text:
User talk:Robinh

Welcome to Wikipedia!
Hello Robinh, welcome to Wikipedia! Thanks for all your contributions. Here are some useful links in case you haven't already found them: If you have any questions, see the help pages, add a question to the village pump or ask me on my talk page. I hope you enjoy editing here and being a Wikipedian!
 * MediaWiki User's Guide
 * How to edit a page
 * How to write a great article
 * Naming conventions
 * Manual of Style

Noldoaran (Talk) 22:19, Dec 8, 2003 (UTC)

Hello and welcome.

Please note the highlighting convention: the title word or title phrase is highlighted at its first appearance. I have entered this correction at Boussinesq approximation and Richardson number. Michael Hardy 02:49, 9 Dec 2003 (UTC)

Hi Robin

Those articles are really good, you're catching the Wiki bug! - I couldn't resist correcting a typo though - sorry ;-)

Anyway, I give in - what's SOC? I googled the two names and they're definitely mathematicians, but they're not in Southampton or perhaps I should say they weren't.

My maths days are long over - I graduated in 1980 - and I always tended towards pure maths. I've been in IT since, which is why I looked up your IP.

Spellbinder 16:54, 10 Dec 2003 (UTC)

Hi Robin, your Logarithm homework help is not quite appropriate for inclusion in an encyclopedia such as this one, though similar articles and your services may be more better suited to a project like Wikibooks. Thanks Dysprosia 22:35, 11 Dec 2003 (UTC)

> Replied on my talk page Dysprosia 22:45, 11 Dec 2003 (UTC)

Hi Robinh, I just found a site that might be another good place for pages like Logarithm homework help, the Know-How Wiki. It looks pretty new and I haven't checked it out in detail yet. Have fun! Tualha 00:41, 13 Dec 2003 (UTC)

Hello - you emailed me about the Euler's equation and Euler equations duplication. I'm not personally that bothered about the title; but it does look as if the former page's content should be merged into the latter's.

Charles Matthews 10:04, 15 Dec 2003 (UTC)

I think you might be exactly who I'm looking for to talk about the organization of the fluid dynamics pages. I'm trying to write aerodynamics (it's been a stub for a long time) and it's going really slowly. It's occuring to me that much of what I'm writing there really belongs in fluid mechanics (like the continuity assumption etc) but then aerodynamics would reduce to a simple "Aerodynamics is fluid mechanics applied to gases" and nothing else, which doesn't work for the importance of the topic. And I keep wanting to insert Bernoulli's equation, the Euler equations, the Navier-Stokes equations, even LaPlace's equation but of course they all have their own pages, so it would just be duplication. And yet nowhere do we have the fact that they are reductions of one another. Also, should I be making new pages for things like Prandtl's lifting-line theory or does it belong in aerodynamics? Anyway, let me know your thoughts, I've started a WikiProject Fluid dynamics to get it going. moink 17:28, 27 Dec 2003 (UTC)

 * Thanks for your comments! We should continue the discussion at WikiProject Fluid dynamics.  moink 19:43, 2 Jan 2004 (UTC)

Hi Robin, I picked up your Red-fronted Serin, it's particularly useful to have contributions on birds from areas other than Europe and North America. The agreed convention is that bird species names are capitalised with a redirect from the lower case form, so to give consistency with the hundreds of other species accounts, I've moved the page and created the redirect. jimfbleak 06:37, 3 Jan 2004 (UTC)

 * to create a redirect, start from the page you have written, eg Syrian Serin. In the browser address box you will see http://en2.wikipedia.org/wiki/Syrian_Serin . Change this to http://en2.wikipedia.org/wiki/Syrian_serin, (first word will be capitalised anyway) and press enter to open the new page. Type #redirect Syrian Serin and save.

The caps convention is somewhere, I'll post again when I find it! Jim

 * Naming_conventions_(fauna), or more clearly at WikiProject_Birds Jim

Lorentz force
Hi noticed your page and did the redirect to our existing page, with the correct spelling. By the way, the Lorentz force isn't Lorentz covariant, per se, but it does transform as the spatial components of a four-vector. Keep up the good work, though. -- Decumanus 22:28, 28 Feb 2004 (UTC)
 * No problem. Happens to me too, those kinds of things. By the way, there is indeed a famous Edward Lorenz, who discovered the Lorenz attractor. -- Decumanus 22:35, 28 Feb 2004 (UTC)

Blocking
Hi, Robin. Can you tell me the address that you were working form that got blocked? Are you on AOL? RickK 14:52, 22 Apr 2004 (UTC)

If you knew the numbers, I could tell you why the account was blocked, but since you don't remember, I'm at a loss. Sorry. RickK 21:51, 25 Apr 2004 (UTC)

Scientific wager
Nice work on Scientific Wager. Fun to read. - Tεx  τ  urε  13:03, 17 Jun 2004 (UTC)

Hotelling's T-square distribution
Hello. What is the quantity you called m? Michael Hardy 17:48, 27 Aug 2004 (UTC)

 * OK, I figured it out. You introduced that variable but only later in the article said what it is. Michael Hardy 18:47, 27 Aug 2004 (UTC)

 * Also, I've added this to list of statistical topics. Could you add them as you create them, and also add any others you know of that are not there?  Thanks. Michael Hardy 17:57, 27 Aug 2004 (UTC)

Hubbell's UNTBB
Based on the title of his book, shouldn't the page actually be titled the "Unified neutral theory of biodiversity and biogeography? Guettarda

Most-perfect magic square
Halló Robinh, I saw the article and want to say Halló! At the name is David Brée not Bree. I worked also on these squares and read about the work of Dame Kathleen Ollerenshaw and David Brée later. I was contacting Harvey Heinz some weeks ago but could not find the work of Ollerenshaw and Brée. Do you know where to get this book? I stoped working at about four weeks ago. I generate only some straight forward patterns. Just take a look. Regards Gangleri 07:53, 2004 Sep 27 (UTC)
 * Halló Robin, Thank you for tha answer. You write: I know your webpage quite well! Do you mean the "linear" generion algorythm? Have you seen it somewhere before? shows a good construction example. If you reload the page you will get another arbitrary square. I am not using an exhaustive method, I just place "the rigth values" arbitraryly at known  "relevant positions". The code is (depending on the programming language) a few line only. For every position in the binary representation there is one if statement with asigns followed by an reasignment statement. Just look here and / or e-mail me.
 * I am aware of 8x8 squares having the property that min { a(i,j)+a(i,j+1)+a(i,j+2)+a(i,j+3) } <> max { (a(i,j)+a(i,j+1)+a(i,j+2)+a(i,j+3) } for every i and every j. Visualy there is no (shifted) horizontal axis where the half row sums are all the same. But the construction method its not as straight forward is in the implemented example.
 * I have never seen a 12x12 Most-perfect. Have you seen / generated one before? Where? / How?
 * Did you know, that the square is showing 27 differnt subqueares with same row, column and diagonal sum?
 * I like visual patterns. For even number squares of order n I like to replace a'(i,j)=(2*n*n+1-2(a(i,j)) and work with odd numbers only. "Gott liebt die ungeraden Zahlen." is refered to Leibniz. The Kabbalah type 4x4 and one of the 8x8 mentioned there (?) givs two straight forwad patterns to. Both regarding the consecutive position of the odd numbers and their sign. Is it worth to show this as a construction method? Regards! Gangleri 09:48, 2004 Sep 28 (UTC)

Most-perfect magic square (2)
Dear Robinh, thanks for your answer and the example. I moved your answer at User talk:Gangleri. If you would post your messages at User talk:Gangleri I would be notified while loging in. Would you like to start writing an article ? Tanks! Gangleri 05:29, 2004 Oct 1 (UTC)

Most-perfect magic square (3)
Dear Robinh, I was reading lots of documentation pages about InterWiki links. I made a note at Talk:Most-perfect magic square. Could you please take a look at it? Thanks! Regards Gangleri 18:37, 2004 Oct 9 (UTC)

 * I moved Most-perfect square to Most-perfect magic square and readjusted all links known to me. Regards Gangleri 15:24, 2004 Oct 17 (UTC)

The Wikification of John Glashan (and his works)
Hello, I see you've just now "Wikified" the page on Jonathan Routh by providing a second link to John Glashan. This surprises me, as there was already a link to him. Or does the start of a new section trigger the need for (or at least desirability of) new links? (I'm new hereabouts, so I really don't know. I guess I could look it up, but I've had my fill of digging around the "Special" pages for one day.)

 * Now I understand. Thank you!

Oh, er, sorry to digress, but can I interest you (or anybody) in my comment within Wikipedia talk:Wikipedia maintenance?

