text:
So, we know how to take the exponential of any complex number now. We do it by converting the exponential into the exponential of the real and imaginary parts separately, and then use the relationship between $e^{ia}$ and the $\cos$ and $\sin$ functions to write everything in terms of functions of real numbers, which we know how to deal with. How about the trigonometric functions applied to complex numbers? Well, we have a pretty good hint already from how we got from the exponential of complex numbers to trigonometric functions of real numbers. In fact we’re just going to give the answer, but you can work it out using Taylor series as well. For a complex number $z$:

$\cos z=\frac{e^{iz}+e^{-iz}}{2}$

$\sin z=\frac{e^{iz}-e^{-iz}}{2i}$

The first thing to check is that this is true when $z$ is a real number. It looks pretty strange at first site, especially the definition of $\sin$ because there’s an $i$ sticking out in the denominator like a sore thumb! How can this give us something real, as we know that it must? Let’s take $z=\theta$ where $\theta$ is real. Then:

$\cos \theta=\frac{e^{i\theta}+e^{-i\theta}}{2}=\frac{\cos\theta+i\sin\theta+\cos(-\theta)+i\sin(-\theta)}{2}=\cos\theta$

$\sin \theta=\frac{e^{i\theta}-e^{-i\theta}}{2i}=\frac{\cos\theta+i\sin\theta-\cos(-\theta)-i\sin(-\theta)}{2i}=\sin\theta$

So that holds. How about trying to understand the behaviour of the trigonometric function of a purely imaginary complex number? Well, we know for sure that trig functions are always between -1 and 1, right? Well, it turns out that this is only true if $\theta$ is purely real. In fact if it’s complex then the trig functions can give you any complex number you like. We’ll see that shortly. Let $z=i b$ where $b$ is a real number, then:

$\cos ib=\frac{e^{-b}+e^{b}}{2}$

$\sin ib=\frac{e^{-b}-e^{b}}{2i}$

Then we can see that $\sin ib$ is purely imaginary and $\cos ib$ is purely real. The other thing that we can note is that for large positive or negative $b$, both of these numbers are going to be large in magnitude. In fact these functions have names $\cos ib=\cosh b$ which is known as hypergeometric cosine, and $-i\sin ib=\sinh b$ which is hypergeometric sine. We can plot both of these functions in the figure below and see that they don’t behave at all like the normal sine and cosine functions that we are used to.

There are hyperbolic trig identities just as there are for normal trig functions, but unlike the case where $\sin^2x+\cos^2x=1$, now $\cosh^2x-\sinh^2x=1$ In fact it is precisely this hyperbolic identity which gives the functions their name. Unlike the sine and cosine functions which describe circular behaviour, so the hyperbolic versions describe the behaviour of things moving along hyperboloids. In the following you can see the differences between hyperolic functions and circular functions, which are very close, up to a single sign in their definitions, but have completely different behaviours

OK, so let’s look at a very general example to see that actually we can have trig functions giving any result we want, not just numbers between -1 and 1 as we had when we were restricted to the real numbers. Let’s ask a very general question. Find $z$ when:

$\sin z=w$

For any complex number $w$. We start by writing the trig function in exponential form and then multiply both sides of the equation by $2i e^{iz}$. This gives:

$e^{2iz}-1=2wie^{iz}$

Now we note that we can write $e^{iz}=p$ and we can happily now write the equation as a normal quadratic equation:

$p^2-2 wip-1=0$

But we can solve this using the normal quadratic recipe (You can prove that this still holds, even for complex numbers, simply by using it and then plugging the result back into the quadratic equation). So:

$p=\frac{2wi\pm\sqrt{-4w^2+4}}{2}=wi\pm\sqrt{1-w^2}$

So, we now have that:

$e^{iz}=wi\pm\sqrt{1-w^2}$

How can we calculate what $z$ must be? Let’s start by saying that $z=a+bi$ so:

$e^{ia-b}=e^{-b}(\cos a+i\sin a)=wi\pm\sqrt{1-w^2}$

We can then solve this by taking the modulus and argument of both sides. First the modulus:

$|e^{-b}(\cos a+i\sin a)|=e^{-b}=|wi\pm\sqrt{1-w^2}|$

and the argument:

$arg\left(e^{-b}(\cos a+i\sin a)\right)=a=\arg\left(wi\pm\sqrt{1-w^2}\right)$

so now, given a $w$, we can calculate precisely the $z$ such that $\sin z=w$. You can see that you would be able to do this for any $w$ you are given, because any $w$ has both a modulus and an argument (though you’d have to be careful about $w=0$). to be a solution to the equation, thus, the full solution is:

$z=\arg\left(wi\pm\sqrt{1-w^2}\right)-i\ln|wi\pm\sqrt{1-w^2}|$

Remember that the argument of a complex number includes additions of $2n\pi$ with $n\in{\mathbb Z}$. This looks a bit abstract, but given specific values of $w$, we can calculate this relatively easily.

In the same vein as in the previous post, this is the mapping of lines in the complex plane under the Cosine function:

 How clear is this post?


text:
# Thread: An unusual simpson's rule question

1. ## An unusual simpson's rule question

Here is a question even the professor couldn't answer.
Show that if f is a polynomial of degree three or lower, then Simpson's Rule gives the exact value of (a bottom) integral (b top) f(x)dx. I would appreciate an answer back as soon as possible. Thanks

2. Originally Posted by desdemoniagirl
Here is a question even the professor couldn't answer.
Show that if f is a polynomial of degree three or lower, then Simpson's Rule gives the exact value of (a bottom) integral (b top) f(x)dx. I would appreciate an answer back as soon as possible. Thanks
Do you have a copy of Smith and Minton's "Calculus - Early Transcendentals". They discuss this on page 415 in the exploratory exercises.

3. ## Book error

Hello, I dont have a copy of Smith's early transcendentals, but i do have a copy of Steward's early transcendentals. Do they give an explination, because I cant find it. thanks in advance

4. Originally Posted by desdemoniagirl
Hello, I dont have a copy of Smith's early transcendentals, but i do have a copy of Steward's early transcendentals. Do they give an explination, because I cant find it. thanks in advance
Well, you can look at the error bound $E_s$ which is given by

$|E_s| \le \frac{K(b-a)^5}{180n^4}$

where

$\left| f^{(4)}(x)\right| \le K$.

If f is cubic the the error is zero.

format: plain


text:
# functions $f=g$ $\lambda$-a.e. for continuous real-valued functions are then $f=g$ everywhere

I am supposed to show that if $f$ and $g$ are continuous, real-valued functions on $\mathbb{R}$, then if $f=g\;\;$, $\lambda$-a.e., then $f=g$ everywhere.

