text:
Glitter

Glitter is an assortment of flat, small, reflective particles that are precision cut and come in a variety of shapes, sizes, and colors. Glitter particles reflect light at different angles, causing the surface to sparkle or shimmer. Glitter is similar to confetti, sparkles and sequins, but somewhat smaller.

Since prehistoric times, glitter has been made from many different materials including stones such as malachite, and mica, as well as insects and glass. Uses for glitter include clothing, arts, crafts, cosmetics and body paint. Modern glitter is usually manufactured from the combination of aluminum and plastic, which is rarely recycled and can find its way into aquatic habitats, eventually becoming ingested by animals, leading some scientists to call for bans on plastic glitter.

Antiquity
Glittering surfaces have been found to be used since prehistoric times in the arts and in cosmetics. The modern English word "glitter" comes from the Middle English word gliteren, possibly by way of the Old Norse word glitra. However, as early as 30,000 years ago, mica flakes were used to give cave paintings a glittering appearance. Prehistoric humans are believed to have used cosmetics, made of powdered hematite, a sparkling mineral.

The Ancient Egyptians produced "glitter-like substances from crushed beetles" as well as finely ground green malachite crystal. Researchers believe Mayan temples were sometimes painted with red, green, and grey glitter paint made from mica dust, based on infrared scans of the remnants of paint still found on the structures in present-day Guatemala.

People of the Americas 8,000 years ago were using powdered galena, a form of lead, to produce a bright greyish-white glittering paint used for objects of adornment. The collecting and surface mining of galena was prevalent in the Upper Mississippi Valley region by the Cahokia native peoples, for regional trade both raw and crafted into beads or other objects.

Development
The first production of modern plastic glitter is credited to the American machinist Henry F. Ruschmann who invented a machine to cut photo films and paper in the 1930s. Sometimes, the machine "stuttered," generating small pieces of glossy cellulose that employees picked up and used as "snow" to decorate their Christmas trees, and modern glitter was born. With his partner, Harry Goetz, Ruschmann cut mica into washers and glitter from metallized cellulose acetate film. During World War II, glass glitter became unavailable so Ruschmann found a market for scrap plastics, which were ground into glitter. In 1943, he purchased Meadowbrook Farm in Bernardsville, New Jersey where he founded Meadowbrook Farm Inventions (MFI) in 1948 to produce industrial glitter. MFI became Meadowbrook Inventions, Inc. in 1953. Ruschmann filed a patent for a mechanism for cross-cutting films as well as other glitter-related inventions. Substrates for cutting glitter expanded from metalized cellulose and aluminum foil to metalized and iridescent film, polyester, PVC, and laminations cut into various shapes.

Production
Today over 20,000 varieties of glitter are manufactured in a vast number of different colors, sizes, and materials. One estimate suggests 10 e6lb of glitter was either purchased or produced between the years of 1989 and 2009, however the source provides no evidence or reference point. Commercial glitter ranges in size from 0.002 to .25 in a side. First, flat multi-layered sheets are produced combining plastic, coloring, and reflective material such as aluminium, titanium dioxide, iron oxide, and bismuth oxychloride. These sheets are then cut into tiny particles of many shapes including squares, triangles, rectangles, and hexagons.

Use
Prior to fabrics made with modern glitter, sequins were sewn or woven on to fabric to give it a glittering appearance. Edible glitter made from gum arabic and other ingredients is even used by culinary artists.

Glitter is used in cosmetics to make the face and nails shiny or sparkly. After the Microbead-Free Waters Act of 2015, the use of microbeads in toothpaste and other "rinse-off" cosmetics has been discontinued in the US, however since 2015 the industry has shifted toward instead using FDA-approved "rinse-off" metallized-plastic glitter as their primary abrasive agent.

Glitter is commonly used in arts and crafts to color, accessorise and texture items. The small, brightly colored particles often stick to clothing, skin, and furniture, and can be difficult to remove. It is also used on optically variable inks.

Glitter coatings or finishes are frequently used on fishing lures to draw attention by simulating the scales of prey fish.

Due to its unique characteristics, glitter has also proven to be useful forensic evidence. Because of the tens of thousands of different commercial glitters, identical glitter particles can be compelling evidence that a suspect has been at a crime scene. Forensic scientist Edwin Jones has one of the largest collections of glitter, consisting of over 1,000 different samples used in comparison of samples taken from crime scenes. Glitter particles are easily transferred through the air or by touch, yet cling to bodies and clothing, often unnoticed by suspects.

Glitter in culture
Glitter can be seen as a tool of fashion used by various subcultures, as it allows for a visible statement to be worn and seen on the body. This is because it has been theorized to be a "flickering signifier", or something that destabilizes known notions of popular culture, identity, and society. Glitter is associated with "fringe cultures", which often use excessive glitz and glamor (such as glitter) to evoke a deeper understanding between the relationships of commercialized popular culture and "high" culture, or "high-brow" art.

Used by glam rockers, such as David Bowie, Gary Glitter and Iggy Pop, glitter is also used as a tool to help blur gender lines. This helped to create the more extreme "glitter rock" – an even more heightened version of glam rock.

Glitter is also used by nail artists and make-up artists to make statements about femininity and beauty standards. The flashy, sparkling nature of glitter allows users to push standard ideas of beauty and what is and is not considered "excessive" in terms of make-up. Glitter is usually associated with nightlife and not professionalism, but wearing it in different settings can push these boundaries.

Because of its tendency to shed off of items it is applied to and stick onto unwanted surfaces, including skin, hair, and clothes, glitter is also used for glitter bombing, which is an act of protest in which activists throw glitter on people at public events. Glitter bombers have frequently been motivated by, though not limited to, their targets' opposition to same-sex marriage. Some legal officials argue glitter bombing is technically assault and battery. It is possible for glitter to enter the eyes or nose and cause damage to the cornea or other soft tissues potentially irritating them or leading to infection, depending on the size of the glitter. Whether a prosecutor would pursue the charges depends on a number of factors.

Environmental impact
Trisia Farrelly, an environmental anthropologist at Massey University, has called for a ban on glitter made of polyethylene terephthalate (PETE) and aluminum, as it is a microplastic that can leach hormonal disruptors into the environment. Furthermore, plastic glitter takes about one thousand years to biodegrade, according to Victoria Miller, a materials and engineering scientist at North Carolina State University. When dozens of British music festivals pledged to ban single-use plastics by 2021, the proposed ban included plastic glitter.

Biodegradable glitter made from eucalyptus tree extract is metaled with aluminium and can be coloured. It is "40% softer and more delicate on the skin than conventional glitter," and it decomposes in soil or water. Cellulose glitter is also available.

According to Chris Flower, director-general of the Cosmetic Toiletry and Perfumery Association, "the total contribution to marine plastic litter from glittery cosmetic products is negligible when compared to the damaging effects of bags and bottles... [While the] total effect of giving up traditional glitter might not be great in comparison with other harmful plastics, we should still do everything we can."

Since October 2023, some types of glitter have been restricted in the European Union as part of a ban on microplastics intentionally added to products.

title: Glitter


text:
Wikipedia:Articles for deletion/Akashic Records

I've read this page three times, and I have no idea what it's about. Whatever it is, it seems to be some kind of bizarro New Age concept with this article written in a very POV manner. Thunderbunny 03:45, 3 Aug 2004 (UTC)
 * Neutral. I've been fussing about with cleaning it up.  See the beginnings of a rewrite I've been attempting at User:Spectatrix/temp/.  In any case, very little has been accomplished in its 11 months on Pages needing attention, so it's high time that it's either rewritten or outright deleted.  Being deleted will merely mean that my rewrite will be put on the backburner compared to some of my other projects. Spectatrix 04:15, 2004 Aug 3 (UTC)
 * Keep. It's an important spirituality/religion/New Age concept, and the article actually isn't all that bad, especially when compared with its class of peers. A few attributions and "is said to be"s in place of a few "is"s, and we're basically there. Now, if you want a true New Age POV mess, see The Mother. And if "considered bizarro by some segment of the population" is the standard, there are hundreds of articles in Category:New Age, Category:New religious movements, and even Category:Religion that can be brought here next, followed by Category:Software engineering, if you catch my drift. --Gary D 04:42, 3 Aug 2004 (UTC)
 * Comment: my main sticking point in rewriting the article (for it does need to be reorganized in addition to be made NPOV) has been finding some good solid historical references to the Akashic Records. Though I've no doubt it's a very old concept, I'd like some actual documents to point to that mention Akasha, or at the very least the concepts now embodied in the phrase "Akashic Records". Spectatrix 05:02, 2004 Aug 3 (UTC)

 * Keep, with major changes. I agree with Spectatrix:  article claims historical evidence goes back to 7500 BC.  Who makes this claim?  Edgar Cayce?  Madam Balvatsky?  And what is the supposed evidence?  And as others have mentioned, needs NPOV work; article is a series of "factual" statements that would probably be better characterized as "religious" or "speculative". Gwimpey 05:20, Aug 3, 2004 (UTC)

 * Keep but cut drastically. It can be reduced to a single sentence, maybe two, explaining what these records are claimed to be and who claims it.  Then add an external link. (And BTW there are no solid historical references to the records, they were invented, like so much else, by Mme. Blavatsky.) Jumbo 13:39, 3 Aug 2004 (UTC)

 * Delete: I really think this is another way to say "Forbidden Knowledge" and such. Merge useful content as a small section in the article on New Age Religion.  A particular point of speculative apocrypha that then goes off to gobble up every culture's version of the dreamtime is a characteristic pseudo-historical move in New Age.  This article alledges that it's true, that it's fact.  Geogre 14:14, 3 Aug 2004 (UTC)
 * While you are indeed correct in evaulating the pseudo-historical tendencies of New Agers, I still feel as though this topic is deserving of its own article because it is a well-known topic amongst New Agers, pagans, and players of Mage: The Ascension (damn my gaming geek tendencies... lol). However, until I can find sufficient reference material to write an article with some real meat to it (as opposed to the fluff in the current article), I would support a merge and redirect with/to New Age. Spectatrix 17:10, 2004 Aug 3 (UTC)
 * Keep: Excellent rewrite. More can be done, but more can always be done.  Acceptably placed in general knowledge now.  Fine work. Geogre 02:52, 9 Aug 2004 (UTC)

 * This actually was an important topic for the Theosophy movement of the 19th cent., and spread from there into contemporary New Age culture. It's become a standard phrase in a lot of mystical and fantastical contexts; I vote to keep, and send to Pages Needing Attention. -FZ 18:03, 3 Aug 2004 (UTC)

 * Terribly POV. As it stands, delete. There may be an encyclopaedic article on the subject, but this isn't it. Fire Star 14:34, 4 Aug 2004 (UTC)

