-08-01
The main purpose of this study is to analyze the thermomechanical behavior of the dry contact between the brake disk and pads during the braking phase. The simulation strategy is based on computer code ANSYS11. The modeling of transient temperature in the disk is actually used to identify the factor of geometric design of the disk to install the ventilation system in vehicles The thermal-structural analysis is then used with coupling to determine the deformation and the Von Mises stress established in the disk, the contact pressure distribution in pads. The results are satisfactory when compared to those of the specialized literature.
20. Disc brake squeal characterization through simplified test rigs
Akay, A.; Giannini, O.; Massi, F.; Sestieri, A.
2009-11-01
This paper presents a review of recent investigations on brake squeal noise carried out on simplified experimental rigs. The common theme of these works is that of approaching the study of squeal noise on experimental set-ups that are much simpler than commercial disc brakes, providing the possibility of repeatable measurements of squeal occurrence. As a consequence, it is possible to build consistent and robust models of the experimental apparatus to simulate the squeal events and to understand the physics behind squeal instabilities.
1. Geostatistical inference of hydraulic conductivity and dispersivities from hydraulic heads and tracer data
E-print Network
Cirpka, Olaf Arie
Geostatistical inference of hydraulic conductivity and dispersivities from hydraulic heads; accepted 25 April 2006; published 10 August 2006. [1] In groundwater, hydraulic heads and solute arrival times depend primarily on the hydraulic conductivity field and hydraulic boundary conditions. The spread
2. Failure analysis of energy storage spring in automobile composite brake chamber
Luo, Zai; Wei, Qing; Hu, Xiaofeng
2015-02-01
This paper set energy storage spring of parking brake cavity, part of automobile composite brake chamber, as the research object. And constructed the fault tree model of energy storage spring which caused parking brake failure based on the fault tree analysis method. Next, the parking brake failure model of energy storage spring was established by analyzing the working principle of composite brake chamber. Finally, the data of working load and the push rod stroke measured by comprehensive test-bed valve was used to validate the failure model above. The experimental result shows that the failure model can distinguish whether the energy storage spring is faulted.
3. Project Startup: Evaluating the Performance of Hydraulic Hybrid Refuse Vehicles
SciTech Connect
2015-09-01
The Fleet Test and Evaluation Team at the National Renewable Energy Laboratory (NREL) is evaluating the in-service performance of 10 next-generation hydraulic hybrid refuse vehicles (HHVs), 8 previous-generation HHVs, and 8 comparable conventional diesel vehicles operated by Miami-Dade County's Public Works and Waste Management Department in southern Florida. The HHVs under study - Autocar E3 refuse trucks equipped with Parker Hannifin's RunWise Advanced Series Hybrid Drive systems - can recover as much as 70 percent of the energy typically lost during braking and reuse it to power the vehicle. NREL's evaluation will assess the performance of this technology in commercial operation and help Miami-Dade County determine the ideal routes for maximizing the fuel-saving potential of its HHVs.
4. 27. Historic drawing, Marine Railway. Detail of Emergency Brake, 1917. ...
Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey
27. Historic drawing, Marine Railway. Detail of Emergency Brake, 1917. Photographic copy of original. Boston National Historical Park Archives, Charlestown Navy Yard. BOSTS 13439, #551-16 - Charlestown Navy Yard, Marine Railway, Between Piers 2 & 3, on Charlestown Waterfront at west end of Navy Yard, Boston, Suffolk County, MA
5. 14 CFR 27.493 - Braked roll conditions.
Code of Federal Regulations, 2011 CFR
2011-01-01
...a)(2); and (b) The structure must be designed to withstand at the ground contact point of each wheel with brakes, a drag load at least the lesser of— (1) The vertical load multiplied by a coefficient of friction of 0.8; and (2) The...
6. 14 CFR 27.493 - Braked roll conditions.
Code of Federal Regulations, 2012 CFR
2012-01-01
...a)(2); and (b) The structure must be designed to withstand at the ground contact point of each wheel with brakes, a drag load at least the lesser of— (1) The vertical load multiplied by a coefficient of friction of 0.8; and (2) The...
7. 14 CFR 29.493 - Braked roll conditions.
Code of Federal Regulations, 2012 CFR
2012-01-01
...2); and (b) The structure must be designed to withstand, at the ground contact point of each wheel with brakes, a drag load of at least the lesser of— (1) The vertical load multiplied by a coefficient of friction of 0.8; and (2)...
8. 14 CFR 29.493 - Braked roll conditions.
Code of Federal Regulations, 2011 CFR
2011-01-01
...2); and (b) The structure must be designed to withstand, at the ground contact point of each wheel with brakes, a drag load of at least the lesser of— (1) The vertical load multiplied by a coefficient of friction of 0.8; and (2)...
9. DISC BRAKE SYSTEM (CENTER), INCLUDING BELT DRIVE TO SECONDARY GENERAL ...
Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey
DISC BRAKE SYSTEM (CENTER), INCLUDING BELT DRIVE TO SECONDARY GENERAL MOTORS ENGINE (LEFT)AND FERREL REDUCTION GEAR CONNECTION TO ALLIS-CHALMERS DIESEL ENGINE (RIGHT), LOOKING NORTH. NOTE TORQUE CONVERTER (TOP) AND THROTTLE (BELOW) LINES CONNECTING TO PRIMARY ENGINE. - Mad River Glen, Single Chair Ski Lift, 62 Mad River Glen Resort Road, Fayston, Washington County, VT
10. 49 CFR 393.42 - Brakes required on all wheels.
Code of Federal Regulations, 2011 CFR
2011-10-01
... a gross weight of 1,361 kg (3,000 pounds) or less which is subject to this part is not required to be equipped with brakes if the axle weight of the towed vehicle does not exceed 40 percent of the sum of the axle weights of the towing vehicle. (4) Any full trailer or four-wheel pole trailer (laden...
11. Sudden Radiative Braking in Colliding Hot-Star Winds
Gayley, K. G.; Owocki, S. P.; Cranmer, S. R.
1997-02-01
Hot, massive stars have strong stellar winds, and in hot-star binaries these winds can undergo violent collision. Because such winds are thought to be radiatively driven, radiative forces may also play an important role in moderating the wind collision. However, previous studies have been limited to considering how such forces may inhibit the initial acceleration of the companion stellar wind. In this paper we analyze the role of an even stronger radiative braking effect, whereby the primary wind is rather suddenly decelerated by the radiative momentum flux it encounters as it approaches a bright companion. We further show that the braking location and velocity law along the line of centers between the stars can be approximated analytically using a simple one-dimensional analysis. The results of this analysis agree well with a detailed two-dimensional hydrodynamical simulation of the wind collision in the WR + O binary V444 Cygni and demonstrate that radiative braking can significantly alter the bow-shock geometry and reduce the strength of the wind collision. We then apply the derived analytic theory to a set of 14 hot-star binary systems, and conclude that radiative braking is likely to be of widespread importance for wind-wind collisions in WR + O binaries with close to medium separation, D <~ 100 R?. It may also be important in other types of hot-star binaries that exhibit a large imbalance between the component wind strengths.
12. Sudden Radiative Braking in Colliding Hot-Star Winds
Gayley, K.; Owocki, S.; Cranmer, S.
1996-05-01
Hot, massive stars have strong stellar winds, and in hot-star binaries these winds can undergo violent collision. Because such winds are thought to be radiatively driven, radiative forces may also play an important role in moderating the wind collision. However, previous studies have been limited to considering how such forces may inhibit the initial acceleration of the companion stellar wind. In this poster we describe the role of an even stronger radiative braking effect, whereby the primary wind is rather suddenly decelerated by the radiative momentum flux it encounters as it approaches a bright companion. We show that the braking location and velocity law along the line of centers between the stars can be approximated analytically using a simple one-dimensional analysis. The results of this analysis agree well with a detailed two-dimensional hydrodynamical simulation of the wind collision in the WR+O binary V444 Cygni, and demonstrate that radiative braking can significantly alter the bow-shock geometry and reduce the strength of the wind collision. We also apply the derived analytic theory to a set of 14 hot-star binary systems, and conclude that radiative braking is likely to be of widespread importance for wind-wind collisions in WR+O binaries with close to medium separation, D <= 100 Rsun. It may also be important in other types of hot-star binaries that exhibit a large imbalance between the component wind strengths.
13. 14 CFR 23.493 - Braked roll conditions.
Code of Federal Regulations, 2013 CFR
2013-01-01
...479 for level landings. (c) A drag reaction equal to the vertical reaction at the wheel multiplied by a coefficient of friction of 0.8 must be applied at the ground contact point of each wheel with brakes, except that the drag reaction...
14. 14 CFR 23.493 - Braked roll conditions.
Code of Federal Regulations, 2012 CFR
2012-01-01
...479 for level landings. (c) A drag reaction equal to the vertical reaction at the wheel multiplied by a coefficient of friction of 0.8 must be applied at the ground contact point of each wheel with brakes, except that the drag reaction...
15. 14 CFR 23.493 - Braked roll conditions.
Code of Federal Regulations, 2014 CFR
2014-01-01
...479 for level landings. (c) A drag reaction equal to the vertical reaction at the wheel multiplied by a coefficient of friction of 0.8 must be applied at the ground contact point of each wheel with brakes, except that the drag reaction...
16. Oxygen-Diffused Titanium as a Candidate Brake Rotor Material
SciTech Connect
Qu, Jun; Blau, Peter Julian; Jolly, Brian C
2009-01-01
Titanium alloys are one of several candidate materials for the next generation of truck disk brake rotors. Despite their advantages of lightweight relative to cast iron and good strength and corrosion resistance, titanium alloys are unlikely to be satisfactory brake rotor materials unless their friction and wear behavior can be significantly improved. In this study, a surface engineering process oxygen diffusion was applied to titanium rotors and has shown very encouraging results. The oxygen diffused Ti-6Al-4V (OD-Ti) was tested on a sub-scale brake tester against a flat block of commercial brake lining material and benchmarked against several other Ti-based materials, including untreated Ti-6Al-4V, ceramic particle-reinforced Ti composites (MMCs), and a thermal-spray-coated Ti alloy. With respect to friction, the OD-Ti outperformed all other candidate materials under the imposed test conditions with the friction coefficient remaining within a desirable range of 0.35-0.50, even under the harshest conditions when the disk surface temperature reached nearly 600 ?C. In addition, the OD-Ti showed significantly improved wear-resistance over the non-treated one and was even better than the Ti-based composite materials.
17. 14 CFR 23.493 - Braked roll conditions.
Code of Federal Regulations, 2011 CFR
2011-01-01
...479 for level landings. (c) A drag reaction equal to the vertical reaction at the wheel multiplied by a coefficient of friction of 0.8 must be applied at the ground contact point of each wheel with brakes, except that the drag reaction...
18. 14 CFR 23.493 - Braked roll conditions.
Code of Federal Regulations, 2014 CFR
2014-01-01
... and ground contacts must be those described in § 23.479 for level landings. (c) A drag reaction equal to the vertical reaction at the wheel multiplied by a coefficient of friction of 0.8 must be applied at the ground contact point of each wheel with brakes, except that the drag reaction need not...
19. 14 CFR 23.493 - Braked roll conditions.
Code of Federal Regulations, 2011 CFR
2011-01-01
... and ground contacts must be those described in § 23.479 for level landings. (c) A drag reaction equal to the vertical reaction at the wheel multiplied by a coefficient of friction of 0.8 must be applied at the ground contact point of each wheel with brakes, except that the drag reaction need not...
20. 14 CFR 23.493 - Braked roll conditions.
Code of Federal Regulations, 2013 CFR
2013-01-01
... and ground contacts must be those described in § 23.479 for level landings. (c) A drag reaction equal to the vertical reaction at the wheel multiplied by a coefficient of friction of 0.8 must be applied at the ground contact point of each wheel with brakes, except that the drag reaction need not...
1. 14 CFR 23.493 - Braked roll conditions.
Code of Federal Regulations, 2012 CFR
2012-01-01
... and ground contacts must be those described in § 23.479 for level landings. (c) A drag reaction equal to the vertical reaction at the wheel multiplied by a coefficient of friction of 0.8 must be applied at the ground contact point of each wheel with brakes, except that the drag reaction need not...
2. 14 CFR 23.493 - Braked roll conditions.
Code of Federal Regulations, 2010 CFR
2010-01-01
... and ground contacts must be those described in § 23.479 for level landings. (c) A drag reaction equal to the vertical reaction at the wheel multiplied by a coefficient of friction of 0.8 must be applied at the ground contact point of each wheel with brakes, except that the drag reaction need not...
3. Dr.-Ing. Norbert Frhleke PIBRAC -Piezoelectrical Brake Actuator
E-print Network
Noé, Reinhold
-mass ultrasonic Power supply and control development Dr.-Ing. Norbert Fröhleke, Department of Power Electronics Böcker, Dr.-Ing. Norbert Fröhleke Current Aircraft Brake Actuator #12;Power Electronics and Electrical" aircraft: · Reduction in volume and weight · Increase in reliability and operating safety · Reduction costs
4. 14 CFR 27.493 - Braked roll conditions.
Code of Federal Regulations, 2010 CFR
2010-01-01
...479(a)(2); and (b) The structure must be designed to withstand at the ground contact point of each wheel with brakes, a drag load at least the lesser of— (1) The vertical load multiplied by a coefficient of friction of 0.8;...
5. 14 CFR 25.493 - Braked roll conditions.
Code of Federal Regulations, 2010 CFR
2010-01-01
...with the load on the main wheels, in accordance with...design ramp weight. A drag reaction equal to the...an airplane with a nose wheel the limit vertical load...design ramp weight. A drag reaction equal to the...contact point of each wheel with brakes. The...
6. 14 CFR 29.493 - Braked roll conditions.
Code of Federal Regulations, 2010 CFR
2010-01-01
...479(a)(2); and (b) The structure must be designed to withstand, at the ground contact point of each wheel with brakes, a drag load of at least the lesser of— (1) The vertical load multiplied by a coefficient of friction of...
7. Wear and related characteristics of an aircraft tire during braking
NASA Technical Reports Server (NTRS)
Mccarty, J. L.
1972-01-01
Wear and related characteristics of friction and temperature developed during braking of size 22 x 5.5, type aircraft tires are studied. The testing technique involved gearing the tire to a driving wheel of a ground vehicle to provide operations at constant slip ratios on asphalt, concrete, and slurry-seal surfaces. Data were obtained over the range of slip ratios generally attributed to an aircraft braking system during dry runway operations. The results show that the cumulative tire wear varies linearly with distance traveled and the wear rate increases with increasing slip ratio and is influenced by the runway-surface character. Differences in the wear rates associated with the various surfaces suggest that runways can be rated on the basis of tire wear. The results also show that the friction coefficients developed during fixed-slip-ratio operations are in good agreement with those obtained by other investigators during cyclic braking, in that the dry friction is insensitive to the tire tread temperature is shown to increase with increasing slip ratio and, at the higher ratios, to be greater during braking on asphalt and slurry seal than on concrete.
8. 30 CFR 57.14102 - Brakes for rail equipment.
Code of Federal Regulations, 2011 CFR
2011-07-01
... 30 Mineral Resources 1 2011-07-01 2011-07-01 false Brakes for rail equipment. 57.14102 Section 57.14102 Mineral Resources MINE SAFETY AND HEALTH ADMINISTRATION, DEPARTMENT OF LABOR METAL AND NONMETAL MINE SAFETY AND HEALTH SAFETY AND HEALTH STANDARDS-UNDERGROUND METAL AND NONMETAL MINES Machinery and Equipment Safety Devices and...
9. 14 CFR 25.493 - Braked roll conditions.
Code of Federal Regulations, 2011 CFR
2011-01-01
...application of maximum braking force as described in paragraphs (b) and (c) of this section. (e) In the absence of a more rational analysis, the nose gear vertical reaction prescribed in paragraph (d) of this section must be calculated according to...
10. 6. OBLIQUE VIEW OF HOIST, SHOWING WOODEN BRAKE SHOES, REDUCTION ...
Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey
6. OBLIQUE VIEW OF HOIST, SHOWING WOODEN BRAKE SHOES, REDUCTION GEARS AND BED FOR (MISSING) CLUTCH/DRIVE GEAR UNIT, LOOKING NORTHWEST - Buffalo Coal Mine, Vulcan Cable Hoist, Wishbone Hill, Southeast end, near Moose Creek, Sutton, Matanuska-Susitna Borough, AK
11. A Laboratory Activity on the Eddy Current Brake
ERIC Educational Resources Information Center
Molina-Bolivar, J. A.; Abella-Palacios, A. J.
2012-01-01
The aim of this paper is to introduce a simple and low-cost experimental setup that can be used to study the eddy current brake, which considers the motion of a sliding magnet on an inclined conducting plane in terms of basic physical principles. We present a set of quantitative experiments performed to study the influence of the geometrical and…
12. Brakes Specialist. Teacher Edition. Automotive Service Series. Second Edition.
ERIC Educational Resources Information Center
Oklahoma State Dept. of Vocational and Technical Education, Stillwater. Curriculum and Instructional Materials Center.
This curriculum guide for automatic brakes service is one in a series of automotive service speciality publications that is based on the National Institute of Automotive Service Excellence task lists. The curriculum is composed of four units. Each unit of instruction may contain some or all of the following components: objective sheet, suggested…
13. Magnetic Braking and Protostellar Disk Formation: Ambipolar Diffusion
Mellon, Richard R.; Li, Zhi-Yun
2009-06-01
It is established that the formation of rotationally supported disks during the main accretion phase of star formation is suppressed by a moderately strong magnetic field in the ideal MHD limit. Nonideal MHD effects are expected to weaken the magnetic braking, perhaps allowing the disk to reappear. We concentrate on one such effect, ambipolar diffusion, which enables the field lines to slip relative to the bulk neutral matter. We find that the slippage does not sufficiently weaken the braking to allow rotationally supported disks to form for realistic levels of cloud magnetization and cosmic ray ionization rate; in some cases, the magnetic braking is even enhanced. Only in dense cores with both exceptionally weak fields and unreasonably low ionization rate do such disks start to form in our simulations. We conclude that additional processes, such as Ohmic dissipation or Hall effect, are needed to enable disk formation. Alternatively, the disk may form at late times when the massive envelope that anchors the magnetic brake is dissipated, perhaps by a protostellar wind.
14. Disk brake squeal prediction using the ABLE algorithm
Lou, G.; Wu, T. W.; Bai, Z.
2004-05-01
Disk brake squeal noise is mainly due to unstable friction-induced vibration. A typical disk brake system includes two pads, a rotor, a caliper and a piston. In order to predict if a disk brake system will generate squeal, the finite element method (FEM) is used to simulate the system. At the contact interfaces between the pads and the rotor, the normal displacement is continuous and Coulomb's friction law is applied. Thus, the resulting FEM matrices of the dynamic system become unsymmetric, which will yield complex eigenvalues. Any complex eigenvalue with a positive real part indicates an unstable mode, which may result in squeal. In real-world applications, the FEM model of a disk brake system usually contains tens of thousands of degrees of freedom (d.o.f.s). Therefore any direct eigenvalue solver based on the dense matrix data structure cannot efficiently perform the analysis, mainly due to its huge memory requirement and long computation time. It is well known that the FEM matrices are generally sparse and hence only the non-zeros of the matrices need to be stored for eigenvalue analysis. A recently developed iterative method named ABLE is used in this paper to search for any unstable modes within a certain user-specified frequency range. The complex eigenvalue solver ABLE is based on an adaptive block Lanczos method for sparse unsymmetric matrices. Numerical examples are presented to demonstrate the formulation and the eigenvalues are compared to the results from the component modal synthesis (CMS).
15. 49 CFR 570.5 - Service brake system.
Code of Federal Regulations, 2014 CFR
2014-10-01
... CFR 571.105, on every new passenger car manufactured on or after January 1, 1968, and on other types... pedal travel. Depress the brake pedal, and with the force applied measure the distance (B) from the... per hour and the vehicle shall be brought to a stop as specified. Measure the distance required...
16. 49 CFR 570.5 - Service brake system.
Code of Federal Regulations, 2010 CFR
2010-10-01
... CFR 571.105, on every new passenger car manufactured on or after January 1, 1968, and on other types... pedal travel. Depress the brake pedal, and with the force applied measure the distance (B) from the... per hour and the vehicle shall be brought to a stop as specified. Measure the distance required...
17. 16 CFR 1512.5 - Requirements for braking system.
Code of Federal Regulations, 2014 CFR
2014-01-01
... as determined by the equivalent ground speed specified in § 1512.18(d)(2)(vi). (2) Hand lever access. Hand lever mechanisms shall be located on the handlebars in a position that is readily accessible to... dimension between the brake hand lever and the handlebars in the plane containing the centerlines of...
18. 16 CFR 1512.5 - Requirements for braking system.
Code of Federal Regulations, 2013 CFR
2013-01-01
... as determined by the equivalent ground speed specified in § 1512.18(d)(2)(vi). (2) Hand lever access. Hand lever mechanisms shall be located on the handlebars in a position that is readily accessible to... dimension between the brake hand lever and the handlebars in the plane containing the centerlines of...
19. 5. FLOOR 3; SHOWS BRAKE LEVER, BLOCK FORMERLY USED TO ...
Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey
5. FLOOR 3; SHOWS BRAKE LEVER, BLOCK FORMERLY USED TO RAISE IT AND HOOK WHICH KEPT IT IN THE 'OFF' POSITION; ALSO SEEN ARE THE LARGE BLOCKS SUSPENDED FROM THE CAP FRAME WHICH HOLD THE TRUCK WHEELS TO CENTER THE CAP - Hayground Windmill, Windmill Lane, East Hampton, Suffolk County, NY
20. 16 CFR 1512.5 - Requirements for braking system.
Code of Federal Regulations, 2011 CFR
2011-01-01
... as determined by the equivalent ground speed specified in § 1512.18(d)(2)(vi). (2) Hand lever access. Hand lever mechanisms shall be located on the handlebars in a position that is readily accessible to... dimension between the brake hand lever and the handlebars in the plane containing the centerlines of...
1. 44. SOUTHWEST TO CIRCA 1900 SHEET METAL BRAKE, THE MACHINE ...
Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey
44. SOUTHWEST TO CIRCA 1900 SHEET METAL BRAKE, THE MACHINE USED TO BEND SHEET METAL TO EXACT ANGLES AS IN STEEL WATER TANK MANUFACTURE. IN THE BACKGROUND IS THE INTERIOR WEST WALL OF THE FACTORY, ITS SHELVES BEARING WATER PUMPS, PARTS FOR PUMPS AND WATER SUPPLY EQUIPMENT, AND NEW OLD STOCK MERCHANDISE. - Kregel Windmill Company Factory, 1416 Central Avenue, Nebraska City, Otoe County, NE
2. Cradle modification for hydraulic ram
SciTech Connect
Koons, B.M.
1995-03-02
The analysis of the cradle hydraulic system considers stress, weld strength, and hydraulic forces required to lift and support the cradle/pump assembly. The stress and weld strength of the cradle modifications is evaluated to ensure that they meet the requirements of the American Institute for Steel Construction (AISC 1989). The hydraulic forces are evaluated to ensure that the hydraulic system is capable of rotating the cradle and pump assembly to the vertical position (between 70{degrees} and 90{degrees}).
3. Analytica Chimica Acta 504 (2004) 199207 Arsenic speciation in Chinese brake fern by ion-pair high-performance
E-print Network
Ma, Lena
2004-01-01
Analytica Chimica Acta 504 (2004) 199207 Arsenic speciation in Chinese brake fern by ion-pair high) and arsenate [As(V)] in Chinese brake fern (Pteris vittata L.). The separation was performed on a reverse in the Chinese brake fern, indicating that Chinese brake fern can convert MMA to DMA by methylation. © 2003
4. Integration in Hydraulics.
ERIC Educational Resources Information Center
Sworder, Steven C.
This paper presents an application of integration to the field of hydraulics. An integral relation for the time required to drop the fluid contained in a cylindrical tank from one level to another using a hole in the tank wall is derived. Procedures for constructing the experimental equipment and procedures for determining the coefficient of…
5. Water Treatment Technology - Hydraulics.
ERIC Educational Resources Information Center
Ross-Harrington, Melinda; Kincaid, G. David
One of twelve water treatment technology units, this student manual on hydraulics provides instructional materials for three competencies. (The twelve units are designed for a continuing education training course for public water supply operators.) The competencies focus on the following areas: head loss in pipes in series, function loss in…
6. Hydraulic Shutdown Monitor
NASA Technical Reports Server (NTRS)
Fleming, S. T.; Harrington, D. B.
1986-01-01
Adding switch allows inappropriate control actions to be overridden. Four-pole, double-throw switch added to front panel of controller to disable tracking-error and endpoint-error circuitry yet still retain overload-detection capability. Previously, it was necessary to use adjustable-voltage-level detection equipment connected with cables to hydraulic "dump" or shutdown circuitry in controller.
7. Correcting Students' Misconceptions about Automobile Braking Distances and Video Analysis Using Interactive Program Tracker
Hockicko, Peter; Trpišová, Beáta; Ondruš, Ján
2014-12-01
The present paper informs about an analysis of students' conceptions about car braking distances and also presents one of the novel methods of learning: an interactive computer program Tracker that we used to analyse the process of braking of a car. The analysis of the students' conceptions about car braking distances consisted in obtaining their estimates of these quantities before and after watching a video recording of a car braking from various initial speeds to a complete stop and subsequent application of mathematical statistics to the obtained sets of students' answers. The results revealed that the difference between the value of the car braking distance estimated before watching the video and the real value of this distance was not caused by a random error but by a systematic error which was due to the incorrect students' conceptions about the car braking process. Watching the video significantly improved the students' estimates of the car braking distance, and we show that in this case, the difference between the estimated value and the real value of the car braking distance was due only to a random error, i.e. the students' conceptions about the car braking process were corrected. Some of the students subsequently performed video analysis of the braking processes of cars of various brands and under various conditions by means of Tracker that gave them exact knowledge of the physical quantities, which characterize a motor vehicle braking. Interviewing some of these students brought very positive reactions to this novel method of learning.
8. Theoretical and experimental studies on a magnetorheological brake operating under compression plus shear mode
Sarkar, C.; Hirani, H.
2013-11-01
The torque characteristics of magnetorheological brakes, consisting of rotating disks immersed in a MR fluid and enclosed in an electromagnetic casing, are controlled by regulating the yield stress of the MR fluid. An increase in yield stress increases the braking torque, which means that the higher the yield strength of the MR fluid, the better the performance of the MR brake will be. In the present research an application of compressive force on MR fluid has been proposed to increase the torque capacity of MR brakes. The mathematical expressions to estimate the torque values for MR brake, operating under compression plus shear mode accounting Herschel-Bulkley shear thinning model, have been detailed. The required compressive force on MR fluid of the proposed brake has been applied using an electromagnetic actuator. The development of a single-plate MR disk brake and an experimental test rig are described. Experiments have been performed to illustrate braking torque under different control currents (0.0-2.0 A). The torque results have been plotted and compared with theoretical study. Experimental results as well as theoretical calculations indicate that the braking torque of the proposed MR brake is higher than that of the MR brake operating only under shear.
9. Aalborg Universitet Hydraulic Yaw System
E-print Network
Pedersen, Henrik C.
Aalborg Universitet Hydraulic Yaw System Stubkier, Søren; Pedersen, Henrik Clemmensen; Mørkholt, M, M. (2012). Hydraulic Yaw System. Poster session presented at AWEA Windpower 2012, Georgia, Atlanta of the art-hydraulic yaw systems for wind turbines. 2011. [10] S. Stubkier and H. C. Pedersen. Design
10. Viscous Hydraulic Jumps Submitted by
E-print Network
Bush, John W.M.
Viscous Hydraulic Jumps Submitted by Jeffrey M. Aristoff, Jeffrey D. Leblanc, Annette E. Hosoi, and John W. M. Bush, Massachusetts Institute of Technology We examine the form of the viscous hydraulic of height 210 mm. Elegaard et al.1 first demonstrated that the axial symme- try of the viscous hydraulic
11. Guidelines for numerical vibration and acoustic analysis of disc brake squeal using simple models of brake systems
Oberst, S.; Lai, J. C. S.; Marburg, S.
2013-04-01
12. Shuttle Rudder/Speed Brake Power Drive Unit (PDU) Gear Scuffing Tests With Flight Gears
NASA Technical Reports Server (NTRS)
Proctor, Margaret P.; Oswald, Fred B.; Krants, Timothy L.
2005-01-01
Scuffing-like damage has been found on the tooth surfaces of gears 5 and 6 of the NASA space shuttle rudder/speed brake power drive unit (PDU) number 2 after the occurrence of a transient back-driving event in flight. Tests were conducted using a pair of unused spare flight gears in a bench test at operating conditions up to 2866 rpm and 1144 in.-lb at the input ring gear and 14,000 rpm and 234 in.-lb at the output pinion gear, corresponding to a power level of 52 hp. This test condition exceeds the maximum estimated conditions expected in a backdriving event thought to produce the scuffing damage. Some wear marks were produced, but they were much less severe than the scuffing damaged produced during shuttle flight. Failure to produce scuff damage like that found on the shuttle may be due to geometrical variations between the scuffed gears and the gears tested herein, more severe operating conditions during the flight that produced the scuff than estimated, the order of the test procedures, the use of new hydraulic oil, differences between the dynamic response of the flight gearbox and the bench-test gearbox, or a combination of these. This report documents the test gears, apparatus, and procedures, summarizes the test results, and includes a discussion of the findings, conclusions, and recommendations.
13. Hydraulic manipulator research at ORNL
SciTech Connect
Kress, R.L.; Jansen, J.F.; Love, L.J.
1997-03-01
Recently, task requirements have dictated that manipulator payload capacity increase to accommodate greater payloads, greater manipulator length, and larger environmental interaction forces. General tasks such as waste storage tank cleanup and facility dismantlement and decommissioning require manipulator life capacities in the range of hundreds of pounds rather than tens of pounds. To meet the increased payload capacities demanded by present-day tasks, manipulator designers have turned once again to hydraulics as a means of actuation. In order to successfully design, build, and deploy a new hydraulic manipulator (or subsystem), sophisticated modeling, analysis, and control experiments are usually needed. Oak Ridge National Laboratory (ORNL) has a history of projects that incorporate hydraulics technology, including mobile robots, teleoperated manipulators, and full-scale construction equipment. In addition, to support the development and deployment of new hydraulic manipulators, ORNL has outfitted a significant experimental laboratory and has developed the software capability for research into hydraulic manipulators, hydraulic actuators, hydraulic systems, modeling of hydraulic systems, and hydraulic controls. The purpose of this article is to describe the past hydraulic manipulator developments and current hydraulic manipulator research capabilities at ORNL. Included are example experimental results from ORNLs flexible/prismatic test stand.
14. Heavy and Overweight Vehicle Brake Testing: Five-Axle Combination Tractor-Flatbed Final Report
SciTech Connect
Lascurain, Mary Beth; Capps, Gary J; Franzese, Oscar
2013-10-01
NASA Technical Reports Server (NTRS)
Kouns, H. H.; Gardner, L. D.
1987-01-01
Outlet pressure adjusted to match varying loads. Electrohydraulic servo has positioned sleeve in leftmost position, adjusting outlet pressure to maximum value. Sleeve in equilibrium position, with control land covering control port. For lowest pressure setting, sleeve shifted toward right by increased pressure on sleeve shoulder from servovalve. Pump used in aircraft and robots, where hydraulic actuators repeatedly turned on and off, changing pump load frequently and over wide range.
16. Independent Orbiter Assessment (IOA): Analysis of the hydraulics/water spray boiler subsystem
NASA Technical Reports Server (NTRS)
Duval, J. D.; Davidson, W. R.; Parkman, William E.
1986-01-01
The results of the Independent Orbiter Assessment (IOA) of the Failure Modes and Effects Analysis (FMEA) and Critical Items List (CIL) are presented. The IOA approach features a top-down analysis of the hardware to determine failure modes, criticality, and potential critical items (PCIs). To preserve independence, this analysis was accomplished without reliance upon the results contained within the NASA FMEA/CIL documentation. This report documents the independent analysis results for the Orbiter Hydraulics/Water Spray Boiler Subsystem. The hydraulic system provides hydraulic power to gimbal the main engines, actuate the main engine propellant control valves, move the aerodynamic flight control surfaces, lower the landing gear, apply wheel brakes, steer the nosewheel, and dampen the external tank (ET) separation. Each hydraulic system has an associated water spray boiler which is used to cool the hydraulic fluid and APU lubricating oil. The IOA analysis process utilized available HYD/WSB hardware drawings, schematics and documents for defining hardware assemblies, components, and hardware items. Each level of hardware was evaluated and analyzed for possible failure modes and effects. Criticality was assigned based upon the severity of the effect for each failure mode. Of the 430 failure modes analyzed, 166 were determined to be PCIs.
17. Anharmonic oscillatory flow braking in the Earth's magnetotail
Panov, E. V.; Wolf, R. A.; Kubyshkina, M. V.; Nakamura, R.; Baumjohann, W.
2015-05-01
Plasma sheet bursty bulk flows often oscillate around their equilibrium position at about 10 RE downtail. The radial magnetic field, pressure, and flux tube volume profiles usually behave differently earthward and tailward of this position. Using data from five Time History of Events and Macroscale Interactions during Substorms (THEMIS) probes, we reconstruct these profiles with the help of an empirical model and apply thin filament theory to show that the oscillatory flow braking can occur in an asymmetric potential. Thus, the thin filament oscillations appear to be anharmonic, with a power spectrum exhibiting peaks at both the fundamental frequency and the first harmonic. Such anharmonic oscillatory braking can explain the presence of the first harmonic in Pi2 pulsations (frequency doubling), which are simultaneously observed by magnetometers on the ground near the conjugate THEMIS footprints.
18. Plasma Jet Braking: Energy Dissipation and Nonadiabatic Electrons
SciTech Connect
Khotyaintsev, Yu. V.; Cully, C. M.; Vaivads, A.; Andre, M.; Owen, C. J.
2011-04-22
We report in situ observations by the Cluster spacecraft of wave-particle interactions in a magnetic flux pileup region created by a magnetic reconnection outflow jet in Earth's magnetotail. Two distinct regions of wave activity are identified: lower-hybrid drift waves at the front edge and whistler-mode waves inside the pileup region. The whistler-mode waves are locally generated by the electron temperature anisotropy, and provide evidence for ongoing betatron energization caused by magnetic flux pileup. The whistler-mode waves cause fast pitch-angle scattering of electrons and isotropization of the electron distribution, thus making the flow braking process nonadiabatic. The waves strongly affect the electron dynamics and thus play an important role in the energy conversion chain during plasma jet braking.
19. Plasma jet braking: energy dissipation and nonadiabatic electrons.
PubMed
Khotyaintsev, Yu V; Cully, C M; Vaivads, A; André, M; Owen, C J
2011-04-22
We report in situ observations by the Cluster spacecraft of wave-particle interactions in a magnetic flux pileup region created by a magnetic reconnection outflow jet in Earth's magnetotail. Two distinct regions of wave activity are identified: lower-hybrid drift waves at the front edge and whistler-mode waves inside the pileup region. The whistler-mode waves are locally generated by the electron temperature anisotropy, and provide evidence for ongoing betatron energization caused by magnetic flux pileup. The whistler-mode waves cause fast pitch-angle scattering of electrons and isotropization of the electron distribution, thus making the flow braking process nonadiabatic. The waves strongly affect the electron dynamics and thus play an important role in the energy conversion chain during plasma jet braking. PMID:21599373
20. Bohmian quantization of the big-brake singularity
Pinto-Neto, Nelson; Pantoja, Diego Moraes
2014-04-01
The aim of this paper is to study the quantum aspects of the big-brake singularity. This is a singularity where the expansion of the universe stops abruptly, with infinity deceleration, caused by the divergence of the pressure of the fluid which describes the matter content of the model. In order to obtain our results, we interpret the quantum solutions of the Wheeler-DeWitt equation obtained from the canonical quantization of the classical model using the de Broglie-Bohm (dBB) quantum theory. Analyzing the Bohmian trajectories, we show that when one approaches the big-brake singularity, the universe still stops expanding, but now with finite deceleration, and initiates a smooth contracting phase. The pressure and the curvature never diverge.
1. Can non-ideal magnetohydrodynamics solve the magnetic braking catastrophe?
E-print Network
Wurster, James; Bate, Matthew R
2015-01-01
We investigate whether or not the low ionisation fractions in molecular cloud cores can solve the magnetic braking catastrophe', where magnetic fields prevent the formation of circumstellar discs around young stars. We perform three-dimensional smoothed particle non-ideal magnetohydrodynamics (MHD) simulations of the gravitational collapse of one solar mass molecular cloud cores, incorporating the effects of ambipolar diffusion, Ohmic resistivity and the Hall effect alongside a self-consistent calculation of the ionisation chemistry assuming 0.1 micron grains. When including only ambipolar diffusion or Ohmic resistivity, discs do not form in the presence of strong magnetic fields, similar to the cases using ideal MHD. With the Hall effect included, disc formation depends on the direction of the magnetic field with respect to the rotation vector of the gas cloud. When the vectors are aligned, strong magnetic braking occurs and no disc is formed. When the vectors are anti-aligned, a disc with radius of 13AU ca...
2. Heat generation in aircraft tires under braked rolling conditions
NASA Technical Reports Server (NTRS)
Clark, S. K.; Dodge, R. N.
1984-01-01
An analytical model was developed to approximate the internal temperature distribution in an aircraft tire operating under conditions of unyawed braked rolling. The model employs an array of elements to represent the tire cross section and considers the heat generated within the tire to be caused by the change in strain energy associated with cyclic tire deflection. The additional heating due to tire slip and stresses induced by braking are superimposed on the previously developed free rolling model. An extensive experimental program was conducted to verify temperatures predicted from the analytical model. Data from these tests were compared with calculations over a range of operating conditions. The model results were in reasonably good agreement with measured values.
3. Thermal design of AOTV heatshields for a conical drag brake
NASA Technical Reports Server (NTRS)
Pitts, W. C.; Murbach, M. S.
1985-01-01
Results are presented from an on-going study of the thermal performance of thermal protection systems for a conical drag brake type AOTV. Three types of heatshield are considered: rigid ceramic insulation, flexible ceramic blankets, and ceramic cloths. The results for the rigid insulation apply to other types of AOTV as well. Charts are presented in parametric form so that they may be applied to a variety of missions and vehicle configurations. The parameters considered include: braking maneuver heat flux and total heat load, heatshield material and thickness, heatshield thermal mass and conductivity, absorptivity and emissivity of surfaces, thermal mass of support structure, and radiation transmission through thin heatshields. Results of temperature calculations presented show trends with and sensitivities to these parameters. The emphasis is on providing information that will be useful in estimating the minimum required mass of these heatshield materials.
4. Analytical Investigation on Squeal Phenomena Generated in Bicycle Disc Brakes
Nakae, Takashi; Sueoka, Atsuo; Ryu, Takahiro
The squeal phenomenon is often generated in bicycle disc brakes. This paper deals analytically with the generation mechanism and the criterion of whether or not the squeal occurs. According to the experimental studies, it has been made clear that the squeal is mainly in-plane vibration in the direction of disc surface with the frequency about 1kHz caused by frictional characteristics with negative slope with respect to the relative velocity. An analytical model of the bicycle disc brake system has been devised to confirm the experimental results, in which a coupled in-plane and out-of-plane vibrating system is composed of the disc, hub, caliper and spokes. The resulting frequency of squeal and the unstable vibration modes of the disc and spokes from the analytical model agreed well with the experimental results.
5. Stellar dynamo driven wind braking versus disc coupling
von Rekowski, B.; Brandenburg, A.
2006-01-01
Star-disc coupling is considered in numerical models where the stellar field is not an imposed perfect dipole, but instead a more irregular self-adjusting dynamo-generated field. Using axisymmetric simulations of the hydromagnetic mean-field equations, it is shown that the resulting stellar field configuration is more complex, but significantly better suited for driving a stellar wind. In agreement with recent findings by a number of people, star-disc coupling is less efficient in braking the star than previously thought. Moreover, stellar wind braking becomes equally important. In contrast to a perfect stellar dipole field, dynamo-generated stellar fields favor field-aligned accretion with considerably higher velocity at low latitudes, where the field is weaker and originating in the disc. Accretion is no longer nearly periodic (as it is in the case of a stellar dipole), but it is more irregular and episodic.
6. An evaluation of short-term exposures of brake mechanics to asbestos during automotive and truck brake cleaning and machining activities.
PubMed
Richter, Richard O; Finley, Brent L; Paustenbach, Dennis J; Williams, Pamela R D; Sheehan, Patrick J
2009-07-01
Historically, the greatest contributions to airborne asbestos concentrations during brake repair work were likely due to specific, short-duration, dust-generating activities. In this paper, the available short-term asbestos air sampling data for mechanics collected during the cleaning and machining of vehicle brakes are evaluated to determine their impact on both short-term and daily exposures. The high degree of variability and lack of transparency for most of the short-term samples limit their use in reconstructing past asbestos exposures for brake mechanics. However, the data are useful in evaluating how reducing short-term, dust-generating activities reduced long-term exposures, especially for auto brake mechanics. Using the short-term dose data for grinding brake linings from these same studies, in combination with existing time-weighted average (TWA) data collected in decades after grinding was commonplace in rebuilding brake shoes, an average 8-h TWA of approximately 0.10 f/cc was estimated for auto brake mechanics that performed arc grinding of linings during automobile brake repair (in the 1960s or earlier). In the 1970s and early 1980s, a decline in machining activities led to a decrease in the 8-h TWA to approximately 0.063 f/cc. Improved cleaning methods in the late 1980s further reduced the 8-h TWA for most brake mechanics to about 0.0021 f/cc. It is noteworthy that when compared with the original OSHA excursion level, only 15 of the more than 300 short-term concentrations for brake mechanics measured during the 1970s and 1980s possibly exceeded the standard. Considering exposure duration, none of the short-term exposures were above the current OSHA excursion level. PMID:18665198
7. 9. VIEW SOUTHWEST OF PRIMARY REDUCING GEARS; NOTE BRAKE WHEEL ...
Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey
9. VIEW SOUTHWEST OF PRIMARY REDUCING GEARS; NOTE BRAKE WHEEL AND PADS AT RIGHT CENTER BEHIND PRIMARY GEAR; MITER GEAR AT CENTER IS PART OF MECHANISM FOR MANUAL OPERATION OF BRIDGE; FLANGE FOR COUPLING THE NORTH AND SOUTH REDUCTION GEAR TRAINS IS AT CENTER OF PHOTOGRAPH BEHIND SOUTH PRIMARY REDUCTION GEAR - East Washington Avenue Bridge, Spanning Pequonnock River at East Washington Avenue, Bridgeport, Fairfield County, CT
8. Energy Efficiency in Heavy Vehicle Tires, Drivetrains, and Braking Systems
SciTech Connect
Peter J. Blau
2000-04-26
This document was prepared to support the primary goals of the Department of Energy, Office of Heavy Vehicle Technologies. These were recently stated as follows: ''Develop by 2004 the enabling technologies for a class 7-8 truck with a fuel efficiency of 10 mpg (at 65 mph) which will meet prevailing emission standards. For Class 3-6 trucks operating on an urban driving cycle, develop by 2004 commercially viable vehicles that achieve at least double the fuel economy of comparable current vehicles (1999), and as a research goal, reduce criteria pollutants to 30% below EPA standards. Develop by 2004 the diesel engine enabling technologies to support large-scale industry dieselization of Class 1 and 2 trucks, achieving a 35 % fuel efficiency improvement over comparable gasoline-fueled trucks, while meeting applicable emissions standards.'' The enabling technologies for improving the fuel efficiency of trucks, include not only engine technologies but also technologies involved with lowering the rolling resistance of tires, reducing vehicle aerodynamic drag, improving thermal management, and reducing parasitic frictional losses in drive train components. Opportunities also exist for making better use of the energy that might ordinarily be dissipated during vehicle braking. Braking systems must be included in this evaluation since safety in truck operations is vital, and braking requirements are greater for vehicles having lowered resistance to rolling. The Office of Heavy Vehicle Technologies has initiated a program to improve the aerodynamics of heavy vehicles through wind tunnel testing, computational modeling, and on-road evaluations. That activity is described in a separate multi-year plan; therefore, emphasis in this document will be on tires, drive trains, and braking systems. Recent, dramatic fluctuations in diesel fuel prices have emphasized the importance of effecting savings in truck fuel economy by implementing new component designs and materials.
9. Evaluation of asbestos exposure during brake repair and replacement.
PubMed
Kakooei, Hossein; Hormozy, Maryam; Marioryad, Hossein
2011-01-01
Occupational exposure to asbestos fiber of brake repair job (auto mechanics) has seldom been evaluated in Iran. Accordingly, we evaluated asbestos fiber concentrations in the breathing zone of auto mechanics between July 2008 and December 2008. The asbestos fiber concentrations of 60 personal air samples collected from 30 cars and trucks brake replacement and they were analyzed by phase-contrast optical microscopy (PCM) and scanning electron microscopy (SEM) by energy-dispersive X-ray analysis. The geometric means of the personal monitoring fiber concentrations were 0.92 PCM f/ml and 0.46 PCM f/ml respectively in car and passenger heavy truck auto shops. There was a significant differences in the asbestos fiber concentrations between the car and truck auto shops (p=0.006). Based on these findings, auto mechanics who worked with asbestos containing brake may have been exposed to asbestos concentrations approximately 7 times higher than the current occupational safety and health agency (OSHA) permissible exposure limit (PEL) of 0.1 f/ml. Fiber morphology and energy dispersive X-ray analysis by SEM revealed that amphibole fibers such as tremolite and actinolite existed in the brakes dust and that the vast majority (>30%) of the airborne chrysotile fibers were greater than 1 ?m in diameter. It can be concluded that the imported chrysotile asbestos contains trace amounts of tremolite and actinolite fibers and they are responsible for the high airborne asbestos levels and occupational exposure to amphibole asbestos in auto mechanics job in Iran. Thus, it is to be expected that the auto mechanics will suffer negative health effects due to exposure to the serpentine and amphibole asbestos fibers. PMID:21372435
10. 49 CFR 393.42 - Brakes required on all wheels.
Code of Federal Regulations, 2010 CFR
2010-10-01
... or four-wheel pole trailer (laden or unladen) with a gross weight of 1,361 kg (3,000 pounds) or less... semitrailer or pole trailer (laden or unladen) with a gross weight of 1,361 kg (3,000 pounds) or less which is subject to this part is not required to be equipped with brakes if the axle weight of the towed...
11. Nonlinear transient and chaotic interactions in disc brake squeal
Oberst, S.; Lai, J. C. S.
2015-04-01
In automotive disc-brake squeal, most numerical studies have been focussed on the prediction of unstable vibration modes in the frequency domain using the complex eigenvalue analysis. However, the magnitude of the positive real part of a complex eigenvalue is an unreliable indicator of squeal occurrence. Although nonlinearities have been shown to play a significant role in brake squeal, transient nonlinear time domain analyses have rarely been applied owing to high computational costs. Here the complex eigenvalue analysis, the direct steady-state analysis and the transient nonlinear time domain analysis are applied to an isotropic pad-on-disc finite element model representing a simple model of a brake system. While in this investigation, in-plane pad-mode instabilities are not detected by the complex eigenvalue analysis, the dissipated energy obtained by the direct steady-state analysis of the model subjected to harmonic contact pressure excitation is negative at frequencies of pad modes, indicating a potential for instabilities. Transient nonlinear time domain analysis of the pad and disc dynamics reveal that in-plane pad vibrations excite a dominant out-of-plane disc mode. For intermittently chaotic pad motion, the disc dynamics is quasi-periodic; and for chaotic motion of the pad, a toroidal attractor is found for the disc's out-of-plane motion. Nonlinear interactions between the pad and the disc highlight that different parts in a brake system display different dynamic behaviour and need to be analysed separately. The type II intermittency route to chaos could be the cause for the experimentally observed instantaneous mode squeal.
12. Simulation study of the plasma-brake effect
Janhunen, P.
2014-10-01
Plasma brake is a thin, negatively biased tether that has been proposed as an efficient concept for deorbiting satellites and debris objects from low Earth orbit. We simulate the interaction with the ionospheric plasma ram flow with the plasma-brake tether by a high-performance electrostatic particle in cell code to evaluate the thrust. The tether is assumed to be perpendicular to the flow. We perform runs for different tether voltage, magnetic-field orientation and plasma-ion mass. We show that a simple analytical thrust formula reproduces most of the simulation results well. The interaction with the tether and the plasma flow is laminar (i.e. smooth and not turbulent) when the magnetic field is perpendicular to the tether and the flow. If the magnetic field is parallel to the tether, the behaviour is unstable and thrust is reduced by a modest factor. The case in which the magnetic field is aligned with the flow can also be unstable, but does not result in notable thrust reduction. We also correct an error in an earlier reference. According to the simulations, the predicted thrust of the plasma brake is large enough to make the method promising for low-Earth-orbit (LEO) satellite deorbiting. As a numerical example, we estimate that a 5 km long plasma-brake tether weighing 0.055 kg could produce 0.43 mN breaking force, which is enough to reduce the orbital altitude of a 260 kg object mass by 100 km over 1 year.
13. Carbon nanotube torsional springs for regenerative braking systems
Liu, Sanwei; Martin, Corbin; Lashmore, David; Schauer, Mark; Livermore, Carol
2015-10-01
The modeling and demonstration of large stroke, high energy density and high power density torsional springs based on carbon nanotube (CNT) yarns is reported, as well as their application as energy-storing actuators for regenerative braking systems. An originally untwisted CNT yarn is cyclically loaded and unloaded in torsion, with the maximum rotation angle increasing incrementally until failure. The measured average extractable energy density values are 2.9?kJ?kg-1??±??1.2?kJ?kg-1 and 3.4?kJ?kg-1??±??0.4?kJ?kg-1 for 1-ply CNT yarns and 2-ply CNT yarns, respectively. Additionally, a regenerative braking system is demonstrated to capture the kinetic energy of a wheel and store it as elastic energy in twisted CNT yarns. When the yarn’s twist is released, the stored energy reaccelerates the wheel. The measured energy and mean power densities of the CNT yarns in the simple regenerative braking setup are on average 3.3?kJ?kg-1 and 0.67?kW?kg-1, respectively, with maximum measured values of up to 4.7?kJ?kg-1 and 1.2?kW?kg-1, respectively. A slightly lower energy density of up to 1.2?kJ?kg-1 and a 0.29?kW?kg-1 mean power density are measured for CNT yarns in a more complex setup that mimics a unidirectional rotating regenerative braking mechanism.
14. Magnetic Braking and Protostellar Disk Formation: The Ideal MHD Limit
Mellon, Richard R.; Li, Zhi-Yun
2008-07-01
Magnetic fields are usually considered dynamically important in star formation when the dimensionless mass-to-flux ratio is close to, or less than, unity (?<~1). We show that, in disk formation, the requirement is far less stringent. This conclusion is drawn from a set of 2D (axisymmetric) simulations of the collapse of rotating, singular isothermal cores magnetized to different degrees. We find that a weak field corresponding to ?~100 can begin to disrupt the rotationally supported disk through magnetic braking, by creating regions of rapid, supersonic collapse in the disk. These regions are separated by one or more centrifugal barriers, where the rapid infall is temporarily halted. The number of centrifugal barriers increases with the mass-to-flux ratio ?. When ?>~100, they merge together to form a more or less contiguous, rotationally supported disk. Even though the magnetic field in such a case is extremely weak on the scale of dense cores, it is amplified by collapse and differential rotation, to the extent that its pressure dominates the thermal pressure in both the disk and its surrounding region. For relatively strongly magnetized cores with ?<~10, the disk formation is suppressed completely, as found previously. A new feature is that the mass accretion is highly episodic, due to reconnection of the magnetic field lines accumulated near the center. For rotationally supported disks to appear during the protostellar mass accretion phase of star formation in dense cores with realistic field strengths, the powerful magnetic brake must be weakened, perhaps through nonideal MHD effects. Another possibility is to remove, through protostellar winds, the material that acts to brake the disk rotation. We discuss the possibility of observing a generic product of the magnetic braking, an extended circumstellar region that is supported by a combination of toroidal magnetic field and rotation-a magnetogyrosphere''-interferometrically.
15. The method of feed-in energy on disc brake squeal
Guan, Dihua; Huang, Jinchun
2003-03-01
Brake squeal is studied in this paper by feed-in energy analysis. Based on the brake closed-loop coupling model, a calculation method of feed-in energy for squeal mode is derived. Result of the feed-in energy indicates squeal tendency of the brake system, while formula for calculating it discloses the relation among brake squeal phenomenon and structural parameters, such as frictional coefficient, geometric shape of brake pads, elastic modulus of frictional material, substructure modal shape, etc. The method also helps to analyze the effectiveness of various structural modification schemes attempted to eliminate the squeal noise. Finally, this method is illustrated by application to a typical squealing disc brake.
16. Computational Fluid Dynamics (CFD) investigation onto passenger car disk brake design
Munisamy, Kannan M.; Kanasan Moorthy, Shangkari K.
2013-06-01
The aim of this study is to investigate the flow and heat transfer in ventilated disc brakes using Computational Fluid Dynamics (CFD). NACA Series blade is designed for ventilated disc brake and the cooling characteristic is compared to the baseline design. The ventilated disc brakes are simulated using commercial CFD software FLUENTTM using simulation configuration that was obtained from experiment data. The NACA Series blade design shows improvements in Nusselt number compared to baseline design.
17. Emission Factor for Antimony in Brake Abrasion Dusts as One of the
E-print Network
Short, Daniel
/ braking/car for PM2.5. These essential data will contribute to the modeling of atmospheric Sb and weighed. From the experimental data, dust emission could be regressed as a function of the initial kinetic) were calculated as 5.8 mg/braking/car for PM10 and 3.9 mg/braking/car for PM2.5. The elemental
18. Fluid Power/Basic Hydraulics. Instructor's Guide.
ERIC Educational Resources Information Center
Stanbery, Richard
This guide is designed to assist industrial vocational instructors in teaching a course on fluid power and basic hydraulics. Covered in the unit on the basics of fluid power and hydraulics are the following topics: the fundamentals of fluid power and hydraulics, basic hydraulic circuits, and servicing a hydraulic jack. The second unit, consisting…
19. Hydraulic mining method
DOEpatents
Huffman, Lester H. (Kent, WA); Knoke, Gerald S. (Kent, WA)
1985-08-20
A method of hydraulically mining an underground pitched mineral vein comprising drilling a vertical borehole through the earth's lithosphere into the vein and drilling a slant borehole along the footwall of the vein to intersect the vertical borehole. Material is removed from the mineral vein by directing a high pressure water jet thereagainst. The resulting slurry of mineral fragments and water flows along the slant borehole into the lower end of the vertical borehole from where it is pumped upwardly through the vertical borehole to the surface.
