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Hello. I think your reformatting in [[probability-generating function]] put lines so close together that it looked cluttered. I've redone it somewhat. [[User:Michael Hardy|Michael Hardy]] 02:00, 21 Nov 2004 (UTC)
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{| cellpadding="0" cellspacing="0" style="background-color: #EEEEEE; text-align: center; margin: auto; font-size: 90%;"
Some tips inspired by your editing of [[Skellam distribution]]:
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* Don't use gratuitous capitalization either in article titles or in the text of an article.
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* There's no need to write (e.g.) <nowiki>[[hyphen|hyphenated]]</nowiki>; one may write <nowiki>[[hyphen]]ated</nowiki>, and it has the same effect (the whole word, not just the part between the brackets, appears as a clickable link).
[[User:Mailer_diablo|About Myself]]
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* There's no need to capitalize the first letter of a link, nor to include underscores. Thus: <nowiki>[[negative binomial distribution]]</nowiki>.
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[[User:Michael Hardy|Michael Hardy]] 04:05, 21 Nov 2004 (UTC)
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Hello - Thanks for the suggestions on the page. I'm obviously new to
[[User:Mailer_diablo/Stats|My WikiStats]]
Wikipedia, and I'm trying to figure a lot of things out, such as is this
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the right way to respond to your message on my talk page? Also, I wanted
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to start a Voigt profile page, which is a convolution of a Doppler profile and
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a Lorentzian profile, or, viewed as probability distributions, a normal
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distribution and a Cauchy distribution. I guess a Voigt profile would translate
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to a Voigt distribution. There are no such profile pages, but there is a
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Lorentzian function page which contains just what a Lorentzian profile page
My Website
should contain. I'm not sure of what to do here, or the etiquette of going
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about doing it. Any suggestions?
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[[User_talk:Mailer_diablo|My TalkPage]]
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!colspan=4 align=center style="border-bottom:2px dashed orange;background:papayawhip"|<big>[http://en.wikipedia.org/w/wiki.phtml?title=User_talk:Mailer_diablo&action=edit§ion=new Leave a Message for mailer_diablo] | </big> ''Archives : [[User_talk:Mailer_diablo/Archive A|A]] [[User_talk:Mailer_diablo/Archive_B|B]] [[User_talk:Mailer_diablo/Archive_C|C]] [[User_talk:Mailer_diablo/Archive_D|D]]''
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'''Hello, and thank you for dropping by my talk page.''' Have something to say or comment about? Just simply begin by clicking on the above link. Be sure to add a title and signature (<nowiki>~~~~</nowiki>) to your messages. If you require a reply, please indicate. I will reply on your talk page. Note that I do not watch talk pages for replies. :)
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:Perhaps moving the [[Lorentzian function]] page to [[Lorentzian profile]] would be the best thing to do, but I don't know this topic. Just click on "move this page". The edit history and discussion page get moved along with it, and the Lorentzian function page will then become a redirect page with an edit history showing that it was created by you at the time of the move. [[User:Michael Hardy|Michael Hardy]] 21:46, 22 Nov 2004 (UTC)
<tr><td><center>'''[[Wikipedia:Babel]]'''</center></td></tr>
<tr><td>{{User en}}</td></tr>
<tr><td>{{User zh-4}}</td></tr>
<tr><td>{{User 1337-2}}</td></tr>
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[[Image:Pagee.jpg|thumb|right|300px|mailer_diablo's latest project, [http://studentssketchpad.blogspot.com The Students' Sketchpad]. For your Singaporean dose of comic relief.]]
