text:
Reference proteomes from uniprot in FASTA format, why is there only one sequence per gene?
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0
Entering edit mode
3 months ago
Jobbe • 0

While downloading the human proteome in fasta format from the uniprot site, I noticed that it was mentioned that there was one protein per sequence (20,594). However, above the protein count is mentioned (81,837) and this made me wonder. I need this file to interpret spectrums obtained from bottom up proteomics experiment. Doesn't this give a very bad representation of the proteins present? Additionally, how is it decided which sequence they display if alternative splicing occurs at a gene? Lastly, is there an alternative approach that searches the entire proteome rather than the gene-centered subset?

uniprot FASTA proteome • 439 views
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Entering edit mode

You could use "unreviewed" Human set (186K): https://www.uniprot.org/uniprotkb?facets=reviewed%3Afalse%2Cmodel_organism%3A9606&query=Human

Use Protein Existence filters in left column to trim this down (transcript level etc).

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Entering edit mode
3 months ago

In the human proteome page, https://www.uniprot.org/proteomes/UP000005640, both protein count and gene count are provided. The gene count is only provided for reference proteomes, and is algorithmically computed: for each gene, a single representative protein sequence is chosen from the proteome. Where possible, reviewed (Swiss-Prot) protein sequences are chosen as the representatives. For more detail, I suggest you look at this help page: https://www.uniprot.org/help/gene_centric_isoform_mapping

There are use cases for both approaches - some users prefer seeing only one entry per gene, others prefer using the complete proteome set with potentially several entries per gene. The latter can be downloaded from the website by clicking on the "Protein count" link in https://www.uniprot.org/proteomes/UP000005640 - or directly at https://www.uniprot.org/uniprotkb?query=proteome:UP000005640

Please don't hesitate to contact the UniProt helpdesk if you have any additional questions.


text:
### Show Posts

This section allows you to view all posts made by this member. Note that you can only see posts made in areas you currently have access to.

### Messages - Laura Campbell

Pages: [1]
1
##### Presentations and discussions / Julia Set
« on: March 14, 2017, 03:18:47 PM »

2
##### Topics / Burgers' Equation
« on: January 24, 2017, 09:58:48 PM »
My presentation topic is Burgers' equation.  My plan is to discuss Burgers' inviscid equation, $u_t+uu_x=0$ and its solution, as well as its solution with particular initial conditions. Then considering the weak solutions to the equation and the Rankine-Hugoniot conditions. Finally, will go over Burgers' viscous equation, $u_t+uu_x= \epsilon u_{xx}$ and some examples of scenarios in which Burgers' equation is used - namely traffic flow and gas dynamics.

Pages: [1]

format: plain


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# My custom theorem/proof environments aren't playing well together

As can be shown in the following MWE, when I have a theorem environment followed by a proof environment, the proof isn't going into the next line; it's rendering right on top of the text I have for the theorem.

\documentclass{book}
\usepackage{color}

\newcounter{theorem}
\setcounter{theorem}{0}
\def\thetheorem{\thesection.\arabic{theorem}}

\newenvironment{theorem}[1][]{%
\refstepcounter{theorem}
\vspace{5mm}
\makebox[-15pt][r]{
\normalfont\large\color{cyan} Theorem\ \thetheorem$\;\;\;\;$}\setbox0\hbox{\ }
\hspace{-\the\wd0}
\ifx\relax#1\relax \else{\large\color{cyan} #1\\[1mm]}\fi
}
{\ignorespacesafterend\medskip}%

\newcounter{example}
\setcounter{example}{0}
\def\theexample{\thesection.\arabic{example}}

\newenvironment{example}[1][]{%
\refstepcounter{example}
\vspace{5mm}
\makebox[-15pt][r]{
\normalfont\large\color{cyan} Example\ \theexample$\;\;\;\;$}\setbox0\hbox{\ }
\hspace{-\the\wd0}
\ifx\relax#1\relax \else{\large\color{cyan} #1\\[1mm]}\fi
}
{\ignorespacesafterend\medskip}%

\newenvironment{proof}{%
\vspace{5mm}
\makebox[-15pt][r]{
\normalfont\large\color{cyan} Proof$\;\;\;\;$}\setbox0\hbox{\ }
\hspace{-\the\wd0}
}
{\ignorespacesafterend\medskip}%

\begin{document}
\begin{theorem}
asdf
\end{theorem}
\begin{proof}
fdsa
\end{proof}

\end{document}

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\ignorespacesafterend should always be last; and it doesn't matter if you end the paragraph at the environment end. Say \newcounter{theorem}[section] if you want that the counter is reset to zero in new sections. –  egreg Feb 16 '13 at 10:03

\medskip and friends don't work in horizontal mode. Put a \par (or a \\) in the environment closure. (And then play with horizontal spacing ;-)

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\par did it.. Thank you very much! –  agent154 Feb 16 '13 at 2:20
\medskip does indeed force a \par; it's \vspace that doesn't. –  egreg Feb 16 '13 at 10:18
@egreg It does in plain TeX; in LaTeX, not. ?!? Checked bla\medskip blaon three computers ;-) –  Sašo Živanović Feb 16 '13 at 10:52
@SašoŽivanović You're right; I was thinking to a different thing. –  egreg Feb 16 '13 at 11:04

You're doing many things in a complicated way and so have very bad control of spaces. Here's a proposal for a better realization.

\documentclass{book}
\usepackage{color}
\usepackage{lipsum} % for mock text

\newcounter{theorem}[section]
\def\thetheorem{\thesection.\arabic{theorem}}

\newenvironment{theorem}[1][]{%
\refstepcounter{theorem}%
\noindent\makebox[0pt][r]{%
\ifx\relax#1\relax \else{\large\color{cyan}#1\\[1mm]}\fi
\ignorespaces}

\newcounter{example}[section]
\def\theexample{\thesection.\arabic{example}}

\newenvironment{example}[1][]{%
\refstepcounter{example}%
\noindent\makebox[0pt][r]{%
\ifx\relax#1\relax\else{\large\color{cyan}#1\\[1mm]}\fi
\ignorespaces}

\newenvironment{proof}{%
\noindent\makebox[0pt][r]{%
\ignorespaces}

\begin{document}
\lipsum[1]

\begin{theorem}
\lipsum*[2]
\end{theorem}

\begin{proof}
\lipsum*[3]
\end{proof}

\end{document}

1. Use \newcounter{theorem}[section] in order to reset the counter at each section.

2. Use \par\addvspace{5mm} so that this won't add space in excess when following other environments that use the same command (such as lists).

3. With \noindent you can control precisely where your label will go. Don't forget \ignorespaces at the end of the "begin part"

4. \ignorespacesafterend is useless in the "end part" since you force a paragraph end; in any case this must be the last token.

5. Be careful with spurious spaces in your definition. I've protected with % more end-of-lines than necessary, but better be safe than sorry.

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+1 for the elegant documented clean rewrite. –  Ethan Bolker Feb 16 '13 at 13:49


text:
# zbMATH — the first resource for mathematics

Weak convergence for empirical processes of associated sequences. (English) Zbl 0968.60019
Let $$(X_n)_{n\in Z}$$ be a stationary and associated sequence of random variables with common continuous distribution function $$F$$. For every integer $$n\geq 1$$ let $$F_n$$ denote the empirical distribution function based on $$X_1,\dots,X_n$$, and $$G_n=\sqrt{n}(F_n-F)$$ the corresponding empirical process. Let $$G$$ be the centered Gaussian process with covariance function $$\text{cov}(G(x),G(y))=\sum_{k\in Z}\text{cov} (1_{X_0\leq x},1_{X_k\leq y})$$. It is shown that the condition $$\text{cov}(F(X_1),F(X_n))=O(n^{-b})$$ for some $$b>4$$ implies weak convergence of $$G_n$$ to $$G$$ in the Skorokhod space $$D[-\infty,\infty]$$. This improves earlier results in which the condition on $$b$$ was more stringent. Applications to linear processes are also given, as well as a comparison of mixing conditions and association.

##### MSC:
 60F05 Central limit and other weak theorems 60F17 Functional limit theorems; invariance principles 62G30 Order statistics; empirical distribution functions
Full Text:


text:
# Tag Info

105

There are two ways in which you can view a Question/Answer site. One is as a real-time "I've asked this question and I want a quick answer now" type of site, and the other is as a longer term repository of questions and definitive answers. I think that many of us here take this latter view of the site. As a result, we have lots of very high quality answers, ...

54

I also often find myself dropping a comment instead of answering. In addition to what was already answered here, my reasons mostly are Might be too localized. If the answer to a huge question is a one-liner, then more often than not the real problem was a little thing the OP overlooked, having nothing to do with the perceived question at all. In that case, ...

38

In general, you are correct that something which answers the question should be given as an answer. However, there are some subtleties to this. The first is as marczellm says that a one-liner may not really 'feel' like an answer: it may be the core of an answer but need expansion, for example. There is then the question of whether the comment really answers ...

29

I like your proposed text block and intend to use it in the future. ("Answering" questions on Meta feels weird)

28

Joseph's post speaks about it slightly, but I would like to add one comment. This often happens when there is not enough information in the question, usually because of a missing MWE. This makes the question difficult to answer, so we often just try to guess what is the problem and we shoot a possible solution, as a comment. If later it is found out that the ...