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# Canadian Journal of Electrical and Computer Engineering
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• ### Obstacle Avoidance in Real Time With Nonlinear Model Predictive Control of Autonomous Vehicles
Publication Year: 2017, Page(s):12 - 22
| | PDF (2539 KB) | HTML
A Nonlinear model predictive control (NMPC) for trajectory tracking with the obstacle avoidance of autonomous road vehicles traveling at realistic speeds is presented in this paper, with a focus on the performance of those controllers with respect to the look-ahead horizon of the NMPC. Two different methods of obstacle avoidance are compared and then the NMPC is tested in several simulated but rea... View full abstract»
• ### Unidirectional HVdc Topology With DC Fault Ride-Through Capability
Publication Year: 2017, Page(s):41 - 49
| | PDF (1915 KB) | HTML
HVdc transmission using modular multilevel converters (MMCs) is becoming increasingly prevalent. However, line-commutated converter (LCC) HVdc transmission remains advantageous in its ability to clear dc faults and restart power transmission without operation of the ac system protection. This paper presents an HVdc system topology that employs both MMC and LCC converters to transmit unidirectional... View full abstract»
• ### Improved Analytical Modeling of Permanent Magnet Leakage Flux in Design of the Coreless Axial Flux Permanent Magnet Generatorx
Publication Year: 2017, Page(s):3 - 11
| | PDF (2508 KB) | HTML
This paper presents an improved magnetic circuit model of a coreless axial flux permanent magnet (AFPM) machine for the evaluation of its air-gap leakage flux. In the coreless AFPM machine, the stator axial length is one of the effective parameters in the calculation of the air-gap leakage flux factor. It is important to correctly update the leakage flux factor value corresponding to the variation... View full abstract»
• ### Impact of EV Charger Load on Distribution Network Capacity: A Case Study in Toronto
Publication Year: 2016, Page(s):268 - 273
| | PDF (1674 KB) | HTML
This paper presents a study of the impact of the electric vehicle (EV) charger load on the capacity of distribution feeders and transformers of an urban utility. A residential neighborhood of the city of Toronto, Canada, is selected to perform the study based on survey results that showed a high tendency for EV adoption. The two most loaded distribution transformers of such a neighborhood are stud... View full abstract»
• ### Energy Storage in Flywheels: An Overview
Publication Year: 2015, Page(s):183 - 193
Cited by: Papers (11)
| | PDF (1039 KB) | HTML
In a deregulated power market with increasing penetration of distributed generators and renewable sources, energy storage becomes a necessity. Renewable energy sources are characterized by a fluctuating and intermittent nature, which simply means that energy may be available when it is not needed, and vice versa. Energy storage devices can help rectify the mismatch between generation and demand at... View full abstract»
• ### Nonlinear Model Predictive Control for Omnidirectional Robot Motion Planning and Tracking With Avoidance of Moving Obstacles
Publication Year: 2014, Page(s):151 - 156
Cited by: Papers (5)
| | PDF (1239 KB) | HTML
This paper presents a nonlinear model predictive control algorithm for online motion planning and tracking of an omnidirectional autonomous robot. The formalism is based on a Hamiltonian minimization to optimize a control path as evaluated by a cost function. This minimization is constrained by a nonlinear plant model, which confines the solution space to those paths which are physically feasible.... View full abstract»
• ### A region-based P300 speller for brain-computer interface
Publication Year: 2009, Page(s):81 - 85
Cited by: Papers (28)
| | PDF (1495 KB) | HTML
A brain-computer interface (BCI) is a system that conveys messages and commands directly from the human brain to a computer. The BCI system described in this work is based on the P300 wave. The P300 is a positive peak of an event-related potential (ERP) that occurs 300 ms after a stimulus. One of the best-known and most widely used P300 applications is the P300 speller designed by Farwell-Donchin ... View full abstract»
• ### Online Neighborhood Watch: The Impact of Social Network Advice on Software Security Decisions
Publication Year: 2016, Page(s):322 - 332
| | PDF (1857 KB) | HTML
Malicious software (malware) is one significant threat to Internet security. Malware is designed to harm a computer or network, and can be installed on one's machine without their consent. Attacks are often done by deceiving people into downloading malicious software that is posing as useful software. We speculated that if people had advice from a trusted source, they would be inclined to use the ... View full abstract»
• ### Cooperative Spectrum Sensing Based on Two-Stage Detectors With Multiple Energy Detectors and Adaptive Double Threshold in Cognitive Radio Networks
Publication Year: 2013, Page(s):172 - 180
Cited by: Papers (13)
| | PDF (1428 KB) | HTML
This paper presents two-stage detectors for spectrum sensing in cognitive radio networks. The first stage consists of multiple energy detectors, where each energy detector (ED) has a single antenna with fixed threshold for making a local binary decision. If required, the second stage comprised of ED with adaptive double threshold is invoked. The detection performance of the proposed scheme is comp... View full abstract»
• ### Application of SFCLs to Inhibit Commutation Failure in HVdc Systems: Position Comparison and Resistance Recommendation
Publication Year: 2017, Page(s):31 - 40
| | PDF (2069 KB) | HTML
Commutation failure is one of the most common failures that may lead to serious consequences in high-voltage direct current (HVdc) systems. Superconducting fault current limiters (SFCLs) have been proved effective to inhibit commutation failures. In this paper, different installation positions of SFCLs are compared through three proposed evaluation indexes. The position between ac and dc systems i... View full abstract»
• ### Secure and Efficient Smart-Card-Based Remote User Authentication Scheme for Multiserver Environment
Publication Year: 2015, Page(s):20 - 30
Cited by: Papers (4)
| | PDF (1476 KB) | HTML
The growth of the Internet and telecommunication technology has facilitated remote access. During the last decade, many secure dynamic identity (ID)-based remote user authentication schemes have been proposed for the multiserver environment using smart cards. Recently, Li et al. point that the Lee et al. scheme is vulnerable to forgery attack, server spoofing attack, improper authentication, and u... View full abstract»
• ### Soil Classification From Large Imagery Databases Using a Neuro-Fuzzy Classifier
Publication Year: 2016, Page(s):333 - 343
| | PDF (1831 KB) | HTML
In this paper, we propose a neuro-fuzzy (NF) classification technique to determine various soil classes from large imagery soil databases. The technique looks at the feature-wise degree of belongings of the imagery databases to obtainable soil classes using a fuzzification method. The fuzzification method builds a membership matrix with an element count equal to the mathematical product of the num... View full abstract»
• ### Offshore Wind Farm Power Control Using HVdc Link
Publication Year: 2016, Page(s):168 - 173
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In this paper, a method is presented to control offshore wind farm output power. This method is able to fix the wind farm output power even during wind speed variations. In the proposed method, the offshore wind farm is connected to the onshore grid through the high-voltage dc (HVdc) cable. Moreover, the power control of the wind turbines is achieved by controlling the HVdc convertors. In the prop... View full abstract»
• ### Fault Ride-Through Capability Improvement of DFIG-Based Wind Turbine by Employing a Voltage-Compensation-Type Active SFCL
Publication Year: 2015, Page(s):132 - 142
Cited by: Papers (7)
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Based on the considerations in creating a smart grid roadmap, an integrated application of renewable energy sources and superconducting power devices may bring more positive effects. This paper suggests a voltage-compensation-type active superconducting fault current limiter (SFCL) to enhance the fault ride-through capability of doubly fed induction generator (DFIG) for wind power generation. Sinc... View full abstract»
• ### A Synchronous Buck Converter Using a New Predictive Analog Dead-Time Control Circuit to Improve Efficiency
Publication Year: 2013, Page(s):181 - 187
Cited by: Papers (4)
| | PDF (1243 KB) | HTML
The one-step predictive dead-time control circuit proposed in this paper consists of a dead-time detection circuit and an analog optimization circuit. The detection circuit, which can be manufactured on the same die as the synchronous MOSFET of the buck converter, provides an accurate detection signal that indicates body diode conduction. The proposed dead-time optimization circuit is an analog ci... View full abstract»
• ### Multivariable Adaptive Sliding-Mode Observer-Based Control for Mechanical Systems
Publication Year: 2015, Page(s):253 - 265
Cited by: Papers (2)
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In this paper, we present the design of an observer-based controller for perturbed mechanical systems using two-independent adaptive sliding-mode structures (ASMSs). The purpose of the proposed method is to compensate for external disturbances and modeling uncertainties of general mechanical plants. Assuming that only position measurements are available, the proposed control approach is based on a... View full abstract»
• ### An efficient 2.4GHz radio frequency identification (RFID) in a standard CMOS process
Publication Year: 2013, Page(s):93 - 101
Cited by: Papers (3)
| | PDF (1953 KB) | HTML
This paper describes the design of an ultra-low-power analog front-end circuitry for a UHF passive RFID transponder. The design includes a voltage multiplier, a voltage regulator, a demodulator, a power-on-reset, a ring oscillator, a matching network and a backscatter modulator. We present a novel charge-pump circuit for improved voltage gain and power efficiency of RFID tags. The charge pump is f... View full abstract»
• ### Application of Integrated Series Compensator in Damping Power Oscillations in Standalone Microgrids
Publication Year: 2015, Page(s):2 - 9
Cited by: Papers (4)
| | PDF (2110 KB) | HTML
This paper is concerned with power oscillation damping in standalone microgrids (MGs) using an integrated series compensator. Power oscillation is the result of dynamic interaction between generating units and/or loads in a power system, which results in increased losses, power quality degradation, and momentary overloading of the converters used in converter-based grid-connected microsources (MSs... View full abstract»
• ### Wireless security through RF fingerprinting
Publication Year: 2007, Page(s):27 - 33
Cited by: Papers (68) | Patents (1)
| | PDF (8124 KB) | HTML
The process of identifying radio transmitters by examining their unique transient characteristics at the beginning of transmission is called RF fingerprinting. The security of wireless networks can be enhanced by challenging a user to prove its identity if the fingerprint of a network device is unidentified or deemed to be a threat. This paper addresses the problem of identifying an individual nod... View full abstract»
• ### Relay Selection Based on Bayesian Decision Theory in Cooperative Wireless Networks
Publication Year: 2015, Page(s):116 - 124
Cited by: Papers (2)
| | PDF (2524 KB) | HTML
Wireless networks use relay nodes as cooperative nodes to gain maximum diversity. Relay selection is one of the key challenging problems in multiuser wireless cooperative networks. This paper addresses the selection problem of the relay node and proposes posterior probability-based relay node selection methods. In these methods, all calculations are derived by either source or destination, conside... View full abstract»
• ### Automatic Modulation Classification Based on Kernel Density Estimation
Publication Year: 2016, Page(s):203 - 209
| | PDF (1899 KB) | HTML
In this paper, we propose an efficient automatic modulation classification (AMC) scheme for a group of narrowband and digitally modulated signals such as quadrature phase-shift keying (QPSK), 16-PSK, 64-PSK, 4-quadratic-amplitude modulation (QAM), 16-QAM, and 64-QAM. The classification was performed by analyzing the probability density distribution for the real and imaginary parts of the modulated... View full abstract»
• ### New Systolic Array Architecture for Finite Field Inversion
Publication Year: 2017, Page(s):23 - 30
| | PDF (1034 KB) | HTML
This paper proposes a new systolic array architecture to perform inversion operation in GF(2m) based on a previously modified extended Euclidean algorithm. This architecture has low area and power complexities and it achieves a moderate speed. This architecture is explored by applying a regular technique to the inversion algorithm. The systolic architecture obtained has simple structure... View full abstract»
• ### Cooperative Energy-Efficient Content Dissemination Using Coalition Formation Game Over Device-to-Device Communications
Publication Year: 2016, Page(s):2 - 10
| | PDF (2322 KB) | HTML
This paper investigates the problem of cooperative energy-efficient content dissemination among a number of cellular user equipments (UEs), with the assumption that these UEs are seeking to receive the same content from a common wireless access point, such as an eNodeB. We formulate the problem as a nontransferable utility coalition formation game, in which a utility function is characterized by t... View full abstract»
• ### Modification in Geometric Structure of Double-Sided Axial Flux Switched Reluctance Motor for Mitigating Torque Ripple
Publication Year: 2015, Page(s):318 - 322
Cited by: Papers (1)
| | PDF (1435 KB) | HTML
Due to very high torque/weight ratio, the axial flux switched reluctance motor (AFSRM) can be appropriately used in many applications, especially electric vehicles and aerospace systems. Since the torque ripple is generally the drawback of SRMs, a new structure is suggested for the double-sided AFSRM in which the torque ripple is significantly reduced. In order to show the effectiveness of the tec... View full abstract»
• ### A New Adaptive Backup Protection Scheme Based on Intelligent Electronic Devices
Publication Year: 2015, Page(s):77 - 88
| | PDF (4280 KB) | HTML
A new adaptive interphase backup protection scheme based on intelligent electronic devices (IEDs) is proposed in this paper. When the system is in normal operation state, the backup protection areas are divided according to the operation status and topology of the primary and secondary devices in the power grid. When fault is detected in the system, each IED will search for the other IEDs in the s... View full abstract»
• ### Leading one detectors and leading one position detectors - An evolutionary design methodology
Publication Year: 2013, Page(s):103 - 110
Cited by: Papers (2)
| | PDF (685 KB) | HTML
Design of leading-one detector (LOD) and leading-one position detector (LOPD) are important as they are used for the normalization process in floating-point multiplication, floating-point addition/subtraction and in logarithmic converters. In this paper, the authors propose various gate-level architectures for LOD and LOPD. The LOD and LOPD circuits are evolved using the evolutionary algorithm (EA... View full abstract»
• ### Vehicular Traffic Monitoring Using Bluetooth Scanning Over a Wireless Sensor Network
Publication Year: 2014, Page(s):135 - 144
Cited by: Papers (2)
| | PDF (2515 KB) | HTML
The ubiquitous nature of Bluetooth equipped devices has made it opportunistic to scavenge information that can be repurposed for applications other than initially intended. One such opportunity is in vehicular traffic monitoring, whereby sampling of Bluetooth radios serve as proxies for vehicles and consequently for traffic density and flow. This paper discusses a complete data collection system d... View full abstract»
• ### Application of combined electric- and magnetic-conductor ground planes for antenna performance enhancement
Publication Year: 2008, Page(s):87 - 98
Cited by: Papers (35)
| | PDF (2902 KB) | HTML
This paper investigates the application of three different ground planes for antenna performance enhancement. They are the conventional perfect electric conductor (PEC), the perfect magnetic conductor (PMC), and their combination. A half-wavelength dipole in free space is considered as the reference case, and its performance over these ground planes is investigated and compared. It is shown that b... View full abstract»
• ### Single-Phase Zero Reactive Power Wireless Power Transfer Topologies Based on Boucherot Bridge Circuit Concept
Publication Year: 2015, Page(s):323 - 337
Cited by: Papers (1)
| | PDF (3858 KB) | HTML
High reliability and cost effectiveness of power electronic components have resulted in high level of interest in wireless power transfer techniques among academic and industrial professionals. Since the major interest is directed toward automotive and rail industries for electromagnetically coupled fast battery charging systems, a special transformer with a large gap and relatively large leakage ... View full abstract»
• ### A Low-Complexity Delta-Sigma Modulator ( $\Delta \Sigma$ ) for Low-Voltage, Low-Power Operation
Publication Year: 2016, Page(s):190 - 199
| | PDF (5240 KB) | HTML
In recent years, inverter-based sigma-delta (ΔΣ) modulators have received great attention as a suitable approach for the design of low-voltage, low-power, switched-capacitor ΔΣ. This method uses digital inverters as the active elements to construct the integrators in the ΔΣ loop. In some applications, a reduced silicon area implementation is an important c... View full abstract»
• ### Circle Views Signature: A Novel Shape Representation for Shape Recognition and Retrieval
Publication Year: 2016, Page(s):274 - 282
| | PDF (4821 KB) | HTML
An important problem in computer vision is object recognition, which has received considerable attention in the literature. The performance of any object recognition system depends on the shape representation used and on the matching algorithm applied. In this paper, we propose a novel circle views (CVs) shape signature for recognizing 2-D object silhouettes. Many views from one circular orbit (or... View full abstract»
• ### A Ring Oscillator-Based PUF With Enhanced Challenge-Response Pairs
Publication Year: 2016, Page(s):174 - 180
Cited by: Papers (1)
| | PDF (938 KB) | HTML
Physical unclonable functions (PUFs) are powerful security primitives that provide cheap and secure solutions for security-related applications. Strong PUFs provide a large set of challenge-response pairs (CRPs) and are suitable for device authentication. Weak PUFs produce a small number of CRPs and can be used for key extraction. In this paper, we propose a novel method to enhance the CRP set of ... View full abstract»
• ### A Near-Threshold Energy-Efficient ASK Transmitter for Biomedical Implants
Publication Year: 2016, Page(s):292 - 296
| | PDF (1572 KB)
A near-threshold amplitude shift keying (NT-ASK) transmitter for biomedical implants is presented in this paper. The ASK transmitter supports a 100-Mb/s baseband data rate with a carrier frequency of 2.4 GHz. The design incorporates an LC voltage-controlled oscillator (VCO), ASK modulator, and a class-E power amplifier. The carrier is generated by a low phase noise LC-VCO, and then directly modula... View full abstract»
• ### Modeling and Fault Analysis of Doubly Fed Induction Generators for Gansu Wind Farm Application
Publication Year: 2015, Page(s):52 - 64
Cited by: Papers (2)
| | PDF (2396 KB) | HTML
Wind power is developing rapidly as a means of handling the world's energy shortage and associated environmental problems. The Gansu provincial wind energy resources have around 237-GW wind power potential in China. In this paper, a study on key technologies of Hexi 750-kV power transmission line protections has been carried out. The project includes some characteristics, such as large-scale wind ... View full abstract»
• ### Fast group sparse classification
Publication Year: 2009, Page(s):136 - 144
Cited by: Papers (29)
| | PDF (367 KB) | HTML
A recent work proposed a novel Group Sparse Classifier (GSC) that was based on the assumption that the training samples of a particular class approximately form a linear basis for any test sample belonging to that class. The Group Sparse Classifier requires solving an NP hard group-sparsity promoting optimization problem. Thus a convex relaxation of the optimization problem was proposed. The conve... View full abstract»
• ### Impact of Solar Panels on Power Quality of Distribution Networks and Transformers
Publication Year: 2015, Page(s):45 - 51
Cited by: Papers (6)
| | PDF (1911 KB) | HTML
This paper presents an investigation on the impact of solar panels (SPs) on the power quality of distribution networks and transformers. Both solar farms and residential rooftop SP are modeled with the distribution network according to Canadian Utility data. Total harmonic distortion of voltages and currents on both sides of the distribution transformer are monitored under different operation cond... View full abstract»
• ### CAR Approach for the Internet of Things
Publication Year: 2016, Page(s):11 - 18
Cited by: Papers (7)
| | PDF (889 KB) | HTML
In this paper, we propose a novel context-aware routing (CAR) approach that uses the cloud as an extra level of data-request processing to improve the network performance in terms of data delivery. Data delivery in the Internet of Things depends heavily on numerous factors, such as the amount of data, end-to-end in-network delay, and setup time. The CAR approach is significantly improving the curr... View full abstract»
• ### A New Adaptive Voltage Protection Scheme for Distribution Network With Distributed Generations
Publication Year: 2013, Page(s):142 - 151
Cited by: Papers (5)
| | PDF (2966 KB) | HTML
A new adaptive voltage protection scheme suitable for distribution networks with potential distributed generation (DG) inserts is proposed in this paper. Firstly, the intelligent electronic devices (IEDs) are utilized to store relevant line parameters, obtain real-time voltage and current data, and facilitate communication among the IEDs. On this basis, the adaptive voltage primary and backup prot... View full abstract»
• ### A new measure of software complexity based on cognitive weights
Publication Year: 2003, Page(s):69 - 74
Cited by: Papers (34)
| | PDF (211 KB) | HTML
One of the central problems in software engineering is the inherent complexity. Since software is the result of human creative activity, cognitive informatics plays an important role in understanding its fundamental characteristics. This paper models one of the fundamental characteristics of software, complexity, by examining the cognitive weights of basic software control structures. Based on thi... View full abstract»
• ### Low Input Resistance CMOS Current Comparator Based on the FVF for Low-Power Applications
Publication Year: 2016, Page(s):127 - 131
| | PDF (1808 KB) | HTML
In this paper, a new low-voltage continuous-time current comparator is presented. The main idea is to use the flipped voltage follower as a key element for the comparator input stage. This configuration delivers a very low input resistance, which is mandatory for current-mode applications. Previous reported current comparators present a high-speed response; nevertheless, only few are suitable for ... View full abstract»
• ### Study on the Application of a Flux-Coupling-Type Superconducting Fault Current Limiter for Decreasing HVdc Commutation Failure
Publication Year: 2015, Page(s):10 - 19
Cited by: Papers (10)
| | PDF (4185 KB) | HTML
Commutation failure is a serious malfunction in high-voltage direct current (HVdc) converters and is mainly caused by ac side faults, where the change of dc current during fault conditions should be given adequate attention. Employing superconducting fault current limiters (SFCLs) for an HVdc system can suppress its dc fault current's amplitude and maintain a small rate of the dc current change, w... View full abstract»
• ### Limit Cycle Occurrence During Reactive Power Generation by Interlinking Converter in Hybrid Microgrids
Publication Year: 2016, Page(s):181 - 189
| | PDF (2343 KB) | HTML
This paper is concerned with the analysis of an instability phenomenon, known as limit cycle, in hybrid microgrids (HMGs). The rapid growth of distributed energy resources and their integration into existing distribution networks has opened a new era for electricity generation and distribution markets. The appearance of microgrids, both in the form of ac and dc, is the result of this integration. ... View full abstract»
• ### Efficient In-Band Spectrum Sensing Using Swarm Intelligence for Cognitive Radio Network
Publication Year: 2015, Page(s):106 - 115
Cited by: Papers (2)
| | PDF (2418 KB) | HTML
Spectrum sensing mechanisms enable cognitive radio networks to detect primary users (Upsi) and utilize spectrum holes for secondary user (SU) transmission. However, precise PU detection leads to longer sensing time and lower achievable throughput. In this paper, we propose a particle swarm optimization (PSO)-based scheme for an in-band local spectrum sensing to address the tradeoff between sensing... View full abstract»
• ### Specific Emitter Identification Based on Nonlinear Dynamical Characteristics
Publication Year: 2016, Page(s):34 - 41
Cited by: Papers (1)
| | PDF (2278 KB) | HTML
Specific emitter identification (SEI) designates the unique transmitter of a given signal, using only external feature measurements called the RF fingerprints of the signal. SEI is often used in military and civilian spectrum-management operations. The SEI technique has also been applied to enhance the security of wireless network, such as VHF radio networks, Wi-Fi networks, cognitive radios, and ... View full abstract»
• ### Coordinated Control of SFCL and SMES for Transient Performance Improvement of Microgrid With Multiple DG Units
Publication Year: 2016, Page(s):158 - 167
Cited by: Papers (1)
| | PDF (4855 KB) | HTML
Aiming at a microgrid system with multiple distributed generation (DG) units, this paper proposes the coordinated control of a flux-coupling-type superconducting fault current limiter (SFCL) and superconducting magnetic energy storage (SMES), so as to improve its transient performance under fault conditions. On the one hand, using the SFCL and the SMES enhances the microgrid's fault ride-through c... View full abstract»
• ### Codesign of Mixer-VGA Downconverter Blocks
Publication Year: 2015, Page(s):199 - 203
| | PDF (2102 KB) | HTML
Two radio frequency integrated circuit (RFIC) downconverters are presented, each consisting of an active mixer and a variable gain amplifier (VGA). The downconverter blocks (DCBs) have identical mixing stages but different VGA topologies. The mixers use a commutating switching network and a low-noise RF transconductance stage to reduce the system noise figure (NF). VGA gain control in one DCB (DCB... View full abstract»
• ### OFDM-CPM signals for wireless communications
Publication Year: 2003, Page(s):19 - 25
Cited by: Papers (3)
| | PDF (355 KB) | HTML
A class of orthogonal frequency division multiplexingcontinuous phase modulation (OFDM-CPM) signals is introduced in which the binary data sequence is mapped to complex symbols using the concept of correlated phase states of a CPM signal. A multiple-symbol-observation receiver is used to decode the received sequence, and an investigation of bit error rate over typical wireless multipath channels w... View full abstract»
• ### Redesigned CMOS (4; 2) compressor for fast binary multipliers
Publication Year: 2013, Page(s):111 - 115
Cited by: Papers (3)
| | PDF (334 KB) | HTML
(4; 2) compressors seem to be the most popular bit-compressing cells with principal application in multi-operand addition and multiplication hardware. Therefore, performance of (4; 2) compressors is particularly influential in the efficiency of multiplication intensive computations. Realization of these cells is mainly based on XOR/XNOR gates, which are functionally equivalent to three simpler one... View full abstract»
• ### Adaptive-backstepping-based design of a nonlinear position controller for an IPMSM servo drive
Publication Year: 2007, Page(s):97 - 102
Cited by: Papers (5)
| | PDF (595 KB) | HTML
This paper presents the design of a novel nonlinear position controller for an interior permanent-magnet synchronous motor (IPMSM) servo drive. The motor model equations provide the basis for the proposed controller, which is designed with the adaptive backstepping technique. Various system uncertainties, particularly mechanical-parameter uncertainties, are incorporated in the design of the contro... View full abstract»
• ### A Directional FM Channel Model for Contemporary Wireless Systems
Publication Year: 2016, Page(s):311 - 321
| | PDF (1861 KB) | HTML
It is anticipated that the existing analog use of the frequency modulation (FM) band (87.5-108 MHz) will ultimately be replaced by contemporary digital systems beyond 3G. Before such a transition is realized, it is important to understand the channel characteristics of the FM band in order to perform preliminary studies before deployment of new systems. Hence, in this paper, for the FM band, we in... View full abstract»
## Aims & Scope
The role of the Canadian Journal of Electrical and Computer Engineering is to provide scientific and professional activity for its members in Canada, the CJECE complements international journals and will be of particular interest to anyone involved in research and development activities in the field of electrical and computer engineering.
Full Aims & Scope
## Meet Our Editors
Editor-in-Chief
Dr. Shahram Yousefi
Dept. of Electrical and Computer
Engineering
Queen's University | {"extraction_info": {"found_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": 0.2778299152851105, "perplexity": 5193.026851432759}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-22/segments/1495463608617.6/warc/CC-MAIN-20170525214603-20170525234603-00551.warc.gz"} |
https://www.toppr.com/guides/physics/sources-of-energy/conventional-sources-of-energy/ | # Conventional Sources of Energy
‘Always surround yourself with positive energy’. You must have heard this phrase quite a lot; what is this energy we’re talking about? Do things have energy in them? And are these things conventional sources of energy? But, before that what are conventional sources of energy? How do we obtain this energy? Since all living beings use energy for various vital activities inside as well as outside their body. So, let us study about various conventional sources of energy below.
## What is Energy?
Energy is one of the most important components of economic infrastructure. In a developing economy, the energy demand is high from sectors like agriculture, industry, residential and economical. Energy resources are very much necessary for the existence of mankind.
## Classification of Energy Sources
Energy sources can be divided into two types based on how quickly can they be replenished:
• Conventional sources of Energy
• Non-conventional sources of Energy
### What is a conventional source of energy?
When we cannot reuse a source of energy after using it once we call them “conventional sources of energy” or “non-renewable energy resources”. They are the most important conventional sources of energy. These include coal, petroleum, natural gas and nuclear energy. Oil is the most widely used source of energy. Coal, petroleum and natural gas account for about 90% of world’s production of commercial energy and hydroelectric and nuclear power account for about 10%.
### Types of Conventional Sources of Energy:
#### Coal
Coal is the most abundant conventional source of energy which could last for at least 200 years. It is a black-brown sedimentary rock. Formation of coal occurs when the remains of plants convert into lignite and then into anthracite. This involves a long process that takes place over a long period of time. Coal helps for various proposes such as heating of the house, as fuel for boilers and steam engines and for generation of electricity by thermal plants. It constitutes about 70% of total commercial energy consumption in the country.
#### Oil
Out of all the conventional sources of energy, oil is used abundantly all over. Considering, oil is one of the most important conventional sources of energy in India, the resources for same are even smaller. The extraction of oil from deposits is known as oil resources.
#### Petroleum and Natural Gas
Petroleum is the mixture of hydrocarbons like alkanes and cycloalkanes. In crude form black liquid is known as petroleum and the formation of a natural gas occurs when the gas comes in contact with petroleum layer. Natural gas is a mixture of 50-90% of Methane, Ethane, Propane, Butane, and Hydrogen sulphide. After refining and purifying crude petroleum, it is available as petrol, diesel, lubricating oil, plastic etc. Natural gas is also making a significant contribution to the household sector. It causes less air pollution as compared to other fossil fuel.
#### Fuel Woods
Rural people use the fuelwood for their day to day cooking which comes from natural forests and plantations. The availability of fuelwood has become difficult due to rapid deforestation. We can avoid this problem by planting more trees on degraded forest land, culturable wasteland, barren land grazing land.
#### Thermal Power Plant
Power stations burn a large number of fossil fuels to heat up water, to produce steam, which further runs the turbine to generate electricity. Transmission of electricity is more efficient than, transporting coal or petroleum over the same distance. It is called as the thermal plant because fuel is burnt to produce heat energy which is converted into electrical energy.
#### Nuclear energy
A small amount of radioactive substance can produce a lot of energy through the nuclear substances all over the world. In order to obtain nuclear energy, nuclear reactions are essential and there are about 300 nuclear reactions. Nuclear energy is one of the most environmentally friendly conventional sources of energy as it produces fewer greenhouse gas emissions during the production of electricity in comparison to sources like coal power plants. Although in case of accidents, this same nuclear energy releases in high amount in the environment. Also, the nuclear waste that remains is radioactive and hazardous.
### Conclusion
• The human race widely uses these conventional sources of energy and therefore the magnitude of usage is so high that the resources are depleting at an even faster rate.
• At present, many countries are overly dependent on fossil fuels to meet their requirement for power.
• The deposits of petroleum in our country are quickly exhausting and if it continues, there will be soon complete exhaustion of all the conventional sources of energy.
## Solved Example for You
Q. Choose the source of energy which is different from others.
a. Wood
b. Falling Water
c. Wind
d. Petroleum
Sol: d. Petroleum
From the given options, wood, water, and wind are the renewable or conventional sources of energy, whereas petroleum is a limited and non-renewable source of energy.
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Get Started | {"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": 0.8308504819869995, "perplexity": 2260.3883474824943}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1679296945381.91/warc/CC-MAIN-20230326013652-20230326043652-00221.warc.gz"} |
https://scicomp.stackexchange.com/questions/27450/correct-use-of-scipys-sparse-linalg-spilu/27451 | # Correct use of scipy's sparse.linalg.spilu
I'm attempting to use scipy's spilu routine as a preconditioner and I'm finding bad performance for my application (solving a global linear system arising from a DG discretization of an time-dependent ADR PDE).
Before I write tests to tune the options and compute the effect of the preconditioner on the eigenvalues of my linear system, I'd like to make sure I'm applying the preconditioning matrix in the scipy intended manner, since the documentation for spilu is pretty spartan...
elif solver == 'spILUPCG': P = sp.sparse.linalg.spilu(A.tocsc()) P = P.L * P.U x = sp.sparse.linalg.cg(A, b, M=P)
If $$\mathbf L$$ and $$\mathbf U$$ give an approximate factorization of $$\mathbf A$$, you wouldn't want to use $$\mathbf P = \mathbf L\cdot \mathbf U$$ as a preconditioner (that's approximately $$\mathbf A$$), you'd want to use $$\mathbf P = \mathbf U^{-1}\cdot \mathbf L^{-1}$$ (that's approximately $$\mathbf A^{-1}$$). Even then, you would not want to multiply them out explicitly into $$\mathbf P$$, it's probably dense. Instead think of $$\mathbf P$$ as an operation/operator that cascades two solve steps (first solve by $$\mathbf L$$, then solve by $$\mathbf U$$).
I would expect there to be some way to inject that operation as a closure/callback to precondition cg(). Sadly I'm not a scipy expert, so I don't know the exact way to do it. But somewhere scipy should have an abstraction for applying the action of a linear operator, and I would expect both their matrix objects and their preconditioner objects to fulfill that abstraction. I suppose I'd try just passing your $$\mathbf P$$ object itself.
• In particular, you don't want to explicitly form $(U^{-1}L^{-1})$ because this is likely to be a dense matrix! Nov 6 '19 at 16:34
• Good clarification, thank you. Nov 6 '19 at 20:29
This question has an example of how to create the preconditioner M with a scipy sparse matrix A of shape NxN
from scipy.sparse.linalg import LinearOperator, spilu
ilu = spilu(A)
Mx = lambda x: ilu.solve(x)
M = LinearOperator((N, N), Mx) | {"extraction_info": {"found_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": 12, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6386682391166687, "perplexity": 1070.9257012826574}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1631780056902.22/warc/CC-MAIN-20210919220343-20210920010343-00671.warc.gz"} |
http://curiouscheetah.com/Museum/Puzzle/Seeknumbers | Curious Cheetah
# Seek Numbers
## Background
The origin of this puzzle is not known.
## Puzzle and Goal
An unsolved puzzle is a rectangular grid. Clues are a start, an end, and number clues.
The goal is to draw a single line that satisfies the clues.
## Rules
The solved grid must satisfy the following conditions:
The line starts at the beginning, ends at the end, and goes through each cell exactly once, travelling orthogonally.
The line may only turn after going through a number X, and then must turn X times before going through another number. | {"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": 0.8384546041488647, "perplexity": 1602.86685005736}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-17/segments/1492917119838.12/warc/CC-MAIN-20170423031159-00409-ip-10-145-167-34.ec2.internal.warc.gz"} |
http://math.stackexchange.com/questions/286814/what-is-the-limit-of-a-sequence-defined-recursively-as-x-1-2-x-n1-1-3-x | # What is the limit of a sequence defined recursively as $x_1=2$, $x_{n+1}=1/(3-x_n)$ with $n \in \mathbb{N}$, and how do I prove it exists?
This is an exercise I've found online.
Find the limit of a sequence defined recursively as $x_1=2$, $x_{n+1}=\dfrac{1}{3-x_n}$ with $n\in \mathbb{N}$. Show that the limit exists before attempting to find it.
So far, I have shown that $\{x_{n}\}$ is bounded below by $0$ and above by $2$ since $\frac{1}{3-x_n}>0$ and $\frac{1}{3-x_n}\le 2$ for all $n$.
I'm stuck here because I'm not sure what to show next, and I don't know precisely how to show the limit exists.
-
Show that $(x_n)$ is a decreasing sequence and then appeal to the fact that a bounded monotone sequence is convergent. – David Mitra Jan 25 '13 at 18:06
At first, you can show that $x_1>x_2$ easily.
If $x_{n-1}>a_n$ holds (and $0\le x_n \le 2$ for all $n$), we get \begin{align} x_{n-1}>x_n & \Longrightarrow & -x_{n-1}<-x_n \\ & \Longrightarrow & 3-x_{n-1}<3-x_n \\ & \Longrightarrow & \frac{1}{3-x_{n-1}}>\frac{1}{3-x_n} \\ & \Longrightarrow & x_n > x_{n+1}\\ \end{align}
so $x_n>x_{n+1}$. So this sequence convergent, by monotone convergence theorem.
-
Is this an inductive proof that $x_{n}>x_{n+1}$? – 000 Jan 25 '13 at 18:13
@Limitless Oh, it is my mistake. – tetori Jan 25 '13 at 18:17
In the last line, how do you arrive at $x_n>x_{n+1}$? Isn't $\dfrac{1}{3-x_{n-1}}=x_{n}$? By definition, if $x_{n+1}=\dfrac{1}{3-x_{n}}$, then a substitution of $x=x'-1$ shows us that $x_{n}=\dfrac{1}{3-x_{n-1}}$. – 000 Jan 25 '13 at 18:26
@DavidMitra I do not follow his or her progression from line 3 to line 4. Is it correct? If so, why? – 000 Jan 25 '13 at 18:30
@Limitless Line 3 had a typo. It is now correct. – David Mitra Jan 25 '13 at 18:31
For limit solve the equation $$l=\frac{1}{3-l} \implies l^2-3l+1=0$$ You get $l=\frac{3+\sqrt 5}{2},\frac{3-\sqrt 5}{2}$. Your limit will be $\frac{3-\sqrt 5}{2}$ since $\frac{3 +\sqrt 5}{2} >2$.
-
If a limit $L$ exists, it must satisfy $$x_{n+1} = \frac{1}{3-x_n} \Rightarrow L = \frac{1}{3-L} \Rightarrow L^2-3L+1=0$$
So that candidates for the limit are $\frac{3\pm \sqrt{5}}{2}$. Since you've proven the series is bounded above by 2, only one of these is possible.
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https://www.physicsforums.com/threads/change-in-momentum.345149/ | # Change in Momentum
1. Oct 12, 2009
### CaptFormal
1. The problem statement, all variables and given/known data
A billiard ball of mass m = 0.15 kg strikes the cushion of a billiard table at θ1 = 48° and a speed v1 = 21 m/s. It bounces off at an angle of θ2 = 670 and a velocity of v2 = 16 m/s. What is the magnitude of its change in momentum (in kg·m/s)?
http://schubert.tmcc.edu/res/msu/mmp/kap6/picts/pool.gif
2. Relevant equations
3. The attempt at a solution
Not sure how to solve this one. Any help will be appreciated.
Sincerely,
CaptFormal
Last edited by a moderator: Apr 24, 2017
2. Oct 12, 2009
### rl.bhat
Take the vertical and horizontal components of v1 and v2.
Find the difference in vertical and horizontal components. Take care of signs.Then take the resultant of these components.
3. Oct 12, 2009
### CaptFormal
Ok, so here is what I got so far.
Vx = 21cos(48) - 16cos(67) = 7.8
Vy = 21sin(48) - 16sin(67) = 0.8779
Now I am not sure what to do. I tried the following:
(7.8^2 + 0.8779^2)^(1/2)
and then took that answer and multiplied it by the mass but it was incorrect. What am I missing?
4. Oct 13, 2009
### rl.bhat
Vx = 21cos(48) - 16cos(67) = 7.8
This is wrong. vx components are in the opposite direction. So the change in vx is
Vx = - 21cos(48) - 16cos(67) = ?
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https://www.ideals.illinois.edu/handle/2142/79144 | ## Files in this item
FilesDescriptionFormat
application/vnd.openxmlformats-officedocument.presentationml.presentation
379845.pptx (5MB)
PresentationMicrosoft PowerPoint 2007
application/pdf
1035.pdf (21kB)
AbstractPDF
## Description
Title: ROTATIONALLY RESOLVED SPECTROSCOPY OF THE B1__ X1_+ AND C1_+_ X1_+ ELECTRONIC BANDS OF CaO Author(s): Sullivan, Michael Contributor(s): Heaven, Michael; Stewart, Jacob Subject(s): Metal containing Abstract: The $B^{1}Pileftarrow X^{1}Sigma^{+}$ and $C^{1}Sigma^{+}leftarrow X^{1}Sigma^{+}$ transitions of CaO, at energies below 30,000 $mathrm{cm^{-1}}$, were previously investigated by Lagerqvistfootnote{A. Lagerqvist, textit{Arkiv F{\"o}r Fysik} textbf{underline{8}}, 83, 1954}. The arc source used in that work yielded spectra at energies above 30,000 $mathrm{cm^{-1}}$ that were too congested for analysis. In the present study we have used jet-cooling of CaO to extend the characterization of the $Bleftarrow X$ and $Cleftarrow X$ band systems up to 35,000 $mathrm{cm^{-1}}$. Analyses of these data and spectroscopic constants will be reported. This work is being carried out in support of two-color photoionization studies of the cation, where the higher energy vibronic levels of the B and C states are used as the first excitation step. Issue Date: 23-Jun-15 Publisher: International Symposium on Molecular Spectroscopy Citation Info: ACS Genre: CONFERENCE PAPER/PRESENTATION Type: Text Language: English URI: http://hdl.handle.net/2142/79144 Date Available in IDEALS: 2016-01-05
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https://spectre-code.org/structSpectral_1_1Swsh_1_1Tags_1_1EthEth.html | Spectral::Swsh::Tags::EthEth Struct Reference
Struct for labeling the $$\eth^2$$ spin-weighted derivative in tags. More...
#include <SwshTags.hpp>
## Detailed Description
Struct for labeling the $$\eth^2$$ spin-weighted derivative in tags.
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Here we are going to see some example problems of solving polynomial of degree 6. Find polynomial with given zeros and y intercept calculator. It also multiplies, divides and finds the greatest common divisors of pairs of polynomials; determines values of polynomial roots; plots polynomials; finds partial fraction decompositions; and more. I can find the zeros (or x-intercepts or solutions) of a polynomial in factored form and identify the multiplicity of each zero. In the complex number system, this statement can be improved. 1 1 In order to simplify the notation, the definition is given in terms of a polynomial in two variables, however the definition naturally scales to any number of variables. Polynomial Functions, Zeros, Factors and Intercepts. Step 2: Find the x- intercepts or zeros of the function. Question: Form a polynomial f (x) with real coefficients having the given degree, zeros and constant. Graph the polynomial function WITHOUT using your graphing calculator. an are the We can use this general equation to find the equation of a family of polynomial functions with a given set of zeros. More › More Courses ›› View Course. form a polynomial function whose real zeros and degree are given. Degree of operating leverage is a financial ratio that helps managers understand how sales affect operating income. The polynomial is degree 3, and could be difficult to solve. The remaining zero can be found using the Conjugate Pairs Theorem. Let P(x) = ∑i pixi be a given polynomial and consider writing P(x) = ∑j Calculate either the monic polynomial with specified zeros, . f(x) = -3<2+5 Number of Extrema: 12. •recognise when a rule describes a polynomial function, and write down the degree of the polynomial, •recognize the typical shapes of the graphs of polynomials, of degree up to 4, •understand what is meant by the multiplicity of a root of a polynomial, •sketch the graph of a polynomial, given its expression as a product of linear factors. Form A Polynomial F(X) With Real Coefficients Having The Given Degree And Zeros. third-degree polynomial must have at least one rational zero. How to Write Polynomial Functions When Given Zeros. ( The degree is the highest power of an x. Look at this example: Find all the rational zeros of: f (x) = 2 x 3 + 3 x 2 - 8 x + 3. Also synonymous with debt and leverage is risk. We can check easily, just put "2" in place of "x":. Degree 5; zeros: -5; -2i; -4+2i If a polynomial has a complex imaginary zero a+bi, then a-bi is also a zero. Let me show you two examples: f(x)= 2(x+3) and x 1(x+10). Understand how the multiplicity of a zero changes how the graph behaves when it hits the x-axis. , x2 - (α + β) x + αβ x2 - (Sum of the …. f (x) is a polynomial with real coefficients. What is Find Cubic Function With Given Zeros Calculator. This technique is performed with less effort than the calculation of the long division method. write a polynomial with integer . Let zeros of a quadratic polynomial be α and β. Insurance, retirement plans, health club memberships, and education reimbursement are just a few examples of compensation in the form of; In exercise, evaluate or simplify each expression without using a calculator. Solve cubic equations or 3rd Order Polynomials. Step 1: Start with the factored form of a polynomial. Let f be a polynomial in two variables, viz. Following how it's constructed. The shape of the pendent can be defined by the equation y = StartFraction 1 Over 20 EndFractio …. A polynomial of degree $5$ is known as a quintic polynomial. 2√2, 3 asked Sep 15, 2020 in Mathematics by darling016. Day 1 Warmup (1) Multiply the polynomial and put in standard form. To find the x-intercept, set y = 0 \displaystyle y=0 y=0. Any first degree polynomial, y= A 1 x+ A 0, has 2 coefficients. Z Worksheet by Kuta Software LLC. Uses the cubic formula to solve a third-order polynomial equation for . PDF Form a polynomial with given zeros and degree calculator. The degree of a polynomial tells you even more about it than the limiting behavior. Finding x-intercepts and y-intercepts. Given a list of "zeros", it is possible to find a polynomial function that has these specific zeros. write a polynomial function of least degree with given zeros calculator. Other conditions on polynomials may include requiring that they be orthogonal to one another as is the case with the. Find Given Function With Zeros Calculator Cubic. Given the graph of a degree 5 polynomial below, complete the table of values for either the x-value of a zero, or the multiplicity of the zero. 4—Complex Zeros of Polynomial Functions. More will be said about these polynomials as they are needed. The first term is the one with the biggest power!. Example 2: Arrange the following . For each zero, state whether the graph crosses the x-axis or touches the x-axis and turns around. There are three given zeros of -2-3i, 5, 5. Select polynomial whose zeros and degree are given. f (x, y) = ∑ i, j a i j x i y j. How To Form A Polynomial With The Given Zeroes December 22, 2020 December 22, 2020 by Veerendra Form A Polynomial With The Given Zeros Let zeros of a quadratic polynomial be α and β. First divide by the leading term, making the polynomial monic. ) Write the function in factored form using the given zeros. LT 5 find the zeros (or x-intercepts or solutions) of a polynomial in factored form and identify the multiplicity of each zero. Calculator shows detailed step-by-step explanation on how to solve the problem. d) Find the total number of zeros (count the multiplicities of all the zeros). calculator Use this calculator to solve polynomial equations with an order of 3 as ax3 + bx2 + cx + d = 0 for x including complex solutions. Unfortunately, in most cases where we need the zeros of a given polynomial function, there is no dependable procedure for finding even one zero in exact form, and with polynomial functions of higher degree, even knowing several zeros may not be enough. ; Find the polynomial of least degree containing all of the factors found in the previous step. ) Symmetries: axis symmetric to the y-axis. Form a polynomial function whose real zeros and degree are given. An online zeros calculator determines the zeros (exact, numerical, real, and complex) of the functions on the given interval. Then the polynomial is given by the following formula. Question 1164186: Form a polynomial whose zeros and degree are given. If the polynomial function f has real coefficients and a complex zero in the form $a+bi\\$, then the complex conjugate. When it's given in expanded form, we can factor it, and then find the zeros! Here is an example of a 3rd degree polynomial we can factor by first taking a common factor and then using the sum-product pattern. The calculator converts a multivariate polynomial to the standard form. Form a polynomial whose real zeros and degree are given. Degree of a Polynomial Calculator. Sum of the zeros = 4 + 6 = 10 Product of the zeros = 4 × 6 = 24 Hence the polynomial formed = x 2 – (sum of zeros) x + Product of zeros = x 2 – 10x + 24. Apr 16, 2017 — Form a polynomial with real coefficients having the given degree and zeros calculator Get the answers you need, now!. 1 The general solution to the quadratic equation There are four steps to nding the zeroes of a quadratic polynomial. 3 Determine the equation of a polynomial given a set of conditions (e. Transcribed image text: Form a polynomial whose zeros and degree are given. Finding a polynomial of a given degree with given zeros - Complex zeros. There are two approaches to the topic of. This online calculator finds the roots of given polynomial. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 2, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7500522136688232, "perplexity": 464.86513491189163}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1652662545326.51/warc/CC-MAIN-20220522094818-20220522124818-00767.warc.gz"} |
https://mathalino.com/reviewer/differential-calculus/problems-caculus-involving-inverse-trigonometric-functions | Problems in Caculus Involving Inverse Trigonometric Functions
The following are problems involving inverse trigonometric functions.
Rate: | {"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": 0.9999929666519165, "perplexity": 4536.687096315333}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-17/segments/1618039508673.81/warc/CC-MAIN-20210421035139-20210421065139-00478.warc.gz"} |
https://hilfe.studip.de/help/4.3/en/Basis/VerschiedenesTeX | # Typesetting formulae with LaTeX
Here you find help on the use of TeX in Stud.IP.
## Mathematical formulae in Stud.IP
Some of you may have noticed that our computer keyboard does not have a sigma sign , an integral sign or similar symbols. Because we occasionally need them for university operations, Stud.IP implemented TeX-Arithmetic (pronounced Tech) in order to be able to insert mathematical symbols and entire formulae.
You generally write:
$$f(x) = e^{x+1}$$
so this becomes, for example:
This means that the bracketed terms form the frame for the formula. Normal TeX code, such as that used by other programmes and websites, can be placed inside the TeX brackets (or TeX tags). The TeX code has become a certain standard, but it will be briefly explained.
## Introduction to TeX
In principal one can write in TeX tags the same way as in other contexts. All formulae, which contain +, -, *, / and whole numbers and letters are written in TeX in the same manner in which one would have written them otherwise. In TeX the other symbols are merely designated by specific character sequences. The character sequence \sum thus results in a sigma sign.
Example:
$$\sum$$ becomes
Similarly, the integral sign is signified by \int etc. A comprehensive list is presented below.
But, to begin with, here are a few syntax rules for TeX. For the sigma sign one wants to specifically state the variables across which the variables are summed (and how often) and for the integral sign the limits of the integration (or quantities). This is performed as follows:
$$\sum_1^9$$ becomes
The _ (underline) always shows the term which should be at the bottom (subscript) (as in the customary Stud.IP syntax as well) and the ^ sign does the same for superscript characters. And this applies for the sigma sign, integral sign but — and now things are getting cool — also for normal variable indices or powers.
Example: $$f(x) = x^7$$ wird zu
In other words this is a notation for everything. If the expressions which are to be subscripts or superscripts are more complicated than one character (and even the number 10 comprises more than one character) one has to write the entire expression in braces { and }, so that it will be considered to be a collective expression. In effect the expression in braces { and } has a character length of 1 for TeX. Now an example for such "complicated“ expressions:
Example: $$\sum_1^100$$ becomes . That is not what we usually desire, thus we have to write $$\sum_1^{100}$$, which becomes . And now another real example: $$\sum_{k = 1}^n 1/k$$ becomes
And now to fractions. In most cases a fraction is well written with the / (slash) character, such as 1/7 for example. But large fractions in particularly become confusing when written in this manner. In TeX fractions can be represented by writing the fraction line as \over. Everything in front of this is considered the numerator; everything behind it is interpreted as the denominator of the fraction.
Example: $$x + 3 \over y + 2$$ becomes
But this becomes problematical when something other than the fraction is to be written. In this case one writes the fraction in braces { and } and everything that is not contained in the braces is not part of the fraction.
Example:
false: $$f(x) = x + 3 \over 5$$ becomes
correct: $$f(x) = x + {3 \over 5}$$ becomes
TeX can also depict compound fractions. To achieve this, one simply writes another fraction in braces in a fraction:
Example: $$f_n(x) = \left {3 + x \over 1 + {1 \over n} }$$ becomes
Unfortunately, the same thing applies in TeX as in real life: one should avoid double fractions. In real life they become confusing and in TeX the characters gradually become too small. At least, a certain minimum size is never exceeded in TeX so that one can use an infinite number of braces.
Example: $$f_n(x) = \left {3 + x \over 1 + {1 \over 1 + {1 \over 1 + {1 \over 1 + {1 \over n}}}} }$$
becomes
It is not pretty, but it works.
The fact that an orderly formula in TeX is rather complicated is beyond dispute. But let’s say it like this: it is more difficult to read TeX code than to write it. Basically, one only has to understand the TeX principle and formulae nearly write themselves.
## Liste of TeX functions
### Vectors and matrices
There are a number of matrices, which all begin with \matrix. The type of matrix is then written in braces (i.e., the type of brackets which should enclose it). Then all cells are written individually from left to right and from top to bottom. An & symbol indicates that a cell should be indented and a // shows that a cell shifts downwards. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9964328408241272, "perplexity": 778.4215766830566}, "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-2019-47/segments/1573496670389.25/warc/CC-MAIN-20191120010059-20191120034059-00155.warc.gz"} |
http://www.akeric.com/blog/?tag=atp | Posts Tagged ‘ ATP
# Overview
I’ve been using removable glass build plates for years on both my Makerbot Replicator 1, and my custom C-Bot: I get double-thick glass cut at my local hardware store (Orchard Supply Hardware has had a great price on this), always thinking it was ‘totally flat’. But is it really? My C-Bot has a 12×12″ heated build platform. When I go to level it with the glass, I get each of the four corners dialed in perfectly. But the middle always sags slightly… even though it’s glass. Double-thick glass. But glass is actually somewhat plastic, and this sag has always bugged me.
Back in December I assembled my 1000mm X-Carve CNC, and it’s been so much fun cutting wood. I knew it could do aluminum as well, but needed a project. And that’s what this post is all about: Using my X-Carve to machine a new removable build plate out of .25″ mic6 aluminum for my 3d printer. I am so happy with the results.
# Sourcing the material
Before I started this, I had no idea what ‘mic6’ aluminum was. It’s also referred to as ‘cast aluminum tooling plate’ or ‘ATP’, since mic6 appears to be a trademarked brand name. Simplistically, it’s a standard for (among other things) a very flat aluminum plate, to .001″. After reading a plethora of forms, and researching my local options, I settled on Midwest Steel And Aluminum’s “Cast Aluminum Tool & Jig Plate“, .25″ thick, 12×12”, which came to about $20, and the ground shipping another$20. I could have bought it locally for \$45 + tax (ugh).
A note on the order: The plate was packaged in one layer of cardboard, that was it. It appeared to have been dropped several times in-transit, 3 of the 4 corners were blunted, and there was an small indentation in the middle of plate itself. If I was using this for something really precision I would have returned it. Just a note to tell them to ship it better if you go this route.
Once it showed up, time to make some cuts!
# Initial cuts
When I first got the plate I knew I had to notch a section out of each corner, since the heads of the bolts that hold the MakerFarm heated build platform stick up about 1/8″ish from it: I didn’t want the plate resting on the bolt-heads, so I need to make little pockets for each. Before I even considered my X-Carve CNC, I figured I could use my drill-press to pocket these. Long story short: It did not work well, and made a mess of the corners. Based on that frustration I went down the ‘how about I use that dormant CNC right next to the drill press…” road.
For all below cuts, I used the same 1/8″ 2-flue upcut carbide endmill.
Since these cuts were so simple, I used Inventable’s Easel: I designed a circle with a diameter of .4″ across, .175″ deep, and used that to pocket each of the four corners already mangled by my drill press. I used the default ‘aluminum’ Easel setting (5 ipm, .003″ doc, DeWalt on speed 1) with the first pocket (which took about 20 minutes), then started cranking it up: By the final pocket I had it running at 20 ipm at .01″ doc, with the DeWalt on speed 2, taking about 5 minutes.. It did great, and the bit was cool to the touch after the cuts. When all four pockets were complete, it fit right on the bed with no collision with the bolt-heads:
All the rough stuff to the right of the bolt-head was the abuse by the drill-press.
I have four bulldog clips that hold the plate on, one on the middle of each side. The issue is even though I’ve bent them down to move them out of the way, parts of them still stick up slightly, and on a large print the nozzle could collide with them. So going back to Easel, I designed a new rectangular pocket that would keep the bulldogs out of the way of the toolhead. These were 2.25″ x .3″, cut .075″ deep. I positioned them in the center of the left\right sides of the build plate, but had to offset them on the front\back based on my leadscrew config.
An in-process cut:
And all four final cuts:
Installed on the printer: No more clearance problems with the bulldogs!
# Prepping the plate
I use a highly secret (50% wood-glue, 50% water) slurry on my build plate to get PLA to stick. But the mic6 is so smooth, I first scoured it with steel wool for several minutes to give the glue something to bite into.