Thanks for any feedback. Hoary 09:46, 15 Nov 2004 (UTC) Feedback received with thanks! Hoary 14:09, 15 Nov 2004 (UTC)

Robinh, I've just written stuff about the excellent guidebooks by John Glashan and Jonathan Routh. I wasn't sure where to put it. Since the four can be described together, I was inclined to put them together, but I couldn't think of a good title for an article ("The Good Loo Guide et seq."?), and I certainly didn't want to create four articles. (As somebody who frequently uses a modem, I hate having to jump around short pages. I'd rather get a long page in a browser window, disconnect, and then read.) Although Glashan's contribution was considerable, it was less than Routh's, so I've put it in the article on Routh. Genius, however, is a different kettle of whatever: it's very much a solo production of Glashan's. I'd thus be inclined to fold both Anode enzyme and Genius (cartoon) into the article on Glashan. Another possibility would be to add a lot to Genius and fold "Anode Enzyme" into it. (Unfortunately all I know of "Genius" is what's reproduced in John Glashan's World.) Comments?

Incidentally, I have most of Glashan's books. Time permitting (and it won't for a month or so), I can say something about all of them. Hoary 04:17, 16 Nov 2004 (UTC)

Granular material
Hi. I merged Granular matter into your article Granular material, since i think Granular material is the better word. Have a look. Nice work on dry quicksand by the way, you beat me by 5 minutes in creating that article. -- Chris 73 Talk 00:08, Dec 10, 2004 (UTC)
 * Thanks. And don't worry about the 5 minutes, happens all the time in wikipedia. I ususally save my progress every few sentences (and hence have a lot of edits), but I thoght who the heck would wanna write an article about dry quicksand. Guess now I know :P Happy editing -- Chris 73 Talk 09:41, Dec 10, 2004 (UTC)

Article Licensing
Hi, I've started a drive to get users to multi-license all of their contributions that they've made to either (1) all U.S. state, county, and city articles or (2) all articles, using the Creative Commons Attribution-Share Alike (CC-by-sa) v1.0 and v2.0 Licenses or into the public domain if they prefer. The CC-by-sa license is a true free documentation license that is similar to Wikipedia's license, the GFDL, but it allows other projects, such as WikiTravel, to use our articles. Since you are among the top 2000 Wikipedians by edits, I was wondering if you would be willing to multi-license all of your contributions or at minimum those on the geographic articles. Over 90% of people asked have agreed. For More Information:
 * Multi-Licensing FAQ - Lots of questions answered
 * Multi-Licensing Guide
 * Free the Rambot Articles Project

To allow us to track those users who muli-license their contributions, many users copy and paste the " " template into their user page, but there are other options at Template messages/User namespace. The following examples could also copied and pasted into your user page:

 * Option 1
 * I agree to multi-license all my contributions, with the exception of my user pages, as described below:

OR
 * Option 2
 * I agree to multi-license all my contributions to any U.S. state, county, or city article as described below:

Or if you wanted to place your work into the public domain, you could replace " " with "  ". If you only prefer using the GFDL, I would like to know that too. Please let me know what you think at my talk page. It's important to know either way so no one keeps asking. -- Ram-Man (comment| talk)

Edit summaries
Hi, Edit summary says "Always fill the summary field." (emphasis in the original). Please fill in the Edit Summary when you edit an article, so the rest of us don't have to resort to a "diff" to see what you did. Thanks! Noel (talk) 23:39, 11 Jan 2005 (UTC)

nice addition...
... to "Bicycle". This section got bandied all over the place last year as editors waged war over just what does keep a bike up. It is now quite complete, and the article may be up to "featured article" level. Sfahey 15:41, 14 Feb 2005 (UTC)

Hi and modular discriminant
Hi, thanks for the compliments on the Weierstrass elliptic functions pictures. See, I hadn't clue that they were fractal; I very accidentally found out that something distantly related was fractal-ish, and followed the leads. Its very odd, to me, that books on chaotic dynamics, fractals, etc. never actually mention these ... but I am now the happier for knowing this. linas 05:25, 15 Feb 2005 (UTC)

Generalized continued fraction needs your help
If you read its discussion page or note the bold Bug notice someone added to the article, you'll see what I mean. 4.250.198.191 05:54, 11 Apr 2005 (UTC)

Theta functions in Weierstrass
Hi, question & remark.

1) Have you been able to confirm that the theta_2 theta_3 etc. that you use in the Weierstrass invariants are consistent with the definitions used given in other articles? There's some mumble-words in the article on theta that make me wonder if all of these really are defined consistently.  I mean, your usage may be correct, but I'm not convinced that all usage in Wikipedia is correct.linas 13:44, 18 May 2005 (UTC)

2) The Weierstrass elliptic article is getting long. I'm thinking it may be time to chop it up. Maybe invariants should get its own page? Then we could have a real subsection called "numerical methods" or something like that.   linas 13:44, 18 May 2005 (UTC)

Votes for deletion/Continuum calculator
Hello Robinh, thanks much for discussing the article. Since I am interested to keep the article I have overworked it a bit and I have added an explanation to the vote list. I would be glad if you had another look. Thanks. -- Karsten88 15:20, 21 May 2005 (CEST)

Metamaterial and Swiss roll (metamaterial)
As of April 2005, someone seems to have filled in the swiss roll (metamaterial) link with information about the "swiss roll" type of jelly roll. Would you be willing to replace this with information on the actual metamaterial you were describing? I don't have the optics expertise to write about it. --Christopher Thomas 20:21, 24 May 2005 (UTC)

Hello...
Hello! William M. Connolley 19:35:18, 2005-08-04 (UTC).

A8 speedies
Hi there. When using undefined, please remember to add the URL it is taken from like this:

otherwise, the admin has to guess and hunt where you spotted it. Thanks. -Splash talk 00:54, 6 October 2005 (UTC)

Cecil Rousseau
Could you please comment on the debate at Articles for deletion/C. C. Rousseau, whether our article on Cecil Rousseau should stay? I think you mentioned him at book (graph theory), which is where I got the idea that you might know something about his work. Thanks, Jitse Niesen (talk) 16:41, 13 October 2005 (UTC)

Dust (relativity)
Hi, please see my query in Talk:Dust (relativity). TIA ---CH (talk) 18:21, 12 November 2005 (UTC)

Shock wave
Hello Robinh. I've undone your partial revert on the Shock_wave page, and I've added my reasons on the talk page of shock wave. it's not that I don't agree that I was too harsh in the first edit, but the quality of the original material was truly abysmal, and I think that some difficult decisions were necessary to prune out everything which wasn't 100% correct. AKAF 13:43, 8 December 2005 (UTC)

Sources for Bulgarian solitaire
Hello, good work on Bulgarian solitaire, and thanks for the contribution. However, you did not provide any references or sources in the article. Keeping Wikipedia accurate and verifiable is very important, and as you might be aware there is currently a push to encourage editors to cite the sources they used when adding content. Can you list in the article any websites, books, or other sources that will allow people to verify the content in Bulgarian solitaire? You can simply add links, or see WP:CITET for different citation methods. Thanks! --best, kevin [kzollman][talk] 17:31, 8 December 2005 (UTC)

 * Thanks for checking on the references. I don't know if you've been keeping track of the news, but wikipedia is comming under fire for having false information.  Everybody is on the lookout!  In that vain, I looked up Varma Division and I cannot find any confirmation of it either.  A quick glance suggests that arguments are good, so my bet is that it is original research.  I have nominated it here.  Thanks for point that out! --best, kevin [kzollman][talk] 03:43, 9 December 2005 (UTC)

Carroll's paradox
Hi Robin. You mentioned you have the solution to this paradox months ago ,please quench my curisoty and expand the article..:) Diza 17:06, 27 December 2005 (UTC)

In litrature.
Hey what's up I just want you to know I deleted your two In Litrature sections of Door Furniture and Door Knockers, the reason I did this was because niethier seemed to have anything really to do with the subject and instead seemed to revolve around quotes you found in which Door knockers were used, I don't find this encyclapedic and it sets a bad example for other users. (We wouldn't want a Toilets in litrature section for example) Thanks for understanding. :) Deathawk 20:43, 26 January 2006 (UTC)

Image copyright problem with Image:WeierstrassP.png
Thanks for uploading Image:WeierstrassP.png. However, the image may soon be deleted unless we can determine the copyright holder and copyright status. The Wikimedia Foundation is very careful about the images included in Wikipedia because of copyright law (see Wikipedia's Copyright policy).

