text:
Talk:Rammed earth

Categories?
I'm wondering whether there should be a category called "sustainable technology" - but perhaps it would overlap too much with categories like Category:Appropriate technology & Category:Renewable energy. For the moment, I'll just use Category:Appropriate technology (which is a subcategory of Category:Development and Category:Sustainability).

In the cases of Rammed earth, Adobe & Dutch brick, I think they reasonably belong in Category:Appropriate technology. At the moment, though, the Appropriate technology aspect of these technologies is not developed in the articles. Anyway, feel free to make a different edit or suggestion.

btw, Mudbrick needs either a lot of work, or to be merged with the Adobe article.

(I posted this comment also on Talk:Adobe) --Singkong2005 03:04, 17 February 2006 (UTC)

 * I know what you mean. A friend of mine visited a rammed earth build in Scotland where the cold and rain had turned most of the site into a muddy quagmire. Given the (normally) high cost of labour in the UK, you could argue that it is most inappropriate technology here, but it still has the sustainability advantages.
 * Categorisation can get quite tricky in the fine details. You really need to find a group of like-minded editors to help sort out the best categorisation structure and then place articles appropriately. A good approach can be to setup a WikiProject on Green Building or the like, to help coordinate activity. Another thing to consider is that articles and list-type articles can also be a useful way of organising related articles and also have the advantage that subtleties can be explained along the way. For example, we don't appear to have an article on sustainable technology, which might be a good start. -- Solipsist 07:53, 17 February 2006 (UTC)

 * Thanks. Maybe the varying things I've read about lifespan of these materials reflects the different environments they were in.
 * I've started the sustainable technology article. --Singkong2005 03:08, 21 February 2006 (UTC)

Green building section merger proposal
User:Lean greener has made significant contributions to the Rammed Earth Construction section of the Green building article. I suggest that that content would be better located here, with a paragraph left behind in the Green building article. Is there any agreement?

User:xxxMicrobexxx I started this article - ironically exactly 3 years ago to the day, March 8th 2004. It seems that the item at Green Building is pretty much a duplication of what is here with a few other pieces of information. Obviously it is preferable to have all the info in one place. Go for it.

With the support of User:xxxMicrobexxx above, User:Greener72 on the Green building talk page and User:Lean greener on his talk page, I have merged the Rammed earth section from Green building into this article.--Jrsnbarn 15:29, 20 March 2007 (UTC)

Old buildings
I'd like examples of old buildings (with pics) still standing with discussion of how they aged. Has this been used for some interesting old palace or mosque or something like that? --84.20.17.84 08:18, 21 September 2007 (UTC)

Hmm...
The current introduction says:
 * Rammed earth construction, also known as pisé de terre or simply pisé, is an age-old building method that has seen a revival in recent years as people seek low-impact building materials and natural building methods.

Isn't rammed earth construction, by definition, high-impact? :-D --Sneftel (talk) 16:04, 25 January 2008 (UTC)

 * Good point, that is jarring, and a bit funny. To keep an encyclopedic tone in the intro, some other phrase, like "more environmentally correct" (although I don't like that phrase either) should be substituted. doncram (talk) 20:52, 24 March 2008 (UTC)

Disagree that this is a good point. Words have different meanings according to their contexts. That's why we know that "shaving off a few points" doesn't refer to literally using a razor, and this issue is still much less likely to cause confusion. The term low-impact here clearly refers to rammed earth's low impact on the environment as a green technology. Its use in this context obviously has nothing to do with how it is formed, even though the latter involves compressing or compacting earth, especially since neither of these processes relates directly to "impact", and only one of them even has a Latin root in common with this word. So "impact" and "compact" are cousins, but are far from synonymous, since compacting is roughly synonymous with compression, but "impact" is not. I see no reason to assume that anyone would confuse these usages here. Edits-to-improve (talk) 20:57, 22 December 2008 (UTC)

Bias
This article extols the virtues of rammed earth without discussing its drawbacks or unsuitable uses to anything like the same extent. 128.232.228.174 (talk) 18:25, 21 May 2008 (UTC)

I assume you know the concept of a wiki... Xxxmicrobexxx (talk) 23:09, 1 August 2008 (UTC)

To me this is a very biased article. In addition many biased claims lack citations too. I am adding the NPOV template to this article. --Stinkypie (talk) 08:03, 16 November 2008 (UTC)

Stinkypie: Please refer to http://en.wikipedia.org/wiki/Wikipedia:NPOVD which says that 'The editor who adds the tag must address the issues on the talk page, pointing to specific issues that are actionable within the content policies' Please state which claims are biased or lack citation and for what reasons. If you fail to justify your claim, please remove the tag. —Preceding unsigned comment added by 88.91.167.196 (talk) 15:54, 24 December 2008 (UTC)

If no justification for claims of bias are made by end of February 2009 I will be removing NPOV templates Xxxmicrobexxx (talk) 06:50, 14 February 2009 (UTC)

xxxmicrobrew, you're late! —Preceding unsigned comment added by 15.203.233.80 (talk) 15:27, 13 March 2009 (UTC)

You're right. But done now Xxxmicrobexxx (talk) 10:18, 24 April 2009 (UTC)

This is quite an engrossing article, I was totally absorbed by the descriptions of rammed earth construction's strength, cheapness and environmentally friendly advantages. However I also say the article is fairly biased too. Particularly, sometimes the article seems to be stating rammed earth with cement combinations are inferior, and also says rammed earth is looked down upon compared to more 'modern' materials. —Preceding unsigned comment added by 123.243.30.245 (talk) 13:07, 10 February 2010 (UTC)

 * The examples of rammed-earth structures are drawn almost entirely from North America and the same goes for the studies cited. I have included a reference to Craterre in the See also list.

Everybody got to be somewhere! (talk) 13:08, 5 April 2021 (UTC)

Stylistic issues
The Green section has much information that is useful in an encyclopedic context, but does not present it in an encyclopedic style. Additionally, parts of the article delve into too much howto-level detail. I don't necessarily think that any information should be deleted; reorganizing and rewriting to maintain NPOV and encyclopedic style should be enough. 75.140.243.0 (talk) 08:24, 14 November 2008 (UTC) As well, it is very convoluted and repeats itself frequently, hard to read or make sense of.

some material removed
I removed a bit of material that is not really encyclopedic to this article.

''The walls require non toxic treatments and have no risk of off-gassing toxic fumes, making it ideal for chemically sensitive dwellers. ''

''In the UK it has been suggested that a compression strength of 2N/mm² (290 pounds per square inch) should be assumed in the absence of data derived from testing of the earth that will be used. Concrete typically used in UK construction is mixed off site and has a compression strength of 12-16N/mm² (1700–2300 pounds per square inch, from a cube strength fcu = 30N/mm² to 40N/mm²), around seven times stronger than rammed earth. However, there are many factors that affect the width of a wall, so a plain concrete wall will not necessarily be much thinner than an equivalent in rammed earth. ''

it might have a place in another one. --Rocksanddirt (talk) 06:10, 14 February 2009 (UTC)

Merge taipa with rammed earth
Taipa (building material) is simply the Portuguese name for rammed earth and that article should be merged with this one. Notice the Portuguese interwiki link here at rammed earth is Taipa (material). —  AjaxSmack   23:28, 26 April 2009 (UTC)

Multiple issues
I have added Multiple issues to the article for several reasons, mainly the odd (to me) arguing style.

I see this issue has been mentioned above: topics "Bias" and "Stylistic issues" above are both still relevant. I do not know this area and I cannot copy-edit myself, so here are notes on some of the problems I found, there are probably more.

The article reads well in most parts - the lede is good for example - but enters "point of view" territory in places. The text sometimes argues the benefits of the building method with insufficient context and insufficient specific explanation. Some examples:

Overview of use section needs copyediting, examples are "Using it involves a", "making a comeback", "modern times",. The sentence starting "However the use of cement is contentious" is jarring and seems out of place for an overview, maybe move it to a section on environmental effects? The rest seems Ok but needs minor copy-editing: "more it cures ", "it is much like". The section also needs citations for the claims. The second paragraph addresses the practical aspects reasonably well but is vague in places, especially at the end.

The paragraphs after the fourth stray outside the concept of use and express a point of view with "significant benefits", "excellent", "virtually", "Depending on conditions", but with no supporting numbers.

I skimmed the rest and saw several odd phrases and vague words, a short list: "millions of dollars", "extensive", "very reasonable".

However, the section "Rammed earth in green building" is clearly written from the pro-point of view, and has dubious uncited claims - the first sentence for example. In places it reads like a brochure extolling the virtues of the method, and it definitely needs work.

-84user (talk) 20:29, 14 May 2010 (UTC)

 * Add to that the tedious repetition - how often does this article mention its thermal mass benefits? Jon (talk) 10:48, 27 June 2010 (UTC)

Zero section
In the intro it says that "traditionally" rammed earth buldings are found on every continent. The article then goes on to show a 19th century building in the US, hardly traditional, but, be that as it may, I challenge the author of that statement to find a "traditional" home or other rammed earth building in Australia. "Traditional" taken to mean "prior to colonisation".KhProd1 (talk) 12:41, 16 November 2010 (UTC)

Pound dirt
"Pounded earth has long been a construction material in human history. Chengziya was surrounded by pounded earth walls as did the Shang dynasty city of Huanbei. The colloquial saying "pound dirt" is a way of saying "get lost" as in go do something menial and tedious. Pounded earth is the base for many traditional homes."

Is this a separate subject? The same subject? OrganicEarth (talk) 18:37, 29 July 2015 (UTC)

Multiple issues (again)
I have added the Multiple Issues template again as it seems many of the things discussed above have not been resolved. First and foremost, much of the article relies on the (currently) fourth reference (named "six" for some reason), which in fact is a "research paper" assigned as part of an English 102 course (frequently American educational institutions number courses by the year they are typically taken — 100- or 1000-level for first year, 300- or 3000-level for third year, etc.) at a community college/technical school, which are not often associated with rigorous scholarship. Basically, it was written by an 18 year old as part of his first college class. It does contain some references (no links, of course), the most recent of which was a Discovery Channel show called Beyond 2000 from 1993; most of the others were from the 1950s or before. Additionally, this article cites a publication from the US Dept. of Agriculture claiming that rammed earth houses are 2/3 the cost of comparable wooden frame houses. The article neglected to mention in the text, until I added it, that said publication was from 1925. Several other references appear to be companies or other organizations with a vested interest in promoting this type of construction. Independent, unbiased, recent research citations are clearly needed. Finally, the article is absolutely full of unreferenced statements. I've been pretty liberal with the Citation Needed template — I apologize for the look it creates, but people need to realize that most of the content is unsubstantiated.