So I have been reading and I think that this question is saying that these two functions are mappings like, $$f,g:=(\mathbb{R},\mathcal{L}) \stackrel{\lambda^{\ast}}{\to} (\mathbb{R},\mathcal{B}(\mathbb{R})).$$

I started my argument by saying:

If $f,g$ are $\lambda$-a.e. on $\mathbb{R}$ then $\exists$ a set $E:=\{x \in \mathbb{R} : f \neq g\}$. But the claim incorporates that $f=g$ everywhere and so there can't exist a set on $\mathbb{R}$ that has Lebesgue outer measure zero, i.e. all sets on $\mathbb{R}$ must have positive Lebesgue measure....

I think the reason there is no set of zero Lebesgue measure is because the preimage of all similar type sets in the Borel algebra, $\mathcal{B}(\mathbb{R})$, is included in a similar set in the algebra of Lebesgue measurable sets $\mathcal{L}$. But, aren't there Lebesgue measurable sets of zero Lebesgue measure - the countable $\mathbb{N}$ for instance? Or does it not count because the preimage is coming from a Borel algebra, even though a Borel set has measure zero too?

Thanks for any help in clearing this up for me.

-
You are making claims that you probably don't want to make: «there can't exist a set on R that has Lebesgue outer measure zero», «all sets on R must have positive Lebesgue measure». They are obviously false. For one thing, every empty subset of $R$ has outer Lebesgue measure zero and does not have positive Lebesgue measure... –  Mariano Suárez-Alvarez Oct 26 '11 at 22:34
There are heaps of sets with Lebesgue outer measure zero. Single points have outer measure zero. This question is asking to show your set $E$ is empty, and the empty set has outer measure zero as well. What you probably do want is that every non-empty open subset of the reals has positive outer measure. –  Ragib Zaman Oct 26 '11 at 22:36
@nate: sets of Lebesgue measure zero do exist! –  Mariano Suárez-Alvarez Oct 26 '11 at 22:38
The set $E$ exists, but it's the empty set, that's what the question wants you to show. –  Ragib Zaman Oct 26 '11 at 22:38
Thank you all for your help - I'll need a few minutes to think about all this –  nate Oct 26 '11 at 22:44

If $f$ and $g$ are a.e. equal, show that the set $\{x\in\mathbb R:f(x)= g(x)\}$ is dense. The using the fact that $f$ and $g$ are continuous, show that $f=g$ on all of $\mathbb R$.

Altenratively, show that if $f\neq g$, then $f$ and $g$ differ on a whole open interval, so that the set $\{x\in\mathbb R:f(x)= g(x)\}$ is not almost $\mathbb R$.

-
I was wondering, for $\mathbb{R}$, what really is the difference between $\lambda$-a.e and dense? $E$ is dense in $\mathbb{R}$ if either every point in $\mathbb{R}$ is in $E$ or is arbitrarily close to a point in $E$. This seems to exclude only singletons - pretty much just like $\lambda$-a.e. What is the difference in this case? Also, the continuity of $f$ and $g$ assures there is a limit at every $x$ in their domain so then if $f$ and $g$ agree everywhere outside of $E$, then this assures that, as their in only 1 limit at $x$ outside $E$, then $f=g$ outside of $E$ too. Not sure about it all –  nate Oct 27 '11 at 0:09
$\mathbb Q$ is dense and most certainly not almost everywhere present! You really need to consider more examples of sets :) –  Mariano Suárez-Alvarez Oct 27 '11 at 0:13
I guess mainly I was unclear as to why denseness was needed to show $f=g$ everywhere, when all that I see needed is continuity ($f=g$ a.e. already) –  nate Oct 27 '11 at 1:17

Consider $f-g$, which is zero almost everywhere and continuous. If $f-g$ is non-zero at some point $x$, then by continuity it is also non-zero in some open ball around $x$. Since this open ball has positive measure, it contradicts the assumption that $f-g$ is zero almost everywhere.

-

If $f\neq g$ everywhere, then there exists $x_0$ such that $f(x_0)>g(x_0)$ (for example). By continuity of $f,g$ it follows that $f(x)>g(x)$ on a neighborhood $(x_0-\varepsilon,x_0+\varepsilon)$ of $x_0$. and that means that the set $[f\neq g]$ has measure at least $2\varepsilon>0$.

-


text:
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 J. Sib. Fed. Univ. Math. Phys.: Year: Volume: Issue: Page: Find

 J. Sib. Fed. Univ. Math. Phys., 2017, Volume 10, Issue 2, Pages 206–215 (Mi jsfu541)

A class of Toeplitz operators in several complex variables

Dmitrii P. Fedchenko

Institute of Mathematics and Computer Science, Siberian Federal University, Svobodny, 79, Krasnoyarsk, 660041, Russia

Abstract: In order to study the Toeplitz algebras related to a Dirac operators in a neighborhood of a closed bounded domain $\mathcal{D}$ with smooth boundary in $\mathbb{C}^n$ we introduce a singular Cauchy type integral. We compute its principal symbol, thus initiating the index theory.

Keywords: Dirac operators, Cauchy type integral, symbol, Toeplitz operators, index.

 Funding Agency Grant Number Ministry of Education and Science of the Russian Federation NSH-9149.2016.1 The research of the author was supported by the Deutscher Akademischer Austauschdienst and by the Russian Federation President grant of support of leading scientific schools NSH-9149.2016.1.

DOI: https://doi.org/10.17516/1997-1397-2017-10-2-206-215

Full text: PDF file (123 kB)
References: PDF file   HTML file

Bibliographic databases:

UDC: 517.983.24
Accepted: 20.02.2017
Language:

Citation: Dmitrii P. Fedchenko, “A class of Toeplitz operators in several complex variables”, J. Sib. Fed. Univ. Math. Phys., 10:2 (2017), 206–215

Citation in format AMSBIB
\Bibitem{Fed17} \by Dmitrii~P.~Fedchenko \paper A class of Toeplitz operators in several complex variables \jour J. Sib. Fed. Univ. Math. Phys. \yr 2017 \vol 10 \issue 2 \pages 206--215 \mathnet{http://mi.mathnet.ru/jsfu541} \crossref{https://doi.org/10.17516/1997-1397-2017-10-2-206-215} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000412014600008}


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# How to become a GMAT teacher / tutor

Author Message
Manager
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How to become a GMAT teacher / tutor [#permalink]

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09 Jan 2014, 10:53
Hi everybody,

First of all, I am sorry if I post this message in the wrong sub forum, was not really sure where to post it !

I passed the GMAT a year ago with a score of 780 (Q51,V45) and now I plan maybe to become a part-time GMAT teacher/tutor. I would like maybe some feedbacks from people working for GMAT prep firms :
- Do GMAT prep firms hire mostly full-time teachers or part-time teachers ? (I plan to keep my current job and do this 5-10h /week on the evening and week-end, is that realistic ?)
- How are working most of the teachers ? Is it "physical" course with a class or mostly internet-based ? This is important because I am currently living in London (where there is mostly likely some physical GMAT course taking place) but I might move to a smaller english city it is unlikely there is.
- Are most of the teachers USA-based or all-around the world ?
- How hard is the selection ? On top of having a good GMAT score, what is required of teachers ? Is it require that teachers hold a MBA or is it not necessary ?
- Any specific advice for getting there ?