 * Good point- it does need pretty major changes, and may well not be worth keeping unless somebody wants to fix it quickly & use any of what's there. The original article is somewhat misleading. I amend my vote to an abstain. -FZ 16:20, 4 Aug 2004 (UTC)

 * Keep. I just did some work on the POV. It's not perfect but I think it's a reasonably good summary of a modern spiritual belief. It could use some trimming though. LeeHunter 02:48, 5 Aug 2004 (UTC)

 * Delete: content is still POV, factually dubious and meandering. If recreated, it should be at Akashic Record, which currently redirects to this article. -Sean Curtin 20:26, 5 Aug 2004 (UTC)

 * Keep: Don't delete ideas that people believe in simply because they stretch credulity. Leave descriptive information in wikipedia. This is an interesting idea. Science Fiction authors use it in conjunction with Everett many-worlds interpretation for short story plots. I came across the term "akashic" just a few days ago and I was delighted to be able to find a semidetailed explanation with references in wikipedia. -Spiderly 21:46, 5 Aug 2004 (UTC)
 * My vote only reflects the sorry state of the article itself, not the subject of it. The concept that everything one does is observed and recorded in another spiritual plane is widespread, from the 94th psalm to the Bodhisattva Akasagarbha. It is just this presentation of the concept that isn't of sufficient calbre to keep around. If someone were to rewrite it properly, I would change my vote. Fire Star 00:48, 6 Aug 2004 (UTC)
 * Can you give an example of language that specifically draws your objections? -Spiderly 18:55, 6 Aug 2004 (UTC)

 * Excellent cleanup- Keep. -FZ 12:41, 9 Aug 2004 (UTC)

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


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Statute of Westminster 1275

The Statute of Westminster of 1275 (3 Edw. 1), also known as the Statute of Westminster I, codified the existing law in England, into 51 chapters. Chapter 5 (which mandates free elections) is still in force in the United Kingdom and the Australian state of Victoria whilst part of Chapter 1 remains in force in New Zealand. It was repealed in Ireland in 1983.

William Stubbs gives a summary of the Statute:

"This act is almost a code by itself; it contains fifty-one clauses, and covers the whole ground of legislation. Its language now recalls that of Canute or Alfred, now anticipates that of our own day; on the one hand common right is to be done to all, as well poor as rich, without respect of persons; on the other, elections are to be free, and no man is by force, malice or menace, to disturb them. The spirit of the Great Charter is not less discernible: excessive amercements, abuses of wardship, irregular demands for feudal aids, are forbidden in the same words or by amending enactments. The inquest system of Henry II of England, the law of wreck, and the institution of coroners, measures of Richard and his ministers, come under review as well as the Provisions of Oxford and the Statute of Marlborough." Though it is a matter of dispute when peine forte et dure (Law French for "hard and forceful punishment") was first introduced, chapter 3 states that those felons standing mute shall be put in prison forte et dure.

History
The Statute of Westminster of 1275 was one of two English statutes largely drafted by Robert Burnell and passed during the reign of Edward I. Edward I had returned from the Ninth Crusade on 2 August 1274 and was crowned King of England on 19 August. His first Parliament was summoned for the quinzaine of the Purification on 16 February 1275 but was prorogued until the day after Easter on 22 April 1275, but did not meet until the week commencing 29 April or, according to Chronicle records, until the beginning of May, for unknown reasons. It met at Westminster, its main work being the consideration of the Statute of Westminster I, the agreement of new levies in Ireland and allowing the King to levy a new tax on wool. This was drawn up, not in Latin, but in Norman French, and was passed "by the assent of Archbishops, Bishops, Abbots, Priors, Earls, Barons, and [all] the Commonalty of the Realm, being thither summoned."

According to Yuen Yuen Ang, the statute replaced a previously communal regime of contract enforcement with one based on "individual responsibility, territorial law, the central administration of justice, and personal collateral."

Chapters
The Statute of Westminster I is composed of 51 chapters:

Ireland
In the early history of the Lordship of Ireland, English statutes were often applied to Ireland. A 1285 writ authorised Stephen de Fulbourn, then Justiciar of Ireland, to apply there English statutes including Westminster I, Westminster II, Gloucester, and those of merchants. A 1320 act of the Parliament of Ireland (13 Edw. 2 c.2) readopted all these statutes. An act of Edward Poynings' 1495 session of the Parliament of Ireland adopted statutes "formerly made for the common weal" in England; later the Maintenance and Embracery Act 1634 adopted all English statutes dealing with champerty and maintenance and embracery. Many chapters of the 1275 English statute were repealed with respect to Ireland by the Statute Law (Ireland) Revision Act 1872. In the Republic of Ireland, the Short Titles Act 1962 assigned the short title "Distress Act 1275" to chapter 16 of the 1275 English statute, as adopted under the 1495 Irish act; and the short title "Maintenance and Champerty Act 1275" to chapters 25 and 28 of the 1275 English statute, as adopted under the 1634 Irish act. The Statute Law Revision Act 1983 repealed the whole of the 1275 English statute and the 1285 and 1320 Irish statutes.

title: Statute of Westminster 1275


text:
Talk:Figwit

First
Urm.... I have been assured that this character does, in fact, exist, by someone who should know; I wasn't really convinced by this page and the website. Could someone provide explanation of where the character came from? Was he a practical joke of the filmmakers, or what? And what is the _actual_ origin of the name figwit -- is that an acronym or a backronym on the page? The explanation you give contradicts the one on the flavor text of the card from decipher.com.

 * As far as I know, the character was at first just one of the many elves sitting in the Council of Elrond, doing nothing important. Then, as the DVD came out, some fans watched the movie over and over again, and for some reason Figwit attracted their attention, maybe because of his funny look . A small fan-community quickly grew out of this phenomenon, they called him Figwit and started to collect every information they could find about this character and actor. It seems that because of this Peter Jacksons gave this character some lines to talk in the third movie of the series. I'm not an expert on this topic, so I may be incorrect in some of these points, feel free to correct me. --Conti|✉ 17:58, Aug 3, 2004 (UTC)

Elf Escort
Surely this is where this page belongs? Rich Farmbrough 15:21, 28 Dec 2004 (UTC)

 * Given that the only notability the character has is as the "fangirl phenomenon" 'Figwit', this is the right place. 'Elf Escort' would refer to any of the escorts, including the non-Figwit unnamed Elves. If the fen would not be so obsessed about the character, no article would be needed. Jordi·✆ 15:26, 28 Dec 2004 (UTC)

Figwit is official
I gave myself the Extended Edition of The Lord of the Rings: The Return of the King for Christmas, and Peter Jackson himself mentions the Figwit phenomenon in his commentary. --Phil | Talk 09:49, Dec 29, 2004 (UTC)

 * Cool, whereabouts? I assume during the "Arwen to the beach" scene…. I mentioned it in the article. Jordi·✆ 09:57, 29 Dec 2004 (UTC)

It's at the point where Figwit himself is on screen, which I think is the scene to which you refer…and, yes, PJ does use the name ;-) --Phil | Talk 10:52, Dec 29, 2004 (UTC)

Melpomaen
Where does the name Melpomaen come from? Pure 'fan' invention? Jordi·✆ 23:57, 29 Mar 2005 (UTC)
 * It sounds a little too Greek-derivative to be any kind of genuine name; while we can't rule out being an offscreen production name, the crediting as 'Elf Escort' seems to make this unlikely too. -- Perey 09:12, 3 Apr 2005 (UTC)
 * The name Melpomaen comes from the Figwit Lives! website - it's a "very loose Elvish translation of 'fig' and 'wit' " I believe it was originally coined to have a more 'elvish' name by which to call the character; this was before the name Aegnor came from the Decipher cards.
 * I went ahead and moved this unlikely and unsourced refource. A reputable source needs to be cited in order for it to be included.
 * I'm also removing these paragraphs, which as they currently stand are excessively fannish:
 * "After the release of The Lord of the Rings: The Return of the King, some Lord of the Rings fans nicknamed another seemingly-innocuous character Fidwis, an acronym for 'Faramir is dead... who is SHE?!?' Fidwis appears in Minas Tirith as Faramir leads a troop of Gondorian soldiers out of the city in an attempt to retake Osgiliath. However, Fidwis's fame never reached the heights of Figwit's, likely because excitement about the Lord of the Rings died down not long after the release of the third movie."
 * "Figwit does little in the movies indeed, but by many Figwit fans he is viewed as a god, so basically he's famous for doing practically nothing."
 * That last paragraph is unnecessary (so no need to fix it) and I'm not sure that the second-to-last is worth mentioning. Basically the idea is a little-known piggyback on an internet phenomenon, not an actual internet phenomenon itself. -Aranel (" Sarah ") 19:40, 4 August 2005 (UTC)

 * However, Fidwis's fame never reached the heights of Figwit's, likely because excitement about the Lord of the Rings died down not long after the release of the third movie. What the heck?! 222.126.73.236 16:35, 7 August 2006 (UTC)

Actual phrase
I read that sentence - "Frodo is great...who is that?" - again and again, and I just couldn't make any sense of it. It's just two disjointed sentences. Then I checked out the original fan site, where the orthography is: "Frodo is grea...who is THAT?!?" This made it clear immediately: a train of thought is interrupted as the spectator's attention is attracted elsewhere on the screen. It makes all the difference in the world!

Presumably some journalist who didn't get it has misrepresented the sentence in an article, and then the error has been perpetuated by lazy cut-and-paste journalism. Even the documentary film makers got it wrong! Anyway, I changed the writing in the article, and referenced it to the original source. Fan sites may not generally be considered reliable sources, but it's different when that was where the phrase actually originated. Lampman (talk) 11:22, 20 August 2008 (UTC)

 * I figured it would be more clear without dropping the letters and using unnecessary capitals, but I see your point, so it's fine. Mr. Absurd (talk) 14:37, 20 August 2008 (UTC)

Same as Lindir
In the audio commentary and bonus material for "An Unexpected Journey" Peter Jackson makes it clear that Findir from The Hobbit (movie) is to be treated as the same character as Figwit from LOTR (movie). Figwit was an unofficial nickname and never appeared in the credits, so they decided to give him a proper canonical name for The Hobbit. This practice of retcon is well known of. I would fix the article myself, but it seems to be a status one. Anything in particular I should know? If not, I'll edit it anyway. 5.164.149.157 (talk) 23:16, 5 January 2014 (UTC)

External links modified
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External links modified
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 * Added archive https://web.archive.org/web/20080804180135/http://www.lotr-models.co.uk/index106.html to http://www.lotr-models.co.uk/index106.html

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title: Talk:Figwit


text:
Talk:Catholic University of America

Untitled section
History. This University is linked in Wikipedia to the gas project in world war 1. According to Theo Emery Hellfire Boys page 50 onward, the American University was a Protestant University. It was founded as a rival to the Catholic University of America, had never prospered. It offered its grounds to the gas project.