The second component of the Multiple Issues template calls into question the article's neutrality. It is clearly pushing the idea that rammed earth construction is a fantastic, inexpensive, strong, environmentally-friendly way to build anything, anywhere. Any drawbacks of the technology are either glossed over or completely ignored, with the possible exception of the discussion regarding cement's contribution to greenhouse gas emissions. Earthquake resistance is briefly mentioned in passing, as are issues with moisture/humidity, but both need to be significantly expanded upon. Structural integrity and building codes around the world need to be addressed, as do questions such as the structural impact of adding doors and windows. Longevity also needs to be critically examined — just because there is an example of a rammed earth structure that has survived in a tectonically-stable desert for thousands of years doesn't mean it's an appropriate building method in a rain forest on an active fault line, for example.

The third template I added was Expert Needed. I'll also be searching for appropriate WikiProjects to notify. Basically, this needs the attention of someone in the fields of materials science, engineering, and/or construction who can comment (and cite) more authoritatively regarding the issues discussed above. This could be a pretty good article, it just needs more and better citations and a more even, encyclopedic tone. I've tried to make some edits where I could, but unfortunately I am not an expert in this field. DadOfBeanAndBug (talk) 03:50, 3 July 2017 (UTC)

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"Citation needed" overuse
It is used 35 times throughout the article, and can be at times very annoying to read. Is there a bot we can ask that can clean it up? Silenceisgod (talk) 03:08, 12 February 2019 (UTC)

"Edifice"
Wow, whoever wrote/corrected this article sure loved to use the word "edifice." It's like, overused to be honest. Spend some time with a thesaurus, would ya?

Excuse-making
"The prevailing perception that such materials and techniques perform poorly in regions prone to earthquakes has prevented their use in much of the world.[citation needed] In Chile, for example, rammed earth edifices normally cannot be conventionally insured against damage or even be approved by the government.[citation needed]"

So, why is this "prevailing perception" wrong? Can we give the Chilean building insurance industry some credit here? If they don't insure rammed earth buildings it's probably for a damned good reason. 2001:8B0:DFDC:12BC:78D9:AC2C:119F:E76C (talk) 14:48, 29 December 2020 (UTC)

 * Studies by the French institute "Craterre" have shown that it is possible to improve the earthquake performance of rammed-earth structures. The structural modifications and techniques have been included in the technical manuals written by Craterre for UNESCO since the 1980s. Everybody got to be somewhere! (talk) 13:02, 5 April 2021 (UTC)

Cob
The article says cob is a similar material. This may be so but cob construction requires a significantly different technology. All earth construction uses similar materials, so perhaps this qualifier could be modified so that the distinction can be usefully made. Everybody got to be somewhere! (talk) 13:17, 5 April 2021 (UTC)

Question: remarkable ´World Heritage Earthen Architecture Programme´ ?
https://whc.unesco.org/en/earthen-architecture/ --Visionhelp (talk) 08:11, 1 August 2021 (UTC)

title: Talk:Rammed earth


text:
Talk:Kissing number

Contradiction of Leech lattice
"In 24 dimensions, the kissing packing places the spheres at the points of the Leech lattice and there is no space at all left over," but from Leech lattice, "It seems to be expected that this configuration also gives the densest packing of balls in 24-dimensional space, but this is still open." These don't seem to agree. Correct me if I'm wrong but this page claims that the Leech latice is the best packing of spheres in 24 dimensions but the Leech latice page says that we aren't sure yet. Which is correct? I'd wager the Leech latice page is but I've never heard of this problem before so I'm not going to change it. Can a mathematician change one of these two pages please? -- Rory ☺ 23:01, May 31, 2004 (UTC)

 * ( It sucks that this has been around for so long without being fixed. There is only an upper bound proven how much better an irregular packing could be in the 24-d case, so the article was clearly wrong. You should have removed the suspect uncited claim as thats always the safe thing to do. --71.191.135.140 (talk) 04:44, 20 September 2008 (UTC)

 * No, the two statements aren't in contradiction with each other. The Leech lattice (lambda-24) has been proven to have the highest possible _kissing number_ among all arrangements, whereas it has not been proven to have the highest _density_ among all arrangements. There is no evidence to suggest that there is a denser packing of 24-dimensional spheres, and, if there is such a packing, it can only be microscopically denser (by a factor of about 10^-30). --Calcyman (talk) 15:34, 11 April 2010 (UTC)

Ref
Could anybody give a ref to the statements in dim 8 and 24? Tosha 15:37, 8 Jul 2004 (UTC)

http://www.research.att.com/~njas/doc/interview.html says this is by Sloane/Odlyzko and V. Levenshtein, independently. Charles Matthews

It's 24! It's 24!
Just a hunch. It rests better with the factors that be. :) --mwazzap 07:50, 29 October 2005 (UTC)

It is 24
It was recently proven by Oleg Musin that in fact the kissing number in four dimensions is 24. See http://arxiv.org/pdf/math.MG/0309430 for a preprint of the article, or http://www.ams.org/notices/200408/fea-pfender.pdf to learn more about the topic.

 * I think the kissing number K(n) of an n-D Euclidean space can be found from K(n–1) by constructing n-D equilateral "triangles"; that is,

K(n)=K(n-1)+(number of admissible new vertices).

Admissible vertices are those at least one diameter apart. The approach gives K(1)=2, K(2)=6, K(3)=12, K(4)=24, but K(5)=48. The last number is larger than the reported bound. Is K(5)=48 correct? The approach also gives an upper bound as K(n)/2n < or =3/2 for large n. 209.167.89.139 16:22, 15 September 2006 (UTC)

math.MG/0608426
This preprint claims better upper bounds for 5, 6, 7, 9, and 10. Melchoir 05:32, 18 August 2006 (UTC)

One dimension ?
You can't draw circles in one dimension, right ?--George (talk) 11:03, 11 March 2008 (UTC)

 * You can have a mathematical equivalent of a circle on 1-dimensional line - it is just the two points that are the same distance either side of some central point. Algebraically, a circle on a 1-dimensional line with centre x and radius y is the two points x-y and x+y, which bound a (closed) 1-dimensional disk which is just the interval or line segment [x-y, x+y]. This is what the very first diagram in the "Known kissing numbers" section is trying to illustrate. Gandalf61 (talk) 12:06, 11 March 2008 (UTC)

Right, thanks --George (talk) 21:08, 11 March 2008 (UTC)

n = 1 to 9
MathWorld and A001116 claim that kissing numbers are known for $$n = 1$$ to $$9$$. VladimirReshetnikov (talk) 20:57, 19 December 2008 (UTC)

 * The values are known for regular arrangements of spheres in 1 to 9 dimensions, where the centres of the spheres occupy points on a lattice. Proving that the maximum kissing number for lattice arrangements is indeed the maximum kissing number for any arrangement of spheres is a much more difficult problem.

 * The maximum kissing number for any arrangement of spheres is only known in 1,2 ,3 4, 8 and 24 dimensions. In each case the best arrangement happens to be a lattice arrangement. However, we know that in 9 dimensions the best arrangement is not a lattice arrangement - the maximum lattice kissing number in 9 dimensions is 272, but a non-lattice arrangement is known with a kissing number of 306. Same applies for dimensions 10 to 14 - a non-lattice arrangement has been found with a higher kissing number than the best lattice arrangement. In 5, 6 and 7 dimensions no one has found a non-lattice arrangement that has a higher kissing number than the best lattice arrangement - but neither has it been proved that one does not exist.

 * I agree that the article could do a better job of explaining the difference between lattice and non-lattice arrangements, and could show the known results for lattice arrangements. Gandalf61 (talk) 12:36, 20 December 2008 (UTC)

 * Can anyone please reconcile or unify the table in this article and that in Wolfram? The two tables give different kissing numbers for 5≤n≤7. If K(n+1)=K(n)+[2×K(n)]/m, no integer m can be found to satisfy K(5) to K(7) in either table. Can we conject that the reported K(n) might be incorrect? Also, why has there been no answer to the question raised about a contradiction to Leech's Lattice for n=24? Thanks. Zymogen (talk) 00:32, 23 December 2008 (UTC)

 * Our table gives known values or bounds for the kissing number across all arrangements, both lattice and non-lattice. Wolfram omits the non-lattice values (column NL in their table) for dimensions 5, 6 and 7 because the highest known kissing number in those dimensions is for a lattice arrangement (column L in Wolfram). However, as I explained above, it has not been proved that this is the highest kissing number across all arrangements, so our table gives the known bounds for those dimensions - the lower bound is, of course, the highest known kissing number, and the upper bound will have been derived from geometric/volumetric arguments. The distinction between known and proven maximum kissing numbers seems to cause some confusion, so I will expand our article at some point over the next few days to give a better explanation. Gandalf61 (talk) 09:02, 23 December 2008 (UTC)

 * I appreciate your clarifications very much. If you do not mind, I would like to ask three more questions: (a) Is a triangular packing a lattice or a non-lattice pattern? (b) Is it true that all K(n) ought to be even, regardless of the pattern? (c) Rory in the first post questioned Leech's K(24) being the largest KN for that dimension. Is he correct? I think he is. Zymogen (talk) 18:53, 23 December 2008 (UTC)

 * I can answer these questions. (a) If by "triangular packing", you mean a packing where the centers of spheres lie on the vertices of a hexagonal lattice, then by definition it is a lattice packing.  (b) The answer to this question is not known.  (c) From my reading of Rory's post, I think he's actually questioning whether the Leech lattice is known to be the densest packing -- in fact it is known to be the configuration which gives the highest kissing number, which is an entirely different question, see these pages from the book by Sloane and Conway.  Akriasas (talk) 22:23, 24 December 2008 (UTC)