Thanks a lot for your help !
Magoosh GMAT Instructor
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Re: How to become a GMAT teacher / tutor [#permalink]

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09 Jan 2014, 11:37
Expert's post
Darmody wrote:
Hi everybody,

First of all, I am sorry if I post this message in the wrong sub forum, was not really sure where to post it !

I passed the GMAT a year ago with a score of 780 (Q51,V45) and now I plan maybe to become a part-time GMAT teacher/tutor. I would like maybe some feedbacks from people working for GMAT prep firms :
- Do GMAT prep firms hire mostly full-time teachers or part-time teachers ? (I plan to keep my current job and do this 5-10h /week on the evening and week-end, is that realistic ?)
- How are working most of the teachers ? Is it "physical" course with a class or mostly internet-based ? This is important because I am currently living in London (where there is mostly likely some physical GMAT course taking place) but I might move to a smaller english city it is unlikely there is.
- Are most of the teachers USA-based or all-around the world ?
- How hard is the selection ? On top of having a good GMAT score, what is required of teachers ? Is it require that teachers hold a MBA or is it not necessary ?
- Any specific advice for getting there ?

Thanks a lot for your help !

Dear Darmody,
I'm happy to respond.

First of all, congratulations on your impressive GMAT performance.

Here's the tricky thing. What does it take to be a good teacher? Well, that's hard to say. Certainly, having expertise in the subject is necessary, but it's not sufficient. There are many folks who know a ton about specific academic fields (math, physics, chemistry, linguistics, etc. ) but are absolutely horrible teachers because they are not effective at communicating what they know in a way that is accessible for others. Without knowing anything about you, I would have no idea about what your talents for teaching might be.

As to your more general questions about the industry. Traditionally, all classes were physical-location, on-site classes --- the older companies (Kaplan, Princeton Review, MGMAT, etc.) all began with that model and still primarily employ it. In our modern interconnected worlds, companies that are 100% web-based (such as Magoosh) are becoming more and more popular, because they are typically cheaper and equally accessible to anyone with an internet connection. Most companies, both web-based and on-site, will hire folks part time: in fact, many times, it's hard to start out with a full-time job at such a company, so the fact that you only want something part-time is good. For the companies that have on-site classes in a physical location, you have to be close that location, but for a web-based company, you could be anywhere in the world. It's not necessary to have an MBA: most GMAT experts don't. I don't have an MBA, but I had twenty years of teaching and tutoring experience before starting to work at Magoosh. If you have never ever done any kind of tutoring or teaching before, you might want to start small, maybe with a few private clients, and build experience before applying with a company. If you charge some very low price (say $10 or$20/hr), then you no doubt will get a few clients who want to work with you, and you can get a sense of how being a tutor feels as well as a sense of how successful you are at it. You would have a much much better chance to land a job with a company if you could approach one, say a year from now, saying, "I have done all this private tutoring, and here are recommendations from my students saying what a wonderful teacher I am." That, combined with a high GMAT score, would open a lot of doors!

Does all this make sense?
Mike
_________________

Mike McGarry
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Re: How to become a GMAT teacher / tutor [#permalink]

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09 Jan 2014, 12:25
Quote:
Here's the tricky thing. What does it take to be a good teacher? Well, that's hard to say. Certainly, having expertise in the subject is necessary, but it's not sufficient. There are many folks who know a ton about specific academic fields (math, physics, chemistry, linguistics, etc. ) but are absolutely horrible teachers because they are not effective at communicating what they know in a way that is accessible for others. Without knowing anything about you, I would have no idea about what your talents for teaching might be.

Yes I completely agree with you ! I consider my GMAT score more of a prerequisite for being a teacher rather than an absolute proof of my quality as a teacher. I have some teaching experience but little and not-GMAT related so I am kinda asking myself what in my background could convince a firm to hire me besides my GMAT score.

Quote:
If you have never ever done any kind of tutoring or teaching before, you might want to start small, maybe with a few private clients, and build experience before applying with a company. If you charge some very low price (say $10 or$20/hr), then you no doubt will get a few clients who want to work with you, and you can get a sense of how being a tutor feels as well as a sense of how successful you are at it.

Yes that would be the ideal thing to do, but I can imagine it is quite hard to find clients on its own. Maybe adds on the internet ? I am not really in connection with a lot of "potential" GMAT test takers. That is why ideally I would like to start with a company so that everything is taken care of and I can focus on teaching.

Quote:
Does all this make sense?

Economist GMAT Tutor Representative
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Re: How to become a GMAT teacher / tutor [#permalink]

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09 Jan 2014, 13:50
Expert's post
Hi Darmody,

All great questions. I think the qualification requirements vary from course to course. Some courses may require a higher degree and some may not.

My suggestion is to take a look at GMAT prep course websites and see if you can find bios of the tutors to see if your qualifications align up. We feature the bios of our tutors here: http://gmat.economist.com/blog/masthead. Also feel free to reach out to test prep companies and see if you can get an informational interview with a tutor or two -- I would bet that there are many who would be happy to share their experiences with you!

Regards,

Elizabeth
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09 Jan 2014, 13:55
Expert's post

gmat-tutors-needed-79157.html
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Re: How to become a GMAT teacher / tutor [#permalink]

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14 Jan 2014, 22:07
The 99th percentile is possible but you gotta do more than one thing. At the very least, do a structured test prep. All said, hiring a private tutor for one-on-one tutoring is the best way to go.
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Re: How to become a GMAT teacher / tutor [#permalink]

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28 Aug 2014, 05:31
Hi, I am searching a course to earn a certificate as GMAT instructor online, but I can't find any information.
I have been teaching GMAT/GRE for 5 years now and I am thinking of having a certificate as a evidence of skills.
Can anybody help? Thank you
Magoosh GMAT Instructor
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How to become a GMAT teacher / tutor [#permalink]

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28 Aug 2014, 11:48
Expert's post
vjosi wrote:
Hi, I am searching a course to earn a certificate as GMAT instructor online, but I can't find any information.
I have been teaching GMAT/GRE for 5 years now and I am thinking of having a certificate as a evidence of skills.
Can anybody help? Thank you

Dear vjosi,
I'm happy to respond. My friend, I don't believe any such certification exists. I teach the GMAT and work for Magoosh --- I have no "certificate," but simply the experience during my time at Magoosh and before. I going to guess that instructors at all the big companies --- MGMAT, Veritas, etc. ---- don't have "certificates" of any kind. I am quite experienced in the GMAT and in GMAT preparation, and I have have never even heard of a separate certificate from some place. I fact, if I did hear about one, I would be quite suspicious.