PS: Also, notice that if you type <nowiki>~~~~</nowiki> in a page you edit, your user name gets signed along with the date and time of the edit, and your user name will appear as a clickable link to your user page. [[User:Michael Hardy|Michael Hardy]] 21:46, 22 Nov 2004 (UTC)
<!--Talkpage template, please leave your messages below this line-->
PPS: The above is appropriate for discussion pages, but not for articles. [[User:Michael Hardy|Michael Hardy]] 21:47, 22 Nov 2004 (UTC)
== PriceThanks equationfor edityour support ==
Thank you for supporting my recent RfA. I was surprised and humbled by the number of positives votes. I'll be monitoring RfA regularly from now on and will look for a chance to "pay it forward". Cheers, --[[User:MarkSweep|MarkSweep]] 01:33, 7 August 2005 (UTC)
Hi, I've seen your major edit on the [[Price equation]] page, and have commented on it in the [[Talk:Price_equation]] page. Please review my comments. --[[User:Aliekens|Anthony Liekens]] 11:04, 30 Nov 2004 (UTC)
== Celebrity Images ==
==Lambert's cosine law==
Hi Mailer diablo,<BR>
I replied on my talk page. [[User:Oleg Alexandrov|Oleg Alexandrov]] 01:24, 1 Jan 2005 (UTC)
I am back again with a query.I just came across a user [[User:Tony619]] who has added numerous images of scantily clad celebrities to many celebrity pages. Though most of the images qualify under fair use as they are magazine covers but I feel that they are not suitable to be displayed on Wikipedia. Moreover in most of the cases he has added images to pages which already had an image. I have left a message at his talk page but I dont know the policy of wikipedia on such images. So, I would be grateful if you could take the necessary steps.[[User:Gaurav1146|Gaurav1146]] 10:50, 7 August 2005 (UTC)
:Thanx for the quick response. The reason that I didn't mark them for deletion was pecisely that Wikipedia has no guidelines for such images. In any case, I felt that adding such images on every page doesn't make sense. If the content of the page requires those kind of image then there is no problem. Moreover why add another image when there is already an existing image on a page until and unless the other image depicts something important. I would be grateful if you could have a look at those pages and take appropriate decision. TIA [[User:Gaurav1146|Gaurav1146]] 04:13, 8 August 2005 (UTC)
::Thanx once again. Right now, I am in office and I would not be fit for me to access those pages from here.I would let you know about the pages by today or tomorrow. As for ''Images for Deletion'' , i had a terrible experience with it.So , I normally prefer directly contacting an administrator.[[User:Gaurav1146|Gaurav1146]] 09:32, 8 August 2005 (UTC)<BR>
::: Here are some of the images where the user has added an image where already another one is existing.
[[Charisma Carpenter]][[Denise Richards]][[Christy Hemme]] [[Bai Ling]]
[[Joanna Krupa]][[Liv Lindeland]][[Torrie Wilson]][[Tia Carrere]][[Nikki Schieler Ziering]][[Jaime Pressly]][[Kristy Swanson]][[Jordan (model)]]. There are many more but it has taken me awfully long to come with this list. So you can check further. The user has uploaded most of the images from an adult magazine.Whether these are obscene and more importantly required or not, that is debatable. I leave it your discretion but in any case, I feel that there should be some guidelines for uploading images based on the content of images.
IMHO adding obscene images in cases where it can be avoided does not add value to a page. [[User:Gaurav1146|Gaurav1146]] 15:39, 8 August 2005 (UTC)
== Image help.... ==
:Oh, and the last sentence on that page, ''For a Lambertian reflector, the light reflected from this source will be the same in all directions, so the radiance seen by any observer will then be proportional that incident flux which will be proportional to the cosine of the incident (not the observing) angle.'' does not sound right. [[User:Oleg Alexandrov|Oleg Alexandrov]] 01:29, 1 Jan 2005 (UTC)
Hah....seems rather rare to see you online, but I really need your advise in the issue of moving imaged to the commons. I listed my imaged in [[Wikipedia:Images and media for deletion]] since August 1, and they are still there. Did I do anything which isnt following proper procedures? Or is there a shortcut which lets me move the images without having to ask for any deletions etc? Thanks! ;)--[[User:Huaiwei|Huaiwei]] 17:09, 7 August 2005 (UTC)
I had some comments here earlier, but removed them. I need to think more about this law. [[User:Oleg Alexandrov|Oleg Alexandrov]] 21:32, 1 Jan 2005 (UTC)
== Re: Fuck hole ==
Hi Paul, Welcome to Wikipedia! I asked a question on [[Talk:Lambert's cosine law]] that I suspect you could answer. Just mentioning it here in case you don't have that page on your watchlist. [[User:Dbenbenn|Dbenbenn]] 02:10, 6 Jan 2005 (UTC)
Hi there. I noticed you just got rid of a bunch of VfDs. While you're online, do you mind taking a look at [[Fuck Hole|this]] page, please? It's been tagged with a speedy, and I'm rather hopeful that it will get deleted ASAP as the contents are simply libelous. Vfd [[Wikipedia:Votes_for_deletion/Fuck_Hole|here]]. Regards—[[User:Encephalon|<font color=#000>Encephalon</font>]] | [[User talk:Encephalon|<font color=#ff0000><sup>ζ</sup></font>]] 18:57:30, 2005-08-20 (UTC) NB. In the unlikely event that you do not often speedy, the proposed deletion is for contravention of [[WP:CSD]] A6. Thank you.—[[User:Encephalon|<font color=#000>Encephalon</font>]] | [[User talk:Encephalon|<font color=#ff0000><sup>ζ</sup></font>]] 19:04:20, 2005-08-20 (UTC)