The copyright holder is usually the creator, the creator's employer, or the last person who was transferred ownership rights. Copyright information on images is signified using copyright templates. The three basic license types on Wikipedia are open content, public domain, and fair use. Find the appropriate template in Image copyright tags and place it on the image page like this:.

Please signify the copyright information on any other images you have uploaded or will upload. Remember that images without this important information can be deleted by an administrator. If you have any questions, feel free to contact me. Thank you. Admrb♉ltz (T | C) 01:56, 28 January 2006 (UTC)
 * All copyright tags can be found at WP:ICT --Admrb♉ltz (T | C) 16:39, 30 January 2006 (UTC)

Image:WeierstrassP.pdf listed for deletion
An image or media file that you uploaded, Image:WeierstrassP.pdf, has been listed at Images and media for deletion. Please look there to see why this is (you may have to search for the title of the image to find its entry), if you are interested in it not being deleted. Thank you. Admrb♉ltz (T | C) 01:56, 28 January 2006 (UTC)

Cramér-Rao inequality
In the Example section in Cramér-Rao inequality, you made an assertion about what the likelihood function is, that simply does not make sense unless normality is assumed. But you began by saying simply: let X be a random variable with expected value ___ and variance ___. That does not imply normality. Michael Hardy 03:35, 26 February 2006 (UTC)

Division ring
I've removed your "Semantics" section on the Division_ring page. Your terminology is wrong, you cite a "Godemont" without reference, and the basic assertion is so far from true that it's silly.

If you were trying to say something sensible here, please rewrite it. 69.107.70.159 15:52, 6 March 2006 (UTC)

PSR J1748-2446ad
With regard to this page that you created I was wondering if you could help me with an interesting question I thought of. If the millisecond pulsar is rotating at that speed and is 4-5 earth radii the outside edge is rotating at way over the speed of light, 383.035581 to 478.794476 times the speed of light to be exact! I know this cannot be though. How I came up with that number was using google caclulator using this equation. So I was wondering if you knew what part of the pulsar is rotating at that speed.

Supplee's paradox
Did I read this wrong? What am I missing? ---CH 21:02, 5 May 2006 (UTC)

Mathematical Coincidence
Hi,

I'd like to continue our discussion at talk:mathematical coincidence. I still don't feel that approximations, like pi ~= 22/7, deserve the name of "coincidence". Hope to hear from you! MrHumperdink 02:23, 9 May 2006 (UTC)

Meaning of "however"
Hi: Thanks for reviewing the article on self-efficacy. This is a bit picky, but I noticed that you changed however to whether or not in the phrase self-efficacy is the belief (however accurate) that one has the power.... One dictionary definition of however is "to whatever degree or extent." This meaning is consistent with its usage in the article. More to the point, "however" implies correctly that accuracy may vary on a continuous scale, but "whether or not" makes it a dichotomy. If no objections, I'll revert. Nesbit 14:21, 26 May 2006 (UTC)

 * Hi Nesbitt. No worries. To me, "self-efficacy is the belief (however accurate) that one has the power..." implies that the statement is true, even as the accuracy approaches perfection. This is the way that such sentences are understood in my field of mathematics. I wanted the emphasis to be on the fact that the accuracy is immaterial. You are right about the the dichotomy, though. How about "...the belief (irrespective of its accuracy) ..."? Robinh 14:50, 26 May 2006 (UTC)

 * I see your point. Your suggested fix sounds fine. Nesbit 22:21, 26 May 2006 (UTC)

Daisyworld generalised
Hi! From where to find model articles of Wikipedia? I am used to scientifical langiuage but my emphasis has typically been in understandability rather than in fine looks. Which sentences you find confused and in which ways? What about if the source is my own thought but which should be easy enough for others to follow just like that? Should I first get them published in some scientifical journal? But that is difficult for a vague subject like Gaia which Wikipedia though includes. I would just like to benefit those interested in the subject. Htervola 10:16, 9 November 2006 (UTC)

Gravitational Tug
I have reverted your partial restoration to the gravitational tug article. Giving such a precise value for delta-v is meaningless here: changing delta v of 0.0019 m/s is the same as 0.002 or 0.005 in this context. What matters is the order-of-magnitude of the delta. The gravitational tug is not relevant in asteroid kinematics. This is a matter of terminolgy: the gravitational tug is used to deflect asteroids. Asteroid kinematics is the motion of asteroids on their own (e.g. 1999 KW4). Michaelbusch 22:33, 24 November 2006 (UTC)

LambertW etc.
Hi, Answered on my own talk page - Don't hesitate if you find I should do more of that type of pictures for other articles Thanks --Xedi 19:56, 25 November 2006 (UTC)
 * I've just done the same for ln, uploading in a few seconds. --Xedi 20:18, 25 November 2006 (UTC)
 * Done, see Natural Logarithm (move it to complex logarithm if you find it better) --Xedi 20:30, 25 November 2006 (UTC)
 * Done the same for exponential, see exponential function --Xedi 21:10, 25 November 2006 (UTC)

Generalized continued fractions
Hello!

I want to add some material to Wikipedia on the subject of continued fractions, particularly the applications of continued fractions in complex analysis. I noticed that you made many of the contributions to generalized continued fractions, and that's why I'm writing to you.

I've already received some friendly advice not to modify the definition appearing at the article about continued fractions. So if I'm going to put a hook into existing articles at all I need to work from the "generalized" case. The problem is that all partial denominators are currently defined to be positive integers.

There are scads of examples from analysis where the partial denominators are complex variables, and I'd like the definition in the "generalized" article to be sufficiently general to allow for these.

Do you care if I change the generalized continued fraction article all around? DavidCBryant 01:18, 2 December 2006 (UTC)

 * Hello again, RobinH!
 * I've added one new article, here, that illustrates how complex numbers can enter into meaningful continued fraction expressions. It's not quite done yet, and I'm still aiming to append a proof (in a separate article). Anyway, if you get a chance to look at it, feedback is always welcome. Thanks! DavidCBryant 12:56, 14 December 2006 (UTC)

 * Hi, RobinH! I'm back!!
 * I've added some new content to the generalized continued fraction article. Please take a look and tell me what you think when you have the time. Merry Christmas! DavidCBryant 00:45, 18 December 2006 (UTC)

Quantum Tic Tac Toe
Hello, Robin! Some months back, I registered with Wikipedia with the intent of writing an article about QT3. Unfortunately, after I had perused some of the policies, guidelines, suggestions, opinions, et cetera ... I was forced to conclude that I could not do so. I am therefore delighted to find that you have created an article referring to the game.

I am yet a WikiNewbie (if I may coin such a word, unless someone else has already done so), and have many questions about the proprieties of this place. I am therefore writing to ask you for help (or at least, pointers to the necessary (more!) reading) so I can figure out whether it is proper for me to add anything to your article. I have an interest, and a possible conflict of interest, in that I am a friend of the inventor of Quantum Tic Tac Toe, and am the author of a version of the game for the Palm PDA.

If you would be so kind as to reply to my (as yet non-existent) talk page, it would be greatly appreciated. And if this is not the appropriate venue for having contacted you, please also let me know that. As I said, I am as yet a stranger here.

Thank you for your kind attention.

Swwright 04:58, 27 December 2006 (UTC)

 * Hello again, Robin!
 * Been working on a draft in my user area, but it's not yet ready for publication. You can probably find it, if you wish to take a look, user pages are not really private in any sense.  Good grief, has it been nearly a year?? — SWWrightTalk 14:23, 19 September 2007 (UTC)

 * Um ... I should note that my article-in-preparation on QT3 is just that: an introduction. You probably have as much information about the game from the AJP article, as you will get from me.  Are you interested in it as a game (i.e., tactics and strategy?) or as a pedagogical tool (i.e. teaching quantum mechanics)? — SWWrightTalk 15:38, 19 September 2007 (UTC)

Orange and Green Marbles
Thank you for providing (yet another) way to answer my question! I have asked the same question in a number of different forums, and have yet to get the same answer twice, yet have gotten three very distinct and very believable anwers (and a host of not so believeable answers). I had no idea there would be such diversity for what I thought was a fairly simple probability question. Now I just have to assess the relative strengths and weaknesses of the three (Bayes, Wilson's interval and the new one you supplied). Do you know if there is a good article or textbook chapter that discusses the various approaches? Thanks again for your excellent answer. dryguy 20:52, 11 January 2007 (UTC)