Note for the future: First, use something like lacquer thinner\acetone\mineral spirits to clean the plate of any oils: Quite to my surprise, after many minutes of scrubbing, I could clearly see my handprint on it. The oils deposited from my hand actually protected it from the steel wool. So I went back and liberally scrubbed it with lacquer-thinner soaked rag, then went back to the steel-wool treatment again: No more handprint. Be sure to wipe it down with lacquer thinner after the steel wool too: The wool actually leaves quite a bit of itself deposited into the aluminum.
After the plate was scrubbed, cleaned, and glue-slurry applied, I did some test prints. And while the flatness was super awesome, I realized something very quickly: The slicer said the bed heated up waaaay faster than it actually did: For big prints in PLA, I’ll heat the bed up to 60c.
It dawned on me that the thermistor that does the temp reading is taped to the bottom of the MakerFarm heated build platform, while the thing being printed is sitting above it on .25″ of aluminum… that is taking much longer to heat up.
After brainstorming, I came up with the idea of cutting a groove into the bottom of the plate, that I could tape the thermistor into: It should then be reading the temp from the removable plate itself, providing a much more accurate temperature. This means I’ll also need to snip the leads running to the thermistor and install a barrel-jack into the mix to allow for the plate to be removed, since there’s now a sensor taped to it.
# Secondary cut
Going back to Easel, I designed a .5″ wide groove cut .0312″ deep that I could recess the tape into, then another smaller groove .2″ across and .1″ deep to run the wires to the thermistor.
Here it is mid-cut:
Cut gotchas:
• Easel has (based on what I’ve experienced) no idea of conventional cuts (bit spinning in the direction of travel) and climb cuts (bit spinning opposite direction of travel). From what I’ve read, climb cuts can provide better finish, but only on ‘professional\beefy’ machines: not the X-Carve. Conventional cuts fare much better on the X-Carve. This (as I found out) can cause dangerous problems.
• When the top cut started, it was all conventional cuts, and cut fine. But when the next layer started, and for every layer down, it was climb cuts. Because of that, I noticed a lot of bit defection, chattering, and even gouging. To avoid catastrophe, I had to manually monitor the cut, and really crank up the spindle speed as needed to compensate.
• Note that MeshCAM gives you the option in the rough-cut to do either conventional or climb cut: For future aluminum projects I’ll be using it for sure.
To help with heat transfer (that is only a theory of mine) and to prevent any sort of plate-slip (which is legit), I shoot the bottom of the plate with rubberized undercoating. I then snipped my thermistor line, soldered barrel-jacks onto either side of it, then taped it into the groove on the bottom of the plate:
Putting it back onto the HPB, I reconnected the barrel-jacks:
# Final thoughts
It works, great.
When the HPB heats up, and it finally gets to temp…. it really feels like the top\bottom are the same temp. And I can level each of the four corners, and the middle is the exact same distance as the rest of them from the toolhead.
Super rewarding project with one machine improving another. | {"extraction_info": {"found_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": 0.5041013956069946, "perplexity": 6254.136209250894}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1518891812405.3/warc/CC-MAIN-20180219052241-20180219072241-00037.warc.gz"} |
https://math.stackexchange.com/questions/191548/combinatorial-proof-of-sum-k-0n-binomnk-1k-binom2nn?noredirect=1 | # Combinatorial proof of $\sum_{k=0}^{n} \binom{n+k-1}{k} = \binom{2n}{n}$ [duplicate]
Possible Duplicate:
Combinatorial proof for two identities
is there a combinatorial proof of equation below? (parallel summation for binomials): $$\sum_{k=0}^{n} \binom{n+k-1}{k} = \binom{2n}{n}$$
It seems like it's easy to prove combinatorically,
yet I cannot find proper proof...
## marked as duplicate by Austin Mohr, leonbloy, Sasha, davidlowryduda♦Sep 5 '12 at 21:36
The righthand side of course counts the number of $n$-element subsets of $\{1,2,\dots,2n\}$.
Now let’s classify these $n$-element subsets by their largest elements. The largest element of such a set must be one of the numbers $n,n+1,\dots,2n$, so it must be of the form $n+k$ for some $k\in\{0,1,\dots,n\}$. Suppose that you want to choose an $n$-element subset of $\{1,2,\dots,2n\}$ whose largest element is $n+k$; you can do it by choosing $n+k$ and then choosing an $(n-1)$-element subset of $\{1,2,\dots,n+k-1\}$. There are $\binom{n+k-1}{n-1}=\binom{n+k-1}k$ ways to do this, and, as previously noted, $k$ can be any integer from $0$ through $n$, so there are $\sum_{k=0}^n\binom{n+k-1}k$ ways to choose an $n$-element subset of $\{1,2,\dots,2n\}$.
Added: A slightly different way to look at it: $\binom{2n}n$ is the number of ways to seat $n$ girls and $n$ boys in a row of $2n$ seats. Suppose that the first $n-k$ seats are occupied by boys and the next seat by a girl (so this is seat $n - k + 1$). That leaves $2n-(n-k+1)=n+k-1$ seats yet to be filled. There are $k$ boys not yet seated, so there are $\binom{n+k-1}k$ ways for them to choose seats. Since $n-k$, the number of boys at the beginning of the row can be anything from $0$ through $n$, $k$ can also be anything from $0$ through $n$, and the number of possible seatings is $\sum_{k=0}^n\binom{n+k-1}k$.
• Please let me know and forgive me for my paltry edit if necessary. I thought it instructive to add to your wonderful answers: the next seat by a girl is the $n - k + 1$ seat. – Greek - Area 51 Proposal Nov 17 '13 at 12:33
First notice that $\displaystyle \binom{n+k-1}{k} = \binom{n+k-1}{n-1}$.
The right-hand side is the number of ways of picking a subset $A$ of size $n$ from a set $X$ of size $2n$. Say for argument's sake that the set we're working with is $X=\{0, 1, \cdots, 2n-1 \}$. We can split it up into cases based on the least element of $A$.
• If the least element of $A$ is $0$ then we pick the remaining $n-1$ elements from a set of size $2n-1 = n+n-1$.
• If the least element of $A$ is $1$ then we pick the remaining $n-1$ elements from a set of size $2n-2 = n+(n-1)-1$.
• $\cdots$
• If the least element of $A$ is $n$ then we pick the remaining $n-1$ elements from a set of size $n-1 = n+0-1$.
So we have the above equality.
The right side is the number of ways of choosing $n$ elements from $\{1,2,3,...,2n\}$.
The number of ways of choosing $n$ elements from that set that starting with ${1,2,...,n-k}$ and not containing ${n-k+1}$ is $\binom{n+k-1}{k}$. | {"extraction_info": {"found_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": 0.9202141761779785, "perplexity": 98.2201935646214}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1568514573832.23/warc/CC-MAIN-20190920050858-20190920072858-00116.warc.gz"} |
https://www.esaral.com/q/the-correct-sequence-of-correct-reagents-for-the-following-transformation-is-11378/ | The correct sequence of correct reagents for the following transformation is :-
Question:
The correct sequence of correct reagents for the following transformation is :-
1. (i) $\mathrm{Fe}, \mathrm{HCl}$
(ii) $\mathrm{Cl}_{2}, \mathrm{HCl}$,
(iii) $\mathrm{NaNO}_{2}, \mathrm{HCl}, 0^{\circ} \mathrm{C}$
(iv) $\mathrm{H}_{2} \mathrm{O} / \mathrm{H}^{+}$
2. (i) $\mathrm{Fe}, \mathrm{HCl}$
(ii) $\mathrm{NaNO}_{2}, \mathrm{HCl}, 0^{\circ} \mathrm{C}$
(iii) $\mathrm{H}_{2} \mathrm{O} / \mathrm{H}^{+}$
(iv) $\mathrm{Cl}_{2}, \mathrm{FeCl}_{3}$
3. (i) $\mathrm{Cl}_{2}, \mathrm{FeCl}_{3}$
(ii) $\mathrm{Fe}, \mathrm{HCl}$
(iii) $\mathrm{NaNO}_{2}, \mathrm{HCl}, 0^{\circ} \mathrm{C}$
(iv) $\mathrm{H}_{2} \mathrm{O} / \mathrm{H}^{+}$
4. (i) $\mathrm{Cl}_{2}, \mathrm{FeCl}_{3}$
(ii) $\mathrm{NaNO}_{2}, \mathrm{HCl}, 0^{\circ} \mathrm{C}$
(iii) $\mathrm{Fe}, \mathrm{HCl}$
(iv) $\mathrm{H}_{2} \mathrm{O} / \mathrm{H}^{+}$
Correct Option: , 3
Solution: | {"extraction_info": {"found_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": 0.9952777624130249, "perplexity": 3511.996865391285}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1652662512229.26/warc/CC-MAIN-20220516172745-20220516202745-00717.warc.gz"} |
http://physics.stackexchange.com/users/5697/terry-giblin?tab=summary | Terry Giblin
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Physics 51 rep 2 | {"extraction_info": {"found_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": 0.3102691173553467, "perplexity": 7068.931777376825}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1466783396538.42/warc/CC-MAIN-20160624154956-00157-ip-10-164-35-72.ec2.internal.warc.gz"} |
https://math.stackexchange.com/questions/3032117/integral-closure-galois-extension-and-dedekind-domain | # Integral Closure, Galois extension,and Dedekind Domain
Let $$A$$: Dedekind domain, $$K$$: $$\operatorname{Frac}(A)$$, $$B$$: Dedekind domain with $$A \subset B$$, $$L$$: $$\operatorname{Frac}(B)$$
Let $$L/K$$: galois extension with galois group: $$G$$.
$$B^G=\{b \in B \mid \sigma(b)=b \text{ for all } \sigma \in G\}=A$$ $$\implies B$$ is the integral closure of $$A$$ in $$L$$
Is this true? I already prove the converse, but not sure if this holds. Thank you in advance.
• I think it's not true. Try to take B=A. Then the fixed ring is A, but unless the extension is trivial, this is not the integral closure. – Madarb Dec 9 '18 at 7:38
• when A=B, then L=K. Since A is dedekind, A is integrally closed and B(=A) is the integral closure of A in L holds, i think. – Kento Dec 9 '18 at 7:56
• I don't think I understood what you say. The claim you want to prove, as I understand it, is that if B is a subring of L, for which the fixed ring under the action of G is A, then B is the integral closure. It is not the true if you take B=A. If I got you wrong, please explain what you wanted to prove :) – Madarb Dec 9 '18 at 8:00
• you understand it right. but i do not get that it does not hold when B=A. when B=A,the extension L/K is trivial, which leads to the conclusion. i think. please tell me if i get something wrong. – Kento Dec 9 '18 at 8:07
• @reuns I think you don't necessarily have $\sigma(B) = B$. A possible counterexample is given below. – pisco Dec 9 '18 at 12:53
Let $$L/K$$ be a Galois extension of number field, let $$\mathfrak{p}$$ be a prime ideal of $$\mathcal{O}_K$$ that splits into more than one primes in $$\mathcal{O}_L$$: $$\mathfrak{p}\mathcal{O}_L = \mathfrak{P}_1 \cdots \mathfrak{P}_r$$
Let $$A = (\mathcal{O}_K)_{\mathfrak{p}}$$, the localization at $$\mathfrak{p}$$ and $$B = (\mathcal{O}_L)_{\mathfrak{P}_1}$$. Both are Dedekind domains. It is easily seen that $$B^G = A$$, but the integral closure of $$A$$ in $$L$$ is the localization of $$\mathcal{O}_L$$ at all $$\mathfrak{P}_1, \cdots, \mathfrak{P}_r$$, which is a proper subset of $$B$$.
• So $K = \mathbf{Q}, L = \mathbf{Q}(i),p=5= (2+i)(2-i), A=\mathbf{Z}_{(5)} = \{\frac{u}{v}, (u,v) \in \mathbf{Z}^2, 5 \nmid v \}$, $B = \mathbf{Z}[i]_{(2+i)} = \{\frac{u}{v}, (u,v) \in \mathbf{Z}[i]^2, v \not \in (2+i)\mathbf{Z}[i] \}$, $\sigma(c+id) = c-id, G= \{\sigma^2,\sigma\}$ then $\frac1{5^n} \not \in B$ so $B^G = \mathbf{Z}_{(5)}$ but $\frac{2+i}{5}=\frac{1}{2-i} \in B$ is not integral over $\mathbf{Z}_{(5)}$. $A,B$ are Dedekind domains since they have only one prime ideal. The problem is that $\sigma(B) \ne B$. – reuns Dec 9 '18 at 23:22
• And replacing $B$ by $\bigcap_{\sigma \in G} \sigma(B)$ makes the claim true – reuns Dec 10 '18 at 18:19 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 27, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9888200163841248, "perplexity": 206.09977802776473}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-18/segments/1555578527135.18/warc/CC-MAIN-20190419041415-20190419063415-00519.warc.gz"} |
https://worldbuilding.stackexchange.com/questions/26773/moons-of-moons-of-moons/26795 | # Moons of Moons of Moons
My question is simple: How many nested moons are physically possible?
If our moon had a moon, that would be a nesting of 1.
I'm assuming it's easily possible for a really big moon to be orbiting a gas giant and have its own moon. If the dimensions were right, that moon could also have a moon?
How many moons deep can we go? Let me know if I'm missing something. I would like answers with calculations not just random guesses! I'm asking what is physically possible, not what is realistically plausible due to the difficulty of such a system forming.
• Definitely related (possibly duplicate): How can you make a stable.... There are no answers there yet, but I suspect any answer there could be extrapolated to an answer here. Oct 1, 2015 at 14:27
• Not the same question, but the answers end up giving similar results: worldbuilding.stackexchange.com/questions/15577/… Oct 1, 2015 at 14:28
• My last sentence negates both of those questions. I did however just find this: astronomy.stackexchange.com/questions/8694/… which is indeed the same question but has one answer which again ignores the last sentence and doesn't answer my question. Oct 1, 2015 at 14:34
• We can't mark cross-site duplicates, but I would say that Do moons have moons? on Astronomy would be a pretty strong candidate if it was possible (particularly considering the answers to it).
– user
Oct 1, 2015 at 14:34
• We already have something like this today. The Moon orbits Earth. Earth orbits the Sun. The Sun orbits the Galaxy (which has a supermassive black hole at its center). The Galaxies of the Local Group orbit and interact with each other. That last part might not be stable, but I just wanted to bring some giant perspective into this. Oct 1, 2015 at 20:55
Let's make a bunch of assumptions:
• The largest primary is about 3 times bigger than Jupiter.
• To really be a parent, the barycenter of a parent-satellite system must be within the parent.
• Everything has approximately the same density
• Orbital stability will magically work itself out (this will give us an upper bound)
Let's call the twice the distance between the barycenter of a parent satellite system and the farthest extent of that system $$D_p$$ then the corresponding diameter for the subsystem $$D_s$$
Now if the mass of the parent is $$M_p$$ and the mass of all the sub satellites together sum to $$M_s$$ then the requirement that barycenter be inside the parent yields:
$$\frac{M_s}{M_P}(D_p-\frac12D_s)<\left(\frac{3M_p}{4\pi\rho}\right)^\frac13$$
Now we know that for each parent none of the satellites can pass within the roche limit of the parent (the limit would actually be farther out due to the fact that the satellite system isn't solid but this will get us an upper bound) Lets call the diameter of the satellite system $$D_s$$ and the diameter of the parent system $$D_p$$. The Roche Limit gives:
$$\frac12 D_p>2.4\left(\frac{3M_p}{4\pi\rho}\right)^\frac13+D_s$$
If we claim that each subsystem is proportionate to the parent system then we have:
$$\left(\frac{D_s}{D_p}\right)^3=\frac{M_s}{M_P+M_s}$$
Now if we're trying to maximize the ratio of satellite mass to parent mass both of these inequalities should be equalities.
Solving the system yields:
$$D_p \approx 2.6 D_s$$
Which means each successive moon would weigh $$17$$ times as much as the previous one.
Now to get from a single atom moon to something 3 times the size of Jupiter would take: $$\frac{\ln\left(3\frac{1.89813 × 10^{27} kg}{1.6726219 × 10^{-27} kg}\right)}{\ln(17)}=42$$
So a system could have a maximum of 42 layers if we stopped at planets as the primary body. Note however, this doesn't consider orbital stability and I have no doubt that even a system with 10 layers would be unstable on the time scale of a century.
## Bigger
If we went up larger and larger, we could eventually incorporate black holes and then relativity plays havoc with the equations. However, I think that at the extremely large end, the expansion of the universe would distort and pull apart any orbits with radii on the order of billions of light years. So if we said that was the limit, then you could nest about $$85$$ layers, which is a lot, but I would hardly call that infinite.
• I'm not sure you can even get to 10 before it becomes untenably chaotic. Pendulums become chaotic if you chain two of them together (which is analogous to a planet/moon/sub moon)!! Oct 1, 2015 at 20:38
• This is the kind of answer I was looking for, well done sir! Oct 1, 2015 at 21:19
• @JoeBloggs: Sheesh, you're not kidding. Oct 2, 2015 at 0:07
• I like this answer but really I think you need a more realistic mininimum size moon than a single atom :p Oct 2, 2015 at 21:21
• I love the fact that the answer here (at least to one question) is 42.
– Alfe
Oct 2, 2015 at 23:40
Theoretically infinite, though the classification would get interesting.
Consider the Moon. It orbits us, the Earth. That's a nesting of 0, right? Now consider the Earth. What's to say that the Earth isn't just a moon of the Sun, apart from arbitrary human classification systems?
On this logic, you could have theoretically infinite moons. If you re-classify any orbiting body as a moon, and you start with a massive enough body, then you can have entire stellar systems orbiting it - giving you big numbers for the nesting. Think: the Sol system, orbiting another larger body, which in turn orbits an even larger body. That gives a nesting of 4 (I think.)
If you're not up for reclassifying, then the potential is small for nesting moons. According to Wikipedia/Natural satellite, the definition of a moon is:
a celestial body that orbits another body (a planet, dwarf planet, or small Solar System body), which is called its primary, and that is not artificial.
That's limiting, because the biggest object you can have a moon orbiting is a planet, which are (comparatively) small. With each orbiting moon, you have a smaller object, and eventually you're left with nothing.
• Good idea with going up instead of down. If you follow the 'smaller and smaller' route you actually hit the planck length surprisingly quickly. Oct 1, 2015 at 15:44
• Could you be able to show mathematical proofs of how it's possible to have infinite nesting? Oct 1, 2015 at 16:52
• Disagree - stars have definitions, as do planets (stars have fusion, planets have cleared their neighborhood, etc). Oct 1, 2015 at 16:54
• @corsiKa: And definitions can change (see Pluto). Oct 1, 2015 at 18:08
• I believe at very large distances the expansion of the universe would prevent one body from orbiting another due to the distances between them growing faster than the speed of light. Thus there is an upper limit on size.
– Rick
Oct 1, 2015 at 20:11
There are some mathematical stability issues which might create sensible bounds, but I'm not qualified to quantify them. In general terms there is no guarantee of long-term stable orbits in a three-body system (such as Sun, Jupiter, Earth, even if Saturn and the rest weren't there). In fact, special cases aside (notably two Lagrange points) there's a proof that there are no infinite-term stable orbits, only chaos. Be reassured that the best astronomical measurements and computer modelling show Earth's present orbit won't change drastically for the next hundred million years or so, after which time we can't say anything about it because of the errors on the observations. It's therefore not impossible that five hundred million years hence, Earth will be a frozen rock wandering the galaxy in interstellar space. (Statistically, it's more likely to stay orbiting the sun until the sun goes nova).
Were you to try to model Asimov's "Nightfall" system (IIRC 4 stars and two planets in a complex dance) you'd find it was unstable on a timescale much shorter than that for the evolution of Terran life. Something would get ejected from the system into interstellar space, or would collide with another body, and so the story is highly improbable (for thermodynamical levels of improbability).
One approach to simplify the N-body problem's maths is perturbation theory: treat the Earth/Moon system as tightly coupled, treat our centre of mass as bound to the Sun and perturbed by Jupiter (the biggest other perturber) on a completely different scale. My guess is that there isn't space for more than around five "levels" before chaos becomes unavoidable on a short timescale. The upper scale is set by the scale of interstellar space and the large number of suns in the galaxy. The lower one, by the weakness of the gravitational force and the fact that other influences such as solar wind and atmospheric drag become dominant for tiny objects orbiting small ones.
Over to anyone with greater higher mathematical skill and knowledge than myself!
• I will point out that our solar system is in fact a chaotic system, that cannot be accurately predicted. We get pretty close, but it is not possible to fully predict.
– Dan
Oct 1, 2015 at 23:52
• @Dan: nothing can be predicted with perfect accuracy; it's a really fundamental thing in physics that every quantity has some uncertainty. But the solar system is in many a sense among the physical systems which we can model most precisely. Oct 3, 2015 at 0:03
• @leftaroundabout I realize that nothing can be predicted with perfect accuracy. However, orbital mechanics are what's called a Chaotic system. The meaning of this is that even a tiny deviation in starting conditions leads to hugely different results, instead of mildly different results. As you pointed out, our ability to get accurate initial conditions for such calculations is limited, therefore we are not able to predict temporally distant future orbital states with great accuracy.
– Dan
Oct 5, 2015 at 15:25
• @Dan: the Lyapunov exponent of the solar system is smaller than 10⁻⁶ yr⁻¹ [web.mit.edu/wisdom/www/measurements.pdf]. Yeah, it is technically chaotic, but I daresay you'll be hard-pressed to find any system with a smaller exponent. So in a sense the solar system is incredibly harmonic. But that would almost certainly not be the case for a system with more nested satellite orbits, like the one proposed in the accepted answer. Oct 5, 2015 at 16:15
• Can moons have moons? Jan 28, 2019 at 1:29
Similar discussions have been marked in comments. I recall previously discussing circumlunar orbits and why a long-lived natural sattelite won't have such an orbit.
Having the primary be uniform rather than lumpy improves the situation.
Having multiple bodies in resonance can stabilize the whole thing. So a pterbation that bumps one sattelite will be corrected by the sisters, on a scale shorter than the long-time averaging out of random outside influences.
Also, don't limit yourself to big-small progressions. Complex star systems, for example, don't have stable 3 or 4 star systems, but do have "hierarchical binaries". Two bodies here in mutual orbit, two bodies there in mutual orbit, and the two pairs in orbit. How does that count in your system, with no "root" object but clearly a hiarchy of what orbits what. | {"extraction_info": {"found_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": 13, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7236871719360352, "perplexity": 879.1370231297775}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1674764500339.37/warc/CC-MAIN-20230206113934-20230206143934-00823.warc.gz"} |
https://infoscience.epfl.ch/record/146697 | Infoscience
Journal article
# Surface Heterogeneity Effects on Regional-Scale Fluxes in Stable Boundary Layers: Surface Temperature Transitions
Large-eddy simulation, with recently developed dynamic subgrid-scale models, is used to study the effect of heterogeneous surface temperature distributions on regional-scale turbulent fluxes in the stable boundary layer (SBL). Simulations are performed of a continuously turbulent SBL with surface heterogeneity added in the form of streamwise transitions in surface temperature. Temperature differences between patches of 6 and 3 K are explored with patch length scales ranging from one-half to twice the equivalent homogeneous boundary layer height. The surface temperature heterogeneity has important effects on the mean wind speed and potential temperature profiles as well as on the surface heat flux distribution. Increasing the difference between the patch temperatures results in decreased magnitude of the average surface heat flux, with a corresponding increase in the mean potential temperature in the boundary layer. The simulation results are also used to test existing models for average surface fluxes over heterogeneous terrain. The tested models fail to fully represent the average turbulent heat flux, with models that break the domain into homogeneous subareas grossly underestimating the heat flux magnitude over patches with relatively colder surface temperatures. Motivated by these results, a new parameterization based on local similarity theory is proposed. The new formulation is found to correct the bias over the cold patches, resulting in improved average surface heat flux calculations.
#### Reference
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https://physics.stackexchange.com/questions/316154/spin-uncertainity | # Spin Uncertainity
In the special case that $\langle S_z\rangle =0$. What does this imply? My guess is that it would imply that $\sigma_{S_z}\sigma_{S_y} \geq 0$ using the general uncertainty formula and [$S_x,S_y$]= $i\hbar S_z$. My gut feelings is that this result does not make sense. In my mind I am envisioning all the spin to be along the $x$ and $y$ axes . Could someone please help me out? Thanks
It simply means that, in your state, the probability of getting spin up is the same as the probability of getting spin down (with up/down defined along the $z$ axis).
It does NOT imply that all your spins are necessarily along $\hat x$ or $\hat y$, although this is one way of getting $\langle S_z\rangle=0$. You could imagine a state such as $$\vert\psi\rangle = \frac{1}{\sqrt{2}}\vert +\rangle + \frac{e^{i\varphi}}{\sqrt{2}}\vert - \rangle$$ without additional restriction on $\varphi$. The resulting state is not in general an eigenstate of either $\sigma_x$ or $\sigma_y$, but for which $\langle S_z\rangle=0$ still holds.
Edit: in answer to some further queries:
The most general spin state has the form $$\vert\psi\rangle = \cos \left(\frac{\theta }{2}\right)\vert +\rangle + e^{i \phi } \sin \left(\frac{\theta }{2}\right)\vert -\rangle$$ with average values $$\langle S_z\rangle=\cos\theta \, ,\qquad \langle S_x\rangle=\sin\theta\cos\phi\, ,\qquad \langle S_y\rangle=\sin\theta\sin\phi\, .$$ It is not hard to see that an appropriate choice of angles $\theta,\phi$ can lead to various triples of average values. In general, if $\hat n=(\sin\theta\cos\phi,\sin\theta\sin\phi,\cos\theta)$ then the state $\vert\psi\rangle$ will be an eigenstate of $\hat n\cdot \vec S:= n_xS_x+n_yS_y+n_zS_z$, and so not of any single spin operator in general.
• what does this say about the uncertainties of spin along the x and y axes though? – Jerry Mar 3 '17 at 20:52
• Not much actually. Their product is $\ge 0$ but you already knew this. – ZeroTheHero Mar 3 '17 at 20:52
• If the expectation value for spin along the z axis was h-bar/2 could we also come up with a state like you did before ? – Jerry Mar 3 '17 at 21:11
• It would have to be of the form $e^{i\varphi}\vert +\rangle$. – ZeroTheHero Mar 3 '17 at 21:19
• so no spin down component? Thanks – Jerry Mar 3 '17 at 21:19 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 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": 0.8391527533531189, "perplexity": 192.78724796353643}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1579251788528.85/warc/CC-MAIN-20200129041149-20200129071149-00115.warc.gz"} |
https://plainmath.net/5910/solve-the-linear-congruence-7x-plus-3y-equal-10-mod-16 | # Solve the linear congruence 7x+3y -= 10(mod 16)
Solve the linear congruence
$7x+3y\equiv 10\left(\text{mod}16\right)$
You can still ask an expert for help
## Want to know more about Congruence?
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Step 1
Consider the linear congruence .
Since gcd (7, 3) = 1 we know at least one solution exists.
However, the difference between a linear congruence in one variable and a
linear congruence in two variables becomes
clear when we see that the congruence has multiple solutions.
The existence of one solution comes to fruition upon converting the aforementioned linear congruence to
the form .
This leads us to the linear congruence .
After multiplying both sides of our congruence by 7, we find . Therefore, one solution to the linear congruence is given by
Step 2
Our difference maker comes into play when we let .
This gives rise to the congruence .
In this case we have .
As a result, we find another solution of is | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 4, "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": 0.9477956295013428, "perplexity": 1036.334781589957}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1656103344783.24/warc/CC-MAIN-20220627225823-20220628015823-00111.warc.gz"} |
https://mathhelpboards.com/threads/p-p-p-1.5401/ | # P ( p ( p ( { 1 } ) ) )
#### Fernando Revilla
##### Well-known member
MHB Math Helper
Jan 29, 2012
661
I quote a question from Yahoo! Answers
If A={1}.FIND NUMBER OF ELEMNTS IN P[P{P(A)}].also write all the elements?
I have given a link to the topic there so the OP can see my response.
#### Fernando Revilla
##### Well-known member
MHB Math Helper
Jan 29, 2012
661
If $|M|$ denotes the cardinal of the set $M$ then, according to a well known property $\left|\mathcal{P}(M)\right|=2^{|M|}$. Then, $$\left|\mathcal{P}(A)\right|=2^{|A|}=2^1=2,\left|\mathcal{P}(\mathcal{P}(A))\right|=2^{ \left|\mathcal{P}(A)\right|}=2^2=4,\\\left |\mathcal{P}(\mathcal{P}(\mathcal{P}(A)))\right|=2^{ \left |\mathcal{P}(\mathcal{P}(A))\right|}=2^4=16$$
We have $\mathcal{P}(A)=\left \{\emptyset,\{1\}\right \}$ and $\mathcal{P}(\mathcal{P}(A))=\left \{\emptyset,\left \{\emptyset \right\},\left \{\{1\} \right\},\left \{\emptyset,\{1\} \right\} \right\}$. For the sake of clarity denote: $$a=\emptyset,\;b=\left \{\emptyset\right \},\;c=\left \{\{1\}\right \},\;d=\left \{\emptyset,\{1\}\right \}\qquad (*)$$
The set $\mathcal{P}(\mathcal{P}(\mathcal{P}(A)))$ is $$\mathcal{P}(\mathcal{P}(\mathcal{P}(A)))=\{ \emptyset,\left \{a\right \},\left \{b\right \},\left \{c\right \},\left \{d\right \},\left \{a,b\right \},\left \{a,c\right \},\left \{a,d\right \},\left \{b,c\right \},\left \{b,d\right \},\left \{c,d\right \},\\\left \{a,b,c\right \},\left \{a,b,d\right \},\left \{a,c,d\right \},\left \{b,c,d\right \},\left \{a,b,c,d\right \}\}$$ Now, we only need to substitute according to $(*)$. For example $\left \{b,c,d\right \}=\left \{\left \{\emptyset\right \},\left \{\{1\}\right \},\left \{\emptyset,\{1\}\right \}\right \}.$ | {"extraction_info": {"found_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": 0.8968647718429565, "perplexity": 1217.0813056084223}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1642320300997.67/warc/CC-MAIN-20220118182855-20220118212855-00575.warc.gz"} |
https://www.vedantu.com/physics/fermi-level | # Fermi Level
## What is the Fermi Level?
In Physics, there are some topics and concepts that can cause headaches to many students. The concept of the Fermi Level can be one such topic. If you want to understand the concept of the Fermi Level, you can refer to this article. This article contains a detailed explanation of the Fermi Level.
We know that atoms consist of n number of energy levels, the Fermi Level is the highest filled energy level in the energy band at zero kelvin. The Fermi Level is the energy level in the energy band diagram for which the probability of occupancy (in other words we can say the presence of majority charge carriers) becomes half. The Fermi Level and Fermi Energy will be changing depending on the type of material. i.e., different materials will have different Fermi Levels and corresponding Fermi Energy.
The concept of Fermi Level and Fermi Energy are the most important topics to be studied in semiconductor Physics to attain a detailed understanding regarding band structure and intrinsic properties of the semiconductor. Let us have a look at a detailed explanation and information about the Fermi Level and the Fermi Energy.
### Fermi Energy:
Now, what is Fermi Energy? Fermi Energy is defined at zero kelvin, in every semiconducting material defined at zero kelvin such that the energy obtained by the electrons at this level will be maximum. Therefore, the Fermi Level is defined as the energy level at which the electrons will have maximum energy or in other words, at zero kelvin there exists an energy level such that no electron will have energy more than this.
### What is the Fermi Level?
So according to the Fermi Energy definition, it is the highest occupied energy level of any material at absolute zero. To be more specific, all the electrons in the material will occupy the energy level at or below that material's Fermi Level at 0k. The concept of the Fermi Level comes from Fermi-Dirac statistics. Electrons are Fermions (the particles with odd half-integral spin) and by the Pauli exclusion principle cannot exist in identical energy states. The energy level corresponds to the Fermi Energy known as the Fermi Level. We have to keep in mind that the Fermi Level is defined for all the temperatures, whereas the Fermi Energy is defined only at the zero kelvin.
So, now the Fermi Level is just the surface of that conductor defined at absolute zero, where no electrons will have enough energy to rise above the surface. The concept of Fermi Energy is a crucially important concept for the understanding of the electrical and thermal properties of solids.
The Fermi Level can also be described as the maximum energy level of an electron at 0 Kelvin at which it can reach. Because all electrons are in the lowest energy state at absolute zero temperature, the Fermi Level falls between the valence and conduction bands. The Fermi Level can be thought of as a sea of Fermions (or electrons) above which no electrons exist due to a lack of energy at 0 Kelvin. As the solids are heated and electrons are added to or removed from them, the Fermi Level changes.
Now, the question arose: why do we need Fermi Level or Fermi Energy? Suppose we increase the temperature of the system by 0K to say 100K then, then some of the electrons lying below the Fermi Level may get excited to certain energy levels, and to determine the density of electrons at that temperature, we introduce the Fermi Dirac distribution.
As the temperature of material increases above absolute zero, the probability of electrons existing in an energy level greater than the Fermi Energy increases and hence there will not be a constant highest occupied energy level.
Let us have a look at the major differences between the Fermi Level and Fermi Energy.
### Difference Between the Fermi Energy and the Fermi Level:
There is not much distinction between these two ideas. According to Wikipedia, Fermi Energy and Fermi Level are two notions that are closely connected. Fermi Energy, according to my knowledge, is the greatest occupied energy level of a system at absolute zero? Is that accurate? What is the distinction between Fermi Energy and Fermi Level, then? The highest energy band (i.e. the conduction band) is half filled in a common metal. Due to the continuity of the conduction band, electrons can be excited by the heat energy which in turn leaves the holes in the lower band. There is no thermal energy at absolute zero, thus electrons fill the band from the bottom up, with a severe cut-off at the highest occupied energy level. Fermi Energy is defined by this energy. Because thermal energy continuously excites electrons within the band at finite temperatures, there is no sharply defined highest energetic electron. The Fermi Level is the best you can accomplish when it comes to defining the energy level with a 50% chance of occupation.
Sl. no. Fermi Energy Fermi Level 1. What is Fermi Energy?Fermi Energy is the energy difference between the lowest and highest occupied single-particle states in the quantum system of non-interacting Fermions at absolute zero temperature. What is the Fermi Level?According to the Fermi Level definition, the Fermi Level is the energy level for the collection of particles at absolute zero temperature. 2. Fermi Energy is defined particularly at absolute zero temperature. The Fermi Level is defined at every temperature, not only at absolute zero temperature. 3. Fermi Energy is the kinetic energy difference between the lowest and highest occupied single-electron states. The Fermi Level corresponds to the total kinetic energy and potential energy of the thermodynamic system. 4. The Fermi Energy of a metal is the energy difference between the Fermi Level and the lowest occupied single electron state or level. The Fermi Level of any metal is the energy of the highest occupied single-particle state at absolute zero temperature. 5. Fermi Energy is defined only for non-interacting Fermions. The Fermi Level can also be defined for the Fermions in the complex interacting systems.
These are a few important and key differences between the Fermi Energy and the Fermi Level. One should not confuse the concept of the Fermi Level and Fermi Energy.
### Did You know:
In metals, Fermi Energy lets us understand information about the velocities of the electrons which participate in ordinary electrical conduction. The total amount of energy that can be given to an electron in such conduction processes is on the order of micro-electron volts, thus only those electrons very close to the Fermi Energy can participate. The Fermi velocity of these conduction electrons can be estimated from the Fermi Energy.
Fermi Energy is crucial in understanding why electrons do not contribute substantially to the specific heat of solids at ordinary temperatures, despite being major contributors to thermal and electrical conductivity. Since only a small percentage of electrons in a metal are within Fermi Energy's thermal energy kT, they are frozen out of the heat capacity.
### What Exactly is the Fermi Paradox?
The Fermi paradox is a debate about the scale and chance of intelligent life existing elsewhere in the universe other than Earth. There is no evidence that it ever existed elsewhere. Enrico Fermi, a Physicist who researched the existence of extraterrestrial civilization, was the first to investigate the Fermi paradox. He had mostly raised the following concerns: There are billions of stars that are billions of years older than the solar system, much like the Sun; There are worlds that are comparable to ours and may have evolved intelligent life; These sophisticated beings may have developed the ability to travel between galaxies.
### Energy Level of Fermi
Because of Pauli's exclusion principle, which stipulates that two Fermions cannot occupy the same quantum state, this energy level exists. Due to this, each Fermion in a system with more than one has its own set of magnetic quantum numbers. The Fermi temperature can be calculated by dividing the energy of the Fermi Level by Boltzmann's constant. The temperature at which the electron's energy equals the Fermi Energy is also known as the Fermi temperature. In metal's lower energy states, it is the number of electrons present in them.
## FAQs on Fermi Level
1. What is Fermi Energy Level? Define Fermi Level.
The Fermi level is just an energy level for the collection of particles at absolute zero temperature. The Fermi level is the surface of that conductor defined at absolute zero where no electrons will have enough energy to rise above the surface.
2. Why is the Fermi Level Important in Semiconductors?
Suppose we increase the temperature of the system from 0K to say 100K, then some of the electrons lying below the Fermi level may get excited to certain energy levels, and in order to determine the density of electrons at that temperature, we introduced the fermi Dirac distribution.
3. What is Fermi?
In physics, Fermi is a unit of measurement and is mostly used in nuclear physics. One should not confuse the Fermi energy and Fermi level with just fermi. One fermi is equal to 10-15m.
4. What is the difference between the Fermi Level and Fermi Energy?
There are a lot of differences in Fermi Level and Fermi Energy. You can define Fermi Level for any particular temperature but if you want to define Fermi Energy, you can do that only at absolute zero or when the temperature is equal to zero Kelvin. Fermi Level, on one hand, is the total energy that includes both kinetic and potential energies but Fermi Energy, on the other hand, is given by the energy difference which is usually corresponding to the kinetic energy.
5. What are the different factors on which Fermi Level depends?
There can be various factors on which Fermi Level depends but the key factor on which Fermi Level depends very much is temperature. If you want to know the exact position of the Fermi Level concerning valence and or conduction bands, you have to consider various parameters which mainly include temperature. Some other factors on which the Fermi Level depends are the number of free electrons & holes and the effective masses of both electrons and holes.
Comment | {"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": 0.9800136685371399, "perplexity": 234.53019334372755}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446710719.4/warc/CC-MAIN-20221130024541-20221130054541-00430.warc.gz"} |
https://www.physicsforums.com/threads/the-smallest-blackhole-possible.52099/ | # The Smallest blackhole possible?
1. Nov 9, 2004
### Alkatran
What is the minimum size of the event horizon of a blackhole? Obviously you need some certain amount of mass for a blackhole, because I don't get sucked into my chair, to overcome the other forces.
I just had an image of a tiny black orb hovering in front of me, and wondered what would happen to the baseball bat I hit it with.
2. Nov 9, 2004
### pervect
Staff Emeritus
I seem to recall reading that the smallest black hole is expected to be around a planck mass. I'm not sure if this is correct, or how it was determined without a full theory of quantum gravity.
3. Nov 9, 2004
### mathman
Try to calculate the circumference of a black hole with the mass of your chair. The formula is 18.5 kilometers x (mass of object)/(mass of sun).
4. Nov 9, 2004
### Wave's_Hand_Particle
Event Horizons around a Blackhole are 'OBSERVER-DEPENDANT', so let me ask you, where are you 'looking' from?..and what is the Area of your theoretical BH?
I ask this because the 'AREA' of a blackhole dictates the 'OBSERVABLE' horizon
P.S.
The situation of your posting is thus:BH = orb..will not be hovering in front of you. its actually the reversed..YOU will be hovering in in an unmovable position with regard to anyone situated 'further away'.
You cannot mainifest the energy needed to move your had to swing the bat to 'hit' the orb..you just cannot do this theoretiaclly or physically!
Last edited: Nov 9, 2004
5. Nov 9, 2004
### Chronos
A Planck mass black hole has a Swarzschild of 1 planck length. Interesting. I'm trying to figure out why I initially found that surprising and then didn't. Talk about confusing yourself.
6. Nov 9, 2004
### Alkatran
I didn't mean I was inside the event horizon. I was just wondering what would happen to a 'rigid' bat, since the part which would hit the black hole would begin travelling through time slower and slower....
7. Nov 9, 2004
### DivineNathicana
Yeah, the minimum size of a black hole is supposedly around the Planck mass... According to string theory. But don't forget guys, there's an enormous amount of tension on a string, and it's a lot heavier than you'd imagine! In fact, it's the weight of an average dust particle. Not much? But think of the size! Around the Planck length, was it? Think of the ratio. So one can see how that is a perfectly plausible candidate for a black hole.
- Alisa
8. Nov 9, 2004
### franznietzsche
If mass is quantized, then it could not be smaller than the Planck amss, it would have to be the planck mass.
9. Nov 10, 2004
### Chronos
I think the limit is more fundamentally tied to the planck length of 1.6E-35 meters, or about 1E-20 times the size of a proton. Mass is quantized in much smaller units than the planck mass: about 2.176E-8 kg. The mass of a hydrogen atom, for example, is about 1.673E-27 kilograms.
10. Nov 10, 2004
### DivineNathicana
Yes, I know that it could not be less than the Planck mass, but I was unsure of whether that was the minimum mass, or whether the latter was actually a bit heavier. But I'm pretty sure that's correct.
What do you think, would the aforementioned supposed black hole be a stable black hole, or would it be more along the lines of a type of quantum fluctuation?
- Alisa
11. Nov 10, 2004
### pervect
Staff Emeritus
Planck units share the characteristic with geometric units that G=c=1, so I'd expect the Schwarzschild _radius_ 2GM/c^2 to be twice the mass. Unless I'm blowing it badly.
12. Nov 11, 2004
### Chronos
Hi pervect! I just did a quick and dirty calculation using the same formula you cited and solved for M, assuming a radius of 1 planck unit. It looked to be about a planck mass. On the other hand, I may have botched the calculation. Not like it would be the first time that ever happened.
13. Nov 11, 2004
### yogi
I will take issue with the Planck mass/size limitations. The whole idea of fundamental units al la Planck is nothing but cosmological numerology. There are other factors that can be combined to yield different values for a unit of mass such as the electron charge and the like. Why attach any significance to the planck mass - why not use the electon mass as a fundamental entity if you must come up with non scientific deductions - in which case the black hole radius would be on the order of 10-57 meters
14. Nov 11, 2004
### Chronos
It's more than numerology. The Planck length is a fundamental unit in nature. Why? Because it is impossible to quantify anything smaller, and this plays a vital role in quantum physics. Consider this:
"There is only one truly fundamental length in nature a length free of all reference to the dimensions and rate of revolution of the planet on which we happen to live, free of any appeal to the complex properties of any solid or gas: free of every reference to the mysterious properties of any elementary particle: what we call today the Planck length,
L=(hG/C^3)1/2= 1.6X10^-33 cm
And what we identify with the characteristic scale of quantum fluctuations in the geometry of space".
- John A Wheeler "At Home in the Universe" p169
And here is a paper that further explains things:
http://xxx.lanl.gov/abs/gr-qc/0201030
Uncertainty in Measurements of Distance
Authors: John C. Baez, S. Jay Olson
And, as suspected, a Planck mass black hole occupies a Planck volume
http://zebu.uoregon.edu/~js/glossary/planck_time.html
"Contained within a Planck volume is a Planck mass (hc/G)1/2, roughly 10-5 g. An object of such mass would be a quantum black hole, with an event horizon close to both its own Compton length (distance over which a particle is quantum mechanically "fuzzy") and the size of the cosmic horizon at the Planck time."
- Encyclopedia Britannica
15. Nov 12, 2004
### hellfire
If I take a look to the vacuum Schwarzschild solution, in which a black hole appears, it seams to me that black holes are only due to singularities which arise in case of point masses with infinite density and not in case of any mass distribution with finite density. Is this incorrect?
16. Nov 12, 2004
### da_willem
Take another good look; I don't believe this is correct. You can find a certain finite mass/radius ratio for wich the schwarzschil metric explodes. The (r,r) term is:
$$-\frac{1}{1-\frac{2MG}{rc^2}}$$
The condition for a black hole to form is that the radius of the object is smaller than $2MG/c^2$. This yields a finite density! The singularities do not follow from general relativity but are predicted by other theories. But no theory of gravity and QM has been found so I would not put your trust in these preditions....
17. Nov 12, 2004
### Chronos
Not at all incorrect and an excellent question, hellfire. I like the planck density as a fundamental limit. Unfortunately, many theorists approaches seem to discount planck and compton lengths as fundamental to anything. It sort of bothers me, but I will get over it.
18. Nov 12, 2004
### hellfire
What you are talking about is the coordinate singularity at r = 2GM in Schwarzschild coordinates. This can be removed chosing proper coordinates to describe the Schwarzschild spacetime.
As far as I know, the condition to have a coordinate independent singularity is an infinite value in the Riemann curvature tensor or any of its contractions. Following S. Carroll (Lecture Notes on General Relativity), in case of the Schwarschild metric:
$$R_{\mu \nu \rho \sigma} R^{\mu \nu \rho \sigma} = \frac {12 G^2 M^2} {r^6}$$
If one considers the interior Schwarschild solution, which looks like the vacuum Schwarzschild solution but with m(r) instead of M, it seams that for a homogeneous mass distribution (m(r) ~ r3), the singularitiy in the mentioned contraction disappears.
Now, suddenly I am aware ( sorry for the confusion) that there are indeed mass distributions which lead to a singularity (m(r) < r3). But I do not know how realistic these distributions are.
Another question is then whether event horizons (and therefore black holes) may exist without singularities (https://www.physicsforums.com/showthread.php?t=52060)
19. Nov 12, 2004
### yogi
Chronos - I am well aware that almost every writer has jumped on the Planck "units" bandwagon - to assert such sweeping generalities based upon nothing that has ever been proven is sheer folly. There is no guarantee that any of the 3 "so called constants" h, c and G that make up planck units are temporally invariant. Show me one single thing that has been proven experimentally that gives support to the notion of their fundamental significance - all you can find is one author quoting another - its another example of modern physics having gone copycat. Why pick Planck's constant h as being more significant than the electron charge e - which leads in combination with c and G to a different (so called) fundamental length, mass and time. There are more interesting cosmic coincidences that result from the electron mass and size that those that occur between the Planck mass and its volume (if you are of a notion that there must be some minimum value that rates a designation as fundamental). Interestingly, John Wheeler held to another view all his life, that all matter was made of electrons (even though he dutifully acknowledged quarks as the constituents of heavier particles).
20. Nov 12, 2004
### da_willem
I agree. But I mentioned this element because it is probably no conicident that exactly at the schwarzschild radius the metric (in certain natural coordinates...) diverges. But the condition for a black hole still stands. The radius of the object has to be smaller than $2MG/c^2$ this yields a minimum density of $3c^6/32M^2G^3$, not infinite! So could you please elaborate on how it follows from the Schwarzschild solution that only point masses with an infinite density lead to black holes. | {"extraction_info": {"found_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": 0.8330821394920349, "perplexity": 870.9439435938609}, "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-2016-44/segments/1476988719192.24/warc/CC-MAIN-20161020183839-00399-ip-10-171-6-4.ec2.internal.warc.gz"} |
https://www.ideals.illinois.edu/browse?rpp=20&order=ASC&sort_by=-1&value=Physics%2C+Condensed+Matter&etal=-1&type=subject&starts_with=N | # Browse by Subject "Physics, Condensed Matter"
• (2004)
I use a combination of alloying and low-energy ion irradiation during film growth to controllably manipulate the nanostructure of TiN-based layers. Ti0.8Ce0.2N films are grown on oxidized Si(001) at 350°C using UHV ...
application/pdf
PDF (6MB)
• (1995)
In this work, a water vapor oxidation process is used to convert high Al composition $\rm Al\sb{x}Ga\sb{1-x}As$ to a stable native oxide. The native oxides described are formed at temperatures in the range of 400$\rm\sp\circ ... application/pdf PDF (3MB) • (1993) Data are presented on the comparison of the chemical stability of oxides of AlAs-GaAs heterostructures formed via atmospheric hydrolysis and by native oxidation at 400$\sp\circ$C for 3 h in a N$\sb2$+ H$\sb2$O vapor. Data ... application/pdf PDF (3MB) • (1967) application/pdf PDF (3MB) • (1983) Single crystal Nb-Ta superlattices with wavelengths from 20 to 800 (ANGSTROM) were fabricated in this work by Molecular Beam Epitaxy (MBE) techniques. For the first time, electronic mean free paths and crystal domain sizes ... application/pdf PDF (5MB) • (1979) application/pdf PDF (15MB) • (1996) This thesis describes NMR measurements involving carbon-13, deuterons, and protons in acetylene ($\rm C\sb2H\sb2\$) adsorbed at room temperature on supported platinum catalysts.
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PDF (4MB)
• (1991)
The author reports the study of diffusion of carbon monoxide on supported palladium and platinum clusters by Nuclear Magnetic Resonance. As part of these studies, a novel NMR technique for studying diffusion (called an ...
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PDF (3MB)
• (1981)
We have studied the ('77)Se NMR in single crystal of 2H-TaSe(,2) to test McMillan's proposal regarding charge density waves (CDW). We compare the temperature dependence of the NMR lineshape from 4.2 K to 130 K with predictions ...
application/pdf
PDF (2MB)
• (1996)
Currently, there is a great deal of interest in metallic multilayer systems, in particular magnetic multilayer structures, for both technological and scientific reasons. Since the growth properties and band structures for ...
application/pdf
PDF (5MB)
• (2009)
We have directly measured the current-phase relation (CPR) of a superconductor-ferromagnet-superconductor (SFS) Josephson junction, and determined that it contains a positive second-harmonic term proportional to sin(2&phis;). ...
application/pdf
PDF (3MB)
• (1989)
This thesis describes work done in two separate areas of the field of superconductivity. The first part describes experiments performed to measure a predicted, but previously unmeasured non-equilibrium effect in superconducting ...
application/pdf
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• (1995)
In this thesis we study certain nonequilibrium properties of mesoscopic superconducting rings, i.e., rings of finite circumference. Two classes of nonequilibrium behavior will be considered: (i) the system is prepared in ...
application/pdf
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• (2009)
We propose a model for the incoherent charge carrier transport in one-dimensional conductors based on the semi-classical Boltzmann transport equation. The electronic transport in these systems is described by treating ...
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• (1980)
Quite large, well-formed single crystals of m(phi)(,3)As(TCNQ)(,2) crystals have been grown. The largest of these crystals are probably the largest TCNQ salt crystals ever grown; they may also be the most perfect.
application/pdf
PDF (3MB)
• (1992)
Structural and magnetic properties of heavy rare earth films and superlattices synthesized by molecular beam epitaxy are investigated. Epitaxial films of rare earth metals, and superlattices of rare earths with Y interlayers, ...
application/pdf
PDF (8MB)
• (2006)
Finally, the initial stage of oxidation was studied for H2O-exposed Si(100) in the presence of Cl. Following H2O dissociation and saturation of the surface with Cl, a mild anneal allowed oxygen atoms to insert into Si dimer ...
application/pdf
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• (1972)
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• (1965)
application/pdf
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• (1974)
application/pdf
PDF (5MB) | {"extraction_info": {"found_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": 0.73670893907547, "perplexity": 7036.874759529781}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1469257829970.64/warc/CC-MAIN-20160723071029-00304-ip-10-185-27-174.ec2.internal.warc.gz"} |
https://www.physicsforums.com/threads/show-that-ln-e-1.352892/ | Show that ln(e)=1.
1. Nov 8, 2009
applegatecz
1. The problem statement, all variables and given/known data
Show that ln(e)=1.
2. Relevant equations
ln(x)=antiderivative from 1 to x of dt/t
3. The attempt at a solution
I assume we have to use the fact that e= lim as n->infinity of (1+1/n)^n, and perhaps can apply l'Hopital's rule to transform that limit -- but I'm not sure where to go from there.
2. Nov 8, 2009
jgens
If $e = \lim_{n \to \infty}(1 + \frac{1}{n})^n$, then we know that $ln(e) = \lim_{n \to \infty}(n)ln(1 + \frac{1}{n})$. Now put this in a form where you can apply L'Hospital's Rule.
3. Nov 8, 2009
applegatecz
Ah, I see! Thank you.
Similar Discussions: Show that ln(e)=1. | {"extraction_info": {"found_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": 0.9943751096725464, "perplexity": 825.5948969598543}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-05/segments/1516084891316.80/warc/CC-MAIN-20180122113633-20180122133633-00740.warc.gz"} |
https://scriptinghelpers.org/questions/97095/how-do-i-put-a-player-name-on-a-textlabel-solved | New: Nitro Boost our Discord server and receive full donation perks here on the website! Join the Scripting Helpers Discord Server to learn more! You can also Support on Patreon as always.
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0
How do I put a player name on a textLabel? [Solved]
Edited by Feahren 14 days ago
I was trying to make a billboardgui that will say the players name. Everything went fine until I started to put the players name on the textLabel. Every time I tried something it would not work.
I don't know if i'm being dumb and the problem is right in my face, but I can't seem to figure out why it does not work.
(This is the code.)
game.Players.PlayerAdded:Connect(function(Plr)
plrNameUI.plrName.Text = Plr.Name
end)
end)
(And This is the line i'm talking about.)
plrNameUI.plrName.Text = Plr.Name
I tried printing out the name and it worked perfectly fine. I also tried while in game to change it. it worked fine. I tried my hardest to find what the problem is, but can't. I hope I explained everything. | {"extraction_info": {"found_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": 0.43911096453666687, "perplexity": 1358.0300362570194}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-16/segments/1585371880945.85/warc/CC-MAIN-20200409220932-20200410011432-00458.warc.gz"} |
https://www.tutorialspoint.com/handling-overflowing-content-using-css | # Handling Overflowing Content using CSS
CSSWeb DevelopmentFront End Technology
We can use CSS overflow property to manage/handle the overflowing content of an element. This property allows user to clip content, provide scrollbars to view clipped content, render content outside the container thus the name overflow.