The Catholic University was also used in this project. But the main campus was the Protestant school. Not the Catholic one. — Preceding unsigned comment added by 2001:8003:a99f:8901:ad59:4a92:1626:e925 (talk) 05:21, 14 August 2022 (UTC)

title: Talk:Catholic University of America


text:
Representation theory of the symmetric group

In mathematics, the representation theory of the symmetric group is a particular case of the representation theory of finite groups, for which a concrete and detailed theory can be obtained. This has a large area of potential applications, from symmetric function theory to quantum chemistry studies of atoms, molecules and solids.

The symmetric group Sn has order n!. Its conjugacy classes are labeled by partitions of n. Therefore according to the representation theory of a finite group, the number of inequivalent irreducible representations, over the complex numbers, is equal to the number of partitions of n. Unlike the general situation for finite groups, there is in fact a natural way to parametrize irreducible representations by the same set that parametrizes conjugacy classes, namely by partitions of n or equivalently Young diagrams of size n.

Each such irreducible representation can in fact be realized over the integers (every permutation acting by a matrix with integer coefficients); it can be explicitly constructed by computing the Young symmetrizers acting on a space generated by the Young tableaux of shape given by the Young diagram. The dimension $$d_\lambda$$ of the representation that corresponds to the Young diagram $$\lambda$$ is given by the hook length formula.

To each irreducible representation ρ we can associate an irreducible character, χρ. To compute χρ(π) where π is a permutation, one can use the combinatorial Murnaghan–Nakayama rule . Note that χρ is constant on conjugacy classes, that is, χρ(π) = χρ(σ−1πσ) for all permutations σ.

Over other fields the situation can become much more complicated. If the field K has characteristic equal to zero or greater than n then by Maschke's theorem the group algebra KSn is semisimple. In these cases the irreducible representations defined over the integers give the complete set of irreducible representations (after reduction modulo the characteristic if necessary).

However, the irreducible representations of the symmetric group are not known in arbitrary characteristic. In this context it is more usual to use the language of modules rather than representations. The representation obtained from an irreducible representation defined over the integers by reducing modulo the characteristic will not in general be irreducible. The modules so constructed are called Specht modules, and every irreducible does arise inside some such module. There are now fewer irreducibles, and although they can be classified they are very poorly understood. For example, even their dimensions are not known in general.

The determination of the irreducible modules for the symmetric group over an arbitrary field is widely regarded as one of the most important open problems in representation theory.

Symmetric groups
The lowest-dimensional representations of the symmetric groups can be described explicitly, and over arbitrary fields. The smallest two degrees in characteristic zero are described here:

Every symmetric group has a one-dimensional representation called the trivial representation, where every element acts as the one by one identity matrix. For n ≥ 2, there is another irreducible representation of degree 1, called the sign representation or alternating character, which takes a permutation to the one by one matrix with entry ±1 based on the sign of the permutation. These are the only one-dimensional representations of the symmetric groups, as one-dimensional representations are abelian, and the abelianization of the symmetric group is C2, the cyclic group of order 2.

For all n, there is an n-dimensional representation of the symmetric group of order n!, called the , which consists of permuting n coordinates. This has the trivial subrepresentation consisting of vectors whose coordinates are all equal. The orthogonal complement consists of those vectors whose coordinates sum to zero, and when n ≥ 2, the representation on this subspace is an (n − 1)-dimensional irreducible representation, called the standard representation. Another (n − 1)-dimensional irreducible representation is found by tensoring with the sign representation. An exterior power $$\Lambda^k V$$ of the standard representation $$V$$ is irreducible provided $$0\leq k\leq n-1$$.

For n ≥ 7, these are the lowest-dimensional irreducible representations of Sn – all other irreducible representations have dimension at least n. However for n = 4, the surjection from S4 to S3 allows S4 to inherit a two-dimensional irreducible representation. For n = 6, the exceptional transitive embedding of S5 into S6 produces another pair of five-dimensional irreducible representations.

Alternating groups
The representation theory of the alternating groups is similar, though the sign representation disappears. For n ≥ 7, the lowest-dimensional irreducible representations are the trivial representation in dimension one, and the (n − 1)-dimensional representation from the other summand of the permutation representation, with all other irreducible representations having higher dimension, but there are exceptions for smaller n.

The alternating groups for n ≥ 5 have only one one-dimensional irreducible representation, the trivial representation. For n = 3, 4 there are two additional one-dimensional irreducible representations, corresponding to maps to the cyclic group of order 3: A3 ≅ C3 and A4 → A4/V ≅ C3.

 * For n ≥ 7, there is just one irreducible representation of degree n − 1, and this is the smallest degree of a non-trivial irreducible representation.
 * For n = 3 the obvious analogue of the (n − 1)-dimensional representation is reducible – the permutation representation coincides with the regular representation, and thus breaks up into the three one-dimensional representations, as A3 ≅ C3 is abelian; see the discrete Fourier transform for representation theory of cyclic groups.
 * For n = 4, there is just one n − 1 irreducible representation, but there are the exceptional irreducible representations of dimension 1.
 * For n = 5, there are two dual irreducible representations of dimension 3, corresponding to its action as icosahedral symmetry.
 * For n = 6, there is an extra irreducible representation of dimension 5 corresponding to the exceptional transitive embedding of A5 in A6.

Kronecker coefficients
The tensor product of two representations of $$S_n$$ corresponding to the Young diagrams $$\lambda,\mu$$ is a combination of irreducible representations of $$S_n$$,

V_\lambda\otimes V_\mu \cong \sum_\nu C_{\lambda,\mu,\nu} V_\nu $$ The coefficients $$C_{\lambda\mu\nu}\in\mathbb{N}$$ are called the Kronecker coefficients of the symmetric group. They can be computed from the characters of the representations :

C_{\lambda,\mu,\nu} = \sum_\rho \frac{1}{z_\rho} \chi_\lambda(C_\rho)\chi_\mu(C_\rho)\chi_\nu(C_\rho) $$ The sum is over partitions $$\rho$$ of $$n$$, with $$C_\rho$$ the corresponding conjugacy classes. The values of the characters $$\chi_\lambda(C_\rho)$$ can be computed using the Frobenius formula. The coefficients $$z_\rho$$ are

z_\rho = \prod_{j=0}^n j^{i_j}i_j! = \frac{n!}{|C_\rho|} $$ where $$i_j$$ is the number of times $$j$$ appears in $$\rho$$, so that $$\sum i_jj = n$$.

A few examples, written in terms of Young diagrams :

(n - 1, 1) \otimes (n - 1, 1) \cong (n) + (n - 1, 1) + (n - 2, 2) + (n - 2, 1,1) $$

(n - 1, 1) \otimes (n - 2, 2) \underset{n>4}{\cong} (n - 1, 1) + (n - 2, 2) + (n - 2, 1, 1) + (n - 3, 3) + (n - 3, 2, 1) $$

(n - 1, 1) \otimes (n - 2, 1,1) \cong (n - 1, 1) + (n - 2, 2) + (n - 2, 1,1) + (n - 3, 2, 1) + (n - 3, 1,1,1) $$

\begin{align} (n - 2, 2) \otimes (n - 2, 2) \cong & (n) + (n - 1, 1) + 2(n - 2, 2) + (n - 2, 1,1) + (n - 3, 3) \\ & + 2(n - 3, 2, 1) + (n - 3, 1,1,1) + (n - 4, 4) + (n - 4, 3, 1) + (n - 4, 2, 2) \end{align} $$ There is a simple rule for computing $$(n-1,1)\otimes \lambda$$ for any Young diagram $$\lambda$$ : the result is the sum of all Young diagrams that are obtained from $$\lambda$$ by removing one box and then adding one box, where the coefficients are one except for $$\lambda$$ itself, whose coefficient is $$\#\{\lambda_i\}-1$$, i.e., the number of different row lengths minus one.

A constraint on the irreducible constituents of $$V_\lambda\otimes V_\mu$$ is

C_{\lambda,\mu,\nu}>0 \implies |d_\lambda-d_\mu| \leq d_\nu \leq d_\lambda+d_\mu $$ where the depth $$d_\lambda=n-\lambda_1$$ of a Young diagram is the number of boxes that do not belong to the first row.

Reduced Kronecker coefficients
For $$\lambda$$ a Young diagram and $$n\geq \lambda_1$$, $$\lambda[n]=(n-|\lambda|,\lambda)$$ is a Young diagram of size $$n$$. Then $$C_{\lambda[n],\mu[n],\nu[n]}$$ is a bounded, non-decreasing function of $$n$$, and

\bar{C}_{\lambda,\mu,\nu} = \lim_{n\to\infty} C_{\lambda[n],\mu[n],\nu[n]} $$ is called a reduced Kronecker coefficient or stable Kronecker coefficient. There are known bounds on the value of $$n$$ where $$C_{\lambda[n],\mu[n],\nu[n]}$$ reaches its limit. The reduced Kronecker coefficients are structure constants of Deligne categories of representations of $$S_n$$ with $$n\in \mathbb{C}-\mathbb{N}$$.

In contrast to Kronecker coefficients, reduced Kronecker coefficients are defined for any triple of Young diagrams, not necessarily of the same size. If $$|\nu|=|\lambda|+|\mu|$$, then $$\bar{C}_{\lambda,\mu,\nu}$$ coincides with the Littlewood-Richardson coefficient $$c_{\lambda,\mu}^\nu$$. Reduced Kronecker coefficients can be written as linear combinations of Littlewood-Richardson coefficients via a change of bases in the space of symmetric functions, giving rise to expressions that are manifestly integral although not manifestly positive. Reduced Kronecker coefficients can also be written in terms of Kronecker and Littlewood-Richardson coefficients $$c^\lambda_{\alpha\beta\gamma}$$ via Littlewood's formula

\bar{C}_{\lambda,\mu,\nu} = \sum_{\lambda',\mu',\nu',\alpha,\beta,\gamma} C_{\lambda',\mu',\nu'} c^{\lambda}_{\lambda'\beta\gamma} c^{\mu}_{\mu'\alpha\gamma} c^\nu_{\nu'\alpha\beta} $$ Conversely, it is possible to recover the Kronecker coefficients as linear combinations of reduced Kronecker coefficients.

Reduced Kronecker coefficients are implemented in the computer algebra system SageMath.

Eigenvalues of complex representations
Given an element $$w\in S_n$$ of cycle-type $$\mu=(\mu_1,\mu_2,\dots,\mu_k)$$ and order $$m=\text{lcm}(\mu_i)$$, the eigenvalues of $$w$$ in a complex representation of $$S_n$$ are of the type $$\omega^{e_j}$$ with $$\omega=e^{\frac{2\pi i}{m}}$$, where the integers $$e_j\in \frac{\mathbb{Z}}{m\mathbb{Z}}$$ are called the cyclic exponents of $$w$$ with respect to the representation.