Shock Wave
Hi Robinh, I'm rather hoping that Genick doesn't make an uninteligable mess of the page like he has oblique shock and moving shock. It would be nice if you could help to correct errors without destroying the article. AKAF 17:47, 1 February 2007 (UTC)
 * Hi Robinh, I would certainly support a merge. If you look at the edit history you'll see that I originally merged oblique shock and shock wave and left a redirect at oblique shock. Actually the stuff at "types of shock wave" is a bit of an embarrasment, but I was having a bit of a low creativity day. The hope was that there would be enough examples of shock waves there that people would get a good ides just from the examples. Perhaps changing the section name to "Examples of shock waves" would be a good start? AKAF 09:36, 2 February 2007 (UTC)

Your undo at Complex number
On 23 February 2007, you undid an edit by. However, that edit was his own reversion of his own error. So you re-introduced his error. Please be more careful in the future to revert only to clean versions. By the way, "undo" only undoes the last change in the difference, even if you push the button while looking at a difference covering more than one change. JRSpriggs 09:45, 24 February 2007 (UTC)

Statistician help needed
The WikiProject Vandalism Studies (WikiProject Vandalism studies) just finished its first study and I was hoping that you being a statistician could help us formalize our findings. You can find our draft conclusions here. Here's an excerpt of what we found so far:

The current study analyzed a sample pool of 100 random articles. Within these 100 articles there were a total of 668 edits during the months of November 2004, 2005, and 2006. Of those 668 edits, 31 (or 4.64%) were a vandalism of some type. The study's salient findings suggest that in a given month approximately 5% of edits are vandalism and 97% of that vandalism is done by anonymous editors. Obvious vandalism is the vast majority of vandalism used. From the data gathered within this study it is also found that roughly 25% of vandalism reverting is done by anonymous editors and roughly 75% is done by wikipedians with user accounts. The mean average time vandalism reverting is 758.35 minutes (12.63 hours), a figure that may be skewed by outliers. The median time vandalism reverting is 14 minutes.

Thanks. Remember 02:26, 26 March 2007 (UTC)

Go Edit
Hi. I think you edited Go (Board game) to introduce the number of moves computer programs considered compared with chess. Unfortunately you provided no source for this claim, could you do so?--ZincBelief 15:51, 12 April 2007 (UTC)

Trivia monacha
Hi! Thank you for adding this article and for expressing interest in expanding Wikipedia's coverage of molluscs. Would you consider adding more to this page? « D. Trebbien ( talk ) 22:08, 8 May 2007 (UTC)

 * Hi Trebbian. Thanks for your feedback.  I'm no great malacologist.  In fact I'm not a biologist at all (except for the mathematics of biodiversity).  I just love the little lemon-shaped shells that Trivia has.  One day I will add a photo.  Best wishes, Robinh 13:21, 9 May 2007 (UTC)

Cfd for Category:Cryptic animals
Hi Robinh, I've nominated this category for deletion as virtually every animal is cryptic in some way or other. Perhaps something like Category:Crypsis would be better, if we can gather together enough articles to populate it. Our material on the subject is so scarce at the moment though; I doubt it could gather many entries. Richard001 11:40, 20 July 2007 (UTC)

Hodgson's paradox
A template has been added to the article Hodgson's paradox, suggesting that it be deleted according to the proposed deletion process. All contributions are appreciated, but this article may not satisfy Wikipedia's criteria for inclusion, and the deletion notice explains why (see also "What Wikipedia is not" and Wikipedia's deletion policy). You may contest the proposed deletion by removing the  notice, but please explain why you disagree with the proposed deletion in your edit summary or on its talk page. Also, please consider improving the article to address the issues raised. Even though removing the deletion notice will prevent deletion through the proposed deletion process, the article may still be deleted if it matches any of the speedy deletion criteria or it can be sent to Articles for Deletion, where it may be deleted if consensus to delete is reached. If you endorse deletion of the article, and you are the only person who has made substantial edits to the page, please tag it with db-author.

Binomial inverse theorem
Would you have any references to this article which you have started, esp. where is the name from, maybe the original paper, please. Or at least where you got it from. Thanks! Jmath666 07:03, 30 September 2007 (UTC)

Crypsis
Hello, I noticed you were the editor who originally provided the description currently being used at crypsis. Do you have any sources for this, or is it just based on your interpretation of the concept? The two main issues are (1) Is avoiding observation supposed to be visual only? and (2) Is crypsis as broad as this? For example is mimicry a form of crypsis, or is crypsis a different concept? I haven't researched this much myself, but it seems hard to pin down a coherent definition of these things. Richard001 01:34, 14 October 2007 (UTC)

 * I've found biological dictionaries tend to refer to it as visual only too, and they tend to use the terms 'crypsis' and 'camouflage' interchangably. I guess we'll have to change the definition of crypsis given then, though it seems there would then be no equivalent term for the broader meaning. I find dictionaries as a whole are usually inadequate at providing reliable definitions, especially for subjects that are difficult to define without lengthy explanations. I'd really like to get the pages crypsis, camouflage and the annoying cryptic coloration (which will have to be merged into one or the other) sorted out, so that's why I brought it up. Richard001 22:21, 15 October 2007 (UTC)

Aerodynamics
Hi Robinh. EMBaero is having a go at cleaning up some pages in the aerodynamics sections, so not would probably be a good time to lob in, if you're so inclined. Amongst other affected: Oblique shock, Moving shock, Shock wave, Shock dynamics, Rayleigh_flow, Fanno flow and Prandtl-Meyer_expansion_fan. Regards AKAF 15:39, 18 October 2007 (UTC)

Wikibooks?
Hi, Robinh, are you the same RobinH on Wikibooks? If so, someone needs to look into a serious COI issue, here. Astonishing that self-promotional work is a featured book!! Sandy Georgia (Talk) 05:53, 2 December 2007 (UTC)

Vandemonde's formula
Hi Robinh. I proposed to merge Your article Vandemonde's formula with Vandermonde's identity. The discussion is at Talk:Vandermonde's identity. —Leo Laursen ( T ¦ C ) 17:43, 30 January 2008 (UTC)

Colin Roberts
A proposed deletion template has been added to the article Colin Roberts, suggesting that it be deleted according to the proposed deletion process. All contributions are appreciated, but this article may not satisfy Wikipedia's criteria for inclusion, and the deletion notice should explain why (see also "What Wikipedia is not" and Wikipedia's deletion policy). You may prevent the proposed deletion by removing the  notice, but please explain why you disagree with the proposed deletion in your edit summary or on its talk page. Also, please consider improving the article to address the issues raised. Even though removing the deletion notice will prevent deletion through the proposed deletion process, the article may still be deleted if it matches any of the speedy deletion criteria or it can be sent to Articles for Deletion, where it may be deleted if consensus to delete is reached. If you agree with the deletion of the article, and you are the only person who has made substantial edits to the page, please add  to the top of Colin Roberts. Jasynnash2 (talk) 09:02, 10 April 2008 (UTC)

Minimax
Hey--I'm removing your recent edit to Minimax, because it's more confusing than helpful in the current state. I'm not sure the best way to deal with it. Possibly get more specific in the assumptions for the theorem? Cretog8 (talk) 22:26, 29 May 2008 (UTC)

I added the condition to the theorem that it's for games with finite strategies. How does that work for you? Cretog8 (talk) 22:39, 29 May 2008 (UTC)

 * Hi Robinh. You're going beyond what I know, so I can't answer at all quickly. Maybe after I study a bit. If you're interested in games on the unit square, and there's a literature on that (so it's not original research, which it looks like it isn't), then it seems like a reasonable article to create. In terms of games with no value, the reason (for instance) Silverman's game has no value (I'm taking that at face value, haven't proven it to myself yet) is that payoffs are defined on open sets and are discontinuous. It's getting into different territory than Minimax and Nash equilibrium which were primarily addressed to finite strategy games. Um, so I'm not sure where I'm going with all this. It's possible that someone at the game theory project would have some input. I'll be happy to look at any new article you create. I might be a good semi-ignorant test audience. Cretog8 (talk) 17:06, 30 May 2008 (UTC)

 * Hi Robinh (just Robin?). I think I was getting various ideas crossed in my head; Silverman's game does not imply it has no value. The stub there definitely wants some work, though. It doesn't describe any solutions to the game. Also, it might be that it's possible to model it as being on the unit square, but it looks like the current definition is on $$\Re^2_+$$. Cretog8 (talk) 16:55, 2 June 2008 (UTC)