## Syntax
Following is the syntax for CSS Overflow property −
Selector {
overflow: /*value*/
}
Let us see an example for CSS overflow property −
## Example
Live Demo
<!DOCTYPE html>
<html>
<title>CSS Overflow</title>
<style>
form {
width:70%;
margin: 0 auto;
text-align: center;
}
* {
margin:5px;
}
input[type="button"] {
}
#containerDiv {
margin: 0 auto;
height: 110px;
overflow: scroll;
}
<body>
<form>
<fieldset>
<legend>CSS Overflow</legend>
<div id="containerDiv">
This is paragraph 1 with some dummy text. This is paragraph 1 with some dummy text. This is paragraph 1 with some dummy text. This is paragraph 1 with some dummy text. This is paragraph 1 with some dummy text. This is paragraph 1 with some dummy text. This is paragraph 1 with some dummy text. This is paragraph 1 with some dummy text. This is paragraph 1 with some dummy text. This is paragraph 1 with some dummy text. This is paragraph 1 with some dummy text. This is paragraph 1 with some dummy text. This is paragraph 1 with some dummy text. This is paragraph 1 with some dummy text. This is paragraph 1 with some dummy text. This is paragraph 1 with some dummy text. This is paragraph 1 with some dummy text.</div>
</fieldset>
</form>
<script>
document.querySelector('#containerDiv').style.overflow = "hidden";
}
</script>
</body>
</html>
## Output
Before clicking ‘Remove Scrollbars’ button −
After clicking ‘Remove Scrollbars’ button −
Let’s see another example for the CSS overflow property −
## Example
Live Demo
<!DOCTYPE html>
<html>
<title>CSS Overflow</title>
<style>
form {
width:70%;
margin: 0 auto;
text-align: center;
}
* {
margin:5px;
}
input[type="button"] {
}
#containerDiv {
margin: 0 auto;
height: 100px;
width: 100px;
overflow: auto;
}
</style>
<body>
<form>
<fieldset>
<legend>CSS Overflow</legend>
<div id="containerDiv">
<img id="image" src="https://www.tutorialspoint.com/sas/images/sas-mini-logo.jpg">
</div>
<input type="button" onclick="fitHeight()" value="Remove Scrollbars">
</fieldset>
</form>
<script>
var divDisplay = document.getElementById("divDisplay");
var imgSelect = document.getElementById("image");
var containerDiv = document.getElementById("containerDiv");
function fitHeight() {
containerDiv.style.height = imgSelect.height+'px';
containerDiv.style.width = imgSelect.width+'px';
containerDiv.style.overflow = 'hidden';
}
</script>
</body>
</html>
## Output
Before clicking any button −
After clicking ‘Remove Scrollbars’ button −
Published on 06-Jan-2020 14:52:25 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 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": 0.8617589473724365, "perplexity": 29480.03462100828}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-50/segments/1606141729522.82/warc/CC-MAIN-20201203155433-20201203185433-00443.warc.gz"} |
https://www.oist.jp/news-center/photos/measuring-transitional-flow | # Measuring Transitional Flow
31 Jan 2018
Sophie Protheroe
Cerbus uses lasers directed at a glass pipe to measure the speed of the flowing water inside.
Free for anyone to re-use, but must be credited to OIST. | {"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": 0.9211680889129639, "perplexity": 9208.335807108571}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1596439735860.28/warc/CC-MAIN-20200804043709-20200804073709-00136.warc.gz"} |
http://tex.stackexchange.com/questions/79257/xecjk-l3-too-old | # xeCJK l3-too-old
I started using XeTeX and whenever I use the xeCJK package I get the following error:
! Critical xeCJK error: "l3-too-old" !
!
! Support package 'expl3' too old.
!
! Please update an up to date version of the bundles
! 'l3kernel' and 'l3packages'
! using your TeX package manager or from CTAN.
!
! See the xeCJK documentation for further information.
! For immediate help type H <return>.
I have updated my entire repository already several times, refreshed my FNDB and so forth but the error keeps popping up and no CJK text appears in my output file.
I am using MikTex 2.9 under Windows 7 Ent 64 Bit.
here is a minimal example:
\documentclass[a4paper,oneside,12pt,bibliography=totoc]{scrartcl}
\usepackage[british]{babel}
\usepackage{xeCJK}
\usepackage[autostyle]{csquotes}
\begin{document}
\end{document}
-
Did you update both in 'standard' and 'Admin' modes? MiKTeX's 'on the fly' installation can result in your packages being distributed between the two. Also, check your log file for the location of the files: this should tell you (or at least us) the likely situation. – Joseph Wright Oct 27 '12 at 7:56
I feel embarrassed for making such a stupid mistake! After I updated as user it works. Thank you! – Paul Oct 27 '12 at 8:15
Welcome to TeX.sx! – Stephen Oct 27 '12 at 8:17 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7152588367462158, "perplexity": 6712.428784398349}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-10/segments/1394026215078/warc/CC-MAIN-20140305133015-00038-ip-10-183-142-35.ec2.internal.warc.gz"} |
https://www.lmfdb.org/EllipticCurve/Q/139650/bt/ | # Properties
Label 139650.bt Number of curves $1$ Conductor $139650$ CM no Rank $1$
# Related objects
Show commands: SageMath
sage: E = EllipticCurve("bt1")
sage: E.isogeny_class()
## Elliptic curves in class 139650.bt
sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
139650.bt1 139650ic1 $$[1, 1, 0, -294515, 360089325]$$ $$-560087524907/10788274176$$ $$-54418222038319104000$$ $$[]$$ $$4290048$$ $$2.4679$$ $$\Gamma_0(N)$$-optimal
## Rank
sage: E.rank()
The elliptic curve 139650.bt1 has rank $$1$$.
## Complex multiplication
The elliptic curves in class 139650.bt do not have complex multiplication.
## Modular form 139650.2.a.bt
sage: E.q_eigenform(10)
$$q - q^{2} - q^{3} + q^{4} + q^{6} - q^{8} + q^{9} + 3 q^{11} - q^{12} + 5 q^{13} + q^{16} - 4 q^{17} - q^{18} - q^{19} + O(q^{20})$$ | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 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": 0.5813950300216675, "perplexity": 10810.558173546431}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1637964358520.50/warc/CC-MAIN-20211128103924-20211128133924-00357.warc.gz"} |
https://asmedigitalcollection.asme.org/tribology/article/139/6/061402/377889/Experimental-Investigation-of-Energy-Dissipation | Interfacial damping in assembled structures is difficult to predict and control since it depends on numerous system parameters such as elastic mismatch, roughness, contact geometry, and loading profiles. Most recently, phase difference between normal and tangential force oscillations has been shown to have a significant effect on interfacial damping. In this study, we conduct microscale (asperity-scale) experiments to investigate the influence of magnitude and phase difference of normal and tangential force oscillations on the energy dissipation in presliding spherical contacts. Our results show that energy dissipation increases with increasing normal preload fluctuations and phase difference. This increase is more prominent for higher tangential force fluctuations, thanks to larger frictional slip along the contact interface. We also show that the energy dissipation and tangential fluctuations are related through a power law. The power exponents we identify from the experiments reveal that contacts deliver a nonlinear damping for all normal preload fluctuation amplitudes and phase differences investigated. This is in line with the damping uncertainties and nonlinearities observed in structural dynamics community.
## Introduction
Interfacial damping arises from frictional shear and slip at the mating surfaces. Frictional energy dissipation is difficult to predict because frictional interactions exhibit high degree of variability, nonlinearity, and uncertainty. Lack of adequate understanding of interfacial damping affects the predictive modeling of assembled structures subjected to vibrations.
One of the main factors that frictional dissipation depends on is the loading conditions imposed on the contacts. Among all possible loading scenarios related to this factor, the case of constant normal load and oscillating tangential force has been studied most extensively [14] and it was shown that the magnitude of energy dissipation increases with the amplitude of oscillations in tangential force as expected from a contact dominated by frictional slip. In addition to how much energy it dissipates, a contact zone is also heavily characterized by the relationship between its energy dissipation and the maximum applied stress. Lazan [5] in his seminal work proposed a simple power-law relation between the maximum applied stress $σ$ and the dissipated energy $ΔW$ to predict the amount of damping at a particular vibration level; i.e.,
$ΔW∼σn$
(1)
This power-law relation holds for both material and interfacial damping [3,6]. Power-law exponents closer to 2 suggest linear damping because in a structure with linear compliance, maximum strain energy scales as the square of the applied stress, and since the damping can be regarded as the ratio of the energy dissipation to the maximum strain energy; the damping scales as $σn−2$, and thus becomes independent of loading if $n=2.$ Therefore, the deviation of $n$ from two signals the degree of nonlinearity in damping.
Mindlin et al. in 1952 [1] proposed the first analytical solution for the interfacial damping. This study showed that under a constant normal load and small amplitude of tangential oscillations, the energy dissipated by frictional slip scaled with the cube of the maximum tangential force, i.e., power-law exponent, $n=3.$ The same analytical solution predicts power-law exponents higher than 3 for larger oscillations. Starting with Johnson’s [2], and Goodman and Brown’s [3] experiments, theoretical estimation of power-law exponents 3 or higher were never observed in measurements of interfacial damping. Experiments with various sample geometries, materials, and instruments the power-law exponents consistently ranged between 2.2 and 2.8 [4,79].
## Problem Statement
In this study, we investigate the effects of normal and tangential fluctuations, and the phase difference between those fluctuations on frictional dissipation in presliding contacts. In particular, we conduct experiments on a contact configuration featuring a rigid sphere-on-deformable half space. As shown in Fig. 1, variable normal $(P)$ and tangential loads $(Q)$ are imposed on this contact. Mean normal load causes tip to penetrate into the sample to a depth of $d,$ and forms a circular contact area with radius, $a.$ Normal load fluctuations following the mean preloading are chosen smaller than 30% of the mean preload to mimic sustained structural vibrations without significant loss of preload. The tangential loading is imposed by tangential displacements fluctuating around zero mean. Fluctuations in tangential displacement are chosen to ensure presliding contact conditions. Mechanical energy losses as measured by the load–displacement response of the contact are used to monitor frictional dissipation. The details of the test samples, experimental setup, loading parameters, and processing of raw data are given in Sec. 3. The results and discussions are presented in Sec. 4. The paper ends with a list of findings and conclusions in Sec. 5.
Fig. 1
Fig. 1
Close modal
## Experiments
### Tested Samples.
The surfaces tested are cut from a 0.5 mm-thick polyimide film and used as received from the supplier (UPILEX). Polyimides are used safely in extreme thermomechanical and chemical conditions, thanks to their high glass transition temperature and low creep properties [21]. Practical uses of polyimide films include electronic circuits, wire insulations, and composite components in aero-engines, turbine blades, and launch vehicles [2225]. We elect to test polyimide samples for several reasons. First of all, polyimide films show linear isotropic response in elastic loading cases [26,27]. Also, we will demonstrate that polyimide exhibit negligible viscoelasticity at the loading rates used in our experiments. Those properties enable us to compare the experimental observations to known analytical solutions of elasticity. Second, polyimide is inert to rigid diamond probes, and thus adhesion is negligible compared to deformation forces. Therefore, frictional slip dominates the interactions between the sample surfaces and probe. Lastly, polyimide delivers more compliant response compared to metals, and thus tangential displacements in presliding regime are comparable to contact radii (∼a few micrometer). Our presliding experiments can resolve and control the tangential displacements on the order of microns with significantly better resolution than nanoscale slips observed at metallic contacts.
Prior to presliding experiments, ultrasonic cleaning with acetone bath is applied to all polyimide samples. After cleaning, the samples are glued to metallic pucks and mounted on the triboindenter (TI950 by Hysitron, Inc., Minneapolis, MN), and roughness of the test surfaces is measured by scanning probe microscopy (SPM). The SPM imaging load, size, and frequency are 2 μN, 10 μm × 10 μm, and 1 Hz, respectively.
Figure 2 shows a representative SPM image of the surface heights of a tested region. The root-mean-square (RMS) and peak-to-valley roughness measured in tested regions vary around 15 and 100 nm, respectively. As will be presented, the mean preload used in the experiments causes penetration depths on the order of 100 nm, and contact radii on the order of 2 μm. The effect of roughness on the indentation response of a spherical contact is investigated elsewhere [28] and the main parameter dictating the amount of deviation is found to be the ratio of RMS roughness to penetration depth. Based on the RMS roughness and penetration depth values, this ratio is around 0.15 in our experiments. In terms of maximum contact pressure, this leads to 12–17% of deviation from the Hertzian theory, whereas the deviation is around 10% for contact radius. In addition, the difference between the surface heights of the contact zone (a 5 μm × 5 μm area in the center) measured before and after experiments (Fig. 2(c)) shows that the change in surface heights range between 4.5 nm and −6.4 nm, which is comparable to the asperity size. This suggests that the loading conditions used in the experiments cause predominantly elastic deformations and the extent of plasticity, if there is any, did not go beyond the asperity scale. Negative values for the height difference between the two images can be attributed to thermal drift, the difference between the two contact detection points preceding SPM imaging sequences or nanoscale debris that is swept out of the contact zone. Spatial matching of the coordinate systems of the before and after images was carried out by offsetting the latter along the x and y directions. Therefore, the calculated differences are also inevitably subjected to some error from rotational mismatch.
Fig. 2
Fig. 2
Close modal
### Presliding Experiments.
After roughness measurements, presliding contact experiments are performed under ambient conditions (26 °C, 37% RH) by using the nanoscratch module of the triboindenter. A spheroconical diamond indenter with a tip radius of 50 μm is first pressed on the polyimide samples. After the initial preloading, normal loading and tangential displacement fluctuations with various amplitudes and phase differences are imposed on the contact. The normal loads and tangential displacements used are expressed as
$P(t)=P0+P1(ω t)$
(2)
$x(t)=x1(ω t−ϕ)$
(3)
where $P0$ is the normal preload, $P1$ and $x1$ are the fluctuations in the normal load and tangential displacement, $w$ is the fluctuation frequency, and $ϕ$ is the phase difference. As shown in Fig. 3, the fluctuations $P1$ and $x1$ are chosen as triangular waves with $w=π/10.$ The mean normal load, $P0$ is set to 1 mN, and the fluctuation amplitudes, $P1$ are adjusted as the 0%, 10%, 20%, and 30% of the mean preload. Note that the first of those fluctuation conditions corresponds to the constant normal load case, which is heavily studied in the literature. For each normal loading condition, the tangential displacement fluctuations are increased from 70 to 120 nm in four equal increments. To ensure presliding conditions, we determined the displacements at the sliding inception by unidirectional sliding experiments on polyimide under a normal load of 1000 μN. As shown in Fig. 4, the tangential displacement (δT) of 60 nm is significantly lower than the displacement at the onset of macrosliding.
Fig. 3
Fig. 3
Close modal
Fig. 4
Fig. 4
Close modal
### Cyclic Indentation Tests.
The mechanical energy loss measured by the hysteresis (friction) loops can be attributed to frictional slip, interface failure, viscoelastic losses, plasticity, and/or surface damage (fracture, wear, etc.) of the polyimide samples. The roughness maps of the tested surfaces before and after presliding tests suggest no noticeable plasticity or damage (see Figs. 2(a) and 2(b)). To identify the relative contribution of viscoelastic losses, we conduct cyclic indentation tests using the triboindenter at the fluctuation frequency used in the presliding experiments (0.05 Hz). Normal loading imposed in these tests is identical to the profile depicted in Fig. 3(a). The phase differences between the normal load and displacement responses are used to monitor the degree of viscous response, and viscoelasticity-born losses. Note that the elastic mismatch between the probe and the samples also causes frictional slip during normal load fluctuations. However, the mismatch-induced slip is expected to be very limited compared to the slip caused by tangential loading. Therefore, phase difference obtained by the cyclic indentation tests can reveal the relative importance of viscoelasticity when compared to the phase differences observed in the hysteresis (friction) loops.
Fig. 5
Fig. 5
Close modal
## Results and Discussion
Fig. 6
Fig. 6
Close modal
Next, we quantify the adhesive strength between the probe and the polyimide samples. Figure 7 shows a representative load versus displacement response in adhesion tests. Note that zero penetration depth corresponds to the undeformed sample surface. In adhesion tests, the probe first approaches to the sample surface, and then penetrates up to 140 nm. This penetration depth is chosen to yield similar normal loads (870–950 μN) as in presliding experiments. Unloading begins immediately after the maximum penetration depth is reached.
Fig. 7
Fig. 7
Close modal
As evident from Fig. 7, the unloading response follows the loading curve with a minute hysteresis. As discussed in cyclic indentation tests, this is thanks to predominantly elastic loading. At the retracting phase, the forces become tensile, and reach a maximum value referred as pull-off force, after which the contact between the probe and the sample is lost momentarily. The pull-off forces obtained in those tests are on the order of 1 μN. (inset figure in Fig. 7). This range is negligibly small compared to the mean preload, and so are the energy losses due to adhesive interactions.
The low adhesive strength that we measured is expected as similar observations are made for adhesion of untreated polyimide films to various metallic and ceramic substrates [32]. In line with this, additional chemical (adhesive promoters) and mechanical (roughness) treatments are required to enhance adhesion of polyimide films in multilayer composites [33]. In addition to the inherently low adhesive characteristics of polyimide, roughness might have contributed to the measured adhesive strength. In order to determine the existence of such an effect, we also estimated the surface energy of polyimide by the JKR theory [34]
$Fpull-off=1.5π ΔγR$
(4)
where $Fpull-off$ is the pull-off force, $Δγ$ is the surface energy, and $R$ is the combined contact radius. This equation returns a surface energy value of 4.24 mJ/m2 when we use 1 μN (from Fig. 7) and 50 μm for $Fpull-off$ and $R$, respectively. This value is significantly small compared to 40 mJ/m2, the surface energy value reported for polyimide [35]. This significant difference confirms that the effect of roughness in our adhesion tests is influential. Regardless of the mechanisms leading to low adhesive strength, we can eliminate adhesive interactions from the list of possible contributors to the mechanical losses, leaving only frictional slip as the dominant contributor.
### Identification of Elastic Properties.
As evident from the roughness measurements before and after presliding experiments, elastic deformations are expected to dominate the contact response. To verify this and identify the Young’s modulus of the polyimide samples, we analyze the initial normal loading portion of the presliding tests where the contact is established and loaded up to a mean normal load of $P0$ (Fig. 3(a)). According to the elastic (Hertzian) contact theory, the normal load, $P$ depends on the normal penetration, $δ$ nonlinearly in a spherical contact as
$P=43E*δ3/2R$
(5)
where $E*=[(1−υ12)/E1+(1−υ22)/E2]−1$ and $R=(1/R1+1/R2)−1$ are the equivalent Young’s modulus and radius of the contact pair, and $E1,2$, $υ1,2$, and $R1,2$ are the Young’s modulus, Poisson’s ratio, and radius of contacting materials 1 and 2, respectively. When the material properties and geometry of the spheroconical diamond probe given in Table 1 are inserted in Eq. (5), the only unknowns are the elastic properties of the polyimide film. The literature reports the Poisson’s ratio of 0.34 for polyimides. With those values, we estimate the Young’s modulus of the polyimide films by the best fits to the normal load versus penetration depth graphs shown in Fig. 8. This procedure is applied to the initial loading stage of all the presliding experiments ($n=112$), and the Young’s modulus is found to range from 1.6 to 2.9 GPa, with a mean of 2.4 GPa. The Young’s moduli range we identify agrees reasonably well with the values reported in the literature [3638]. The analytical predictions of Eq. (5) with the minimum, maximum, and mean values of Young’s moduli are also overlaid on the experimental data in Fig. 8. The match between the analytical curves and the experimental data is quite significant beyond ∼20 nm of penetration depth, whereas below that level, experimental data exhibit a slightly smaller slope than 3/2. This is in support of the previously presented argument that once the penetration depth exceeds the RMS roughness of the surface, the indentation curves gradually converge to the Hertzian response. This also agrees with the use of the normal loading portion of the tests in estimating Young’s modulus as an alternative to the Oliver–Pharr method.
Fig. 8
Fig. 8
Close modal
Table 1
Young’s modulus (GPa)Poisson’s ratio, υRadius of curvature (μm)
Polyimide1.6–2.9 (avg. 2.4)0.34
Diamond11000.250
Young’s modulus (GPa)Poisson’s ratio, υRadius of curvature (μm)
Polyimide1.6–2.9 (avg. 2.4)0.34
Diamond11000.250
For each experiment, we determined the residual normal displacement upon complete unloading. Then, we calculated the total thermal drift by multiplying the thermal drift rate measured and total test duration. The mean and standard deviation values were calculated to be 5.84 nm and 5.4 nm for residual normal displacements and 26.98 nm and 11.39 nm for thermal drift values. This shows that experimentally observed residual normal displacements lie within the uncertainty of thermal drifts. Hence, we conclude that the extent of plasticity is minimal.
We will use the elastic properties identified experimentally in the analytical interpretation of the presliding experiments in Sec. 4.3.
### Presliding Experiments and Energy Dissipation.
We conduct a total of 112 presliding experiments to study the effect of loading fluctuations and phase differences on the frictional dissipation. Those experiments can be grouped into three major categories according the loading conditions: (i) no normal load fluctuation (Fig. 9(a)); (ii) normal and tangential load fluctuations with low phase (LP) difference (Fig. 9(b)); and (iii) normal and tangential load fluctuations with high phase (HP) difference (Fig. 9(c)). Loading condition in Fig. 9(a) is extensively studied in the literature both experimentally and analytically. We will apply this loading condition on the polyimide samples to validate the experiments against analytical solutions. Loading conditions in Figs. 9(b) and 9(c) differ from each other by the phase difference between the normal and tangential fluctuations. As evident from the loading curves, Fig. 9(b) approximates in-phase linear loading (i.e., oblique loading), whereas the loading in Fig. 9(c) causes an elliptical loading in $P−Q$ plane. Those extreme cases provide sufficiently large contrast between loading conditions, and thus enable us to study the effect of phase difference on frictional energy losses.
Fig. 9
Fig. 9
Close modal
Figure 10 shows the hysteresis loops obtained from the eighth cycle of loading for the constant normal load case under four different maximum tangential fluctuations. The areas inside those loops will be studied as the frictional losses at the steady state.
Fig. 10
Fig. 10
Close modal
Figure 11 shows the frictional dissipation as a function of maximum tangential load for all testing configurations. Starting with the constant normal load case, we observe that higher tangential loads cause larger frictional dissipation. This is expected since higher tangential loads lead to larger frictional slip. Frictional slip and associated energy dissipation in spherical contacts under cyclic loading conditions are worked out by Mindlin and Deresiewicz [10], yielding the following expression for the energy loss:
Fig. 11
Fig. 11
Close modal
$ΔW=9μ2P02G*10a{1−[1−QmaxμP0] 5/3−5Qmax6μP0[1+(1−QmaxμP0)2/3]}$
(6)
where $G*=(2−υ1)/G1$ and $G1$ and $υ1$ are the shear modulus and Poisson’s ratio of the test material, respectively; $a$ is the contact radius, and $μ$ is the coefficient of friction of the test surface.
To estimate the energy dissipation using Eq. (6), we need the material properties, contact radius, loading conditions, and the coefficient of friction, all of which we discussed in Secs. 3.2 and 4.2 except for the last one. We conduct sliding friction tests using the same experimental procedure as in presliding tests but with larger tangential displacements to obtain the coefficient of friction of polyimide samples. Upon five trials, we find the mean value of coefficient of friction of 0.2, and substituting the elastic properties listed in Table 1 and contact radius estimated from the experimental data using the Hertzian assumption in to Eq. (6), we estimate the energy dissipation predictions. We calculated the shear modulus of polyimide ($G1$) using $G=E/2(1+υ)$. Since the experimental Young’s moduli of polyimide varied across a range of values between 1.6 GPa and 2.9 GPa, we calculated minimum and maximum shear moduli corresponding to the same measured range, and plotted Eq. (6) for these two values separately. The band formed by these two theoretical curves as presented in Fig. 11 correlates reasonably well with the measured frictional dissipations, confirming the frictional slip as the major dissipation mechanism observed in the experiments. Among all the cases tested, high preload fluctuation with HP difference between tangential loads yields the maximum frictional dissipation. As the preload fluctuations decrease, so does the energy dissipation, and thus, constant normal load case yields the minimum frictional dissipation. For a fixed maximum tangential load, one can alter the frictional dissipation by a factor of two by adjusting the fluctuation amplitudes and phase difference. Albeit being subtler, we also find that the HP difference cases consistently dissipate more energy than the LP difference cases. Those observations are in line with the analytical solutions of Putignano et al. [15] and Patil and Eriten’s numerical results [39] stating that maximum frictional dissipation occurs when the normal and tangential components are approximately 90 deg out of phase. Similar conclusions are also made earlier for contacts under more complicated loading conditions that could result in sliding and separation [13]. The influence of normal fluctuation amplitudes and phase difference on the frictional dissipation vanishes as the maximum tangential fluctuation amplitude decreases, and thus, all the dissipation values cluster closely as shown around $Qmax=90μN.$ However, when the fluctuations are high, the differences are more pronounced, and controlling dissipation with both fluctuation amplitudes and phase difference is possible. Remarkably, frictional dissipations can be tuned over an order of magnitude from low to high amplitude vibrations when phase difference is increased from low to high; i.e., the triangles at around $Qmax=90μN$ to circles at around $Qmax=150μN.$
Furthermore, we estimated the dissipation due to normal loading over the last fluctuation cycle of 20 s (i.e., starting from P0 to P1 rising up to P0 + P1 and falling back to P0 − P1). The mean and standard deviation values of the residual normal displacements from this mini normal loading/unloading cycle are 1.49 nm and 0.4 nm, respectively, whereas the same parameters are calculated to be 3.34 nm and 1.55 nm for thermal drift that occurs over the same cycle. Since the residual displacements are lower than thermal drift, the energy dissipation due to normal load fluctuations around the mean preload of P0 is unquantifiable. Our presliding experiments, however, are conducted under tangential displacements that are an order of magnitude higher than thermal drift. Therefore, frictional energy loss is expected to be quantifiably larger than drift and viscoelasticity-related losses as presented in Figs. 10 and 11.
Another possible source of energy dissipation in normal loading is elastic mismatch between the probe and the polyimide samples. Due to elastic mismatch, normal and tangential tractions are coupled; i.e., normal loading causes shear tractions around edges of a spherical contact, and shear tractions influence normal displacements and thus contact area and normal tractions. Munisamy et al. [40] showed that when the product of elastic mismatch parameter (Dundurs constant) and friction coefficient is less than 0.1, the effects of mismatch on contact parameters and thus dissipation can be neglected. In our experiments, that product attains a value of 0.048 (Dundurs constant ∼0.24 × friction coefficient ∼ 0.2). Therefore, the contribution of mismatch on the dissipation observed in the normal loading cycles is expected to be negligible.
### Power-Law Exponents.
Next, we estimate the power-law exponents giving the dependence of energy dissipation on the maximum tangential load; i.e., the exponent n in $ΔW∼Qmaxn$. Note that for a given loading condition, we find the best fits to 16 sets of energy loss and $Qmax.$ Table 2 lists the estimated power-law exponents for seven loading conditions tested. The power-law exponent is 2.5 for the constant normal load case. Note that this case was treated analytically by Mindlin and Deresiewicz [10], and power-law exponents of 3 were found at the small vibration approximation. For larger vibrations, the power-law exponents were predicted even higher than 3. However, experimental studies featuring constant normal loading reported power-law exponents ranging from 2.2 to 2.8 [2,8]. Our results fall into this observed range. Spatial, temporal, and load-dependent variations in coefficient of friction, plasticity, and roughness are possible reasons for the mismatch between the analytical and experimental power-law exponents. In our study, we control the loading conditions, contact geometry, and surface roughness to suppress the effects of plasticity and roughness. However, the spatial and temporal variations in frictional behavior, which links normal and tangential tractions over the contact area, might still be influential. For the fluctuating normal load cases, the power-law exponents vary between 2.3 and 2.7 with higher phase differences consistently leading to lower power-law exponents. This is in close agreement with the analytical [15] and numerical [39] observations made in the literature. Both works state that power-law exponents closer to 2 are attainable with 90 deg out-of-phase normal and tangential fluctuations. Besides, Kim and Jang investigated an axisymmetric Hertzian contact problem under cyclic loading and obtained a power-law exponent of 2 [41]. Although the trends in our experiments correlate well with the theoretical and numerical predictions, we could not obtain power-law exponents close to 2 with the loading configurations we tested. Note that any deviation from two introduces nonlinear damping into a dynamic system. Therefore, our experiments assert that nonlinear damping is inevitable in an assembled structure containing frictional contacts even when the loading conditions, contact geometry, and roughness are controlled within a reasonable degree of accuracy.
Table 2
Power-law exponents for scratch tests on polyimide
02.49
Low2.54Low phase
Intermediate2.56Low phase
High2.67Low phase
Low2.32High phase
Intermediate2.48High phase
High2.53High phase
02.49
Low2.54Low phase
Intermediate2.56Low phase
High2.67Low phase
Low2.32High phase
Intermediate2.48High phase
High2.53High phase
## Conclusions
The relationship between frictional energy dissipation in spherical contacts and two main loading parameters has been investigated: magnitude of and phase difference between fluctuations in normal and tangential loads. 0%, 10%, 20%, and 30% of normal load fluctuations around a mean preload of 1000 μN and four different maximum tangential loads covering the range between ∼90 μN and ∼150 μN were used in two different phase difference scenarios, i.e., ∼0 deg and ∼90 deg. Pull-off and cyclic normal loading experiments conducted prior to the presliding experiments verified that energy losses observed in the presliding experiments can be fully attributed to frictional dissipation. Major findings of the study include:
• Energy dissipation have been shown to increase with increasing tangential force fluctuations primarily because of larger frictional slip;
• The maximum dissipation values were observed in the large normal and tangential load fluctuations and HP difference, whereas the minimum dissipation was obtained under constant normal load and small tangential fluctuations;
• For the same tangential loading and phase difference, energy dissipation increases as normal load fluctuations increase;
• As the maximum tangential load increases, the range of energy dissipation values observed for different normal loading and phase difference scenarios widens making it possible to tune energy dissipation over a wide range;
• In contrast to the theoretical predictions of 3, the power-law exponents linking the tangential fluctuation magnitudes to energy dissipations were found to be 2.49 for the constant normal loading case. Additionally, none of the loading cases studied delivered power-law exponents close to 2; i.e., nonlinear damping prevailed for all the contact cases investigated.
• For the same normal and tangential loading parameters, energy dissipation increased and power-law exponents decreased with increasing phase difference.
## Acknowledgment
This work is supported by the U.S. National Science Foundation (NSF) under Grant No. NSF CMMI-1462870.
## References
1.
Mindlin
,
R. D.
,
Mason
,
W. P.
,
Osmer
,
T. F.
, and
Deresiewicz
,
H.
,
1952
, “
Effects of an Oscillating Tangential Force on the Contact Surfaces of Elastic Spheres
,”
First U.S. National Congress of Applied Mechanics
, Chicago, IL, June 11–16, pp.
203
208
.
2.
Johnson
,
K. L.
,
1955
, “
Surface Interaction Between Elastically Loaded Bodies Under Tangential Forces
,”
Proc. R. Soc. London Ser. A
,
230
(
1183
), pp.
531
548
.
3.
Goodman
,
L. E.
, and
Brown
,
C. B.
,
1962
, “
,”
ASME J. Appl. Mech.
,
29
(
1
), p.
17
.
4.
Johnson
,
K. L.
,
1962
, “
Discussion: “Energy Dissipation in Contact Friction: Constant Normal and Cyclic Tangential Loading” (Goodman, L. E., and Brown, C. B., 1962, ASME J. Appl. Mech., 29, pp. 17–22)
,”
ASME J. Appl. Mech.
,
29
(
4
), p.
763
.
5.
Lazan
,
B. J.
,
1968
,
Damping of Materials and Members in Structural Mechanics
, Pergamon Press, Oxford, UK.
6.
Goodman
,
L.
,
1976
, “
Material Damping and Slip Damping
,”
Shock and Vibration Handbook
, McGraw-Hill, New York, pp.
1
28
.
7.
Segalman
,
D. J.
,
Bergman
,
L. A.
, and
Starr
,
M. J.
,
2006
, “
Joints Workshop 2006 Final Report
,” NSF and Sandia National Laboratories, Arlington, TX, Report No. Sandia-2007-7761.
8.
Segalman
,
D. J.
,
Gregory
,
D. L.
,
Starr
,
M. J.
,
Resor
,
B. R.
,
Jew
,
M. D.
, and
Lauffer
,
J. P.
,
2009
, Handbook on Dynamics of Jointed Structures,
Sandia National Laboratories
,
Albuquerque, NM
, Report No.
SAND2009-4164
.
9.
Eriten
,
M.
,
Polycarpou
,
A. A.
, and
Bergman
,
L. A.
,
2011
, “
Effects of Surface Roughness and Lubrication on the Early Stages of Fretting of Mechanical Lap Joints
,”
Wear
,
271
(
11–12
), pp.
2928
2939
.
10.
Mindlin
,
R. D.
, and
Deresiewicz
,
H.
,
1953
, “
Elastic Spheres in Contact Under Varying Oblique Forces
,”
ASME J. Appl. Mech.
,
20
, pp. 327–344.
11.
Griffin
,
J. H.
, and
Menq
,
C.-H.
,
1991
, “
Friction Damping of Circular Motion and Its Implications to Vibration Control
,”
ASME J. Vib. Acoust.
,
113
(
2
), pp.
225
229
.
12.
Menq
,
C.-H.
,
Chidamparam
,
P.
, and
Griffin
,
J. H.
,
1991
, “
Friction Damping of Two-Dimensional Motion and Its Application in Vibration Control
,”
J. Sound Vib.
,
144
(
3
), pp.
427
447
.
13.
Jang
,
Y. H.
, and
Barber
,
J. R.
,
2011
, “
Effect of Phase on the Frictional Dissipation in Systems Subjected to Harmonically Varying Loads
,”
Eur. J. Mech., A: Solids
,
30
(
3
), pp.
269
274
.
14.
Barber
,
J. R.
,
Davies
,
M.
, and
Hills
,
D. A.
,
2011
, “
,”
Int. J. Solids Struct.
,
48
(
13
), pp.
2041
2047
.
15.
Putignano
,
C.
,
Ciavarella
,
M.
, and
Barber
,
J. R.
,
2011
, “
Frictional Energy Dissipation in Contact of Nominally Flat Rough Surfaces Under Harmonically Varying Loads
,”
J. Mech. Phys. Solids
,
59
(
12
), pp.
2442
2454
.
16.
Davies
,
M.
,
Barber
,
J. R.
, and
Hills
,
D. A.
,
2012
, “
Energy Dissipation in a Frictional Incomplete Contact With Varying Normal Load
,”
Int. J. Mech. Sci.
,
55
(
1
), pp.
13
21
.
17.
Barber
,
J. R.
,
2012
, “
Frictional Systems Under Periodic Loads—History-Dependence, Non-Uniqueness and Energy Dissipation
,”
J. Phys. Conf. Ser.
,
382
(
1
), p.
012002
.
18.
Ciavarella
,
M.
,
1998
, “
The Generalized Cattaneo Partial Slip Plane Contact Problem. I—Theory
,”
Int. J. Solids Struct.
,
35
(
18
), pp.
2349
2362
.
19.
Ciavarella
,
M.
,
1998
, “
The Generalized Cattaneo Partial Slip Plane Contact Problem. II—Examples
,”
Int. J. Solids Struct.
,
35
(
18
), pp.
2363
2378
.
20.
Jäger
,
J.
,
1998
, “
A New Principle in Contact Mechanics
,”
ASME J. Tribol.
,
120
(
4
), pp.
677
684
.
21.
Xu
,
Y.
,
Bhargava
,
P.
, and
Zehnder
,
A.
,
2016
, “
Time and Temperature Dependent Mechanical Behavior of HFPE-II-52 Polyimide at High Temperature
,”
Mech. Mater.
,
100
, pp.
86
95
.
22.
Sroog
,
C. E.
,
1996
, “
History of the Invention and Development of Polyimides
,”
Polyimides: Fundamentals and Applications
, Marcel Dekker, New York.
23.
McDanels
,
D. L.
,
Serafini
,
T. T.
, and
DiCarlo
,
J. A.
,
1986
, “
Polymer, Metal, and Ceramic Matrix Composites for Advanced Aircraft Engine Applications
,”
J. Mater. Energy Syst.
,
8
(
1
), pp.
80
91
.
24.
Bowman
,
C. L.
,
Sutter
,
J. K.
,
Thesken
,
J. C.
, and
Rice
,
B. P.
,
2001
,
“Characterization of Graphite Fiber/Polyimide Composites for RLV Applications,”
2001 Material and Processes Odyssey, 46th International SAMPE Symposium and Exhibition, Long Beach, CA, May 6–10, pp.
1515
1529
.
25.
Ivosevic
,
M.
,
Knight
,
R.
,
Kalidindi
,
S. R.
,
Palmese
,
G. R.
, and
Sutter
,
J. K.
,
2003
, “
Erosion/Oxidation Resistant Coatings for High Temperature Polymer Composites
,”
High Perform. Polym.
,
15
(
4
), pp.
503
517
.
26.
Bower
,
A. F.
, 2009, “
Constitutive Laws—3.2 Linear Elasticity
,”
Applied Mechanics of Solids
, CRC Press, Boca Raton, FL.
27.
Feger
,
C.
,
1993
,
Advances in Polyimide: Science and Technology
,
Technomic Publishing, Inc.
, Lancaster, PA.
28.
Greenwood
,
J. A.
, and
Tripp
,
J. H.
,
1967
, “
The Elastic Contact of Rough Spheres
,”
ASME J. Appl. Mech.
,
34
(
1
), pp.
153
159
.
29.
Ovcharenko
,
A.
, and
Etsion
,
I.
,
2009
, “
Junction Growth and Energy Dissipation at the Very Early Stage of Elastic-Plastic Spherical Contact Fretting
,”
ASME J. Tribol.
,
131
(
3
), p.
031602
.
30.
Yoshizawa
,
H.
,
Chen
,
Y. L.
, and
Israelachvili
,
J.
,
1993
, “
Fundamental Mechanisms of Interfacial Friction. 1. Relation Between Adhesion and Friction
,”
J. Phys. Chem.
,
97
(
16
), pp.
4128
4140
.
31.
Comer
,
A. C.
,
2011
, “
Dynamic Relaxation Properties of Aromatic Polyimides and Polymer Nanocomposites
,”
Ph.D. thesis
, University of Kentucky, Lexington, KY.
32.
Minges
,
M. L.
,
1989
,
Electronic Materials Handbook: Packaging
,
ASM International
, Materials Park, OH.
33.
Buchwalter
,
L. P.
,
1990
, “
Adhesion of Polyimides to Metal and Ceramic Surfaces: An Overview
,”
,
4
(
1
), pp.
697
721
.
34.
Johnson
,
K. L.
,
Kendall
,
K.
, and
Roberts
,
A. D.
,
1971
, “
Surface Energy and the Contact of Elastic Solids
,”
Proc. R. Soc. London A
,
324
(1558), pp.
301
313
.
35.
Troughton
,
M. J.
,
2008
,
Handbook of Plastics Joining: A Practical Guide
,
William Andrew
, Norwich, NY.
36.
Maseeh
,
F.
,
Schmidt
,
M. A.
,
Allen
,
M. G.
, and
Senturia
,
S. D.
,
1988
, “
Calibrated Measurements of Elastic Limit, Modulus, and the Residual Stress of Thin Films Using Micromachined Suspended Structures
,” IEEE Solid State Sensor and Actuator Workshop (
SOLSEN
), Hilton Head Island, SC, June 6–9, pp. 84–87.
37.
Odegard
,
G. M.
,
Clancy
,
T. C.
, and
Gates
,
T. S.
,
2005
, “
Prediction of Mechanical Properties of Polymers With Various Force Fields
,”
AIAA
Paper No. 2005-1850.
38.
DuPont, 2017, “
Extreme Versatility and Thermal Performance Provides Unlimited Potential|DuPontTM Kapton®|DuPont USA
,” DuPont, Wilmington, DE, accessed Aug. 22, 2016, http://www.dupont.com/products-and-services/membranes-films/polyimide-films/brands/kapton-polyimide-film.html
39.
Patil
,
D. B.
, and
Eriten
,
M.
,
2015
, “
Frictional Energy Dissipation in Spherical Contacts Under Presliding: Effect of Elastic Mismatch, Plasticity and Phase Difference in Loading
,”
ASME J. Appl. Mech.
,
82
(
1
), p.
011005
.
40.
Munisamy
,
R. L.
,
Hills
,
D. A.
, and
Nowell
,
D.
,
1994
, “
Static Axisymmetric Hertzian Contacts Subject to Shearing Forces
,”
ASME J. Appl. Mech.
,
61
(
2
), pp.
278
283
.
41.
Kim
,
J. H.
, and
Jang
,
Y. H.
,
2014
, “ | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 53, "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": 0.7639545202255249, "perplexity": 2458.658010113596}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1656103556871.29/warc/CC-MAIN-20220628142305-20220628172305-00632.warc.gz"} |
http://mactex-wiki.tug.org/wiki/index.php/TeX_Helpers | # TeX Helpers
Jump to: navigation, search
Your helpful TeX on Mac wiki depends on you to support it by adding your valuable information!
This page lists software which, while not primarily or solely designed for use with TeX, complements it. Some of the software, such as asymptote, includes a TeX interface or package of some kind; some of it, such as gnuplot, is used by TeX packages; and some of it, such as pdfcrop, offers functionality which may be essential to a TeX-centric workflow.
## Fonts
This section includes software which may be helpful to those who wish to install or use different fonts for use with TeX, or in resolving font issues of various kinds.
### FontForge
by George Williams
Open source ("essentially" revised BSD)
From the project homepage:
An outline font editor that lets you create your own postscript, truetype, opentype, cid-keyed, multi-master, cff, svg and bitmap (bdf, FON, NFNT) fonts, or edit existing ones. Also lets you convert one format to another. FontForge has support for many macintosh font formats.
FontForge may be compiled from source or installed using one of the packages available for OS X. Alternatively, it can be installed using i-Installer and may be available from MacPorts or Fink.
Note: FontForge uses the freetype library and some of its functionality depends on a build of freetype compiled with the byte code interpreter enabled. The byte code interpreter is disabled by default as it infringes on patents owned by Apple. If you own a licence or if you live somewhere where the patents do not apply, you may wish to compile freetype with the byte code interpreter enabled and to build FontForge against this library in order to enable those features of FontForge which depend on this. MacPorts provides a "variant" called "with_freetype_bytecode". If you do not enable the byte code interpreter, FontForge will still work but some features will be disabled.
### fondu
by George Williams
Open source (BSD)
A set of utilities for dealing with fonts in Mac-specific formats. The utilities perform various conversions between Mac-specific and other font formats.
Fondu font utilities
Utility
Input formats
Output formats
fondu macbinary (.bin)
binhex (.hqx)
bare resource fork
data fork resource (.dfont)
postscript (.pfb)
truetype (.ttf)
opentype (.otf)
bitmap (.bdf)
afm (.afm)
ufond bitmap (.bdf)
truetype (.ttf)
opentype (.otf)
postscript (.pfb)
macbinary (.bin)
bare resource fork
data fork resource (.dfont)
binhex (.hqx)??
dfont2res data fork resource (.dfont) (bare?) resource fork
lumper bitmap (.bdf)
truetype (.ttf)
opentype (.otf)
family info. (FOND)
data fork resource (.dfont)
showfond bitmap (.bdf)
truetype (.ttf)
opentype (.otf)
family info. (FOND)
information dump
In addition:
• tobin produces a macbinary (.bin) file from a series of files;
• frombin unwraps a macbinary (.bin) file.
fondu may be compiled from source or installed from the Mac OS X package provided. Alternatively, fondu may be installed using i-Installer and may be available from MacPorts or Fink.
Given that Mac OS X can now make direct use of fonts in many of the unix formats, these utilities may be of most use to those interested in using fonts in Mac-specific formats with TeX, such as the fonts supplied with Mac OS X. The exception concerns fonts in unix postscript format (.pfb etc.) which still require wrapping for use with OS X applications.
### pkfix
by Heiko Oberdiek
Open source (LPPL)
A very useful terminal script to fix old ps files which were produced by the old dvips and use bitmap (pk) fonts. These files look good in gv (ghostview) but look really ugly when converted by ps2pdf, pstopdf or Apple Preview. Because such converted files do not include a text layer, they cannot be searched. This script substitutes postscript (type 1) fonts for the bitmap (pk) fonts and then conversion to pdf works well.
pkfix may be missing from some (older) TeX distributions.
## Graphics
This section includes software which can be useful in the production of various sorts of graphics for use with TeX, including images, diagrams, graphs etc.
### asymptote
Open source (LGPL)
Terminal command %asy and %xasy for built-in drawing tool. Asymptote 1.44 brought major new feature (creation of pdf with embedded prc 3d models).
See this thumbnail:
.
Requires Adobe Reader to see the model. Current version 1.66; enabled OpenGL renderer with antialiasing to MacOS (10.4 and 10.5) (Victor Ivrii 19:05, 25 December 2008 (UTC))
Now part of TeXLive and is updated regularly Victor Ivrii 11:39, 16 November 2009 (UTC)
### gnuplot
Other/Proprietary licence
Plotting routine that can generate numerous high quality graphics format. (eps, pdf, metapost, etc.)
If \write18 enabled http://sourceforge.net/projects/pgf/ pgf with tikz] (very powerful graphics package for TeX and LaTeX) can use gnuplot for providing some data)
Example:
\usepackage{tikz}% in preamble
\begin{tikzpicture}
\draw[domain=0:2.5,scale=0.4, smooth]
plot[parametric,id=parametric-example] function{-0.8*t*t*t+2.6,t*t+0.2*t*t*t*t} node[right]{$\mathcal Q$};
\end{tikzpicture}
To use as a standalone application in Aqua (standard Mac OS) environment you may need Aquaterm
### ImageMagick
Open source (BSD)
A suite of image manipulation and conversion utilities with X11 and command line interfaces.
The MacTeX distribution installs the convert command line utility from ImageMagick in /usr/local/bin. To benefit from the full range of utilities provided by ImageMagick or to install the GUI (X11) interface, you need to use another installation method. If you install ImageMagick before MacTeX, you may wish to preserve your existing convert command by customising the MacTeX installation.
Note that ImageMagick may be installed using i-Installer which will include the GUI tools if X11 is available as well as the command line utilities.
MacPorts and Fink offer alternative installation methods, and precompiled binaries are available on macupdate and other Mac sites.
### Ipe
by Otfried Cheong (version: 7.0.14, link: http://tclab.kaist.ac.kr/ipe/, licence: GPL with exception allowing distribution of binaries linked against CGAL, manual: http://ipe7.sourceforge.net/manual/manual.pdf)
An extensible drawing editor with embedded LaTeX support which can also be used to create complete presentations. Text and mathematics can be input as LaTeX source so that LaTeX markup can be easily included in drawings. Output is postscript or PDF.
Ipe is a serious replacement of the loved 'xfig' tool. If the core of your figure is produced, for example, by gnuplot into a PDF format to be incorporated in your LaTeX document, you can use the Ipe tool pdftoipe and edit this core figure with IPE in order to incorporate mathematics in texboxes anywhere. Ipe will display your figure as well as the formatted LaTeX mathematics (you can compile your local LaTeX texboxes from Ipe). Texboxes can then be moved, rotated, colored etc.
• An advantage over xfig is that instead of using the burden of 'special', 'export to both' with xfig, you can more precisely and rapidly adjust your maths to the figure.
• But instead of having a single LaTeX compilation which allows cross-references, you are using an independent on line compilation of the mathematics included in your figure.
Useful links:
Installation: Ipe 7.0.14 depends on cairo, fontconfig, freetype2, lua and some other more common libraries supplied by OS/X. You can compile the source yourself if you use fink for the less common libraries or use a MacPort port which already exists for the program as well as for the Ipe tools.
### jfig
by Norman Hendrich
Dual licence (shareware for non-commercial use only)
The homepage describes jfig as a multi-platform
2D graphics and diagram editor based on the FIG file format.
written in Java with LaTeX support and a GUI based on xfig. A number of complementary programs are available on the download page.
### Xfig
by Supoj Sutanthavibul, Brian V. Smith, Paul King et al.
Open source (details)
Xfig is an interactive drawing tool which runs under X Windows. In xfig, figures may be drawn using objects such as circles, boxes, lines, spline curves, text, etc.
## Mathematics
This section includes software which may be useful to those typesetting mathematics in TeX.
## JavaScript TeX parsers
JavaScript suites allowing to direct input of TeX into web pages. While these suites do not use TeX installation and are not designed to load packages or to process large TeX documents (albeit under certain restrictions could be used for this task as well) they are specifically designed to process TeX snippets (equation-type environments) embedded into web pages (including those which are parts of wikis, blogs, forums and CMS (context management systems)). In contrast to equation->(dvi->eps)->png approach do not create png images of equations and thus are much more portable.
While not mac-specific they have mac aspects as designed to work with multiple browsers
### jsMath
by Davide P. Cervone
Open source (Apache Licence v2.0)
The first widely used suite of this type. Development is frozen.
### MathJax
by Davide P. Cervone and others
Open source (Apache Licence v2.0)
Successor of jsMath. Allows MathMl snippets and TeX<->MathMl conversion. Works with variety of browsers including those for mobile devices.
Very nice demo MathJax + Geogebra http://ams.org/samplings/feature-column/fcarc-geo-dft#2
MathJax internals are MathML. MathJax is not TeX despite using TeX inputs. It does not use any TeX distribution and has completely different goals and scope.
### MacQTeX
Restricted freeware (academic institutional use only)
Quiz management software.
Commercial
Equation editor.
### MATLAB/GNU Octave
#### MATLAB
by The MathWorks, Inc.
Commercial
From the homepage:
MATLAB® is a high-level language and interactive environment that enables you to perform computationally intensive tasks faster than with traditional programming languages such as C, C++, and Fortran.
#### GNU Octave
by John W. Eaton et al.
Open source (GPL)
From the homepage:
GNU Octave is a high-level language, primarily intended for numerical computations. It provides a convenient command line interface for solving linear and nonlinear problems numerically, and for performing other numerical experiments using a language that is mostly compatible with Matlab. It may also be used as a batch-oriented language.
#### Sage
Open source (GPL)
Sage is a free open-source mathematics software system licensed under the GPL. It combines the power of many existing open-source packages into a common Python-based interface. Mission: Creating a viable free open source alternative to Magma, Maple, Mathematica and Matlab.
#### latexcmd
by Peder Axensten
Licence?
Provides access to MATLAB results in LaTeX documents.
#### poly2tex.m
by Joseph C. Slater
Licence?
Converts polynomials into LaTeX source strings.
#### matrix2tex.m
by Joseph C. Slater
Licence?
Converts matrices into LaTeX source strings.
## Postscript/PDF
### epspdf and epspdftk
by Siep Kroonenberg
Open source (GPL v2)
A multiplatform GUI- and command-line converter for [e]ps and pdf. It can be used for cropping, grayscaling and much more of (e)ps and pdf-files (both graphics and documents). It is available for several platforms. On Mac OS X, there is a graphical user interface.
Included in TeX Live.
### ghostscript
Open source (GPL but varies with version)
Interpreter for PostScript and PDF.
Can convert ps/pdf files to many raster formats for printing on printers without postscript capability.
Can convert ps to pdf, and pdf to ps files (with some limitations).
Included in MacTeX 2008.
### pdfcrop
by Heiko Oberdiek
Open source (LPPL)
terminal script which crops pdf files (according to specified parameters; usually it is enough to type %pdfcrop foo.pdf which crops according to bounding box. Very useful if external pdf graphics is used in TeX or LaTeX documents).
For example, one can use LaTeX package pgf with tikz to make pdf pictures (with \pagestyle{empty}), then use pdfcrop to crop them, then use as external graphics file.
### pdftk
by Sid Steward
Open source (GPL)
pdftk is a command-line utility to post-process PDF-files. Among other things, it can add decryption, password-protection, Watermarks. You can deny the reader to copy from the pdf or to print it. You can modify the metadata (Author, Title, description, keywords, creator, ...) and so on.
From the homepage:
If PDF is electronic paper, then pdftk is an electronic staple-remover, hole-punch, binder, secret-decoder-ring, and X-Ray-glasses. Pdftk is a command-line tool for doing everyday things with PDF documents. Keep one in the top drawer of your desktop and use it to:
• Merge PDF Documents
• Split PDF Pages into a New Document
• Decrypt Input as Necessary (Password Required)
• Encrypt Output as Desired
• Fill PDF Forms with FDF Data and/or Flatten Forms
• Apply a Background Watermark
• Report on PDF Metrics such as Metadata, Bookmarks, and Page Labels
• Update PDF Metadata
• Attach Files to PDF Pages or the PDF Document
• Unpack PDF Attachments
• Burst a PDF Document into Single Pages
• Uncompress and Re-Compress Page Streams
• Repair Corrupted PDF (Where Possible)
The latest version is 1.4.4 (hosted on http://www.pdflabs.com/). There is a bug requiring full-path call
% /opt/pdflabs/pdftk/bin/pdftk
but fixed version could be downloaded
It may be incompatible with some features of pdf-1.6 (aka Acrobat/Adobe Reader 1.7). Now it comes with MacOSX installer and is tested under MacOSX 10.6 but may work under older systems. Installer does not work under older systems. Victor Ivrii 00:10, 3 November 2010 (UTC) </noinclude>
## Spelling
### CocoAspell
Freeware (interface)
Open source (Aspell)
CocoAspell is Mac OS X implementation of Aspell -- A more intelligent Ispell -- that is being developed by Kevin Atkinson. Here is a brief snippet of how Kevin describes Aspell on his web site: Aspell is an Open Source spell checker designed to eventually replace Ispell. Its main feature is that it does a much better job of coming up with possible suggestions than Ispell does. In fact recent tests shows that it even does better than Microsoft Word 97's spell checker or just about any other spell checker I have seen. It also has support for checking (La)TeX and HTML files, and run time support for other non English languages.
CocoAspell is included in MacTeXtras.
### Excalibur
by Rick Zaccone
Open source (GPL)
Excalibur is a very nice spell checker for any Macintosh text file or the clipboard, but it is specifically designed for use with LaTeX files. Features include:
• Excalibur will offer suggestions for how to correct a word.
• Excalibur can spell check the clipboard. This makes it a good spelling checker for any text based application such as Alpha or SimpleText.
• Excalibur also works with Eudora Pro, BBEdit, MT NewsWatcher, Communicate, Nisus Writer, AppleWorks (formerly ClarisWorks), WordPerfect, and any other program that supports Word Services.
• You can teach it about new LaTeX commands and environments that you define.
• You can create your own dictionaries.
• Works on any plain TEXT file. (type TEXT)
• Works on formatted files via Word Services.
• You will need Mac OS 8.6 or higher to run Excalibur 4.0.
• Version 3.0.2 of Excalibur will run on System 7.1 or higher, but it requires the Classic environment on Mac OS X. It is still available from the Excalibur ftp server.
• Version 2.6 of Excalibur is still available too. It will run on System 6.0.5 or greater, and it will run on any Macintosh since the Mac Plus.
• The "Standard Dictionary" (American English) distributed with Excalibur has over 162,000 words.
Excalibur is included in both MacTeX and MacTeXtras. | {"extraction_info": {"found_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": 0.6875019073486328, "perplexity": 10260.24297357801}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-13/segments/1490218189198.71/warc/CC-MAIN-20170322212949-00157-ip-10-233-31-227.ec2.internal.warc.gz"} |
https://cloud.originlab.com/doc/OriginC/guide/Mathematics | # 1.12.1 Mathematics
## Normalize
The following example shows how to pick a point in a data plot (curve) and then normalize all curves in the layer to the same value at that point. This snippet of code assumes a graph layer with multiple curves is active and all curves share the same X values. This assumption is typical in spectroscopy.