 * Thank you very much for your answers. (a) By "triangular packing", I mean the centers of n-D hyper-spheres lie on the vertices of n-D hyper-triangles. (b) For the aforementioned packing pattern, I think it ought to be possible to use an n-D hyper-triangle as a base to build an (n+1)-D hyper-triangle. Each base will introduce two out-of-plane apexes, one on the positive x(n+1) axis and another one on the negative x(n+1) axis. Since K(1)=2, all K(n) thereafter ought to be even. Anyway, that is just a thought. (c) Do you think a K(24) much larger than that given by Leech Lattice could exist? Zymogen (talk) 02:49, 25 December 2008 (UTC)

pi's revenge
Just for fun, I did a linear regression on the means of the logarithms of the known bounds, and got $$e^{0.451309n+1.33904}$$, which is fascinatingly close to $$3.815\left(\frac\pi2\right)^n$$. Does anyone know whether this possibility for the base of the (presumed) exponential growth has been investigated, and perhaps ruled out? --Tardis (talk) 23:30, 21 May 2009 (UTC)

 * This is interesting. How accurate are the coefficients in that regression? Is it possible that the base isn't pi/2 but, say, the Golden ratio?  The two are only off by only 3%, and phi^n would make this problem a cousin of the Fibonacci sequence. Owen×  ☎  01:18, 22 May 2009 (UTC)

 * $$e^{0.451309}=0.499863\pi$$ (to that precision, given the precision to which I gave my coefficient), which is 0.027% low. Obviously the uncertainty in my fit parameters is much larger, since I have only a few data points, most of them are estimates (the geometric means), and the inputs are integers that cannot lie exactly on any exponential.  But it's (whether by happenstance or not) a lot closer than 3% to $$\pi/2$$ .  --Tardis (talk) 19:38, 22 May 2009 (UTC)

 * You are right, it is closer to pi/2 up to n=24. But do we have reason to believe it rises exponentially at all? From n=4 to n=8, it grows proportionally to 1.7782^n, while from n=8 to n=24, it's 1.5208^n. If you go all the way to n=48 (52416000), it's 1.2621^n, which is nowhere near pi/2. Perhaps asymptotically it isn't exponential at all. Owen×  ☎  01:16, 23 May 2009 (UTC)

 * We do know that it's exponential — there are known exponential upper and lower bounds. It's just that the base of the exponent in the upper bounds is different from the one in the lower bounds, so we don't know what the correct exponential function is. π/2 seems like a very interesting guess for the correct base of the exponential. —David Eppstein (talk) 01:29, 23 May 2009 (UTC)

 * It may be easy to prove an exponential as an upper bound. I don't have any values beyond n=128, but for any range with n>24, pi/2 seems like a gross overestimate for the base, and the value for the base keeps shrinking as we move higher. If you chart the function on a log scale, you'll see it clearly growing slower than exponentially, although of course that's far from an actual proof. Owen× ☎  01:36, 23 May 2009 (UTC)
 * It is very easy to prove a 2n + 1 upper bound. Suppose one has a collection of k unit spheres, all touching a central unit sphere centered at the origin. Then each of the given spheres has at least half of its volume inside of a sphere of radius 2 centered at the origin. Therefore, the sum of the volumes of the k unit spheres is at most twice the volume of the radius-2 sphere. But the volume of a sphere scales as the nth power of its radius, so the volume of the radius-2 sphere is 2n times that of the unit sphere. Therefore, k must be at most 2n + 1, or else all the little half-spheres inside the radius-2 sphere would be bigger than the radius-2 sphere itself. —David Eppstein (talk) 02:04, 23 May 2009 (UTC) This argument isn't right (it would give √5n not 2n) but anyway Bezdek cites a tighter known bound. —David Eppstein (talk) 03:26, 23 May 2009 (UTC)

 * As I've said, an exponential upper bound is obvious. But the actual kissing number seems to rise much slower than exponential, as per my comment above. Owen× ☎  03:08, 23 May 2009 (UTC)

 * As I said above (but maybe you didn't notice), exponential lower bounds are also known. Specifically, according to Bezdek, there is a lower bound of approximately 1.1547n due to.

I just looked again at the Bezdek survey I cited above. It mentions a known upper bound of approximately 1.320n, less than π/2. So I guess this guess at the base of the exponential cannot be π/2. Oh well. The reference given by Bezdek is.

 * Sorry, I missed your comment about an exponential lower bound. I wasn't aware of Bezdek's work--thanks for bringing it to my attention! I guess the 1.2621^n I mentioned wasn't that far off... Owen×  ☎  12:48, 23 May 2009 (UTC)

Musin?
The link to Oleg Musin is to an article about a football player. Same person? There's no mention of a mathematical career in the article.

 * Yes, link definitely points to wrong Oleg Musin, so I have removed it. Gandalf61 (talk) 08:41, 25 September 2009 (UTC)

Musin's subtle trick
The "Known kissing numbers" section currently has the text Oleg Musin proved the kissing number for n = 4 to be 24, using a subtle trick, followed by a reference. This doesn't seem quite right. If we're going to tell our readers it was a subtle trick, shouldn't we also tell them at least something about what the trick was?

It would be sifferent if subtle trick was in quotes, but that phrase doesn't appear in the JAMS (Pfender & Ziegler) article. They seem to be actually discussing Musin's ideas from a preprint, unrefereed form of the paper, and include the opinion "The bad news about Musin’s approach is that it forces him to compute, at least approximately...", so it's not clear exactly how clever the whole thing is, since it seems to rely on approximations (and I realize that a lot of higher math proofs latterly use that approach). But the subtle trick bit of the article looks like a paraphrase of two people's opinion, which may or may not be confirmed over time and in any case is not properly explained within the text body.

So what I'm suggesting is: add a rudimentary explanation of what the trick actually was; quotationize the phrase and make it true to the reference, so any of "clever modification", "beautiful idea", "clever way" would work fine; or just drop the subtle trick synthesis. I'm not even close to competent at interpreting the actual maths, so I suppose my own response would be to pull the phrase. I'll leave it in the hands of editors better able to explicate this stuff. Regards! Franamax (talk) 07:40, 6 October 2009 (UTC)

Questionable bounds
Based on my observation, I suspect the upper bound for 22 is no greater than 75600...--Billymac00 (talk) 23:38, 6 November 2009 (UTC)

Maximum number?
The intro definition seems to imply the kissing number is the maximum for a given dimension, while other contexts talk about maximum known kissing number. Is it wrong to say a kissing number of a given lattice/packing is X, even if X<maximum? 75.146.178.58 (talk) 21:30, 10 July 2010 (UTC)

The Conway reference,, page 21, section 2.2 says:
 * The kissing numbers in other dimensions. More generally we may define the kissing number (usually denoted by τ) of a sphere packing in any dimension to be the number of spheres that touch one sphere. For a lattice packing τ is the same for every sphere, but for an arbitrary packing τ may vary from one sphere to another. Other names for τ that have been used are Newton number (after the originator of the problem), contact number, coordination number of ligancy (the last being chemist's terms.)

So anyway, it looks like kissing number isn't the maximum itself, but a property of a given packing. This ought to be written in to the article. I'd try but not really my domain of confidence. :) 75.146.178.58 (talk) 21:41, 10 July 2010 (UTC)

 * I also notice that Kissing number redirects here which actually is called Kissing number problem, which is the content of the article, but I'll try adding the more general definition. 75.146.178.58 (talk) 21:48, 10 July 2010 (UTC)

My question is : Are the coordinates of centers of hyperspheres for the lowest bounds of certain dimension 4<n<9 known (40, 72, ...)? I've only found coords for n=1,2,3,4,8,24 ... Thanks — Preceding unsigned comment added by 77.38.2.194 (talk) 09:48, 2 December 2012 (UTC)

Which ones are "tight"?
It would be good for the article to say which ones are tight - in the sense that there is no slack. The two-dimensional case is tight, but three and four are not. IIRC, 8 and 24 are tight, but I'm not sure. Bubba73 You talkin' to me? 04:32, 21 March 2016 (UTC)

Inconsistency
The intro paragraph of this page is currently inconsistent:

"In geometry, a kissing number is defined as the greatest number of non-overlapping unit spheres that can be arranged such that they each touch a common unit sphere. For a lattice packing the kissing number is the same for every sphere, but for an arbitrary sphere packing the kissing number may vary from one sphere to another."

The first sentence describes a property of a space while the second sentence describes a property of a particular sphere within a particular sphere packing (within a particular space). I am going to make both possible notions clear and distinct, but if it only is supposed to be one, feel free to correct.Jess_Riedel (talk) 15:43, 30 May 2020 (UTC)

Update
if anyone is interested, they can update the known bounds with these two sources: and — Preceding unsigned comment added by Dintre (talk • contribs) 20:27, 30 March 2023 (UTC)

 * These appear not to have been peer-reviewed and published, so they do not yet meet Wikipedia's standards for reliable sources. —David Eppstein (talk) 22:14, 30 March 2023 (UTC)
 * Here's an arXiv link to the first one. Henry Cohn's page has already been updated with these sources, FWIW. Double sharp (talk) 06:54, 14 December 2023 (UTC)

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

title: Talk:Kissing number


text:
Talk:Friendship of peoples

Lenin appears to call Tsarist Russia the "prison of the peoples", in On the National Pride of the Great Russians, which surely could be a simple translation difference. However, he refers to it not as his own phrase, "... in a country which has been rightly called..."

Later in the same paper, Lenin quotes Chernyshevsky of referring to Russia as "A wretched nation, a nation of slaves, from top to bottom—all slaves." -Rholton 23:01, 31 May 2004 (UTC)

 * Thanks for the link and the exact quote, I incorporated them into the article. Can't find the author yet.  ←Humus sapiens←Talk 00:36, 1 Jun 2004 (UTC)

 * Nice bit of detective work on the origins of the phrase. It's almost worth an article page of its own. -Rholton 06:27, 5 Jun 2004 (UTC)

Deleting the reference to Hamlet; he doesn't mean anything like what is meant by the phrase "prison of the peoples"; it's rhetoric referring to the way he, personally, feels imprisoned by the limits of his role in the court of Denmark. Winterbadger (talk) 17:51, 8 April 2010 (UTC)

WTF?