 * Hey--Minimax as it stands right now is kinda a mess, a disorganized jumble of different applications of the notion of minimax. It probably wants a major re-write. Thinking about how to do that makes my head hurt. I'm new enough to wiki-ness that I'm not sure if a separate article on the minimax theorem would be appropriate. Maybe some advice at Cretog8 (talk) 11:42, 3 June 2008 (UTC)
 * I don't feel like it's particularly important to provide counterexamples to the minimax theorem. That's mostly because I think the theorem is pretty clear about its limitations. Not sure... Possibly in a nontechnical part there could be counter-examples for those who want to get the gist of the theorem but don't want to think math. Cretog8 (talk) 11:52, 3 June 2008 (UTC)

Dreaming spires
Hi Robin. How goes it in Cambridge's ivory towers? Has your turn to The Dark Side paid off yet? I hope so. Have they granted you any special powers yet? Sith statistics perhaps? Anyway, I just spotted that you've been editing demerara - any chance of getting hold of your recipe for tablet? ;-) Best regards, --P LUMBAGO  13:07, 9 September 2008 (UTC)

 * Hello mate. Well things are settling down here . . . although I would characterize economics as the Dismal Science, certainly in the field of climate mitigation.   As for special powers, I am hoping to procure a working computer before my contract expires.  Heh.  My main problem is selling my house in Romsey.  Wanna buy it?   On another matter, are you going to the Tyndall Assembly tomorrow?  Robinh (talk) 13:15, 9 September 2008 (UTC)

 * Sadly not. I'm stuck here for the time being.  My contract's up in a few weeks time, so I'm scrambling around trying to finish bits and bobs of work off.  I'm hopefully going to be interviewed for a position here before the end, but we'll see.  Failing that, Bob seems to be in the business of conjuring up money.  And failing that, there's always Sainsburys!  The Christmas rush is doubtless coming up, so they'll need extra staff.  ;-)  Anyway, as the foregoing implies, I'm afraid property ownership is not something I'm considering in the immediate future.  Good luck selling your place off.  Do your Dark Side colleagues have any pertinent advice on that front?  One would presume that it's their bread and butter.  Cheers, --P LUMBAGO  13:26, 9 September 2008 (UTC)

Typo Eradication Advancement League
Recreated at User:Robinh/sandbox. Let me know if you have any questions/comments or need help. seicer | talk  | contribs  04:10, 30 September 2008 (UTC)

Mathematical notation

 * Incorrect: k-1
 * Better but still incorrect: k-1
 * Better still but not yet correct: k - 1
 * Correct: k − 1

All four next to each other:
 * k-1
 * k-1
 * k - 1
 * k − 1

Please see Manual of Style (mathematics). Michael Hardy (talk) 08:13, 28 November 2008 (UTC)

Re: Generalization of Lambert W function
Hello Robin

Thanks about your comments concerning the generalization to the Lambert W function. Will do. I am new to this kind of forum and I could use a few pointers w.r.t. adding and editing articles and/or discussion threads. When it came to pointing out that an article was incomplete, I was following the guidelines and posted a comment on the discussion forum.

best wishes

Tony —Preceding unsigned comment added by 76.21.16.147 (talk) 20:52, 5 December 2008 (UTC)

Re: necklace
I first thought I should change the first necklace appearance to Necklace (combinatorics), but then decided that the math context is really different, so "see also" section was a compromize... Mhym (talk) 22:08, 5 December 2008 (UTC)

Consensus division
I intend turning Consensus division into a disambiguaion page for the reasons in Talk:Consensus division. Dmcq (talk) 11:35, 31 December 2008 (UTC)

Latin hypercube (combinatiorics)
Sorry, I didn't know you were going to create that article, or I would not have reverted the edit. Sorry! Next time, put that you're going to create the article in the edit summary please.

Thanks and sorry,

-Axmann8  ( Talk )  10:48, 20 March 2009 (UTC)

Type III Sum of Squares
I realize that it's been over a year since you made this edit, but what is your basis for calling Type III SS "a discredited technique formerly used in statistics?" Admittedly, I'm only a first year Masters student, but nothing that I've seen thus far supports that claim. —Preceding unsigned comment added by Cjh57 (talk • contribs) 05:58, 1 April 2009 (UTC)

Edit war possibility at Mathematical coincidence
I see that you were around at the beginning (originated) article, are still here, and communicated intensively with the contributor of my pet coincidence (from among those on the page at present). I thought I would tell you about the current threat and ask if MrHumperdink provided the sourcing of pi^4+pi^5~=e^6 that appeared in the article ("personal communication by...") temporarily. Some think that attribution of a print source is a requirement, but I think the standard should be that it's only a preference. In any case, personal communications are a form of attribution at least, though not of notability necessarily.Julzes (talk) 06:49, 28 May 2009 (UTC)

Just to let you know: WP:OR's exception on routine calculations refers to the sources of the numbers used in calculations, and I am reasoning that the sources, as far as that goes, are the numbers themselves, as opposed to cases where a number has some other meaning as a datum (birthday, weight of something, etc.).Julzes (talk) 09:40, 28 May 2009 (UTC)

Found net reference (Ph.D. from CalTech :) ). zhurnaly.com/cgi-bin/wiki/CoincidentalTaxonomy.Julzes (talk) 13:38, 29 May 2009 (UTC)

Something you might appreciate
Howdy. How go things over in the city of dreaming spires and ivory towers? Hopefully all well. Things here pass more or less as usual. Sooner or later someone will find out that I'm a charlatan! ;-) Anyway, I came across this and thought that you'd appreciate it.  Actually, I imagine that many in the community might find it both amusing and rather apposite.  Best regards, --P LUMBAGO  08:20, 20 July 2009 (UTC)

Hi there! great to hear from you, and I enjoyed the link very much; a peculiar conjugation of Godwin's law! I don't know about dreaming spires or ivory towers...more like dozy roofs and dreary garretts! Could we talk by email? google me by name and "Cambridge". Best wishes, Robinh (talk) 07:51, 22 July 2009 (UTC)

Most-perfect magic square (4)
Dear Robinh, how are you? I had some new ideas about most-perfect magic squares and generated some at fr:talk:Carré magique plus que parfait. I beleive that the number of squares of order n is

 * $$2^n \cdot (\frac{n}{2}!)^2 \cdot \prod_{k=1}^{M} \binom {2 \cdot e_k}{e_k}$$

when

 * $$n=p_1^{e_1} \cdot \ldots \cdot p_M^{e_M} = \prod_{k=1}^{M} p_k^{e_k}$$, $$p_i$$ < $$p_j$$ for i < j

as mentioned at de:talk:Vollkommen perfektes magisches Quadrat. For n = 36 = 2^2 * 3^2 this is 1.01406E+44 and not 2.7E+44 essentially different as mentioned in the article.

 * Do you have some possibilities to verify the figures?
 * Do you have the book written by Kathleen Ollerenshaw and David Bree?
 * Do you know the book of T.V.Padmakumar, Number Theory and Magic Squares, Sura books, ISBN 9788184493214 ?

·לערי ריינהארט·T·m:Th·T·email me· 16:05, 26 July 2009 (UTC)

 * I worked on the formula. The amount of squares is

 * $$2^n \cdot (\frac{n}{2}!)^2 \cdot \beth(e_1,..., e_M)$$

 * where $$\beth(2, 2) = 786$$ and $$\beth(2, 1, 1) = 2316$$ . Best regards
 * ·לערי ריינהארט·T·m:Th·T·email me· 14:49, 6 August 2009 (UTC)

Please see also wikiversity:portal talk:Mathematics#Most-perfect magic square. Regards

·לערי ריינהארט·T·m:Th·T·email me· 01:48, 22 August 2009 (UTC)

AfD nomination of Douglas Warrick
An article that you have been involved in editing, Douglas Warrick, has been listed for deletion. If you are interested in the deletion discussion, please participate by adding your comments at Articles for deletion/. Thank you.Please contact me if you're unsure why you received this message. Abductive (reasoning) 02:24, 30 October 2009 (UTC)

needing your help
Dear Robinh; please take a look at project talk:WikiProject Spam#ein Schildbürgerstreich. I am travelling and can neither be online nor on IRC. Thanks for your help in advance!

invitation to commons:category:Collaborative work
Dear Robinh;

I kindly invite you to participate at the development of a new game at commons:category:Collaborative work. Please take a look at the related talk page. You might be interested on some card tricks. Just look at Medias (examples). Best regards Gangleri

·לערי ריינהארט·T·m:Th·T·email me· 10:43, 7 November 2009 (UTC)

Unreferenced BLPs
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Proposed deletion of Game of Mr Paint and Mrs Correct

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Help with covariance matrix
I noticed that you made the change in the covariance article regarding Complex Random Vectors. You stated that "The matrix so obtained will be Hermitian positive definite." Do you have any prove that the matrix in fact will be positive definite? Do you know any books or other references for this? I've been cracking my head to think if it's actually positive definite or just positive semidefinite, like any other covariance matrix from real valued vectors. Felipe (talk) 19:36, 7 July 2010 (UTC)