*Kind of you, Mailer diablo. Yeah, Zscout Sd'd it soon after I posted here. I've never posted at an admin's page asking for an SD, but this particular one perhaps merited it. Glad it's gone.—[[User:Encephalon|<font color=#000>Encephalon</font>]] | [[User talk:Encephalon|<font color=00ff00><sup>ζ</sup></font>]] 05:53:21, 2005-08-21 (UTC)
==Lévy flightMy user page ==
In the [[Lévy flight]] article you recently changed "the direction of each step follows a [[uniform distribution]]" to "the direction of each step follows a [[Lévy distribution]]". Although the '''length''' of each step may follow a Lévy distribution, doesn't the '''direction''' of the step have to be uniformly distributed - otherwise the random walk would not be isotropic ? I've checked ''The Fractal Geometry of Nature'', which definitely says that Lévy flight random walks are isotropic. [[User:Gandalf61|Gandalf61]] 10:27, Jan 21, 2005 (UTC)
Congrats, you're the first signed in user to edit my user page without vandalizing it! :P [[User:Redwolf24|Redwolf24]] 07:18, 21 August 2005 (UTC)
:Thank you for your response. I guess the definition of "direction" depends on the dimension of the process. For a 1-dimensional Lévy flight then I agree the direction of each step is either "up" or "down", with equal probability. For a 2-dimensional Lévy flight (which is the type that Mandelbrot describes in ''FGoN'') then the direction of each step can take any value between 0 and 360 degrees, so in this context I think the distribution of the direction would be uniform on the interval [0,360]. But the important characteristic of Lévy flights is, as you say, the distribution of the step length. I have split up the opening paragraph of the article to make it more readable, but I have not changed your new explanation, which is very clear. [[User:Gandalf61|Gandalf61]] 12:00, Jan 22, 2005 (UTC)
:Thanks for the typo fix on my User page. [[User:BlankVerse|<font color=green>''Blank''</font><font color= #F88017>''Verse''</font>]]<font color=#2554C7> </font>[[User talk:BlankVerse|<font color=#F660AB>∅</font>]] 14:29, 28 August 2005 (UTC)
==GSL link==
== Abby Hayes ==
As far as I could see, the GSL link you want to include does not contain anything about the gamma function except its definition. It is only potentially useful for someone who wants to compute it, but then they have to have GSL installed already and that gives them the docs readily accessible on their machine. Futhermore there are lots of bits of code out there that can compute the gamma function, including some large libraries like IMSL and NAG, and packages like Maple, Mathematica, probably Matlab. Do a google search for <"gamma function" procedure> and you'll get pages of them. There is no special reason to give just GSL. We should provide links that give information about the function, not just programming manuals. That's my opinion. --[[User:Zero0000|Zero]] 11:55, 23 Jan 2005 (UTC)
== Sinc ==
I notice you edited [[Sinc function]], though I think there may be a problem with the definition overall. Could you take a look at [[Talk:Sinc function]]? Thanks [[User:Dysprosia|Dysprosia]] 08:59, 1 Feb 2005 (UTC)
Heya. Just to let you know that you made a mistake on the [[Abby Hayes]] vfd. It's not a vanity page, because Abby Hayes is the protagonist of a popular American series of children's novels - I think >11K Google hits is enough to disprove the "non-notable" claim, yes? To be fair, the article was extremely poorly written, focusing almost exclusively on the character's personal life to the near-total exclusion of the fact that "oh, by the way, she's a fictional character". And you're a male Malaysian college student in Singapore, not a twelve-year-old American girl, so you wouldn't know about the books (and neither did I until I googled). I've since cleaned up the article substantially - might you change your vote? [[User:DragonflySixtyseven|DS]] 13:23, 21 August 2005 (UTC)
== German "Sun" article ==
== [[Slovenian or Slovene]] ==
Thanks for the Babelfish translation, there's still a lot of work to be done, especially with the terminology. I have no idea what "hauptreihenstern" means for example :) so it might be a good idea for some of the german folk to help with that :). After a brief look at the article I think I can recover about 2/3 of the information for incorporation in the enlish version article. And I just want to briefly introduce myself, I go by the nickname of Smartech and I'm heading a major Solar System effort in bg: and I was looking for article about the Sun. Anyway, thanks for your efforts. Regards. --[[User:Smartech|Smartech]] 01:16, 14 Mar 2005 (UTC)
Unless you're one of avid the supporters of the [[rules lawyer]]ing, autocratic, foaming-at-the-mouth inclusionism that was flaunted at the RfC of [[user:Tony Sideaway|Tony Sideaway]] you can't possibly interpret obne vote to '''keep''' against four ''delete''' or '''merge''' votes as no consensus. I redirected the page in question and I would be most grateful if I wasn't forced to VfD it again after only a week or so.