There is a combinatorial description of the cyclic exponents of the symmetric group (and wreath products thereof). Defining $$\left(b_\mu(1),\dots,b_\mu(n)\right) = \left(\frac{m}{\mu_1},2\frac{m}{\mu_1},\dots, m, \frac{m}{\mu_2},2\frac{m}{\mu_2},\dots, m,\dots\right)$$, let the $$\mu$$-index of a standard Young tableau be the sum of the values of $$b_\mu$$ over the tableau's descents, $$\text{ind}_\mu(T) = \sum_{k\in \{\text{descents}(T)\}} b_\mu(k)\bmod m$$. Then the cyclic exponents of the representation of $$S_n$$ described by the Young diagram $$\lambda$$ are the $$\mu$$-indices of the corresponding Young tableaux.

In particular, if $$ w $$ is of order $$n$$, then $$b_\mu(k)=k$$, and $$\text{ind}_\mu(T)$$ coincides with the major index of $$T$$ (the sum of the descents). The cyclic exponents of an irreducible representation of $$S_n$$ then describe how it decomposes into representations of the cyclic group $$ \frac{\mathbb{Z}}{n\mathbb{Z}}$$, with $$\omega^{e_j}$$ being interpreted as the image of $$w$$ in the (one-dimensional) representation characterized by $$e_j$$.


text:
Liahona (Book of Mormon)

In to the Book of Mormon, the Liahona is a brass ball with two spindles, one of which directs where Lehi and his companions should travel after they leave Jerusalem at the beginning of the narrative. Some early participants in the Latter Day Saint movement, believing contrary to mainstream findings that the Book of Mormon described genuinely historical events, claimed to have seen the Liahona. The Church of Jesus Christ of Latter-day Saints and its members have used the Liahona as a namesake, such as in the name of the magazine the Liahona and in the idea of "Liahona Mormons".

Background
The Book of Mormon, published in 1830, is one of the primary religious texts of Mormonism, also known as the Latter Day Saint movement. Founder Joseph Smith said that an angel of the Christian God directed him to uncover metal plates inscribed with the history of an ancient American people and that by miraculous means he translated the writing on these plates, producing the Book of Mormon. Most in the Latter Day Saint movement regard the Book of Mormon as being genuinely ancient and historical, contrary to mainstream academic archaeology's finding that Book of Mormon historicity is implausible and unproven.

Depiction
In the Book of Mormon, a man named Lehi and his family live in Jerusalem prior to the Babylonian captivity. God communicates with Lehi and directs him to lead his family away from Jerusalem. While they camp in the wilderness, the Liahona is found one morning at Lehi's tent door. It is not named as the Liahona at this point. It is described as a "brass ball" of "curious workmanship" with "two spindles", one of which indicate the direction that his party should travel. On occasion writing mystically appears on the ball that displayed additional instructions from God. Using the Liahona, Lehi and his party travel through a wilderness and across an ocean. The Liahona works "according to the faith and diligence" with which they heed its direction, and ceases functioning at times when the members of the party demonstrate a loss of faith in God's commandments, notably when Nephi's brothers rebelled against Lehi during their ocean crossing.

In the Book of Alma, Alma identifies the object as "Liahona" when speaking to his son Helaman, saying, "our fathers called it Liahona, which is, being interpreted, a compass".

Cultural reception
Joseph Smith and three compatriots of his—Oliver Cowdery, David Whitmer, and Martin Harris, known as the Three Witnesses to the Book of Mormon—said that God promised to show them the Liahona and did show it to them in what they believed was a miraculous vision. This claimed promise is included in the Doctrine and Covenants, a Mormon religious text that compiles documents that adherents believe to be divine revelations. The Church of Jesus Christ of Latter-day Saints, the largest denomination in the Latter Day Saint movement, named one of its magazines, the Liahona, after the object, referencing its purpose of directing people. A 1967 essay categorized approaches to Latter-day Saints worship as being either like the Iron Rod (another object from the Book of Mormon)—rigid and unambiguous—or like the Liahona, flexible and based on experiencing what Latter-day Saints believe to be revelation. This has been called the "Iron Rod–Liahona scales". The concept of "Liahona Mormons" circulated among Latter-day Saints, and it was acknowledged in the denomination's General Conference.

title: Liahona (Book of Mormon)


text:
Garrett Brown

Garrett Brown (born April 6, 1942) is an American inventor, best known as the creator of the Steadicam. Brown's invention allows camera operators to film while walking without the normal shaking and jostles of a handheld camera. The Steadicam was first used in the Hal Ashby film Bound for Glory (1976), receiving an Academy Award (Best Cinematography), and since used on such films as Rocky, filming Rocky's running and training sequences, and Return of the Jedi, where Brown walked through a Redwood forest with the Steadicam shooting film at 1 frame per second to achieve the illusion of high speed motion during the speeder-bike chase.

The sequence in Rocky that took the audience up what would later be known as the Rocky Steps of the Philadelphia Museum of Art for the triumphant moment at the top was first filmed during tests for the original Steadicam system. The system was used extensively on Stanley Kubrick's 1980 classic horror film The Shining, starring Jack Nicholson. Brown's Steadicam work can be seen in over seventy motion pictures.

Brown has also invented the SkyCam (for football games), DiveCam (following olympic divers) and MobyCam (underwater camera following olympic swimmers).

Garrett Brown is the father of TV Director Jonathan Brown. Both worked together as Steadicam operators on the film Bulworth, directed by and starring Warren Beatty. A member of the American Society of Cinematographers and the Directors Guild of America, Garrett Brown was recipient of an Oscar for Scientific or Technical Achievement from the Academy of Motion Picture Arts and Sciences and an Emmy Award from the National Academy of Television Arts and Sciences for his invention of the Steadicam.

Early years
After his graduation from Haverford High School, he matriculated at Tufts University, where he met Al Dana. Together, they formed the folk duo Brown & Dana, and recorded the classic "It Was a Very Good Year", among others. Brown also attained a cult following for his radio advertisements with Anne Winn, especially for Molson Golden beer. Their witty repartee became a template for others.

Inventions
Garrett Brown has invented multiple camera supports focusing mostly on camera stabilization.

 * Equipois: A mechanical arm for heavy equipment.
 * FlyCam: A closed loop, stabilized tracking camera system.
 * DiveCam: The first dropping vertical camera system.
 * GoCam: The ultra-light high speed camera tracking system.
 * MobyCam: The first submarine tracking camera system.
 * SkyCam: The first suspended flying camera system.
 * Steadicam: The original handheld stabilizing system.
 * Steadicam Merlin: Next generation hand held Steadicam system.
 * Steadicam Tango: A new Steadicam accessory for floor-to-ceiling boom range.
 * SuperFlyCam: An ultralight stabilized 35mm wire-borne flying camera.
 * Zeen: Elevating walker chair. http://gozeen.com/

Awards and recognitions

 * 2013 – Joined the National Inventors Hall of Fame for his "Equipment for Use with Hand Held Motion Picture Cameras" Patent No. 4,017,168 the Steadicam® Camera Stabilizer.
 * 2012 – Steadicam Guild Life Achievement Award.

Academy Award

 * 2006 – Scientific and Engineering Award – For the original concept of the Skycam flying camera system - the first use of 3D volumetric cable technology for motion picture cinematography.
 * 2001 – American Society of Cinematographers – President's Award
 * 1999 – Technical Achievement Award – Shared with: Jerry Holway For the creation of the Skyman flying platform for Steadicam operators.
 * 1978 – Academy Award of Merit – (The Cinema Products Corporation. Engineering Staff under the supervision of John Jurgens). For the invention and development of Steadicam.

Society of Camera Operators

 * 2008 – Technical Achievement Award Shared with: Jerry Holway (inventor) (The Tiffen Company [us] (developer) ). For the Ultra2 Steadicam camera support system.
 * 1998 – Historical Shot for: Bound for Glory (1976).
 * 1992 – Technical achievement award Shared with: Ed Di Giulio (ceo Cinema Products) (Cinema Products (developer) ). For the Steadicam camera stabilizing system.

Nikola Tesla Satellite Award

 * 2014 – For visionary achievement in filmmaking technology

title: Garrett Brown


text:
Talk:Potomac, Maryland

Affluency
Are there any sources for the affluency stuff, esp. the 90210 show? Also, I'd like to tone down "rich professionals" as it almost seems derogative. Any comments? --Sarcasticninja 03:57, Aug 3, 2004 (UTC)

Why should it be toned down? It's true. Trust me, I know. I live five minutes away. - Big Brother

The Beverly Hills 90210 is indeed a fact. I'll look into citing it. It also appears in the Beverly Hills 90210 article here on Wikipedia. Now, your other point is probably something that should be fixed. The list itself is quiet long and difficult to read. Someone (perhaps me) should look at other affluent neighborhoods and see how Notable Residency is handled. Edaru 21:37, 22 August 2006 (UTC) — Preceding comment signed as by Edaru (talk • contribs) actually added by W Ed (talk • contribs)

Is this really the kind of information people would want to know? I feel like this article has been gobbled up by realtors and high school students with sloppy setance construction habits. I grew up there. I'd be interested in seeing 1) geography, 2) history, 3) economy, 4) land usage (the land usage pattern is unusal: there are a lot of mature trees for a suburban area.)

I think all the affluent talk and the list of celebs is a big gouche, and to say the least could be a bit better organized, and perhpas deprioritized. —Preceding unsigned comment added by 71.34.22.127 (talk • contribs) 05:11, 14 May 2007

Cleanup
This article needs major help. It's completely unsourced, appears to be WP:OR and most of the article is a list of notable residents which is WP:Trivia. Toddstreat1 01:02, 26 September 2007 (UTC)

 * I concur. I went through and reformatted the article to conform a bit better with the WikiProject:Cities format, removed the redlinked "celebrities", and tagged the neighborhoods section as unencyclopedic. That whole section reads like a real estate brochure, and adds nothing to the article except fluff. It appears that most of the editing of this article is vandalism and reversion rather than actual improvements, which is rather pathetic. I just added the WikiProject Maryland template, which might get some knowledgeable editors to fix this fiasco. Horologium t-c 12:17, 20 October 2007 (UTC)

"Peacock Terms"
I got rid of the "peacock terms" on the Copenhaver neighborhood article. The comments on it were pretty much just promoting the neighborhood's features. I am going to clean-up all of the peacock terms in the neighborhood section soon (note the peacock notice on top of the neighborhood section).

Are we realators or Wikipedians? This advertising isn't appropriate for Wikipedia articles. Sections about neighborhoods should be brief, not a huge paragraph on how great the neighborhood's pools and tennis courts are.