Cross-covariance
I'm sorry for the messages, but I just can't see the trivial prove to the statement. I've been trying a lot of things and can't seem to figure it out. If you could really help me I would gladly appreciate it. Also, would it apply to cross-covariance matrices (between two different complex random vectors)? Or it's positive definitive only for the case of the a vector with itself? Felipe (talk) 21:29, 7 July 2010 (UTC)

Citation from long ago: Polaris
Hi, I'm looking for a citation for a change you added a very long time ago... in 2004. It was on changes in brightness to the North star (Polaris) and you said it was from Science, but I tried searching in the Science archives and I didn't find anything. You wouldn't happen to remember any information that would help me track it down? Thanks, Lepidoptera (talk) 00:56, 13 December 2010 (UTC)

Leopard on PowerPC?
Hello,

I just noticed your post recently on the Computing RefDesk. It says you have Leopard running on a PowerPC. I was unaware that was even possible - I thought Leopard was for Intel-only machines. Can you confirm this? Also, is there anything extra-special that needs to be done to get this to work? I have Tiger on my G3 PPC iBook, but wouldn't mind trying Leopard (I really doubt it would work, though). Cheers. -- KägeTorä - (影虎) (TALK) 20:13, 6 January 2011 (UTC)

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Nomination of Hugh Howitt for deletion
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Talkback
 Rcsprinter  (talk)  12:00, 22 July 2011 (UTC)

Applications of Bochner's theorem
Hi,

the articles Bochner's theorem and positive-definite function contain an (almost identical) paragraph about statistical applications, which I think you wrote. Could you please provide a reference?

Thank you very much, Sasha (talk) 18:47, 25 August 2011 (UTC)

Proposed deletion of Buckle bunny

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Nomination of Buckle bunny for deletion
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Proposed deletion of Journal of Mundane Behavior

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 * Journal that existed only briefly without leaving much of a trace.

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Nomination of Journal of Mundane Behavior for deletion
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Need your advice/help
Hello! I hope you are well. I need your help. I face a peculiar problem which forces me to contact you rather anonymously rather than the wiki userid I have been using for years (I'll explain). If you recall, I had contacted you w.r.t. a generalization of the Lambert W function and you recommended that I be bold. I showed you the papers and made the changes to the site according to your suggestions/directives. Since then, a lot of good work has been done w.r.t. that generalization with positive updates. It has been cited and used in fundamental Physics. It has even been cited by the very so-called "owners" of that function e.g. Rob Corless and D. Jeffries for the better. This is all well and good and positive and I thank you. However, I now face a peculiar problem namely a self-appointed vigilante who calls himself "HelpUsStopSpam", a fanatic with an issue concerning ResearchGate but whose major contributions consist in tearing down wikipedia contribution to shreds because he views anything he does not like as "spam". He often quotes Wikipedia's policy of self-citation and he removes without proof that the wiki userid is indeed making a self-citation to remove said citation and contribution. The Conflict of interest policy (COI) in wikipedia clearly states: "Using material you have written or published is allowed within reason, but only if it is relevant, conforms to the content policies, including WP:SELFPUB, and is not excessive. Citations should be in the third person and should not place undue emphasis on your work. When in doubt, defer to the community's opinion." However, he ignores agreements made with other editors, like the one we had, and just cuts away. This is why I am contacting you, this self-appointed vigilante looks at my list of contributions and applies his own criteria as a means of cutting away the contributions, I and others, have built over the years! This is why I am contacting you anonymously. His talk-page is filled of complaints from others in this regard but he just ignores them. I have myself bogged down in some kind of editor warfare. In my defense, he is the aggressor and I (and others) am the defender. He uses his own criteria way above and beyond Wikipedia's expressed policies like citations without understanding that e.g. impact factors change from IT to Science to Mathematics. The trouble is I don't want to break e.g. the 3-revert rule, etc... A part of me wants to lodge a complaint with the Wikipedia administrators but I fear this could backfire. I do not want to appear as the aggressor. A few questions, if I may? Part of the problem is that agreements on talk page can be erased over time. Ours is still there for the W function but some editing over the years has been applied to other sites (this vigilante started in early 2016). Is there something like a statute of limitations w.r.t. Wikipedia entries? I.e. you should not be allowed to veto or cut or remove changes done in previous years because policies change over time? What are my options?
 * I also think this "HelpUsStopSpam" is a bit dangerous for Wikipedia. E.g. He has this openly professed "jihad" against ResearchGate, he has added fuel to the fire on the Wiki site for ResearchGate just recently. ResearchGate faces criticisms but Wikipedia is not one of the players against ResearchGate in current and past lawsuits but "HelpUsStopSpam" insists on forcing his own point of view here (and on all of Wikipedia). I submit Wikipedia has to remain objective and remain outside of such disputes.  I know this sounds subjective but in a way he reminds me of Harry Potter's evil Dolores Umbridge except that Dolores was empowered to do as she did.  I cannot see how "HelpUsStopSpam" is empowered apart from being just another wiki editor - sorry to say.  He is not an administrator but he acts as if he was.  He seems to act as if he was the grim reaper.

Group theory question
Thanks for asking your RD/MA question. It's been a couple of decades since the modicum of algebra I studied, so I enjoy pondering those questions which show up on the ref desk and appear to be within the scope of my limited subject knowledge. After pondering on your question for a while I was just about to give up and ask you what the explicit isomorphism was when the very simple and obvious answer struck me. I then wondered if you made the connection to Parity bit. Cheers! -- ToE 01:34, 19 December 2017 (UTC)

Ways to improve Akivis algebra
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Wasysym moved to draftspace
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Median of Chi-square distribution
Back in '04 you contributed this formula. Do you know where it came from? Dicklyon (talk) 01:54, 15 August 2020 (UTC)

Rearranged parallelepiped
On the parallelepiped page, I renamed lexicography to etymology and rearranged things with the aim to make it more readable. Feel free to take a look and adjust. 'wɪnd (talk) 11:00, 19 May 2022 (UTC)

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text:
Richardson number

The Richardson number (Ri) is named after Lewis Fry Richardson (1881–1953). It is the dimensionless number that expresses the ratio of the buoyancy term to the flow shear term:

\mathrm{Ri} = \frac{\text{buoyancy term}}{\text{flow shear term}} = \frac{g}{\rho} \frac{\partial \rho/\partial z}{(\partial u / \partial z)^2} $$

where $$g$$ is gravity, $$\rho$$ is density, $$u$$ is a representative flow speed, and $$z$$ is depth.

The Richardson number, or one of several variants, is of practical importance in weather forecasting and in investigating density and turbidity currents in oceans, lakes, and reservoirs.

When considering flows in which density differences are small (the Boussinesq approximation), it is common to use the reduced gravity g'  and the relevant parameter is the densimetric Richardson number

\mathrm{Ri} = \frac{-\partial g'/\partial z}{(\partial u / \partial z)^2} $$

which is used frequently when considering atmospheric or oceanic flows.

If the Richardson number is much less than unity, buoyancy is unimportant in the flow. If it is much greater than unity, buoyancy is dominant (in the sense that there is insufficient kinetic energy to homogenize the fluids).

If the Richardson number is of order unity, then the flow is likely to be buoyancy-driven: the energy of the flow derives from the potential energy in the system originally.

Aviation
In aviation, the Richardson number is used as a rough measure of expected air turbulence. A lower value indicates a higher degree of turbulence. Values in the range 10 to 0.1 are typical, with values below unity indicating significant turbulence.

Thermal convection
In thermal convection problems, Richardson number represents the importance of natural convection relative to the forced convection. The Richardson number in this context is defined as

\mathrm{Ri} = \frac{g \beta (T_\text{hot} - T_\text{ref})L}{V^2} $$

where g is the gravitational acceleration, $$\beta$$ is the thermal expansion coefficient, Thot is the hot wall temperature, Tref is the reference temperature, L is the characteristic length, and V is the characteristic velocity.

The Richardson number can also be expressed by using a combination of the Grashof number and Reynolds number,

\mathrm{Ri} = \frac{\mathrm{Gr}}{\mathrm{Re}^2}. $$

Typically, the natural convection is negligible when Ri < 0.1, forced convection is negligible when Ri > 10, and neither is negligible when 0.1 < Ri < 10. It may be noted that usually the forced convection is large relative to natural convection except in the case of extremely low forced flow velocities. However, buoyancy often plays a significant role in defining the laminar–turbulent transition of a mixed convection flow. In the design of water filled thermal energy storage tanks, the Richardson number can be useful.