It seems what you are really seeking is some sort of credibility that you can demonstrate to others. Certainly your own GMAT score would be a strong credential. I would suggest beginning by getting testimonials from former students. If a prospective student can look at your website and see that some previous student began at, say, a 530, and with your help was able to achieve, say, a 720, then that would be a strong inducement for the new student to work with you. Evidence of former success is one of the best credentials.

Does all this make sense?
Mike
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Re: How to become a GMAT teacher / tutor [#permalink]

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28 Aug 2014, 13:08
Expert's post
I'm actually someone who often looks for GMAT tutors to refer my clients to, as I don't work with that part of the MBA application. I just work on the actual application itself: resume, essays and interview prep through my firm.

You do have an excellent score. Most GMAT tutors are going to be in person, so your business would be city and state dependent, but I recommend getting in touch with people who run MBA consulting firms, yet based on their web presence obviously don't have a GMAT component. Partnering with an already established business is the way to go!

Jillian, President & Founder
MBA Ivy League

www.MBAIvyLeague.com
_________________

For more free MBA & EMBA tips and advice, check out my MBA Admissions Blog: http://www.MBAIvyLeague.com/Blog

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Re: How to become a GMAT teacher / tutor [#permalink]

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29 Aug 2014, 00:27
mikemcgarry wrote:
vjosi wrote:
Hi, I am searching a course to earn a certificate as GMAT instructor online, but I can't find any information.
I have been teaching GMAT/GRE for 5 years now and I am thinking of having a certificate as a evidence of skills.
Can anybody help? Thank you

Dear vjosi,
I'm happy to respond. My friend, I don't believe any such certification exists. I teach the GMAT and work for Magoosh --- I have no "certificate," but simply the experience during my time at Magoosh and before. I going to guess that instructors at all the big companies --- MGMAT, Veritas, etc. ---- don't have "certificates" of any kind. I am quite experienced in the GMAT and in GMAT preparation, and I have have never even heard of a separate certificate from some place. I fact, if I did hear about one, I would be quite suspicious.

It seems what you are really seeking is some sort of credibility that you can demonstrate to others. Certainly your own GMAT score would be a strong credential. I would suggest beginning by getting testimonials from former students. If a prospective student can look at your website and see that some previous student began at, say, a 530, and with your help was able to achieve, say, a 720, then that would be a strong inducement for the new student to work with you. Evidence of former success is one of the best credentials.

Does all this make sense?
Mike

I totally agree! And that's the way I have been working up to now, with recommendations from previous students but sometimes I get calls from prospective students that ask if I have any qualifications. And my response has always been I have a Master Degree and took GMAT myself, but as it seems it is not enough for them. So I for some time I have been asking if there is such a qualification.But now I know that it doesn't exist and and it makes sense. Thank you!
Re: How to become a GMAT teacher / tutor   [#permalink] 29 Aug 2014, 00:27
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# How to become a GMAT teacher / tutor

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As you can see, the sequence name can be most anything (e.g. mySeq, A, B, or Bob's_your_uncle). If you start a sequence with a new sequence name the numbering restarts with 1. Look at Mary's first chore in the right hand column. Here you see the reset switch \r1 was used. This switch directs Word to restart the sequence named "A" with "1" at this point.

The partial sums themselves form a sequence {\displaystyle (S_{N})_{N\in \mathbb {N} }} , which is called the sequence of partial sums of the series {\displaystyle \sum _{n=1}^{\infty }a_{n}} . If the sequence of partial sums converges, then we say that the series {\displaystyle \sum _{n=1}^{\infty }a_{n}} is convergent, and the limit {\displaystyle \lim _{N\to \infty }S_{N}} is called the value of the series. The same notation is used to denote a series and its value, i.e. we write {\displaystyle \sum _{n=1}^{\infty }a_{n}=\lim _{N\to \infty }S_{N}} .
Typically the second option of saving as a CSV file is the one to choose for use with Data Merge. Click the create button to choose a file name and location, make sure that a header has been assigned and click OK. This creates the CSV file that contains the sequential numbers that can then be used in a Data Merge by opening the Data Merge palette, clicking the flyout and clicking Select Data Source…
Is there a way to delete old or no longer used email addresses that appear in the drop down box when I am addressing a new email? Shebubba wrote: > Is there a way to delete old or no longer used email addresses that appear in > the drop down box when I am addressing a new email? That is the nickname cache. Search and delete the .nk2 file. That's the cache for nicknames (i.e., your manually entered e-mail addresses). If you only want to delete some of them, highlight an entry and hit the delete key. If that doesn't work, use Nirsoft's NK2 Viewer utility (it e...
As I indicated, because you want to only generate this number just before saving, I would put this code behind a Save button or another event that runs just before you save the record. So if you want to prevent duplications, you don’t use the expression as a control source, but put the code behind a button or event. Since you have a Save button, put it there.
You won’t use any of the standard List Number styles for SEQ field numbering. You need to create your own style if you want correct indentation and alignment with the tab position of the first word after the number. In this example, I’ll create a new style called Step Number, but you can call it whatever you want. In this example, I’ve also used the default settings for tab and hanging indent positions — you can change these later if you want.
In a legal document, it's rare for every paragraph in the document to be numbered. Usually, you change between numbered paragraphs and non-numbered (plain) paragraphs of text. When Word sees you switching between these types of formats, it usually tries to help by restarting your numbered list back at "1" (or the first value of your list, such as "A"). There are a few different ways to make the number follow the last number of your paragraphs. In Word, this is called Continue from Previous List.
I like where your idea is going, but I cannot figure out how to consecutively number across text frames on one document. So far I have created a csv document in Excel, drew a textbox, imported the csv file into the Data Merge window and dragged it into the text frame. Now, I've got "<<00001>>" in the text frame. When I click "Create Merged Document" I get an error message: "Cannot creat merged document because no placeholders are present..." Now what?
How do I set up the basic template for text numbering in Word 2008 for the Mac? Here is what is driving me nuts: I want to generate numbered lists - lots and lots of them. The first level numbered lines will have second level under them in many cases, also numbered and indented below the first level. The second level will also have third level under them, intended some more and also numbered. This "sort-of" works fine. It USED to work excellently. Here is what I do. I click the Numbering button in the Bullets and Numbering palette. The line indents and a 1) is aut...

### Footnotes, after all, are always numbered sequentially and update when you add or remove one. The problem is that each time you add a footnote you get an extra space down at the bottom of the column. The solution? Make a paragraph style for your footnotes that specifies a .1 pt tall size with a 0 (zero) leading, then choose that paragraph style in the Document Footnote Options dialog box.