27

Here is my proposed answer: While [tag:MathJax] uses LaTeX syntax, it uses Javascript and HTML's DOM model rather than TeX technology, making it mostly off topic for this site. You might try instead searching among the [questions tagged with mathjax on Stack Overflow](http://stackoverflow.com/questions/tagged/mathjax), or in the official [mathjax-users](...

27

I think an important pedagogical angle also needs to be emphasised. A significant point of the OP providing an attempt at coding is that it is an indication of their level of expertise. It's not just about helping with problems but knowing at what level you need to start your discussion from. Neither of the code blocks as presented emphasise this enough I ...

24

It may be that people don't consider a one-liner solution to be worth an Answer. There's the feeling that an Answer with capital A is something more detailed. This feeling is (at least in my case) strengthened by the fact that somehow, on this site, there are much more detailed answers than one-liners. The Answerers usually go to great detail even about ...

21

I sometimes posted advice in a comment, because of being pretty sure that the question has been answered before and I just did not find the duplicate yet. As soon as I would find the duplicate, I would add a link. It would be good to check for a duplicate at first, before quickly firing answer for rep and badges. I guess commenters often avoid adding an ...

20

As on all StackExchange sites, the idea of comments here is that they are ways of allowing clarification or feedback on questions/answers but should always be viewed as 'less important' than the material they are attached to. In particular, they may be deleted where moderators deem this appropriate. In terms of 'Thanks' comments, they are not encouraged ...

19

To be honest, I think we'd be better without boiler plate text blocks for this kind of thing, If a situation isn't worth writing a custom comment, it's probably not worth making a comment at all.

18

Documentation & Definition of commands (La)TeX core Difference between optional and delimited arguments Are all commands with an optional argument fragile? [Are all commands with an optional argument fragile?](https://tex.stackexchange.com/q/497356) What is the difference between Fragile and Robust commands? [What is the difference between Fragile ...

15

We don't follow the Thanks removal rule. It is a SO thing. Some of us approve Thanks removing edits. Some don't. I don't. Some notes for future reference and responding to a hypothetical SO user arriving here. I'm not bothered with Thanks word. It's a word. Why don't we get equally bothered by those voting arrows next to the question or those colorful ...

15

Since other text blocks that we paste in sometimes have alternatives, perhaps both this one and the original one can be preserved, and people can use whichever one suits their degree of formality/hypocrisy.

15

I don't consider this an issue, since people who see that message are already on this site. The suggestion is not "Go to TeX.SX" or "Visit TeX.SX". As an aside: For those posting Welcome to TeX.SX! verbatim as a comment, they could consider changing this to Welcome to TeX.SE! as the .SE suffix is more commonly used to represent the Stack Exchange ...

15

The current highest-voted comment has a score of 208: You can run a SEDE query to see the top 100 highest-voted comments.

14

It's a protection mechanism to prevent people to delete too much of their contribution on the site. It also hinders an hacker to do the same. Actually your action triggered an automatic moderator attention flag by the system, which I cleared just now. I guess from time to time some people, mainly from the bigger stackexchange sites, may become frustrated ...

14

This varies and depends on a number of circumstances. I'll reflect on a couple from personal experience: You're too slow to respond. The OP doesn't wait long enough for you to respond and asks a new follow-up question before you can get around smoothing out anything further to help. You forget. This happens, believe it or not. Some days/weeks are more ...

14

You can see your comments on your activity tab: https://tex.stackexchange.com/users/28474/ppr?tab=activity&sort=comments - this is not as sophisticated as views on Qs and As, because you can only see them ordered from newest to oldest, but they should all be there.

13

Well my personal opinionated response to that is So What? (in a very playful tone). You can even misshoot the click while scrolling the page and it lands on the other comment which is completely wrong but still, so what? No damage is done. It doesn't measure anything and it certainly doesn't effect anything. If it seems correct temporarily then upvote it ...

13

Yes, moderators can choose to see deleted comments and flag history (including 'handled' flags). So we can see the context of flags or later comments.

13

Instead formulate your confusion that apparently made you uncomfortable into smaller pieces and throw it to our TikZ lions and PSTricks piranha (animals are in alphabetical order don't bother :P) In other words, instead of am I doing wrong? questions, convert them into why do I do this? shouldn't it be happening such and such etc. questions with ...

13

This is already partly provided when rejecting a suggested edit: You are provided with a number of canned responses, including a custom message where you can "clearly explain why you are rejecting the edit": Here is an example of a rejected edit I made displaying a custom message*: The suggester of the edit can review their suggestions by clicking on the ...

13

Yes it is possible for moderators to edit comments. In practice this is normally done only if the commenter requests it (as they've spotted an error but have missed the editing window) or where there is a typo that is clear and correctable. (Both cases are rare so I can't readily point to an example, though I know I've corrected things for people on occasion;...

12

Jeff Atwood wrote: multiple lines are not supported in comments, and will never be Comments are treated as a single line, so multi-line code is impossible. I guess one reason is rendering speed.

12

TikZ Difference between "right of=" and "right=of" in PGF/TikZ [Difference between "right of=" and "right=of" in PGF/TikZ](https://tex.stackexchange.com/q/9386) Should \tikzset or \tikzstyle be used to define TikZ styles? [Should \tikzset or \tikzstyle be used to define TikZ styles?](https://tex.stackexchange.com/...

12

There are two sets of comments: Those submitted by you and those submitted by others to you (are to posts that you made). The former is available under the Comments section of your Activity tab in your User profile, and found at the following URL (since it's user-specific): https://tex.stackexchange.com/users/<userid>?tab=activity&sort=comments ...

12

According to the help on Markdown, StackExchange has programmed "[comments to] support only bold, italic, code and links; in addition, a few shorthand links [...]". Comments, in general, should be used only or limited interaction between posters and other contributors. As such, providing the same markdown capabilities has (most likely) been decided as not ...

12

You can only link the two databases containing posts and comments using the SEDE. The following query lists questions on the main site, sorted by their last activity date (oldest to newest) with these attributes: No comment No answer Not closed Positive score select top 1000 p.id as [Post Link], p.lastactivitydate as [Last Active] from posts p left ...

11

I hope people will forgive me if I use the freedom of the Meta group format to add a commentary that is too long for a comment. @AlanMunn's answer is one that I find extremely helpful for clarifying the culture of TeX.SE. The other answers are also very helpful. However, I think those who function as leaders in TeX.SE should consider the possibility that ...

Only top voted, non community-wiki answers of a minimum length are eligible


text:
## Recursos de colección

#### Project Euclid (Hosted at Cornell University Library) (198.174 recursos)

Proceedings of the Japan Academy, Series A, Mathematical Sciences

1. #### A note on transcendental entire functions mapping uncountable many Liouville numbers into the set of Liouville numbers

Lelis, Jean; Marques, Diego; Ramirez, Josimar
In 1906, Maillet proved that given a non-constant rational function $f$, with rational coefficients, if $\xi$ is a Liouville number, then so is $f(\xi)$. Motivated by this fact, in 1984, Mahler raised the question about the existence of transcendental entire functions with this property. In this work, we define an uncountable subset of Liouville numbers for which there exists a transcendental entire function taking this set into the set of the Liouville numbers.

2. #### An explicit formula of the unramified Shintani functions for $(\mathbf{GSp}_{4},\mathbf{GL}_{2} \times_{\mathbf{GL}_{1}} \mathbf{GL}_{2})$ and its application

Gejima, Kohta
Let $F$ be a non-archimedean local field of arbitrary characteristic. In this paper, we announce an explicit formula of the unramified Shintani functions for $(\mathbf{GSp}_{4}(F),(\mathbf{GL}_{2} \times_{\mathbf{GL}_{1}} \mathbf{GL}_{2})(F))$. As an application, we compute a local zeta integral, which represents the spin $L$-factor of $\mathbf{GSp}_{4}$.

3. #### Semi-discrete finite difference schemes for the nonlinear Cauchy problems of the normal form

We consider the Cauchy problems of nonlinear partial differential equations of the normal form in the class of analytic functions. We apply semi-discrete finite difference approximation which discretizes the problems only with respect to the time variable, and we give a proof for its convergence. The result implies that there are cases of convergence of finite difference schemes applied to ill-posed Cauchy problems.

4. #### Examples of genus two fibrations with no sections on rational surfaces

Kitagawa, Shinya
We construct explicit examples of genus two fibrations with no sections on rational surfaces by the double covering method. For the proof of non-existence of sections, we use the theory of the virtual Mordell-Weil groups.

5. #### Symmetry breaking operators for the restriction of representations of indefinite orthogonal groups $O(p,q)$

Kobayashi, Toshiyuki; Leontiev, Alex
For the pair $(G, G') =(O(p+1, q+1), O(p,q+1))$, we construct and give a complete classification of intertwining operators (\textit{symmetry breaking operators}) between most degenerate spherical principal series representations of $G$ and those of the subgroup $G'$, extending the work initiated by Kobayashi and Speh [Mem. Amer. Math. Soc. 2015] in the real rank one case where $q=0$. Functional identities and residue formul{æ} of the regular symmetry breaking operators are also provided explicitly. The results contribute to Program C of branching problems suggested by the first author [Progr. Math. 2015].