"Even though the USSR often claimed to make significant progress on that path, its dissolution put an end to that goal." — Preceding unsigned comment added by 108.171.128.174 (talk) 10:41, 9 October 2017 (UTC)

title: Talk:Friendship of peoples


text:
Category talk:Romance languages

Untitled
where Spanish, Catalan, occitan, mirandese, etc...-Pedro 23:01, 31 May 2004 (UTC)
 * waiting for someone to add them? :) Lupin 23:35, 31 May 2004 (UTC)
 * where can I add? -Pedro 17:30, 18 Jun 2004 (UTC)

Spanish, italian, et al
So should they be new subcategories, or made into a new section? I'd think that they'd get their own subcategories, but I'm not quite a language expert :)

Cleaning up
I cleaned up this category, mostly according to Romance languages tree at Ethnologue.

I put specific languages under their respective groups. This includes major ones like Italian and Spanish.

In the meantime i am only leaving here a few languages whose categorization is disputed. --Amir E. Aharoni 16:58, 6 August 2007 (UTC)

title: Category talk:Romance languages


text: Category:Aircraft

title: Category:Aircraft


text: Category:Vehicles

title: Category:Vehicles


text: Category:Transportation

title: Category:Transportation


text:
User:Rimdo

My Homepage

title: User:Rimdo


text:
Nina Webster

Nina Webster is a fictional character from The Young and the Restless, an American soap opera on the CBS network, portrayed by Tricia Cast. She was introduced during the episode airing on June 26, 1986, as a pregnant teenager whom Christine Blair (Lauralee Bell) befriends. Cast remained a regular cast member for fifteen years before asking for a contract release and departing onscreen in February 2001. In 2008, the actress returned for several guest spots, and the following year, she returned for a bigger storyline, and has continued to make occasional appearances until 2014. Cast later returned in 2020 to present.

Cast described Nina as "someone who is confused generally". After her child was stolen from her hands at birth, Nina was later involved in a romance with Phillip Chancellor III (Thom Bierdz), which resulted in another child, Phillip Chancellor IV (John Driscoll). Phillip III then died—which many years later proved to be faked—and Nina raised Phillip IV as a single mother. She became a novelist and screenwriter, also having marriages to David Kimble (Michael Corbett) and Ryan McNeil (Scott Reeves). Nina was also involved with a man named Tomas Del Cerro (Francesco Quinn), a publisher interested in a novel of hers about her stolen son. In 2010, Nina met her long lost son, revealed to be Ronan Malloy (Jeff Branson). In 1992, Cast won a Daytime Emmy Award for her portrayal.

Casting
Cast debuted in the role onscreen on June 26, 1986, with her first run lasting fifteen years. She went on to reveal in 1993 that she only expected her role to be short term on the soap opera. In September 2000, it was announced that Cast had requested to be released from her contract, leading to much speculation as to why she chose to leave. Cast's publicist later issued a statement, saying: "Tricia has decided to take a sabbatical from Hollywood for an indefinite period of time. She is looking forward to spending some quality time with her new husband in Tennessee." Her last airdate was January 31, 2001. In 2008, it was announced that Cast would be returning for several guest appearances along with various other previous actors, airing from November 14 to 20, 2008. In April 2009, Cast was announced to be reprising the role again for a bigger storyline. She then remained on a recurring status with the soap opera for the following three years. She then made guest appearances in September 2013 and on August 27, 2014.

In October 2020, Entertainment Weekly announced Cast would return to the role in "early November," as well as the week of November 30 of the same year, to celebrate the soap's 12,000th episode. Cast returned to the show on November 18, 2020.

1986–2001
After getting pregnant by a man named Jimmy, Nina Webster ran away from her home and spent nights on a park bench in Genoa City, before being found by Christine Blair, with whom she soon became friends. She found a place to live at Rose DeVille's home, but had no idea that Rose was involved in a black-market baby snatching. When Nina gave birth to a son, she decided to keep the baby, but Rose made sure that this would not happen as she stole the baby and sold him to a couple, the Lansings, who were desperate to adopt, afterwards Rose left town. Nina decided to get her life back on track, but things did not seem to work out well. She set her sights on Christine's boyfriend Phillip Chancellor III (Thom Bierdz), seduced him and ended up pregnant yet again. In a rare act of unity, Phillip's mother Jill Foster Abbott and her sworn enemy Katherine Chancellor attempted to pay Nina to leave town, but she refused.

After a difficult delivery, Nina gives birth to a baby boy named Phillip Chancellor IV. She and Phillip marry and not even Jill or Kay can separate the happy couple; however, their happiness is ruined when Phillip dies from injuries sustained after a car accident. She ended up with a considerable fortune despite Jill and Katherine's attempt to keep Nina away from the Chancellor fortune.

Soon after, Nina began dating Jill's former assistant David Kimble. Nina's friends Christine and Danny Romalotti warned Nina against David, but Nina and David continued their romance. David even threatened Christine to keep away from Nina, and when Christine told Nina, she did not believe her. Nina and David ended up quickly eloping and he signed a prenuptial agreement, but David ended up having an affair with a mailroom attendant Diane Weston. It was soon discovered that David had killed his first wife Rebecca and when Rebecca's friend showed up in Genoa City to prove David killed her, she herself was killed. Christine and Danny continued to look into David, and David tried to frame Danny for cocaine possession in retaliation. Nina ended up learning from Diane that David was going to kill her and Phillip IV. Soon after, Nina shot David five times and was in turn arrested for attempted murder. It was later dropped when she convinced the jury that she shot David in self-defense.

By 1991, David returned in disguise and with the name of Jim Adams, and began romancing Nina's mother Florence. He was able to convince Nina to change her will to make Florence and him the co- beneficiaries of Nina's estate. At a masquerade ball, David intended to kill Nina, Christine, and Danny, but his ex-lover Diane warned them. They ended up tricking David to think that he killed them all and was soon being investigated by the police. He hid in a garbage chute at one point and was then killed by a garbage compactor.

She then started an affair with Ryan McNeil, who at the time was married to Victoria Newman. Their relationship continued after Ryan and Victoria's marriage ended, and Nina ended up pregnant once again, leaving Ryan with no choice but to marry her. Nina miscarried, and it was then when Ryan realized how much he loved her. During their marriage though, Nina fell for Cole Howard, who incidentally was another one of Victoria's husbands. Cole didn't want to be with her and Nina was having hard time dealing with the truth, and her marriage to Ryan suffered because of it. Ryan fell for another woman, Tricia Dennison, and the feelings of rejection from both Cole and Ryan caused her to try to die by suicide. Ryan convinced her not to do this but a shot was fired and she lost her memory. She survived, however Ryan was believed to have shot Nina, who later regained her memory and told the police the truth.

Nina evolved into a more mature woman; she continued writing novels and began a friendship with a man named Tomas Del Cerro, a world-renowned novelist. Their friendship soon evolved into a relationship. Nina's career took an upswing when Tomas' publisher became interested in her novel "A Cry in Thin Air", which involved her story regarding her long-lost child. He decided to propose to Nina and she reluctantly accepted, but their relationship was soon over when Tomas was unable to get over Nina's success as a writer. Tomas disappeared from Genoa City, and Nina left town to escape her past.

2008–2014
In 2008, Nina returned to Genoa City to attend Katherine's funeral (although in truth, Katherine was alive, and it was her lookalike Marge Cotrooke who had died). She revealed that she is still writing screenplays, although without much success and that her son Phillip IV was now enlisted in the army and currently serving in Iraq. Nina returned to town again for Katherine's wedding to Patrick Murphy. She discovered a drunken Jill at the door as she was arriving; she promptly tied Jill up and hid her in the hall closet so she would not disturb the ceremony. However, she wasn't in there for long, as Lauren Fenmore Baldwin heard her muffled screams and let her out. After the wedding, she decided to approach Katherine with the idea of turning her recently published autobiography into a film; Katherine complied under the condition that her collaborator, Amber Moore, co-write the movie with her.

During Nina's long absence from Genoa City, it was revealed that Jill's son Phillip III was switched shortly after birth by a jealous and alcoholic Katherine. Jill's true son was taken to Australia, returning years later under the name Cane Ashby. The other child, whose true identity remains unknown, was raised as Phillip and eventually married Nina. Following his wedding to Lily Winters, Cane recalled his telephone conversation two years earlier with a man regarding their joint plan to con Jill and Katherine. The man bore a startling resemblance to the supposedly deceased Phillip. It was revealed that Phillip was indeed the other gentleman, and that he is still very much alive; unknown to everyone except Cane.

Nina shocks Katherine and Jill by stating that she is having Phillip III's body exhumed for a DNA test. She explains that her motives are not only to find out if the body is actually that of Phillip III, but to obtain some crucial information about her son. Nina informs Jill and Katherine that before being deployed in Iraq, her son had a physical and explained some symptoms he had been experiencing. The doctor asked if he had any family history of the deadly Huntington's disease. She explains that she isn't a carrier of the disease, and if his father wasn't either then Phillip IV will be in the clear. Jill informs Nina that the results from the previous exhumation of Phillip III's body should still be on file at the lab. After a couple of phone calls, it was revealed that the lab had no record of such a test, and the doctor who signed the autopsy report that Jill had on file had previously falsified forensic evidence and had disappeared. Nina goes back to her original plan of having Phillip III's body exhumed. After much pleading from both Jill and Katherine, Nina agrees to only have the test for Phillip IV done rather than both DNA tests. Once Katherine and Jill leave the room however, Nina calls the lab back to order the second DNA test. The body of Phillip III is exhumed, and Nina requests to be present for the opening of the casket. When it is discovered that Phillip's casket is empty and in fact never contained a corpse at all, Nina demands that Cane submit to DNA testing to verify his status as Jill's biological son. Upon learning of Nina's demand, Cane retrieves a vial of Phillip's blood from a carousel of vials he has kept in a hidden freezer for use in DNA testing. Thus, it becomes apparent that Phillip III, not Cane, is Jill's biological son. Nina confronts Cane accusing him of tampering with the blood samples for the DNA test. The blood had been frozen at one time, and the lab detected that. Cane finally breaks down and admits that he is not Phillip, but has no time to explain why he did what he did as Phillip III makes his grand return to Genoa City. Nina stands there with a horrified look upon her face as she sees her husband who was long thought deceased standing before her very much alive.