GraphLayer gl = Project.ActiveLayer();
if( !gl )
return;
// Allow user to click and select one particular point of one particular curve
GetGraphPoints mypts;
mypts.SetFollowData(true);
mypts.GetPoints(1, gl);
vector vx, vy;
vector<int> vn;
if(mypts.GetData(vx, vy, vn) == 1)
{
// Save index and y value of picked point
int nxpicked = vn[0] - 1;
double dypicked = vy[0];
// Loop over all data plots in layer
foreach( DataPlot dp in gl.DataPlots )
{
// Get the data range and then the y column for current plot
XYRange xy;
Column cy;
if(dp.GetDataRange(xy) && xy.GetYColumn(cy))
{
// Get a vector reference to y values from the y column
vectorbase &vycurrent = cy.GetDataObject();
// Scale vector so y value matches user-picked point
vycurrent *= dypicked/vycurrent[nxpicked];
}
}
}
## Interpolation/Extrapolation
The ocmath_interpolate function is used to do interpolation/extrapolation with modes of Linear, Spline and B-Spline.
// Make sure there are 4 columns in active worksheet
// The first two columns are source xy data,
// 3rd column has input x data, 4th column to put output y.
Worksheet wks = Project.ActiveLayer();
wks.SetSize(-1, 4);
DataRange drSource;
drSource.Add(wks, 0, "X"); // 1st column - source x data
drSource.Add(wks, 1, "Y"); // 2nd column - source y data
vector vSrcx, vSrcy;
drSource.GetData(&vSrcx, 0);
drSource.GetData(&vSrcy, 1);
DataRange drOut;
drOut.Add(wks, 2, "X"); // 3rd column - input x data
drOut.Add(wks, 3, "Y"); // 4th column - interpolated y data
vector vOutx, vOuty;
drOut.GetData(&vOutx, 0);
int nSrcSize = vSrcx.GetSize();
int nOutSize = vOutx.GetSize();
vOuty.SetSize(nOutSize);
int nMode = INTERP_TYPE_BSPLINE;
double dSmoothingFactor = 1;
int iRet = ocmath_interpolate(vOutx, vOuty, nOutSize, vSrcx, vSrcy, nSrcSize,
nMode, dSmoothingFactor);
drOut.SetData(&vOuty, &vOutx);
## Integration
Origin C provides access to NAG's integral routines to perform integration. With Origin C and NAG you can do integration on a normal integrand, an integrand with parameters, an integrand with oscillation, an infinite integral, higher dimension integration, and more. The following examples show how to do integration with NAG.
Your Origin C code will need to include the NAG header file at least once before your code calls any NAG functions.
#include <OC_nag.h> // NAG declarations
### Simple Integral Function
The first example shows how to do a basic integration on a simple integrand with only one integration variable.
// NAG_CALL denotes proper calling convention. You may treat it
// like a function pointer and define your own integrand
double NAG_CALL func(double x,Nag_User *comm)
{
int *use_comm = (int *)comm->p;
return (x*sin(x*30.0)/sqrt(1.0-x*x/(PI*PI*4.0)));
}
void nag_d01sjc_ex()
{
double a = 0.0;
double b = PI * 2.0; // integration interval
double epsabs, abserr, epsrel, result;
// you may use epsabs and epsrel and this quantity to enhance your desired
// precision when not enough precision encountered
epsabs = 0.0;
epsrel = 0.0001;
// The max number of sub-intervals needed to evaluate the function in the
// integral. For most cases 200 to 500 is adequate and recommmended.
int max_num_subint = 200;
NagError fail;
Nag_User comm;
static int use_comm[1] = {1};
comm.p = (Pointer)&use_comm;
d01sjc(func, a, b, epsabs, epsrel, max_num_subint, &result, &abserr,
&qp, &comm, &fail);
// For the error other than the following three errors which are due to
// bad input parameters or allocation failure. You will need to free
// the memory allocation before calling the integration routine again
// to avoid memory leakage
if (fail.code != NE_INT_ARG_LT && fail.code != NE_BAD_PARAM &&
fail.code != NE_ALLOC_FAIL)
{
NAG_FREE(qp.sub_int_beg_pts);
NAG_FREE(qp.sub_int_end_pts);
NAG_FREE(qp.sub_int_result);
NAG_FREE(qp.sub_int_error);
}
printf("%g\n", result);
}
### Integral Function with Parameters
The next example shows how to define and perform integration on an integrand with parameters. Notice that the parameters are passed to the integrator by a user-defined structure. This avoids having to use static variables as parameters of the integrand, and makes it thread-safe.
This example can also be adapted to use NAG's infinite integrator. For instance, by enabling the line calling the infinite integrator d01smc function, the example can be used to perform infinite integration.
struct user // integrand parameters
{
double A;
double Xc;
double W;
};
// Function supplied by user, return the value of the integrand at a given x.
static double NAG_CALL f_callback(double x, Nag_User *comm)
{
struct user *param = (struct user *)(comm->p);
return param->A * exp(-2 * (x - param->Xc) * (x - param->Xc)
/ param->W / param->W) / (param->W * sqrt(PI / 2));
}
Now, we set parameter values for the function and define the additional parameters necessary to perform the integration. The integration is then performed by a single function call, passing the parameters as arguments.
void nag_d01sjc_ex()
{
double a = 0.0;
double b = 2.0; // integration interval
// The following variables are used to control
// the accuracy and precision of the integration.
double epsabs = 0.0; // absolute accuracy, set negative to use relative
double epsrel = 0.0001; // relative accuracy, set negative to use absolute
int max_num_subint = 200; // max sub-intervals, 200 to 500 is recommended
// Result keeps the approximate integral value returned by the algorithm
// abserr is an estimate of the error which should be an upper bound
// for |I - result| where I is the integral value
double result, abserr;
// The structure of type Nag_QuadProgress, it contains pointers
// allocated memory internally with max_num_subint elements
// The NAG error parameter (structure)
NagError fail;
// Parameters passed to integrand by NAG user communication struct
struct user param;
param.A = 1.0;
param.Xc = 0.0;
param.W = 1.0;
Nag_User comm;
comm.p = (Pointer)¶m;
// Perform integration
// There are 3 kinds of infinite boundary types you can use in Nag infinite
// integrator Nag_LowerSemiInfinite, Nag_UpperSemiInfinite, Nag_Infinite
/*
d01smc(f_callback, Nag_LowerSemiInfinite, b, epsabs, epsrel, max_num_subint,
&result, &abserr, &qp, &comm, &fail);
*/
d01sjc(f_callback, a, b, epsabs, epsrel, max_num_subint,
&result, &abserr, &qp, &comm, &fail);
// check the error by printing out error message
if (fail.code != NE_NOERROR)
printf("%s\n", fail.message);
// For errors other than the following three errors which are due to
// bad input parameters, or allocation failure,
// you will need to free the memory allocation before calling the
// integration routine again to avoid memory leakage.
if (fail.code != NE_INT_ARG_LT && fail.code != NE_BAD_PARAM
&& fail.code != NE_ALLOC_FAIL)
{
NAG_FREE(qp.sub_int_beg_pts);
NAG_FREE(qp.sub_int_end_pts);
NAG_FREE(qp.sub_int_result);
NAG_FREE(qp.sub_int_error);
}
printf("%g\n", result);
}
### Multi-dimension Integral Function
For integrals of dimension higher than 2, you can call the NAG integrator function d01wcc to perform the integration.
Our user defined call back function will be passed to the NAG d01wcc function.
double NAG_CALL f_callback(int n, double* z, Nag_User *comm)
{
double tmp_pwr;
tmp_pwr = z[1]+1.0+z[3];
return z[0]*4.0*z[2]*z[2]*exp(z[0]*2.0*z[2])/(tmp_pwr*tmp_pwr);
}
Main function:
void nag_d01wcc_ex()
{
// Input variables
int ndim = NDIM; // the integral dimension
double a[4], b[4];
for(int ii=0; ii < 4; ++ii) // integration interval
{
a[ii] = 0.0;
b[ii] = 1.0;
}
int minpts = 0;
int maxpts = MAXPTS; // maximum number of function evaluation
double eps = 0.0001; // set the precision
// Output variable
double finval, acc;
Nag_User comm;
NagError fail;
d01wcc(ndim, f_callback, a, b, &minpts, maxpts, eps, &finval, &acc,
&comm, &fail);
if (fail.code != NE_NOERROR)
printf("%s\n", fail.message);
if (fail.code == NE_NOERROR || fail.code == NE_QUAD_MAX_INTEGRAND_EVAL)
{
printf("Requested accuracy =%12.2e\n", eps);
printf("Estimated value =%12.4f\n", finval);
printf("Estimated accuracy =%12.2e\n", acc);
}
}
## Differentiation
The ocmath_derivative function is used to do simple derivative calculations without smoothing. The function is declared in ocmath.h as shown below.
int ocmath_derivative(
const double* pXData, double* pYData, uint nSize, DWORD dwCntrl = 0);
The function ignores all missing values and computes the derivative by taking the average of the two slopes between the point and each of its neighboring data points. If the dwCntrl argument uses the default value of 0, the function fills in the average when data changes direction.
if( OE_NOERROR == ocmath_derivative(vx, vy, vx.GetSize()) )
out_str("successfully");
If dwCntrl is set to DERV_PEAK_AS_ZERO, the function fills in zero if data changes direction.
if( OE_NOERROR == ocmath_derivative(vx, vy, vx.GetSize(), DERV_PEAK_AS_ZERO) )
out_str("successfully"); | {"extraction_info": {"found_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": 0.6859985589981079, "perplexity": 14349.997161915513}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662534773.36/warc/CC-MAIN-20220521014358-20220521044358-00028.warc.gz"} |
https://www.scm.com/highlights/uncovering-the-capacitive-mechanism-of-birnessite-with-experiments-and-reaxff/ | # Capacitive mechanism of birnessite uncovered by experiments and simulations
The adsorption and intercalation of ions from the electrolyte into the interlayers of the electrode material is a key process in electrochemical energy storage. It is described by two adsorption extremes: 1) adsorption involving mainly electrostatic interactions, leading to non-Faradaic electric double layer (EDL), and 2) specific adsorption involving chemical bonding, leading to Faradaic pseudocapacitance. Typically, these mechanisms are considered to be mutually exclusive.
While cyclic voltammetry and galvanostatic cycling experiments suggest an EDL formation in birnessite (a hydrated layered manganese oxide – δ-MnO2; AxMnO2·yH2O, where A is an alkali ion, ~0.1<x<0.7 and 0.3<y<2), measurements of changes in structure, bonding, and Mn oxidation state suggests a pseudocapacitive behavior.
To resolve this distinction between EDL and pseudocapacitance in birnessite, researchers at NC State, Penn State, ORNL, and UC Riverside have investigated the effects of interlayer confinement and hydration using a multimodal experimental and computational study in a recent Nature Materials paper.
The study revealed that the capacitive behavior of birnessite originates from the cation intercalation into a hydrated interlayer. The majority of the changes in structure and mass can be attributed to the cation (de)intercalation, as shown by XRD, EQCM, AFM dilatometry, DFT, and ReaxFF-Grand Canonical Monte Carlo (GCMC) simulations. The ReaxFF-GCMC simulations demonstrated that the most probable intercalants are H2O and K+, as opposed to H3O+ or SO42-, and the local inhomogeneity in the interlayer leads to the flexibility of the birnessite layers. However, the distance between the interlayer K+ and the surface oxygen remains large (~3Å), considering the smaller solvation shell due to confinement.
Therefore, the capacitive charge storage under confinement is not purely EDL or pseudocapacitive, but a continuum based on the interaction distance between the intercalated ion and the host material.
More info: GCMC, ReaxFF (the simulations in the paper were performed with the standalone ReaxFF in AMS2019.3) | {"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": 0.9218724370002747, "perplexity": 7929.130285665349}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1642320300849.28/warc/CC-MAIN-20220118122602-20220118152602-00109.warc.gz"} |
https://deustotech.github.io/dycon-toolbox-documentation/posts/03-DynamicsInterface/T03_DynamicsInterface/ | # Interface for Dynamics (ODEs)
DyCon Toolbox aims to group all the problems studied by the research team of the chair of mathematics. That is why it is necessary to create a common interface for you dissolve studied equations. To get an idea of the variety of equations involved we will name some:
• Heat Equation
• Population Dynamics
• Collective Behavior
• Schrodinger Equation
• Burgers Equation
• Waves Equation
Since these equations can be solved in different ways, we have opted to create a communication interface with external programs. All the equations that are defined in DyCon toolbox they will be represented by programming classes. So that the classes defined are compatible with the entire system must meet the following requirements.
• They must have a property InitialCondition, which will be a vector double of $[n \times 1]$ dimensions
• They must have a tspan property, indicating the integration intervals. This must be a vector double $[1 \times Nt]$ , where Nt is the number of points in time.
• They must have a method ‘solve’, which resumes the dynamics for that initial condition and for that interval ‘tspan’, This method must accept an optional parameter ‘Control’, which allows solving the dynamics dependent on a function over time. This optional parameter must be an array of dimensions $[m \times Nt]$, where m is the dimension of the control vector
These simple requirements allow to make conenxiones to other specialized programs in the resolution of the different types of equations, previously mentioned. Dycon Toolbox has already implemented a general version to define ODEs. If we wanted to define the following ODE:
We could define as follows:
Symbolic State and Control Vectors
Y = sym('y',[2 1]); U = sym('u',[2 1]);
%% Dynamics Definition
F = @(t,Y,U,Params) [ U(1) + sin(Y(1)*Y(2)) + (Y(1)*Y(2)) ; ...
U(2) + Y(2) + cos(Y(1)*Y(2)) ] ;
dynamics = ode(F,Y,U);
The class ode allows you to store all the information related to the dynamics, and meets all requirements. If we look inside this function
dynamics
dynamics =
ode with properties:
StateVector: [1x1 struct]
Control: [1x1 struct]
DynamicEquation: [1x1 SymNumFun]
Params: [0x0 param]
Derivatives: [1x1 odeDerivatives]
InitialCondition: [2x1 double]
FinalTime: 1
Nt: 10
MassMatrix: [2x2 double]
label: ''
Solver: @eulere
SolverParameters: {}
tspan: [1x10 double]
ControlDimension: 2
StateDimension: 2
dt: 0.1000
You can see the InitialCondition property.
There is also the solver method that allows solving the dynamics.
[tspan,solution] = solve(dynamics); | {"extraction_info": {"found_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": 0.6086548566818237, "perplexity": 2761.229126186608}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-35/segments/1566027320156.86/warc/CC-MAIN-20190824084149-20190824110149-00031.warc.gz"} |
https://dzone.com/articles/euro-2016-predictions-using-team-rating-systems | {{announcement.body}}
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# Euro 2016 Predictions Using Team Rating Systems
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# Euro 2016 Predictions Using Team Rating Systems
### Complex mathematics to rank European soccer teams through the 2016 championship and doing predictive analytics. Focus on Data Science.
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The 2016 UEFA European Championship is about to kick-off in a few hours in France with 24 national teams looking to claim the title. In this post, we’ll explain how to utilize various football team rating systems in order to make Euro 2016 predictions.
## Rating Systems for Football Teams
Have you ever wondered how to predict the outcome of a football match? One of the basic techniques for doing so is to use a rating system. Usually, a rating system assigns each team a single parameter — its rating — based on its performance in previous games. These ratings can then be used to generate predictions for future matches. However, there are many rating systems to choose from. In this post, we will review several methods used for rating football a.k.a. soccer teams (of course, these methods can also be applied to other sports). Next, we will use these rating systems to generate our Euro 2016 predictions.
### Elo Rating System
However, before getting started with football, we’ll have to briefly discuss… chess. In the previous century, Arpad Elo, a Hungarian-American physicist, proposed a rating system to assess chess players’ performance. Since its development, the system has been widely adapted for other sports and online gaming. It also serves as the foundation for other rating systems, such as: Glicko or TrueSkill. The Elo model’s appealing formulation, elegance and, most importantly, accuracy, contributed to its popularity.
Let’s briefly introduce the Elo model. The general idea is that the Elo model updates its ratings based on what result it expects prior to the game and its actual outcome. There are two steps in compiling team ratings. First of all, given two team ratings ri and rj, one can derive the expected outcome of their match by using the so-called sigmoid function applied to the difference in their ratings. This function takes values from 0 to 1 and has a direct interpretation as a probability estimate. The exact formula is:
p_{ij} = \frac{1}{1 + e^{-a(r_{i}\ -\ r_{j} +\ h)}},
Where a is a scaling factor and h is an extra points parameter for the home team, which has a slight advantage over the visiting team (in chess, a parallel advantage is given to the ‘White’ player who always makes the first move). Given the predicted outcome pij and actual outcome oij equal to 1 in case of team i‘s win, 0.5 in case of a tie and 0 for team j’s win, the ratings are updated as follows:
r_i^{new} = r_i + k \cdot (o_{ij} -\ p_{ij})
And accordingly for the second team:
r_j^{new} = r_j -\ k \cdot (o_{ij} -\ p_{ij})
Here, k is the so-called K-factor, which governs the magnitude of rating changes. Note that in its original formulation the Elo system only predicts binary outcomes with 0.5 being interpreted as a draw. To generate the probability of a tie we used a simple method suggested here.
As far as football is concerned, Elo ratings’ implementation is maintained at EloRatings.net website. Moreover, the system is also the basis of the FIFA Women’s World Ranking. Notably, these systems have been documented to work better than FIFA’s Men’s Ranking when considering the ranking systems’ predictive capabilities. We will employ both versions of the Elo model in their original formulation to generate the predictions below.
### Ordinal Logistic Regression Ratings
Another way of estimating team ratings is to use an ordinal regression model. This model is an extension of the basic logistic regression model to ordered outcomes – in this case win, draw and loss. Somewhat analogous to the Elo system, the probabilities of the occurrence of these events, given the two teams’ ratings ri and rj are determined as:
\begin{align*}
\mathbb{P}(\textrm{team}\ i\ \textrm{wins}) &= \frac{1}{1+e^{c\ -\ (r_i -\ r_j +\ h)}},\\
\mathbb{P}(\textrm{draw}) &= \frac{1}{1+e^{-c\ -\ (r_i -\ r_j +\ h)}}\ -\ \frac{1}{1+e^{c\ -\ (r_i -\ r_j +\ h)}},\\
\mathbb{P}(\textrm{team}\ j\ \textrm{wins}) &= 1\ -\ \frac{1}{1+e^{-c\ -\ (r_i -\ r_j +\ h)}},
\end{align*}
Where c > 0 is a parameter governing draw margin and h is used to adjust for home team advantage. Here, unlike in the original Elo model, the probability of a draw is modeled explicitly (in case c = 0 we arrive at the Elo’s expected outcome equation provided previously). Using these equations and the method of maximum likelihood, one can estimate team ratings ri, c and the home team advantage parameters.
### Least Squares Method
The next rating system is based on a simple observation that the difference si – sj in the scores produced by the teams should correspond to the difference in ratings:
s_i -\ s_j = r_i -\ r_j + h
Again, h is a correction for the home team i advantage. The rating system’s name originates from its estimation method: one finds ratings ri such that the sum of squared differences (over a set of games) between the two sides of the above equation is minimal. Kenneth Massey’s website, among others, compiles and maintains a version of the rating system for various sports.
For the least squares model, we still need to generate probabilities for particular outcomes. Once again, we do this by using the sigmoid function analogously to the Elo model.
### Poisson Model
The final rating system that we’ll discuss is based on the assumption that the goals scored by a team can be modeled as a Poisson distributed variable. This distribution is applicable in situations in which we deal with count data, e.g., the number of accidents, telephone calls or… goals scored — the mean rate of this variable is dependent on the attacking capabilities of a team and the defensive skills of its opponent. This extends ratings to two parameters — offensive and defensive skills per team as opposed to a single parameter in the methods discussed above.
Given the attacking and defensive skills of teams i and j, ai, aj and di, dj, respectively, the rates of Poisson variables for a home team i and visiting team j, λ and μ respectively, are modeled as:
\log(\lambda) = i + h + a_i -\ d_j
\log(\mu) = i + a_j -\ d_i
Given a dataset of matches, one can estimate the team rating parameters using the maximum likelihood method. Here, we employ the basic version of the model that assumes that the Poisson variables modeling the goals scored by the teams, given their rating parameters, are independent.
## Tuning the Predictive Power
We used the rating systems presented here to estimate win, draw and loss probabilities for every pair of possible matchups among the 24 teams participating in Euro 2016. Given these probabilities, we simulated the tournament multiple times and computed each team’s probability of winning it all. We used the database of international football match results provided at this website (thanks to Christian Muck for generously exporting the data).
First of all, the rating systems involve some adjustable parameters e.g., weights for importance of matches (friendly vs. World Cup final), a weighing function for most recent results and regularization (to avoid overfitting of rating models to historical results). We then tuned these parameters to maximize the predictive accuracy of the models: using a sample of games, we predicted their results and evaluated them. For tuning the parameters, we chose matches from major international tournaments – World Cup finals, European Championships and Copa America (South American continental championships).
The parameters of ratings systems are chosen for World Cup finals held between 1994 and 2010 (5 tournaments), UEFA European Championships 1996 – 2008 (4) and Copa America finals 1999 – 2011 (5). This accounts for a set of 562 matches. The prediction accuracy is evaluated using logarithmic loss (so-called logloss). It is an error metric that is often used to evaluate probabilistic predictions. Perhaps a more direct interpretation is provided by accuracy – this is just the percentage of matches that were correctly predicted by a given method. The table below presents logloss for probabilities of match outcome as well as accuracy of predictions for each method.
Method Logloss Accuracy EloRatings.net 0.9818 52% FIFA Women World Rankings 0.9934 52% Ordinal Logistic Regression 0.9638 53% Least Squares 0.9553 55% Poisson Ratings 0.9646 55%
The estimates below might be overly optimistic since they were chosen so as to minimize the prediction error on this specific set of games. To validate the methods more thoroughly, we used 121 other matches from the three most recent tournaments – the 2014 World Cup finals, the 2012 European championships and 2015 Copa America finals. The results are presented below. To provide some context for the numbers, we present a benchmark solution of random guessing and probabilities derived from an average of bookmakers’ odds. A random guess yields a logarithmic loss of -log(1/3) ≈ 1.1 and accuracy of 33% for a three-way outcome.
Method Logloss Accuracy EloRatings.net 1.0074 55% FIFA Women World Rankings 1.0032 54% Ordinal Logistic Regression 0.9972 50% Least Squares 0.9949 56% Poisson Ratings 0.9981 55% Random guess 1.0986 33% Bookmakers 0.9726 52% Ensemble 0.9919 55%
The results achieved by bookmakers (in terms of logloss) are better than all the individual rating methods. Of course, the bookmakers can include some additional information on player injuries, suspensions or a team’s form during the contest — this provides them with an advantage over the models. Including such external information would be the next step to enhancing the accuracy of the presented models. In any case, the accuracy of predictions is slightly better in case of the rating systems. The bottom row of the table presents results for an ensemble method – which is the average of predictions for the three best performing methods: least squares, Poisson and ordinal regression ratings. It is a simple method for increasing the predictive power of individual models. We observe that this method slightly improves logloss while maintaining accuracy.
The rating methods presented here have some limitations. There are many factors influencing match results and we only covered simple predictive models based on historical data. Naturally, one could use some external and more sophisticated information e.g., players and their skills, and include it in a model. We encourage you to think about other factors playing a role in match outcomes which could be included in a model. This could greatly improve the models’ accuracy!
## Euro 2016 Predictions
Given match outcome probabilities for each possible matchup, we simulated 1,000,000 Euro 2016 tournaments. We sampled only win, draw and loss results. If – after considering head-to-head results – the teams are still tied in the group stage, we resolved such ties randomly. According to the tournament’s official rules, we should use goal differences, however, this information is not available in our simulation. Notably, coin-tosses (random outcome) were used to resolve ties (if the game was tied after extra-time) before the penalty shoot-out was “invented.” For instance, on its way to winning Euro 1968, Italy “won” its semifinal with the USSR through a coin toss. Although we do not support this manner of deciding the outcomes of sporting events, we employ drawing lots if teams are tied at the end of the tournament’s group stage. If there is a draw in the playoffs, we sample the result again.
And… here are the predictions generated using the ensemble of the three best-performing ratings systems! The consecutive columns indicate the probability of advancing to a given stage of the competition. For example, the number next to Portugal in the first column indicates that there is a 91.37% chance that it will advance past the group stage. On the other hand, in the case of Spain, there is a 33.95% chance that it will reach the Euro 2016 final. The last column indicates a team’s chance of winning the whole tournament.
Team Last 16 Quarterfinals Semifinals Final Champions France 98.01% 82.6% 67.71% 51.21% 37.55% Spain 92.6% 72.24% 51.11% 33.95% 19.08% Germany 94.71% 70.41% 45.99% 24.88% 13.21% England 93.52% 67.5% 40.87% 22.25% 10.4% Belgium 84.38% 48.2% 26.1% 11.51% 4.55% Portugal 91.37% 54.7% 26.31% 12.09% 4.42% Italy 72.43% 33.38% 14.83% 5.26% 1.55% Ukraine 76.81% 37.05% 15.5% 5.53% 1.52% Croatia 66% 31.92% 14.65% 5.27% 1.5% Russia 75.34% 37.84% 13.07% 4.29% 1.14% Turkey 61.9% 27.97% 12.07% 4% 1.05% Switzerland 69.98% 30.49% 11.8% 3.97% 0.88% Poland 67.4% 26.58% 9.35% 2.77% 0.6% Sweden 57.89% 20.76% 7.45% 2.11% 0.47% Romania 62.64% 23.82% 8.07% 2.35% 0.45% Austria 71.63% 27.01% 7.46% 2.07% 0.43% Slovakia 63.66% 25.57% 6.96% 1.79% 0.37% Republic of Ireland 54.68% 18.64% 6.38% 1.72% 0.35% Czech Republic 46.28% 16.19% 5.6% 1.44% 0.29% Hungary 56.86% 16.08% 3.37% 0.69% 0.11% Iceland 47.81% 11.32% 2.02% 0.36% 0.05% Albania 31.46% 6.62% 1.26% 0.19% 0.02% Wales 34.29% 7.98% 1.19% 0.16% 0.02% Northern Ireland 28.32% 5.11% 0.88% 0.13% 0.01%
Some of you might find these predictions surprising – and our discussion thread is now open! As far as our thoughts are concerned, first of all, we see that France tops the ranking. The 12th man is behind them – they are playing at home and the methods we used give them some edge due to this fact. On the other hand, the prediction for four-time World Cup winners Italy is somewhat discouraging. In recent years, Italy has seen disappointing results, including draws with Armenia, Haiti and Luxembourg (not to mention their 2010 and 2014 World Cup records). However, what the rating system could not infer is the fact that the Italian team usually rises to the occasion when faced with a major challenge – which usually happens at the big tournaments. Russia’s perhaps surprisingly high position in the ranking might be partially attributed to the easier (according to the rating systems that we used) group stage opponents they will face: Wales, Slovakia and England.
All in all, no team is condemned to lose before the start of the tournament and that is the very beauty of sports. We might well end up with a surprising result, such as Greece’s Euro 2004 triumph… so, which team will upset the favorites this year?
Topics:
big data, big data analytics, deep learning, machine learning
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Published at DZone with permission of Jan Lasek , DZone MVB. See the original article here.
Opinions expressed by DZone contributors are their own. | {"extraction_info": {"found_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": 0.4681685268878937, "perplexity": 5103.1551015909035}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-34/segments/1596439738950.31/warc/CC-MAIN-20200812225607-20200813015607-00010.warc.gz"} |
https://www.easyfreeware.com/font_xplorer_lite-12710-freeware.html | # Font Xplorer Lite
License: Freeware Size: 799.0 KB Date Added: 06 January, 2009 Category: Desktop / Fonts Author: Moon Software
Easy to use and free font viewer program Font Xplorer Lite is an easy to use and free font viewer program.
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http://mathhelpforum.com/calculus/27301-separable-variables-differential-equations.html | # Math Help - Separable Variables-Differential Equations
1. ## Separable Variables-Differential Equations
Hello,
I am having trouble solving the 2 following problems.
Given the differential equation solve by separation of variables.
1. sec^2(x) dy + csc(y) dx =0
I have tried to get the y's on the left and the x's on the right and integrate, but I cannot get the correct solution. This is what I have so far....
1/(csc(y)) dy = 1/(sec^2(x))
But I'm just not getting 4cos(y)=2x+sin(2x)+c
2. dy/dx = (xy + 3x - y-3) / (xy - 2x + 4y -8)
On this problem I am not sure where to start.
Any help is greatly appreciated. Thanks!
2. Originally Posted by yellowrose
Hello,
I am having trouble solving the 2 following problems.
Given the differential equation solve by separation of variables.
1. sec^2(x) dy + csc(y) dx =0
I have tried to get the y's on the left and the x's on the right and integrate, but I cannot get the correct solution. This is what I have so far....
1/(csc(y)) dy = 1/(sec^2(x))
But I'm just not getting 4cos(y)=2x+sin(2x)+c
$\sec^2 x ~dy + \csc y ~dx = 0$
$\Rightarrow \sec^2 x ~dy = - \csc y ~dx$
$\Rightarrow \sin y ~dy = - \cos^2 x ~dx$
now continue
3. Originally Posted by yellowrose
Hello,
I am having trouble solving the 2 following problems.
Given the differential equation solve by separation of variables.
1. sec^2(x) dy + csc(y) dx =0
I have tried to get the y's on the left and the x's on the right and integrate, but I cannot get the correct solution. This is what I have so far....
1/(csc(y)) dy = 1/(sec^2(x))
Mr F says: $\Rightarrow \sin y \, dy = \cos^2 x \, dx \Rightarrow \int \sin y \, dy = \int \cos^2 x \, dx$.
Note that from the double angle formula $\cos (2x) = 2 \cos^2 x - 1$, $\cos^2 x = \frac{1}{2} (\cos(2x) + 1)$.
[snip]4cos(y)=2x+sin(2x)+c
[snip]
..
4. Originally Posted by yellowrose
[snip]
2. dy/dx = (xy + 3x - y-3) / (xy - 2x + 4y -8)
On this problem I am not sure where to start.
Any help is greatly appreciated. Thanks!
Note that $\frac{dy}{dx} = \frac{xy + 3x - y-3}{xy - 2x + 4y} = \frac{y(x - 1) + 3(x - 1)}{y(x + 4) - 2(x + 4)}$
$= \frac{y + 3}{y\left(\frac{x+4}{x-1} \right) - 2\left(\frac{x+4}{x-1} \right)} = \frac{y + 3}{\left(\frac{x+4}{x-1} \right) (y - 2)} = \left(\frac{x-1}{x+4} \right) \left( \frac{y + 3}{y - 2} \right)$.
*Ahem* or you could just spot that $\frac{xy + 3x - y-3}{xy - 2x + 4y} = \frac{x(3 + y) - (3 + y)}{x(y - 2) + 4(y - 2)} = \frac{(x - 1)(3 + y)}{(x + 4)(y - 2)}$ .......
I'll come back to this point if you still need help with it. Suffice to say, it's now separable .....
5. Originally Posted by Jhevon
$\sec^2 x ~dy + \csc y ~dx = 0$
$\Rightarrow \sec^2 x ~dy = - \csc y ~dx$
$\Rightarrow \sin y ~dy = - \cos^2 x ~dx$
now continue
I integrated that and got
-cos(y)=-.5(sin(x)cos(x)+x)+c
I'm sorry I just can't figure out how to get this into simplier terms. So that I just have a y on the left.
6. Originally Posted by yellowrose
I integrated that and got
-cos(y)=-.5(sin(x)cos(x)+x)+c
I'm sorry I just can't figure out how to get this into simplier terms. So that I just have a y on the left.
well, you could take the arccosine of both sides (remove the minus signs). but i don't think you have to get the answer any simpler than what you have
7. Originally Posted by mr fantastic
..
Thanks for your help. I understand that I need to use the rule you gave me, but I'm not sure how. Do I use this before or after I integrate? I guess I'm just really confused about this problem.
8. Originally Posted by yellowrose
Thanks for your help. I understand that I need to use the rule you gave me, but I'm not sure how. Do I use this before or after I integrate? I guess I'm just really confused about this problem.
The rule I gave for $cos^2 x$ gets used before integrating .... it's used to facilitate the integration of $cos^2 x$.
9. Originally Posted by mr fantastic
Note that $\frac{dy}{dx} = \frac{xy + 3x - y-3}{xy - 2x + 4y} = \frac{y(x - 1) + 3(x - 1)}{y(x + 4) - 2(x + 4)}$
$= \frac{y + 3}{y\left(\frac{x+4}{x-1} \right) - 2\left(\frac{x+4}{x-1} \right)} = \frac{y + 3}{\left(\frac{x+4}{x-1} \right) (y - 2)} = \left(\frac{x-1}{x+4} \right) \left( \frac{y + 3}{y - 2} \right)$.
*Ahem* or you could just spot that $\frac{xy + 3x - y-3}{xy - 2x + 4y} = \frac{x(3 + y) - (3 + y)}{x(y - 2) + 4(y - 2)} = \frac{(x - 1)(3 + y)}{(x + 4)(y - 2)}$ .......
I'll come back to this point if you still need help with it. Suffice to say, it's now separable .....
Some further help:
$\frac{dy}{dx} = \left(\frac{x-1}{x+4} \right) \left( \frac{y + 3}{y - 2} \right) \Rightarrow \int \frac{y - 2}{y + 3} \, dy = \int \frac{x-1}{x+4} \, dx$.
Note that:
$\frac{y - 2}{y + 3} = \frac{(y + 3) - 5}{y + 3} = 1 - \frac{5}{y + 3}$
$\frac{x - 1}{x + 4} = \frac{(x + 4) - 5}{x + 4} = 1 - \frac{5}{x + 4}$
10. Originally Posted by mr fantastic
Note that $\frac{dy}{dx} = \frac{xy + 3x - y-3}{xy - 2x + 4y} = \frac{y(x - 1) + 3(x - 1)}{y(x + 4) - 2(x + 4)}$
$= \frac{y + 3}{y\left(\frac{x+4}{x-1} \right) - 2\left(\frac{x+4}{x-1} \right)} = \frac{y + 3}{\left(\frac{x+4}{x-1} \right) (y - 2)} = \left(\frac{x-1}{x+4} \right) \left( \frac{y + 3}{y - 2} \right)$.
*Ahem* or you could just spot that $\frac{xy + 3x - y-3}{xy - 2x + 4y} = \frac{x(3 + y) - (3 + y)}{x(y - 2) + 4(y - 2)} = \frac{(x - 1)(3 + y)}{(x + 4)(y - 2)}$ .......
I'll come back to this point if you still need help with it. Suffice to say, it's now separable .....
I separated them, took the integral of both sides, raised it to the e, and got
e^y(y+3)^5=e^x(x+4)^5
but the ans states e^x(y+3)^5=e^y(x+4)^5
could you tell me what I'm doing different....or is what I have still correct? Thanks!
11. Originally Posted by yellowrose
I separated them, took the integral of both sides, raised it to the e, and got
e^y(y+3)^5=e^x(x+4)^5
but the ans states e^x(y+3)^5=e^y(x+4)^5
could you tell me what I'm doing different....or is what I have still correct? Mr F says: Your answer is not the same as the book's answer. The exponent terms are switched!
Thanks!
Originally Posted by mr fantastic
Some further help:
$\frac{dy}{dx} = \left(\frac{x-1}{x+4} \right) \left( \frac{y + 3}{y - 2} \right) \Rightarrow \int \frac{y - 2}{y + 3} \, dy = \int \frac{x-1}{x+4} \, dx$.
Note that:
$\frac{y - 2}{y + 3} = \frac{(y + 3) - 5}{y + 3} = 1 - \frac{5}{y + 3}$
$\frac{x - 1}{x + 4} = \frac{(x + 4) - 5}{x + 4} = 1 - \frac{5}{x + 4}$
So you have:
$\int 1 - \frac{5}{y + 3} \, dy = \int 1 - \frac{5}{x+4} \, dx$
$\Rightarrow y - 5 \ln |y + 3| = x - 5 \ln |x + 4| + C$
$\Rightarrow y + \ln |x + 4|^5 = x + \ln |y + 3|^5 + C$
Exponentiate both sides, and let $A = e^C$:
$\Rightarrow e^y (x + 4)^5 = Ae^x (y + 3)^5$
which is the same as you book's answer (except that your book did a very bad thing and either forgot to include the arbitrary constant of integration or conveniently set A = 1).
I could guess what mistake you made, but I'll bet that the mistake is obvious in hindsight | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 31, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9633151888847351, "perplexity": 613.5576017065118}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-48/segments/1448398468396.75/warc/CC-MAIN-20151124205428-00112-ip-10-71-132-137.ec2.internal.warc.gz"} |
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# A woman sold 100 oranges at $12.10, some at the rate of 3 Question banks Downloads My Bookmarks Reviews Important topics Author Message TAGS: Director Joined: 07 Jun 2004 Posts: 614 Location: PA Followers: 3 Kudos [?]: 277 [4] , given: 22 A woman sold 100 oranges at$12.10, some at the rate of 3 [#permalink] 26 Jul 2010, 07:39
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A woman sold 100 oranges at $12.10, some at the rate of 3 for 35 cents and the rest at 7 for 85 cents. How many were sold at the first rate? A. 45 B. 21 C. 9 D. 15 E. 12 [Reveal] Spoiler: OA _________________ If the Q jogged your mind do Kudos me : ) Manager Joined: 02 Apr 2010 Posts: 103 Followers: 5 Kudos [?]: 98 [11] , given: 18 Re: Oranges sold at different rates [#permalink] 26 Jul 2010, 08:58 11 This post received KUDOS 1 This post was BOOKMARKED This can be solved like a classical mixture problem but numbers are awkward to deal with. It's easier to just look at the answer choices. You know that a multiple of 3 oranges has to be sold at the first rate, and a multiple of 7 at the second rate. You simple subtract the answer choices for the first rate from 100 and check whether the remainder (i.e. the number of oranges sold at the second rate) is a multiple of 7. 100 - 45 = 55 => not a multiple of 7 so exclude 100 - 21 = 79 => not a multiple of 7 so exclude 100 -9 = 91 => a multiple of 7 so keep 100 - 15 = 85 => not a multiple of 7 so exclude 100 - 12 = 88 => not a multiple of 7 so exclude Hence, answer choice 9 is correct. Senior Manager Status: mba here i come! Joined: 07 Aug 2011 Posts: 271 Location: Pakistan Concentration: Strategy, Marketing GMAT 1: 680 Q46 V37 GMAT 2: Q V Followers: 32 Kudos [?]: 782 [5] , given: 48 Re: Oranges sold at different rates [#permalink] 29 Feb 2012, 09:03 5 This post received KUDOS $$\frac{35}{3}x+\frac{85}{7}(100-x)=1210$$ solve and you'll get x = 9 _________________ press +1 Kudos to appreciate posts Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 5461 Location: Pune, India Followers: 1337 Kudos [?]: 6797 [3] , given: 177 Re: Oranges sold at different rates [#permalink] 15 Mar 2012, 21:45 3 This post received KUDOS Expert's post GMATD11 wrote: $$\frac{35}{3}x+\frac{85}{7}(100-x)=1210$$ Can you pls explain the Right hand side of equation. Won't it be 12.10 The equation equates the total selling price. He gets$12.10 i.e. 1210 cents.
If he sold x oranges for 35/3 cents and (100-x) for 85/7 cents, this is a total of
(35/3) * x + (85/7) * (100-x) cents. You equate cents to cents.
Also, you can use the weighted average formula here:
w1/w2 = (85/7 - 121/10)/(121/10 - 35/3) = 9/91
Total 9+91 is 100. So he sells 9 oranges at 35 for 3 and 91 oranges at 85 for 7.
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Re: Oranges sold at different rates [#permalink] 15 Mar 2012, 20:18
$$\frac{35}{3}x+\frac{85}{7}(100-x)=1210$$
Can you pls explain the Right hand side of equation.
Won't it be 12.10
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Re: Oranges sold at different rates [#permalink] 16 Aug 2012, 23:47
GMATD11 wrote:
$$\frac{35}{3}x+\frac{85}{7}(100-x)=1210$$
Can you pls explain the Right hand side of equation.
Won't it be 12.10
Hi,
Because we are taking all the values in cents so we have converted $12.10 into cents which is 1210 cents. as 1 cent =0.01 Dollar Hope this helps. Try and fail but never fail to try. GMAT Club Legend Joined: 09 Sep 2013 Posts: 4784 Followers: 296 Kudos [?]: 52 [0], given: 0 Re: A woman sold 100 oranges at$12.10, some at the rate of 3 [#permalink] 29 Sep 2013, 07:23
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Re: A woman sold 100 oranges at $12.10, some at the rate of 3 [#permalink] 01 Oct 2013, 04:31 for such question need a will power to take on some random complicated numbers. i derived the equation but goofed up with the numbers _________________ “Confidence comes not from always being right but from not fearing to be wrong.” GMAT Club Legend Joined: 09 Sep 2013 Posts: 4784 Followers: 296 Kudos [?]: 52 [0], given: 0 Re: A woman sold 100 oranges at$12.10, some at the rate of 3 [#permalink] 02 May 2015, 00:35
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Re: A woman sold 100 oranges at $12.10, some at the rate of 3 [#permalink] 02 May 2015, 08:14 simple question.... killer calculation.. WOW... rxs0005 wrote: A woman sold 100 oranges at$12.10, some at the rate of 3 for 35 cents and the rest at 7 for 85 cents. How many were sold at the first rate?
A. 45
B. 21
C. 9
D. 15
E. 12
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Re: A woman sold 100 oranges at $12.10, some at the rate of 3 [#permalink] 02 May 2015, 08:14 Similar topics Replies Last post Similar Topics: 3 A woman is planning a trip that involves 3 connecting trains 3 13 Jan 2014, 12:07 If x = (-100)^1/3 * (100)^3 0 02 Sep 2013, 02:14 Prepare some Orange juice 2 25 Mar 2010, 21:55 1 Jacob purchased 100 boxes of oranges at$8.00 per box. He 1 09 Oct 2008, 05:07
Of the 25 cars sold at a certain dealership yesterday, some 5 09 Sep 2007, 15:25
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http://mathhelpforum.com/advanced-statistics/129060-how-do-probability.html | # Thread: How to do probability >-<
1. ## How to do probability >-<
Jerseys will sell for $30. Random variable X is number of jerseys that will be sold. E(X)=100 and R is the total revenue (R=30X). What is the expected revenue. I have no idea what formula to use. I thought conditional probability because revenue is dependent on the sale of the jerseys, but the formula does not match my data, or I am writing it back the front. Why is it not$3000...?
I think if I knew the formula I could work it out~ maybe :-)
2. Originally Posted by char111
Jerseys will sell for $30. Random variable X is number of jerseys that will be sold. E(X)=100 and R is the total revenue (R=30X). What is the expected revenue. I have no idea what formula to use. I thought conditional probability because revenue is dependent on the sale of the jerseys, but the formula does not match my data, or I am writing it back the front. Why is it not$3000...?
I think if I knew the formula I could work it out~ maybe :-)
Definition of the expectation of a function of a RV:
$E(f(X))=\int f(x) p_X(x)\; dx$
so:
$
E(30X)=\int 30\; x\; p_X(x)\;dx=30 E(X)
$
where the integrals are over the support of $p_X$.
Make the obvious modification or interpretation for a discrete RV.
CB
3. Thanks Captain Black~ obviously I have no idea because I have not seen this formula before in class nor can I find it in my book.
100 x (30x100)...is that how I plug in my numbers...?
This topic just confuses me the more I try to understand it~ give me SPSS anytime :-) | {"extraction_info": {"found_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": 3, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8299506902694702, "perplexity": 1358.4622697327218}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-22/segments/1495463609054.55/warc/CC-MAIN-20170527191102-20170527211102-00292.warc.gz"} |
http://ask.sagemath.org/question/56047/how-to-solve-a-combined-problem-of-ip-boolean-satisfiability-and-maximization/ | # How to solve a combined problem of IP, Boolean Satisfiability and Maximization? edit
I have a problem in mind that I want to solve, and after doing some research I believe it is a maximization problem that uses both Integer Programming and Boolean Satisfiability.
Now, it's easy enough for me to declare the variables, and assign them a range. But I simply don't know how to go on from there with Sage. So I was hoping that if I explain a thought up example of what I need to do, someone could point me in the right direction.
So I have some sum equations with a lot of variables, and all of the variables are positive integers, including zero. For example, one such equation could be like this:
(A or B) + (C or D or E)=10
This means, that at LEAST one combination of the variables in those two groups must sum up to 10. It could for example be A+C, B+D, A+E, but A+B doesn't matter. And there could be more than one combination thereof that sums up to 10, that also doesn't matter, just whether there's at least one that does.
Now I combine the sum equations I have, into groups, which is where the Boolean part comes in. Any such group can either be true or false. True, if all the sum equations can be solved, i.e. at least one combination in the equation sums up to the desired number. False, if even one of the equations cannot be solved.
So one such group could consist of two equations:
(A or B) + (C or D or E)=10
(A or D) + (B or E)=10
Because I have a lot of different variables, and a lot of equations, I doubt all the groups I will need to make, can all be solved, i.e. all are true. And that is where the Maximization problem comes in. The problem I actually need to solve, is to make as many as the aforementioned groups of equations True. Once I know this, and which groups and thus equations can be solved, I have my solution. And if there are more than one way to achieve the maximum number of solved groups, all those count and are of interest to me.
So this is where I'm at, with a problem I want to solve, and no idea on how to go about solving it with Sage.
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For technical details on solving MILP in Sage and examples, you can refer to the documentation.
As for your specific problem, let us enumerate all clauses appearing in the equations in arbitrary order. For each variable $Q$ present in clause number $i$, let's introduce a binary indicator variable $s_{Q,i}$ telling whether variable $Q$ is taken from this clause. Also, let $t_{Q,i}$ be an integer variable with the value $Q\cdot s_{Q,i}$, which is enforced by the constraints: $$\begin{cases} t_{Q,i} \geq Q - L(1-s_{Q,i}), \\ t_{Q,i} \leq Q + L(1-s_{Q,i}), \\ t_{Q,i} \geq - L s_{Q,i}, \\ t_{Q,i} \leq L s_{Q,i}, \\ \end{cases}$$ where $L$ is a large positive constant (larger than the maximum possible value for $|Q|$).
Now, without loss of generality, suppose that the clauses (A or B) and (C or D or E) in the equation (A or B) + (C or D or E)=10 have numbers 1 and 2, respectively. Then in addition to the above 4 inequalities for each pair $(Q,i)\in \{ (A,1), (B,1), (C,2), (D,2), (E,2)\}$, we introduce the following constraints: $$\begin{cases} s_{A,1} + s_{B,1} = 1, \\ s_{C,2} + s_{D,2} + s_{E,2} = 1, \\ t_{A,1} + t_{B,1} + t_{C,2} + t_{D,2} + t_{E,2} = 10.\qquad (\star) \end{cases}$$ Here the first two constraints enforce that only one variable is taken from each clause, while the constraint $(\star)$ represents the equation itself.
Finally, to deal with the groups of equations, let's enumerate them, and for a group number $j$ let's introduce a binary indicator variable $p_j$ telling whether the group is satisfied. Suppose that the group formed by equations (A or B) + (C or D or E)=10 and (A or D) + (B or E)=10 has number $1$. Then we replace the equation labeled $(\star)$ above, which corresponds to the first equation, with \begin{cases} t_{A,1} + t_{B,1} + t_{C,2} + t_{D,2} + t_{E,2} \geq 10 - M(1-p_1), \\ t_{A,1} + t_{B,1} + t_{C,2} + t_{D,2} + t_{E,2} \leq 10 + M(1-p_1) \end{cases} and similarly for the second equation in the group, where $M$ is a large positive constant (larger than the maximum absolute value of the l.h.s. of the equations).
The objective function to maximize is $\sum_j p_j$, which gives the number of satisfied groups of equations.
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Alright, so before I posted this question, I had a look around the forum, and I noticed that a lot of commenters posted code as answers. So it threw me back that you decided to post math instead, and I've had to use some time to digest it all, as it's been a long time since I've had to deal with that notation.
I understand that the constants L and M are either zero, or their value, because you substract binary variables from 1. But I don't understand how choosing two large constants help enforce the constraints in those equations.
Also, since the s variable is binary, what happens if SC,2 and SE,2 are both 1? Because as I said, I need at least one combination to equal the sum, but not exactly one, there CAN be more.
Finally, I'm not sure how ...(more)
( 2021-03-12 12:45:38 +0200 )edit
Math is needed to solve the problem. My answer explains how to approach your problem. If you concern about actual Sage code, you'd need to give a particular example of the problem for illustration.
Constants $L$ and $M$ are not zero -- they must be large positive constants. Perhaps, you meant them multiplied by a coefficients, which may be 0 or 1. The idea is that whenever these constants come in the inequality with coefficient 1, the corresponding inequality becomes silent (i.e., automatically satisfied).
Both $s_{C,2}$ and $s_{E,2}$ cannot be 1 at the same time, because they must satisfy the constraint $s_{C,2}+s_{D,2}+s_{E,2} = 1$. But there may exist one solution, say, with $s_{C,2}=1$ and $s_{D,2}=s_{E,2}=0$, and another solution with $s_{E,2}=1$ and $s_{C,2}=s_{D,2}=0$.
( 2021-03-12 15:03:03 +0200 )edit
Overall, your question makes an impression that you have trouble with formalizing/posing your problem as MILP (which is quite irrelevant to Sage), and this is what my answer explains how to do. As soon as your problem is formalized as MILP, it can be solved with Sage or any other solver (e.g., CPLEX, Gurobi, etc.).
If you have troubles with Sage specifically within the context of your problem, please let me know what they are.
( 2021-03-12 17:41:38 +0200 )edit | {"extraction_info": {"found_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": 0.7193208932876587, "perplexity": 298.2457064224965}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1618038084601.32/warc/CC-MAIN-20210415065312-20210415095312-00362.warc.gz"} |
http://mathhelpforum.com/pre-calculus/189725-end-point-extrema-print.html | # end-point extrema
• October 7th 2011, 01:22 AM
Stuck Man
1 Attachment(s)
end-point extrema
Is this book wrong about point B? I think it is an end-point but not an end-point minimum. The function at 0 has a lower value.
• October 7th 2011, 02:03 AM
magicka
Re: end-point extrema
Book is correct here:
And end-point minimum if there exists a region in the domain for which B is an end-point (you agreed it's true) and for which $f(B)\leq x, \forall x$. Note: if exists a region, so it doesn't have to be for every region (that would be definition of minimum), but only for a region (in this example use $[3,4]$)
• October 7th 2011, 04:11 AM
Stuck Man
Re: end-point extrema
Thanks. I had started to think it is correct. Surely you are talking about B not A?
• October 7th 2011, 04:19 AM
magicka
Re: end-point extrema
yes, my mistake, I've edited previous post!
• October 7th 2011, 05:50 AM
Stuck Man
1 Attachment(s)
Re: end-point extrema
In this example C and D are end-point minimums aren't they?
• October 7th 2011, 07:12 AM
magicka
Re: end-point extrema
Nope; even though they satisfy second condition they are not endpoints!
• October 7th 2011, 07:44 AM
Stuck Man
Re: end-point extrema
They are end-points of the second and third functions. The book definitely describes these as end-points.
• October 7th 2011, 07:55 AM
magicka
Re: end-point extrema
Could you please copy here how end-point is exactly defined?
And you are watching endpoints of $f(x)$, not every part of it. By that logic you could split function above (one that is defined on -2 to 4) split into infinite many parts and have infinite many end-points.
• October 7th 2011, 08:07 AM
Stuck Man
Re: end-point extrema
Unfortunately it is not defined.
• October 7th 2011, 08:10 AM
Stuck Man
Re: end-point extrema
The book does talk about C and D as being at end-points of the subdomains.
• October 7th 2011, 08:35 AM
Stuck Man
Re: end-point extrema | {"extraction_info": {"found_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": 3, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6923530101776123, "perplexity": 5996.309590657488}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-41/segments/1410657135930.79/warc/CC-MAIN-20140914011215-00159-ip-10-234-18-248.ec2.internal.warc.gz"} |
http://clay6.com/qa/1275/find-the-integrals-of-the-functions | # Find the integrals of the functions$\frac{1}{\sin x\cos^3x}$
$\begin{array}{1 1} \frac{\tan^2x}{2}+\log|\tan x|+c \\ \frac{\tan^2x}{2}-\log|\tan x|+c \\ \frac{\cot^2x}{2}+\log|\tan x|+c \\ \frac{\tan^2x}{2}+\log|\cot x|+c \end{array}$
Toolbox:
• $(i)\;\sin^2x+\cos^2x=1.$
• $(ii)\;Method\;of\;substitution.$
• Let f(x)=t.
• Therefore f'(x)dx=dt.Thus $\int f(x)dx=\int t.dt.$
Given:$I=\int\frac{1}{\sin x\cos x}dx.$
This can be written as,
$I=\frac{\sin^2x+\cos^2x}{\sin x\cos^3x}dx.$
Separating the terms we get,
$I=\int\frac{\sin^2x}{\sin x\cos^3x}dx+\int\frac{\cos^2x}{\sin x\cos^3x}dx.$
$\;\;\;=\int\frac{\sin x}{\cos x}\frac{1}{\cos^2x}dx+\int\frac{\cos x}{\sin x}\frac{1}{\cos^2x}dx.$
$\;\;\;=\int\tan x.\sec xdx+\int\frac{\sec^2}{\tan x}dx.$
Let tan x=t.
On differentiating we get,
$\sec^2xdx=dt.$
By substituting t we get,
$I=\int t.dt+\int\frac{1}{t}.dt.$
On integrating we get,
$\;\;\;=\frac{t^2}{2}+log |t|+c.$
Substituting for t we get,
$\int\frac{\sin^2x+\cos ^2x}{\sin x\cos^3x}dx=\frac{\tan^2x}{2}+log|\tan x|+c.$ | {"extraction_info": {"found_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": 0.9998670816421509, "perplexity": 13601.458417548021}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-05/segments/1516084891316.80/warc/CC-MAIN-20180122113633-20180122133633-00118.warc.gz"} |
https://open.kattis.com/problems/railroad2 | Kattis
Theta likes to play with her DUPLO railway set. The railway set she has consists of pieces of straight tracks, curved tracks, Y-shaped switches, and X-shaped level junctions, as well as bridges that allow one track to cross over another. There are also straight tracks that are railroad crossings to allow car traffic to cross.
Close-ups of some of the pieces are shown below:
To play, she picks a number of X-shaped level junctions and a number of Y-shaped switches and connects them with straight and curved pieces, using bridges as necessary.
Because the set doesn’t include any bumpers, she wants to build a closed track, like all the examples shown in the manual that came with the set:
Unfortunately, sometimes, this doesn’t seem to work with the number of X-shaped level junctions and Y-shaped switches she starts out with.
She quickly figures out exactly when it is possible to build a closed track - can you figure it out, too?
Write a program that outputs if it is possible to build a railroad that does not require any bumpers (i.e., which does not have any dead-end tracks).
## Input
The input consists of a single test case with two integer numbers $X$ ($0 \le X \le 1000$) and $Y$ ($0 \le Y \le 1000$) denoting the number of level junctions and switches, respectively. You may assume that Theta has sufficiently many straight and curved pieces as well as bridges.