6. #### Symmetry breaking operators for the restriction of representations of indefinite orthogonal groups $O(p,q)$

Kobayashi, Toshiyuki; Leontiev, Alex
For the pair $(G, G') =(O(p+1, q+1), O(p,q+1))$, we construct and give a complete classification of intertwining operators (symmetry breaking operators) between most degenerate spherical principal series representations of $G$ and those of the subgroup $G'$, extending the work initiated by Kobayashi and Speh [Mem. Amer. Math. Soc. 2015] in the real rank one case where $q=0$. Functional identities and residue formulæ of the regular symmetry breaking operators are also provided explicitly. The results contribute to Program C of branching problems suggested by the first author [Progr. Math. 2015].

7. #### An algebraic proof of determinant formulas of Grothendieck polynomials

Matsumura, Tomoo
We give an algebraic proof of the determinant formulas for factorial Grothendieck polynomials obtained by Hudson–Ikeda–Matsumura–Naruse in~[6] and by Hudson–Matsumura in~[7].

8. #### An algebraic proof of determinant formulas of Grothendieck polynomials

Matsumura, Tomoo
We give an algebraic proof of the determinant formulas for factorial Grothendieck polynomials obtained by Hudson–Ikeda–Matsumura–Naruse in [6] and by Hudson–Matsumura in [7].

9. #### A character of the Siegel modular group of level 2 from theta constants

Xiong, Xinhua
Given a characteristic, we define a character of the Siegel modular group of level 2, the computations of their values are obtained. Using our theorems, some key theorems of Igusa~[2] can be recovered.

10. #### A character of the Siegel modular group of level 2 from theta constants

Xiong, Xinhua
Given a characteristic, we define a character of the Siegel modular group of level 2, the computations of their values are obtained. Using our theorems, some key theorems of Igusa [2] can be recovered.

11. #### Semicomplete vector fields on non-Kähler surfaces

We investigate semicomplete meromorphic vector fields on complex surfaces, those where the solutions of the associated ordinary differential equations have no multivaluedness. We prove that if a non-Kähler compact complex surface has such a vector field, then, up to a bimeromorphic transformation, either the vector field is holomorphic, has a first integral or preserves a fibration. This extends previous results of Rebelo and the author to the non-Kähler setting.

12. #### Semicomplete vector fields on non-Kähler surfaces

We investigate semicomplete meromorphic vector fields on complex surfaces, those where the solutions of the associated ordinary differential equations have no multivaluedness. We prove that if a non-Kähler compact complex surface has such a vector field, then, up to a bimeromorphic transformation, either the vector field is holomorphic, has a first integral or preserves a fibration. This extends previous results of Rebelo and the author to the non-Kähler setting.

13. #### Corrigendum On the class groups of pure function fields

Ichimura, Humio

14. #### Corrigendum On the class groups of pure function fields

Ichimura, Humio

Horie, Taro

Horie, Taro

17. #### A Thermodynamic formalism for one dimensional cellular automata

Namiki, Takao

18. #### A Thermodynamic formalism for one dimensional cellular automata

Namiki, Takao

19. #### The Bergman kernel on weakly pseudoconvex tube domains in $\mathbf {C}^2$

Kamimoto, Joe

20. #### The Bergman kernel on weakly pseudoconvex tube domains in $\mathbf {C}^2$

Kamimoto, Joe

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text:
# taking stock

The one thing harder than to start blogging after a long period of silence is to stop when you think you’re still in the flow.

(image credit Putnam Consulting)

The Januari 1st post a math(arty) 2018 was an accident. I only wanted to share this picture, of a garage-door with an uncommon definition of prime numbers, i saw the night before.

I had been working on a better understanding of Conway’s Big Picture so I had material for a few follow-up posts.

It was never my intention to start blogging on a daily basis.

I had other writing plans for 2018.

For years I’m trying to write a math-book for a larger audience, or at least to give it an honest try.

My pet peeve with such books is that most of them are either devoid of proper mathematical content, or focus too much on the personal lives of the mathematicians involved.

An inspiring counter-example is ‘Closing the gap’ by Vicky Neal.

From the excellent review by Colin Beveridge on the Aperiodical Blog:

“Here’s a clever way to structure a maths book (I have taken copious notes): follow the development of a difficult idea or discovery chronologically, but intersperse the action with background that puts the discovery in context. That’s not a new structure – but it’s tricky to pull off: you have to keep the difficult idea from getting too difficult, and keep the background at a level where an interested reader can follow along and either say “yes, that’s plausible” or better “wait, let me get a pen!”. This is where Closing The Gap excels.”

So it is possible to publish a math-book worth writing. Or at least, some people can pull it off.

Problem was I needed to kick myself into writing mode. Feeling forced to post something daily wouldn’t hurt.

Anyway, I was sure this would have to stop soon. I had plans to disappear for 10 days into the French mountains. Our place there suffers from frequent power- and cellphone-cuts, which can last for days.

Thank you Orange.fr for upgrading your network to the remotest of places. At times, it felt like I was working from home.

I kept on blogging.

Even now, there’s material lying around.

I’d love to understand the claim that non-commutative geometry may offer some help in explaining moonshine. There was an interesting question on an older post on nimber-arithmetic I feel I should be following up. I’ve given a couple of talks recently on $\mathbb{F}_1$-material, parts of which may be postable. And so on.

Problem is, I would stick to the same (rather dense) writing style.

Perhaps it would make more sense to aim for a weekly (or even monthly) post over at Medium.

Medium offers no MathJax support forcing me to write differently about maths, and for a broader potential audience.

I may continue to blog here (or not), stick to the current style (or try something differently). I have not the foggiest idea right now.

# the monster dictates her picture

The monstrous moonshine picture is a sub-graph of Conway’s Big Picture on 218 vertices. These vertices are the classes of lattices needed in the construction of the 171 moonshine groups. That is, moonshine gives us the shape of the picture.

(image credit Friendly Monsters)

But we can ask to reverse this process. Is the shape of the picture dictated by group-theoretic properties of the monster?

That is, can we reconstruct the 218 lattices and their edges starting from say the conjugacy classes of the monster and some simple rules?

Look at the the power maps for the monster. That is, the operation on conjugacy classes sending the class of $g$ to that of $g^k$ for all divisors $k$ of the order of $g$. Or, if you prefer, the $\lambda$-ring structure on the representation ring.

Rejoice die-hard believers in $\mathbb{F}_1$-theory, rejoice!

Here’s the game to play.

Let $g$ be a monster element of order $n$ and take $d=gcd(n,24)$.

(1) : If $d=8$ and a power map of $g$ gives class $8C$ add $(n|4)$ to your list.

(2) : Otherwise, look at the smallest power of $g$ such that the class is one of $12J,8F,6F,4D, 3C,2B$ or $1A$ and add $(n|e)$ where $e$ is the order of that class, or, if $n > 24$ and $e$ is even add $(n | \frac{e}{2})$.

A few examples:

For class 20E, $d=4$ and the power maps give classes 4D and 2B, so we add $(20|2)$.

For class 32B, $d=8$ but the power map gives 8E so we resort to rule (2). Here the power maps give 8E, 4C and 2B. So, the best class is 4C but as $32 > 24$ we add $(32|2)$.

For class 93A, $d=3$ and the power map gives 3C and even though $93 > 24$ we add $(93|3)$.

This gives us a list of instances $(n|e)$ with $n$ the order of a monster element. For $N=n \times e$ look at all divisors $h$ of $24$ such that $h^2$ divides $N$ and add to your list of lattices those of the form $M \frac{g}{h}$ with $g$ strictly smaller than $h$ and $(g,h)=1$ and $M$ a divisor of $\frac{N}{h^2}$.

This gives us a list of lattices $M \frac{g}{h}$, which is an $h$-th root of unity centered as $L=M \times h$ (see this post). If we do this for all lattices in the list we can partition the $L$’s in families according to which roots of unity are centered at $L$.

This gives us the moonshine picture. (modulo mistakes I made)

The operations we have to do after we have our list of instances $(n|e)$ is pretty straightforward from the rules we used to determine the lattices needed to describe a moonshine group.

Perhaps the oddest part in the construction are the rules (1) and (2) and the prescribed conjugacy classes used in them.

One way to look at this is that the classes $8C$ and $12J$ (or $24J$) are special. The other classes are just the power-maps of $12J$.

Another ‘rationale’ behind these classes may come from the notion of harmonics (see the original Monstrous moonshine paper page 312) of the identity element and the two classes of involutions, 2A (the Fischer involutions) and 2B (the Conway involutions).

For 1A these are : 1A,3C

For 2A these are : 2A,4B,8C

For 2B these are : 2B,4D,6F,8F,12J,24J

These are exactly the classes that we used in (1) and (2), if we add the power-classes of 8C.

Perhaps I should take some time to write all this down more formally.

# From the Da Vinci code to Habiro

The Fibonacci sequence reappears a bit later in Dan Brown’s book ‘The Da Vinci Code’ where it is used to login to the bank account of Jacques Sauniere at the fictitious Parisian branch of the Depository Bank of Zurich.

Last time we saw that the Hankel matrix of the Fibonacci series $F=(1,1,2,3,5,\dots)$ is invertible over $\mathbb{Z}$
$H(F) = \begin{bmatrix} 1 & 1 \\ 1 & 2 \end{bmatrix} \in SL_2(\mathbb{Z})$
and we can use the rule for the co-multiplication $\Delta$ on $\Re(\mathbb{Q})$, the algebra of rational linear recursive sequences, to determine $\Delta(F)$.