When Phillip appears, Nina is shocked, and Katherine collapses. Phillip briefly disappears, but is found at the hospital by Murphy, who keeps him there until Nina arrives. They all go into Katherine's hospital room to have a sort of family meeting. Nina listens as Phillip explains why he and Cane deceived everyone. When Phillip explains that he didn't want to live the life he had 20 years earlier. Nina is furious at Phillip for faking his death, leaving her to raise their son by herself. Phillip claims that he faked his own death for his son, stating that he wouldn't have been a good father while suicidal and alcoholic. Nina, Jill and Katherine are left in a very familiar place, in a hospital room, filled with pain, rage and guilt, exactly the same as 20 years earlier when Phillip "died".

Nina then demands more answers from Phillip, who is reluctant to reveal anything else. He follows her when she storms out of the Chancellor Mansion, and tells her to ask him anything she wants. After their conversation, Phillip reveals that he always wanted to call Nina and their son but didn't know what to say. He then reveals that he is gay, and has always been. Nina seems to support him, and even convinces him to tell Jill and Katherine. Phillip IV returned from his tour of duty in Iraq, now going by the nickname Chance. This allowed for Chance to finally meet his father, but the two get into an argument. Nina wanted Phillip and Chance to develop relationship, but Phillip wanted Nina to let things be. Over time Phillip and Chance develop a relationship. Yet, Phillip ended up moving back to Australia, but returns occasionally.

Nina then began dating Paul Williams. Christine returns to Genoa City fully aware about the truth about Nina's son being Ronan Malloy, an FBI agent working undercover at the Genoa City Police Department. However, for security reasons, Christine cannot tell Nina. Ronan and Chance became enemies at the department as Chance thought Ronan was a corrupt cop. Chance ended up being framed for drug possession and pleaded guilty in order to infiltrate corrupt police schemes. Chance is later released on bail.

At the premiere Gloria and Jeffrey Bardwell's nightclub, Gloworm, Paul and Christine shared a kiss in remembrance of it being their wedding anniversary. Nina sees this and disappointingly walks away. The next day, when Nina sees the two of them she believes that the two of them had sex. The two of them deeply apologizes to her and assure her that they did not have sex. However Paul and Christine later kiss again almost to the point of them having sex. Christine abruptly leaves with Paul chasing after her. Nina sees Paul chasing after Christine. Paul confess to Nina about this. Nina is so mad slaps Paul on his face and storm out the room. Paul later begs for Nina's forgiveness and reminds her that he is still committed to finding her son. However, Chance is accidentally shot by Ronan and is pronounced dead at the scene just as Nina finally discovered the truth about Ronan.

It was revealed that Chance faked his death and entered into the Witness Protection Program. Only his parents, Nina and Phillip, as well as Ronan and Christine knew before Chance later returned to donate his kidney to Ronan. When Chance returned, Katherine, Jill, as well as everyone else found out about Chance. He left Witness Protection before he left again to pursue a career at the Pentagon. In 2012, When Paul is arrested for the shooting death of his son Ricky, Nina returns for moral support. She remains in town until Paul is proven to have only shot Ricky because he was threatening the life of Eden Baldwin. She is ready to continue a relationship with Paul until she sees him with Christine and leaves him and Genoa City.

In September 2013, Nina returned to Genoa City for Katherine Chancellor's memorial service. She made her peace with Paul and Christine on the advice of a letter written by Katherine before her death. The service ended with an impromptu wedding ceremony between Paul and Christine, in which Nina ended up being Christine's maid of honor. She returned the following August for Katherine's remembrance party.

title: Nina Webster


text:
User:Maximus Rex/monobook.js

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text: Category:Physical chemists

title: Category:Physical chemists


text: Category:Chemists

title: Category:Chemists


text: Category:Physicists

title: Category:Physicists


text:
Category:Assassinations

 * Assassination is the targeted killing of a public figure.
 * Assassinations may be prompted by ideological, political, military, or financial reasons.

title: Category:Assassinations


text:
Category:Crimes

This category includes articles on specific types and instances of crime. For articles on crime in general, see Category:Crime. Articles which only allege that a crime has occurred should not be included in these categories (e.g. an article about a person or company that is indicted but whose case is later dismissed). For specific alleged crimes which have not been proven in a court of law, consider using Category:Scandals or a subcategory instead.

title: Category:Crimes


text: Category:Transition metals

title: Category:Transition metals


text:
Min-max theorem

In linear algebra and functional analysis, the min-max theorem, or variational theorem, or Courant–Fischer–Weyl min-max principle, is a result that gives a variational characterization of eigenvalues of compact Hermitian operators on Hilbert spaces. It can be viewed as the starting point of many results of similar nature.

This article first discusses the finite-dimensional case and its applications before considering compact operators on infinite-dimensional Hilbert spaces. We will see that for compact operators, the proof of the main theorem uses essentially the same idea from the finite-dimensional argument.

In the case that the operator is non-Hermitian, the theorem provides an equivalent characterization of the associated singular values. The min-max theorem can be extended to self-adjoint operators that are bounded below.

Matrices
Let $A$ be a $n × n$ Hermitian matrix. As with many other variational results on eigenvalues, one considers the Rayleigh–Ritz quotient $R_{A} : C^{n} \ {0} → R$ defined by

 * $$R_A(x) = \frac{(Ax, x)}{(x,x)}$$

where $(⋅, ⋅)$ denotes the Euclidean inner product on $C^{n}$. Clearly, the Rayleigh quotient of an eigenvector is its associated eigenvalue. Equivalently, the Rayleigh–Ritz quotient can be replaced by

 * $$f(x) = (Ax, x), \; \|x\| = 1.$$

For Hermitian matrices A, the range of the continuous function RA(x), or f(x), is a compact interval [a, b] of the real line. The maximum b and the minimum a are the largest and smallest eigenvalue of A, respectively. The min-max theorem is a refinement of this fact.

Min-max theorem
Let $A$ be Hermitian on an inner product space $V$  with dimension $n$, with spectrum ordered in descending order $\lambda_1 \geq ... \geq \lambda_n$.

Let $v_1, ..., v_n$ be the corresponding unit-length orthogonal eigenvectors.

Reverse the spectrum ordering, so that $\xi_1 = \lambda_n, ..., \xi_n = \lambda_1$.

$$

$$

Counterexample in the non-Hermitian case
Let N be the nilpotent matrix

 * $$\begin{bmatrix} 0 & 1 \\ 0 & 0 \end{bmatrix}.$$

Define the Rayleigh quotient $$ R_N(x) $$ exactly as above in the Hermitian case. Then it is easy to see that the only eigenvalue of N is zero, while the maximum value of the Rayleigh quotient is $1⁄2$. That is, the maximum value of the Rayleigh quotient is larger than the maximum eigenvalue.

Min-max principle for singular values
The singular values {σk} of a square matrix M are the square roots of the eigenvalues of M*M (equivalently MM*). An immediate consequence of the first equality in the min-max theorem is:

 * $$\sigma_k^{\uparrow} = \min_{S:\dim(S)=k} \max_{x \in S, \|x\| = 1} (M^* Mx, x)^{\frac{1}{2}}=\min_{S:\dim(S)=k} \max_{x \in S, \|x\| = 1} \| Mx \|.$$

Similarly,

 * $$\sigma_k^{\uparrow} = \max_{S:\dim(S)=n-k+1} \min_{x \in S, \|x\| = 1} \| Mx \|.$$

Here $$\sigma_k=\sigma_k^\uparrow$$ denotes the kth entry in the increasing sequence of σ's, so that $$\sigma_1\leq\sigma_2\leq\cdots $$.

Cauchy interlacing theorem
Let $A$ be a symmetric n × n matrix. The m × m matrix B, where m ≤ n, is called a compression of $A$ if there exists an orthogonal projection P onto a subspace of dimension m such that PAP* = B. The Cauchy interlacing theorem states:

 * Theorem. If the eigenvalues of $A$ are $α_{1} ≤ ... ≤ α_{n}$, and those of B are $β_{1} ≤ ... ≤ β_{j} ≤ ... ≤ β_{m}$, then for all $j ≤ m$,
 * $$\alpha_j \leq \beta_j \leq \alpha_{n-m+j}.$$

This can be proven using the min-max principle. Let βi have corresponding eigenvector bi and Sj be the j dimensional subspace $S_{j} = span{b_{1}, ..., b_{j}},$ then

 * $$\beta_j = \max_{x \in S_j, \|x\| = 1} (Bx, x) = \max_{x \in S_j, \|x\| = 1} (PAP^*x, x) \geq \min_{S_j} \max_{x \in

S_j, \|x\| = 1} (A(P^*x), P^*x) = \alpha_j.$$

According to first part of min-max, $α_{j} ≤ β_{j}.$ On the other hand, if we define $S_{m−j+1} = span{b_{j}, ..., b_{m}},$ then

 * $$\beta_j = \min_{x \in S_{m-j+1}, \|x\| = 1} (Bx, x) = \min_{x \in S_{m-j+1}, \|x\| = 1} (PAP^*x, x)= \min_{x \in S_{m-j+1}, \|x\| = 1} (A(P^*x), P^*x) \leq \alpha_{n-m+j},$$

where the last inequality is given by the second part of min-max.

When $n − m = 1$, we have $α_{j} ≤ β_{j} ≤ α_{j+1}$, hence the name interlacing theorem.

Compact operators
Let $A$ be a compact, Hermitian operator on a Hilbert space H. Recall that the spectrum of such an operator (the set of eigenvalues) is a set of real numbers whose only possible cluster point is zero. It is thus convenient to list the positive eigenvalues of $A$ as

 * $$\cdots \le \lambda_k \le \cdots \le \lambda_1,$$

where entries are repeated with multiplicity, as in the matrix case. (To emphasize that the sequence is decreasing, we may write $$\lambda_k = \lambda_k^\downarrow$$.) When H is infinite-dimensional, the above sequence of eigenvalues is necessarily infinite. We now apply the same reasoning as in the matrix case. Letting Sk ⊂ H be a k dimensional subspace, we can obtain the following theorem.