## Output
Output possible if she can build a closed track using all level junctions and all switches without any dead ends, or impossible otherwise.
Sample Input 1 Sample Output 1
1 0
possible
Sample Input 2 Sample Output 2
0 2
possible
Sample Input 3 Sample Output 3
1 3
impossible | {"extraction_info": {"found_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": 0.40923935174942017, "perplexity": 1444.803966995954}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1558232258147.95/warc/CC-MAIN-20190525164959-20190525190959-00029.warc.gz"} |
https://mathtuition88.com/2018/02/17/characteristic-polynomial-eigenvalues-eigenvectors/ | ## Characteristic Polynomial, Eigenvalues, Eigenvectors
Characteristic Polynomial, $\det(\lambda I-A)$
\begin{aligned} \lambda\ \text{is an eigenvalue of }A&\iff\det(\lambda I-A)=0\\ &\iff \lambda\ \text{is a root of the characteristic polynomial}. \end{aligned}
Eigenspace
The solution space of $(\lambda I-A)\mathbf{x}=0$ is called the eigenspace of $A$ associated with the eigenvalue $\lambda$. The eigenspace is denoted by $E_\lambda$.
Sum/Product of Eigenvalues
– The sum of all eigenvalues of $A$ (including repeated eigenvalues) is the same as $Tr(A)$ (trace of $A$, i.e. the sum of diagonal elements of $A$)
– The product of all eigenvalues of $A$ (including repeated eigenvalues) is the same as $\det(A)$. | {"extraction_info": {"found_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": 12, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9789413213729858, "perplexity": 587.8788053461467}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1544376824912.16/warc/CC-MAIN-20181213145807-20181213171307-00023.warc.gz"} |
http://www.ques10.com/p/1622/mass-transfer-operation-1-question-paper-dec-201-1/ | Question Paper: Mass Transfer Operation - 1 : Question Paper Dec 2015 - Chemical Engineering (Semester 5) | Mumbai University (MU)
0
Mass Transfer Operation - 1 - Dec 2015
Chemical Engineering (Semester 5)
TOTAL MARKS: 100
TOTAL TIME: 3 HOURS
(1) Question 1 is compulsory.
(2) Attempt any four from the remaining questions.
(3) Assume data wherever required.
(4) Figures to the right indicate full marks.
1(a) Nickel carbonyl (B) is to be produced by passing Carbon monoxide (A) through a bed of nickel spheres. Find $$\dfrac{N_A}{N_A+N_B}$$
Ni+4CO = Ni(CO)4
(2 marks)
1(b) Derive the equation for adiabatic saturation temperature.(8 marks) 1(c) Estimate the diffusivity of benzene in toluene and toluene in benzene at 110°C. The physical properties are as follows :
Component M Boiling point 0C VA at B.P. cm3/ mol μ at 110 0C Cp Benzene 78.11 80.1 86.5 0.24 Toluene 92.13 110.6 118.3 0.26
(10 marks) 2(a) The air pressure in a tyre reduces from 2 bars to 1.99 bars in five days. The volume of air in the tube=0.0253, the surface area 0.5m3 and wall thickness 0.01 metre. The solubility of air in rubber is 0.07 m3/m3. Estimate the diffusivity of air in rubber.(10 marks) 2(b) Derive relation between individual and overall mass transfer coefficient when
(i) Gas phase resistance is controlling
(ii) Liquid phase resistance is controlling
(10 marks)
3(a) An ammonia air mixture containing 2% by volume ammonia is to be scrubbed with water at 10°C in a tower packed with 1.27 cm Ranching rings. The water and gas rates are 1) 70 kg/hr m2 each, based on empty tower cross selection. Estimate the height of tower required if 98% of ammonia in the entering gas is to be absorbed. The tower operates at 1 atm pressure. The equilibrium relation is given by the following equation.
Ye =0.74x
Ye= mole fraction of ammonia in air
X= Mole fraction of ammonia in solution with water.
the height of transfer unit may be taken as equal to z meter.
(12 marks)
3(b) Compare packed tower with tray tower.(8 marks) 4(a) It is desired to dry a certain type of fibre board in sheets 0.131 meter by 0.162 meter by 0.071 meter from 58% to 5% moisture (wet basis) content. Initially from laboratory test data with this fibre board, the rate of dying at constant rate period wad found to be 8.9 kg/m2hr. The critical moisture content was 24.9% and the equilibrium moisture content was 1%. The fiber board is to be dried from one side only and has a bone-dry density of 210kg/m3. Determine the times required for drying. The falling rate may be assumed linear.(10 marks)
Write short note on :-
4(b)(i) Drum dryer(5 marks) 4(b)(ii) Tray dryer(5 marks) 5(a) Give classification of cooling tower. Explain mechanical draft cooling tower in detail.(10 marks) 5(b) Explain loading and flooding in packed column.(5 marks) 5(c) Write short note on welted wall column.(5 marks)
Write short note on any four.
6(a) Humid heat(5 marks) 6(b) Venture scrubber(5 marks) 6(c) Fisk's first law of diffusion(5 marks) 6(d) Diffusion through polymers(5 marks) 6(e) Absorption factor and striping factor.(5 marks) | {"extraction_info": {"found_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": 0.8060692548751831, "perplexity": 10559.568233347183}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-09/segments/1550247489343.24/warc/CC-MAIN-20190219041222-20190219063222-00376.warc.gz"} |
https://www.pims.math.ca/scientific-event/181116-uwcsb | ## University of Washington Colloquium: Sara Billey
• Date: 11/16/2018
• Time: 03:30
Lecturer(s):
Sara Billey
Location:
University of Washington
Topic:
Patterns in Standard Young Tableaux
Description:
Standard Young tableaux are fundamental in combinatorics, representation theory, and geometry. In this talk, we will define these objects and discuss some of their remarkable properties. In particular, we will discuss the connection between the major index generating functions for standard Young tableaux and the $S_n$-representation theory of the coinvariant algebras. The major index statistic was originally defined 100 years ago for permutations and has been very successfully extended to tableaux.
In recent joint work with Matjaz Konvalinka and Joshua Swanson, we study the probability distribution of major index on standard tableaux of fixed partition shape chosen uniformly in terms of the corresponding generating function. We give an explicit hook length style formula for all of the cumulants of these distributions using recent work of Chen--Wang--Wang and Hwang--Zacharovas. The cumulant formula allows us to classify all possible limit laws for any sequence of shapes in terms of a simple auxiliary statistic, aft. We show that any such sequence of distributions with aft approaching infinity is asymptotically normal. This leads to a series of questions concerning locations of zero coefficients, unimodality, and asymptotic estimates for the major index generating functions over all standard tableaux of a fixed shape. We give conjectured answers concerning unimodality and asymptotic estimates.
Sara Billey is a Professor and John Rainwater Faculty Fellow at the University of Washington. Her PhD is from UCSD, and she was at MIT before coming to UW. She is a Fellow of the American Math Society.
Other Information:
When: Friday, November 16, 2018 - 3:30 to 4:30
Where: MEB 248 | {"extraction_info": {"found_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": 0.8662536144256592, "perplexity": 731.5431601600012}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662550298.31/warc/CC-MAIN-20220522220714-20220523010714-00181.warc.gz"} |
https://qetlab.com/wiki/index.php?title=Negativity&oldid=815 | # Negativity
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Other toolboxes required Negativity Computes the negativity of a bipartite density matrix none PartialTransposeTraceNorm Entanglement measures yes (convex)
Negativity is a function that computes the negativity of a bipartite density matrix, which is defined as follows: $\mathcal{N}(\rho) := \frac{1}{2}\big( \|\rho^\Gamma\|_1 - 1 \big),$ where $\rho^\Gamma$ is the partial transpose of $\rho$ and $\|\cdot\|_1$ is the trace norm. Equivalently, the negativity of $\rho$ is the absolute value of the sum of the negative eigenvalues of $\rho^\Gamma$.
## Syntax
• NEG = Negativity(RHO)
• NEG = Negativity(RHO,DIM)
## Argument descriptions
• RHO: A bipartite density matrix.
• DIM (optional, by default has both subsystems of equal dimension): A specification of the dimensions of the subsystems that RHO acts on. DIM can be provided in one of two ways:
• If DIM is a scalar, it is assumed that the first subsystem has dimension DIM and the second subsystem has dimension length(RHO)/DIM.
• If $X \in M_{n_1} \otimes M_{n_2}$ then DIM should be a row vector containing the dimensions (i.e., DIM = [n_1, n_2]).
## Examples
### PPT states have zero negativity
States with positive partial transpose have zero negativity. The following code verifies this fact for one particular Chessboard state:
>> rho = ChessboardState(1,2,3,4,5,6);
>> Negativity(rho)
ans =
1.1102e-16
### Can be used with CVX
This function is convex and can be used in the objective function or constraints of a CVX optimization problem. For example, the following code finds the maximum overlap of a density matrix $\rho$ with the maximally-entangled pure state, subject to the constraint that its negativity is no larger than 1/2:
>> d = 3;
>> phi = MaxEntangled(d);
>> phi = phi*phi'; % the maximally-entangled pure state, represented as a rank-1 density matrix
>> cvx_begin sdp quiet
variable rho(d^2,d^2) hermitian;
maximize trace(phi*rho);
subject to
trace(rho) == 1;
rho >= 0;
Negativity(rho) <= 1/2;
cvx_end
cvx_optval
cvx_optval =
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https://inperc.com/wiki/index_title_Grayscale_images.html | Computer Vision & Math contains: mathematics courses, covers: image analysis and data analysis, provides: image analysis software. Created and run by Peter Saveliev.
# Grayscale images
(Redirected from Grayscale Images)
A slightly more advanced presentation of this material: Graph representation of the topology of gray scale images
Previously we developed a general approach to topological analysis of Binary Images. However, images are rarely binary in computer vision applications.
## What we are trying to find in the image
Before we start to develop the algorithm for analysis of gray scale images, let’s first figure out what we are looking for.
We want to find objects in the image. It seems clear that there are 4 light objects on the dark background in the image on the left. Its negative on the right has 4 dark objects on the light background. Now we need to teach the computer see what we see.
The image:
Its blurry version:
So, what are those "objects"? The idea comes from considering binary images. Indeed, objects in a binary image are either clusters of adjacent black pixels surrounded by white background, or clusters of adjacent white pixels surrounded by black background, like the one on the right.
Therefore, objects in a gray scale image should be either connected darker regions surrounded by lighter background, or connected lighter regions surrounded by darker background. On the pixel level this is what we see:
4 black objects, one with a hole:
3 dark objects, one with a hole:
To confirm that this approach makes sense in real life, see these examples of image analysis or simply run Pixcavator.
Two dark objects each with a hole:
For more on this see Objects in gray scale images.
## Objects as maxima and minima of the gray scale function
The level of gray of each pixel is given by a number between 0 and 255. These numbers together form the gray scale function of the image. An example is on the right.
A grayscale image:
The gray scale function of the image on the left:
The image on the left is accompanied by its gray scale function. Higher means lighter and lower means darker.
The objects in the image correspond to maxima and minima of the gray scale function. This way, as before, they are either connected darker regions surrounded by lighter background, or connected lighter regions surrounded by darker background. Just like with binary images we have to choose one of these two options. Once again we choose the former.
Grayscale images are treated as if they have dark objects on light background.
Here, the image has 12 dark and 8 light objects. Keep in mind that since the light objects are holes, the ones that touch the border are not counted.
The gray level function of the original image:
The three light objects contained in the image:
The way we capture light objects may be described as “cutting off mountaintops”, as shown here. On the left, we have the gray level function of the (1-dimensional) image. The maxima and minima are clearly identified as objects. Now, to extract a given dark object as a separate gray scale image, cut off all other maxima.
Similarly, we capture dark objects by "filling in valleys" or removing all other minima.
A gray scale image and its two objects represented as gray scale images:
For more, see Gray scale function.
## Thresholding
Our objective is to extend the method described in Binary images to gray scale images. Recall our approach:
Every image is represented as a combination of binary images.
In this case the combination will be a sequence. For a given gray scale image we will create a sequence of binary images which we will call frames. Each frame is obtained through thresholding, as follows:
Given a number, threshold, T between 0 and 255,
create a $T$-th frame by replacing all the pixels
with gray level lower than or equal to T with black (0),
the rest with white (1).
For example, the pixel with gray level of 100 will be white in the first 101 binary images in the sequence and black in the rest. The procedure is illustrated in the picture below. Now, if we let T run from 0 to 255, we end up with a sequence of 256 binary images.
The diagram below illustrates the thresholding procedure and creation of frames. The original gray scale image is at the top. It has 8 levels of gray. Thresholding produces only 4 binary frames because some intermediate levels of gray do not appear in the image. Here P(i,j) stands for the value of the pixel $(i,j)$ in the original, while $B(i,j)$ is the value of that pixel in the binary frame.
For more details see Thresholding.
## Counting objects in the sequence of frames
Once the frames have been created, each of them can be - separately - analyzed by the algorithm from Binary images. For example, in the sequence above the algorithm will produce the following: 0, 1, 2, and 1 objects respectively. The total count of 4 would of course be wrong as the number of objects in the gray scale image which is 2. The key is, therefore, not to over-count objects as you move from frame to frame.
To ensure the correct count, the following rule may be applied: Don't count an object that has a predecessor in the previous frame. Then only A and C should be counted below.
The following, equivalent, rule will prove itself more convenient:
Don't count objects that have single successors in the next frame.
In other words, we count objects that merge with others in the next frame. According to this rule only B and C should be counted.
Note: The last frame is always all black. So, this object is never counted unless it's the only object. Sometimes, the last frame, or any all black frame, and the first frame, or any all white frame, will be simply ignored.
These relations are easier to visualize with a graph, below. The merge of B and C is clearly shown.
We will call this the topology graph. Transition from frame to frame involves Adding Pixels. As a result, each arrow in this graph hides multiple intermediate steps.
For more, see Topology graph.
## Using cycles to capture objects
Both objects and holes are captured by cycles. Until later, by cycles we will understand circular sequences of edges. There are 0- and 1-cycles:
• 0-cycles represent objects or connected components of the image,
• 1-cycles represent holes.
This results in a natural and unambiguous representation of the regions by the curves that enclose them. A 0-cycle is traversed clockwise (on the outside of the object like a rubber band) and a 1-cycle is traversed counterclockwise. Observe that in the either case black is on the left.
The binary image. Topological analysis: Two components, the first one with two holes:
The topological features are captured by cycles. Here A and B are 0-cycles, C and C’ are 1-cycles (outside components clockwise and inside holes counterclockwise):
The analysis should be similar for gray scale images, in spite of the blur. There should be cycles capturing components and holes. The only difference is that there will be more then one possible answer.
The blurred version of the above binary. A possible topological analysis: Two components, the first one with two holes:
The topological features are captured by cycles. The result does not have to match that of the binary image:
The result of this topological analysis is a partition of the image. A partition is a collection of non-overlapping regions, connected sets of black pixels and connected sets of white pixels, that covers the whole image. The partition is achieved by finding boundaries of these regions as 0- and 1-cycles. These cycles are closed curves made of vertical and horizontal edges of pixels.
## The output
The primary output of the algorithm will be the full graph of the frame sequence with framed nodes identified. Based on this information, the topology graph can be extracted. It captures the complete information about the internal structure of the image sequence, including the hierarchy of objects. It is fair, therefore, to call the method lossless, as before.
During processing of each frame, the areas, perimeters, etc of the objects are computed as before, see Binary Images#The output of the algorithm . The algorithm also evaluates certain new characteristics. The main are contrast and "saliency".
By contrast we understand the difference of the gray level of the object and that of the area surrounding the object from the outside measured in levels of gray. The possible levels run from 0 to 255. The lowest setting always produces a copy of the original image, the highest a blank image.
Saliency is what we decided to call the volume under the graph of the function that represents the gray scale image. It is computed by adding the (binary) areas in consecutive frames. Based on that the gray scale centroids are also computed. A direct way to compute them is here [1], in MATLAB.
The distribution of these parameters also serves as output. This output can be used in image recognition and image-to-image search. This is why it is important that the count of objects is not significantly affected by rotations. The output for the original 640×480 fingerprint in this image is 3121 dark and 1635 light objects. For the rotated version, it is 2969-1617. By considering only objects with area above 50 pixels, the match becomes better: 265-125 and 259-124, respectively.
Stretching the image does not affect the number of objects. The distribution of objects with respect to area is affected but in an entirely predictable way. Shrinking makes objects merge. If the goal, however, is to count and analyze large features, limited shrinking of the image does not affect the outcome. The counting is also stable under “salt-and-pepper” noise or mild blurring. Our experience has shown that the output corresponds well with what humans see. The only case when there is a mismatch is when the size, or the contrast of the object, or its connection to another object are imperceptible to the human eye.
Indirectly, cycles as sequences of edges are captured. This data can be used as follows. (1) The cycles can be plotted in black to reveal boundaries of a gray-scale image. This creates a black-and-white “drawing”, below. (2) If they are filled with an appropriate choice of colors, the user can view a new, simplified, image. (3) The interior of the cycles can be recolored randomly to exhibit them. (4) The cycles can be used for further, possibly manual, editing by the user. For example, they can be moved around or deformed. (5) Besides visualization, the boundaries can be extracted and used elsewhere. For example, they can be matched with cycles collected from another image, or used for picture enlargement, or separation of foreground from background.
Example of the output: the first is the original image and the second is some of its cycles.
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https://terrytao.wordpress.com/tag/global-well-posedness/ | You are currently browsing the tag archive for the ‘global well-posedness’ tag.
A few days ago, I released a preprint entitled “Localisation and compactness properties of the Navier-Stokes global regularity problem“, discussed in this previous blog post. As it turns out, I was somewhat impatient to finalise the paper and move on to other things, and the original preprint was still somewhat rough in places (contradicting my own advice on this matter), with a number of typos of minor to moderate severity. But a bit more seriously, I discovered on a further proofreading that there was a subtle error in a component of the argument that I had believed to be routine – namely the persistence of higher regularity for mild solutions. As a consequence, some of the implications stated in the first version were not exactly correct as stated; but they can be repaired by replacing a “bad” notion of global regularity for a certain class of data with a “good” notion. I have completed (and proofread) an updated version of the ms, which should appear at the arXiv link of the paper in a day or two (and which I have also placed at this link). (In the meantime, it is probably best not to read the original ms too carefully, as this could lead to some confusion.) I’ve also added a new section that shows that, due to this technicality, one can exhibit smooth $H^1$ initial data to the Navier-Stokes equation for which there are no smooth solutions, which superficially sounds very close to a negative solution to the global regularity problem, but is actually nothing of the sort.
Let me now describe the issue in more detail (and also to explain why I missed it previously). A standard principle in the theory of evolutionary partial differentiation equations is that regularity in space can be used to imply regularity in time. To illustrate this, consider a solution $u$ to the supercritical nonlinear wave equation
$-\partial_{tt} u + \Delta u = u^7$ (1)
for some field $u: {\bf R} \times {\bf R}^3 \to {\bf R}$. Suppose one already knew that $u$ had some regularity in space, and in particular the $C^0_t C^2_x \cap C^1_t C^1_x$ norm of $u$ was bounded (thus $u$ and up to two spatial derivatives of $u$ were bounded). Then, by (1), we see that two time derivatives of $u$ were also bounded, and one then gets the additional regularity of $C^2_t C^0_x$.
In a similar vein, suppose one initially knew that $u$ had the regularity $C^0_t C^3_x \cap C^1_t C^2_x$. Then (1) soon tells us that $u$ also has the regularity $C^2_t C^1_x$; then, if one differentiates (1) in time to obtain
$-\partial_{ttt} u + \Delta \partial_t u = 7 u^6 \partial_t u$
one can conclude that $u$ also has the regularity of $C^3_t C^0_x$. One can continue this process indefinitely; in particular, if one knew that $u \in C^0_t C^\infty_x \cap C^1_t C^\infty_x$, then these sorts of manipulations show that $u$ is infinitely smooth in both space and time.
The issue that caught me by surprise is that for the Navier-Stokes equations
$\partial_t u + (u \cdot \nabla) u =\Delta u -\nabla p$ (2)
$\nabla \cdot u = 0$
(setting the forcing term $f$ equal to zero for simplicity), infinite regularity in space does not automatically imply infinite regularity in time, even if one assumes the initial data lies in a standard function space such as the Sobolev space $H^1_x({\bf R}^3)$. The problem lies with the pressure term $p$, which is recovered from the velocity via the elliptic equation
$\Delta p = -\nabla^2 \cdot (u \otimes u)$ (3)
that can be obtained by taking the divergence of (2). This equation is solved by a non-local integral operator:
$\displaystyle p(t,x) = \int_{{\bf R}^3} \frac{\nabla^2 \cdot (u \otimes u)(t,y)}{4\pi |x-y|}\ dy.$
If, say, $u$ lies in $H^1_x({\bf R}^3)$, then there is no difficulty establishing a bound on $p$ in terms of $u$ (for instance, one can use singular integral theory and Sobolev embedding to place $p$ in $L^3_x({\bf R}^3)$. However, one runs into difficulty when trying to compute time derivatives of $p$. Differentiating (3) once, one gets
$\Delta \partial_t p = -2\nabla^2 \cdot (u \otimes \partial_t u)$.
At the regularity of $H^1$, one can still (barely) control this quantity by using (2) to expand out $\partial_t u$ and using some integration by parts. But when one wishes to compute a second time derivative of the pressure, one obtains (after integration by parts) an expansion of the form
$\Delta \partial_{tt} p = -4\nabla^2 \cdot (\Delta u \otimes \Delta u) + \ldots$
and now there is not enough regularity on $u$ available to get any control on $\partial_{tt} p$, even if one assumes that $u$ is smooth. Indeed, following this observation, I was able to show that given generic smooth $H^1$ data, the pressure $p$ will instantaneously fail to be $C^2$ in time, and thence (by (2)) the velocity will instantaneously fail to be $C^3$ in time. (Switching to the vorticity formulation buys one further degree of time differentiability, but does not fully eliminate the problem; the vorticity $\omega$ will fail to be $C^4$ in time. Switching to material coordinates seems to makes things very slightly better, but I believe there is still a breakdown of time regularity in these coordinates also.)
For later times t>0 (and assuming homogeneous data f=0 for simplicity), this issue no longer arises, because of the instantaneous smoothing effect of the Navier-Stokes flow, which for instance will upgrade $H^1_x$ regularity to $H^\infty_x$ regularity instantaneously. It is only the initial time at which some time irregularity can occur.
This breakdown of regularity does not actually impact the original formulation of the Clay Millennium Prize problem, though, because in that problem the initial velocity is required to be Schwartz class (so all derivatives are rapidly decreasing). In this class, the regularity theory works as expected; if one has a solution which already has some reasonable regularity (e.g. a mild $H^1$ solution) and the data is Schwartz, then the solution will be smooth in spacetime. (Another class where things work as expected is when the vorticity is Schwartz; in such cases, the solution remains smooth in both space and time (for short times, at least), and the Schwartz nature of the vorticity is preserved (because the vorticity is subject to fewer non-local effects than the velocity, as it is not directly affected by the pressure).)
This issue means that one of the implications in the original paper (roughly speaking, that global regularity for Schwartz data implies global regularity for smooth $H^1$ data) is not correct as stated. But this can be fixed by weakening the notion of global regularity in the latter setting, by limiting the amount of time differentiability available at the initial time. More precisely, call a solution $u: [0,T] \times {\bf R}^3 \to {\bf R}^3$ and $p: [0,T] \times {\bf R}^3 \to {\bf R}$ almost smooth if
• $u$ and $p$ are smooth on the half-open slab $(0,T] \times {\bf R}^3$; and
• For every $k \geq 0$, $\nabla^k_x u, \nabla^k_x p, \nabla^x_u \partial_t u$ exist and are continuous on the full slab $[0,T] \times {\bf R}^3$.
Thus, an almost smooth solution is the same concept as a smooth solution, except that at time zero, the velocity field is only $C^1_t C^\infty_x$, and the pressure field is only $C^0_t C^\infty_x$. This is still enough regularity to interpret the Navier-Stokes equation (2) in a classical manner, but falls slightly short of full smoothness.
(I had already introduced this notion of almost smoothness in the more general setting of smooth finite energy solutions in the first draft of this paper, but had failed to realise that it was also necessary in the smooth $H^1$ setting also.)
One can now “fix” the global regularity conjectures for Navier-Stokes in the smooth $H^1$ or smooth finite energy setting by requiring the solutions to merely be almost smooth instead of smooth. Once one does so, the results in my paper then work as before: roughly speaking, if one knows that Schwartz data produces smooth solutions, one can conclude that smooth $H^1$ or smooth finite energy data produces almost smooth solutions (and the paper now contains counterexamples to show that one does not always have smooth solutions in this category).
The diagram of implications between conjectures has been adjusted to reflect this issue, and now reads as follows:
I’ve just uploaded to the arXiv my paper “Localisation and compactness properties of the Navier-Stokes global regularity problem“, submitted to Analysis and PDE. This paper concerns the global regularity problem for the Navier-Stokes system of equations
$\displaystyle \partial_t u + (u \cdot \nabla) u = \Delta u - \nabla p + f \ \ \ \ \ (1)$
$\displaystyle \nabla \cdot u = 0 \ \ \ \ \ (2)$
$\displaystyle u(0,\cdot) = u_0 \ \ \ \ \ (3)$
in three dimensions. Thus, we specify initial data ${(u_0,f,T)}$, where ${0 < T < \infty}$ is a time, ${u_0: {\bf R}^3 \rightarrow {\bf R}^3}$ is the initial velocity field (which, in order to be compatible with (2), (3), is required to be divergence-free), ${f: [0,T] \times {\bf R}^3 \rightarrow {\bf R}^3}$ is the forcing term, and then seek to extend this initial data to a solution ${(u,p,u_0,f,T)}$ with this data, where the velocity field ${u: [0,T] \times {\bf R}^3 \rightarrow {\bf R}^3}$ and pressure term ${p: [0,T] \times {\bf R}^3 \rightarrow {\bf R}}$ are the unknown fields.
Roughly speaking, the global regularity problem asserts that given every smooth set of initial data ${(u_0,f,T)}$, there exists a smooth solution ${(u,p,u_0,f,T)}$ to the Navier-Stokes equation with this data. However, this is not a good formulation of the problem because it does not exclude the possibility that one or more of the fields ${u_0, f, u, p}$ grows too fast at spatial infinity. This problem is evident even for the much simpler heat equation
$\displaystyle \partial_t u = \Delta u$
$\displaystyle u(0,\cdot) = u_0.$
As long as one has some mild conditions at infinity on the smooth initial data ${u_0: {\bf R}^3 \rightarrow {\bf R}}$ (e.g. polynomial growth at spatial infinity), then one can solve this equation using the fundamental solution of the heat equation:
$\displaystyle u(t,x) = \frac{1}{(4\pi t)^{3/2}} \int_{{\bf R}^3} u_0(y) e^{-|x-y|^2/4t}\ dy.$
If furthermore ${u}$ is a tempered distribution, one can use Fourier-analytic methods to show that this is the unique solution to the heat equation with this data. But once one allows sufficiently rapid growth at spatial infinity, existence and uniqueness can break down. Consider for instance the backwards heat kernel
$\displaystyle u(t,x) = \frac{1}{(4\pi(T-t))^{3/2}} e^{|x|^2/(T-t)}$
for some ${T>0}$, which is smooth (albeit exponentially growing) at time zero, and is a smooth solution to the heat equation for ${0 \leq t < T}$, but develops a dramatic singularity at time ${t=T}$. A famous example of Tychonoff from 1935, based on a power series construction, also shows that uniqueness for the heat equation can also fail once growth conditions are removed. An explicit example of non-uniqueness for the heat equation is given by the contour integral
$\displaystyle u(t,x_1,x_2,x_3) = \int_\gamma \exp(e^{\pi i/4} x_1 z + e^{5\pi i/8} z^{3/2} - itz^2)\ dz$
where ${\gamma}$ is the ${L}$-shaped contour consisting of the positive real axis and the upper imaginary axis, with ${z^{3/2}}$ being interpreted with the standard branch (with cut on the negative axis). One can show by contour integration that this function solves the heat equation and is smooth (but rapidly growing at infinity), and vanishes for ${t<0}$, but is not identically zero for ${t>0}$.
Thus, in order to obtain a meaningful (and physically realistic) problem, one needs to impose some decay (or at least limited growth) hypotheses on the data ${u_0,f}$ and solution ${u,p}$ in addition to smoothness. For the data, one can impose a variety of such hypotheses, including the following:
• (Finite energy data) One has ${\|u_0\|_{L^2_x({\bf R}^3)} < \infty}$ and ${\| f \|_{L^\infty_t L^2_x([0,T] \times {\bf R}^3)} < \infty}$.
• (${H^1}$ data) One has ${\|u_0\|_{H^1_x({\bf R}^3)} < \infty}$ and ${\| f \|_{L^\infty_t H^1_x([0,T] \times {\bf R}^3)} < \infty}$.
• (Schwartz data) One has ${\sup_{x \in {\bf R}^3} ||x|^m \nabla_x^k u_0(x)| < \infty}$ and ${\sup_{(t,x) \in [0,T] \times {\bf R}^3} ||x|^m \nabla_x^k \partial_t^l f(t,x)| < \infty}$ for all ${m,k,l \geq 0}$.
• (Periodic data) There is some ${0 < L < \infty}$ such that ${u_0(x+Lk) = u_0(x)}$ and ${f(t,x+Lk) = f(t,x)}$ for all ${(t,x) \in [0,T] \times {\bf R}^3}$ and ${k \in {\bf Z}^3}$.
• (Homogeneous data) ${f=0}$.
Note that smoothness alone does not necessarily imply finite energy, ${H^1}$, or the Schwartz property. For instance, the (scalar) function ${u(x) = \exp( i |x|^{10} ) (1+|x|)^{-2}}$ is smooth and finite energy, but not in ${H^1}$ or Schwartz. Periodicity is of course incompatible with finite energy, ${H^1}$, or the Schwartz property, except in the trivial case when the data is identically zero.
Similarly, one can impose conditions at spatial infinity on the solution, such as the following:
• (Finite energy solution) One has ${\| u \|_{L^\infty_t L^2_x([0,T] \times {\bf R}^3)} < \infty}$.
• (${H^1}$ solution) One has ${\| u \|_{L^\infty_t H^1_x([0,T] \times {\bf R}^3)} < \infty}$ and ${\| u \|_{L^2_t H^2_x([0,T] \times {\bf R}^3)} < \infty}$.
• (Partially periodic solution) There is some ${0 < L < \infty}$ such that ${u(t,x+Lk) = u(t,x)}$ for all ${(t,x) \in [0,T] \times {\bf R}^3}$ and ${k \in {\bf Z}^3}$.
• (Fully periodic solution) There is some ${0 < L < \infty}$ such that ${u(t,x+Lk) = u(t,x)}$ and ${p(t,x+Lk) = p(t,x)}$ for all ${(t,x) \in [0,T] \times {\bf R}^3}$ and ${k \in {\bf Z}^3}$.
(The ${L^2_t H^2_x}$ component of the ${H^1}$ solution is for technical reasons, and should not be paid too much attention for this discussion.) Note that we do not consider the notion of a Schwartz solution; as we shall see shortly, this is too restrictive a concept of solution to the Navier-Stokes equation.
Finally, one can downgrade the regularity of the solution down from smoothness. There are many ways to do so; two such examples include
• (${H^1}$ mild solutions) The solution is not smooth, but is ${H^1}$ (in the preceding sense) and solves the equation (1) in the sense that the Duhamel formula
$\displaystyle u(t) = e^{t\Delta} u_0 + \int_0^t e^{(t-t')\Delta} (-(u\cdot\nabla) u-\nabla p+f)(t')\ dt'$
holds.
• (Leray-Hopf weak solution) The solution ${u}$ is not smooth, but lies in ${L^\infty_t L^2_x \cap L^2_t H^1_x}$, solves (1) in the sense of distributions (after rewriting the system in divergence form), and obeys an energy inequality.
Finally, one can ask for two types of global regularity results on the Navier-Stokes problem: a qualitative regularity result, in which one merely provides existence of a smooth solution without any explicit bounds on that solution, and a quantitative regularity result, which provides bounds on the solution in terms of the initial data, e.g. a bound of the form
$\displaystyle \| u \|_{L^\infty_t H^1_x([0,T] \times {\bf R}^3)} \leq F( \|u_0\|_{H^1_x({\bf R}^3)} + \|f\|_{L^\infty_t H^1_x([0,T] \times {\bf R}^3)}, T )$
for some function ${F: {\bf R}^+ \times {\bf R}^+ \rightarrow {\bf R}^+}$. One can make a further distinction between local quantitative results, in which ${F}$ is allowed to depend on ${T}$, and global quantitative results, in which there is no dependence on ${T}$ (the latter is only reasonable though in the homogeneous case, or if ${f}$ has some decay in time).
By combining these various hypotheses and conclusions, we see that one can write down quite a large number of slightly different variants of the global regularity problem. In the official formulation of the regularity problem for the Clay Millennium prize, a positive correct solution to either of the following two problems would be accepted for the prize:
• Conjecture 1.4 (Qualitative regularity for homogeneous periodic data) If ${(u_0,0,T)}$ is periodic, smooth, and homogeneous, then there exists a smooth partially periodic solution ${(u,p,u_0,0,T)}$ with this data.
• Conjecture 1.3 (Qualitative regularity for homogeneous Schwartz data) If ${(u_0,0,T)}$ is Schwartz and homogeneous, then there exists a smooth finite energy solution ${(u,p,u_0,0,T)}$ with this data.
(The numbering here corresponds to the numbering in the paper.)
Furthermore, a negative correct solution to either of the following two problems would also be accepted for the prize:
• Conjecture 1.6 (Qualitative regularity for periodic data) If ${(u_0,f,T)}$ is periodic and smooth, then there exists a smooth partially periodic solution ${(u,p,u_0,f,T)}$ with this data.
• Conjecture 1.5 (Qualitative regularity for Schwartz data) If ${(u_0,f,T)}$ is Schwartz, then there exists a smooth finite energy solution ${(u,p,u_0,f,T)}$ with this data.
I am not announcing any major progress on these conjectures here. What my paper does study, though, is the question of whether the answer to these conjectures is somehow sensitive to the choice of formulation. For instance:
1. Note in the periodic formulations of the Clay prize problem that the solution is only required to be partially periodic, rather than fully periodic; thus the pressure has no periodicity hypothesis. One can ask the extent to which the above problems change if one also requires pressure periodicity.
2. In another direction, one can ask the extent to which quantitative formulations of the Navier-Stokes problem are stronger than their qualitative counterparts; in particular, whether it is possible that each choice of initial data in a certain class leads to a smooth solution, but with no uniform bound on that solution in terms of various natural norms of the data.
3. Finally, one can ask the extent to which the conjecture depends on the category of data. For instance, could it be that global regularity is true for smooth periodic data but false for Schwartz data? True for Schwartz data but false for smooth ${H^1}$ data? And so forth.
One motivation for the final question (which was posed to me by my colleague, Andrea Bertozzi) is that the Schwartz property on the initial data ${u_0}$ tends to be instantly destroyed by the Navier-Stokes flow. This can be seen by introducing the vorticity ${\omega := \nabla \times u}$. If ${u(t)}$ is Schwartz, then from Stokes’ theorem we necessarily have vanishing of certain moments of the vorticity, for instance:
$\displaystyle \int_{{\bf R}^3} \omega_1 (x_2^2-x_3^2)\ dx = 0.$
On the other hand, some integration by parts using (1) reveals that such moments are usually not preserved by the flow; for instance, one has the law
$\displaystyle \partial_t \int_{{\bf R}^3} \omega_1(t,x) (x_2^2-x_3^2)\ dx = 4\int_{{\bf R}^3} u_2(t,x) u_3(t,x)\ dx,$
and one can easily concoct examples for which the right-hand side is non-zero at time zero. This suggests that the Schwartz class may be unnecessarily restrictive for Conjecture 1.3 or Conjecture 1.5.
My paper arose out of an attempt to address these three questions, and ended up obtaining partial results in all three directions. Roughly speaking, the results that address these three questions are as follows:
1. (Homogenisation) If one only assumes partial periodicity instead of full periodicity, then the forcing term ${f}$ becomes irrelevant. In particular, Conjecture 1.4 and Conjecture 1.6 are equivalent.
2. (Concentration compactness) In the ${H^1}$ category (both periodic and nonperiodic, homogeneous or nonhomogeneous), the qualitative and quantitative formulations of the Navier-Stokes global regularity problem are essentially equivalent.
3. (Localisation) The (inhomogeneous) Navier-Stokes problems in the Schwartz, smooth ${H^1}$, and finite energy categories are essentially equivalent to each other, and are also implied by the (fully) periodic version of these problems.
The first two of these families of results are relatively routine, drawing on existing methods in the literature; the localisation results though are somewhat more novel, and introduce some new local energy and local enstrophy estimates which may be of independent interest.
Broadly speaking, the moral to draw from these results is that the precise formulation of the Navier-Stokes equation global regularity problem is only of secondary importance; modulo a number of caveats and technicalities, the various formulations are close to being equivalent, and a breakthrough on any one of the formulations is likely to lead (either directly or indirectly) to a comparable breakthrough on any of the others.
This is only a caricature of the actual implications, though. Below is the diagram from the paper indicating the various formulations of the Navier-Stokes equations, and the known implications between them:
The above three streams of results are discussed in more detail below the fold.
Mark Keel, Tristan Roy, and I have just uploaded to the arXiv the paper “Global well-posedness for the Maxwell-Klein-Gordon equation below the energy norm“, submitted to Discrete and Continuous Dynamical Systems. This project started about eight years ago, and was in fact a partial result was essentially finished by 2002, but managed to get put on the backburner for a while due to many other priorities. Anyway, this paper applies the I-method to the Maxwell-Klein-Gordon system of equations in the Coulomb gauge (a simplified model for the hyperbolic Yang-Mills equations) in three spatial dimensions. Previously to this paper, it was known that the Cauchy problem was globally well-posed in the energy norm (which is essentially $H^1({\Bbb R}^3)$) and locally well-posed in $H^s({\Bbb R}^3)$ for $s > 1/2$, with this condition being essentially best possible except for the endpoint. Here we manage to lower the regularity threshold for global wellposedness to $s > \sqrt{3}/2 \approx 0.866$. (The partial result alluded to earlier was for $s > 7/8 = 0.875$; at one point we had announced an improvement to $5/6 \approx 0.833$, but the argument turned out to be flawed.) This is part of what is now quite a large family of such “global well-posedness below the energy norm” results, but there are some notable technical features here which were not present in earlier works. Firstly, we can show that there is no smoothing effect in the nonlinearity, ruling out use of the Fourier truncation method. Secondly, due to our use of rescaling, supercritical quantities such as the $L^2$ norm are not under control, which necessitates some unusual treatment of the low frequency portions of the scalar and vector fields. Namely, they are estimated in $L^p$ spaces rather than $L^2$ ones. This complicates a number of tasks, ranging from controlling the elliptic theory, to understanding the coercive nature of the Hamiltonian, to establishing the nonlinear commutator estimates underlying the almost conservation law. | {"extraction_info": {"found_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": 164, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9234665632247925, "perplexity": 324.81362829557503}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1480698544097.11/warc/CC-MAIN-20161202170904-00118-ip-10-31-129-80.ec2.internal.warc.gz"} |
https://docs.nersc.gov/performance/case-studies/amrex-gpu/ | # AMReX¶
## Background¶
AMReX is a software framework for the development and implementation of massively parallel algorithms using block-structured adaptive mesh refinement (AMR). Block-structured AMR provides the basis for the temporal and spatial discretization strategy for a large variety of applications of interest to the DOE. AMReX provides a unified infrastructure with the functionality needed for applications to be able to effectively and efficiently utilize machines from laptops to exascale accelerator-based architectures. AMR reduces the computational cost and memory footprint compared to a uniform mesh while preserving accurate descriptions of different physical processes in complex multi-physics algorithms. AMReX supports algorithms that solve systems of partial differential equations (PDEs) in simple or complex geometries, and those that use particles and/or particle-mesh operations to represent component physical processes.
Key features of AMReX include:
• Support for block-structured AMR with optional subcycling in time
• Support for cell-centered, face-centered and node-centered data
• Support for hyperbolic, parabolic, and elliptic solves on hierarchical grid structure
• Support for hybrid parallelism model with MPI and OpenMP
• Support for particles, collisions and particle-mesh operations.
• Support for embedded boundary based on the cut-cell methodology
• Support for GPU systems through AMReX's portability layer.
• Basis of mature applications in combustion, astrophysics, cosmology, accelerator physics, multiphase modeling, wind modeling and porous media
• Demonstrated successful scaling on all major DOE supercomputers as well as other large machines
• Source code freely available
AMReX has developed a unique portability layer to achieve high performance on both CPU and GPU based supercomputers. An overview of this layer's design features is presented here:
## GPU Porting Strategy¶
AMReX has developed its own portability layer for GPU systems to allow user readability, GPU portability and performance. This layer targets the native programming model for each GPU architechture: CUDA for NVIDIA, HIP for AMD, and DPC++ for Intel, and gives AMReX immediate access to the newest features and performance gains without adding any additional overhead or dependencies.
AMReX's portability layer has been effective by utilizing a flexible system of wrappers designed specifically for its users' needs. AMReX includes well designed loop iterators and specialized launch macros to achieve targetted, optimized performance that is maintainable by AMReX developers and understandable to AMReX users.
One major concern when running on GPU systems is allocation overhead: the cost of allocating and freeing data is substantial and limiting. This is especially true in codes such as AMReX, which regularly changes the problem distribution, fidelity and extent over time. Reducing this overhead has lead to the widespread implementation of memory pools, called Arenas in AMReX, which reuse chunks of contiguous memory to eliminate unneeded allocations and frees. Arena have been integrated into all AMReX data structures, increasing flexibility and control of memory in a performant, tracked manner. The Arenas use a standard alloc and free interface that's portable to CPU and GPU systems:
// Direct use of AMReX's default Arena, 'The_Arena'.
auto dp = (char*)(amrex::The_Arena()->alloc( size ));
amrex::The_Arena()->free(dp);
// Build a new MultiFab in device memory,
// using AMReX's built-in Arena, 'The_Device_Arena'.
// 'mf' Will use this arena for all allocations, resizes and frees.
MultiFab mf(boxarray, distmap, ncomp, nghost,
MFInfo().SetArena(The_Device_Arena()));
// Build a vector that uses a device memory allocator and interacts
// with the memory in a safe, performant manner.
DeviceVector dvect(...);
Once data is properly allocated, accessing data on the device is handled by lightweight, device-friendly objects that contain non-owning pointers and indexing information. For particles, these are the ArrayOfStructs and StructOfArray objects, which allow access to the data in the most performant way. For meshes, this is the Array4 object, which allows a Fortran-like, interface to the underlying data:
MultiFab mf(boxarray, distmap, ncomp, nghost,
MFInfo().SetArena(The_Cpu_Arena()));
// Find the box (the memory block) that contains
// the point of interest.
IntVect cell(/* Target index */);
int comp = /* Target component */;
for (int i=0; i<boxarray.size(); ++i)
{
if (boxarray[i].contains(cell))
{ bx_id = i; break; }
}
// GPU safe, Fortran-like accessor and indexing object.
// This example is done on the CPU.
Array4<Real> arr = mf.array(bx_id);
Real val = arr(cell, comp);
Real valB = arr(cell[0], cell[1], cell[2], comp);
Working on the device with these objects is done through AMReX's lambda launch system, ParallelFor. The ParallelFor launch takes a lambda function and a launch configuration and performs work over the configuration on either the CPU or GPU. AMReX has designed launches for a box of mesh points, a number of particles, or with a user-defined launch configuration. These options cover the majority of parallel algorithms of interest to AMReX's users and developers, allowing AMReX to give highly optimized performance, portable performance.
// Function version of ParallelFor,
// Called over a number of objects, N.
const int MyProc = amrex::ParallelDescriptor::MyProc();
amrex::ParallelFor(N, [=] AMREX_GPU_DEVICE (int idx) noexcept
{
amrex::ULong seed = MyProc*1234567ULL + 12345ULL ;
int seqstart = idx + 10 * idx ;
AMREX_HIP_OR_CUDA( hiprand_init(seed, seqstart, 0, &d_states_d_ptr[idx]);,
curand_init(seed, seqstart, 0, &d_states_d_ptr[idx]); )
});
// Macro version of ParallelFor
// Called over a box, bx, and number of components, ncomp:
Real add = val;
Array4<T> const& a = mf->array();
AMREX_HOST_DEVICE_PARALLEL_FOR_4D(bx, ncomp, i, j, k, n,
{
a(i,j,k,n) += val;
});
These ParallelFor lambda launch calls have been integrated into the workflow of AMReX's custom iterators to create a consistent, portable and performant workflow pattern for users. AMReX's custom iterators, MFIter to iterate over boxes and ParIter to iterate over particles, include GPU workflow control features that create a consistent pattern for users automatically. This pattern is typically the performant option, but can be altered with appropriate flags at runtime. The custom iterators include automatically launching on round-robin rotated GPU streams to complete each iteration's launches in order but independently, explicitly synching the device in the iterator's destructor to ensure safe data use, and optional kernel fusing to reduce launch overhead whenever possible. By creating a default pattern that users is generally optimial but users can tune as needed, the AMReX iterator loops are portable, performant, understandable, and focus on the science:
bool sync = /* Set at iterator destructor. True by default. */
for (MFIter mfi(mf_xi, MFInfo().SetDeviceSync(sync)); mfi.isValid(); ++mfi)
{
// Start on GPU stream "0"
const Box& bx = mfi.tilebox();
auto const& mfab_1 = mf_1.array(mfi);
auto const& mfab_2 = mf_2.array(mfi);
auto const& mfab_3 = mf_3.array(mfi);
// ... Prep first launch
amrex::ParallelFor(bx,
[=] AMREX_GPU_DEVICE (int i, int j, int k) noexcept
{
func_1(i, j, k, mfab_1, obj1);
});
// ... Prep second launch
amrex::ParallelFor(bx,
[=] AMREX_GPU_DEVICE (int i, int j, int k) noexcept
{
func_2(i, j, k, mfab_1, mfab_2, obj2);
});
// ... Prep third launch
amrex::ParallelFor(bx,
[=] AMREX_GPU_DEVICE (int i, int j, int k) noexcept
{
func_3(i, j, k, mfab_2, mfab_3, obj3);
func_4(i, j, k, mfab_1, mfab_3, obj4);
});
// mfi++ operator will cycle to the next GPU stream
} // Device synch in MFIter destructor
From this basic pattern, AMReX has explored a variety of performance optimizations and has established some guidelines for AMReX app developers to use when building GPU codes or porting existing codes to GPUs:
• Build initially in managed memory to make porting easier and allow developers to focus on the most critical features first.
• Whenever possible, put data on the device and leave it there. Additional features, such as Asynchoronous I/O, have been developed in AMReX to help ensure that's possible throughout user's codes. Initially, use this limitation to define the number of GPUs to run across for a given problem's size.
• Inline device functions. Grid-and-particle codes are limited by register usage on modern GPU architechtures. Inlining device operations reduces the number of function pointers, and therefore registers, needed for a given device operation, improving overall performance.
AMReX also includes wrappers and functions for other common operations, including reductions, random number generators, atomics and scans. Some of these operations have been special wrapped with hand-written AMReX code to maximize performance and functionality, such as reductions:
// Reduction to determine the next time step size:
Real estdt = amrex::ReduceMin(S, 0,
[=] AMREX_GPU_HOST_DEVICE (Box const& bx, Array4<Real const> const& fab) -> Real
{
return cns_estdt(bx, fab, dx, *lparm);
});
estdt *= cfl;
ParallelDescriptor::ReduceRealMin(estdt);
and some simply wrap around the available libraries provided by vendors, such as InclusiveSum and ExclusiveSum for CUDA versions greater than 11:
// amrex wrapper around CUB's InclusiveSum
template <typename N, typename T, typename M=std::enable_if_t<std::is_integral<N>::value> >
T InclusiveSum (N n, T const* in, T * out, RetSum a_ret_sum = retSum)
{
#if defined(AMREX_USE_CUDA) && defined(__CUDACC__) && (__CUDACC_VER_MAJOR__ >= 11)
void* d_temp = nullptr;
std::size_t temp_bytes = 0;
AMREX_GPU_SAFE_CALL(cub::DeviceScan::InclusiveSum(d_temp, temp_bytes, in, out, n,
Gpu::gpuStream()));
d_temp = The_Arena()->alloc(temp_bytes);
AMREX_GPU_SAFE_CALL(cub::DeviceScan::InclusiveSum(d_temp, temp_bytes, in, out, n,
Gpu::gpuStream()));
T totalsum = 0;
if (a_ret_sum) {
Gpu::dtoh_memcpy_async(&totalsum, out+(n-1), sizeof(T));
}
Gpu::streamSynchronize();
The_Arena()->free(d_temp);
AMREX_GPU_ERROR_CHECK();
#elif /* HIP, DPC++ and CPU versions */
...
}
These decisions are made on a case-by-case basis to create an understandable, portable, performant, and manageable framework for AMReX developers and users.
Communications operations have also been heavily optimized for AMReX's GPU port. As the GPUs have substantially reduced calculation time, the relative amount of time spent in communications algorithmsi has skyrocketed. As such, AMReX's halo and copy operations have undergone extensive testing to maximize performance. This includes GPUDirect testing, fusing and buffer packing optimization. In addition, clean, simple, non-blocking versions of the comm operations have been created to allow users to hide latency where possible inside of their applications:
dst.ParallelCopy_nowait(src, src_comp, dst_comp, n_comp);
// Perform work on data sets other than 'dst' while MPI completes.
dst.ParallelCopy_finish();
AMReX apps have found this unique porting strategy to be widely accessable, beneficial and performant:
### ExaWind¶
Snapshot of the instantaneous flowfield for an NM-80 rotor using the hybrid ExaWind simulation solver suite. The image shows the tip vortices rendered using q-criterion and the contour colors show the magnitude of the x-velocity field. Credit: Mike Brazell, Ganesh Vijayakumar and Shreyas Ananthan (NREL), AmrWind.
The ExaWind project’s scientific goal is to advance fundamental understanding of the flow physics that govern whole wind plant performance, including wake formation, complex terrain impacts, and turbine-turbine interaction effects. ExaWind uses AMReX for a background structured mesh used to gain considerable speed-ups over a pure unstructured solution. This AMR-based structured code is named AMR-Wind.
AMR-Wind has been able to go from zero to a fully-functional AMReX-based background solver for ExaWind in less than a year using AMReX's incompressible flow solver, incflo, as the starting point. The codebase can run all the target problems on current and pre-exascale hardware. The background solver has been coupled with the structured solver, Nalu-Wind, using an overset-mesh methodology. AMR-Wind has also coupled it to a full-turbine structural solver, OpenFAST, to model structural loading under realistic atmospheric conditions. The top components of AMR-Wind's success are:
• AMReX's GPU abstractions: The ParallelFor and DeviceVector type abstractions make it easy to develop code quickly. Once the initial code example is in place, application users have been able to adapt for their use cases easily without needed to know the details about the GPU. 80% of the time, users write and test code on CPU and it works on GPU without issues, albeit there's typically tuning that can be done.
• Linear solvers: MLMG (on structured grid) was critical in achieving AMR-Wind's time-to-solution goals given the problem sizes and spatial scales that have to be resolved. Over the last year, AMReX has added several linear solver enhancements (i.e., overset masking, improvements to hypre interface) that were required to support the hybrid nalu/amr simulations.
Compared to the original Nalu-Wind pathway for ABL/actuator line simulations, AMR-Wind gives a 5x performance benefit on CPUs and GPUs (coming from using MLMG over the AMG/GMRES solvers). Aa 24 hour ABL simulation can be completed in faster than real time (~10 hours). Shreyas Ananthan, ExaWind researcher at NREL, has been able to run a 51.5 billion cell mesh on 4096 summit nodes using GPUs, demonstrating reasonable weak scaling at full scale. This was all unimaginable about a year ago.
### Pele¶
Cavity flame: Reflecting shocks in a supersonic channel flow interact with a cavity-stabilized flame that is fueled by direct injection of H2 fuel from the boundary within the cavity. Computed on ORNL’s Summit computer using PeleC, an adaptive mesh compressible combustion code based on the AMReX library.
The Pele project's goal is to enable high fidelity combustion fluid dynamics simulations within complex geometries. It is a suite of applications, mainly PeleLM and PeleC, which perform simulations in the low-mach and compressible regimes, respectively. Here are the highlights of PeleC's implementation of AMReX and capabilities that have been achieved:
PeleC was originally written in BoxLib (which transitioned into AMReX). PeleC adopted a typical programming model for AMR applications which was to do overall application orchestration in C++ and write the computational kernels in Fortran. For targeting Intel Xeon Phi architectures, MPI+OpenMP was introduced which allowed simulations to run with less MPI ranks and increase scalability.
To transition to GPUs, PeleC attempted to keep its Fortran code by developing a prototype of the code using OpenACC. Concurrently, PeleC was prototyped in AMReX's C++ framework for GPUs as well. While performance was found to be quite similar between both prototypes, the C++ method had several advantages for the Pele project, while preserving the Fortran kernels only saved developer time in the short term.
PeleC was originally 12k lines of C++ and 38k lines of Fortran. Using AMReX's C++ framework, PeleC is at the time of this writing, 20k lines of entirely C++ code. PeleC experienced a 2x speedup in simulations on the CPU. The application is able to run on NVIDIA, Intel, and AMD GPUs using their native language implementations as backends in AMReX. Inclusion of the GPU capabilities has also allowed for the MPI+OpenMP model for CPUs to be preserved. Developers of PeleC have found the transition to C++ code to be more readable, more succinct, easier to debug, increased the number of compatible compilers, increased compatibility across the toolchain for code profiling, etc, and generally improved performance.
Utilizing the GPU capabilities in AMReX, PeleC has been demonstrated to scale to 100% of the Summit machine with a parallel efficiency loss of 35%. This was observed when weak scaling from a single Summit node to all of the 4608 available Summit nodes, using 27648 NVIDIA V100 GPUs:
Use of AMReX has also enabled PeleC to demonstrate a 72 billion cell calculation on Summit. Using PeleC on Summit GPUs has improved time to solution for simulations by around 125x when comparing the original Fortran programming model using GCC on Summit CPUs (one MPI rank per CPU core) to the Summit GPUs (one MPI rank per GPU).
In general, the Pele project has stated AMReX to be a lightweight, highly capable, highly scalable, and inviting framework in which to develop their CFD applications. | {"extraction_info": {"found_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": 0.19937027990818024, "perplexity": 10177.857962167243}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296943484.34/warc/CC-MAIN-20230320144934-20230320174934-00534.warc.gz"} |
https://cn.overleaf.com/articles/latex-assignment-4/rjdqzptjcsfv | # LaTeX Assignment 4
Author
Jonathan Guiang
AbstractThis was an assignment for a college physics course. Please let me know what you think! :) | {"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": 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": 0.9619624614715576, "perplexity": 1123.319562269397}, "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-2020-50/segments/1606141181482.18/warc/CC-MAIN-20201125071137-20201125101137-00358.warc.gz"} |
http://mathhelpforum.com/algebra/24427-reciprocals.html | # Math Help - reciprocals
1. ## reciprocals
Are there 21 different positive whole numbers such that the sum of their reciprocals is 1?