For a general integral linear recursive sequence the corresponding Hankel matrix is invertible over $\mathbb{Q}$, but rarely over $\mathbb{Z}$. So we need another approach to compute the co-multiplication on $\Re(\mathbb{Z})$.

Any integral sequence $a = (a_0,a_1,a_2,\dots)$ can be seen as defining a $\mathbb{Z}$-linear map $\lambda_a$ from the integral polynomial ring $\mathbb{Z}[x]$ to $\mathbb{Z}$ itself via the rule $\lambda_a(x^n) = a_n$.

If $a \in \Re(\mathbb{Z})$, then there is a monic polynomial with integral coefficients of a certain degree $n$

$f(x) = x^n + b_1 x^{n-1} + b_2 x^{n-2} + \dots + b_{n-1} x + b_n$

such that for every integer $m$ we have that

$a_{m+n} + b_1 a_{m+n-1} + b_2 a_{m+n-2} + \dots + b_{n-1} a_{m+1} + a_m = 0$

Alternatively, we can look at $a$ as defining a $\mathbb{Z}$-linear map $\lambda_a$ from the quotient ring $\mathbb{Z}[x]/(f(x))$ to $\mathbb{Z}$.

The multiplicative structure on $\mathbb{Z}[x]/(f(x))$ dualizes to a co-multiplication $\Delta_f$ on the set of all such linear maps $(\mathbb{Z}[x]/(f(x)))^{\ast}$ and we can compute $\Delta_f(a)$.

We see that the set of all integral linear recursive sequences can be identified with the direct limit
$\Re(\mathbb{Z}) = \underset{\underset{f|g}{\rightarrow}}{lim}~(\frac{\mathbb{Z}[x]}{(f(x))})^{\ast}$
(where the directed system is ordered via division of monic integral polynomials) and so is equipped with a co-multiplication $\Delta = \underset{\rightarrow}{lim}~\Delta_f$.

Btw. the ring structure on $\Re(\mathbb{Z}) \subset (\mathbb{Z}[x])^{\ast}$ comes from restricting to $\Re(\mathbb{Z})$ the dual structures of the co-ring structure on $\mathbb{Z}[x]$ given by
$\Delta(x) = x \otimes x \quad \text{and} \quad \epsilon(x) = 1$

From this description it is clear that you need to know a hell of a lot number theory to describe this co-multiplication explicitly.

As most of us prefer to work with rings rather than co-rings it is a good idea to begin to study this co-multiplication $\Delta$ by looking at the dual ring structure of
$\Re(\mathbb{Z})^{\ast} = \underset{\underset{ f | g}{\leftarrow}}{lim}~\frac{\mathbb{Z}[x]}{(f(x))}$
This is the completion of $\mathbb{Z}[x]$ at the multiplicative set of all monic integral polynomials.

This is a horrible ring and very little is known about it. Some general remarks were proved by Kazuo Habiro in his paper Cyclotomic completions of polynomial rings.

In fact, Habiro got interested is a certain subring of $\Re(\mathbb{Z})^{\ast}$ which we now know as the Habiro ring and which seems to be a red herring is all stuff about the field with one element, $\mathbb{F}_1$ (more on this another time). Habiro’s ring is

$\widehat{\mathbb{Z}[q]} = \underset{\underset{n|m}{\leftarrow}}{lim}~\frac{\mathbb{Z}[q]}{(q^n-1)}$

and its elements are all formal power series of the form
$a_0 + a_1 (q-1) + a_2 (q^2-1)(q-1) + \dots + a_n (q^n-1)(q^{n-1}-1) \dots (q-1) + \dots$
with all coefficients $a_n \in \mathbb{Z}$.

Here’s a funny property of such series. If you evaluate them at $q \in \mathbb{C}$ these series are likely to diverge almost everywhere, but they do converge in all roots of unity!

Some people say that these functions are ‘leaking out of the roots of unity’.

If the ring $\Re(\mathbb{Z})^{\ast}$ is controlled by the absolute Galois group $Gal(\overline{\mathbb{Q}}/\mathbb{Q})$, then Habiro’s ring is controlled by the abelianzation $Gal(\overline{\mathbb{Q}}/\mathbb{Q})^{ab} \simeq \hat{\mathbb{Z}}^{\ast}$.

# in praise of libraries

I’m back in Antwerp for over a week now, and finally got hold of our copy of Shimura’s “Introduction to the arithmetic theory of automorphic functions”.

The sad story of disappearing libraries at our university, and possibly elsewhere (everywhere?).

Over 20 years ago our maths department shared a building with the language departments, as well as a library.

The ground floor was taken up by languages, science books were in the cellar. There were years I spend more time on the ground floor than in the maths section.

I must have read most of the Dutch novels published between 1980 and 2000. For some time I could even pass as a Joyce-scholar, at least to those interested in a tiny part of Finnegans Wake.

All that changed when they united the three different branches of Antwerp university and we had to move to another campus.

We were separated from the language departments (they moved to the center of town) and, sadly, also from their library.

On the positive side, we moved to a nice building with a gorgeous library. And, an added bonus, it was on the same floor as my office. To kill an hour it was fun to stroll over to the library and spend some time between books and journals.

Then, some years ago, they closed down the maths-library and moved a tiny fraction of it to the science-library (located at a different campus).

Administration argued that too few people visited the library to keep it open.

But more important, they needed the space to create what they call a ‘study landscape’: a lounge where students can hang out, having enough power outlets for all their computers and smartphones.

So, the maths-library had to go for a place where, during term, students can recharge their phones, and during examination periods like now, students can sit together to study.

It seems that millennials need to have visual confirmation that their fellow students are also offline.

Today even the science-library is transformed into such a study-landscape, and only a handful of math-books remain on the shelves (well-hidden behind another door).

For the few odd ones, like me, who still want to browse through a book occasionally, you have to request for it online.

A few days later you get an email saying that your request is granted (they make it sound as if this is a huge favour), and then they need some more days to get the book from the storehouse and deliver it (sometimes randomly) to one of the few remaining university libraries, sorry, study landscapes…

# The return of the Scottish solids

In Januari’s issue of the Notices of the AMS there’s a paper by Mohammad Ghomi Dürer’s Unfolding Problem for Convex Polyhedra.

Here are the opening lines:

“Convex polyhedra are among the oldest mathematical objects. Indeed the five platonic solids, which constitute the climax of Euclid’s books, were already known to the ancient people of Scotland some 4,000 years ago; see Figure 1.”

It sure would make a good story, the (ancient) Scotts outsmarting the Greek in discovering the five Platonic solids. Sadly, the truth is different.

Once again, hat tip to +David Roberts on Google+ for commenting on the AMS announcement and for linking to a post by John Baez and a couple of older posts here refuting this claim.

Perhaps the most readable of the two posts is:


text:
# Getting Image name given a canvas WPF

I have a bunch of images I'm using for a chess game in a canvas using wpf, xaml, and C#. I want to use

Canvas.SetTop(image, position);

to set the position of this image. However I am given the index of child in my canvas and that is it.

myCanvas.children[index]

I tried

Canvas.SetTop(myCanvas.children[index], position);

but that did not work. How can I change the position of the image given only the index of the image in the canvas?

Edit: Another option would be to change the position of the canvas child. But I couldn't find anything for that.

Since you're using WPF I expect you don't plan to use a lot of animation, so a better way to do this would be with a Grid:

<!-- XAML -->
<Grid x:Name="Board">
<Grid.RowDefinitions>
<RowDefinition/>
<RowDefinition/>
<RowDefinition/>
<RowDefinition/>
<RowDefinition/>
<RowDefinition/>
<RowDefinition/>
<RowDefinition/>
</Grid.RowDefinitions>
<Grid.ColumnDefinitions>
<ColumnDefinition/>
<ColumnDefinition/>
<ColumnDefinition/>
<ColumnDefinition/>
<ColumnDefinition/>
<ColumnDefinition/>
<ColumnDefinition/>
<ColumnDefinition/>
</Grid.ColumnDefinitions>
</Grid>

To place something in a cell:

void SetPosition(UIElement element, int x, int y)
{
if (!Board.Children.Contains(element))

myCanvas.Children[index].SetValue(Canvas.TopProperty, position);


text:
# Finite Element Method¶

In the sequel the theory of the Finite Element is discussed in a compact way. This discussion is by no means comprehensive. Therefore one is invited to dive in more complete textbooks. The key contribution of this reader is that it is supported by many examples that can be easily extended and customized into efficient, production ready code. To this end, the examples are in C++14, and are specifically written such that they are mostly ‘what you see is what you get’. The entire structure is in the main-file, and not hidden somewhere in a library. To simplify your life we do use several libraries, each of which however only with a dedicated task, which can be understood, used, and checked independently of the Finite Element Method or any specific application. More specifically we use:

• GooseMaterial

Provides the constitutive response (and optionally the constitutive tangent) of several materials.

• cppmat

Provides tensor classes and operations. (The amount of tensor-operations is limited in the main program, and even non-standard, but this library is crucial to compute the material response implemented in GooseMaterial.)

• Eigen3

A linear algebra library. As you will notice, Eigen plays an important role in GooseFEM, and glues everything together since in the end the Finite Element Method is just a way to cast a problem into a set linear or linearized equations. Most of the efficiency of the final program will depend on the efficiency of the implementation of the linear algebra. In several examples we will simplify the structure by using dense matrices together with a simple solver which solves the resulting linear system. In reality one should always use sparse matrices combined with a more efficient solver. As you will notice, many examples need only few changes to be transformed in a production code.