Tell me if you want them back, but I strongly disagree. (Wikipedian1234 (talk) 00:24, 20 February 2008 (UTC))

UPDATE I deleted most of the neighborhood section. Should we delete the celebrity section to? I also deleted the part of the history where it explained "the night life of Potomac Towne" and how many shops were in it and how it was and when the article was explaining how the town inspired a TV show. This has nothing to do with history at all. This is starting to get rediculous. (Wikipedian1234 (talk) 15:52, 8 March 2008 (UTC))

I added the expansion icon to the history article, because that is what needs to happen.--(Wikipedian1234 (talk) 20:47, 6 April 2008 (UTC))

I deleted the part of the history section that talks about the community meet-up. This has nothing to do with the history of Potomac--(Wikipedian1234 (talk) 23:48, 8 April 2008 (UTC))

Alright I'm back. I deleted the neighborhood part of the article because it was clearly unneeded and stuffed with peacock terms. This article should only be about the town, not about its residents or about how rich everyone is- (Wikipedian1234 (talk) 05:14, 28 May 2009 (UTC))

Notable people
Most of the individuals listed under this articles section on notable residents are simply not very notable among members of the general public.

Marriott hotel founder - fine Doug Ingram President of the Ingram group - who in hell is this schmuck?? —Preceding unsigned comment added by 68.33.186.110 (talk) 23:23, 20 March 2008 (UTC)

I agree. There should only be "notable residents" that are known to the general public. Half of them are just a bunch of Potomac aristocrats that not many people care about. And by the way, who brout the neighborhoods section back? and you below me, quit talking about your weed fantasies.-(Wikipedian1234 (talk) 19:21, 21 March 2008 (UTC))

General Flavor of the Potomac, Maryland entry

I lived in Potomac from 1960-1975 and made various contributions to the article. The page used to have some real feeling as to what the town is like. However, other contributors seem bent on sanitizing it. Pretty soon it will just be the latitude, longitude and population.Seth1066 (talk) 10:13, 11 December 2009 (UTC)

Seth, The character of Potomac has changed significantly since you lived there. (I live there now - have for about 20 years.) The town used to be unique. Now, it's more sanitized in the same way that the article has been! For the most part, neighborhoods and stores in Potomac look just like those of its neighbors. A few pockets of the old Potomac remain but it is largely no longer stereotypical Potomac from the times you lived there. --Donlibes (talk) 16:59, 14 May 2017 (UTC)

Canaze Indian nation
I was trying to find out more about this, but a Google search does not lead to any info about this nation. The only results are things that quote this article. Could this be a misspelling of something else? Inf-in MD (talk) 19:53, 28 August 2021 (UTC)

title: Talk:Potomac, Maryland


text:
Henry B. Eyring

Henry Bennion Eyring (born May 31, 1933) is an American educational administrator, author, and religious leader. Eyring has been the second counselor to Russell M. Nelson in the First Presidency of the Church of Jesus Christ of Latter-day Saints (LDS Church) since January 14, 2018. Previously, Eyring was the first counselor to Thomas S. Monson in the First Presidency from 2008 until Monson's death on January 2, 2018. Eyring was the second counselor to Gordon B. Hinckley in the First Presidency from October 6, 2007, until Hinckley's death on January 27, 2008.

While he has been a general authority of the church, Eyring has also served in the Quorum of the Twelve Apostles, the First Quorum of the Seventy, and the Presiding Bishopric. Eyring has served twice as commissioner of the Church Educational System. Currently, he is the fourth most senior apostle among the ranks of the church.

Early life
Eyring was born in Princeton, New Jersey, the second child of Henry Eyring, then a professor at Princeton and later the dean of the graduate school at the University of Utah and president of the American Chemical Society, and his wife, Mildred Bennion. His father's sister, Camilla Eyring, married Spencer W. Kimball, making Henry B. the nephew of Kimball, who was the twelfth president of the LDS Church.

He lived in Princeton until his early teenage years. Until the start of World War II they attended LDS meetings at the branch in New Brunswick, New Jersey, but with the gasoline rationing of the war, they received permission to hold meetings in their home, which often had only the Eyring family. As a teenager, Eyring and his family moved to Salt Lake City, where his father took a post at the University of Utah.

Military service and education
Eyring spent two years in the U.S. Air Force, stationed at Sandia Base in New Mexico. In New Mexico, Eyring served as a district missionary for the LDS Church. Eyring had been in the ROTC at the University of Utah. While in the Air Force, he served as a liaison between military officers and scientists. His main responsibility was to analyze data from weapons tests of nuclear weapons. At the end of the assignment, he gave a report and ended up meeting in person with a collection of several leading generals.

He had previously received a bachelor's degree in physics from the University of Utah. He went on to earn both master's and doctoral degrees in business administration from the Harvard Business School, before embarking on a career in academia. Over the summer after his first year at Harvard, Eyring did an internship with Arthur D. Little as a consultant for Abitibi Power and Paper Company. He did an analysis to study how to improve the process of river logging. His suggestion was to abandon river logging and turn to truck transport of logs, but a combination of not studying the issue deeply enough and having a CEO of the company who had risen through the ranks from being a river logger prevented Eyring's suggestions from being adopted then.

While studying at Harvard, Eyring was heavily influenced by Georges Doriot, who offered Eyring a chance to work with him and Ken Olsen, the founder of Digital Equipment Company. Eyring chose instead to pursue a doctorate in business.

Academic and business career
In the fall of 1962, Eyring began work as a professor at Stanford University. He finished his doctorate in business in the summer of 1963. That summer, Eyring completed a fellowship with the RAND Corporation. Eyring had married his wife, Kathleen, the summer before he started at Stanford, and they spent their first year of married life moving through various homes his real estate developer father-in-law was in the process of refurbishing. They then spent the next ten years living in the guest house of his in-laws' property.

Among Eyring's associates at Stanford were Roger Sant and Ed Zschau. Eyring worked with Zschau in the founding of the computer company System Industries.

Eyring was an associate professor of business at the Stanford Graduate School of Business from 1962 to 1971. He was also a Sloan Visiting Faculty Fellow at the Massachusetts Institute of Technology. At MIT, he took multiple courses in human behavior, including courses from Douglas McGregor, who died of a heart attack while Eyring was at MIT, and also Ed Schein and Warren Bennis.

Eyring has served twice as commissioner of church education, from September 1980 to April 1985, and from September 1992 to January 2005, when he was replaced by W. Rolfe Kerr.

LDS Church service
Among other callings in the LDS Church, Eyring has served as a regional representative, bishop and member of the Sunday School General Board. Eyring served as an early-morning seminary teacher early in his time as a professor at Stanford University, and as bishop of the Stanford singles ward later on.

Eyring served as president of Ricks College from 1971 to 1977, as a counselor to Presiding Bishop Robert D. Hales from 1985 to 1992, and as a member of the First Quorum of the Seventy, from 1992 to 1995.

Following the death of church president Howard W. Hunter, Eyring was sustained as a member of the church's Quorum of the Twelve Apostles on April 1, 1995 and ordained an apostle later that week.

Eyring was sustained as second counselor in the church's First Presidency on October 6, 2007, filling the vacancy left by the death of James E. Faust, on August 10, 2007. When the First Presidency was reorganized following the death of Gordon B. Hinckley, Eyring was called and set apart as the first counselor on February 3, 2008. The new First Presidency, with Monson as president, was announced on February 4, 2008.

As a member of the First Presidency, Eyring has dedicated the San Salvador El Salvador, Gilbert Arizona, Payson Utah, Indianapolis Indiana, and Philadelphia Pennsylvania Temples where he had also presided at the groundbreaking in 2011 as well as rededicating the Buenos Aires Argentina and Mexico City Mexico Temples.

In 2014, after a meeting with Pope Francis, Eyring spoke at Humanum, "an International Interreligious Colloquium on The Complementarity of Man and Woman," held in Vatican City. It was the first time that a pope and a top LDS general authority ever met.

Family
Eyring and his wife, Kathleen Johnson, met at a YSA meeting held at Rindge, New Hampshire at the Cathedral of the Pines in the spring of 1960. They became further acquainted at a meeting at the LDS Longfellow Park Chapel in Cambridge, Massachusetts, the next summer. Johnson was a native of Palo Alto and was a student at Stanford University. She had previously studied summers at the University of Vienna and University of Paris and was studying at Harvard University the summer she met Eyring. Wilbur Cox, the LDS Church's district president (to whom Eyring was serving as a counselor), made accommodations to facilitate Eyring's dating Johnson. After an intense courtship that first summer, Eyring and Johnson continued courting with her making multiple cross-country airplane trips until they were engaged early in 1961. They were married in the LDS Church's Logan Temple on July 27, 1962, with the ceremony performed by his uncle, Spencer W. Kimball. The couple were married for 61 years until Kathleen's death on October 15, 2023, at the age of 82.

They are the parents of six children (four sons and two daughters). Their sons include Henry J. Eyring, past president of BYU–Idaho (2017 to 2023); and Matthew J. Eyring, the chief strategy innovation officer of Vivint, a home automation company in North America. Eyring is a first cousin once-removed of former Michigan governor George W. Romney; his paternal grandmother was Romney's aunt.

Honors

 * Honorary Doctor of Humane Letters, University of Utah (2015)
 * Honorary Doctor of Humane Letters, Utah Valley University (2017)

Published works

 * . Database:PsycINFO Electronic, accessed March 12, 2009
 * . Database:PsycINFO Electronic, accessed March 12, 2009
 * . Database:PsycINFO Electronic, accessed March 12, 2009
 * . Database:PsycINFO Electronic, accessed March 12, 2009
 * . Database:PsycINFO Electronic, accessed March 12, 2009
 * . Database:PsycINFO Electronic, accessed March 12, 2009
 * . Database:PsycINFO Electronic, accessed March 12, 2009
 * . Database:PsycINFO Electronic, accessed March 12, 2009

 * Speeches

title: Henry B. Eyring


text:
Kitty Dukakis

Katharine "Kitty" Dukakis (née Dickson; born December 26, 1936) is an American author. She is married to former Massachusetts governor Michael Dukakis.

Life and career
Dukakis was born Katharine Virginia Dickson in Cambridge, Massachusetts, the daughter of Jane (née Goldberg) and Harry Ellis Dickson. Her paternal grandparents were Russian Jews; her mother was born to an Irish Catholic father and a Hungarian Jewish mother, and had been adopted by a family of German Jewish descent. Her father was a member of the first violin section of the Boston Symphony Orchestra for 49 years and also served as Associate Conductor of the Boston Pops Orchestra.

She graduated from Brookline High School in 1954 and attended Pennsylvania State University. She dropped out of college in 1956 and married John Chaffetz in 1957. They had one son, John. After four years and several moves the marriage ended in divorce, and she returned to Cambridge. Her former husband later remarried and had a son, Jason Chaffetz, who was a Republican Congressman from Utah. Kitty received her B.A. from Lesley College in 1963, the same year she married Michael Dukakis. She received a M.A. degree from Boston University College of Communication in 1982.