[[User:Karmosin|Peter]] <sup>[[User talk:Karmosin|Isotalo]]</sup> 10:37, 28 August 2005 (UTC)
== EmailSFTPPlus ==
I saw you closed [[Wikipedia:Votes for deletion/SFTPPlus]] with "dealt with as a copyvio". I actually skipped that one as I was not sure what to do with, so I'm glad to see what has happened. However, you didn't remove the VfD notice of the article [[SFTPPlus]] itself. I assumed you simply forgot it (it does not make much sense to have a link to a closed debate, does it), so I did it for you, but please correct me if I am wrong. -- [[User:Jitse Niesen|Jitse Niesen]] ([[User talk:Jitse Niesen|talk]]) 12:08, 3 September 2005 (UTC)
Hi Oleg - do you have an email set in preferences? I sent an email, but got no reply
[[User:PAR|PAR]] 13:14, 18 Mar 2005 (UTC)
== Thanks ==
: I just replied. Sorry for the delay. [[User:Oleg Alexandrov|Oleg Alexandrov]] 16:56, 18 Mar 2005 (UTC)
Hi Mailer Diablo: <br />
== Fourier Series ==
[[image:WikiThanks.png]] Thanks for support and your confidence in me in my recent RFB nomination. I'm now WP's newest bureaucrat. :) Regards, {{User:Nichalp/sg}} 19:56, September 6, 2005 (UTC)
==SGCOTW==
:Hi Michael - I was about to revert edits by 142.150.160.187 on the [[Fourier series]] article (please see its
Thanks for setting up the page! ;) Nut I was wondering if we should make it a weekly, fortnightly, or monthly affair? :D --[[User:Huaiwei|Huaiwei]] 21:24, 7 September 2005 (UTC)
discussion page for reasons) but I noticed you had edited it for style. I want to make sure this doesn't constitute
an endorsement of the article as it stands (please, I hope not!) [[User:PAR|PAR]] 17:22, 18 Mar 2005 (UTC)
==Metroblogging VFD==
I didn't look at it closely; I was just doing some stylistic adjustments. I have noticed that that person has written some dubious things in some math articles, so go ahead and delete his stuff if necessary. [[User:Michael Hardy|Michael Hardy]] 23:57, 18 Mar 2005 (UTC)
Hey, just a quick note: When you close a AFD you need to put a note on the talk page of the article about the outcome as well. Looks like you missed it on that one. Cheers! --[[User:Gmaxwell|Gmaxwell]] 23:08, 8 September 2005 (UTC)
== Brownian MotionThanks! ==
Thanks for the support on my RfA. I was very pleasantly surprised to see so much support throughout the week. Please do keep an eye on me and my logs, especially while I'm learning the ropes with the new buttons. Thanks again! -[[User:Splash|Splash]] 00:03, 10 September 2005 (UTC)
I liked your BM-Picture. How did you make it?<br>
I tried to do the same in the German wikipedia: [[de:Brownsche_Molekularbewegung]] any help for me? :)<br>
Thomas
== Photography (Singapore) ==
:Yours looks good. I just used a Gaussian random number generator in the x and y directions and plotted it. You could just use the image on the English page for the German page if you wanted to, after all, all images are in the public ___domain. I have grabbed an image off the German [[de:Sonne]] article for the English [[Sun]] article. [[User:PAR|PAR]] 16:29, 22 Mar 2005 (UTC)
Hello, photos of Singapore are actually laying everywhere around Wikipedia, (and you some of the most significant pieces of work) perhaps its time for some organisation, and consolidate into a single venue. I find that the Singapore page at [http://commons.wikimedia.org/wiki/Singapore Wikimedia Commons] quite a suitable place. Let me hear what do you have to say. [[User:Slivester|Slivester]] 10:41, 11 September 2005 (UTC)
:I know that I could grab it, but I wanted to make my own one as nice as yours and I wanted to be sure that it's really [[Brownian Motion]] (I published the [[R programming language|R]] source code as well, just two gaussian random walks). What software did you use? Any ideas for improving it?<br>
:This and many related articles in the german wikipedia are quite poor: a lot of work to do...<br>
:Thomas, --[[User:128.130.51.96|128.130.51.96]] 08:08, 23 Mar 2005 (UTC)
== My RFA ==
:I wrote the program in [[IDL_programming_language|IDL]]. It looks something like this:
Thank you very kindly for your support for my nomination. I promise your trust will not be misplaced; I may occasionally be slightly buzzed with power, but never drunk. ;) · [[User:Katefan0|'''Katefan0''']]<sup>[[User talk:Katefan0|(scribble)]]</sup> 22:10, September 12, 2005 (UTC)
n=1000
seed=0
x=randomn(seed,n)
y=randomn(seed,n)
plot,x,y
== Android79's RfA ==
:where randomn() is a random number generator, which generates an n-element, 1-dimensional array of normally distributed random numbers. Seed is the random number seed, and its returned value is different from its input value. [[User:PAR|PAR]] 13:21, 23 Mar 2005 (UTC)
Thank you for your support on my RfA. <font color="green">[[User:Android79|android]]</font><font color="purple">[[User talk:Android79|79]]</font> 15:28, 13 September 2005 (UTC)
I believe you did '''not''' this: In your example x and y are normally distributed, but for Brownian Motion ''incements'' should be normally distributed. I guess (quick first look) this is the case in your picture.
Just in the case you are curious: I added another picture in the German wikipedia, where you can see (well, execute the R-code and you really see it ;) ) the convergenace of a discrete process towards BM.