Erica Gamet has been involved in the graphics industry for an unbelievable 30 years! She is a speaker, writer, and trainer, focusing on Adobe InDesign and Illustrator, Apple Keynote and iBooks Author, and other print- and production-related topics. She is a regular presence at CreativePro Week’s PePcon and InDesign Conferences, and has spoken at ebookcraft in Canada and Making Design in Norway. You can find Erica’s online tutorials at CreativeLive and through her YouTube channel. When she isn’t at her computer, she can be found exploring her new homebase of Seattle and the greater Pacific Northwest.
Hi, this is a great write up. I am very new to InDesign and i print onto a range of products and my first order with sequential numbering came up (serial numbers), I have the template made in illustrator and i also have the numbers added (00001 on all of the art work). A friend told me InDesign has a function for automatically incrasing the numbers by 1 for each art work. I have 105 pieces per template, is there a way to import the design and then sort the number (already text edible) and then save as a pdf then send to print?
Please tell me there is a way to accomplish this.  As stated, if two users launch the initial submission form with the lookup field populated with P1234 for example, the first user to submit get the number, and the second user now has started there purchasing with a duplicated/invalid number.  Can we increment the field on submission load?  Also, the ability to instead show the purchasing number on event completion doesn't work either, too bad.
There are a couple of ways you can set up Word 2007/2010 to use SEQ fields for numbering — you can set them up as AutoCorrect entries or as Quick Parts. Both ways work; the method you choose is up to you. This long article describes how to create the SEQ fields and the numbering style in your Normal.dotm template; how to save the SEQ fields as AutoCorrect entries in Word 2007/2010 (and how to use them); and how to save (and use) them as Quick Parts. The most consuming part of this process is settings up the fields and the style; once they’re set up, using them is super easy.
Budget is our income and sometimes this is positive. I need to make this column in a query all negitive values. I am using the IIf function but it is not working. Budget: [budget_amount] IIf ([budget_amount] >=0, [budget_amount]*-1, [budget_amount]) or is there another function I could use? On Mon, 29 Oct 2007 19:18:00 -0700, Tamm Fox wrote: > Budget is our income and sometimes this is positive. I need to make this > column in a query all negitive values. > > I am using the IIf function but it is not working. > > Budget: [budget_amount] IIf ([budget_amount] &g...
Set up a matrix in Excel, one column for each ticket position (stack) and one row for each sheet, plus one for field names. Fill the first column down in consecutive order, then the second, starting where the first column leaves off, and so on. Afet a couple of columns are filled, you can auto fill across the rows, too, so the whole thing takes only a couple of minutes. Name the stacks and use a different field for each position on the page when you do the merge. The trick is to set up using a custom file for the total number of tickets or whatever, divided into the correct number of stacks and sheets.
You can define a section prefix to label section pages automatically. For example, if you specify A– for Section Prefix on page 16 of a document and include the section prefix, the page will appear in the table of contents or index as A–16. Text you type for a section marker appears when you choose Type > Insert Special Character > Markers > Section Marker.
To define a sequence by recursion, one needs a rule to construct each element in terms of the ones before it. In addition, enough initial elements must be provided so that all subsequent elements of the sequence can be computed by the rule. The principle of mathematical induction can be used to prove that in this case, there is exactly one sequence that satisfies both the recursion rule and the initial conditions. Induction can also be used to prove properties about a sequence, especially for sequences whose most natural description is recursive.

I’d like to use this for Exhibits/Appedices. If we refer to the same Exhibit # in a footnote or elsewhere in the document, and then the Exhibit reference is moved, it causes an error in the footnote or reference. Is there a way to cross-reference this, or to have it cross-reference automatically? Lawyers want to use this but I can’t see them bothering to cross-reference the footnotes. Thanks.
For example, in our law practice, we submit briefs with hundreds of attachments. Those attachments are constantly being reorganized (thus renumbered) and we had to develop a scheme to keep each attachment (and reference to each attachment) organized and accurate. We created a master list of attachments, and captured the dynamic field code in a bookmark. We can then cross-reference to that bookmark (which will return a number) through our documents. Example Public Attachment 68 (where 68 represents a field sequence code, is captured in a bookmark we will call SR_112). The bookmark name is a code name supplied by the drafting lawyer. That way, when the lawyer refers throughout the document to Public Attachment ___, we insert a cross reference to bookmark SR_112, and it always returns an accurate number, even if we reorganize the order of our attachments.
For controlname you need to use the name of the control bound to your Project ID# field. However, the # may be complicating things. Type the Me. and Intellisense should give you a list of controls and methods. Press the P key to go to Ps and scroll until you find the controlname. Selecting the name from the Intellisense list will make sure you are using the correct control. That control needs to have a ControlSource of the Project ID# field. If you do this correctly, then pressing the button should populate the control with the next number. It will also save the record.
Understanding outline numbering and how outline numbering interacts with styles is crucial to your success in using Word with legal documents. Basic outline numbering can be handled much the same way as bullets and numbering. Seven default outline numbered lists come with Word. Three of the lists format the paragraphs with outline numbers. These lists are in the top row of the dialog box. The remaining four format the paragraphs with outline numbers and apply heading styles to the paragraphs and can be found in the bottom row.
Step 4: Go to your coupons, page 1. Select the first text box (Command + Shift + Click to release from master page) and paste. The numbers will populate all of the boxes on that page (0001-0008). Now, here's where I'm not sure if I have a plugin doing this or not. The document should add pages to correspond to all of the numbers you have. If it doesn't (and it's doing it on mine because of a plugin), you can select the little red plus in the bottom right text box, add a page and hold down the shift key when pasting into the top left text box of page 2. That will add pages as needed.
I have two fields that should match, but one includes special characters while the other does not. Example: Field1 00ABCD123456123 Filed2 00/ABCD/123456/123/SBZ I need to find records where these two fields don't match, either by changing the display of one of them, or a query to compare Field1 character 7-15 with Field2 characters 9-14, 16-18. Hope this makes sense. Can anyone help? Thanks! Take a look at the following from the Access Help file it might be what you're looking for... Extract a part of a text value The following table lists examples of expressions that ...
I've also been using NumberPress for about a year and it is awesome. You can easily position numbers as many up per form and as many up on a sheet as you will ever need. Easily change font, color, point size, angle, number of digits and can even customize prefix-ex: instead of No. you can print ABC or a form number. It also does variable data (I've only used a couple of times).Took a little while to learn but is now a piece of cake.
The second thing you need to do is make sure that Word is configured so that it updates fields when it prints. Now, when you run the macro, you are asked how many copies to print and what starting number to use. The document variable is updated and a single copy of the document is printed. These steps are repeated for the number of times that you chose to print.
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My issue is trying to create small dot labels or equivalent to make up sequential alpha numeric labels to identify each individual item that I have in my shop, retrospectively. I have possibly 6-8thousand individual items that need coding for stock take purposes yet I can find no outlet that supply such thing. Do you have any suggestions. My line is antiques/collectables, predominantly china with items ranging in size from 2-3cm to 5/600cm. I would be most grateful for any solutions or suggestions. Best regards. Pete.