During the 1988 presidential election, several false rumors were reported in the media about the Dukakises, including the claim by Idaho Republican Senator Steve Symms that Kitty had burned an American flag to protest the Vietnam War. Republican strategist Lee Atwater was accused of having initiated these rumors.

In 1989, Dukakis was briefly hospitalized after drinking rubbing alcohol. In 1991, Dukakis published her memoir, Now You Know, in which she candidly discussed her ongoing battle with alcoholism. The book also discussed the pressures of being a political wife and her disappointment over her husband's defeat in the 1988 election. In the mid-1990s, Dukakis graduated from the Boston University School of Social Work with a master's degree in Social Work, successfully performing her practicum at Charles River Hospital in Wellesley, Massachusetts. In 2006, her book Shock revealed that she had undergone electroconvulsive therapy treatment beginning in 2001 in order to treat major depression. Dukakis is a leading proponent of using ECT to treat depression.

In 2007, the Lemuel Shattuck Hospital in Jamaica Plain, Massachusetts, opened a center for addiction treatment named after Dukakis.

Dukakis appears in the 2008 documentary on Lee Atwater, Boogie Man: The Lee Atwater Story.

Published works

 * Cowritten with Larry Tye.
 * Cowritten with Larry Tye.

Public service
Dukakis has served on the President's Commission on the Holocaust, on the United States Holocaust Memorial Council, on the board of the Refugee Policy Center, and on the Task Force on Cambodian Children.

title: Kitty Dukakis


text:
Jeffrey R. Holland

Jeffrey Roy Holland (born December 3, 1940) is an American educator and religious leader. He served as the ninth president of Brigham Young University (BYU) and is the acting president of the Quorum of the Twelve Apostles of the Church of Jesus Christ of Latter-day Saints (LDS Church). As a member of the Quorum of the Twelve, Holland is accepted by the church as a prophet, seer, and revelator. Currently, he is the third most senior apostle in the church.

Holland was born and raised in St. George, Utah. After graduating from high school, his college education began at Dixie College and he also served as a missionary for the LDS Church in Great Britain. After returning from his mission, he transferred to BYU and graduated with a bachelor's degree in English. He later earned a master's degree in religious education at BYU. Holland received a second master's degree and later a PhD in American studies at Yale University. In 1974, Holland was appointed BYU's dean of religious education, then two years later he was appointed as the eleventh commissioner of the Church Educational System (CES), replacing Neal A. Maxwell. In 1980, Holland became BYU's ninth president, replacing Dallin H. Oaks.

Early life and education
Holland was born in St. George, Utah. His father, Frank D. Holland, was a convert to the LDS Church while his mother, Alice, came from a long line of Latter-day Saints. As a youth, he worked as a newspaper carrier, a grocery bagger, and a service station attendant. As a young man, Holland served in what was then known as the British Mission. His mission president was Marion D. Hanks, a church general authority. He and Quentin L. Cook were missionary companions.

Holland graduated from Dixie High School in 1959. He helped the Flyers capture state high school championships in football and basketball. He began his college education at Dixie College before his mission. After returning from his mission, he served as co-captain of the Dixie basketball team. In 2011, the school broke ground for the Jeffrey R. Holland Centennial Commons Building, a building to honor both Holland and the school's 2011 centennial. The completed building was dedicated in September 2012.

Holland transferred to BYU, where he graduated with a bachelor's degree in English. He did graduate study in religious education, receiving a Master of Arts (M.A.) degree in 1966 with a thesis on selected changes to the text of the Book of Mormon, while also teaching religion classes part-time. After earning his master's degree, Holland became an Institute of Religion teacher in Hayward, California. He later worked as an institute director in Seattle, Washington. Holland then studied American studies at Yale University, where he received a second M.A. and a PhD in 1972. At Yale, Holland studied with American literary scholar and critic R. W. B. Lewis and authored a dissertation on the religious sense of Mark Twain. He was an instructor at the LDS Church's institute in Hartford while he was a student at Yale.

While studying at Yale, Holland served as a counselor in the presidency of the LDS Church's Hartford Connecticut Stake.

Leadership at BYU and CES
Holland served as an institute director in Salt Lake City after earning his PhD. He also served as director of the Melchizedek Priesthood MIA and as chair of the Young Adult Committee for the LDS Church. In 1974, at age 33, Holland was appointed Dean of Religious Education at BYU. As dean, Holland founded BYU’s Religious Studies Center and became its first director. From 1976 to 1980, he served as the eleventh commissioner of CES, replacing Neal A. Maxwell, who was called to the First Council of the Seventy. During this time, Holland also served on the board of directors of both LDS Hospital and the Polynesian Cultural Center.

In 1980, Holland was appointed to succeed Dallin H. Oaks as BYU's president. After a search committee was formed, as a favorite candidate of N. Eldon Tanner, First Counselor in the LDS Church's First Presidency, and the protégé of the chair of the executive committee of the BYU Board of Trustees, Gordon B. Hinckley, Holland was appointed less than two days later. As the church's commissioner of education at the time Oaks was released, Holland was supposed to compile a list of candidates to be the next BYU president. Instead, he was unexpectedly notified of the First Presidency's intention to make him president. After his appointment, rumors on campus cited the decision as "politically motivated". Before he arrived at BYU, Holland reduced the number of vice-presidents to four and increased the number of assistant and associate vice-presidents over academics.

Holland easily transitioned into the role of president. He was familiar with the president's duties, since he had worked closely with Oaks as the commissioner of education. He placed emphasis on upgrading programs and improving relationships with faculty rather than focusing on physical expansion of the campus. In order to supplement the school's funds, Holland launched a fundraiser called "Excellence in the Eighties" which sought to raise $100 million from 1982 to 1987. Specific funds were raised for student scholarships, academic programs, faculty salaries, and extension programs. He emphasized hiring more qualified faculty and purchasing more library and research materials. He supervised the building of the Crabtree Technology Building, but didn't promise more than ten new buildings during his presidency.

A significant achievement during Holland's presidency was the founding of the BYU Jerusalem Center. Also during his presidency, the BYU Center for International Studies was renamed the David M. Kennedy Center for International Studies and had its role at BYU re-emphasized. There had been a large amount of debate about BYU's dress code throughout the previous administration. Holland clarified his support for dress code rules. Regarding violations of the Honor Code, if a student requested their names be removed from the church records, Holland instituted a policy in which they would have to receive special permission from the board of trustees in order to remain enrolled in school.

During Holland's presidency, the weekly independent student newspaper, The 7th East Press was shut down due to writing about controversial topics. However, student editor, Dean Huffaker, believed that Holland had tried to prevent them from being banned because Holland was conscious of public relations and didn't want to cause controversy. The students stated that they believed the ban came from one of the LDS Church's general authorities.

Holland had the re-establishment of religious instruction as the "hub" of BYU's academics as one of his significant administrative goals. While he did not initiate any significant changes along these lines, his public communications regularly emphasized the importance of religious education. As BYU's president, Holland encouraged academic excellence in an atmosphere of faith. Holland emphasized that BYU could not do everything but would seek excellence in what it did choose to do.

Holland served as the president of the American Association of Presidents of Independent Colleges and Universities (AAPICU) and as a member of the NCAA's presidents' committee. He also received the "Torch of Liberty" award from the Anti-Defamation League.

LDS Church service
Holland was called as a general authority and member of the First Quorum of the Seventy on April 1, 1989, bringing an end to his term as BYU's president. As a member of the Seventy, Holland was a counselor in the general presidency of the church's Young Men organization from 1989 to 1990.

Prior to his call as a general authority, Holland served as bishop of a single adult ward in Seattle, as a counselor in the presidency of the Hartford Connecticut Stake, and as a regional representative. He also served in the presidency of two other stakes and as a stake high councilor.

From 1990 to 1993, Holland and his wife lived in Solihull, England, where he served as president of the church's Europe North Area.

On June 23, 1994, Holland was called and ordained as an apostle by new church president Howard W. Hunter. The vacancy was created by the death of Ezra Taft Benson and subsequent reorganization of the First Presidency. This timing differed from the typical sustaining of new apostles in a general conference and ordaining them afterward. Holland also met with the media on the day of his ordination. His call to the apostleship was subsequently ratified by the church during the October 1994 General Conference.

In 2000, Holland became the chair of the Missionary Curriculum Task Force which worked to develop Preach My Gospel.

Holland lived in Santiago and served as president of the church's Chile Area from 2002 to 2004.

In church general conferences in the fall of 2007 and spring of 2008, Holland gave sermons that directly answered accusations that Latter-day Saints are not Christians. At the April 2009 general conference, Holland gave a sermon about the crucifixion of Jesus Christ and the importance of Christ's statement, "my God, my God, why hast thou forsaken me". This talk was later reformatted with music and put on a church website where it had been viewed over 500,000 times by August 2009.

In 2012, Holland was the member of the Quorum of the Twelve with responsibility for the affairs of the LDS Church in Africa. Early in that year, he went to Sierra Leone, Liberia, and Ghana to meet with members and missionaries. He also met with the Vice President of Sierra Leone, Samuel Sam-Sumana. In December 2012, Holland organized the LDS Church's 3,000th stake, located in Freetown, Sierra Leone. On March 12, 2012, the Harvard Law School hosted Holland for a "Mormonism 101" series. On June 10, 2015, he addressed the All-Party Parliamentary Group on Foreign Affairs in the House of Lords at the UK Parliament. In 2016, Holland was keynote speaker at the Boy Scouts of America's (BSA) Duty to God breakfast, as part of his assignment as the LDS Church's chief BSA representative.

From 2015 to 2023, among his other assignments, Holland served on the Church Board of Education and Boards of Trustees, where he also served as chairman of the Board's Executive Committee from January 2018 to May 2023.

In November 2018, Holland spoke at a major inter-religious conference at Oxford University. During the same trip, Holland met with Theresa May, Prime Minister of the United Kingdom. This may have been the first official meeting of an LDS Church apostle and a British prime minister.

In January 2019, Holland presided at the groundbreaking for the church's Urdaneta Philippines Temple. He also spoke at a multi-stake conference in the Philippines that week. In 2020, as chairman of the executive committee of the BYU-Hawaii board of trustees, he announced the appointment of John S. K. Kauwe III as the institution's new president.

In August 2021, Holland spoke at BYU's annual conference for faculty and staff and the speech sparked controversy within the LGBTQ+ community. In the address, Holland asked the faculty to defend the doctrine of the LDS Church, BYU's institutional sponsor, with the use of metaphorical "musket fire."

In April 2023, the church reported that Holland would take a two-month hiatus from service to focus on his health. He had been undergoing dialysis for a kidney issue and had also contracted COVID-19. In early June, Holland began to gradually return to church service.

After the death of M. Russell Ballard on November 12, 2023, Holland was appointed and set apart as the acting president of the Quorum of the Twelve Apostles on November 15, 2023.