Thomas, --[[User:128.130.51.96|128.130.51.96]] 09:48, 24 Mar 2005 (UTC)
:Yes, you are right, sorry about that. I deleted the old code and was trying to rewrite from memory. This is
more like what I did:
n=1000
seed=0
x=randomn(seed,n)
y=randomn(seed,n)
for i=1,n-1 do x[i]=x[i-1]+x[i]
for i=1,n-1 do y[i]=y[i-1]+y[i]
plot,x,y
:I don't understand the phrase "convergence of a discrete process towards BM". BM is a discrete process, right?
:I think you're doing some good work on that page. I will check with it occasionally to make sure the English page is competitive. Also, you might want to check out a related topic [[Levy flight]]. Its sort of a generalized Brownian motion for other stable distributions.
Brownian motion is definitely ''not'' discrete, but continous (and, btw nowhere differentiable). But it is constructed the way I tried to draw the second picture: Take an interval [t-1, t] and two normally distributed numbers B_t and B_{t-1}. Then devide the interval by two and add in the center another random number B_{t-1/2}. This process is discrete. Now you let the mesh go to zero and the discrete process tends to something that really exists (Wiener proved it first), it is continous and we call it BM. Correct me if I'm wrong.
I'd really like to improve especially the german wikipedia on this (and related) topic and there is really a lot of work to do, but I am not very expereinced yet...
Thomas, --[[User:128.131.219.28|128.131.219.28]] 22:54, 24 Mar 2005 (UTC)
:I just assumed that Brownian motion referred to e.g. the motion of a particle in a liquid as it is hit by the molecules of the liquid. This is a discrete process, (assuming the duration of the impact is short compared to the free travel time between collisions). I have never tracked down the precise definition of Brownian motion, however. Are you saying that the motion of particles under molecular bombardment is only a discrete approximation to Brownian motion? This seems strange to me. [[User:PAR|PAR]] 03:14, 25 Mar 2005 (UTC)
I reffered to BM as a mathematical object, that's right.
But never the less I think that BM is continous. I do not want to start a philosophical question, but I can't imagine molecules that move discrete. As far as I know discrete moving does just exist in [[quantum physics]] (read this article! or just this [[Quantum_physics#Description_of_the_theory|paragraph]]) for [[electron]]s and other particles. (But honestly I know ''nothing'' about Quantum physics)
So I think that the mathimatical model "BM" is a quite good model for "random" movements of molecular particles - they are both very rough and not discrete, but continous.
Thomas, --[[User:128.131.219.28|128.131.219.28]] 23:47, 25 Mar 2005 (UTC)
:Hello Thomas - The way I picture it is that a particle gets hit by a molecule, which instantaneously changes its direction and speed. Then it travels as a free particle for some distance L1, at which point it gets hit again.
:It changes direction and speed again, and moves L2, until it is hit again. This motion, described by [L1,L2,...] is discrete, not continuous. There is no quantum physics involved, just classical free particles, undergoing collisions, like billiard balls. Maybe you are saying that if we go to the limit of infinitely many collisions per second, and infinitely small distances between collisions, that that is sufficiently accurate to describe what is really a discrete situation? [[User:PAR|PAR]] 01:01, 26 Mar 2005 (UTC)
You think of billiard balls? Very good! They definitely can't move in a discrete way. Discrete moving means, that the billiard ball is now at one end of the table and an instant later (not one second, not 0.00000001 [[Millisecond|msec]] later) at the other end of the table. It did not move very fast, no it '''jumped'''. You were talking about '''immediatement change of the direction''' (and speed) of the ball. I would say this means that (at some point in space and time) the movement of the ball is not differentiable.
Think of the following: billiard balls and molecules move the same way. In one dimension (on the x-axis you plot the time, on y the position) a crash lookes somehow like [[Absolute value|abs(x)]]. If we assume [[Continuous time]] a '''discrete movement''' could be modeled by a discrete function like the [[Sign function]].