Note

Compilation

Unless otherwise mentioned, the examples can be compiled as follows. Provided that pkg-config is set-up correctly one can use

clang++ pkg-config --cflags Eigen3 cppmat GooseMaterial GooseFEM -std=c++14 -o example example_name.cpp

(whereby clang++ can be replaced by for example g++). If one does not want to use pkg-config, one has to specify -I/path/to/library for each of the libraries.

For further development it is strongly advised to include the options -Wpedantic -Wall to get on top of mistakes. Once the code is ready, one should compile with optimization (-O3) and without assertions (-DNDEBUG). The Eigen3 documentation further recommends the option -march=native to enable vectorization optimized for you architecture.

## Statics¶

### The conceptual idea¶

We begin our discussion by considering a static, solid mechanics, problem. Loosely speaking the the goal is to find a deformation map, , that maps a body to a deformed state that satisfies equilibrium and the boundary conditions applied on .

As is the case in the illustration, the body can be subjected to two kinds of boundary conditions:

• Essential or Dirichlet boundary conditions on , whereby the displacements are prescribed.
• Natural or Neumann boundary conditions on , whereby the tractions are prescribed. (Whereby traction-free is also perfectly acceptable.)

In practice, we are not explicitly looking for the map , but for the deformation gradient , or in fact for a displacement field . To make things a bit more explicit, the deformation gradient is defined as follows:

hence

### Momentum balance¶

We start from the linear momentum balance:

where is the Cauchy stress which depends on the new position and thus on the displacement . It has been assumed that all actions are instantaneous (no inertia) and, for simplicity, that there are no body forces. Loosely speaking the interpretation of this equation is that the sum of all forces vanishes everywhere in the domain

Note

The following nomenclature has been used

The crux of the Finite Element Method is that this non-linear differential equation is solved in a weak sense. I.e.

where are test functions. For reasons that become obvious below, we apply integration by parts, which results in

Note

Use has been made of the following chain rule

together with the symmetry of the Cauchy stress

and the following nomenclature:

The right-hand-side of this equation can be reduced to an area integral by employing Gauss’ divergence theorem. The result reads

Note

Gauss’ divergence theorem states that

where is the normal along the surface .

### Discretization¶

The problem is now discretized using nodes that are connected through elements, which define the discretized domain . Shape functions are used to extrapolate the nodal quantities throughout the domain (and ), as follows:

Following standard Galerkin

Note

Applied to our problem sketch, a discretization might look like this. The nodes are clearly marked as circles. The lines connecting the nodes clearly mark the elements which are in this case three-node triangles (Tri3 in GooseFEM)

Applied to the balance equation we obtain

from which the dependency on can be dropped:

This corresponds to (non-linear) set of nodal balance equations:

with:

• Internal forces

• Boundary tractions

which is zero in the interior of the domain, i.e. in , while they can be zero or non-zero in depending on the problem details.

### Iterative solution – small strain¶

A commonly used strategy to solve the non-linear system, is the iterative Newton-Raphson scheme (see inset below). The idea is thereby to formulate an initial guess for the solution, determine possible residual forces, and use these forces to come to a better guess for the solution. This is continued until the solution has been found, i.e. when the residual vanishes.

This solution technique is discussed here in the context of small deformations, while it is later generalized. Assuming the deformations to be small allows us to assume that , and thus that . Also we define a strain tensor

and use some non-linear relationship between it and the stress

To simplify our discussion we assume the boundary tractions to be some known constant. Our nodal equilibrium equations now read

with

To come to an iterative solution, we linearize as this point. This results in

where

where the left part is the constitutive tangent operator and the right part comes from the strain definition. Note that this right part, the symmetrization using , can often be omitted as many constitutive tangent operators already symmetrize.

In a shorter notation, this is our iterative update:

with

and

Note

This is a good point to study some examples:

• Linear statics – small strain

We slowly work up to an iterative scheme starting from a linear problem, written however in such a way that the step towards a non-linear problem is small.

• Non-linear statics – small strain

Here we employ Newton-Raphson to solve the non-linear equilibrium equation. It is easy to see that once the above examples have been understood this step is indeed trivial.

Note

Newton-Raphson in one dimension

We try to find such that

We will make a guess for and (hopefully) iteratively improve this guess. This iterative value is denoted using . Therefore we will make use of the following Taylor expansion

where

We now determine by neglecting higher order terms, which results in

From which we obtain as

Thereafter we set

And check if we are have reached our solution within a certain accuracy :

If not, we repeat the above steps until we do.

The iterative scheme is well understood from the following illustration:

## Dynamics¶

### Momentum balance¶

We continue with our balance equation and add inertia an damping to it:

where is the density and the viscosity (a.k.a. the damping coefficient). The first and second time derivative of the position are respectively the velocity and the acceleration .

We can generalize this as follows (which will also simplify our proceedings below)

Note

To retrieve the original form

But, we can now use also other expressions. For example the damping equivalent of linear elasticity:

with

where is the bulk viscosity while is the shear viscosity. Furthermore

Our original form is retrieved when , both are independent of , and possesses the necessary symmetries.

Like before, we will solve this equation in a weak sense

Integration by parts results in

Which we will discretize as before:

Which is independent of the test functions, hence:

Which we can denote as follows

whereby we have introduced:

• Mass matrix

• Boundary tractions

• Internal forces

Note

In many problems it make sense to assume the mass matrix constant, as any change of volume results in an equivalent change of the density, i.e.

This results in the following expression for the mass matrix:

### Time discretization¶

Here we will discuss several common time discretization steps. To simplify notation we will denote the velocity and the acceleration .

Note

Most time integration schemes result is some form like

where contains the boundary tractions and internal forces, including their damping equivalents. The subscript indicates that the variable is a known quantity, while indicates that it is an unknown quantity. To enhance computational efficiency, it may be a good option to approximate the mass matrix in such a way that it becomes diagonal. Consequently, no system has be solved to find . One only has to invert an array of scalars. Since in addition the mass matrix is almost often assumed constant, this factorization has to be performed only once for the entire simulation.

Physically one can interpret this assumption as assuming the damping to be concentrated on the nodes.

See: Diagonal mass matrix.

#### Velocity Verlet with damping¶

1. Compute the position at :

2. Estimate the velocity at :

1. Correct :

## Shape functions¶

In the Finite Element Method a geometry is discretized using nodes. The nodes are grouped in elements which define the domain . The crux of the method is that nodal quantities, for example , are extrapolated throughout the discretized domain using shape functions . Each shape function is globally supported, however in such a way that only in the elements containing node . It is furthermore imposed that , i.e. it is one in the node , and zero in all other nodes.

For a one-dimensional problem comprising four linear elements and five nodes the shape functions are sketched below (whereby the node numbers are in color, while the element numbers are in black, in between the nodes).

From this it becomes obvious that is polynomial through each of the nodes, and that is discontinuous across element boundaries. Note once more that each of the shape functions is globally supported, but zero outside the elements that contain the node . For node 2, the shape function is thus:

As we can see, node 2 is only non-zero in elements 1 and 2, while it is zero everywhere else. To evaluate we therefore only have to integrate on these elements (using Isoparametric transformation and quadrature):

By now it should be clear that the above allows us assemble element-by-element. For this example, graphically this corresponds to the following sum:

where the indices show that the shape functions are evaluated compared to some generic element definition (see Isoparametric transformation and quadrature).

## Isoparametric transformation and quadrature¶

A very important concept in the Finite Element Method is the isoparametric transformation. It allows us to map an arbitrarily shaped element with volume onto a generic isoparametric element of constant volume . By using this mapping it is easy to perform numerical quadrature while even reusing an existing implementation (for example the one of GooseFEM).

The mapping between the generic domain and the physical domain is as follows

where the column contains the real position vectors of the element nodes. In order to perform the quadrature on we must map also the gradient operator:

or

with

Using the above:

We can now determine the mapping between the real and the master volume:

For example for the internal force this implies

Numerical quadrature can be formulated (exactly) on the master element. It corresponds to taking the weighted sum of the integrand evaluated at specific quadrature points (or integration-points). Again, for our internal force:

Note

To obtain , , and , simply replace with in the first equation. For this reason the same element implementation (of for example GooseFEM) can be used in small strain and finite strain (total Lagrange and updated Lagrange), proving either or as input.

Note

The details depend on the element type. Several standard elements types are implemented in GooseFEM.


text:
Ask your own question, for FREE!
Mathematics
OpenStudy (anonymous):

5 sqrt10(18 - sqrt6)

OpenStudy (anonymous):

Are you asking $5\sqrt{10(18-\sqrt{6})}$?

OpenStudy (anonymous):

no 5 sqrt10 (18- sqrt6)

OpenStudy (anonymous):

So... $5\sqrt{10}(18-\sqrt{6})$?

OpenStudy (anonymous):

yes

OpenStudy (anonymous):

$90\sqrt{10}-5\sqrt{60}$ $90\sqrt{10}-10\sqrt{15}$

OpenStudy (anonymous):

how did you get the 15?

OpenStudy (anonymous):

5*sqrt(60) = 5*sqrt(4)*sqrt(15)=5*2*sqrt(15)=10*sqrt(15).

OpenStudy (anonymous):

ok thanks i got it can i ask another question?

OpenStudy (anonymous):

Sure... just post another one, unless your question pertains to the one you just asked me.