 * Theorem (Min-Max). Let $A$ be a compact, self-adjoint operator on a Hilbert space $H$, whose positive eigenvalues are listed in decreasing order $... ≤ λ_{k} ≤ ... ≤ λ_{1}$. Then:
 * $$\begin{align}

\max_{S_k} \min_{x \in S_k, \|x\| = 1} (Ax,x) &= \lambda_k ^{\downarrow}, \\ \min_{S_{k-1}} \max_{x \in S_{k-1}^{\perp}, \|x\|=1} (Ax, x) &= \lambda_k^{\downarrow}. \end{align}$$

A similar pair of equalities hold for negative eigenvalues.

$$

Self-adjoint operators
The min-max theorem also applies to (possibly unbounded) self-adjoint operators. Recall the essential spectrum is the spectrum without isolated eigenvalues of finite multiplicity. Sometimes we have some eigenvalues below the essential spectrum, and we would like to approximate the eigenvalues and eigenfunctions.

 * Theorem (Min-Max). Let A be self-adjoint, and let $$E_1\le E_2\le E_3\le\cdots$$ be the eigenvalues of A below the essential spectrum. Then

$$E_n=\min_{\psi_1,\ldots,\psi_{n}}\max\{\langle\psi,A\psi\rangle:\psi\in\operatorname{span}(\psi_1,\ldots,\psi_{n}), \, \| \psi \| = 1\}$$.

If we only have N eigenvalues and hence run out of eigenvalues, then we let $$E_n:=\inf\sigma_{ess}(A)$$ (the bottom of the essential spectrum) for n>N, and the above statement holds after replacing min-max with inf-sup.

 * Theorem (Max-Min). Let A be self-adjoint, and let $$E_1\le E_2\le E_3\le\cdots$$ be the eigenvalues of A below the essential spectrum. Then

$$E_n=\max_{\psi_1,\ldots,\psi_{n-1}}\min\{\langle\psi,A\psi\rangle:\psi\perp\psi_1,\ldots,\psi_{n-1}, \, \| \psi \| = 1\}$$.

If we only have N eigenvalues and hence run out of eigenvalues, then we let $$E_n:=\inf\sigma_{ess}(A)$$ (the bottom of the essential spectrum) for n > N, and the above statement holds after replacing max-min with sup-inf.

The proofs use the following results about self-adjoint operators:

 * Theorem. Let A be self-adjoint. Then $$(A-E)\ge0$$ for $$E\in\mathbb{R}$$ if and only if $$\sigma(A)\subseteq[E,\infty)$$.

 * Theorem. If A is self-adjoint, then

$$\inf\sigma(A)=\inf_{\psi\in\mathfrak{D}(A),\|\psi\|=1}\langle\psi,A\psi\rangle$$

and

$$\sup\sigma(A)=\sup_{\psi\in\mathfrak{D}(A),\|\psi\|=1}\langle\psi,A\psi\rangle$$.

title: Min-max theorem


text: Category:Scientists

title: Category:Scientists


text: Category:North Germanic languages

title: Category:North Germanic languages


text: User talk:205.157.110.11

title: User talk:205.157.110.11


text:
Cook's Bay (Ontario)

Cook's Bay is the southernmost bay of Lake Simcoe in Ontario, Canada. Most of the southern part of the bay is within the jurisdiction of Georgina, a town in the Regional Municipality of York. Its western end is in Simcoe County, and a small portion from the mouth of the Holland River to the Simcoe County border is within Bradford West Gwillimbury. The largest community on the shores of the bay is Keswick.

It was named by John Graves Simcoe, the first Lieutenant-Governor of Upper Canada, for James Cook, who had served as master aboard HMS Pembroke (1757) in 1759 under the command of Captain John Simcoe, the Lieutenant-Governor's father.

The bay is used for fishing, and is especially known for yellow perch. It attracts windsurfers and kitesurfers throughout the year, and its northern end features many cottages that are part of Ontario's cottage country. Marinas and motel accommodations are available.

title: Cook's Bay (Ontario)


text: Category:German people

title: Category:German people


text: Category:Germany

title: Category:Germany


text: Category:Baltic languages

title: Category:Baltic languages


text:
Category:Analytic number theory

Analytic number theory is the branch of number theory that uses methods from mathematical analysis. Its first major success was the application of complex analysis in the proofs of the prime number theorem based on the Riemann zeta function.

title: Category:Analytic number theory


text: Category:Cancer treatments

title: Category:Cancer treatments


text:
User:Kylefr635

Hi. My name is Brandon. I'm 16. There was a quote by ToddLo114 that fits me perfectly. He says "I have a problem. I'm addicted to knowledge." That statement probably fits a lot of us here at Wikipedia, or we wouldn't be here.

Any way, I don't feel like writing my biography right now so see my blurb on the New Users page. Look under kylefr635. I fill this out later.

Until,

Brandon

title: User:Kylefr635


text:
Maid of the Mist

The Maid of the Mist is a sightseeing boat tour of Niagara Falls, N.Y., U.S.A., starting and ending on the American side, crossing briefly into Canada during a portion of the trip.

James V. Glynn is chairman and chief executive officer of Maid of the Mist Corp. He joined Maid of the Mist in 1950 as a ticket seller and purchased the company in 1971. During his tenure, Maid of the Mist expanded operations, achieving ten-fold growth.

The current fleet, the result of the innovation of Maid of the Mist President Christpher M. Glynn, consists of two vessels, both of which launched in 2020. The James V. Glynn was named in honor of the Maid of the Mist Chairman and CEO James V. Glynn, who in 2020 celebrated 70 years with the company, and the Nikola Tesla, for the man who developed a type of alternating current (AC) motor. Nikola Tesla's patents were licensed by George Westinghouse whose company later won the bid to build the first AC power plant at Niagara Falls. Prior to the current two boats, all prior ships had been named Maid of the Mist, dating back to 1846. The first ships were steam-powered; these were replaced by diesel-powered vessels from 1955 until 2019, and later replaced with the current two boats powered by lithium-ion battery-powered electric motors.

The name, Maid of the Mist, could be a reference to the Iroquois myth of Lelawala.

The United States
The original Maid of the Mist was built at a landing near Niagara Falls on the American side of the border. The boat was christened in 1846 as a border-crossing ferry; its first trip was on September 18, 1846. The two-stage barge-like steamer was designed primarily as a link for a proposed ferry service between New York City and Toronto. It was a 72-foot-long side-wheeler with an 18-foot beam which was powered by steam produced from a wood- and coal-fired boiler. It could carry up to 100 passengers.

The ferry did well until 1848, when the opening of a suspension bridge between the United States and Canada cut into the ferry traffic. It was then that the owners decided to make the journey a sightseeing trip, plotting a journey closer to the Falls.

The present day Maid of the Mist Corporation was formed in 1884 by Captain R. F. Carter and Frank LaBlond, who invested in a new Maid that would launch in 1885. Captain Carter and Mr. LaBlond hired Alfred H. White from Port Robinson, Ontario to build the new ship. A letter in the archives of the Buffalo Historical Society from Mr. LaBlond to Alfred White says that they are well pleased with the vessel and asks Alfred to add a wale onto the boat.

The service is run by Maid of the Mist Corp. of Niagara Falls, New York. Maid of the Mist has been owned by the Glynn family since 1971.

James V. Glynn is chairman and chief executive officer of Maid of the Mist Corp. Glynn joined Maid of the Mist in 1950 as a ticket seller, and purchased the company in 1971. During his tenure, Maid of the Mist expanded operations, achieving ten-fold growth.

Canada
Access to the river-level attraction on the Canadian side was provided by the Maid of the Mist Incline Railway, a funicular railway, between 1894 and 1990, to travel between street level and the boat dock. As this service proved increasingly inadequate in transporting the growing passenger base of the 1990s, four high-speed elevators replaced the railway in 1991. On the American side, the dock is reached by four elevators enclosed in the observation tower.

The Russel Brothers of Owen Sound, Ontario made two all-steel Maids for the Niagara Falls Gorge, in 1955 and 1956. The first one is now based in Parry Sound, Ont. and runs dinner cruises and day excursions. The second Maid was sold in 1983 to the United Pentecostal Church of Ontario and destined for missionary service in the Amazon. Maid of the Mist II took part in the July 9, 1960, rescue of Roger Woodward, a seven-year-old boy who became the first person to survive a plunge over the Horseshoe Falls with nothing but a life jacket. Maid of the Mist II served as a Maid of the Mist until 1983. Subsequently she was relocated to the Amazon River, where she served as a missionary ship for some years.

A partial history of Maid of the Mist is featured in the IMAX film Niagara: Miracles, Myths and Magic.

Notable passengers
While on his 1860 tour of Canada, Albert Edward, Prince of Wales (later King Edward VII), rode on Maid of the Mist.

June 1952: Marilyn Monroe rode the Maid of the Mist while in Niagara Falls to film the movie, Niagara.

Mikhail Gorbachev was a passenger in 1983.

1991: Prince Charles and Princess Diana, and their two young sons, Princes William and Harry, rode on Maid of the Mist.

1996: Former U.S. President Jimmy Carter was a passenger, escorted by James V. Glynn.

2003: BBC Scotland's popular comedy sitcom Still Game made mention of the Maid of the Mist when lead characters Jack and Victor visited the formers family in Canada, and Victor takes Jack's grandson's aboard off screen.

2003: Maid of the Mist was featured in a scene of the movie Bruce Almighty, where Jim Carrey's character Bruce Nolan, a news anchor, has a mental breakdown after being told over his earpiece that his rival was given a promotion he himself was eyeing.

2009: NBC-TV's popular sit-com The Office filmed scenes on Maid of the Mist. The episode centered on the wedding of the characters Jim and Pam.

2018: ESPN's Monday Night Countdown recorded a segment before a Buffalo Bills game.

2020: NFL great DeMarcus Ware and a crew from NFL Films were onboard James V. Glynn in 2020 ahead of the Buffalo Bills - New England Patriots game.

2022: Maid of the Mist was featured in the 2022 motion picture, A Man Called Otto, starring Tom Hanks.

Original ships
The first series boats to bear the "Maid of the Mist" moniker were steam-powered wooden-hulled ferries. These were in use until an early-season fire destroyed the last of them in 1955.