Is there a way to do this: I have a form called "List of Proposals Written" that is listed by th Proposal number. Is there a way to display on another excel spreadsheet, the mos current Proposal number? I know Access you use something like Dmax(ProposalID)+1 What should I do in Excel:confused: Any help would be greatly appreciated! Michae -- Message posted from http://www.ExcelForum.com "daniels012 >" < wrote > I have a form called "List of Proposals Written" that is listed by the > Propos...
If the sequence of real numbers (an) is such that all the terms are less than some real number M, then the sequence is said to be bounded from above. In other words, this means that there exists M such that for all n, an ≤ M. Any such M is called an upper bound. Likewise, if, for some real m, an ≥ m for all n greater than some N, then the sequence is bounded from below and any such m is called a lower bound. If a sequence is both bounded from above and bounded from below, then the sequence is said to be bounded.
In summary, paragraph numbering is really just an exercise in logic, and this blog post is showing the numbering styles for a very specific project. Your project may be similar, but not exactly the same. You just need to think though the levels and how you want to restart the numbers. I do my best to think it through correctly the first time, set it up, and then try as hard as I can to break it, so that I can find my errors. The good news is that once you get your numbers working, you shouldn’t ever have to think about it again.
Hello, When I enter 100, it display 1, When I enter 1000, it display 10, ChefChaudart, Is that bad ? That is one of those things that everyone runs into you change the option and it doesn't seem to do anything so you leave it changed. If you enter a decimal point everything is normal i.e. 1000. or 1000.50 but if you fail to enter a decimal point your option in Tools, Options, Edit (tab), [x] fixed decimals 2 will be used. Remove the checkmark and you'll be fine. You can try that on your boss at April Fool's time as long as their not doing your sal...

# All I want to know is, how do you link fields, like {SEQ}, to a style – so that if I select/apply style “Figure Caption” (my style, I also have “Table Caption”), I get not just the attributes of the style (what it looks like, where it is on the page etc.) but I get a chapter (or section) number + a sequence number added, (e.g. “2-3”). I know about STYLEREF and SEQ Figure # and/or calling a section number (if required) – but I can’t find out how to take the simple and to me obvious step to have sequential numbering (prefixed with either “Figure” or “Table”) attached to my Figure Caption style. It all seems to be a two-step process: (i) select the style, (ii) select the numbering. I want to do both at style level. I want to see/get (e.g.) “Figure 2-3: Linking figure numbering to styles” just by applying my “Figure Caption” style to my figure caption text “Linking figure numbering to styles”. Please, only tell me how to do that, how to link chapter/sequence numbering via a style – i.e. in just one step – applying the style.

Bullets and Numbering options in InDesign aren’t just for boring lists. You can auto-number items like captions, even incorporating prefixes like figure labels. Depending on how your document is set up, there are two ways to achieve this. Both involve setting up a paragraph style that incorporates numbering from the Bullets and Numbering feature. Generally I create a temporary text frame—often on my pasteboard—and set some items to create my style, pasting the text into my actual caption frames after the fact.
Although sequences are a type of function, they are usually distinguished notationally from functions in that the input is written as a subscript rather than in parentheses, i.e. an rather than f(n). There are terminological differences as well: the value of a sequence at the input 1 is called the "first element" of the sequence, the value at 2 is called the "second element", etc. Also, while a function abstracted from its input is usually denoted by a single letter, e.g. f, a sequence abstracted from its input is usually written by a notation such as {\displaystyle (a_{n})_{n\in A}} , or just as {\displaystyle (a_{n})} . Here A is the domain, or index set, of the sequence. sequential numbering in word


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# Perturbation Theory Help

1. May 8, 2010

### phrozenfearz

Perturbation Theory Help!!

Hello physicsforums.com,

The last two weeks of my nuclear engineering course covered a mathematical topic known as 'perturbation theory'. It was offered as a 'method to solve anything' with; the problem is, however, that nobody in my class understands it.

Basic google searching has not yielded any great results, so I turn to the wise physicsforums.com community to perhaps help give new perspective or recommend some relatively easy to follow readings.

2. May 9, 2010

### HallsofIvy

Re: Perturbation Theory Help!!

Well, it's a method to approximately solve anything! Specifically, it is a method to approximately solve non-linear equations, in particular functional equations like differential equations or integral equations. The "WKB" method used in quantum mechanics is a perturbation method.

The basic idea of "perturbation" theory is to write the solution to your problem (typically, a differential equation or integral equation although it will work for other kinds of problems) as a power series, $y= y_0+ \epsilon y_1+ \epsilon^2 y_2+ \cdot\cdot\cdot$ where "$\epsilon$" is some small number inherent in your problem. Write out both sides of your equation as power series in $\epsilon$ and set coefficients of the same powers of $\epsilon$ equal. The $\epsilon^0$ term gives the solution to the approximate linear problem, y_0, and the other equations will give solutions in terms of previous solutions- that is, $y_1$, $y_2$ in terms of $y_0$ and $y_1$, etc.

Here's a trivial example: Imagine that we know how to solve equations of the form $x^2= a$ by just taking the square root but we don't know the "quadratic formula".

Now, we want to solve the equation $x^2+ \epsilon x- 4= 0$ where $\epsilon$ is a very, very small (positive) number. We could argue that since $\epsilon$ is small, that equation is very nearly $x^2= 4$ which has solutions 2 and -2 and so our equation must have solutions very close to 2 and -2.

Is that true? If it is, how could we prove it is true? And how could we use that information to get a better approximation to the true solution?

Let $x= x_0+ x_1\epsilon+ x_2\epsilon^2+ \cdot\cdot\cdot$, a power series in $\epsilon$. We will assume that $\epsilon$ is small enough that we can ignore $\epsilon^3$ (assuming that $\epsilon$ was small enough to ignore $\epsilon^1$ would give y_0 the linear solution).

If $x= x_0+ x_1\epsilon+ x_2\epsilon^2$, then $x^2= x_0^+ 2x_0x_1\epsilon+ 2x_0x_2\epsilon^2+ x_1^2\epsilon^2$ where I have dropped the terms $2x_1x_2\epsilon^3$ and $x_2^2\epsilon^4$ since they are of higher than second dergee.

$x^2+\epsilon x- 4$, then is $x_0^2+ 2x_0x_1\epsilon+ 2x_0x_2\epsilon^2+ x_1^2\epsilon^2+ x_0\epsilon+ x_1\epsilon^2- 4$ where I have dropped the term $x_2\epsilon^3$ from $\epsilon x$ as it is, again, of higher than degree 2.

The equation becomes $(x_0^2- 4)+ (2x_0x_1+ x_0)\epsilon+ (2x_0x_2+ x_1^2)\epsilon^2= 0$. Equating corresponding components, we have $x_0^2- 4= 0$, $2x_0x_1+ x_0= x_0(2x_1+ 1)= 0$ and $2x_0x_2+ x_2^2= 0$.