$1/2+1/3+\frac{1/2+1/3}{6}$ = 35/36
$1/2+1/3+\frac{1/2+1/3}{6}+\frac{\frac{1/2+1/3}{6}}{6}$ = $\frac{6^3-1}{6^3}$
We can keep doing this forever so the sum of any even number of reciprocals of natural numbers can represent $\frac{6^n-1}{6^n}$ | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 4, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7976512908935547, "perplexity": 633.1332123465011}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-14/segments/1427131304412.34/warc/CC-MAIN-20150323172144-00046-ip-10-168-14-71.ec2.internal.warc.gz"} |
http://www.pandora.com/noisia/getdarker-presents-this-is-dubstep-2011/alpha-centauri-excision-datsik-remix | It is taking longer than expected to fetch the next song to play. The music should be playing soon. If you get tired of waiting, you can try reloading your browser.
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# Alpha Centauri (Excision & Datsik Remix)
on GetDarker Presents - This Is Dubstep 2011
## Features of This Track
danceable beats
use of modal harmonies
the use of chordal patterning
light drum fills
a busy bass line
synth riffs
subtle use of arpeggiated synths
light synth fx
a dry recording sound
trippy soundscapes
These are just a few of the hundreds of attributes cataloged for this track by the Music Genome Project.
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It makes me want to dance
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This bass drop is amazing
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Gkokphiokojp j o n l o k p g o g m o n p n p b l j h i n o h p h o l o y l o k o v o h l h i h i b b i k p v i b o v i b p b l b o n o v t b p b k b o b j b l b i b o k o k o b k d b i b o b p n p k l k o n o b i v o v u b o k g i r i v u r y i b u r t u r u b u v u r y o v u t y o h u t y o j u r y i j u t y i v y r b y t h h e v r k b r i h u r v h r u v j r u j u e u e u v j r t o b u r y i h u r y o j u t y o h u t y o j u t y i h y t y i h y t v u t v y u b j t u v u r y o b u b i b u r u b u r y i h y r y i h y r v y r u
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G
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Irt
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Re
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T
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Irt
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Fj
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Glhojkhogkvl b l n j o k l b o b k c k c i y l o g e i j i r y i b o r y i b o e u i j o e k k o n o v h b o b k v g b l n r v l b l k o n o b l i e h u n g t u p o n l j u s j m k o k o n l l h m m m m m m j o j i k o h i k o k p l p l o p k o j i n i k o t i y p j k l l p k k v l m p k p k l j o l p n l j k l o l o k p k o j u l j j g i k o t u k b i r y i j o r y o b i t y o b i t y i v k t y i b o r i b o t o i t y i b u b o g t v p h i n p l m p p q z j t s e u g e e e u g s e y t e r y g d r y g j i k k k k d d j f u r r r r r t d r
Siri
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Bobikovubuon o v g b o j i n p k k h u k p b i n p n i j i j i j u s j j u e t u v u e y u v h r y i h y r y i h y r y i v u r y i k i t b u u r j b j r y k n k n k k k k g o b i j p h o g l l n m k o n o j p h i g i l i b o h i v o b i b j o b l v o g g i f o b p l k l g o k o m i o
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Íe ibm kvo kbobi inobictbovkv i k m v j v o c t v k v i b o b o v u e i v i e h i v i e y i v u r y i b i e y i v u e y i v u e j u h u e y i v i e h i b o e g i v k r h i b r krbirijirjib j r y i b j r o b u r y o j u r y o b u r y o b u r k j u t i r u h v i r i j u r t i j u r t i j u r j h y r y i v y r t i j u e v h x k g i h o f u l p j p j o j i b p g i c l f l n m j l o k p h o c l h o l n m j o h o y l k o n o k i h j t p i n o k m j u k j o i i u p j o k o k o j o k y k o h u b j o b o j u j f l x j lno
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Wohnovubovhb o g b l b i b o h j n o b i e i b o b o l p b u v i b t b o b i v g b o b u b k b l n i b k v g b i b u kvibojobunpv u b o b i v y n o v u b i b i n o b u v k b i l o n o b i n o b y v o b i n o n k k o n i v u b o b o b o b i v i l b k b o b k b k b i b k b o b i b o b h v i v t b l b i n i j u v i n o u i u ibibibuctbov y v k v i b i v u v o v t b o ibibijivujif t i u t i h r t i j u t i v j g t k b k b k k k j l c
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NANA
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Dc
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Nrlguxtscefz g q d q e q q q e s r s r z e z f t s h f j g k b k t j y y r u y i y f t f r e y e h r h r y e h r t f t f t
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Co
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Xo
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58\$858\$(@!!! ! ! ! ! ! 8 ! \$ & 9 & 8 ! 6 ! 9 ! 6 ) 6 ! 8 ) 5 ! 9 ! 6 \$ 9 & 9 4 & 7 ! ! ! ! ' n n
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Op
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Vi
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Ho
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Rijeujirtinu r t i n i e p e b i e j i b i e t i b j e t o b i e y i b j b o b i v r b o b j o n o b u b o b j b o e i b u b o b y b o b i b i k p b y g j b i p n j f k h k k k k y k f i f o l i l i f u k k k u p h p k o j o g p p j i g l p n o j p h i l i k o j o g k k o k o l k l o k p j l i k j o k p h i j j u k c o g i j i b i g h m o k p k o j o j o j i g i f l u u b u j i m o f o b i o i p k i r j j o r y u n k e t i n k r y i k e y i n k e y i k r y o b i e t i b i e t o k r t i i r y o k e h o n k r y o n i r y o i r y o j r y o b j r y o n i f y o i r y j n i r y i n i t t i n i f y o b i r y o j o r y o i r y o
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Mime
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P
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Rosé Nyand
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Vieubiehinov g o h ibijbueubibo n p b i b o b i k p v y b o b i n o b u n o b i n p b u n o g u n p j i b o n u j o b y b h b i i b i j e i j i e t i j i e k j o k o j o k o k o j h b o b y k p h u g u k p k u u
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Up
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Iririryiurti v y t y i g t t y i g t t b y v y t y k k j i t b y b u t t i v f b i r b u n o n o b i r i n i r g o n j TNO hnobybobybob u n o b j b i g r b o v y b o v y b o b u v i f e b h
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Excision's sounds tend to be heavily distorted while Datsik's sounds tend to be very robotic.
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Amazing. nuff said.
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Can't get loud enough!
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Top Three!
I have a lot of top 3s
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This Music FEEDS me!!
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These 2 are awesome alone but when they work together they R legendary
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Harmonic!!!! ! !
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I like how you can definitely 100% tell who did this song just by listening to it. You can clearly hear the influences of Noisia, Excision, and Datsik.
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Yyyeah, Datsik and Excision are magical when they work together.
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YES
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Love when these 2 work together :)
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This song absolutely kills
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Vip
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Yessssssssss s s s s s s s s s s s s s s . Noisia, Excision, AND Datsik! "And" is definitely better than "or" in this situation.
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Noisia, Excision & Datsik... So epic!
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Varien is a bit better in my opinion buy they are very different
We're sorry, but a browser plugin or firewall may be preventing Pandora from loading. | {"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": 0.9850958585739136, "perplexity": 2612.292703326489}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1454701164268.69/warc/CC-MAIN-20160205193924-00238-ip-10-236-182-209.ec2.internal.warc.gz"} |
http://physics.stackexchange.com/questions/44541/thermal-expansion-of-sphere/44546 | # Thermal expansion of Sphere
How would one go about writing an expression of the expansion of the volume of a sphere of a given material? I noticed a few sources give it as
$\Delta V= 3\gamma V\Delta T$
where V is the initial volume; $\gamma$ is the expansivity coefficient and $\Delta T$ is change in temperature of sphere.
Other texts leave out the 3, but with everything else the same.
Any suggestions?
- | {"extraction_info": {"found_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": 0.8794043064117432, "perplexity": 254.5130934165217}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1368704234586/warc/CC-MAIN-20130516113714-00067-ip-10-60-113-184.ec2.internal.warc.gz"} |
http://www.koreascience.or.kr/article/ArticleFullRecord.jsp?cn=KHGGB3_2014_v23n3_447 | Characteristics of the Number and the Mass Concentrations and the Elemental Compositions of PM10 in Jeju Area
Title & Authors
Characteristics of the Number and the Mass Concentrations and the Elemental Compositions of PM10 in Jeju Area
Kang, Chang-Hee; Hu, Chul-Goo;
Abstract
The number concentrations, the mass concentrations and the elemental concentrations of $\small{PM_{10}}$ have measured at Gosan site in Jeju, Korea, from March 2010 to December 2010. And the correlation and the factor analysis for the number, the mass and the elemental concentrations of $\small{PM_{10}}$ are performed to identify their relationships and sources. The average $\small{PM_{10}}$ number concentration is observed $\small{246\;particles/cm}$$\small{^3}$($\small{35.7{\sim}1,017\;particles/cm^3}$) and the average $\small{PM_{10}}$ mass concentration is shown $\small{50.1{\mu}g/m^3}$($\small{16.7{\sim}441.4{\mu}g/m^3}$) during this experimental period. The number concentrations are significantly decreased with increasing particle size, hence the concentrations for the smaller particles less than $\small{2.5{\mu}m}$($\small{PM_{2.5}}$) are contributed 99.6% to the total $\small{PM_{10}}$ number concentrations. The highest concentration of the 20 elements in $\small{PM_{10}}$ determined in this study is shown by S with a mean value of $\small{1,497ng/m^3}$ and the lowest concentration of them is found by Cd with a mean value of $\small{0.57ng/m^3}$. The elements in $\small{PM_{10}}$ are evidently classified into two group based on their concentrations: In group 1, including S>Na>Al>Fe>Ca>Mg>K, the elemental mean concentrations are higher than several hundred $\small{ng/m^3}$, on the other hand, the concentrations are lower than several ten $\small{ng/m^3}$ in group 2, including Zn>Mn>Ni>Ti>Cr>Co>Cu>Mo>Sr>Ba>V>Cd. The size-separated number concentrations are shown positively correlated with the mass concentrations in overall size ranges, although their correlation coefficients, which are monotonously increased or decreased with size range, are not high. The concentrations of the elements in group 1 are shown highly correlated with the mass concentrations, but the concentrations in group 2 are shown hardly correlated with the mass concentrations. The elements originated from natural sources have been predominantly related to the mass concentrations while the elements from anthropogenic sources have mainly affected on the number concentrations of $\small{PM_{10}}$.
Keywords
$\small{PM_{10}}$;Number concentration;Mass concentration;Element composition;Correlation analysis;Factor analysis;Jeju;
Language
Korean
Cited by
1.
대기 중 입자상 에어로솔 분석법: 물리적 특성 및 금속성분과 수용성 화합물 분석방법을 중심으로,엄지원;이보경;
분석과학, 2015. vol.28. 3, pp.139-159
References
1.
Bae, G. N., Kim, M. C., Lim, D. Y., Moon, K. C., Baik, N. J., 2003, Characteristics of Urban Aerosol Number Size Dictriution in Seoul during the Winter Season of 2001, J. of Korean Society for Atmospheric Environment, 19(2), 167-177.
2.
Choi, G. H., Kim, K. H., Kang, C. H., Lee, J. H., 2003, The Influence of the Asian Dust on the Metallic Composition of Fine and Coarse Particle Fractions, J. of Korean Society for Atmospheric Environment, 19(1), 45-56.
3.
Chun, Y. S., Kim, J. Y., Choi, J. C., Shin, D. S., 1999, The characteristics of the aerosol number concentration observed in seoul and Anmyondo during an yellow sand phenomenon, J. of Korean Society for Atmospheric Environment, 15(5), 575-586.
4.
Hieu, N. T., Lee, B. K., 2010, Characteristics of particulate matter and metals in the ambient air from a residential area in the largest industrial city in Korea, Atmospheric Research, 98, 526-537.
5.
Jung, C. H., Chun, Y. S., Choi, B. C., 2003, Characteristics of Aerosol Size Distribution from OPC Measurement in Seoul, 2001, J. of Korean Society for Atmospheric Environment, 19(5), 515-528.
6.
Jung, C. H., Cho, Y. S., Lee, J. T., 2005, Characteristics of Incheon Aerosol during Asian Dust Period in 2004 using Optical Particle Counter(OPC), J. of Environmental Sciences, 14(6), 565-575.
7.
Kim, H. S., Byun, K. T., Chung, Y. S., Choi, H. J., Kim, M. J., 2012, An Analysis of Aerosol Mass Concentrations and Elemental Constituents Measured at Cheongwon depending on the Backward Trajectories of Air Parcel in East Asia in 2011, J. of Environmental Sciences, 21(7), 855-863.
8.
Kim, J. Y., Choi, B. C., 2002, Aerosol Size Distributions and Their Regional Characteristics of over Korea, J. of the Korean Meteorological Society, 38(2), 95-104.
9.
Lee, D. E., Kim, W. H., Ko, H. J., Oh, Y. S., Kang, C. H., 2013, Chemical Composition Characteristics of Size-fractionated Particles during Heavy Asian Dust Event in Spring, 2010, J. of Korean Society for Atmospheric Environment, 29(3), 325-337.
10.
Lee, S. B., Jung, D. S., Cho, E. K., Kim, H. A., Hwang, E. Y., Kang, C. H., 2011, Composition and pollution characteristics of $PM_{10}$ and $PM_{2.5}$ particles at Gosan site of Jeju Island in 2008, Analytical Science & Technology, 24(4), 310-318.
11.
Lundgren, D. A., Hlaing, D. N., Rich, T. A., Marple, V. A., 1996, $PM_{10}/PM_{2.5}/PM_{1}$ Data from a Trichotomous Sampler, Aerosol Science and Technology, 25, 353-357.
12.
Monkkonen, P., Uma, R., Srinivasan, D., Koponen, I. K., Lehtinen, K. E. J., Hameri, K., Suresh, R., Sharma, V. P., Kulmala, M., 2004, Relationship and variations of aerosol number and $PM_{10}$ mass concentrations in a highly polluted urban environment- New Delhi, India, Atmospheric Environment, 38, 425-433.
13.
Na, D. J., Lee, B. K., 2000, A Study on the Characteristics of $PM_{10}$ and Air-borne Metallic Elements Produced in the Industrial City, J. of Korean Society for Atmospheric Environment, 16(1), 23-35.
14.
Park, K. Y., Lee, H. G., Suh, M. S., Jang, K. M., Kang, C. H., Hu, C. G., Kim, Y. J., 1994, Analysis of Air Pollution Concentrations at Cheju Baseline Measurement Station, J. of Korean Air Pollution Research Association, 10(4), 252-259.
15.
Shaheen, N., Shah, M. H., Khalique, A., Jaffar, M., 2005, Metal Levels in Airborne Particulate Matter in Urban Islamabad, Pakistan, Environmental Contamination and Toxicology, 75, 739-746.
16.
Song, S. H., Park, D. M., Lee, Y. M., Lee, C. W., Park, J. H., Yu, S. D., 2012, Ambient Fine and Ultrafine Particles Measurements and Their Correlations with Particulate PAHs at an Elementary School Near a Highway, Asian J. of Atmospheric Environment, 6(2), 96-103.
17.
Vyziene, R., Girgzdys, A., 2009, Investigation of aerosol number concentration in jonava town, Journal of Environmental Engineering and Landscape Management, 17(1), 51-59.
18.
Yan, F., Hu, H., Yu, T., 2004, Analysis of particulate mass concentration, aerosol number concentration and visibility in beijing, China Particuology, 2(1), 25-30.
19.
Zang, R., Han, Z., Shen, Z., Cao, J., 2008, Continuous Measurement of Number Concentration and Elemental Concentration of Aerosol Particles for a Dust Storm Event in Beijing, Advances Atmospheric Sciences, 25(1), 89-95. | {"extraction_info": {"found_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": 20, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7457610964775085, "perplexity": 16580.87173032388}, "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-2018-05/segments/1516084891105.83/warc/CC-MAIN-20180122054202-20180122074202-00039.warc.gz"} |
http://mathhelpforum.com/math-topics/22666-angle-refraction.html | 1. ## Angle of refraction
Hi, I am having some trouble with this question.
The index of refraction of light passing from air to water is 1.33. If the angle of incidence is 38 deg, find the angle of refraction.
Thank you!
2. using snell's law we get:
theta = arcsin[(n1/n2)*sin(38)] ~ 55.2
3. ^ I do not quite get Snell's law =( Can you possibly explain a bit of the steps to me.
What I know is that the formula is like this:
sin theta 1 / sin theta 2 = v1 / v2
v1 / v2 = index of refraction
we are given the angle of incidence which the value of v1 .
so it would be
sin 38 deg / sin theta 2 = 1.33 ?_?
4. I have always thought snells law was:
n1 sin theta1=n2 sin theta2
where n1 is the refractive index of the first substance,
theta1 is the angle of incidence,
n2 is the refractive index of the second substance and
theta2 is the angle of refraction
Therefore, n1=1.00 (absolute refractive index of air)
n2=1.33 (absolute refractive index of water)
theta1=38 deg
so n1 sin theta 1=n2 sin theta 2
1 sin 38=1.33sin theta2
theta2=sin^-1 (sin38/1.33)
theta2=27.57deg
Hope that helps
5. Originally Posted by trent19
I have always thought snells law was:
n1 sin theta1=n2 sin theta2
where n1 is the refractive index of the first substance,
theta1 is the angle of incidence,
n2 is the refractive index of the second substance and
theta2 is the angle of refraction
Therefore, n1=1.00 (absolute refractive index of air)
n2=1.33 (absolute refractive index of water)
theta1=38 deg
so n1 sin theta 1=n2 sin theta 2
1 sin 38=1.33sin theta2
theta2=sin^-1 (sin38/1.33)
theta2=27.57deg
Hope that helps
I second that.
I've always thought snell's law was n1 sin(theta)1 = n2 sin(theta)2 as well!
So the question should provide you with index of refraction for both substances. | {"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": 0.9624374508857727, "perplexity": 3126.1821154669415}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-22/segments/1495463608642.30/warc/CC-MAIN-20170526051657-20170526071657-00024.warc.gz"} |
https://search.datacite.org/works/10.4230/LIPICS.STACS.2012.326 | ### Lower Bounds on the Complexity of MSO_1 Model-Checking
Robert Ganian, Petr Hlineny, Alexander Langer, Jan ObdrÂáLek & Peter Rossmanith
One of the most important algorithmic meta-theorems is a famous result by Courcelle, which states that any graph problem definable in monadic second-order logic with edge-set quantifications (MSO2) is decidable in linear time on any class of graphs of bounded tree-width. In the parlance of parameterized complexity, this means that MSO2 model-checking is fixed-parameter tractable with respect to the tree-width as parameter. Recently, Kreutzer and Tazari proved a corresponding complexity lower-bound---that MSO2 model-checking is not... | {"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": 0.9548024535179138, "perplexity": 2338.5006912779127}, "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-2018-05/segments/1516084887600.12/warc/CC-MAIN-20180118190921-20180118210921-00634.warc.gz"} |
https://www.physicsforums.com/threads/greens-theorem-question.271101/ | # Homework Help: Green's theorem question
1. Nov 11, 2008
### Nick89
1. The problem statement, all variables and given/known data
For a > 0, let $C_a$ be the circle $x^2 + y^2 = a^2$ (counter-clockwise orientation). Let $$\textbf{F} : R^2$$ \ {0} $$\rightarrow R^2$$ be the following vectorfield:
$$\textbf{F}\left(x,y\right) = F_1\left(x,y\right)\textbf{i} + F_2\left(x,y\right)\textbf{j}$$
Also given:
$$\frac{\partial F_2}{\partial x} - \frac{\partial F_1}{\partial y} = \frac{1}{\sqrt{x^2+y^2}}$$
$$\oint_{C_1} \textbf{F} \cdot d \textbf{r} = 1$$
Determine:
$$\oint_{C_a} \textbf{F} \cdot d \textbf{r}$$
for arbitrary a > 0.
2. Relevant equations
Green's theorem:
$$\oint_{C} \textbf{F} \cdot d \textbf{r} = \iint_R \left( \frac{\partial F_2}{\partial x} - \frac{\partial F_1}{\partial y} \right) \, dA$$
3. The attempt at a solution
It is obvious that we should use Green's theorem, even if it's not explicitly mentioned in the question, but I fear that I'm using it where it is not valid...
Using Green's theorem directly I calculate:
(R is the interior (surface) of the circle C_a)
$$\oint_{C_a} \textbf{F} \cdot d \textbf{r} = \iint_R \left( \frac{\partial F_2}{\partial x} - \frac{\partial F_1}{\partial y} \right) \, dA = \iint_R \frac{dA}{\sqrt{x^2+y^2}}$$
$$= \iint_R \frac{dA}{a} = \frac{1}{a} \times \text{surface of R} = \pi a$$
This answer is wrong, and my question is actually why?
I don't need the actual answer to the question (I have it right here in fact) but I need to know why I cannot use green's theorem like this.
I can see two possible reasons:
1. F needs to be smooth (0 is not included in the domain of F)
2. The $$\frac{\partial F_2}{\partial x} - \frac{\partial F_1}{\partial y}$$ part needs to be smooth (it's now undefined at 0)
Which is the right reason? Or are they equivalent? I can't remember my teacher telling us F needs to be smooth but I expect he simply forgot...
2. Nov 11, 2008
### gabbagabbahey
Hmmmm... does $$\frac{1}{\sqrt{x^2+y^2}}$$ Really equal $\frac{1}{a}$ everywhere in your region....or just on the boundary of the region?
3. Nov 11, 2008
### Nick89
Oh wow, that was probably the worst mistake I ever made LOL!
Thanks for spotting that... :p
4. Nov 12, 2008
### mhill
from the definition of the problem and since the line integral would not be defined at r=0 my idea is that the line integral is not 0 but $$2\pi$$
it is a similar problem to 'Cauchy integral formula' on the complex plane but know we miss the ' i'
5. Nov 12, 2008
### Nick89
Actually the answer is 1 + 2 pi (a - 1)
Let D be the region enclosed by the curves $$C_1$$ and $$C_a$$.
For a < 1 we have:
$$\oint_{C_1} \textbf{F} \cdot \textbf{dr} - \oint_{C_a} \textbf{F} \cdot \textbf{dr} = \iint_D \frac{1}{\sqrt{x^2+y^2}}\,dx\,dy = \int_0^{2\pi} \int_a^1 dr\,d\theta = 2\pi \left(1 - a\right)$$
And since the first integral on the left hand side is 1 (see problem statement) we have:
$$\oint_{C_a} \textbf{F} \cdot \textbf{dr} = 1 - 2\pi(1-a) = 1 + 2\pi (a - 1)$$
And a similar argument for a > 1 yields the same value. | {"extraction_info": {"found_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": 0.9774632453918457, "perplexity": 571.4046287026027}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-43/segments/1539583512750.15/warc/CC-MAIN-20181020121719-20181020143219-00303.warc.gz"} |
https://www.gamedev.net/forums/topic/342345-shadow-volume-flickering/ | This topic is 4519 days old which is more than the 365 day threshold we allow for new replies. Please post a new topic.
## Recommended Posts
i've implemented the shadow volume algorithme after the good tutorial on gamasutra. now my problem is that while the algorithme works well on distance i get disturbing results if getting close to a model. if i am at medium distance the shadow is correct. if i get closer to the model the shadows start to 'fade' away or 'pop' up on the model. it looks to me like the z-buffer values used during shadowing and rendering are not the same. for rendering the shadow volume and rendering i use an infinite matrix using this:
decMatrix decMatrix::CreateProjectionInfinite(int width, int height, float fov, float fovRatio, float znear){
if( width<1 || height<1 || fov<=0 || fov>=PI || fovRatio==0 ) THROW(dueInvalidParam);
decMatrix m;
float a = (float)width / (float)height;
float fx = 1.0f / tan(fov * 0.5f);
float fy = a / tan(fov * fovRatio * 0.5f);
float e = 0.0001f;
m.a11=fx; m.a12=0; m.a13=0; m.a14=0;
m.a21=0; m.a22=fy; m.a23=0; m.a24=0;
m.a31=0; m.a32=0; m.a33=1-e; m.a34=znear*(e-2);
m.a41=0; m.a42=0; m.a43=1; m.a44=0;
return m;
}
multiplied with a small translation matrix (translate z around 0.0001) to avoid z-fighting. how can it happen that getting close to objects in my scene (funny not all of them) show this strange behaviour? is the z-offset not good? or is the matrix not fully correct?
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Quote:
Original post by RPTDmultiplied with a small translation matrix (translate z around 0.0001) to avoid z-fighting.
Excuse me, but why do you think that any z-fighting will occur in this case? Do you render different geometry/apply different vertex shaders when you are doing the second pass?
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You shouldn't need the translation matrix. Just render each geometry pass with the same exact vertices and use LEQUAL as your depth function, and you should be fine.
Which API are you using, OpenGL or DirectX? I think your infinite projection matrix may need an adjustment, but it depends on the API. (The matrix in the gamasutra article is correct for OpenGL.)
-- Eric Lengyel
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Quote:
Original post by Generic Guest
Quote:
Original post by RPTDmultiplied with a small translation matrix (translate z around 0.0001) to avoid z-fighting.
Excuse me, but why do you think that any z-fighting will occur in this case? Do you render different geometry/apply different vertex shaders when you are doing the second pass?
i'm using this anti-z-flickering as if i am not using it all shadows on surfaces are flickering like hell. with that small fix i got all shadows working except this case with the model very close to the camera.
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Quote:
Original post by Eric LengyelYou shouldn't need the translation matrix. Just render each geometry pass with the same exact vertices and use LEQUAL as your depth function, and you should be fine.Which API are you using, OpenGL or DirectX? I think your infinite projection matrix may need an adjustment, but it depends on the API. (The matrix in the gamasutra article is correct for OpenGL.)-- Eric Lengyel
i'm using opengl on linux on a ati radeon. and my matrix implementation inside my engine is a directx-like matrix which i convert to opengl format upon setting it (special render module system to separate engine and os).
// setup stuff for shadow rendering OGL_CHECK( glClear(GL_STENCIL_BUFFER_BIT) ); OGL_CHECK( glEnable(GL_STENCIL_TEST) ); OGL_CHECK( glStencilFunc(GL_ALWAYS, 0, ~0) ); OGL_CHECK( glEnable(GL_DEPTH_TEST) ); OGL_CHECK( glDepthFunc(GL_LESS) ); OGL_CHECK( glColorMask(GL_FALSE, GL_FALSE, GL_FALSE, GL_FALSE) ); OGL_CHECK( glDepthMask(GL_FALSE) ); pSetMatrix( GL_PROJECTION, zSafeProjMat );
this is what i took out of the gamasutra article unless i understood something wrong there.
shadowing itself i do like this (i think this should be correct):
void deoglShadowVolume::RenderShadows(deGraphicOpenGl *ogl, deoglMeshData *mesh, bool renderCaps){ // first pass if(renderCaps){ OGL_CHECK( glCullFace(GL_FRONT) ); OGL_CHECK( glStencilOp(GL_KEEP, GL_INCR_WRAP_EXT, GL_KEEP) ); }else{ OGL_CHECK( glCullFace(GL_BACK) ); OGL_CHECK( glStencilOp(GL_KEEP, GL_KEEP, GL_INCR_WRAP_EXT) ); } pRenderShadowPass(mesh, renderCaps); // second pass if(renderCaps){ OGL_CHECK( glCullFace(GL_BACK) ); OGL_CHECK( glStencilOp(GL_KEEP, GL_DECR_WRAP_EXT, GL_KEEP) ); }else{ OGL_CHECK( glCullFace(GL_FRONT) ); OGL_CHECK( glStencilOp(GL_KEEP, GL_KEEP, GL_DECR_WRAP_EXT) ); } pRenderShadowPass(mesh, renderCaps);}
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using LEQUAL and leaving out the anti-z-fight matrix yields z-fighting, like seen here:
can it be that the matrix is wrong? i see nothing wrong there though.
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i managed to narrow down the problem. it is not the perspective matrix. if rendering Depth-pass without caps i have no flickering, if i render all in Depth-fail with caps though it flickers like hell.
altering the 'e' value in the matrix i posted doesn't solve the problem hence i don't think the far clipping plane is the bad guy. i assume it is the near clipping plane but from my current understanding of this technic i don't get how this can be a problem with Depth-fail. somebody can give me some pointers or knows what problem i have run into?
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The blockiness in your image has driver bug written all over it.
For the caps, are you sure that the vertex program is producing the exact same vertex positions that are used in the shadow extrusion and the mesh itself? Can you post your vertex programs/shaders for the extrusion and caps?
Also, this is a long shot, but you wouldn't happen to have GL_POINT_SPRITE_ARB or GL_VERTEX_PROGRAM_POINT_SIZE_ARB enabled? I've noticed similar blockiness problems on ATI hardware in the past with these enabled (even though they have nothing to do with what you're rendering).
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about the caps i don't get exactly what you are refering too, but it should always use the same vertices.
this vertex-program is used to project the shadow volume:
!!ARBvp1.0## OpenGL Graphic Module Vertex Program## Copyright (C) 2004, Plüss Roland ( rptd@gmx.net )# # This program is free software; you can redistribute it and/or # modify it under the terms of the GNU General Public License # as published by the Free Software Foundation; either # version 2 of the License, or (at your option) any later # version.## This program is distributed in the hope that it will be useful,# but WITHOUT ANY WARRANTY; without even the implied warranty of# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the# GNU General Public License for more details.# # You should have received a copy of the GNU General Public License# along with this program; if not, write to the Free Software# Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA.## input data##############ATTRIB inPos = vertex.position; # position object space# output data###############OUTPUT outHPos = result.position; # homogenous position# constants############## eyePARAM pEyePos = program.local[0]; # eye position in object space# lightPARAM pLightPos = program.local[1]; # object spacePARAM pLightDir = program.local[2]; # object spacePARAM pLightColor = program.local[3];PARAM pLightOptions = program.local[4]; # type, power, cutoff, spotexp# opengl states#################PARAM pMatMVP[4] = { state.matrix.mvp };# variables#############TEMP t1;# transform the vertex with the matrix## t1 = inPos.w * pLightPos + (inPos - pLightPos, 0)ADD t1.xyz, inPos, -pLightPos;MOV t1.w, 0;MAD t1, pLightPos, inPos.w, t1;## outHPos = oglMatProj * (oglMatMdl * inPos);DP4 outHPos.x, t1, pMatMVP[0];DP4 outHPos.y, t1, pMatMVP[1];DP4 outHPos.z, t1, pMatMVP[2];DP4 outHPos.w, t1, pMatMVP[3];# end of program# 4 instructions# 1 temp registersEND
this one used for the mesh (it's the ambient shader but the light shaders are all the same except some additional parameters calculated):
!!ARBvp1.0## OpenGL Graphic Module Vertex Program## Copyright (C) 2004, Plüss Roland ( rptd@gmx.net )# # This program is free software; you can redistribute it and/or # modify it under the terms of the GNU General Public License # as published by the Free Software Foundation; either # version 2 of the License, or (at your option) any later # version.## This program is distributed in the hope that it will be useful,# but WITHOUT ANY WARRANTY; without even the implied warranty of# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the# GNU General Public License for more details.# # You should have received a copy of the GNU General Public License# along with this program; if not, write to the Free Software# Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA.## input data##############ATTRIB inPos = vertex.position; # position object spaceATTRIB inColor = vertex.color.primary; # ambient + emissiveATTRIB inTexPos = vertex.texcoord[0]; # texture coordinates# output data###############OUTPUT outHPos = result.position; # homogenous positionOUTPUT outColor = result.color.front.primary; # ambient + emissiveOUTPUT outTexPos = result.texcoord[0]; # texture coordinates# constants############## opengl states#################PARAM pMatTex1[4] = { state.matrix.texture[0] };PARAM pMatMVP[4] = { state.matrix.mvp };# variables############## calculate texture coordinates## outTexPos = oglMatTex1 * inTexPosDPH outTexPos.x, inTexPos, pMatTex1[0];DPH outTexPos.y, inTexPos, pMatTex1[1];# color is ambient + emissive## outColor = ambient + emissive;MOV outColor, inColor;# transform the vertex with the matrix## outHPos = oglMatProj * (oglMatMdl * inPos);DPH outHPos.x, inPos, pMatMVP[0];DPH outHPos.y, inPos, pMatMVP[1];DPH outHPos.z, inPos, pMatMVP[2];DPH outHPos.w, inPos, pMatMVP[3];# end of program# 7 instructions# 0 temp registersEND
about the extensions i'm not using them but it may be well the driver as i have also witnessed once texture-compression bugs where the driver compressed textures which he should not without asking me.
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Try changing your extrusion code to the following:
# transform the vertex with the matrix## t1.xyz = (inPos.w < 0.5) ? inPos - pLightPos : inPos;## t1.w = inPos.w;SLT t1.w, inPos.w, 0.5;MAD t1.xyz, pLightPos, -t1.w, inPos;MOV t1.w, inPos.w;## outHPos = oglMatProj * (oglMatMdl * inPos);DP4 outHPos.x, t1, pMatMVP[0];DP4 outHPos.y, t1, pMatMVP[1];DP4 outHPos.z, t1, pMatMVP[2];DP4 outHPos.w, t1, pMatMVP[3];
I've found that some processors with lower floating-point precision can cause problems when you try to do a + b - a, as I suggested in the gamasutra article. (At the time, it worked fine on all available GPUs, but on some newer GPUs you don't necessarily get exactly b back.) The above code is guaranteed to preserve your vertex position if its w component is 1.
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i'll try this one out once. one question though: what is SLT doing? don't remeber this command somehow.
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i tried out your suggestion and received a strange result. on components (models made with a 3d app) do work with this and procude no more flickering. terrain patches though (single sided, non closed, grid-like patch) does still flicker like hell. now this makes no sense as no matter which of both i use both end up as a triangle-list which is then shadow-rendered (hence it should be the same for both).
*scratch head*... anyways... it is a beginning (50% works now *grin*). one problem though still stays. if i get very close to a model surface the shadow gets wrong, even without the z-fight-matrix applied. can you look once more at the matrix and the shaders? i see no reason why very near to the camera-plane this effect happens. if the model moves roughly 10m away from you the effect vanishes. seen something like this?
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Quote:
one question though: what is SLT doing?
That's Set if Less Than -- it returns (ra < rb) ? 1.0 : 0.0.
Quote:
can you look once more at the matrix and the shaders?
I just noticed that the (3,3) and (4,3) entries of your projection matrix are negated (they should be e-1 and -1). Was there a reason for that? OpenGL won't be too happy without m.a43 = -1. It could be the source of your problems. | {"extraction_info": {"found_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": 0.25577619671821594, "perplexity": 7876.752657242485}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-05/segments/1516084887253.36/warc/CC-MAIN-20180118111417-20180118131417-00398.warc.gz"} |
http://science.sciencemag.org/content/163/3874/1445 | Reports
# Areal Spread of the Effect of Cloud Seeding at the Whitetop Experiment
See allHide authors and affiliations
Science 28 Mar 1969:
Vol. 163, Issue 3874, pp. 1445-1449
DOI: 10.1126/science.163.3874.1445
## Abstract
With reference to arguments that weather modification technology is sufficiently advanced for the federal government to finance cloud-seeding operations as a means of alleviating water shortages, an analysis of the Whitetop rain stimulation experiment was performed. The average 24-hour precipitation in six concentric regions up to 180 miles from the center of the target on 102 days of cloud seeding was less than that on the 96 experimental days without seeding. For distances less than 30 miles, the apparent loss of rain due to seeding was 32 percent. With the increase in distance, this apparent loss decreased to a minimum of 9 percent for gages between 120 and 150 miles from the center. However, the 48 gages at distances between 150 and 180 miles showed a 22 percent apparent loss of rain due to seeding. The estimated average loss of rain within the whole region of about 100,000 square miles was 21 percent of what would have fallen without seeding. When a 5-year experiment, expected to produce a 5 to 10-percent increase, shows a 20-percent decrease in rainfall, the relevant technology does not appear reliable enough for practical use. | {"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": 0.914621889591217, "perplexity": 1851.1486416788498}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-13/segments/1552912203123.91/warc/CC-MAIN-20190324002035-20190324024035-00411.warc.gz"} |
https://www.legacysurvey.org/dr8/updates/ | DR8 is the first release to integrate data from all of the individual Legacy Surveys (BASS, DECaLS and MzLS). In addition, observations for the Legacy Surveys were completed in March 2019, before the release of DR8. As such, a major push was made to update the DR7 code and data model to prepare for the final Legacy Surveys Data Releases. This page briefly documents those updates.
## Algorithmic changes for optical data
• Data from DECam has been trimmed to only observations after 2014-03-14 (to avoid problems with scattered light in early DECam data).
• Contaminating foreground sources have been treated more consistently:
• Such foreground sources include bright stars, medium-bright stars, globular clusters and large galaxies.
• The foreground sources consist of pre-defined geometrical masks (which are elliptical for galaxies).
• These mask regions are ignored in the local-sky-fitting calibration code.
• Within the mask regions for bright stars, globular clusters and large galaxies, sources are forced to be TYPE=PSF (except for the large galaxies themselves).
• Within all of the mask regions, a constant sky level is fit in the mask blob for each exposure; this appears to preferentially classify sources as TYPE=PSF around Gaia stars.
• Cosmic rays & other artifacts are now detected across multiple images.
• PSF wings around bright stars are now partially subtracted.
• All Gaia sources are forced to have fixed positions after accounting for proper motion and parallax.
• Sources that pass a star/galaxy cut in the Gaia catalog are forced to be TYPE=PSF using the Gaia excess noise parameter as follows:
• For $G < 18$: $\mathrm{astrometric\_excess\_noise} < 10^{0.5}$
• For $G \geq 18$: $\mathrm{astrometric\_excess\_noise} < 10^{(0.5 + 0.2(G-18))}$
• Astrometry is now tied entirely to Gaia Data Release 2.
## Algorithmic changes for WISE
• PSFs are now pixelized.
• Astrometry has been improved.
• Sky modeling is now more accurate, which should remove biases for faint sources.
• WISE coadds are generated on the same brick projections as for the optical ($g,r,z$) imaging.
• WISE bitmasks are now much more richly featured, as detailed in Aaron Meisner's unWISE documentation.
• The unWISE inverse variance map has been regularized.
## Other algorithmic changes
• External catalogs are now matched to using a 1.5 arcsecond radius (the matching radius was 1.0 arcsec prior to DR8).
## Data model changes
• The directory structure is now split into two distinct sub-directories:
• A new morphological type TYPE=DUP has been added for Gaia sources that are coincident with an extended source.
• No optical flux is assigned to DUP sources, but they are retained such that all Gaia sources appear in the source catalogs.
• The maskbits-* files have been updated with extra bits as documented on the DR8 bitmasks page.
• The BRIGHTSTARINBLOB boolean column has been dropped in favor of the integer column BRIGHTBLOB, which contains extra bits as documented on the DR8 bitmasks page.
• Additional Gaia columns have been added to the Tractor and sweeps catalogs:
• GAIA_PHOT_BP_RP_EXCESS_FACTOR
• GAIA_ASTROMETRIC_SIGMA5D_MAX
• GAIA_ASTROMETRIC_PARAMS_SOLVED
• Additional Gaia columns have been propagated from the Tractor catalogs to the sweeps catalogs:
• REF_CAT
• REF_EPOCH
• Additional columns now appear in the random catalogs:
• PSFSIZE_G/R/Z
• APFLUX_G/R/Z
• APFLUX_IVAR_G/R/Z
• PHOTSYS
• Additional columns now appear in the survey-ccds- files:
• plver (this was previously only in the ccds-annotated- files)
• procdate
• plprocid
• airmass
• ccdskysb
• ccdnastrom
• ccdnphotom
• A column has been removed from the survey-ccds- files:
• ccdnmatch
• Any columns denoting quantities in $u$, $i$ or $Y$ filters have been removed from the Tractor catalogs (e.g. flux_u, flux_i, flux_Y).
• The calib/*/splinesky files now contain many additional statistics characterizing the sky fitting.
• New metrics files have been added in the metrics directories: | {"extraction_info": {"found_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": 0.7700446844100952, "perplexity": 9021.648543102037}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1596439738746.41/warc/CC-MAIN-20200811090050-20200811120050-00393.warc.gz"} |
https://math.stackexchange.com/questions/1909203/are-neg-p-lor-q-lor-p-and-p-lor-neg-p-logically-equivalent | # Are $\neg p \lor q \lor p$ and $p \lor \neg p$ logically equivalent?
I'm not sure if this question makes sense or not, but if one assesses the following question:
Are $\neg p \lor q \lor p$ and $p \lor \neg p$ logically equivalent?
How could they be? The question doesn't seem to make sense.
Let's assume a truth table:
My Truth Table
Is this what the question is asking? It's a very vague question. I am just wondering if it is asking that given $p$ and $q$, that the values are equivalent based on the values taken from the truth table. Thanks! | {"extraction_info": {"found_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": 0.9390590786933899, "perplexity": 248.92131844011618}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1600401598891.71/warc/CC-MAIN-20200928073028-20200928103028-00008.warc.gz"} |
https://www.mathematik.uni-rostock.de/veranstaltungen/regelmaessige-veranstaltungen/forschungskolloquium/2017/ | ### Mathematisches Kolloquium 2017
• Assistant Professor Dimitri Boiroux (Technical University of Denmark)
"Mathematical modeling of neurons: Perspectives for the treatment of epilepsy"
Abstract: Epilepsy is a neurological disorder affecting around 40 million people worldwide, and is characterized by sudden occurrences of seizures. Currently, the main treatment is anti-epileptic drugs, but these drugs do not work for about a third of the patients. Neuromodulation, i.e. the alteration of neuronal activity through external stimuli, may be an alternative to drugs. The aim of this talk is to present the perspectives of closed-loop neuromodulation for epilepsy. I will provide a review of the models used for simulations of a single neuron and a network of interconnected neurons. I will also present the state of the art of treatments using open- and closed-loop control and discuss the possible future trends for the treatment of neurological disorders.
13.12.2017, 15:15 Uhr, HS 326 (Ulmenstr. 69, Haus 3)
Kolloquiumsleiter: Prof. Dr. Jens Starke
• Prof. Dr. Alexander Pott (Otto-von-Guericke Universität Magdeburg)
"Almost perfect nonlinear functions"
Abstract: Viele symmetrische Verschlüsselungsverfahren basieren auf der Anwendung von Funktionen, die hochgradig nichtlinear sind. Es gibt dabei verschiedene Kriterien, wie Nichtlinearität gemessen werden kann. Eine Möglichkeit wird durch sogenannte "almost perfect nonlinear functions" (APN) realisiert. Das sind Abbildungen auf einem endlichen Körper der Charakteristik 2, die sich von allen linearen Abbildungen stark unterscheiden. Die inverse Abbildung beispielsweise ist eine solche APN Funktion, die in einem der am weitesten verbreiteten Systeme (AES) verwendet wird.
In dem Vortrag gebe ich einen Überblick über die Entwicklung in diesem Gebiet in den letzten 10 Jahren und diskutiere einige offene Fragen.
29.11.2017, 16:15 Uhr, HS 228 (Ulmenstr. 69, Haus 3)
Kolloquiumsleiter: Prof. Dr. Gohar Kyureghyan
• Prof. Dr. Ferruh Özbudak (Middle East Technical University, Ankara, Turkey)
"Bent functions, plateaued functions and Alltop functions"
Abstract: We recall some definitions and basic facts on bent functions, plateaued functions and Alltop functions over arbitrary finite fields. We give some new characterizations. We also explain some applications related to cryptography, coding theory and communications briefly.
29.11.2017, 15:15 Uhr, HS 228 (Ulmenstr. 69, Haus 3)
Kolloquiumsleiter: Prof. Dr. Gohar Kyureghyan
• Prof. Dr. Kathrin Padberg-Gehle (Leuphana Universität Lüneburg)
"Coherent sets in nonautonomous dynamics"
08.11.2017, 16:00 Uhr, HS 326 (Ulmenstr. 69, Haus 3)
Kolloquiumsleiter: Prof. Dr. Jens Starke
• Dr. Christos Pelekis (The Czech Academy of Sciences, Institute of Computer Science)
"A generalised isodiametric problem"
Abstract: According to Bieberbach's inequality the area of a planar set whose diameter is 2 cannot be larger than \pi. What can we say about the maximum area of a planar set A, having the property that among any three points in A at least two are at distance less than or equal to 2? In the first part of the talk I will discuss the, devious, motivation behind the formulation of this question and I will sketch proofs of certain results and bounds on the maximum area of A. In the second part I will describe how the question gives rise to a "geometric analogue" of Turán's graph theorem and I will present some recent results on the corresponding extremal problem.
08.11.2017, 15:00 Uhr, HS 228 (Ulmenstr. 69, Haus 3)
• Dr. Giacomo Micheli (University of Oxford)
"Regular Pattern of Irreducible Polynomials"
Abstract: In this talk we explain a new connection between the theory of irreducible polynomials over finite fields and the theory of finite automata. This is a joint work with A. Ferraguti (University of Cambridge) and R. Schnyder (University of Zurich). In particular, we set up an infrastructure which allows the use of machinery from automata theory to address irreducibility questions for a special class of polyno- mials which has been widely studied in the literature (i.e. decomposable polynomials). Interestingly enough, such bridge can be constructed by means of elementary tools. In turn, it seems that this idea allows synergic combination of tools from the theory of finite fields and from the theory of regular languages. As an example, we are able to show non-trivial rational patterns in certain infinite subsets of primes of F q [x], where F q is a finite field (see [3, Theorem 3.10]). The theory seems also to lift quite naturally to the context of local fields. New questions arise naturally from this framework.
12.10.2017, 15:15 Uhr, HS 228 (Ulmenstr. 69, Haus 3)
Kolloquiumsleiter: Prof. Dr. Gohar Kyureghyan
• Dr. Valentin Suder (University of Versailles-St-Quentin-en-Yvelines)
"Differential Equivalences of SBoxes"
Abstract: In this work, we discuss two notions of differential equivalence on Sboxes. First, we introduce the notion of DDT-equivalence which applies to vectorial Boolean functions that share the same difference distribution table (DDT). Next, we compare this notion, to what we call the γ-equivalence, applying to vectorial Boolean functions whose DDTs have the same support. We discuss the relation between these two equivalence notions and provide an algorithm for computing the DDT-equivalence and the γ-equivalence classes for a given function. We study the sizes of these classes for some families of Sboxes. Finally, we prove a result that shows that the rows of the DDT of an APN permutation are pairwise distinct.
12.10.2017, 14:00 Uhr, HS 228 (Ulmenstr. 69, Haus 3)
Kolloquiumsleiter: Prof. Dr. Gohar Kyureghyan
• Dr. Thomas Kalinowski (The University of Newcastle)
"Extended formulations for convex hulls of graphs of bilinear functions "
Abstract: Many methods in global optimization require the approximation of convex and concave envelopes of functions. For bilinear functions, a classic approach is the McCormick relaxation: introduce additional variables representing products of pairs of original variables and write down linear constraints approximating the bilinear terms. The McCormick relaxation can be strengthened by adding more inequalities. In this direction, the Boolean Quadric Polytope (BQP) is best possible in the sense that its projection is the convex hull of the graph of the function, in other words, it provides an extended formulation for this graph. Unfortunately, in general the BQP has exponentially many facets and no complete list is known. In the talk I will discuss a method which in certain cases allows the identification of a small subset of facets of the BQP describing an extended formulation for the graph of the function.
(joint work with Natashia Boland, Akshay Gupte, Fabian Rigterink and Hamish Waterer)
19.07.2017, 15:45 Uhr, HS 228 (Ulmenstr. 69, Haus 3)
• Prof. Dr. Uwe Leck (Europa-Universität Flensburg)
"Problems and conjectures related to possible sizes of maximal antichains"
Abstract: We will address the following two problems:
1. For given n, which cardinalities are attainable by maximal antichains in the Boolean lattice B_n?
2. For given m and k, which cardinalities can the shadow of a k-uniform family of m sets in B_n have?
Some general conjectures will be stated and motivated. Strategies and partial results will be presented.
19.07.2017, 15:15 Uhr, HS 228 (Ulmenstr. 69, Haus 3)
• Prof. Dr. Jerry Griggs (University of South Carolina)
"Poset-free Families of Subsets"
Abstract: Given a finite poset P, we consider the largest size La(n,P) of a family of subsets of [n]:={1,...,n} that contains no (weak) subposet P. Early theorems of Sperner and Katona solve this problem when P is the k-element chain (path poset) P_k, where it is the sum of the middle k-1 binomial coefficients in n. Katona and his collaborators investigated La(n,P) for other posets P. It can be very challenging, even for small posets.
Based on earlier results we conjectured with Lu (2008) that pi(P), which is the limit as n goes to infinity, of La(n,P)/{n\choose{n/2}}, exists for general posets P. Moreover, it is an integer obtained in a specific way. The conjecture has been verified for various families of posets.
For most k at least 2, our work with Li verifies the conjecture for D_k, which is the k-diamond poset {A< B_1,...,B_k < C}. Yet, the case k=2 remains open, after considerable effort by researchers. We expect pi(D_2)=2, the easy lower bound. Recently, Grosz, Methuku, and Tompkins brought the upper bound down below 2.21. Tools used on these problems include probabilistic reasoning, such as bounding the average number of times a random full chain meets a P-free family F, called the Lubell function of F.
19.07.2017, 14:00 Uhr, HS 228 (Ulmenstr. 69, Haus 3)
• Prof. Dr. Alois Kneip (Universität Bonn)
"On the Optimal Reconstruction of Partially Observed Functional Data"
Abstract: We propose a new linear prediction operator that aims to recover the missing parts of a function given the observed parts. The structure of an optimal linear predictor is analyzed theoretically. Our estimation theory allows for autocorrelated functional data and considers the practically relevant situation where each function (in total n many) is observed at m discretization points. We derive uniform rates of consistency for our nonparametric estimation procedures using a double asymptotic that allows investigate all data scenarios from almost sparse to dense functional data. The finite sample properties are investigated through simulations and a real data application.
12.07.2017, 15:00 Uhr, HS 326/327 (Ulmenstr. 69, Haus 3)
Kolloquiumsleiter: Prof. Dr. A. Meister
• Dr. rer. nat. habil. Michael Maiwald (BAM)
"Low field NMR spectroscopy for process control - robust automated data preparation and analysis as prerequisites"
12.07.2017, 10:15 Uhr, Raum 427 (Ulmenstr. 69, Haus 3)
Kolloquiumsleiter: Prof. Dr. Klaus Neymeyr
• Dr. Romanos Malikiosis (TU Berlin)
"Formal Duality in Finite Cyclic Groups"
05.07.2017, 15:00 Uhr, HS 228 (Ulmenstr. 69, Haus 3)
Kolloquiumsleiter: Prof. Dr. A. Schürmann
• apl. Prof. Heidemarie Bräsel (im Ruhestand)
"Faszination Mathematik"
Abstract: „Faszination Mathematik – Malerei und mehr“, so hieß die Ausstellung, die ich anlässlich des 50. Jahrestages der Gründung der Spezialklasse für Mathematik und Naturwissenschaften an der damaligen Technischen Hochschule Magdeburg im Herbst 2014 gestaltet habe. Die Ausstellung war so erfolgreich, dass mein Mann und ich beschlossen haben, mit ihr auf Wanderschaft zu gehen.
In meinem Vortrag möchte ich Ihnen einen Überblick über die Inhalte der Bilder und Computergrafiken, über die mathematischen Experimente und über das Zahlensammelsurium geben. Dabei spannt sich der Bogen vom Satz des Pythagoras, dem Goldenen Schnitt und den Fibonaccizahlen und Fibonaccispiralen hin zu den Fraktalen, der Geometrie der Natur.
Bei den Experimenten zu magischen und lateinischen Quadraten sollen neue Erfahrungen zur Konstruktion und Auffüllbarkeit solcher Quadrate und auch über ihren Zusammenhang gewonnen werden. Ein Modell aus 49 Würfeln, die 6 paarweise orthogonale lateinische Quadrate der Ordnung 7 enthalten, lädt zum Staunen ein. Natürlich darf auch mathematisch gepuzzelt werden.
Schließlich wird noch auf die Plakatserie des Sammelsurium eingegangen, das Kurioses, Wissenswertes und Symbolisches über die Zahlen von 0 bis 12 enthält.
Ich bin sicher, dass ich Ihnen nicht viel Neues aus der Mathematik erzählen werde, schließlich will ich vor einem Fachpublikum vortragen, aber ich erzähle es Ihnen anders: Mathematik zum Anschauen, Staunen, neugierig und aktiv werden, Begreifen und Lernen. Seien Sie neugierig!
17.05.2017, 15:00 Uhr, HS 228 (Ulmenstr. 69, Haus 3)
Kolloquiumsleiter: Prof. Dr. G. Kyureghyan
• Prof. Dr. Benjamin Klopsch (Universität Düsseldorf)
"Zetafunktionen von zulässigen Darstellungen kompakter p-adischer Liegruppen"
Abstract: Die gewöhnliche’ Darstellungszetafunktion einer kompakten p-adischen Liegruppe G ist eine Dirichlet-Erzeugendenfunktion, mittels derer (endlich dimensionale) irreduzible komplexe Darstellungen von G abgezählt werden. Zunächst werde ich diese Art von Zetafunktionen motivieren und einige zugehörige Resultate skizzieren. Allgemeiner läßt sich jeder geeigneten’ unendlich dimensionalen Darstellung von G eine Zetafunktion zuordenen; die `gewöhnliche’ Darstellungszetafunktion ist dann - bis auf Skalierung - gerade die Zetafunktion der regulären Darstellung von G. In meinem Vortrag werde ich über gemeinsame Ergebnisse mit Steffen Kionke berichten und dabei den Schwerpunkt auf Zetafunktionen induzierter Darstellungen setzen. Eine sehr einfache und schöne Quelle von expliziten Beispielen erschließt sich aus distanztransitiven Wirkungen von pro-endlichen Gruppen auf verwurzelten Bäumen, weitere dann schon kompliziertere Beispiele lassen sich mit Hilfe der Kirillovschen Bahnenmethode und Werkzeugen aus der p-adischen Integrationstheorie gewinnen.
03.05.2017, 15:00 Uhr, SR 228 (Ulmenstr. 69, Haus 3)
Kolloquiumsleiter: Prof. Dr. J.-C. Schlage-Puchta
• Prof. Dr. Angelika Rohde (Albert-Ludwigs-Universität Freiburg)
Abstract: We develop honest and locally adaptive confidence bands for probability densities. They provide substantially improved confidence statements in case of inhomogeneous smoothness, and are easily implemented and visualized. The article contributes conceptual work on locally adaptive inference as a straightforward modification of the global setting imposes severe obstacles for statistical purposes. Among others, we introduce a statistical notion of local Hölder regularity and prove a correspondingly strong version of local adaptivity. We substantially relax the straightforward localization of the self-similarity condition in order not to rule out prototypical densities. The set of densities permanently excluded from the consideration is shown to be pathological in a mathematically rigorous sense. On a technical level, the crucial component for the verification of honesty is the identification of an asymptotically least favorable stationary case by means of Slepian's comparison inequality. This is a joint work with Tim Patschkowski.