Personal life
Holland and his wife, Patricia Terry, were married on June 7, 1963, in the St. George Temple. They are the parents of three children. Their oldest son, Matthew S. Holland, served as president of Utah Valley University from 2009 to 2018 and has been a general authority since April 2020. Their youngest son, David F. Holland, is the John A. Bartlett Professor of New England Church History and Interim Dean of Harvard Divinity School. Patricia died on July 20, 2023, from causes incident to age and health.

Works

 * Books

 * Speeches

 * — unofficial transcript
 * — unofficial transcript
 * — unofficial transcript
 * — unofficial transcript
 * — unofficial transcript

Awards

 * Eagle Scout Award by the Boy Scouts of America (1955)
 * Distinguished Eagle Scout Award by the National Eagle Scout Association
 * Torch of Liberty Award by the Anti-Defamation League of B'nai B'rith
 * Washington County Exemplary Manhood Award (July 2013)

title: Jeffrey R. Holland


text:
Talk:Vector field

n-dimensional real vector space
Hey, up to isomorphism there is only one real n-dimensional vector space. Up to isomorphism there is only one real-dimensional Slawomir Bialy. Of course, Slawomir Bialy is always changing, but there is a reasonable equivalence class, and we call the equivalence class Slawomir Bialy. There are many different elements of the equivalence class called the `the n-dimensional real vector space' where equivalence is isomorphism. This is common usage in mathematics. In any case, it's rude to delete undo all changes while objecting only to one. — Preceding unsigned comment added by Lost-n-translation (talk • contribs) 16:49, 1 February 2011 (UTC)

 * This is true, but of course a vector field is not just a function into another vector space up to isomorphism, it is a mapping into a particular vector space (in mathematics, the tangent space at a point; in physics, it is characterized by a contravariant transformation law). Either way, it's misleading to say that a vector field is a mapping into the n-dimensional real vector space; there is strictly more structure than that.   Sławomir Biały  (talk) 17:17, 1 February 2011 (UTC)

Example 1
If we write the vectors of the vector field as (1, 0) in polar coordinates, that means we're using different coordinate systems for these vectors at different positions in the original R2. The theta=zero direction of each tangent space would be identified with the r direction of the original space. Is that really a good choice? In the second part using cartesian coordinates, the coordinate systems of all tangent spaces are parallel to that of the original space, which means that in most of the tangent spaces we don't have the usual transformation between polar and cartesian coordinates. Isn't that a bit confusing? —  H HHIPPO  20:33, 26 September 2012 (UTC)

 * Careful, the polar coordinates $$(r,\theta)$$ refer to polar coordinates on $$\mathbb{R}^2$$. The tangent spaces carry the linear coordinates induced by the differentials $$dr,d\theta$$.   Sławomir Biały  (talk) 23:53, 26 September 2012 (UTC)

 * Ahh, I see. That is actually a very obvious choice of coordinates. I hadn't fully digested that the codomain of a vector field is a tangent bundle, which only for Cartesian coordinates looks like a single vector space. Thanks! —  H HHIPPO  18:57, 27 September 2012 (UTC)

 * Should the definition of $$v_{polar}$$ in Example 1 be changed to $$(1,0)$$ so that it would map the argument into the tangent space? Additionally, the present definition of $$v_{polar}$$ does not transform contravariantly. Tommi Höynälänmaa (talk) 12:03, 29 October 2016 (UTC)

Picture of vector field on sphere
Normally the indicated map in the picture of the sphere with the red arrows would not be regarded as vector field, since on the equator some arrows seem to be orthogonal to the surface rather than tangent to it. They must be tangent otherwise its not a vector field. — Preceding unsigned comment added by 131.220.132.179 (talk) 21:36, 16 November 2012 (UTC)
 * The picture is very bad. Someone should upload a better one.   Sławomir Biały  (talk) 22:00, 16 November 2012 (UTC)

Definition needs work.
The definition claims (fV)(p):= f(p)V(p) is scalar multiplication (for real valued function f:S → R). This may be an example of scalar multiplication, it is not scalar multiplication: scalar multiplication is multiplication by a scalar, not by a function.

I have tried to understand why the definition is so awkward, and I can't figure it out. You can NOT define a vector field in terms of two vector fields! Come on!

A vector field is the mathematical structure in which each element in the field has associated with it a direction and magnitude. A vector field is a ring (a commutative (Abelian) group having (at least) two operations, addition and multiplication, defined over it. Addition is abelian, while multiplication is monoid (that is, every element may not have a multiplicative inverse).

I don't know the exact definition of a vector field (if I did, I wouldn't be looking it up). All of the vector fields I am familiar with have the following additional characteristics which may or may not be required: Scalar multiplication is defined. The direction of the field is in the same space as the field.

The definition here fails to explain these things, as well as what the common properties are: (commutation, distribution of multiplication over addition, associativity, inverse, division, subtraction, (in)finiteness, closedness, magnitude, dot product, inner product, outer product, cross product...)

I KNOW that the vector fields are NOT limited to Euclidean Spaces, since I am currently working with them in Special Relativity. The lede is misleading or simply wrong.

All in all, this needs a bit of work...whether it goes from the narrow case (Euclidean) to the general case or vice versa is a matter or pedagogy, (I personally prefer general to specific then back to general, but I am not competent to write it).216.96.79.149 (talk) 20:19, 18 February 2014 (UTC)
 * It's not clear to me what perspective you're coming from, but it's very likely the source of your confusion is not this article. Vector fields do not form a ring.  The scalar fields are just functions.  While it's true that Euclidean space is not the most general setting for vector fields, it is one that we can expect all readers of this article at least to be familiar with.   Sławomir Biały  (talk) 17:55, 19 February 2014 (UTC)

Modified "Index of vector field" section
I have modified the section Index of vector field so that

 * Several false statements have been removed and replaced with correct ones (e.g., the false statement that the index at a saddle singularity in an n-dimensional manifold is necessarily equal to -1).

 * Some inappropriate statements have been removed, such as the statement that the index at an isolated singularity of a vector field in the plane is equal to "the winding number". (The winding number of what??? The winding number in the plane is defined for an oriented curve with respect to a point not lying on the curve, but no curve had been mentioned.)

 * Some ungrammatical sentences have been replaced with grammatical ones, in particular several sentences in which independent clauses were spliced together with commas.

 * Some less-than-clear wording has been replaced with clearer wording.Daqu (talk) 13:15, 22 April 2016 (UTC)

Small mistake in the example of Complete vector fields
It appears to me that there is a small error in the example of (in)complete vector fields, under the header Flow Curves. The unique solution is given as
 * $$\frac{1}{x_0 - t}$$,

while a calculation yields that this should be
 * $$\frac{1}{\tfrac{1}{x_0} - t}$$.

Could the main editor of this page verify and correct this?

Definition of "Flow Curve"
There is a section entitled "Flow Curves", and there is a definition for "integral curves"/"trajectories"/"flow lines", but there seems to be no definition for the term "flow curves". Are these 4 terms used interchangeably?

title: Talk:Vector field


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William Ladd

William Ladd (May 10, 1778 – April 9, 1841) was one of the earliest American anti-war activists, and the first president of the American Peace Society.

Biography
Ladd was born in Exeter, New Hampshire as a direct lineal descendant of Daniel Ladd, Sr. (1613–1693). After he graduated from Harvard in 1797 he shipped as a seaman from Portsmouth, New Hampshire in a vessel owned by his father, a local merchant. At 20 years old he was a capable New England captain and had seen much of the world. He briefly had a plantation in Florida which ultimately failed as he refused to use slave labor.

A disbeliever in war for any purpose, he turned at the outbreak of the War of 1812, when the British blockade temporarily stopped commerce. He moved to Minot, Maine, became a prosperous farmer, and devoted both his tongue and his pen to preaching non-resistance. In 1823 he wrote the first of 32 Essays on Peace and War, published in the Christian Mirror of Portland, Maine, which laid out a Christian case for pacifism. These essays were published pseudonymously as a book in 1825 (Portland, ME: Shirley & Edwards) under the title The Essays of Philanthropos on Peace and War; a second revised and corrected edition was published in 1827 (Exeter, NH: J. T. Burnham in behalf of the Exeter and other peace societies). Subsequent essays would criticize the slave trade and the raising of the Bunker Hill Monument in Charlestown, Massachusetts as a memorial to war.

State and local "peace societies" already existed in the 1820s, but in 1828 the American Peace Society was formed with Ladd as its first president. The first meeting was held in New York City. Ladd wrote and published the society's newspaper, The Harbinger of Peace (later The Calumet) from his house in Minot, Maine. In 1837, due to Ladd's influence and against the arguments of other members, including the president of Bowdoin College, the constitution of the American Peace Society was amended to declare that all war was contrary to the Christian Gospel.

In 1840 Ladd proposed a plan for a World Congress and Court of Nations, somewhat similar to the later League of Nations or United Nations. He published An Essay on a Congress of Nations (1840). He was partly influenced by the military build-up the year before in his home state of Maine because of a border dispute with Britain, the so-called Aroostook War.