OpenStudy (anonymous):

sqrt5 divided by 18 + sqrt3

OpenStudy (anonymous):

Are you trying to rationalize it?

OpenStudy (anonymous):

i don't know. i think i just need to simplify it

OpenStudy (anonymous):

It is basically simplified already. Rationalize means that there can't be any roots in the denominator.

OpenStudy (anonymous):

yes - rationalize it please

OpenStudy (anonymous):

sqrt(5)/(18+sqrt(3)). Multiply both the top and bottom by 18-sqrt(3). On the top, you have sqrt(5)(18-sqrt(3)). On the bottom, you have 18^2-3. I hope you can simplify from here.

OpenStudy (anonymous):

what does the ^ sign mean?

OpenStudy (anonymous):

power or exponentiation.

Can't find your answer? Make a FREE account and ask your own questions, OR help others and earn volunteer hours!

Join our real-time social learning platform and learn together with your friends!
Can't find your answer? Make a FREE account and ask your own questions, OR help others and earn volunteer hours!

Join our real-time social learning platform and learn together with your friends!


text:
# Prove(5)

• January 22nd 2010, 03:05 AM
Punch
Prove(5)
Prove $cos^2A-cos^2B=sin(B-A)sin(B+A)$

I attempted the question start with the RHS, using the addition formulae and ended off with cot^2A-cot^2B...
• January 22nd 2010, 04:37 AM
Quote:

Originally Posted by Punch
Prove $cos^2A-cos^2B=sin(B-A)sin(B+A)$

I attempted the question start with the RHS, using the addition formulae and ended off with cot^2A-cot^2B...

lets start from the RHS .

$(\sin B\cos A-\cos B\sin A)(\sin B\cos A+\cos B\sin A)$

this is in the form of $(a+b)(a-b)=a^2-b^2$

$\sin^2 B\cos^2 A-\cos^2 B\sin^2 A$

$(1-\cos^2 B)\cos^2 A-\cos^2 B(1-\cos^2 A)$

$\cos^2 A-\cos^2 A\cos^2 B-\cos^2 B+\cos^2 B\cos^2 A$


text:
To get the best deal on Tutoring, call 1-855-666-7440 (Toll Free)
Top

# Inductance Formula

Inductance is the property of a conductor by which a change in current flowing through it induces (creates) a voltage (electromotive force) in both the conductor itself (self-inductance) and in any nearby conductors (mutual inductance).  Inductance is defined as opposing of changes of current. The inductance value is represented as L and its unit is Henry. One Henry value is equal to the induced one volt by changing of current in one ampere per second in an inductance value. The inductance value is of two types. One is self inductance and another one is mutual inductance. Let us see the applications of inductance value.
The self inductance in an electrical circuit is
Where,
V is voltage in volts,
L is inductance value,
i is the current in A,
t is time taken

The reactance of inductance is given by
Where,
X is reactance in henry,
f is the frequency in Hz,
L is inductance in Henry

The total series inductance is
The parallel inductance is
Where, L1, L2, L3 ..... Ln are the inductance values.

 Related Calculators Inductance Calculator Inductive Reactance Calculator Acceleration Formula Calculator Area of a Circle Formula Calculator

## Inductance Problems

Lets see some examples on inductance:

### Solved Examples

Question 1: Calculate the equivalent resistance if inductors of 5H, 2H and 7 H are connected in series ?
Solution:

Given: L1 = 5H, L2 = 2H, L3 = 7H
The series inductance is given by
L = L1 + L2 + L3
= 5H + 2H + 7H
= 14 H.

Question 2: A inductor of 50 H is connected in a circuit and a frequency of 200 Hz is applied. Calculate the reactance ?
Solution:

Given: Reactance x= ?, frequency f = 200 Hz, inductance L = 50 Henry
The reactance is given by
X = 2 $\pi$ f L
= 2 $\times$ $\pi$ 200 Hz $\times$ 50 H
= 4000 $\Omega$.

 More topics in Inductance Formula Transformer Formula Induced Voltage Formula Inductive Reactance Formula
*AP and SAT are registered trademarks of the College Board.


text:
### (PDF) Computational aeroacoustics:progress on nonlinear

Computational aeroacoustics:progress on nonlinear problems of sound generation. Progress in Aerospace Sciences, 2004. Prasanth Kutchu (PDF) Deep temperatures and surface heat flow distribution computation of subsurface î a change of 1,0%o in. surface . HF corresponds to T materials having . proper thermal conductivity an average thickness of about 50 km (Della. Vedova . et al

### (PDF) Engineering mechanics solved problems pdf provide

14 Full PDFs related to this paper. READ PAPER. Engineering mechanics solved problems pdf (PDF) Langmuir mechanism of low-frequency stimulated thermal conductivity (d uring the l aser pulse, hea t wave diffu sion l ength i s ~10 0 n m g iven water thermal conductivity s cm / 10 1 .9 = 2 5 ), we get the final heating temperature Chapter 2 Magnetic Materials and Their CharacteristicsThe permeability of a magnetic material is a measure of the ease in magnetizing the material. Permeability, u, is the ratio of the flux density, B, to the magnetizing force, H. D =, [permeability] [2-1] H The relationship between B and H is not linear, as shown in the hysteresis loop in Figure 2-1. Then, it is

### Computational aeroacoustics:progress on nonlinear

Aug 01, 2004 · We will take A = 0.095 and B = 5.5, along with L (x) = 1.4 1 / 2 (x) and u 0 (x) = 0.25 U c (x) to make estimates for (x-x 0) / D j 6. The virtual origin of the jet, x 0 , is known to depend on the conditions at the nozzle exit; a nearly laminar boundary layer has the effect of shifting the location where the potential core ends, while a Sample papers Archives - Page 20418 of 20639 - (SOLVED) Consider the satellite attitude control system shown in the Figure 5-80(a). The output of this system exhibits continued oscillations. About Us. About Us. This category contains various papers that have been submitted by other students in various universities for the award of marks. Categories. Sample papers. Recording and Simulation studies of carbon nanotube field-effect Simulation studies of carbon nanotube field-effect transistors (CNFETs) are presented using models of increasing rigour and versatility that have been systematically developed. Firstly, it is demonstrated how one may compute the standard tight-binding band structure. From this foundation, a self-consistent solution for computing the equilibrium energy band diagram of devices with Schottky

### Solved:Consider a large plate of thickness L and thfermal

Consider a large plate of thickness L and thfermal conductivity k" in which heat is generated uniformly at a rate of e gen.One side of the plate is insulated while the other side is exposed to an environment at T x. with a heat transfer coefficient of h.(a) E the differential equation and the boundary conditions for steady one-dimensional heat conduction through the plate, (b) determine Synthesis and physiochemical characterization of Studies showed that many types of surfactants can be used at low concentrations (0.05-0.2%) to achieve low interfacial tension on the order of 10 2 dynes/cm or less (Ge and Wang, 2015 [Solved] Consider a silicon sample doped with $$\rm N_D Question:Consider a silicon sample doped with \(\rm N_D = 1×10^{15}/cm^3$$ donor atoms. Assume that the intrinsic carrier concentration $$\rm n_i = 1.5×10^{10}/cm^3$$.If the sample is additionally doped with $$\rm N_A = 1×10^{18}/cm^3$$ acceptor atoms, the approximate number of $$\rm electrons/cm^3$$ in the sample, at $$\rm T=300\ K$$, will be _____.


text:
## Introduction – Logosouk IGNITE

I am here to share my ideas and adding knowledge from this forum.

If anyone has questions or suggestions, let me know.

Thank You

Logosouk – IGNITE

## script – Did the introduction of VerifyScript cause a backwards incompatible change to consensus?

My question is about the changes to bitcoin done by commit range `(a75560d8, 6ff5f718)`, and their effect on consensus.
Out of this range of four commits (all attributed to satoshi) during the dates July 30th-31st 2010, only the first and last commits are relevant to the question (the two in the middle seem like a build system change, not code).

The two commits (first and second from now on), `a75560d8` and `6ff5f718` are attributed to fixing quite a few vulnerabilities in bitcoin script semantics and execution. For example, in the first commit :

1. Constraints were applied to push and stack sizes
2. The so-called script versioning mechanism was removed, and the various `NOP#` opcodes were added in its place
3. Constraints were applied to bignum operations
4. `OP_RETURN` was changed from merely terminating the script to returning `false` for the entire execution

In the second commit :

1. Constraints were applied on the maximum number of opcodes in the script
2. Execution of unknown opcodes was set to return `false` for the execution
3. The maximum size of the script was reduced by half to 10kb
4. A change to `*SHIFT` opcodes was done (I don’t really uderstand it though)
5. A function called `VerifyScript` was introduced into bitcoin which changed the behavior of script execution

This question is about this list of changes, and whether any of them might be non backwards compatible. Specifically, I will focus on change (5) from the second commit : 6ff5f718:script.cpp

Before this change, at the point of txout redemption, a redeeming transaction’s input’s `scriptSig` and the prevout’s `scriptPubKey` were joined to form a single script by placing an `OP_CODESEPARATOR` between them, and passing the result to `EvalScript` which would execute the script.

Inside `EvalScript`, an empty stack was created and results from the various operations done in the script are pushed onto it. When script execution completes without errors, a boolean is returned; if the stack is not empty then the top element is passed to a `CastToBool` function and and returned (`true` or `false`), and if the stack is empty then `false` is returned.