But perhaps I missunderstood you (my poor English?) or I am wrong... we just discuss! :)
I hope that now be are both happy with the layout of our discussion :) (I changed your postings as well, I hope you don't mind)
Thomas, --[[User:128.131.219.28|128.131.219.28]] 10:22, 26 Mar 2005 (UTC)
: Ok, good - I think we agree on the mechanism of the motion of a particle undergoing BM. It is just the definition of "discrete" that we had trouble with. I agree - the motion of the particle is continuous except perhaps at the points of impact with molecules. I was using "discrete" to mean that the distance travelled between collisions is small, but not zero. [[User:PAR|PAR]] 11:13, 26 Mar 2005 (UTC)
==Quantum chaos==
Any chance you have a reference to the article by what's-his-name on a quantum-mechanical derivation of particles-in-a-box? Its a fascinating article: the wave functions are shown to be fractal, and space-filling the entire box. The energy levels of each eigenfunction are shown to extremely close to each other (spacing as 1/avogadro's N). Thus, for example, if you start with all of the particles on one side of the box at time=0, the wave functions, though technically filling the whole box, are destructively interfering on the empty side of the box. But at time!=0 they rather quickly fill the box. You also get a very strong sense of why irreversibility happens (due to the closeness of the spacing of the energy levels, and the fractal-space-fillingness). The author is from UC santa barbera or UC san diego .. I lost the reference... [[User:Linas|linas]] 17:40, 26 Mar 2005 (UTC)
: No, sorry, I don't know of that article. Let me know if you find it, I would be interested. [[User:PAR|PAR]] 20:40, 26 Mar 2005 (UTC)
==[[discrete]] is a disambiguation page==
... so it's usually better to link to one of the pages listed on it than to it directly. [[User:Michael Hardy|Michael Hardy]] 23:16, 3 Apr 2005 (UTC)
== Entropy ==
Just noticed you added the "entropy" entry to the [[chi-square distribution]] infobox. How did you evaluate that integral? I've tried, but obviously I'm missing something. Presumably the same technique would also work for the [[gamma distribution]]. --[[User:MarkSweep|MarkSweep]] 20:17, 10 Apr 2005 (UTC)
: I used Mathematica. It wouldn't give the integral directly but these three statements gave that result:
:: f=(1/2)^(k/2)/Gamma[k/2]
:: logp=Log[f]+(k/2-1)*Log[x]-x/2
:: Simplify[PowerExpand[Integrate[-p[x]*logp,{x,-Infinity,Infinity}]]]
: There is a on-line Mathematica integrator at http://integrals.wolfram.com/ but it only gives indefinite integrals, so I'm not sure if it will help, if you don't have Mathematica. Looking at the page, I realized that the psi or polygamma function is not mentioned, so I will fix that. [[User:PAR|PAR]] 20:42, 10 Apr 2005 (UTC)
::Strange, I can't get Mathematica 5.0 to symbolically evaluate that integral. Which version did you use? --[[User:MarkSweep|MarkSweep]] 21:39, 10 Apr 2005 (UTC)
: I'm using an old version, 2.2. The troublesome part of the integral is
::Integrate[x^(k/2-1)Exp[-x/2]*Log[x],{x,-Infinity,Infinity}]
:which returns an expression involving the PolyGamma(0,k/2) term. I tried it on the Mathematica web page and it too solved the integral, but gave an expression involving HypergeometricPFQ. Whether the two are equivalent, I don't know. Looking at Abramowitz & Stegun, I don't see any integrals involving a Log() defining the Digamma function. [[User:PAR|PAR]] 22:20, 10 Apr 2005 (UTC)
::I see. Can you try to evaluate the corresponding definite integral for the standard [[Gamma distribution]] (i.e. with scale parameter equal to one)? The difficult part is again to compute <math>\mathrm{E}(\ln(x))</math>. I end up with the following:
:::<math>(1-k)\,\Gamma'(k+1) + k + \ln\Gamma(k)</math>
::The indefinite integral corresponding to the expectation of ln(''x'') is expressed in terms of a hypergeometric 2F2 function that I know nothing about. Only the definite integral seems to have a simple closed form. --[[User:MarkSweep|MarkSweep]] 23:20, 10 Apr 2005 (UTC)
I put in these Mathematica lines:
:f=1/(s^k*Gamma[k])
:logp=Log[f]+(k-1)*Log[x]-x/s
:Simplify[PowerExpand[Integrate[-p[x]*logp,{x,xmin,xmax}]]]
and it returned:
:k + Log[s] + Log[Gamma[k]] + PolyGamma[0, k] - k PolyGamma[0, k]
For s=1 thats almost the same as yours, since <math>\Gamma'(x)/\Gamma(x)=\psi(x)</math> = Polygamma(0,x) [[User:PAR|PAR]] 23:59, 10 Apr 2005 (UTC)
== Linking, etc. ==
Looking at several edits you've made (such as [[:Image:PoissonDistribution.png]]), you don't seem to know how to *link* to images and categories.
To link to an image or category, preceed it with a colon: <nowiki>[[:Image:PoissonDistribution.png]]</nowiki> will create [[:Image:PoissonDistribution.png]].
Also, don't put text immediately after <nowiki>{{ifd}}</nowiki> otherwise it will
make text act like fixed-width font and put a block around it
[[User:Cburnett|Cburnett]] 03:18, Apr 11, 2005 (UTC)
: I picked up on the linking to categories after you mentioned it on the template talk page. I didn't know about the ifd thing or the
first space causing a box.