First Maid of the Mist
 * Years of service: 1846–1854
 * Type: double-stack steamboat ferry
 * Engine: one sidewheel steam

Second Maid of the Mist
 * Years of service: 1854–1860
 * Length: 72 ft
 * Type: single-stack steamer
 * Engine: paddle boat

Third Maid of the Mist Fourth Maid of the Mist
 * Years of service: 1885–1955
 * Type: steam boat
 * Years of service: 1892–1955
 * Type: white oak steamboat
 * Length: 89 ft
 * Engine: two-engine steam

Diesel vessels
After a fire destroyed the last of the wooden-hulled steamers, they were replaced by steel-hulled, diesel-powered ferries, launched in 1955 and 1956. About every 20 years or so, new ships were added to the fleet, of increasingly larger capacity; the initial Maid of the Mist held only 101 passengers, while the last of the diesel-powered vessels, Maid of the Mist VII, could hold up to 600. The last of these were retired in 2019, to be replaced by an electric-powered fleet that can both hold 600 passengers.

Maid of the Mist I
 * Years of service: 1955–1990
 * Length: 66 ft
 * Engine: 200 hp diesel engines
 * Passengers: 101

Maid of the Mist II
 * Years of service: 1956–1983
 * Type: all-steel boat, twin of I
 * Engine: 200 hp diesel engines
 * Passengers: 101

Maid of the Mist III
 * Years of service: 1972–1997
 * Length: 65 ft
 * Gross tonnage: 75
 * Engine: single 250 hp diesel
 * Passengers: 210

Maid of the Mist IV
 * Years of service: 1976–2013
 * Length: 72 ft
 * Gross tonnage: 75
 * Engine: two 250 hp diesel
 * Passengers: 300

Maid of the Mist V
 * Years of service: 1983–2013
 * Length: 72 ft
 * Gross tonnage: 74
 * Engine: two 355 hp diesel
 * Passengers: 300

Maid of the Mist VI
 * Years of service: 1990–2019
 * Length: 74 ft
 * Breadth: 30 ft
 * Depth: 10 ft
 * Gross tonnage: 155
 * Engine: two 355 hp diesel
 * Passengers: 600

Maid of the Mist VII
 * Years of service: 1997–2020
 * Length: 80 ft
 * Breadth: 30 ft
 * Depth: 10 ft
 * Gross tonnage: 155
 * Engine: two 350 hp diesel
 * Passengers: 600

Electric vessels
Beginning with the 2020 season, the Maid of the Mist launched two all-new electric ships, with a similar size and capacity to the prior diesel-powered ones.

James V. Glynn
 * Years of service: 2020–present
 * Length: 90 ft
 * Breadth: 34 ft
 * Depth: 6 ft
 * Propulsion system: lithium-ion battery packs power the all-electric motor
 * Passengers: 600

Nikola Tesla
 * Years of service: 2020–present
 * Length: 90 ft
 * Breadth: 34 ft
 * Depth: 6 ft
 * Propulsion system: lithium-ion battery packs power the all-electric motor
 * Passengers: 600

title: Maid of the Mist


text: Category:Medical treatments

title: Category:Medical treatments


text:
Cave of the Winds

Cave of the Winds may refer to:
 * Cave of the Winds (New York), a former cave and current tourist attraction at Niagara Falls
 * Cave of the Winds (Colorado)
 * Cave of the Winds (Malaysia), a cave at Gunung Mulu National Park, Sarawak, Borneo

title: Cave of the Winds


text:
Category:Love Hina

__NOGALLERY__

title: Category:Love Hina


text: Category:Barristers

title: Category:Barristers


text:
InterVarsity Christian Fellowship

InterVarsity Christian Fellowship/USA (IVCF) is an inter-denominational, evangelical Christian campus ministry founded in 1941, working with students and faculty on U.S. college and university campuses. InterVarsity is a charter member of the International Fellowship of Evangelical Students, a network of similar campus ministries around the world.

It is a collective campus ministry found in hundreds of American colleges whose collegiate members involve themselves in Christian student activist movements.

Organization
InterVarsity is governed by a board of directors. Tom Lin became the eighth president of InterVarsity on August 10, 2016. The president works with a team of four Executive Vice Presidents. InterVarsity is a tax exempt organization under the provisions of Section 501(C)(3) of the Internal Revenue Code. In the fiscal year ending 30 June 2018, InterVarsity had $107M in revenue (with over 70% coming from charitable donations) and $106.6M in expenditures.

InterVarsity is a charter member of the Evangelical Council for Financial Accountability (ECFA), and uses more than 85% of its revenue for staff-worker salaries and other on-campus work. InterVarsity was rated 4 stars (out of 4) by Charity Navigator for eight straight years. Michael Thatcher, the president of Charity Navigator, reported: "Only 3% of the charities we evaluate have received at least 8 consecutive 4-star evaluations, indicating that InterVarsity Christian Fellowship/USA outperforms most other charities in America." In 2019 InterVarsity slipped just below the cut-off for the four-star rating, and based on the latest available IRS Form 990 data (for Fiscal Year 2020) is currently rated at three stars by Charity Navigator. However, InterVarsity continued to maintain a 100 percent score in Accountability and Transparency.

InterVarsity strives to maintain the highest level of accountability with its ministry partners and is also rated by sites such as Guidestar and MinistryWatch. InterVarsity (as of 2018) met 18 of the 20 Better Business Bureau's "Standards for Charity Accountability".

History
InterVarsity Christian Fellowship/USA became an official organization in November, 1941. But the organization traces its roots to a movement of British university students, starting at Cambridge University in 1877. The movement spread to Canada before reaching the U.S. In 1938 Stacey Woods, the Canadian Inter-Varsity director, met with students on the University of Michigan campus. As an immediate result of that visit, students formed the first InterVarsity chapter in the United States. InterVarsity's first three staff members came on loan from Canada, and Stacey Woods served as the organization's General Secretary (CEO). In 1947 InterVarsity USA became one of ten founding members of the International Fellowship of Evangelical Students, a federation of national Christian student movements. By 1950 there were 35 staff workers serving students in 499 InterVarsity chapters and by the early seventies, the on-campus staff had grown to more than 200.

In September 2019, the U.S. District Court for the Southern District of Iowa ruled that the University of Iowa violated the First Amendment when it expelled the group from campus for requiring its leaders to uphold Christian beliefs. A similar ruling was issued against Wayne State University in April 2021.

Statement of Faith
In 2016, InterVarsity clarified its requirements for staff, asking that they affirm traditional, orthodox views of sexuality that are shared by most evangelical denominations. Staff are asked to affirm a twenty-page document which affirms the Hebrew Bible and the New Testament sexual ethic that limits sexual expression to marriage between a man and a woman. However, this change in policy has prompted controversy, especially from LGBTQ Christians and their supporters.

College ministry
Of the 772 campuses where InterVarsity is present, many have multiple chapters which might focus individually on Greek life students, international students, nursing students, graduate students, athletes, artists, and members of ethnic minorities, or be more generalized depending on the campus. These include 71 ethnic-specific chapters ministering to Blacks, Asians, Native Americans, Filipinos, and Latinos. Of the 34,750 active InterVarsity students, 15,198, or 44%, identify themselves as ethnic minority or multiracial students.

Nurses Christian Fellowship (NCF) is unique among the ministries of InterVarsity; it is a professional organization as well as a student ministry. In addition to campus ministry, NCF offers continuing education courses and the professional publication, Journal of Christian Nursing, to practicing nurses.

Bible Study
Bible study has always been an important part of InterVarsity's campus ministry. InterVarsity staff worker Paul Byer is credited with developing the Manuscript Study method of inductive Bible study, a useful tool for inductive Bible studies. After graduating from the University of Southern California with a degree in architecture, Byer became one of the leading forces in InterVarsity, as both a campus staff worker and as the West Coast Regional Director, and was the developer of the Manuscript Study method. Through his innovative approach to Bible Study, extensive mentoring, and long tenure he helped shape the theology and culture of the entire movement. The Manuscript Study method continues to be used heavily by InterVarsity as one of many tools to help students investigate and learn from the teachings of the Bible.

Other early staff members laid more of the foundation for InterVarsity's commitment to Bible study. Jane Hollingsworth learned inductive Bible study in seminary and in turn trained staff members in the 1940s. She wrote the first Bible study guide published by InterVarsity, Discovering the Gospel of Mark. In the 1960s, veteran staff member Barbara Boyd developed what became the Bible and Life Training Courses, experienced by decades of students.

Missions
InterVarsity, as a member movement, participates in the global student ministry network, the International Fellowship of Evangelical Students (IFES), by sending staff and recent graduates to work under the authority of local IFES staff in countries around the world.

Training
InterVarsity operates several training centers, Campus by the Sea Catalina Island, CA; Toah Nipi, Rindge, NH; Cedar Campus, Cedarville, MI; Bear Trap Ranch, Colorado Springs, CO; and, until recently, Forest Springs, WI. These camps are used for weekend conferences during the school year, week-long training sessions at the beginning and end of summer break, and faculty and alumni retreats.

InterVarsity Press
In 1947 the InterVarsity/USA Board of Trustees determined that the Fellowship should develop its own publishing arm. With this action, InterVarsity Press (IVP) became an official part of InterVarsity's ministry, overseeing the publication and distribution of books, booklets and Bible study guides in support of the campus work.

title: InterVarsity Christian Fellowship


text:
User talk:Neiltest

 * pi : area of a circle with radius 1
 * e : Eulers number

title: User talk:Neiltest


text: Category:Iraq

title: Category:Iraq


text:
Tricia Cast

Patricia M. Cast (born November 16, 1966) is an American actress. She is best known for her portrayal of Nina Webster on the CBS soap opera The Young and the Restless.

Career
Cast came to prominence on the television series The Bad News Bears in 1979 as Amanda Whirlitzer, the role originated by Tatum O'Neal in the 1976 film of the same name. After years of acting in television films, she starred with Jason Bateman as his sister on the television series It's Your Move. This performance led to a short stint on the soap opera Santa Barbara.