After the change, the `VerifyScript` function wraps around two separate calls to `EvalScript`, executing `scriptSig` and `scriptPubKey` separately one after the other. The empty stack which was previously created within `EvalScript` is instead created in `VerifyScript` before any script execution begins, and the final check of the stack’s contents (or lack thereof) and `CastToBool` was also moved to `VerifyScript`, to the point after both `scriptSig` and `scriptPubKey` completed their execution.

In `VerifyScript`, first the `scriptSig` from the redeeming transaction is passed to `EvalScript` along with the empty stack. The machine executes the script and results from the operations are pushed to the stack that was passed in with it. If no errors occurred during execution, `true` is returned to `VerifyScript`.
Secondly, if indeed `true` was returned, the `scriptPubKey` from the funding transaction is passed to `EvalScript` along with the stack, which at that point holds the contents left over from `scriptSig`‘s execution.
The `scriptPubKey` is executed, which further manipulates the stack’s contents and if no errors occured, returns `true` back to `VerifyScript`.
Lastly, if `true` was returned, then the check for empty stack and `CastToBool` are done, which determines the final result of script verification.

The reason for this change was cited as being a fix to a possible vulnerability in Script : SE answer, BCTalk thread.
Although it’s orthogonal to this question, it’s why I included the list of changes from commit `a75560d8`.

It’s not too hard to see that considering simple (lacking a checksig) scripts, this change is indeed backwards compatible. At worst, some scripts might become unspendable, but there doesn’t seem to be a case where a previously unspendable script might become spendable as a result of this change.

Even for scripts with a checksig like `p2pk`, `p2pkh` and multisig, the `CHECKSIG` opcode is always taking place in `scriptPubKey`, which was separated from the elements of `scriptSig` by an `OP_CODESEPARATOR` prior to this change. Seemingly, the semantics remained the same – until about two years later.

Looking at the wiki page for `OP_CHECKSIG` wiki-checksig, steps (2) to (4) explain how to go from `scriptCode` to `subScript`, and specifically what happens when an `OP_CODESEPARATOR` exists in `scriptCode` :

1. A new subScript is created from the `scriptCode` (the `scriptCode` is the actually executed script – either the `scriptPubKey` for non-segwit,
non-P2SH scripts, or the `redeemscript` in non-segwit P2SH scripts). The
script from the immediately after the most recently parsed
`OP_CODESEPARATOR` to the end of the script is the `subScript`. If there
is no `OP_CODESEPARATOR` the entire script becomes the `subScript`
2. Any occurrences of `sig` are deleted from subScript, if present (it is not standard to have a signature in an input script of a
transaction)
3. Any remaining `OP_CODESEPARATORS` are removed from `subScript`

Now, prior to commit `6ff5f718`, when `scriptSig` and `scriptPubKey` were joined to form a single script, the `scriptCode` would look like :

``````<scriptSig> CODESEPARATOR <scriptPubKey>
``````

With checksig operations taking place in `scriptPubKey`, making `subScript` be everything to the right of `CODESEPARATOR` – basically `<scriptPubKey>` itself (unless more codeseparators or if signatures consumed by a checksig also exist in `scriptPubKey`).

After the commit, there would actually be two separate executions with `scriptSig` first and `scriptPubKey` second, where each execution would have its own `scriptCode` and subsequently its own `subScript`.
Now, Because checksig operations are still only being done in `scriptPubKey`, it appears that `subScript` would remain the same, but what would happen if a `CHECK(MULTI)SIG` opcode gets executed in `scriptSig`?

In January 24th 2012, block 163685 was mined which contained transaction `eb3b82c0884e3efa6d8b0be55b4915eb20be124c9766245bcc7f34fdac32bccb`.
This transaction, the two immediately after it, and its funding at `b8fd633e7713a43d5ac87266adc78444669b987a56b3a65fb92d58c2c4b0e84d` which were also mined in the same block are all mentioned in BIP-17, which is an alternative implementation of `p2sh` semantics :

• `OP_CHECKHASHVERIFY` will re-define the existing `OP_NOP2` opcode, and will function as follows when executed:

• First, hash the end of the prior script (in the general case, `scriptSig`; if no prior script, a null string is hashed) beginning
from the last evaluated `OP_CODESEPARATOR` onward (or from the
beginning of the script, if no `OP_CODESEPARATOR` was present)

• Then, compare this with the item on the top of the stack (if there is none, the script fails immediately)
• If the hashes match, do nothing, proceed as if an `OP_NOP`; if they do not match, the script fails immediately. Note that in the case of a
matched hash, the top stack item (the hash being compared with) is not
popped off the stack. This is for backward compatibility.

Notice how in bip17 the `redeemScript` is given as an actual executable script in `scriptSig`, rather than a single data push of a blob as is the case with bip16. Even though older nodes will not enforce the `hash160` of `scriptSig` to be equal to the 20 bytes value from prevout’s `scriptPubKey`, they would still have to execute it and validate any `CHECK(MULTI)SIG` operations within.

I’m assuming here that these bip17 example transactions were mined and validated by nodes running software that was recent in Jan. 2012, but suppose there were still nodes on the network running older software, and specifically ones running versions `v0.3.6` and lower. Would these older nodes be able to come to consensus with the newer nodes about the validity of block 163685?

Going over the funding transaction `b8fd633e7713a43d5ac87266adc78444669b987a56b3a65fb92d58c2c4b0e84d`, and looking at the output at index 1, we see the `scriptPubKey` (`NOP2` is actually a non active `OP_CHECKHASHVERIFY`)

``````0x14 0x2a9bc5447d664c1d0141392a842d23dba45c4f13 NOP2 DROP
``````

And in the spending transaction `eb3b82c0884e3efa6d8b0be55b4915eb20be124c9766245bcc7f34fdac32bccb`, from the input at index 1, we have the `scriptSig`

``````0 0x47 0x30440220276d6dad3defa37b5f81add3992d510d2f44a317fd85e04f93a1e2daea64660202200f862a0da684249322ceb8ed842fb8c859c0cb94c81e1c5308b4868157a428ee01 CODESEPARATOR 1 0x21 0x0232abdc893e7f0631364d7fd01cb33d24da45329a00357b3a7886211ab414d55a 1 CHECKMULTISIG
``````

Consider first how software from `v0.3.7` and above would construct the `subScript` for the `CHECKMULTISIG` in `scriptSig`. We begin with a `scriptCode` which is exactly `scriptSig`, and since a `CODESEPARATOR` is executed, `subScript` becomes :

``````1 0x21 0x0232abdc893e7f0631364d7fd01cb33d24da45329a00357b3a7886211ab414d55a 1 CHECKMULTISIG
``````

Now consider how software from `v0.3.6` and below would construct the `subScript` for the same `CHECKMULTISIG`. Our `scriptCode` is no longer made from only `scriptSig`, but from a joining of it and `scriptPubKey` by a `CODESEPARATOR`. The `scriptCode` would look like :

``````0 0x47 0x30440220276d6dad3defa37b5f81add3992d510d2f44a317fd85e04f93a1e2daea64660202200f862a0da684249322ceb8ed842fb8c859c0cb94c81e1c5308b4868157a428ee01 CODESEPARATOR 1 0x21 0x0232abdc893e7f0631364d7fd01cb33d24da45329a00357b3a7886211ab414d55a 1 CHECKMULTISIG CODESEPARATOR 0x14 0x2a9bc5447d664c1d0141392a842d23dba45c4f13 NOP2 DROP
``````

Recall the rules from the wiki. At the point when `CHECKMULTISIG` is executed, `subScript` is everything from the point after the last executed `CODESEPARATOR` and until the end of the script, with all `CODESEPARATOR`s on the right hand side of the checksig operator removed :

``````1 0x21 0x0232abdc893e7f0631364d7fd01cb33d24da45329a00357b3a7886211ab414d55a 1 CHECKMULTISIG 0x14 0x2a9bc5447d664c1d0141392a842d23dba45c4f13 NOP2 DROP
``````

If this is correct, then it appears that old nodes with versions `v0.3.6` and below cannot agree on which is the correct `sighash` for this spending transaction, but since I can’t realistically run any such old version software, I can’t be absolutely sure. I did patch a recent bitcoin core version with some changes that enabled me to simulate validation of tx `eb3b82c0884e3efa6d8b0be55b4915eb20be124c9766245bcc7f34fdac32bccb`, and as expected it did not pass validation. I will add the two sighashes below along with the public key and signature for comparison.

So my question is, is there something I’m misunderstanding or perhaps missed that would allow pre-`v0.3.7` and post-`v0.3.7` nodes to come to consensus about the validity of block 163685?