:Thanks for the help on that. [[User:PAR|PAR]] 03:34, 11 Apr 2005 (UTC)
== Cburnett's admin nomination ==
I was nominated for administrator and I'd like to hear your opinion at [[Wikipedia:Requests for adminship/Cburnett]]. [[User:Cburnett|Cburnett]] 07:23, Apr 24, 2005 (UTC)
== Source of Parthenon image ==
You recently uploaded ParthenonGoldenRatio.png. I am interested in an image without the white lines. Can you tell me the source of this image? Thank you in advance! --[[User:Wolfgangbeyer|Wolfgangbeyer]] 07:48, 30 Apr 2005 (UTC)
== [[204.184.37.2]] ==
Someone removed the earlier block because it was too long. I've reblocked for one year.--[[User:Duk|Duk]] 18:22, 2 May 2005 (UTC)
== Image:Autorecessive.png ==
Thanks for improving the image! --[[User:Cprompt|cprompt]] 14:54, May 4, 2005 (UTC)
==Trilobites==
Hi, probably best not to make so many trilobite articles with only a taxobox and no text. They are likely to get deleted. I'd love more trilobite articles, but they have to have ''some'' text. Also, some of the taxa might need to be combined into single articles because the differences between them are not that great to merit separate articles (e.g. between a superfamily and family). Thanks for the effort though and feel free to ask me any questions. --[[User:DanielCD|DanielCD]] 00:33, 7 May 2005 (UTC)
:Ok, no problem. Its just that I looked at Phacops rana, and the next available link upwards was order Phacopida, so I clicked on that and then all of the suborders had no links downward. It seemed to me that (maybe) I was filling in some blanks. [[User:PAR|PAR]] 05:49, 7 May 2005 (UTC)
== [[Wikipedia:WikiProject Mathematics]] ==
Hi Paul. Just wondering, are you aware of the math project? Its talk page is where a lot of math issues on Wikipedia are discussed, and could be of interest to a mathematician to have on the watchlist (sort of like math news). There is also a list of participants to sign on. All this assuming you don't mind rubbing shoulders with other mathematicians. :) [[User:Oleg Alexandrov|Oleg Alexandrov]] 03:09, 5 Jun 2005 (UTC)
: Thanks, Oleg - Its now on my watch list. It looks interesting. [[User:PAR|PAR]] 03:27, 5 Jun 2005 (UTC)
==[[Pareto distribution]]==
Why link ''likelihood'' to [[maximum likelihood]] rather than to [[likelihood function]]? The method of maximum likelihood is not the only use of likelihood functions. [[User:Michael Hardy|Michael Hardy]] 22:29, 12 Jun 2005 (UTC)
:Hi Michael - The technique shown in the [[:Pareto distribution]] article is directly addressed in the [[:maximum likelihood]] article (section="philosophy of the MLE"). Thats the only reason. I think it should be one jump to the relevant section. I will revert it soon if you have no objection. [[User:PAR|PAR]] 23:17, 12 Jun 2005 (UTC)
==A theorem by Boltzmann==
I thought I'd ask you, since you've contributed to statistical physics articles here: In the article on [[maximum entropy probability distribution]]s it says under the heading [[maximum entropy probability distribution#A theorem by Boltzmann|A theorem by Boltzmann]]:
:''All the above examples are consequences of the following theorem by [[Boltzmann]].''
(The theorem is about the form of the maxent distribution when the expectation of a family of functions is known.)
The article doesn't provide any explicit source for that statement. I'm not doubting the veracity of the statement or the theorem it refers to (I've seen it proved by Jaynes), just wondering where Boltzmann stated or proved that theorem. Would you happen to know the primary source, or could you point me to the secondary literature? Thanks! --[[User:MarkSweep|MarkSweep]] 14:05, 13 Jun 2005 (UTC)
: Hi Mark - I've seen the theorem before, but no, I don't know of the primary (or secondary) sources. I'm sure it was in some statistical mechanics course or book. [[User:PAR|PAR]] 16:36, 13 Jun 2005 (UTC)
::Ok, I'll check some textbooks. --[[User:MarkSweep|MarkSweep]] 16:58, 13 Jun 2005 (UTC)
== Correlation dimension ==
Sorry I didn't back to you sooner. I haven't looked at it carefully, but as it progresses on the queue of to do's I'll get to it. It generally looks OK, though. No bogosity alarms went off.--[[User:CSTAR|CSTAR]] 20:24, 22 Jun 2005 (UTC)
== Hypergeometric functions==
Hmm, I created that category hoping it would cover the theory of hypergeometric functions, rather than listing various special functions that are special cases. Oh well, I'll have to regroup, I guess, and maybe start a category [[:Category:Hypergeometric function theory]] or something like that. No problem, I just want to keep a distinction between the theory and the list of miscellaneous special functions. [[User:Linas|linas]] 05:27, 27 Jun 2005 (UTC)
: Well, lets do the right thing. I mean, there's the possibility of two sub-categories of hypergeometric functions instead of just one. [[User:PAR|PAR]] 28 June 2005 13:44 (UTC)
== Dilogarithm - your opinion ==
Hi,
I looked through the article on the [[polylogarithm]] and noticed that you are one of the main contributors to that topic. Here the dilogarithm is mentioned as a special case. I feel tempted to initiate a stub article on the dilogarithm, because it is a function that relatively often pops up in physics. However, I noticed that you have made a redirection from the dilogarithm to the polylogarithm - and based on this I began wondering whether it is to specialize too much to mention the dilogarithm explicitly???