$x_0^2- 4= 0$ gives $x_0= 2$ or $x_0= -2$. Since that is not 0, we can divide both sides of $x_0(2x_1+ 1)= 0$ by x_0 and get $x_1= -\frac{1}{2}$ for both values of $x_0$.

If $x_0= 2$ and $x_1= -1/2$, then the third equation is $4x_2+ \frac{1}{4}= 0$ so $x_2= -1/16$.

If $x_0= -2$ and [iterx]x_1= -1/2[/itex], then the third equation is $-4x_2+ \frac{1}{4}= 0$ so $x_2= 1/16$.

That is, our two solutions are $x= 2- (1/2)\epsilon- (1/16)\epsilon^2$ and $x= -2- (1/2)\epsilon+ (1/16)\epsilon^2$.

If, for example, $\epsilon= .001$, then those solutions are $2- .0005- 0.0000000625= 1.9994999375$ and $-2- .0005+ 0.0000000625= -2.0004999375. We can use the quadratic formula (which we were pretending we did not know) to actually solve [itex]x^2+ .001x- 4= 0$, getting $x= (-.001\pm\sqrt{0.000001+ 16})/2[/quote] which gives x= 1.99950006 and -2.00050006 so what we got using "perturbation theory" was certainly better than 2 and -2 and also show that 2 and -2 are good first approximations. A equation of the form [itex]\epsilon x^2+ 2x- 4= 0$ is a much harder problem. Here, just ignoring $\epsilon$, the equation becomes 2x- 4= 0 which has the single solution x= 2 while we expect a quadratic equation like this to have two solutions. For this problem we need "singular perturbation" which is a whole different story!

3. May 14, 2010

### macmosher

Re: Perturbation Theory Help!!

I had an additional question to what you have explained. I have used the perturbation method for solving a set of non-linear differential equations where $$\epsilon$$ was not small, however the terms $$x_0,x_1,x_2$$...etc. get progressively smaller.

I have worked out the equations and they seem to match up quite accurately to the solution found by using ode45 in matlab (while having time-varying parameters in the function).

I am trying to find some sort of reassurance that this is ok. Everything that I have found all suggests that epsilon must be small.

4. Sep 9, 2011

### Gabrielwer

Re: Perturbation Theory Help!!

Many of the ab initio quantum chemistry methods use perturbation theory directly or are closely related methods. Møller–Plesset perturbation theory uses the difference between the Hartree–Fock Hamiltonian and the exact non-relativistic Hamiltonian as the perturbation. The zero-order energy is the sum of orbital energies. The first-order energy is the Hartree–Fock energy and electron correlation is included at second-order or higher. Calculations to second, third or fourth order are very common and the code is included in most ab initio quantum chemistry programs. A related but more accurate method is the coupled cluster method.


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OCaml Planet

## October 23, 2014

### OCamlCore Forge News

Earlier today, I was connected while the Forge was under heavy load. This has often been the case before most of the recent reboot. This time I was able to identify the process causing the problem and stop it early. Unfortunately, an intruder was able to exploit shellshock through gitweb.cgi. This means that the attacker was able to run a process on the server as www-data for a few hours. I have studied the script used and it is a IRC server in Perl. I think the main goal of the server was to attack other computers. I am not sure that any files were compromised. The script has been removed and my security tool (rkhunter) cannot find any other problems. I have upgraded the system to squeeze-lts to fix the shellshock CVE. The following script can test the files, that have been uploaded to the forge, against what is currently on the server (see the link). AFAIK, none of my tarball have been changed. Please check your files as well and contact me if you find any problems. Sorry for the inconvenience Sylvain Le Gall Use this command to run the script: $> ocaml download-test.ml */dist/*.tar.gz https://forge.ocamlcore.org/frs/download.php/1478/download-test.ml ### OCaml Platform #### OPAM 1.2.0 Released We are very proud to announce the availability of OPAM 1.2.0. ### Upgrade from 1.1 Simply follow the usual instructions, using your preferred method (package from your distribution, binary, source, etc.) as documented on the homepage. NOTE: There are small changes to the internal repository format (~/.opam). It will be transparently updated on first run, but in case you might want to go back and have anything precious there, you're advised to back it up. ### Usability Lot of work has been put into providing a cleaner interface, with helpful behaviour and messages in case of errors. The documentation pages also have been largely rewritten for consistency and clarity. ### New features This is just the top of the list: • A extended and versatile opam pin command. See the Simplified packaging workflow • More expressive queries, see for example opam source • New metadata fields, including source repositories, bug-trackers, and finer control of package behaviour • An opam lint command to check the quality of packages For more detail, see the announcement for the beta, the full changelog, and the bug-tracker. ### Package format The package format has been extended to the benefit of both packagers and users. The repository already accepts packages in the 1.2 format, and this won't affect 1.1 users as a rewrite is done on the server for compatibility with 1.1. If you are hosting a repository, you may be interested in these administration scripts to quickly take advantage of the new features or retain compatibility. ## October 22, 2014 ### Sylvain Le Gall #### Release of OASIS 0.4.5 On behalf of Jacques-Pascal Deplaix I am happy to announce the release of OASIS v0.4.5. OASIS is a tool to help OCaml developers to integrate configure, build and install systems in their projects. It should help to create standard entry points in the source code build system, allowing external tools to analyse projects easily. This tool is freely inspired by Cabal which is the same kind of tool for Haskell. You can find the new release here and the changelog here. More information about OASIS in general on the OASIS website. Here is a quick summary of the important changes: • Build and install annotation files. • Use builtin bin_annot and annot tags. • Tag .mly files on the same basis as .ml and .mli files (required by menhir). • Remove 'program' constraint from C-dependencies. Currently, when a library has C-sources and e.g. an executable depends on that library, then changing the C-sources and running '-build' does not yield a rebuild of the library. By adding these dependencies (rather removing the constraint), it seems to work fine. • Some bug fixes Features: • no_automatic_syntax (alpha): Disable the automatic inclusion of -syntax camlp4o for packages that matches the internal heuristic (if a dependency ends with a .syntax or is a well known syntax). • compiled_setup_ml (alpha): Fix a bug using multiple arguments to the configure script. This new version is a small release to catch up with all the fixes/pull requests present in the VCS that have not yet been published. This should made the life of my dear contributors easier -- thanks again for being patient. I would like to thanks again the contributor for this release: Christopher Zimmermann, Jerome Vouillon, Tomohiro Matsuyama and Christoph Höger. Their help is greatly appreciated. ## October 21, 2014 ### Caml Weekly News ## October 19, 2014 ### Shayne Fletcher #### Tail-recursion ### Tail-recursion Stack overflow refers to a condition in the execution of a computer program whereby the stack pointer exceeds the address space allocated for the stack. The usual result of "blowing the stack" is swift and brutal abnormal termination of the program. The amount of memory allocated by the operating system for a given program's stack is finite and generally little can be done by the programmer to influence the amount that will be made available. The best the programmer can really do is to use what's given wisely. We can get a sense of the limits of the stack in practical terms with a program like the following. let rec range s e = if s >= e then [] else s :: range (s + 1) elet rec loop i = let n = 2.0 ** (i |> float_of_int) |> int_of_float in try let _ = range 0 n in loop (i + 1) with | Stack_overflow -> Printf.printf "Stack overflow at i = %d, n = %d\n" i n let () = loop 0 range is a function that produces the half-open range$\left[s, e\right)$- the ordered sequence$\left\{s, s + 1, s + 2, \dots, e - 2, e - 1\right\}$. Note that range is defined in terms of itself, that is, it is a recursive function. The idea is to use it in an unbounded loop to build sequences of increasing lengths of powers of$2$:${2^0, 2^1, 2^2, \dots}$. We set it off and when we encounter stack overflow, terminate the program gracefully reporting on the power of$2$found to give rise to the condition. In my case I found that I was able to make$\approx 2^{19} = 524,288$recursive calls to range before the stack limit was breached. That's very limiting. For realistic programs, one would hope to be able to produce sequences of lengths much greater than that! What can be done? The answer lies in the definition of range and that thing called tail-recursion. Specifically, range is not tail-recursive. To be a tail-recursive function, the last thing the function needs do is to make a recursive call to itself. That's not the case for range as written as the recursive call to itself is the second to last thing it does before it returns (the last thing it does is to 'cons' a value onto the list returned by the recursive call). Why being tail-recursive is helpful is that tail-calls can be implemented by the compiler without requiring the addition of a new "stack frame" to the stack. Instead, the current frame can be replaced in setting up the tail-call being modified as necessary and effectively the recursive call is made to be a simple jump. This is called tail-call elimination and its effect is to allow tail-recursive functions to circumvent stack overflow conditions. Here's a new definition for range, this time implemented with tail-calls. let range s e = let rec aux acc s e = if s >= e then acc else aux (s :: acc) (s + 1) e in List.rev (aux [] s e) With this definition for range I find I can build sequences of length up to around$\approx 2^{26} = 67,108,864$elements long without any sign of stack overflow which is a huge improvement! At around this point though, my sequence building capabilities start to be limited by the amount of physical memory present on my PC but that's a different story entirely. ## October 17, 2014 ### Erik de Castro Lopo #### Haskell : A neat trick for GHCi Just found a really nice little hack that makes working in the GHC interactive REPL a little easier and more convenient. First of all, I added the following line to my ~/.ghci file.  :set -DGHC_INTERACTIVE  All that line does is define a GHC_INTERACTIVE pre-processor symbol. Then in a file that I want to load into the REPL, I need to add this to the top of the file:  {-# LANGUAGE CPP #-}  and then in the file I can do things like:  #ifdef GHC_INTERACTIVE import Data.Aeson.Encode.Pretty prettyPrint :: Value -> IO () prettyPrint = LBS.putStrLn . encodePretty #endif  In this particular case, I'm working with some relatively large chunks of JSON and its useful to be able to pretty print them when I'm the REPL, but I have no need for that function when I compile that module into my project. ## October 16, 2014 ### WODI #### OCaml 4.02.1 released Windows binary builds for OCaml 4.02.1 are now available. Download links for the 32-bit and 64-bit build can be found in the download section. You can upgrade from an existing installation of OCaml 4.02.0 with godi_upgrade  or from source code with: godi_update godi_perform -rebuild -newer  The OCaml 4.02.0 builds are not longer maintained. If you still want to continue to use the binary builds for this OCaml version (or revert back to it), you have to change the repository address at /opt/wodi(32|64)/etc/godi.conf from GODI_BINPKG_SERVER=http://dl.arirux.de/7/binaries${MINGW_WORDSIZE}/