(also relevant : this SE question)

``````Pubkey : 0232abdc893e7f0631364d7fd01cb33d24da45329a00357b3a7886211ab414d55a
``````

Pre-`v0.3.7` sighash (does not validate) :

``````01000000
02
00
FFFFFFFF
3C 51210232abdc893e7f0631364d7fd01cb33d24da45329a00357b3a7886211ab414d55a51ae142a9bc5447d664c1d0141392a842d23dba45c4f13b175
FFFFFFFF
02
E0FD1C0000000000 19 76a914380cb3c594de4e7e9b8e18db182987bebb5a4f7088ac
C0C62D0000000000 17 142a9bc5447d664c1d0141392a842d23dba45c4f13b175
00000000
01000000

sha256  : 1EB276326D72CB358F6C275D6542F76EED4E36364727CB82D40A116244EBDDB5
sha256d : 11491E74778E1FA8C40CC8E07E1F835677CF1AC81F54255EC1C7125C1894939A
``````

Post-`v0.3.7` sighash (does validate) :

``````01000000
02
00
FFFFFFFF
25 51210232abdc893e7f0631364d7fd01cb33d24da45329a00357b3a7886211ab414d55a51ae
FFFFFFFF
02
E0FD1C0000000000 19 76a914380cb3c594de4e7e9b8e18db182987bebb5a4f7088ac
C0C62D0000000000 17 142a9bc5447d664c1d0141392a842d23dba45c4f13b175
00000000
01000000

sha256  : 3858A592C15A47F3058010689883DECCD4AF41F5367B9776429613DFB3339883
``````

## What is a sitemap? Do you really need it? This short introduction should help you make the decision! | Proxies-free

JavaScript is deactivated. For a better experience, please enable JavaScript in your browser before continuing.

Regardless of whether you don't have much (or no) background information about web improvement, you are probably familiar with search engine optimization (SEO). This is a broad term for an enormous number of procedures that you can use to improve the ranking of your website in web search engines. A large number of the SEO strategies that you will learn to focus on are keywords. However, there are various tasks that are similarly basic.

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## introduction

Hello everybody,

I am Prajith Khan

I just joined this forum a few hours ago and look forward to receiving and sharing a lot of useful insights here!😃

## Introduction to Forex – Discussions & Help

The TopGold Forum quickly becomes the most important online financial goal on the Internet.

We are an authority and a first class forum for professional investors, forex traders, affiliates and individuals looking to make a living online or just want to make more money.

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## Proof theory – reasons for the inapplicability of the complete introduction to the tour expansion

It is known that the expansion of tours is a rather bad heuristic to generate short Hilton cycles even in the planar Euclidean case. This is surprising when you learn about it for the first time.
The surprise is due to the fact that the heuristic appears to resemble full induction if you start with the convex hull of the set of points as the base case and then insert the next point as the point that causes the least increase in length of the tour:

Framework:

• The relative order of the points on the convex hull is the same as for the shortest tour of all points.

Induction step:

• if that's the tour $$T_n$$ through the first $$left | CH right | + n$$ points is optimal, then the shortest tour $$T_ {n + 1}$$ with an additional point is optimal again ($$left | CH right |$$ is the number of points on the convex hull and $$n geq 0)$$,

Question:

What are the reasons that prove that the greedy expansion of the tour is not a variant of the full introduction?

What I am looking for is evidence that clearly indicates which of the conditions for the applicability of full induction are violated by a greedy extension of the tour.

## problem

The problem definition is here. For a brief summary:

• An IntCode program is an array of Ints
• The program counter begins with index 0, reads an opcode there, followed by 0 or more arguments for the next indexes, and then goes to the index after the last argument
• opcode 1 takes 3 arguments, `a`. `b`, and `z`and sets `program(z) = program(a) + program(b)`
• opcode 2 does the same thing, but multiplies instead
• opcode 99 takes 0 arguments and stops the program

In part 1 we take the input, replacing index 1 with 12 and index 2 with 2 (`restore 12 2`), run the program and return index 0.

In part 2 (not shown in the link unless you solve part 1) we find which Ints have to replace indices 1 and 2 to get a result where index 0 is 19690720.

With this code, I think it could probably be easier. I tried to separate the program counter logic from the command execution logic (`interpret` vs `step`), but apparently you needed a strange combiner `whileWith`, I was wondering if there are better combiners to express this type of loop or if there is a completely different approach.

I was considering wrapping `step` in the `ContT` or `ExceptT`This would make it possible to reduce part of the nesting by using the early exit instead. However, I wasn't sure which way was the best in terms of extensibility.

## code

``````import Control.Arrow (second)
import Data.Array
import Data.Array.ST
import Data.List (find)

data Status = InvalidOp | Terminated | Running | InvalidAddress
deriving (Show, Eq)

newtype Program = Program {
getInts :: Array Int Int
} deriving (Show)

-- Execute the instruction starting at `start`
step :: STArray s Int Int -> Int -> Int -> ST s Status
step arr len start = do
case op of
99 -> return Terminated
_ -> do
(i, j, store) <- forM (start+1..start+3) (readArray arr)
if not \$ all inBounds (i, j, store) then
else do
(a, b) <- forM (i, j) (readArray arr)
case op of
1 -> writeArray arr store (a+b) >> return Running
2 -> writeArray arr store (a*b) >> return Running
_ -> return InvalidOp

where inBounds ix = 0 <= ix && ix < len

interpret :: Program -> Program
interpret (Program prog) = Program \$ runSTArray \$ do
let len = succ . uncurry subtract \$ bounds prog
mArr <- thaw prog
whileWith (== Running) (0, 4..len-1)
(step mArr len)
return mArr

let nums = fmap read \$ split ',' str
in
Program \$ listArray (0, length nums - 1) nums

restore :: Int -> Int -> Program -> Program
restore a b = Program . (// ((1, a), (2, b))) . getInts

-- pt 2

findNounVerb :: Program -> Int -> Maybe (Int, Int)
findNounVerb prog target =
find ((== target) . (! 0) . getInts . interpret . (\$ prog) . uncurry restore) \$
((n, v) | n <- (0..1000), v <- (0..n))

-- util --

split :: Eq a => a -> (a) -> ((a))
split _ () = ()
split k xs = curr : split k rest
where (curr, rest) = second (drop 1) \$ span (/= k) xs

whileWith :: (Monad m) => (ret -> Bool) -> (inp) -> (inp -> m ret) -> m ()
whileWith _ () _ = return ()
whileWith pred (x:xs) step = do
res <- step x
when (pred res) \$
whileWith pred xs step

-- end util --

main :: IO ()
main = do

-- pt 1:
putStrLn "Part 1:"
let output = (! 0) . getInts . interpret . restore 12 2 \$ prog
putStrLn \$ "Output: " ++ show output
putStrLn ""

-- pt 2:
putStrLn "Part 2:"
let Just (noun, verb) = findNounVerb prog 19690720
putStrLn \$ "Noun: " ++ show noun ++ "n" ++ "Verb: " ++ show verb
print \$ 100*noun + verb

$$```$$
``````

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Marina One Residences Prices can be observed excitingly in the upward trend of the real estate market. In block 21, only limited units remain with a very attractive price of 2,200 psf on average.

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Contact the New Condo Launch 2020 development team at 6100 3447 or visit http://www.condolaunchsg.com/properties/ma…one-residences/ for more information on Marina 1.

## Javascript – Is there a discussion about the introduction of aliases for window.URL.createObjectURL ()?

Is there a suggestion for ES2020 (or later) regarding the introduction of aliases for `window.URL.createObjectURL()` ?

So that I can write the following:

``````let myBlobURL = window.URL.createObjectURL(myBlob, 'my-blob-url');
``````

and then:

``````example.com/my-blob-url
``````

is a alias that points to the generated URL that was created by `window.URL.createObjectURL()` ?

## Introduction!!!

Hello everybody,

I am new to this forum, my name is Debby Tompkins. I love to know why I'm here. I hope to get some really good ideas for trading and the digital ways of making money.

Many thanks


text:
# Through which route an SMPS propagates and picks up the switching noise?

I have seen that some switch mode power supplies are injecting noise to the electrical power network. I guess this noise is common mode noise. That switching noise then propagates through and enters to another power supply and even can appear at the DC output.

1) Regarding the switching noise originates from an SMPS, does it propagate on neutral, line or earth wire?

2) And in the affected SMPS, how does it pass this switching noise all the way to its DC outputs? From its line, neutral or earth terminal?

3) Why is this type of noise is called common mode noise?

I would like to see the actual trace/path the noise travels from the injector to the receiver SMPS.

• A lot of the noise is differential; the switching mechanism in an SMPS creates a diff signal that gets conducted to the L and N wires at the top and bottom of the bridge rectifiers conduction points. Plenty of SMPS have diff filters. – Andy aka Dec 11 '18 at 9:03
• @Andyaka Thanks for the comment but I dont understand in real. Why do you call it differential if it is appearing both at neutral and line? And where does the noise current flow through all the way from the smps to the other smps. A illustrative answer would help a lot. – panic attack Dec 11 '18 at 10:04
• Appearing on both lines simultaneously and having the same amplitude and phase is called common-mode. If either the amplitude or the phase are unequal then a combined differential and common signal is produced. The main switching element produces a signal that is largely differential. If you don't understand this then you should do some research and then adjust your question above. – Andy aka Dec 11 '18 at 10:09
• What I understand from your words the noise initially common at both lines but because of in balance it will become as differential. If the noise at line is 10 and the noise at neutral is 8 the difference is 2. Th CM filter still helps because if it has attenuation factor of 10 the line noise will be 1 and the neutral noise will be 0.8 resulting s differential noise of 0.2. Thats what I have in mind. Is that totally wrong. If it is I will go and do more research as you recommend. – panic attack Dec 11 '18 at 10:16

Finally, you measure all these conducted perturbation with a line impedance stabilization network or LISN configured in such a way that you can isolate DM and CM noises. You have to separate CM and DM as each requires a different cure. The LISN offers a constant 50-$$\\Omega\$$ output resistance along the analyzed frequency band. The final EMI plot to check PASS or FAIL mixes them of course.