In the article I plan to start out by defining <math>\mathrm{Li}_2(z) \equiv -\int_{0}^{z} \frac{\ln(1-z)}{z} dz</math> for general complex variables, show the series expansion for <math>|z|<1</math>. Then I will focus a little on real, negative arguments, show the asymptotic form, and a useful relation for converting a dilog with an argument smaller than -1 into the <math>]-1;0[</math> range.
Finally, I plan to add a reference to : Lewin, Polylogarithms
Not at all as comprehensive as the polylog article...but a start
Anyway, I would like to hear your opinion on this. I have never written a wikipedia article before, and today is the first time I have seen one. I am just exited to see all the material that is in here, and I began wondering if I could contribute with anything usefull...
[[User:KimViborg|KimViborg]] 29 June 2005 22:35 (UTC)
:I think that would be an excellent idea. Any material that is specific to the dilogarithm, but not to the polylogarithm could go in a separate article. If there is enough material, then it SHOULD go in a separate article. If you have results that apply to the polylogarithm AND the dilogarithm, please put it in the polylogarithm article as well. Not that I am an expert, but if you have any questions, just ask. [[User:PAR|PAR]] 30 June 2005 03:27 (UTC)
== Fluctuation theorem ==
I thought you might be interested in this article based on your user page: [[Fluctuation theorem]] :-) --[[User:HappyCamper|HappyCamper]] 3 July 2005 20:28 (UTC)
==Polylogs==
Hi, I replied on [[Talk:Polylogarithm]] [[User:Linas|linas]] 8 July 2005 19:22 (UTC)
==Grassmann==
If you look at the biography of [[Grassmann]], you'll see it mentions his color work. The law comes, I believe, from his article "Theory of compound colors", Philosophical Magazine 4 (7), 1854, 254-264. You can cross-check in a few library catalogues under, e.g. Sources of color science, ed. David L. MacAdam, MIT Press [1970]. --[[User:Macrakis|Macrakis]] 23:35, 11 July 2005 (UTC)
Web search finds Grassmann's three color laws covered in http://wwwzenger.informatik.tu-muenchen.de/lehre/vorlesungen/graphik/info/csc/COL_11.htm. See also http://www.colorsystem.com/grundlagen/bibl1.htm for more bibliography. Then there is Grassmann's Law in historical linguistics. --[[User:Macrakis|Macrakis]] 13:47, 12 July 2005 (UTC)
== Revived WikiProject on probability and statistics ==
Hi PAR, got your message. I've started to revive [[Wikipedia:WikiProject Probability]], which had been more or less dormant for well over a year. I think this would be a natural place to discuss guidelines for probability related articles, open tasks, etc. My plan is to expand it and clean it up a bit, and then notify the people who are already signed up on the WikiProject page, as well as the regular contributors on [[Template talk:probability distribution]], and perhaps others who might be interested. What do you think? --[[User:MarkSweep|MarkSweep]] 03:00, 18 August 2005 (UTC)
: Yes, sounds like a good idea to me. Whats the time frame on this? [[User:PAR|PAR]] 06:11, 18 August 2005 (UTC)
::Don't know how long it's going to take. I personally don't have a lot of time at the moment, and the project page needs a bit more work. But I've cleaned out [[Wikipedia talk:WikiProject Probability]], which could be used for discussions right away. --[[User:MarkSweep|MarkSweep]] 06:54, 18 August 2005 (UTC)
== ''[[Balcoracania dailyi]]'' ==
If you don't know the authority for a name, you can use {{[[Template:Taxobox section binomial simple|Taxobox section binomial simple]]}}. That allows taxoboxes without authorities to be found and fixed. It's not a good idea to guess; ''Balcoracania dailyi'' wasn't named by Daily — that would have been the height of vanity! — but by Pocock. [[User talk:Gdr|Gdr]] 23:29:43, 2005-08-22 (UTC)
: Ok, I understand. Thanks for pointing that out. [[User:PAR|PAR]] 01:07, 23 August 2005 (UTC)
==[[Tent map]]==
Really nice bifurcation diagram - thanks ! You are right, I had got the Julia set wrong in my original description of the behaviour for μ between 1 and 2 - it is not the whole of the interval from 0 to μ/2, but just the part from μ-μ^2/2 to μ/2. I have fixed this in the article. I am interested in your views on how the explanation of the map's dynamic behaviour can be improved - which parts are still not very clear, for example ? [[User:Gandalf61|Gandalf61]] 15:28, 13 September 2005 (UTC)
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