to

## October 15, 2014

### OCamlCore Forge News

#### OCaml Forge maintenance

Recently the OCaml forge has required a lot of hardware reboots. The server is probably near end of life and I need to upgrade the whole infrastructure to a recent server. Rackspace Cloud, as part of their developer support program, is kindly providing a new host for the forge. You may encounter a few more problems in the coming weeks, due to this migration. Ping me if anything is utterly wrong (sylvain ... le-gall.net).


text:
# integer factorization

Given an integer $n$, its integer factorization (or prime factorization) consists of the primes $p_{i}$ which multiplied together give $n$ as a result. To put it algebraically,

 $n=\prod_{i=1}^{\omega(n)}{p_{i}}^{a_{i}},$

with each $p_{i}$ distinct, all $a_{i}>0$ but not necessarily distinct, and $\omega(n)$ being the value of the number of distinct prime factors function. Theoretically, an integer is a product of all the prime numbers,

 $n=\prod_{i=1}^{\infty}{p_{i}}^{a_{i}},$

with many $a_{i}=0$.

For example, the factorization of 32851 is $7\times 13\times 19\times 19$, more usually expressed as $7\times 13\times 19^{2}$. Because of the commutative property of multiplication, it does not matter in what order the prime factors are stated in, but it is customary to give them in ascending order (http://planetmath.org/AscendingOrder), and to group them together by the use of exponents.

The factorization of a positive integer is unique (this is the fundamental theorem of arithmetic). For a negative number $n<0$ one could take the factorization of $|n|$ and randomly give negative signs to one (or any odd number) of the prime factors. Alternatively, the factorization can be given as $-1\cdot{p_{1}}^{a_{1}}\cdot\ldots$ (this is what Mathematica opts for).

The term “factorization” is often used to refer to the actual process of determining the prime factors. There are several algorithms to choose from, with trial division being the simplest to implement.

Title integer factorization IntegerFactorization 2013-03-22 16:39:09 2013-03-22 16:39:09 PrimeFan (13766) PrimeFan (13766) 8 PrimeFan (13766) Definition msc 11A41 prime factorization


text:
DiPAS is a framework for differentiable simulations of particle accelerators.

## Project description

DiPAS is a program for differentiable simulations of particle accelerators. It acts as a framework and thus supports a wide range of use cases such as particle tracking or optics calculations such as closed orbit search or computation of Twiss parameters.

The involved computations are backed by the PyTorch package which also provides the relevant functionality for differentiation of user-defined quantities as well as a variety of gradient-based optimizers that integrate with the thus derived quantities.

The DiPAS program can parse MADX lattice definitions and hence allows for zero-overhead importing of existing lattices. In addition, it supports custom lattice definitions from provided element classes.

DiPAS can also be used via command line interface, see dipas --help for more information.

## Example usage

Minimizing loss along beamline by tuning quadrupoles:

import numpy
from dipas.build import from_file
import torch

while True:
tracked, loss_val = lattice.linear(particles, recloss='sum')
lost = 1 - tracked.shape[1] / particles.shape[1]
if lost < 0.01:  # Fraction of particles lost less than 1%.
break
loss_val.backward()
optimizer.step()

## Project details

Uploaded source
Uploaded py3