In 1986, Cast began her most notable role, Nina Webster on the soap opera The Young and the Restless, where she was reunited with her good friend and Bad News Bears co-star, Kristoff St. John. In 1992, she won a Daytime Emmy Award for her portrayal. Cast went on to reveal in 1993 that she only expected her role to be short term on the soap opera. In September 2000, it was announced that Cast had requested to be released from her contract, leading to much speculation as to why she chose to leave. Cast's publicist later issued a statement, saying: "Tricia has decided to take a sabbatical from Hollywood for an indefinite period of time. She is looking forward to spending some quality time with her new husband in Tennessee." She made her last appearance on January 31, 2001. In 2008, it was announced that Cast would be returning for several guest appearances along with various other previous actors, airing from November 14-20, 2008. In April 2009, Cast was announced to be reprising the role again for an extended run, remaining on a recurring status with the soap opera for the next three years. In 2011, she was nominated for another Daytime Emmy Award in a different category.

Personal life
Cast was married to Jack Allocco, a composer for The Young and the Restless and The Bold and the Beautiful, from 1989 to 2000. On July 20, 2000, Cast married Bat McGrath and they remained married until his death in 2019.

title: Tricia Cast


text:
Category:Endocrinology

Endocrinology is the field of medicine that diagnoses and treats diseases of the endocrine organs or dysregulation of hormone homeostasis.

title: Category:Endocrinology


text: Category:Irish heads of government

title: Category:Irish heads of government


text: Category:Web browsers

title: Category:Web browsers


text:
Category:Analytical chemistry

Analytical chemistry is the analysis of material samples to gain an understanding of their chemical composition and structure.

title: Category:Analytical chemistry


text:
Larry Ridley

Larry Ridley (born September 3, 1937) is an American jazz bassist and music educator.

Biography
Ridley was born and reared in Indianapolis, Indiana. He began performing professionally while still in high school in the 1950s. He studied at the Indiana University School of Music and later at the Lenox School of Jazz. Ridley has been involved in jazz education, heading the jazz program at Rutgers University.

David Baker, another Indianapolis native and notable jazz musician, was one of his prime mentors. Ridley was bassist for David Baker's Big band during his studies at Indiana University.

Ridley served as chairman of the Jazz Panel of the National Endowment for the Arts (NEA) and was the organization's National Coordinator of the "Jazz Artists in Schools" Program for five years (1978–1982). Ridley is a recipient of the MidAtlantic Arts Foundation's "Living Legacy Jazz Award", a 1998 inductee the International Association for Jazz Education Hall of Fame (IAJE), an inductee of the Downbeat Magazine Jazz Education Hall of Fame, a recipient of the Benny Golson Jazz Award from Howard University, and was honored by a Juneteenth 2006 Proclamation Award from the New York City Council. Ridley is currently the executive director of the African American Jazz Caucus, Inc., an affiliate of IAJE. He is also the IAJE Northeast Regional Coordinator. He continues to actively teach as Professor of Jazz Bass at the Manhattan School of Music. Ridley is currently serving as Jazz Artist in Residence at the Harlem based New York Public Library/Schomburg Center for Research in Black Culture. He established an annual series there dedicated to presenting the compositions of jazz masters that are performed by Ridley and his Jazz Legacy Ensemble.

As leader

 * 1975: Sum of the Parts (Strata-East)
 * 1989: Live at Rutgers University (Strata-East)

As sideman
With Chet Baker With Bill Barron With Kenny Burrell With Al Cohn With Dameronia With Teddy Edwards With Red Garland With Dexter Gordon With Stéphane Grappelli and Joe Venuti 'With Bunky Green With Slide Hampton With Roy Haynes With Freddie Hubbard With Jackie McLean With Hank Mobley With James Moody With Wes Montgomery and Wynton Kelly With Lee Morgan With Horace Silver With Lucky Thompson With Gerald Wilson
 * Chet Baker Quartet/Live in France 1978, one track only, (Gambit Records, 2005)
 * Hot Line (Savoy, 1962 [1964])
 * Groovin' High (Muse, 1981 [1984])
 * Play It Now (Xanadu, 1975)
 * To Tadd with Love (Uptown, 1982)
 * Look Stop Listen (Uptown, 1983)
 * Live at the Theatre Boulogne-Billancourt Paris (Soul Note, 1989 [1994])
 * The Inimitable Teddy Edwards (Xanadu, 1976)
 * The Nearness of You (Jazzland, 1961)
 * The Panther! (Prestige, 1970)
 * Venupelli Blues (Affinity, 1969)
 * My Babe (Vee-Jay, 1960 [1965])
 * Somethin' Sanctified (Atlantic, 1960)
 * Cracklin' (New Jazz, 1963)
 * Cymbalism (New Jazz, 1963)
 * Hub Cap (Blue Note, 1961)
 * Blue Spirits (Blue Note, 1965)
 * The Night of the Cookers (Blue Note, 1965)
 * Destination... Out! (Blue Note, 1963)
 * Jacknife (Blue Note, 1965)
 * Dippin' (Blue Note, 1965)
 * Straight No Filter (Blue Note, 1989)
 * Feelin' It Together (Muse, 1973)
 * Maximum Swing: The Unissued 1965 Half Note Recordings (Resonance, 1965)
 * Cornbread (Blue Note, 1965)
 * The Jody Grind (Blue Note, 1966)
 * Goodbye Yesterday (Groove Merchant, 1973)
 * New York, New Sound (Mack Avenue, 2003)

title: Larry Ridley


text:
Talk:Carinthians

The whole first bullet is very suspect. "Kranjci" would be called "Carniolans" in English, not "Carinthians", and there is at present definitely no "ethnic group" called that. Before 1848, the term "Kranjci" was frequently used to mean "Slovenians". It's not even much used as a regional designation anymore - it's been mostly supplanted by "Dolenjci", "Gorenjci" and "Notranjci" (Upper Carniolans, Lower Carniolans and Inner Carniolans).

I think that this page should be deleted (possibly redirected to Carinthia). I'll wait a couple of days for possible citation of sources, though. Zocky 23:36, 31 May 2004 (UTC)

 * Oh, Igor. Say no more. --Joy [shallot]   11:32, 27 Aug 2004 (UTC)

title: Talk:Carinthians


text:
Penny Black (research project)

The Penny Black Project is a Microsoft Research project that tries to find effective and practical ways of fighting spam. Because identifying spams consumes a recipient's time, the idea is to make the sender of emails "pay" a certain amount for sending them. The currency or the mode of payment could be CPU cycles, Turing tests or memory cycles. Such a payment would limit spammers' ability to send out large quantities of emails quickly.

The project's name is derived from the Penny Black, the world's first adhesive stamp used for prepaid postage.

Objective
The goal of the project is to move the e-mail costs from the receiver to the sender. The general idea is that if the sender must prove that they have expended a certain amount of effort specifically for the receiver and the message alone.

The project aims to devise a method to do this without introducing additional challenge-response mechanisms and third parties, and without requiring extra maintenance and updates, while retaining the current architecture of the e-mail system.

Ticket server
One of the project's ideas was the "ticket server", a credit-based method for validating emails. Tickets would be required to perform actions, such as sending emails. There are three operations the ticket server provides: "request ticket", "cancel ticket", and "refund ticket".

The server would allow the user to request a ticket in exchange for a proof of work: expending CPU cycles solving hard algorithms with processing power, Turing tests, or even just by paying money. The server could also cancel a ticket. For example, after receiving an email with a ticket, the receiver could request the ticket to be cancelled so it cannot be reused. The person who cancels a ticket also has the option to refund the ticket to the sender. This causes the original sender to regain a new ticket. For example, a user might refund a ticket that came with an email if it was not spam.

Using this, friendly and trusted emails would have little to no cost as tickets would be frequently refunded. However, spammers would be required to invest either a lot of computing time or money in order to create enough tickets to send large numbers of e-mails.

title: Penny Black (research project)


text: Category:Netherlands

title: Category:Netherlands


text:
Epaphroditus Champion

Epaphroditus Champion (April 6, 1756 – December 22, 1834) was an American politician and military officer from Connecticut. He served as a U.S. Representative from Connecticut.

Early life
Champion was born in Colchester in the Connecticut Colony, son of Colonel Henry Champion and Deborah (Brainard) Champion. He was educated both by private tutors and in the common schools.

Champion's brother Henry Champion was a major in the Continental Army during the Revolutionary War and served in the Connecticut state house of representatives.

Career
During the American Revolutionary War, Connecticut Governor Jonathan Trumbull directed Champion's father, Connecticut state commissary Colonel Henry Champion, to collect cattle and drive them to Valley Forge. Champion helped his father gather a herd of 300 cattle at Hartford, Connecticut and drive them west to King's Ferry, across the Hudson, into New Jersey, across the Delaware to Washington's famished troops west of the Schuylkill. They were devoured in five days prompting Champion to remark that the cattle were so thoroughly eaten that "you might have made a knife out of every bone." Champion was named assistant commissary to Trumbull in 1776, and was the first Commissary General of the Continental Army.

Champion moved to East Haddam, Connecticut in 1782. He served as a captain in the Twenty-fourth Regiment of the Connecticut State militia from 1784 to 1792, as major from 1793 to 1794, as lieutenant colonel from 1795 to 1798, and as brigadier general of the Seventh Brigade from 1800 to 1803.

He worked as a merchant, shipowner, exporter and importer. He was successful in conducting trade in the West Indies. Champion was a member of the Connecticut state assembly from 1791 to 1806. He was elected as a Federalist candidate to the Tenth United States Congress and to the four succeeding Congresses, serving from March 4, 1807 to March 3, 1817. After serving in Congress, he resumed his former business activities. Champion served as commissary general of provisions for army pensioners in 1832.

Personal life
In 1781, Champion married Lucretia Hubbard (1760–1836). Together, they had three children:

 * Lucretia Champion (1783–1882)
 * Clarissa Champion (1785–1801)
 * Epaphroditus Champion, Jr. (1786–1841).

Champion died on December 22, 1834, in East Haddam, Connecticut. He is interred in Riverview Cemetery in East Haddam. His epitaph reads, "Talents, benevolence and integrity characterized his spotless life."

Legacy
Champion's home in East Haddam is included in the East Haddam Historic District, which is listed on the National Register of Historic Places. The home is named the General Epaphroditus Champion House and was built in a late-Georgian style.

title: Epaphroditus Champion


text: Category:Postage stamps

title: Category:Postage stamps