Meteorology
In atmospheric science, several different expressions for the Richardson number are commonly used: the flux Richardson number (which is fundamental), the gradient Richardson number, and the bulk Richardson number.

 * The flux Richardson number $$Ri_{f}$$ is the ratio of buoyant production (or suppression) of turbulence kinetic energy to the production of turbulence by shear. Mathematically, this is:

Ri_{f} = \frac{(g/T_{v}) \overline{w' \theta'}}{\overline{u' w'} \frac{\partial \overline{u}}{\partial z} + \overline{v' w'} \frac{\partial \overline{v}}{\partial z}} $$, where $$T_{v}$$ is the virtual temperature, $$\theta_{v}$$ is the virtual potential temperature, $$z$$ is the altitude, $$u$$ is the $$x$$ component of the wind, $$v$$ is the $$y$$ component of the wind, and $$w$$ is the $$z$$ (vertical) component of the wind. A prime (e.g. $$w'$$) denotes a deviation of the respective field from its Reynolds average.

 * The gradient Richardson number $$Ri_{g}$$ is arrived at by approximating the flux Richardson number using "K-theory". This results in:

Ri_{g} = \frac{(g/T_{v}) \frac{\partial \theta_{v}}{\partial z}}{(\frac{\partial u}{\partial z})^2 + (\frac{\partial v}{\partial z})^{2}} $$.

 * The bulk Richardson number $$Ri_{b}$$ results from making a finite difference approximation to the derivatives in the expression for the gradient Richardson number, giving:

Ri_{b} = \frac{(g/T_{v0})\Delta \theta_{v} \Delta z}{(\Delta u)^2 + (\Delta v)^2} $$. Here, for any variable $$f$$, $$\Delta f := f_{z1} - f_{z0}$$, i.e. the difference between $$f$$ at altitude $$z1$$ and altitude $$z0$$. If the lower reference level is taken to be $$z0=0$$, then $$u_{z0}=v_{z0}=0$$ (due to the no-slip boundary condition), so the expression simplifies to:

Ri_{b} = \frac{(g/\theta_{v0})(\theta_{vz1} - \theta_{v0})z}{(u_{z1})^2 + (v_{z1})^{2}} $$.

Oceanography
In oceanography, the Richardson number has a more general form which takes stratification into account. It is a measure of relative importance of mechanical and density effects in the water column, as described by the Taylor–Goldstein equation, used to model Kelvin–Helmholtz instability which is driven by sheared flows.

 * $$\mathrm{Ri} = \frac{N^2}{(\mathrm{d}u/\mathrm{d}z)^2} $$

where N is the Brunt–Väisälä frequency and u the wind speed.

The Richardson number defined above is always considered positive. A negative value of N² (i.e. complex N) indicates unstable density gradients with active convective overturning. Under such circumstances the magnitude of negative Ri is not generally of interest. It can be shown that Ri < 1/4 is a necessary condition for velocity shear to overcome the tendency of a stratified fluid to remain stratified, and some mixing (turbulence) will generally occur. When Ri is large, turbulent mixing across the stratification is generally suppressed.

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: Richardson number


text:
User talk:Thdenney

THDenney, the part that was "Excised" is right here - >Ethiopian_Airlines_Flight_961 WhisperToMe 02:01, 5 Mar 2004 (UTC)

title: User talk:Thdenney


text:
Scotts Bluff National Monument

Scotts Bluff National Monument is located west of the City of Gering in western Nebraska, United States. This National Park Service site protects over 3,000 acres of historic overland trail remnants, mixed-grass prairie, rugged badlands, towering bluffs and riparian area along the North Platte River. The park boasts over 100,000 annual visitors.

The monument's north bluff is named after Hiram Scott, who was a clerk for the Rocky Mountain Fur Company and died near the bluff in 1828. The bluff served as an important landmark on the Oregon Trail, California Trail and Pony Express Trail, and was visible at a distance from the Mormon Trail. Over 250,000 westward emigrants passed by Scotts Bluff between 1843 and 1869. It was the second-most referred to landmark on the Emigrant Trails in pioneer journals and diaries.

Scotts Bluff County and the city of Scottsbluff, Nebraska, were named after the landmark.

Geography
Although called "Scotts Bluff National Monument," the site includes two separate bluffs, "South Bluff" and the northern bluff called "Scotts Bluff." There are five major outcroppings on the bluffs, known as Dome Rock, Crown Rock, Sentinel Rock, Eagle Rock and Saddle Rock. The area between Scotts Bluff and the North Platte River is known as the "Badlands."

Charting the landmark
The collection of bluffs was first charted in 1812 by the Astorian Expedition of fur traders traveling along the river. The expedition party noted the bluffs as the first large rock formations along the North Platte River where the Great Plains started giving way to the foothills of the Rocky Mountains. Their findings were not widely communicated because of the War of 1812. Explorers rediscovered the route to the Rocky Mountains in 1823, and fur traders in the region relied on the bluffs as a landmark. European Americans named the north, and most prominent bluff, after Hiram Scott, a fur trader who died in 1828 near the bluffs. The local Native Americans had called it Me-a-pa-te, "the hill that is hard to go around."

Emigrant trail landmark
Fur traders, missionaries, and military expeditions began regular trips past Scotts Bluff during the 1830s. Beginning in 1841, multitudes of settlers passed by Scotts Bluff on their way west along the Great Platte River Road to Oregon, and later California and Utah. All these groups used the bluff as a major landmark for navigation.

Although a natural gap existed between South Bluff and Scotts Bluff, the area was not easily traversed. So initially the Oregon Trail passed to the south of the Scotts Bluff area at Robidoux Pass and the Mormon Trail passed to the north of the bluff, on the other side of the North Platte River. In the early 1850s a road was constructed in the gap, which later became known as Mitchell Pass. Beginning in 1851, this new passage became the preferred route of the Oregon and California Trails; although the Mormon Trail continued to pass the bluff only at a distance. Who built the road through Mitchell Pass about 1850 is unknown, although one possibility includes soldiers from Fort Laramie. Many emigrants preferred this route rather than trying to traverse the badlands on the north side of the bluffs or detouring south to the older trail at Robidoux Pass. Use of the Emigrant Trail tapered off in 1869 after the trail was superseded by the completion of the transcontinental railroad.

Settlement in the Scotts Bluff area
The town of Gering, Nebraska, was founded near the base of the bluff in 1887, and the city of Scottsbluff was founded across the North Platte River from the bluff in 1900. Separated (or joined) by the river, the two cities have since grown together and now form the 6th-largest urban area in Nebraska.

Once permanent settlements had been established nearby, residents and travelers went to the bluff as a destination because of its extensive views of the flat land stretching to the east, the hills and mountains to the west, and the river valley in between. Developers built various trails up the bluff over the years, but most were precarious and dangerous. In the early 20th century, the National Park Service constructed a safer, more modern trail for improved access.

National Monument
The Department of Interior designated Scotts Bluff and several nearby bluffs as a National Monument on December 12, 1919; they were placed for management under the National Park Service, created just three years prior.

The Oregon Trail Museum and Visitor Center was built at the base of the bluff which serves as a start for hiking tours of the bluffs. Exhibits focus on the westward expansion and pioneers, the drawings and paintings of William Henry Jackson, and the geology and paleontology of the region.

In the 1930s, a roadway leading to the top of Scotts Bluff was constructed by the Civilian Conservation Corps, organized by President Franklin D. Roosevelt's administration. The road goes through three tunnels on its way to the top and provides easy access to the summit.

All historic sites administered by the National Park Service were listed on the National Register of Historic Places on October 15, 1966, when it was established.

The naming of Scotts Bluff
According to Washington Irving, around 1825 a fur trapping party was “descending the upper part of the (Nebraska) River in canoes when their frail barks were overturned and all their powder spoiled. Their rifles being thus rendered useless they were unable to procure food by hunting and had to depend upon roots and wild fruits for subsistence. After suffering extremely from hunger, they arrived at Laramie’s Fork, a small tributary of the north branch of the Nebraska, about sixty miles above the cliffs just mentioned. Here, one of their party by the name of Scott was taken ill; and his companions came to a halt, until he should recover health and strength sufficient to proceed. While they were searching round in quest of edible roots they discovered a fresh trail of white men, who had evidently but recently preceded them. What was to be done? By a forced march they might overtake this party, and thus be able to reach the settlements in safety. Should they linger they might all perish of famine and exhaustion. Scott, however, was incapable of moving; they were too feeble to aid him forward, and dreaded that such a clog would prevent them coming up with the advance party. They determined, therefore, to abandon him to his fate. Accordingly, under pretense of seeking food, and such simples as might be efficacious in his malady, they deserted him and hastened forward upon the trail. They succeeded in overtaking the party of which they were in quest, but concealed their faithless desertion of Scott; alleging that he had died of disease.