Ladd is buried in Portsmouth, New Hampshire

title: William Ladd


text: User talk:202.133.195.117

title: User talk:202.133.195.117


text: File:Manuel Mendez Ballester.jpg

title: File:Manuel Mendez Ballester.jpg


text:
Wikipedia:Articles for deletion/Vacuum propeller

I followed the external link. This looks like voodoo science, like antigravity drives and such. AlainV 04:05, 3 Aug 2004 (UTC)
 * Delete. Unoriginal reasearch, if there is such a thing, by an anon. The external link is to part of a site explaining how flying saucers work. Andrewa 05:02, 3 Aug 2004 (UTC)
 * Keep, maybe. The site linked-to is not a kook site.  It's mostly useful information from the founder of Autodesk with a couple of speculative articles such as this.  There is all sorts of weirdness in the vacuum at the quantum level (particles appearing and disappearing and whatnot), and he explicitly states that he's not proposing a violation of conservation laws.  Maybe a better physicist than I am could offer some insight.  Gwimpey 05:14, Aug 3, 2004 (UTC)
 * Comment: Speculative all right, quote: Why do people report such a bewildering variety of objects? Because they're living, space-dwelling creatures. Consider the range of creatures which inhabit the Earth's oceans. The ocean of space is immeasurably more vast and deeper than any planetary ocean. No change of vote. Andrewa 06:00, 3 Aug 2004 (UTC)
 * Keep. It is discussed by particle physicists and cosmologists. Suggest however to move it to Cleanup and have it reviewed and edited by somebody knowledgable in quantum physics. (In my opinion, John Walker of FourmiLab is definitively not a crank.) --Palapala 07:25, 2004 Aug 3 (UTC)
 * Keep. (though I'm not sure I've been around long enough for my vote to be significant.) Read his article on demonstrating universal gravitation in your basement, and read the disclaimer where he says everything in the /goldberg directory, including what you quoted Andrewa, is a work of speculative fiction, nothing more. This guy's no kook, he knows his shit. And while that doesn't mean his article on vacuum propulsion doesn't violate conservation of momentum, it isn't entirely clear that it does, either, and I'm willing to give him the benefit of the doubt based on the quality of his other writing. Presuming the original author is not the submitter, perhaps we could appeal to the original author to come to Wikipedia and explain himself directly. Glenn Willen (Talk)   07:37, 3 Aug 2004 (UTC) (Resolved edit conflict with Palapala.)
 * Comment: The vote is whether we delete this article. Whether this guy is a crank is irrelevant, and I certainly didn't say he was one. Call the article speculative fiction if you like, fine, so what? It's still a delete unless it's significant enough in the literature to be encyclopedic when clearly labelled as that. No change of vote. Andrewa 03:33, 4 Aug 2004 (UTC)
 * Delete. Original research and obscure one. Google returns only 116 hits, when searched for "vacuum propeller", from a small number of websites. (The number of relevant hits is even slightly smaller, because some hits are about a company producing vaccum cleaners.) I do not buy the claim that this is being "discussed by particle physicists and cosmologists", as the google search found almost nothing on university/research sites. Andris 07:55, Aug 3, 2004 (UTC)
 * Delete. [The] vacuum propeller [..] is a hypothetical solution to the rocket problem. Yes, and the perpetuum mobile is a hypothetical solution to the energy problem, manna falling from heaven is a hypothetical solution to the world hunger problem and sanity the is a hypothetical solution to nonsense Wikipedia articles. -- Pjacobi 09:04, 3 Aug 2004 (UTC)
 * Comment: There are articles dealing with perpetuum mobile, manna and sanity; so why not this one? --Palapala 17:51, 2004 Aug 3 (UTC)
 * Delete: Original research. When space turns out to push back, this will all be science, and then it is encyclopedic.  At present, it is speculation by solo dreamers.  We can applaud their vision without including their visions. Geogre 14:10, 3 Aug 2004 (UTC)
 * Delete. Well put, Geogre! Denni ☯ 01:03, 2004 Aug 7 (UTC)
 * Delete. Interesting but still original research. Article can be rewritten when it is an established concept published and discussed in multiple forums. If anyone can provide evidence that this is in fact discussed by particle physicists or cosmologists, I will change my vote. Rossami 14:19, 3 Aug 2004 (UTC)
 * Comment: Propellantless Propulsion has been discussed in the open for years; see e.g. BPP (NASA Breaktrough Propulsion Physics program). --Palapala 09:01, 2004 Aug 4 (UTC)
 * Thank you. Tentative keep. If you can find one or two more reputable references that this is an openly discussed topic, then I will fully support keeping the article if it is moved to the correct commonly used description. ("Vacuum propeller" is not actually used in the article you cite.)  To me, the only relevant point is proving that this is not original research. As someone elegantly said in an earlier discussion, Stephen Hawking could not publish a new theory on Wikipedia. Rossami 18:06, 4 Aug 2004 (UTC)
 * How about the external links I added to the article today? --Palapala 20:29, 2004 Aug 4 (UTC)
 * Now a strong keep. Palapala has provided enough credible references to convince me that this is not original research. There should still be a discussion (on the article's talk page) about whether this is the right title for the article. Rossami 22:28, 4 Aug 2004 (UTC)
 * Delete - "space screw" says it all - Tεx  τ  urε  17:27, 3 Aug 2004 (UTC)
 * "somehow push against space itself"? I've got an idea for a rocket that will "somehow generate thrust without using needing fuel". Delete. DJ Clayworth 17:39, 3 Aug 2004 (UTC)
 * I think talking about how realistic the science is gets off-track from the real question of whether it's encyclopedia-worthy or not. On the former question, I would point out that zero-point energy, virtual particles, and the Casimir effect are all real phenomena; Stephen Hawking used virtual particles to explain a mechanism by which black holes could radiate (I believe that was in A Brief History of Time), and it is not unreasonable to postulate similar mechansims for virtual-particle propulsion. Energy is still being conserved, and one can frame it in such a way that momentum is as well. The science isn't absurd, though I can understand how people would think it is. As for the second question, of whether it is a subject worthy of an encyclopedia: I prefer to err on the side of keeping information around. Besides, we have an article about the technological singularity, for crying out loud. Tell me that's more worthy than this. Glenn Willen (Talk)   20:39, 3 Aug 2004 (UTC)
 * Delete. This isn't a theory that has the backing of recognized experts in the field, it's original research/pseudoscience. As is Technological singularity, BTW, since it presupposes that we'll be able to create a human-equivalent machine intelligence. Personally, I think if we ever do create an actual intelligence, we'll be completely unimportant to it... - Kenwarren 03:21, Aug 4, 2004 (UTC)
 * Delete - original research at best. -- Cyrius|✎ 19:09, 6 Aug 2004 (UTC)


text:
Ajou University

Ajou University (Korean: 아주대학교; Hanja: 亞洲大學校; lit. Asia University) is a private research university located in Suwon, Gyeonggi-do, South Korea. It was founded in 1973. Ajou University started as Ajou Engineering College with the aim of exchanging technology and culture through education between France government and South Korea government.

Ajou is located on a single campus with details, affiliated research hospital, Gwanggyo Bio-Techno Valley, Samsung Electronics headquarters, CJ Blossom Park, a food bio-convergence research institute. Gyeonggi-do Pharmaceutical Association has signed MOUs with Ajou. Its School of Business is a member of both the AACSB and EFMD certification bodies.EPAS

Ajou University Hospital, an affiliated hospital of the medical school and a base hospital in Gyeonggi-do, is opening Ajou University Intermediate Care Hospital, Ajou University Pyeongtaek Hospital, Ajou University Paju Hospital. The affiliated medical center is conducting research on human aging.

In 2020, Ajou established a campus in Tashkent, Uzbekistan which boasts strong engineering programs.

Notable academic programs

 * Exchange student: As of 2021 years, it was held with 325 schools in 67 countries. It is a program that exchanges students with foreign universities and institutions where academic exchange agreements are signed. By paying tuition to the main school and studying at an overseas university for a semester, credits taken from overseas universities are recognized as the main school. Ajou is a member of ISEP (International Student Exchange Program), CREPUQ (Conference of Rectors and Principals of Quebec Universities), HUMAP (Hyogo University Mobility in Asia and the Pacific), "n+i" Network(French Union of Technology Universities), AUF(Federation of French Universities).
 * Multiple degrees: A program that takes 1/2 of its graduation credits and takes the remaining credits from other schools, earning both Ajou University and other schools' degrees. It is currently operated by the Illinois Institute of Technology and Stony Brook University in the United States.
 * Blue Ladder: The business of the Ministry of Education of Korea. Despite the difficult environment, it supports overseas training experiences to college students who have dreams and passion for self-development and career development. Each university in charge selects students and proceeds with the program. Ajou University was selected in 2018 and runs for three years. The schools include the University of Michigan and the University of Washington in the United States, and Shanghai Transportation University in China.
 * Global Internship: A program that sends students to companies in about 20 countries around the world for internships to provide more diverse and challenging overseas experience opportunities. It will provide opportunities to learn the senses and explore career in overseas industrial sites related to majors. It will be dispatched to INKE (World Korean Venture Network), IDB (US Development Bank), KOTRA (Korea Trade and Investment Promotion Corporation), CKP (USA Asia Accounting Corporation), W-OKTA (World Korean Trade Association), HMART, etc. It is recognized as a credit for the third and fourth grade internship courses.
 * Short-term dispatch: It is a program that is sent to sister universities abroad for about four weeks during the vacation. Participation in language training, international training programs, etc. at sister universities may be recognized as credits. Part of the program participation fee may be supported by scholarships.
 * Global Leadership in Business Administration
 * ABIZ Global Supporter(AGS)

Reputation and rankings

 * 2024 QS : World 631~640th
 * 2023 QS : World 488th
 * 2021 QS 50 Under 50 : World 101-150th.
 * 2019 JoongAng Ilbo University Evaluation(Korean Press): Nation 11th.
 * 2019 Employment and Start-up Evaluation of Hankyung(Korean Press) : Nation 5th.
 * 2021 WURI Global Top 100 Innovative Universities : World 62nd.
 * 2019 REUTERS Asia Pacific's Most Innovative Universities : Asia 24th.
 * 2021 THE Impact Rankings : 201-300th.

Symbol

The Statue of Pioneer is the symbol of Ajou University. It is located at the school's main entrance.

Central Library
In order to contribute to the learning, cultivation and research of students and faculty members through the collection, accumulation and distribution of information, the Central Library was established on March 15, 1973. It was opened together with the opening of the prefecture elementary and junior college. At the time of opening, there were 120 seats of the first floor of the main building. From April 12, 1973, 1,272 books were purchased with one librarian. In 1983, Daewoo Group Kim Dae-woo, chairman of the Daewoo Group, donated 5 billion won to renovate the Central Library. The new total floor space was 4,026 pyeong. On October 16, 2017, the entire library on the second floor was converted into a community lounge through remodeling. In addition, on the first floor, the space that was previously used for the corridor was expanded to build a café, allowing rest space and convenience facilities.

Dining halls
The campus is mainly served by two large cafeterias and many minor restaurants. The biggest restaurant is close to the dormitories and is called the Dormitory Restaurant. It has two floors and serves both Korean and Western style foods with a daily rotating menu. The second biggest restaurant is called the Student Restaurant, and is located in the Student Union building. There are also smaller restaurants in Paldal hall, Dasan hall and Jonghap Hall.

Dormitories
There are five big dormitories on campus: Nam-jae dormitory, Yong-Ji dormitory, Hwa-hong dormitory, Kwang-Gyu dormitory and the newly built International dormitory. Nam-jae and Yong-ji dormitories are exclusively boys' dormitories while Kwang-gyu is a girls' dormitory. Hwa-hong houses both males and females (on separate floors; girls' floors are female-keycard access only) and is one of two dormitories open to foreigners as exchange students or regular students. The other one open for foreigners is the newly built International dormitory. Except for Hwa-hong and International dormitory, all the dormitories have rooms with four occupants each. International and Hwa-hong have two-bed and four-bed rooms. They also have single rooms for visiting professors. Ajou University International Dormitory VIDEO

Notable alumni

 * Ahn Jung-Hwan, football player
 * Ha Seok-Ju, football player
 * Jee Seok-jin, entertainer
 * Kim Ji-hoon, actor
 * Lee Min-Sung, football player
 * Woo Sung-Yong, football player
 * Eon Tae Ha, CEO of Hyundai Motor Company
 * Lee Guk-jong, Head of the trauma lab at the University Institute for Advanced Medicine, trauma specialist.
 * Chi Hwan Lee, biomedical engineer, academic, and researcher
 * Suh Jin-suck, medical professor

title: Ajou University