21.04.2017, 15:00 Uhr, HS 125 (Ulmenstr. 69, Haus 3)
Kolloquiumsleiter: Prof. Dr. A. Meister
• Prof. Dr. Kim Jong-Min (University of Minnesota-Morris)
"Mixture of D-vine copulas or modeling dependence"
Abstract : The identification of an appropriate multivariate copula for capturing the dependence structure in multivariate data is not straightforward. The reason is because standard multivariate copulas (such as the multivariate Gaussian, Student-t, and exchangeable Archimedean copulas) lack flexibility to model dependence and have other limitations, such as parameter restrictions. To overcome these problems, vine copulas have been developed and applied to many applications. In order to reveal and fully understand the complex and hidden dependence patterns in multivariate data, a mixture of D-vine copulas is proposed incorporating D-vine copulas into a finite mixture model. As a D-vine copula has multiple parameters capturing the dependence through iterative construction of pair copulas, the proposed model can facilitate a comprehensive study of complex and hidden dependence patterns in multivariate data. The proposed mixture of D-vine copulas is applied to simulated and real data to illustrate its performance and benefits.
Keywords: Dependence, Multivariate data, Pair-copula, Vines.
16.02.2017, 10:30 Uhr, HS 125 (Ulmenstr. 69, Haus 3)
Kolloquiumsleiter: Prof. Dr. W.-D.Richter
• Dr. Francesco Chiacchio (Universität Neapel)
"Sharp Poincar´e inequalities"
Abstract: Let µ1(Ω) be the first nontrivial Neumann eigenvalue for the Laplace operator in a Lipschitz, bounded domain Ω of Rn. We will present two type of lower bounds for µ1(Ω), involving different geometrical features of Ω. In the first estimate, obtained in [1] via “symmetrization arguments”, it appears Kn(Ω) the isoperimetric constant relative to Ω. In [2] we consider planar domains consisting of the points on one side of a fixed curve γ, within a suitable distance δ from it. In this last case the estimate is given in terms of the length of γ, its curvature and δ.
References:
[1] B. Brandolini, F. Chiacchio, C. Trombetti, Optimal lower bounds for eigenvalues of linear and nonlinear Neumann problems. Proc. Roy. Soc. Edinburgh Sect. A 145 (2015), no. 1, 31-45.
[2] B. Brandolini, F. Chiacchio, E. B. Dryden, J. J. Langford, Sharp Poincar´e inequalities in a class of non-convex sets, arXiv:1608.01236v1.
25.01.2017, 17:00 Uhr, HS 125 (Ulmenstr. 69, Haus 3)
Kolloquiumsleiter: Prof. Dr. Friedemann Brock
• Prof. Dr. Sergej Bezrukov (University of Wisconsin - Superior)
"New families of edge-isoperimetric graphs"
Abstract: We present new infinite families of regular graphs whose all cartesian powers admit nested solutions in the edge-isoperimetric problem. For a given graph the problem is to specify a subgraph of a given order m that has maximum number I(m) of induced edges among all subgraphs of that order. Our results include as special cases most previously published results in this area. The graphs are specified by means of so-called delta-sequences of the length given by the number of vertices in the graph. The m-th element of the sequence d(m) is the difference I(m) - I(m-1). We also present a construction for regular graphs admitting these sequences. We show that by ordering the vertices of the n-th cartesian power of our graphs lexicographically (where n is at least 2), the subgraph induced by any initial segment of this order spans maximum number of edges.
As a byproduct, based on a special representation of graphs as a union of disjoint cliques, we introduce a new technique for extending a graph admitting nested solutions in the edge-isoperimetric problem to a larger one with that property.
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http://fora.xkcd.com/search.php?author_id=34856&sr=posts | ## Search found 150 matches
Mon Apr 01, 2013 7:55 pm UTC
Topic: 1193: Externalities
Replies: 505
Views: 152706
### Re: 1193: Externalities
I have pyskein 0.7.1 and am matching what the website gives except for in the one case where I tried using some curse words and numbers mixed together
Wed Jan 13, 2010 2:53 am UTC
Forum: Mathematics
Topic: Is there a such thing as a cardinality under aleph null?
Replies: 18
Views: 1924
### Re: Is there a such thing as a cardinality under aleph null?
If a set is infinite, you can remove any finite number of objects and it maintains being infinite. In particular you can remove one object, then another object, then another object, etc. So you can map aleph 0 into your infinite set (by counting the objects you removed) and hence aleph 0 must be at ...
Thu Jan 07, 2010 1:58 pm UTC
Forum: Mathematics
Topic: Group theory: do some sets have implied operations?
Replies: 10
Views: 1653
### Re: Group theory: do some sets have implied operations?
R* is used to denote the ring of units but someone taking group theory for the first time may not have seen that notation. As an example of how obvious the group operation in question is let's take a look at Z 2 . I claim there are two possible groups 1) The operations addition operation as we know ...
Sat Dec 05, 2009 7:35 pm UTC
Forum: Mathematics
Topic: Number of paths under diagonal
Replies: 10
Views: 1426
### Re: Number of paths under diagonal
Fri Jun 12, 2009 11:32 am UTC
Topic: 0596: "Latitude"
Replies: 84
Views: 23877
### Re: "Latitude" Discussion
Hmm... I thought Megan bought a sexbot and installed an arc welder on it
Fri Jun 05, 2009 3:20 pm UTC
Forum: Mathematics
Topic: Real-world examples of -x * -y = +z
Replies: 66
Views: 8352
### Re: Real-world examples of -x * -y = +z
Sure it is. All you have to do is interpret the two numbers differently: one is a point on the number line, and one is a scale factor. Negative scale factors are "orientation-reversing." Yes, you have positive times positive is positive because three groups of four apples is twelve apples...
Fri Jun 05, 2009 7:08 am UTC
Forum: Mathematics
Topic: Most frequently occuring digit
Replies: 17
Views: 1893
### Re: Most frequently occuring digit
Does 1x10^10 have two zeroes or ten zeroes?
Mon Jun 01, 2009 5:12 am UTC
Topic: 0591: "Troll Slayer"
Replies: 178
Views: 187022
### Re: "Troll Slayer" Discussion
This comic was awesome. Then I read the alt-text. Genius!
And good call pyro
Tue Apr 28, 2009 5:47 am UTC
Forum: Mathematics
Topic: Good problem for a 10th grader?
Replies: 32
Views: 3027
### Re: Good problem for a 10th grader?
Lol, you're right quintopia. I normally don't write it that way, so when I saw your quote I thought you were bolding my text
Mon Apr 27, 2009 11:22 pm UTC
Forum: Mathematics
Topic: Good problem for a 10th grader?
Replies: 32
Views: 3027
### Re: Good problem for a 10th grader?
3,5,7 is not the only set of consecutive primes all of which are odd. In fact, all but one set of three consecutive primes are all odd. I thought that you'd say that, but I don't see how you can interpret it that way from the sentence structure. I avoided saying three consecutive odd primes for a r...
Mon Apr 27, 2009 10:49 pm UTC
Forum: Mathematics
Topic: Good problem for a 10th grader?
Replies: 32
Views: 3027
### Re: Good problem for a 10th grader?
quintopia, what's the other interpretation?
Mon Apr 27, 2009 7:13 pm UTC
Forum: Mathematics
Topic: Good problem for a 10th grader?
Replies: 32
Views: 3027
### Re: Good problem for a 10th grader?
The solution is incredibly easy to understand, so even if the problem is too hard it's simple to just ask the question, have her struggle over it, then give the solution. Then use this as a jumping off point to other similar questions. If the question's too easy, that's fine, because you can use it ...
Sun Apr 26, 2009 2:39 am UTC
Forum: Mathematics
Topic: question that I have no Idea how to go about
Replies: 10
Views: 1212
### Re: question that I have no Idea how to go about
It's obvious that if the die is not a 2 or a 1 you re-roll it. If you get a 2 on your first die, my gut instinct is that it's better to re-roll, because you have lots of chances to get a 2 again, and are fairly unlikely to get straight 1's on your other dice.
Sun Apr 26, 2009 2:26 am UTC
Forum: Forum Games
Topic: Name a smaller (closer to zero) number.
Replies: 52
Views: 4950
### Re: Name a smaller (closer to zero) number.
Previous number divided by -2
Sat Apr 25, 2009 10:48 pm UTC
Forum: Mathematics
Topic: My question might annoy those who know the answer
Replies: 13
Views: 1405
### Re: My question might annoy those who know the answer
I'll try again
∅rly?
Sat Apr 25, 2009 6:24 pm UTC
Forum: Mathematics
Topic: Math: Fleeting Thoughts
Replies: 434
Views: 161371
### Re: Math: Fleeting Thoughts
Did you divide by the volume of an M&M?\
You might want to find the height and diameter and assume it's a box shape instead because they don't fit together perfectly
Fri Apr 24, 2009 5:30 am UTC
Topic: 0573: "Parental Trolling"
Replies: 78
Views: 19974
### Re: "Parental Trolling" Discussion
BlueEyedGreen wrote:I love how everything in the future is curvy, and how computers are just sleek glowing membranes floating at desk level.
I didn't even notice that
Fri Apr 24, 2009 5:19 am UTC
Topic: 0573: "Parental Trolling"
Replies: 78
Views: 19974
### Re: "Parental Trolling" Discussion
Let's be honest, this comic would only be mildly amusing except for the use of 'bleegle warble yargle' for when she can't speak
Fri Mar 27, 2009 8:39 pm UTC
Forum: Mathematics
Topic: Here's a fun problem...
Replies: 27
Views: 3741
### Re: Here's a fun problem...
A sucker would expect a heads to increase the chance of a tails coming up next. Most people aren't suckers, so will pick heads to come up next. He knows most people aren't suckers, so the coin's rigged to come up tails. More seriously, itaibin, I can't believe that him flipping the coin and it landi...
Mon Mar 23, 2009 7:50 pm UTC
Forum: Mathematics
Topic: Alternative definitions of the derivative
Replies: 15
Views: 2283
### Re: Alternative definitions of the derivative
I should be using math fonts but I forget the syntax. If f : R^n -> R^m is differentiable at a E R^n. There exists a linear transformation L : R^n -> R^m such that lim h-> 0 |(f(a + h) - f(a) - L(h))|/|h| = 0 The function L is refered to as the derivative of f at a. real-valued single-variable func...
Sun Mar 22, 2009 1:47 pm UTC
Forum: Mathematics
Topic: Uncountably many vertical asymptotes?
Replies: 18
Views: 2161
### Re: Uncountably many vertical asymptotes?
Something that sort of fits what you're looking for: f(x) = 0 if x is irrational and if x is rational, say x = m/n, then f(x) = n f is locally unbounded everywhere. You don't get the limit of f approaching infinity as x approaches a point (since it doesn't exist) but the limsup does for every point....
Thu Mar 19, 2009 6:32 pm UTC
Forum: Mathematics
Topic: Different definitions of an open set
Replies: 18
Views: 1633
### Re: Different definitions of an open set
Define T to be the closure of T' under finite intersection and countable union. Then T happens to match all of the requirements of a topology on S.
You need uncountable unions also
Thu Mar 12, 2009 11:49 pm UTC
Forum: Mathematics
Topic: Math problem help
Replies: 9
Views: 1034
### Re: Math problem help
You should have a formula describing distance as a function of time and acceleration which you can solve
Tue Mar 10, 2009 2:14 pm UTC
Forum: Mathematics
Topic: Graph: F(x)=x^∞
Replies: 25
Views: 3355
### Re: Graph: F(x)=x^∞
For a quick answer: \lim_{x\to\infty}\frac{1}{x^2}=\frac{1}{\infty^2} = \frac{1}{\infty} = 0 \lim_{x\to\frac{\pi}{2}}\frac{1}{cos(x)}=\frac{1}{cos(\frac{\pi}{2})} = \frac{1}{0} = \infty Meaning, in the context of limits at least (an underlying basis of many other things like derivat...
Mon Mar 09, 2009 1:24 pm UTC
Forum: Mathematics
Topic: Find if a number has a root
Replies: 8
Views: 1263
### Re: Find if a number has a root
There are all kinds of algorithms. A not very efficient one is: Given a number y for which we are trying to find positive integer roots, we will find them only if y is a positive integer. Write the equation x^n=y. This is the same as finding roots for x^n-y=0. If there is an integer root k, (x-k) i...
Sun Feb 08, 2009 2:33 am UTC
Forum: Mathematics
Topic: The probability of impossible
Replies: 63
Views: 7531
### Re: The probability of impossible
It should be noted that as long as your sample space is countable, that p(x)=0 does in fact imply that x is impossible. It's only when you have uncountable sample spaces, like the set of real numbers or the set of infinite sequences H or T that you start getting into these problems (if problem is th...
Mon Nov 24, 2008 3:12 pm UTC
Forum: Logic Puzzles
Topic: Right and Left - Truth and Lies.
Replies: 23
Views: 3466
### Re: Right and Left - Truth and Lies.
Holy cow! What if they're ambidextrous!
Fri Nov 21, 2008 5:38 pm UTC
Forum: Mathematics
Topic: Favorite math jokes
Replies: 1452
Views: 494127
### Re: Favorite math jokes
Why did the vector cross the road? He wanted to be normal A baseball coach once had the most talented team he'd ever seen. Unfortunately, it all got flipped upside down when he put his naturals in a field. An infinite number of mathematicians walk into a bar. The first one orders a beer. The second ...
Fri Nov 21, 2008 5:14 pm UTC
Forum: Mathematics
Topic: Analysis success suggestions?
Replies: 3
Views: 780
### Re: Analysis success suggestions?
Become more than familiar with definitions, what they mean, and alternative formulations. Continuity is a good example, you have the standard epsilon-delta definition of a continuous function, but you also have a function is continuous if and only if for all convergent sequences (x k ) (converging t...
Fri Nov 14, 2008 5:32 pm UTC
Forum: Mathematics
Topic: Which is bigger?
Replies: 35
Views: 3653
### Re: Which is bigger?
Maybe you shouldn't have bought them so much food
Thu Nov 13, 2008 10:39 pm UTC
Forum: Mathematics
Topic: Which is bigger?
Replies: 35
Views: 3653
### Re: Which is bigger?
Even larger than 3->3->65->3?
Thu Nov 13, 2008 7:42 pm UTC
Forum: Mathematics
Topic: Minimum bit string (shortest common superstrings)
Replies: 20
Views: 2366
### Re: Minimum bit string
If you start with the string of n 1's, then you add a 0, you get the string with a 0 at the end... adding on more 1's gives you each string with a single 0 placed somewhere inside the string. You can't extend this exactly for two zeros as far as I can tell, but that's a bit more of a systematic star...
Thu Nov 13, 2008 5:54 pm UTC
Forum: Mathematics
Topic: Adding Repeating Decimals (not *quite* .999...=1)
Replies: 28
Views: 2990
### Re: Adding Repeating Decimals (not *quite* .999...=1)
If I have a distinct .000....1 and I multiply it by 10, what do I get? This is the biggest problem with trying to use an intuitive decimal notation for a 'super small' number
Thu Nov 13, 2008 12:29 pm UTC
Forum: Logic Puzzles
Topic: Equilibrium Strategy for "Tension"
Replies: 14
Views: 1869
### Re: Equilibrium Strategy for "Tension"
If the number of bins is less than the number of people,
Spoiler:
then n people each putting all their chips into a different of the bins gives an equilibrium (the rest of the players don't bid at all). It's not a very interesting one though
Wed Nov 12, 2008 9:24 pm UTC
Forum: Mathematics
Topic: Direct proof of compactness
Replies: 18
Views: 1791
### Re: Direct proof of compactness
Proving the Heine Borel theorem and then using the Heine Borel theorem is still using the Heine Borel theorem.
Wed Nov 12, 2008 6:33 pm UTC
Forum: Mathematics
Topic: Direct proof of compactness
Replies: 18
Views: 1791
### Re: Direct proof of compactness
"Unroll" the definition of the Heine-Borel theorem and apply it. If whatever grading authority says that's still using the Heine-Borel theorem, add a line in the unrolled definition stating "For all b in B, the set of bananas, b is a banana". Because the Heine-Borel theorem neve...
Wed Nov 12, 2008 3:04 pm UTC
Topic: 0503: "Terminology"
Replies: 292
Views: 48543
### Re: Terminology
Re: Africa. Let's be honest. Rome beat Carthage, the Persians took Egypt, and it was pretty much game over for the whole continent. It's kind of like getting zerg-rushed
I think we should refer to Antarctica as the deep south from now on
Mon Nov 10, 2008 10:40 pm UTC
Forum: Mathematics
Topic: Direct proof of compactness
Replies: 18
Views: 1791
### Re: Direct proof of compactness
If there's an open cover of K, it must be 0 is contained in one of the covering sets. What else does that covering set cover (hint: A lot of other points)
Thu Nov 06, 2008 7:12 pm UTC
Forum: Mathematics
Topic: How do you prove that a function is continuous?
Replies: 12
Views: 7660
### Re: How do you prove that a function is continuous?
And yet you're the only person who didn't understand what level of math answers should be at. Someone working with rings of continuous functions over a compact space does not need to know how to prove sinx + 2 is continuous
Wed Nov 05, 2008 11:33 pm UTC
Forum: Forum Games
Topic: Word Chain II
Replies: 51
Views: 4524
### Re: Word Chain II
tricky77puzzle wrote:
Office_Shredder wrote:freed to slave
Spoiler:
freed
feed
fed
lave
slave
He asked for slave to free, not freed.
Oh, whatever. Just change it to
free
freed
repeat
That was trivially fixable without comment I think | {"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": 0.8570677042007446, "perplexity": 2426.1443003682784}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1566027315618.73/warc/CC-MAIN-20190820200701-20190820222701-00203.warc.gz"} |
http://mathhelpforum.com/algebra/146324-percentage-change-between-percentages.html | # Math Help - Percentage change between percentages
1. ## Percentage change between percentages
Hi all,
Let's say that 20% of the population had a computer in 1990 and 35% of the population had a computer in 2000. What is the percentage change between 1990 and 2000?
Is it [(35-20)/20]*100=75% or 35-20=15%?
2. 15%
3. Thanks slovakiamaths!
I know, i know.... i suck at math!! | {"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": 0.9936730861663818, "perplexity": 2578.0803568129672}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-22/segments/1432207930259.97/warc/CC-MAIN-20150521113210-00051-ip-10-180-206-219.ec2.internal.warc.gz"} |
https://arxiv.org/abs/1006.3061 | astro-ph.SR
(what is this?)
Title:Surface flux transport modeling for solar cycles 15--21: effects of cycle-dependent tilt angles of sunspot groups
Abstract: We model the surface magnetic field and open flux of the Sun from 1913 to 1986 using a surface flux transport model, which includes the observed cycle-to-cycle variation of sunspot group tilts. The model reproduces the empirically derived time evolution of the solar open magnetic flux, and the reversal times of the polar fields. We find that both the polar field and the axial dipole moment resulting from this model around cycle minimum correlate with the strength of the following cycle.
Comments: Accepted for publication by ApJ Subjects: Solar and Stellar Astrophysics (astro-ph.SR) DOI: 10.1088/0004-637X/719/1/264 Cite as: arXiv:1006.3061 [astro-ph.SR] (or arXiv:1006.3061v1 [astro-ph.SR] for this version)
Submission history
From: Robert Cameron [view email]
[v1] Tue, 15 Jun 2010 19:44:24 UTC (69 KB) | {"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": 0.8238162398338318, "perplexity": 4852.03173188237}, "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-2019-04/segments/1547584336901.97/warc/CC-MAIN-20190123172047-20190123194047-00271.warc.gz"} |
http://www.tug.org/pipermail/tex-k/2002-October/000555.html | [tex-k] fonts for dvips
Timothy Murphy tim@maths.tcd.ie
Sat, 19 Oct 2002 22:51:09 +0100
On Fri, Oct 18, 2002 at 02:41:34PM -0400, Kevin Cahill wrote:
> But when using the slides documentclass,
> I can't get dvips to find the fonts it needs,
> e.g., most subscripts and superscripts
> were missing.
but I've always found the seminar class
superior in almost every way to the slides class.
===============================================
\documentclass[a4,12pt,semhelv,portrait]{seminar}
\pagestyle{empty}
\begin{document}
\begin{slide*}
...
\end{slide*}
\end{document}
===============================================
--
Timothy Murphy
e-mail: tim@maths.tcd.ie
tel: 086-233 6090
s-mail: School of Mathematics, Trinity College, Dublin 2, Ireland | {"extraction_info": {"found_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": 0.9060313701629639, "perplexity": 26536.40433433715}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-05/segments/1516084891316.80/warc/CC-MAIN-20180122113633-20180122133633-00785.warc.gz"} |
http://tex.stackexchange.com/questions/23718/labelling-and-drawing-at-rotated-shifted-objects | # Labelling and drawing at rotated/shifted objects
I'm trying to draw an image from a mathematical publication (see the crop at the end of my post). You can find a recent version of the drawing at page 37 of my script (PDF). The complete source is here.
I drew a rhomb with those squares in it and shifted all pieces to the right place:
\begin{tikzpicture}
\draw (0,0) -- (4,1) -- (8,0) -- (4,-1) -- (0,0);
\draw[thick] (6,.5) -- (4,1) -- (4,-1) -- (6,-.5)
[yshift=4cm] (6,.5) -- (4,1) -- (4,-1) -- (6,-.5);
\draw[thick,dashed] (6,.5) -- (6,-.5)
[yshift=4cm] (6,.5) -- (6,-.5);
I did the same with the squares around those figures. Now I want to label each square (R_0, R_1) and draw arrows from one box to another.
I'm looking for a better way than to write something like \draw[->] (2,2) -- (2,0);. So adding nodes sounds like the right idea, but I found no working solution. What would you recommend for drawing arrows and adding some labels?
-
You can use the shapes tikz-library. I am including an example, but you should read section 48.3 Geometric shapes on page 420 from the tikz manual. Here is the example
\documentclass{minimal}
\usepackage{tikz}
\usetikzlibrary{shapes}
\usetikzlibrary{positioning}
\begin{document}
\begin{tikzpicture}
\node[draw=lightgray,rectangle,inner sep=0.5cm,outer sep=5pt,label=245:$R_0$] (top) {\tikz{
\node[draw,trapezium,trapezium angle=75,shape border rotate=270,outer sep=0pt] (top trap)
{$\sigma(S_0)$};
\draw[white,postaction={draw=black,dashed}]
(top trap.bottom left corner) -- (top trap.bottom right corner);
}};
\node[draw=lightgray,rectangle,inner sep=0.5cm,below=2cm of top,outer sep=5pt,label=245:$R_0$] (bottom) {\tikz{
\node[draw,trapezium,trapezium angle=75,shape border rotate=270,outer sep=0pt] (trap)
{$T_0$};
\draw[white,postaction={draw=black,dashed}] (trap.top left corner) -- (trap.top right corner);
}};
\draw[->] (top) -- (bottom) node[pos=0.5,right] {$\varphi|_{R_0}$};
\end{tikzpicture}
\end{document}
The result is
- | {"extraction_info": {"found_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": 0.9234413504600525, "perplexity": 2187.4370836065427}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-48/segments/1448398446300.49/warc/CC-MAIN-20151124205406-00093-ip-10-71-132-137.ec2.internal.warc.gz"} |
http://link.springer.com/article/10.1007%2FBF01199323 | , Volume 97, Issue 1-2, pp 259-285
# Laplace asymptotics for reaction-diffusion equations
Rent the article at a discount
Rent now
* Final gross prices may vary according to local VAT.
## Summary
We obtain sharp (i.e. non logarithmic) asymptotics for the solution of non homogeneous Kolmogorov-Petrovski-Piskunov equation depending on a small parameter ε, for points ahead of the Freidlin-KPP front. | {"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": 0.8906754851341248, "perplexity": 5027.5753367261805}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1408500832662.33/warc/CC-MAIN-20140820021352-00396-ip-10-180-136-8.ec2.internal.warc.gz"} |
http://math.stackexchange.com/questions/93019/visualizing-homologous-elements | # Visualizing homologous elements
For the fundamental group it's easy to visualize when two loops are homotopic. I was wondering if there are any ways to look at the equivalent problem for homology? I guess this might be tricky for singular homology, but are there nice ways to think about this for say simplicial and cellular homology?
-
By definition, two $k$-chains $a$ and $b$ are homologous if they represent the same homology class; that is to say that $a-b = \partial C$ for some $k+1$-chain $C$. Let's restrict our attention to surfaces for the moment, for simplicity, and let's set $k=1$ just to see how this goes. A $2$-chain will just be some two-dimensional subsurface, possibly with boundary. For instance, $C$ might be a cylindrical subsurface sitting inside the torus (a quarter-donut, if you will). The boundary of $C$ in this case will consist of two loops, and (having properly oriented everything) these two loops will be homologous, precisely because together they bound a subsurface.
Similarly, in some simply-connected space, like $\mathbb{R}^2$, say, all $1$-chains are homologous to zero, since we can always find a $2$ chain to "fill in" any holes; if we have a map of the circle, we can always extend it to a map of the $2$-disk. But of course, we can't always fill in holes in spaces with more interesting topology; i.e. a loop going around the hole in a torus can't be filled in, hence this will not represent zero in homology.
The introduction to Chapter 2 of Hatcher's $\textit{Algebraic Topology}$ has a nice discussion motivating the transition from homotopy to homology that you might enjoy looking at. | {"extraction_info": {"found_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": 0.9025288224220276, "perplexity": 128.23281761516088}, "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-2014-10/segments/1394011267211/warc/CC-MAIN-20140305092107-00053-ip-10-183-142-35.ec2.internal.warc.gz"} |
http://mathematica.stackexchange.com/users/973/fred-kline?tab=activity&sort=posts | Fred Kline
Reputation
697
Top tag
Next privilege 1,000 Rep.
May18 asked Why can Reduce solve for Integers but not for Reals? May8 asked Question about a catalytic equality? Jan25 asked Is there a notebook to create entries for OEIS? Oct28 asked Can degenerating Nicomachus' triangle down to $0$ area by using Graph be done? Oct24 asked How can we get this infinite prism lattice to look more like PolyhedronData[{“Prism”, 3}]? Oct16 answered Can you compute more terms in this sequence? Sep12 wiki created experimental-mathematics excerpt May24 asked Is there a better way to create my rotational-symmetric (180 degrees) rectangles? May20 answered Solve within a range? May18 asked Using a variable for two different purposes Apr17 asked Why the complicated pattern in this 3D plot? Feb17 answered Convert number to exponent form with highest power possible Feb2 asked Question about inequality plot Aug6 answered Collatz Tool Box — any speed ups possible? Aug5 asked Can we compile using only Integers Of Unusual Size? Jul31 asked Collatz Tool Box — any speed ups possible? Jun20 answered Stop Computation - Is Exit[] overkill? Jun9 asked Wallis Formula and Pippenger Product---How do we get symbolic output? May22 asked Are there any functions that can determine the disorder between two lists? May22 answered Correct behavior of lock file in hsqldb connection | {"extraction_info": {"found_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": 0.23034802079200745, "perplexity": 10471.217496020457}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-22/segments/1432207928923.85/warc/CC-MAIN-20150521113208-00155-ip-10-180-206-219.ec2.internal.warc.gz"} |
http://mathoverflow.net/questions/124943/qustions-on-r-bryants-papaer-calibrated-embeddings-in-the-special-lagrangian-a | # Qustions on R.Bryant's papaer “Calibrated embeddings in the special Lagrangian and coassociative cases”
I am reading the paper "Calibrated embeddings in the special Lagrangian and coassociative cases" by R.Bryant (here the link: http://arxiv.org/abs/math/9912246) and there are certain things that are unclear to me.
1. Bryant defines on page 11 in is paper the set $V_{n}(\mathcal{I},\pi) =$ {$E\in V_{n}(\mathcal{I})|D_{u}\pi : E \rightarrow T_{\pi(u)}M$ is injective} and claims that $V_{n}(\mathcal{I},\pi) \subset Gr_{n}(TF)$ is a submanifold of codimension $np$, where $p$ is the codimension of $G \subset SO(n)$ in $SO(n)$. My question is: why is this so? I tried to use several chart representations or the implicite function theorem but without any succes.
2. On page 12 there are the subspaces $\mathfrak{h}_{k}$ defined. Then he computes that $H(E _ {k}) = E + ( \mathfrak{h} _ {k} ) _ {u}$. Why does this hold?
3. How does he show that $SU(n)$ is reglarly presented in $SO(2n)$?
I hope that some of you have the answers to some of my questions.
Best regards Mario
-
1. This is a consequence of the claim, proved in the reference [Br$_2$], that the condition of being torsion-free is $np$ first order PDE for a section $\sigma:M\to S=F/G$ that defines a $G$-structure (where $n$ is the dimension of the manifold and $p$ is the codimension of $G$ in $\mathrm{SO}(n)$). The hypothesis of strong admissibility implies (indeed, it is equivalent to the condition) that all of these equations are captured by the condition of closure of the differential forms associated to the $G$-structure, which is exactly the condition that an $n$-plane $E$ be an integral element of $\mathcal{I}$.
2. If you unwind the definitions, you will see that the spaces ${\frak{h}}_k$ were defined so as to make this equation true. This computation is best carried out up on $F$, where one can write out the definition of $\hat \alpha$ in a coframing of $F$ given by the structure equations and compute $d\hat\alpha$ explicitly. (When I have more time, maybe I can put in a brief description of this computation.)
3. I didn't claim to give the proof that $\mathrm{SU}(n)\subset\mathrm{SO}(2n)$ is regularly presented for all $n$, I just said that it can be proved. You can get an indication of how the proof goes by looking a little further along in the paper where, on pages 13–14, I do (briefly) give the argument for $n=3$, the case of most interest in the article. | {"extraction_info": {"found_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": 0.9611868262290955, "perplexity": 200.77583722878637}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1469257824113.35/warc/CC-MAIN-20160723071024-00283-ip-10-185-27-174.ec2.internal.warc.gz"} |
http://hackage.haskell.org/package/hakyll-4.9.8.0/docs/Hakyll-Core-Rules-Internal.html | hakyll-4.9.8.0: A static website compiler library
Hakyll.Core.Rules.Internal
Synopsis
# Documentation
Constructors
data RuleSet Source #
Constructors
RuleSet FieldsrulesRoutes :: RoutesAccumulated routesrulesCompilers :: [(Identifier, Compiler SomeItem)]Accumulated compilersrulesResources :: Set IdentifierA set of the actually used filesrulesPattern :: PatternA pattern we can use to check if a file *would* be used. This is needed for the preview server.
Instances
Source # Methodsmconcat :: [RuleSet] -> RuleSet #
Constructors
RulesState FieldsrulesRoute :: Maybe Routes rulesCompiler :: Maybe (Compiler SomeItem)
newtype Rules a Source #
The monad used to compose rules
Constructors
Rules FieldsunRules :: RWST RulesRead RuleSet RulesState IO a
Instances
Source # Methods(>>=) :: Rules a -> (a -> Rules b) -> Rules b #(>>) :: Rules a -> Rules b -> Rules b #return :: a -> Rules a #fail :: String -> Rules a # Source # Methodsfmap :: (a -> b) -> Rules a -> Rules b #(<\$) :: a -> Rules b -> Rules a # Source # Methodspure :: a -> Rules a #(<*>) :: Rules (a -> b) -> Rules a -> Rules b #(*>) :: Rules a -> Rules b -> Rules b #(<*) :: Rules a -> Rules b -> Rules a # Source # Methods
Run a Rules monad, resulting in a RuleSet | {"extraction_info": {"found_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": 0.28609776496887207, "perplexity": 26640.709350586483}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1521257645280.4/warc/CC-MAIN-20180317174935-20180317194935-00677.warc.gz"} |
https://economics.stackexchange.com/questions/32718/prove-quasi-concavity-of-utility-function | # Prove quasi-concavity of utility function [closed]
How do you prove from definition (no Hessians) that $$U(x_1,x_2)=x_1^2 x_2$$ is quasi-concave?
• What is the definition of Quasi-Concavity? – Brennan Nov 12 '19 at 18:40
Take $$(1,1)$$ and $$(-1,1)$$: we have that $$U(1,1)=U(-1,1)=1$$. However, $$U(\frac12(1,1) + \frac12(-1,1)) = U(0,1) - 0 < 1 = \min\{U(1,1),U(-1,1)\}$$. Hence the function, at least defined globally over $$\mathbb R^2$$ is not quasi-concave.
Just to build up on @201p answer:
You probably wanted to prove that the utility function $$u: \mathbb{R^2_{++}} \to \mathbb{R}$$ given by: $$u(x_1,x_2) = x^2_1 x_2$$ is quasiconcave. As @201p pointed - allowing the function to be defined globally over $$\mathbb{R^2}$$ gives you trouble.
To see the intuition behind it, let's start with a definition. The function $$u$$ of many variables defined on a convex set $$S$$ is quasiconcave if every upper level set of function $$u$$ is convex.
Draw a level set of aforementioned utility function allowing it to be defined globally over $$\mathbb{R^2}$$:
Shaded area is the upper level set (at some level of utility). You can clearly see that it is not convex, therefore utility function defined that way is not quasiconcave.
However, if you allow utility function to be $$u: \mathbb{R^2_{++}} \to \mathbb{R}$$ given by: $$u(x_1,x_2) = x^2_1 x_2$$. The level set would consist only with the part on the right, clearly being convex.
Let $$u: \mathbb{R^2_{++}} \to \mathbb{R}$$ given by: $$u(x_1,x_2) = x^2_1 x_2$$.
Another way of thinking about it could be:
Proposition. The function $$f$$ of many variables defined on a convex set $$S$$ is quasiconcave if and only if for all $$x \in S$$ and $$x' \in S$$ such that $$f(x) ≥ f(x')$$ we have $$f((1−λ)x + λx') ≥ f(x')$$ for all $$λ ∈ [0, 1]$$.
But all this actually means is that a function is quasiconcave if and only if the line segment joining the points lying on two level curves lies nowhere below the level curve corresponding to the lower value of the function. Higher level curve represents higher utility. Let point $$A$$ represent higher utility and $$B$$ lower utility. If the segment joining $$A$$ and $$B$$ lies on or above the indifference curve corresponding to the smaller value of the utility function (speaking about point $$B$$), then the function $$u$$ of many variables is quasiconcave.
For more interesting examples you should check out: https://mjo.osborne.economics.utoronto.ca/index.php/tutorial/index/1/qcc/t
Finally, Cobb-Douglas function $$f: \mathbb{R^2_{++}} \to \mathbb{R}$$ given by: $$u(x_1,x_2) = x^a_1 x^b_2$$ for positive $$a,b>0$$ is:
• strictly concave if $$a + b < 1$$
• concave if $$a + b = 1$$
• neither concave nor convex if $$a + b > 1$$
• quasiconcave for all $$a,b > 0$$
For proofs you could check out this! | {"extraction_info": {"found_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": 37, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9700878262519836, "perplexity": 307.89713559655}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-34/segments/1596439738913.60/warc/CC-MAIN-20200812171125-20200812201125-00212.warc.gz"} |
https://www.wyzant.com/resources/answers/838571/probability-question | Leanna G.
# Probability Question
A spinner has 10 equal pieces, 4 white, 3 black and 3 gray. Linda spun it 50 times. She got 17 White, 14 Gray, and 19 black. Assuming that the spinner is fair, compute the theoretical probability of landing on white. | {"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": 0.8813397884368896, "perplexity": 2667.8261050370515}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1620243991943.36/warc/CC-MAIN-20210513173321-20210513203321-00241.warc.gz"} |
http://mathoverflow.net/questions/64492/continuity-of-borel-measurable-gleason-frame-functions | # Continuity of Borel measurable Gleason frame functions
Gleason's theorem (Journal of Mathematics and Mechanics, Vol. 6, No. 6, 1957) classifies measures on the closed subspaces of a separable Hilbert space. A key lemma toward the proof of the theorem asserts the following. Let f be a nonnegative real-valued function on the 2-sphere in 3-space with the property that its sum on any triple of orthogonal points is independent of the triple. Then f is continuous. The question is whether the conclusion remains valid if one drops the nonnegativity assumption and assumes Borel measurability instead.
- | {"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": 0.9654258489608765, "perplexity": 104.43035358551793}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-40/segments/1443737913039.71/warc/CC-MAIN-20151001221833-00210-ip-10-137-6-227.ec2.internal.warc.gz"} |
https://www.gradesaver.com/textbooks/math/algebra/algebra-and-trigonometry-10th-edition/prerequisites-p-3-polynomials-and-special-products-exercises-page-31/1 | ## Algebra and Trigonometry 10th Edition
$n, a_n, a_0$
Look at the definitions of the degree of a polynomial, leading coefficient of a polynomial and the constant term of a polynomial on page 28. Degree of a polynomial = n (It is the maximum of the degrees of its monomials / terms with non-zero coefficients.) Leading coefficient of a polynomial = $a_n$ (The coefficient of the term with the highest power) Constant term of a polynomial = $a_0$ ( term of degree 0) | {"extraction_info": {"found_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": 0.8529732823371887, "perplexity": 188.62884739871612}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1652662587158.57/warc/CC-MAIN-20220525120449-20220525150449-00751.warc.gz"} |
https://quantumcomputing.stackexchange.com/questions/14196/how-exactly-does-grovers-algorithm-crack-symmetric-key-encryption | # How exactly does Grovers algorithm “crack” symmetric key encryption?
How exactly does Grovers algorithm "crack" symmetric key encryption? I searched around on the internet, and found that it could make the key length effectively half as long, meaning you only needed to double the lenth of your key for the encryption to be viable again. But how exactly could it brute force the password?
• I think it would be incorrect to say that Grover can "crack" any particular cryptosystem. Grover merely provides a quadratic speedup over classical search algorithms. For instance if you have to search for a key in say $n$-bit strings there are $2^n$ keys to brute force check. Grover search can effectively square root the search space but this means there are still $2^{n/2}$ keys to brute force... still an exponential number of keys (with respect to $n$) to check. – Condo Oct 16 '20 at 14:07
Grover's algorithm is a Circuit SAT solver that finds a satisfying assignment in around $$2^{n/2}$$ evaluations of the circuit, where $$n$$ is the number of inputs. You can build a circuit that takes a key as input and checks whether it can successfully decrypt a ciphertext with that key (perhaps by verifying an authenticator), returning 1 if it can. Grover's algorithm then gives you a working key in around $$2^{n/2}$$ decryptions where $$n$$ is the key length. | {"extraction_info": {"found_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": 4, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.43449288606643677, "perplexity": 574.5003623838188}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-25/segments/1623487610841.7/warc/CC-MAIN-20210613192529-20210613222529-00203.warc.gz"} |
https://cstheory.stackexchange.com/questions/20814/polynomial-time-solvable-instances-of-max-sat/21384 | # Polynomial time solvable instances of Max-Sat
The problem Max-Sat ask you to find an assignment of a CNF formula which satisfy as many clauses as possible.
For the simpler problem SAT there are many known special cases which can be solved in polynomial time, e.g. we can solve 2-SAT in polynomial time.
For Max-Sat the situation is different since Max-Sat is NP-hard even for 2-CNF formulas (each clause contains only 2 variables).
Is there any interesting special inputs for which Max-Sat is polynomial?
In particular I would be interested in a standard reference for solving Max-Sat when the incedence graph has bounded treewidth.
• Planar max-cut is a special case of max-cut, which is (in a sense) a special case of max-2-sat. – Jukka Suomela Jan 31 '14 at 19:19
This does not answer directly your Max-SAT problem but the references may guide you to the complete answer.
Szeider showed that Satisfiability is fixed-parameter tractable when parameterized by the treewidth of the incidence graph. Samer and Szeider gave an efficient dynamic programming algorithm.
References
S. Szeider. On fixed-parameter tractable parameterizations of SAT. In Proc. 6th International Conference on Theory and Applications of Satisfiability (SAT’03), Selected and Revised Papers, vol. 2919 of LNCS, pages 188–202. Springer-Verlag, 2004.
M. Samer and S. Szeider. Algorithms for propositional model counting. In Proc. 14th Internationial Conference on Logic for Programming, Artificial Intelligence and Reasoning (LPAR’07), vol. 4790 of LNCS, pages 484–498. Springer-Verlag, 2007.
Samer and Szeider, Fixed-parameter tractability. In A. Biere, M. Heule, H. van Maaren, and T. Walsh, editors, Handbook of Satisfiability, part 1, chapter 13. IOS Press
• I know some of Stefan Szeiders work, a more recent paper shows that #SAT is polynomial when the incedence graph has bounded clique-width which also imlies bounded tree-width (although here we have XP runtime instead of FPT). Friedrich Slivovsky and Stefan Szeider, Model Counting for Formulas of Bounded Clique-Width, Algorithms and Computation, vol. 8283,p. 677-687, LNCS,2013 I know that these type of results often would translate into MAX-SAT, but it would be much easier have a reference where this is already done instead of doing it myself. – Martin Vatshelle Jan 31 '14 at 20:22
We found one kind of such property:
For a formula $F$ , if $F$ has a linear ordering of the variables and clauses such that for any variable $x$ occurring in clause $C$, if $x$ appears before $C$ then any variable between them also occurs in $C$, and if $C$ appears before $x$ then $x$ occurs also in any clause between them. Then we can solve MAX-SAT in polynomial time.
Are there any other such properties known? | {"extraction_info": {"found_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": 0.8637893795967102, "perplexity": 1180.6707444969798}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1593655890105.39/warc/CC-MAIN-20200706042111-20200706072111-00495.warc.gz"} |
http://mathoverflow.net/questions/148756/a-new-continuum-hypothesis-revised-version?answertab=votes | # A New Continuum Hypothesis (Revised Version)
Define $N_n$ as $n$ th natural number: $N_0=0, N_1=1, N_2=2, ...$.
What happens after exponentiation?
We have the following equation: $2^{N_n}=N_{2^{n}}$.
(Which says: For all finite cardinal $n$ we have: $2^{n~\text{th finite cardinal}}=2^{n}~\text{th finite cardinal}$).
What this means?
The gap between $N_n$ and $2^{N_n}$ is rapidly increasing in exponential speed.
Now look at the $\text{GCH}$. It says that the gap between an infinite cardinal $\kappa$ and $2^{\kappa}$ is just a constant number $1$ in cardinals. Even in models for total failure of $\text{GCH}$ we usually have a finite gap between $\kappa$ and $2^{\kappa}$. Now if we look at the infinite cardinals as generalization of natural numbers it seems we should restate continuum hypothesis with more acceleration for the function $\kappa \mapsto 2^{\kappa}$ in order to uniform the behavior of exponentiation function in finite and infinite cardinals. Note to the following statement:
For all cardinal $\kappa$ we have $2^{\kappa~\text{th infinite cardinal}}=2^{\kappa}~\text{th infinite cardinal}$.
This is a direct generalization of the equation $\forall n\in \omega~~~~~2^{N_n}=N_{2^n}$ to the following form:
Natural Continuum Hypothesis (NCH): $~~~\forall \kappa\in Card~~~~~2^{\aleph_{\kappa}}=\aleph_{2^{\kappa}}$
Unfortunately $\text{NCH}$ is contradictory by Konig's lemma because assuming $\text{NCH}$ we have: $\aleph_{\aleph_0}<cf(2^{\aleph_{\aleph_0}})=cf(\aleph_{\aleph_1})\leq \aleph_1$ a contradiction.
(Thanks to Ramiro and Emil for their advices.)
But the acceleration problem remains open. The main question here is this:
Can we have a rapidly increasing gap between carinals by exponentiation? In the other words:
Question 1: Assuming consistency of $\text{ZFC}$ (plus some large cardinal axiom or axiom of constructibility), is the following statement consistent with $\text{ZFC}$?
$\forall \kappa\in Card~~~\exists \lambda \in Card~;~~~~~\lambda\geq 2^{\kappa}~\wedge~2^{\aleph_{\kappa}}=\aleph_{\lambda}$
Definition 1: Let $\kappa$ be a (finite or infinite) cardinal. Define $\kappa$-based beth function as follows:
$\beth_{(\kappa)}:Ord\longrightarrow Card$
$\beth_{(\kappa)}(0):=\kappa$
$\forall \alpha\in Ord~~~\beth_{(\kappa)}(\alpha +1):=2^{\beth_{(\kappa)}(\alpha)}$
$\forall \alpha\in LimitOrd~~~\beth_{(\kappa)}(\alpha):=\bigcup_{\beta \in \alpha}\beth_{(\kappa)}(\beta)$
Definition 2: Let $F:Card\longrightarrow Card$ be an increasing function and $\delta$ an ordinal. We say that $F$ has acceleration rank $\delta$ if $\delta=min\{\alpha\in Ord~|~\forall \kappa\in Card~~~\beth_{(\kappa)}(\alpha)\leq F(\kappa) < \beth_{(\kappa)}(\alpha+1)\}$.
For example the functions $\kappa\mapsto \kappa^{+}$, $\kappa\mapsto 2^{\kappa}$, $\kappa\mapsto 2^{2^{\kappa}}$ have acceleration ranks $0, 1, 2$ respectively.
Question 2: Is there any limitation for acceleration of the continuum function? Precisely is the following statement true?
"For any ordinal $\delta$ there is an increasing function $F:Card\longrightarrow Card$ with acceleration rank $\delta$ such that assuming consistency of $\text{ZFC}$ (and some large cardinal axiom) one can prove the consistency of $\text{ZFC}$ with the statement $\forall \kappa\in Card~~~2^{\aleph_{\kappa}}=\aleph_{F(\kappa)}$."
According to Emil's interesting comment I added his question here:
Question 3: Assuming consistency of $\text{ZFC}$ (and some large cardinal axiom or axiom of constructibility), is the following consistent with $\text{ZFC}$?
$\forall \kappa\in Card~~~~\exists \lambda\in Card~~~~~2^{\aleph_{\kappa}}=\aleph_{\lambda}$
Note that it is not trivial that one can have a "cardinal index" for $\aleph$ as value of $2^{\aleph_{\kappa}}$ everywhere. Perhaps we will need some non-cardinal ordinals as indexes to avoid inconsistency.
-
Wouldn't $NCH$ imply $2^{\aleph_\omega}=\aleph_{\omega_1}$? – Ramiro de la Vega Nov 13 '13 at 14:16
@RamirodelaVega: Yes. We have $\text{NCH}\longrightarrow \text{CH}\wedge\neg \text{GCH}$ so $2^{\aleph_{\aleph_{0}}}=\aleph_{2^{\aleph_{0}}}=\aleph_{\aleph_{1}}$. – user42090 Nov 13 '13 at 14:24
So, doesn’t that imply that NCH is contradictory, as ZFC proves $\mathrm{cf}(2^\kappa)>\kappa$ for every infinite $\kappa$? – Emil Jeřábek Nov 13 '13 at 14:35
Very good! I deleted my answer (showing that NCH has large cardinal lower bounds in strength) in light of Ramiro's observation that NCH is inconsistent. – Joel David Hamkins Nov 13 '13 at 14:40
I can't really see the point made by your five introductory lines. Your function $N$ is the identity, so all it seems to me that it says is that "exponentiation behaves in an exponential fashion". – James Cranch Nov 13 '13 at 15:31
In the following answer, by Foreman-woodin model, I mean the model constructed by them in the paper "The generalized continuum hypothesis can fail everywhere. Ann. of Math. (2) 133 (1991), no. 1, 1–35. "
Questions 1 and 3 have positive answer: In Foreman-Woodin model for the total failure of GCH the following hold:
1) For all infinite cardinal $\kappa, 2^{\kappa}$ is weakly inaccessible, and hence a fixed point of the $\aleph-$function,
2) If $\kappa \leq \lambda< 2^{\kappa},$ then $2^{\lambda}= 2^{\kappa}.$
In this model for all infinite cardinals $\kappa, 2^{\kappa}=\aleph_{ 2^{\kappa}}$ in particular for all fixed points $\kappa$ of the $\aleph-$function, $2^{\aleph_\kappa}=\aleph_{ 2^{\kappa}}$. Also note that in this model for all infinite cardinals $\kappa,$ if we let $\lambda=2^{\aleph_\kappa},$ then $\lambda \geq 2^\kappa,$ and $2^{\aleph_\kappa}=\aleph_\lambda.$ So both of questions 1 and 3 have a positive answer.
For your question 2, $\delta$ can be arbitrary large: Start with GCH+there exists a supercompact cardinal $\kappa$+ there are infinitely many inaccessibles above it. Now let $\delta$ be any ordinal $<\kappa.$ Force with Foreman-Woodin construction above $\delta$ (in the sense that let the first point of the Radin club added during their forcing construction be above $\delta$). In their final model (which is $V_\kappa$ of some extension of the ground model) for all infinite cardinals $\lambda <\kappa, 2^\lambda \geq \lambda^{+\delta}$. So if $F$ is defined in the ground model by $F(\kappa)=\kappa^{+\delta},$ then the acceleration rank of $F$ is $\delta$ (using GCH), and in the finial model for all infinite cardinals $\kappa, 2^\kappa \geq F(\kappa).$
Remark. I may note that we can not define the function $F$ in the ground model, such that it is the realization of power function in the extension, but we can find some inner model of the final extension in which $GCH$ holds and such a function $F$ is definable.
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Very nice Mohammad. This phenomenon happens under assumption of $\text{NCH}$, i.e. $\text{NCH}$ implies for each fixed point of $\aleph$ function like $\kappa$, $2^{\kappa}$ is also a fixed point of $\aleph$ function. – user42090 Nov 13 '13 at 19:04
Excellent answer Mohammad. Please introduce some references for Foreman-Woodin construction. But about question 2, why the acceleration rank of the function $\kappa\mapsto \kappa^{+\delta}$ is $\delta$? What about Emil's upper bound on possible acceleration rank of continuum function? – user42090 Nov 14 '13 at 8:35
Under GCH, $\beth_\kappa(\alpha)=\kappa^{+\alpha}$ – Mohammad Golshani Nov 14 '13 at 10:20
Ah! Of Course. So is Emil's answer incorrect? – user42090 Nov 14 '13 at 10:29
The problem of definability once again! Thank you Mohammad. – user42090 Nov 14 '13 at 12:42
Let me provide a large cardinal lower bound for the statement in question 1. Since $\kappa\lt\kappa+1\lt 2^\kappa$ for $\kappa>1$, the statement implies that there is a universal failure of the GCH above $\aleph_1$ at cardinals of the form $\aleph_\kappa$ for $\kappa$ a cardinal. In particular, this implies that the negation of the singular cardinals hypothesis SCH. Since $\neg\text{SCH}$ is known to have large cardinal strength, we have large cardinal lower bounds for the consistency strength of your statement.
Meanwhile, since the statement also implies violations of the SCH arbitrarily high in the cardinals, it follows by a result of Solovay that it is inconsistent with the existence of strongly compact cardinals.
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Really interesting. Thanks. Please introduce some references for Solovay's result. – user42090 Nov 13 '13 at 14:18
I adapted my answer for the revised question. – Joel David Hamkins Nov 13 '13 at 15:07
NCH is inconsistent with ZFC:
First, under NCH, we have: $$2^{\aleph_{\aleph_{\aleph_0}}} = \aleph_{2^{\aleph_{\aleph_0}}} = \aleph_{\aleph_{2^{\aleph_0}}} = \aleph_{\aleph_{\aleph_1}} .$$
Under NCH, $\aleph_{\aleph_{\aleph_0}}$ is strong limit, since, for any $n \in \omega$: $$2^{\aleph_{\aleph_n}} = \aleph_{2^{\aleph_n}} = \aleph_{\aleph_{2^n}} < \aleph_{\aleph_{\aleph_0}} .$$
Now, consider the Theorem 7.3 in Chapter 14 (Cardinal Arithmetic - Abraham and Magidor) of the Handbook of Set Theory (page 1210):
Suppose that $\delta$ is a limit ordinal and ${|\delta|}^{\operatorname{cf}(\delta)} < \aleph_{\delta}$. Then $${\aleph_{\delta}}^{\operatorname{cf}(\delta)} < \aleph_{({|\delta|}^{+4})} .$$
Then we have, under NCH: $$2^{\aleph_{\aleph_{\aleph_0}}} = {(\aleph_{\aleph_{\aleph_0}})}^{\aleph_0} < \aleph_{{(\aleph_{\aleph_0})}^{+4}} = \aleph_{\aleph_{\omega + 4}} .$$
However, $$\aleph_{\aleph_{\aleph_1}} > \aleph_{\aleph_{\omega + 4}} .$$
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As has been pointed out by Ramiro de la Vega, and mentioned in the question itself, NCH is inconsistent with ZFC because of König’s lemma. No need to involve pcf theory. – Emil Jeřábek Nov 13 '13 at 15:39
What an amazing answer by pcf theory! Thanks for your effort, Alberto. – user42090 Nov 13 '13 at 16:23
As for question 2, if $\forall\kappa\,2^{\aleph_\kappa}=\aleph_{F(\kappa)}$, then $F$ does not have an acceleration rank.
If the rank were $\delta\ge2$, we could take $\kappa$ to be any fixpoint of the $\aleph$ function to obtain a contradiction: $$2^{\aleph_\kappa}=2^\kappa\le\aleph_{2^\kappa}=\aleph_{\beth_{(\kappa)}(1)}.$$ On the other hand, a finite acceleration rank is impossible: this would imply $F(n)<\omega$ for every $n<\omega$, i.e., $\aleph_\omega$ is strongly limit. In particular, $\omega\le F(\omega)\le\beth_{(\omega)}(\delta+1)=\beth_{\delta+1}<\aleph_\omega$, hence $\mathrm{cf}(2^{\aleph_\omega})=\mathrm{cf}(\aleph_{F(\omega)})=F(\omega)<\aleph_\omega$, contradicting König’s lemma.
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Interesting answer Emil. Thank you very much. – user42090 Nov 13 '13 at 15:54
Your answer imposes an upper bound on the possible growth speed of continuum function. It is really surprising. – user42090 Nov 13 '13 at 16:19
Oh! What a strange result! It seems I should change some parameters in my intuition about continuum function. – user42090 Nov 13 '13 at 17:49
Emil, I added some edits in the definition of acceleration rank in order to clarify the difference between growth rate of the functions $\kappa\mapsto \kappa^{+}$, $\kappa\mapsto 2^{\kappa}$, $\kappa\mapsto 2^{2^{\kappa}}$. Please add updates in your answer. Thanks. – user42090 Nov 13 '13 at 19:37
F is defined in the ground model, and it is asked it to be realized as a power function in some extension. See my answer. – Mohammad Golshani Nov 14 '13 at 4:19 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 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": 0.9901524782180786, "perplexity": 409.0238666657611}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-48/segments/1448398458511.65/warc/CC-MAIN-20151124205418-00217-ip-10-71-132-137.ec2.internal.warc.gz"} |