“On the ensuing summer, these very individuals, visiting these parts in company with others, came suddenly upon the bleached bones and grinning skull of a human skeleton, which by certain signs, they recognized for the remains of Scott. This was sixty long miles from the place where they had abandoned him; and it appeared that the wretched man had crawled that immense distance before death put an end to his miseries. The wild and picturesque bluffs in the neighborhood of his lonely grave have ever since borne his name.”

Another version of the legend portrays Scott's companions in more favorable terms: "A melancholy tradition accounts for the name of this spot. A party who had been trading with the Indians were returning to the States and encountering a band of hostile savages, were robbed of their peltries and food. As they struggled homeward, one of the number, named Scott, fell sick and could not travel. The others remained with him, until the sufferer, despairing of ever beholding his home, prevailed on his companions to abandon him. They left him alone in the wilderness, several miles from this spot. Here human bones were afterwards found; and, supposing he had crawled here and died, the subsequent travelers have given his name to the neighboring bluff."

Proper spelling
There has always been some disagreement as to the proper spelling of this geomorphic feature, specifically with regard to the apostrophe. For example, an 1843 map titled Map of an Exploratory Expedition to the Mountains in 1842 by John C. Frémont labeled the feature Scott's Bluff (with an apostrophe). Another early military map of Nebraska and the Dakotas published in 1875 by G.K. Warren dropped the apostrophe and labeled the feature simply as Scotts Bluff. There are numerous other examples in the late 19th and early 20th centuries in which the name has been spelled with or without an apostrophe. In a final decision by the United States Board on Geographical Names rendered on June 11, 1941, the name Scotts Bluff (without an apostrophe) was officially adopted. The nearby town of Scottsbluff is spelled as one word.

Geology
The oldest rocks visible within the monument are the Oligocene siltstones and mudstones of the Orella Member of the Brule Formation. The overlying Whitney Member in the same formation has volcaniclastic siltstones originating from volcanic centers to the west. An unconformity separates the Brule from the overlying Gering Formation, composed of fluvial sediments. Next in the geologic sequence is the Miocene Monroe Creek–Harrison Formations that include eolian features such as cross-bedding and ripple marks. These formations include the caprock, composed of hard, lime-cemented ledges called “pipy” concretions formed when calcium carbonate (lime) precipitated from groundwater.

Trails at the Monument
Summit Trails

The North Overlook Trail is a 0.5 mi paved trail that leaves from the summit parking lot and overlooks the North Platte River Valley. Visitors can reach the highest point on the bluff at 4659 ft above sea level.

The South Overlook Trail is a 0.4 mi paved trail that leaves from the summit parking lot towards the south. From the overlook, visitors can see the Visitor Center and Mitchell Pass.

Saddle Rock Trail begins at the Visitor Center and climbs 435 ft in 1.6 mi. The first third of the trail is relatively level from the Visitor Center to Scott's Spring. From here, the trail climbs rapidly most of the 435 ft in 0.8 mi to the summit parking lot.

The Oregon Trail Pathway is a short trail ascending 85 ft in 0.5 mi. The trail begins at the display of a Murphy and Conestoga wagons and ends in Mitchell Pass.

The Bike Path is the only trail available to users other than hikers. It runs from the Visitor Center to the eastern boundary of the park. It drops 50 ft in 1.2 mi.

Legacy
Scotts Bluff County and the city of Scottsbluff were named after the landmark.

During World War II, the United States built hundreds of T2 oil tanker ships and named many of them after national monuments. The SS Scotts Bluff was built in 1944, served in the war, and then its name was changed when it was sold to France in 1948.

title: Scotts Bluff National Monument


text:
Boussinesq approximation (buoyancy)

In fluid dynamics, the Boussinesq approximation (, named for Joseph Valentin Boussinesq) is used in the field of buoyancy-driven flow (also known as natural convection). It ignores density differences except where they appear in terms multiplied by $g$, the acceleration due to gravity. The essence of the Boussinesq approximation is that the difference in inertia is negligible but gravity is sufficiently strong to make the specific weight appreciably different between the two fluids. Sound waves are impossible/neglected when the Boussinesq approximation is used since sound waves move via density variations.

Boussinesq flows are common in nature (such as atmospheric fronts, oceanic circulation, katabatic winds), industry (dense gas dispersion, fume cupboard ventilation), and the built environment (natural ventilation, central heating). The approximation is extremely accurate for many such flows, and makes the mathematics and physics simpler.

The approximation
The Boussinesq approximation is applied to problems where the fluid varies in temperature (or composition) from one place to another, driving a flow of fluid and heat transfer (or mass transfer ). The fluid satisfies conservation of mass, conservation of momentum and conservation of energy. In the Boussinesq approximation, variations in fluid properties other than density $ρ$ are ignored, and density only appears when it is multiplied by $g$, the gravitational acceleration. If $u$ is the local velocity of a parcel of fluid, the continuity equation for conservation of mass is
 * $$ \frac{\partial\rho}{\partial t} + \nabla\cdot\left(\rho\mathbf{u}\right) = 0.$$

If density variations are ignored, this reduces to

The general expression for conservation of momentum of an incompressible, Newtonian fluid (the Navier–Stokes equations) is
 * $$\frac{\partial \mathbf{u}}{\partial t} + \left( \mathbf{u}\cdot\nabla \right) \mathbf{u} = -\frac{1}{\rho}\nabla p + \nu\nabla^2 \mathbf{u} + \frac{1}{\rho}\mathbf{F},$$

where $$ (nu) is the kinematic viscosity and $F$ is the sum of any body forces such as gravity. In this equation, density variations are assumed to have a fixed part and another part that has a linear dependence on temperature:
 * $$\rho = \rho_0 - \alpha\rho_0(T-T_0),$$

where $ν$ is the coefficient of thermal expansion. The Boussinesq approximation states that the density variation is only important in the buoyancy term.

If $$F = \rho \mathbf{g}$$ is the gravitational body force, the resulting conservation equation is

In the equation for heat flow in a temperature gradient, the heat capacity per unit volume, $$\rho C_p$$, is assumed constant and the dissipation term is ignored. The resulting equation is

where $α$ is the rate per unit volume of internal heat production and $$k$$ is the thermal conductivity.

The three numbered equations are the basic convection equations in the Boussinesq approximation.

Advantages
The advantage of the approximation arises because when considering a flow of, say, warm and cold water of density $ρ_{1}$ and $ρ_{2}$ one needs only to consider a single density $$: the difference $Δρ = ρ_{1} − ρ_{2}$ is negligible. Dimensional analysis shows that, under these circumstances, the only sensible way that acceleration due to gravity $$ should enter into the equations of motion is in the reduced gravity $J$ where

 * $$g' = g\frac{\rho_1-\rho_2}{\rho}.$$

(Note that the denominator may be either density without affecting the result because the change would be of order $ρ$.) The most generally used dimensionless number would be the Richardson number and Rayleigh number.

The mathematics of the flow is therefore simpler because the density ratio $ρ_{1}⁄ρ_{2}$, a dimensionless number, does not affect the flow; the Boussinesq approximation states that it may be assumed to be exactly one.

Inversions
One feature of Boussinesq flows is that they look the same when viewed upside-down, provided that the identities of the fluids are reversed. The Boussinesq approximation is inaccurate when the dimensionless density difference $Δρ⁄ρ$ is approximately 1, i.e. $Δρ ≈ ρ$.

For example, consider an open window in a warm room. The warm air inside is less dense than the cold air outside, which flows into the room and down towards the floor. Now imagine the opposite: a cold room exposed to warm outside air. Here the air flowing in moves up toward the ceiling. If the flow is Boussinesq (and the room is otherwise symmetrical), then viewing the cold room upside down is exactly the same as viewing the warm room right-way-round. This is because the only way density enters the problem is via the reduced gravity $g$ which undergoes only a sign change when changing from the warm room flow to the cold room flow.

An example of a non-Boussinesq flow is bubbles rising in water. The behaviour of air bubbles rising in water is very different from the behaviour of water falling in air: in the former case rising bubbles tend to form hemispherical shells, while water falling in air splits into raindrops (at small length scales surface tension enters the problem and confuses the issue).

title: Boussinesq approximation (buoyancy)