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SUMMARY / RELATED TOPICS

Singularity theory

In mathematics, singularity theory studies spaces that are manifolds, but not quite. A string can serve as an example of a one-dimensional manifold. A singularity can be made by balling it up, dropping it on the floor, flattening it. In some places the flat string will cross itself in an approximate "X" shape; the points on the floor where it does this are one kind of singularity, the double point: one bit of the floor corresponds to more than one bit of string. The string will touch itself without crossing, like an underlined "U"; this is another kind of singularity. Unlike the double point, it is not stable, in the sense that a small push will lift the bottom of the "U" away from the "underline". Vladimir Arnold defines the main goal of singularity theory as describing how objects depend on parameters in cases where the properties undergo sudden change under a small variation of the parameters; these situations are called bifurcations or catastrophes. Classifying the types of changes and characterizing sets of parameters which give rise to these changes are some of the main mathematical goals.

Singularities can occur in a wide range of mathematical objects, from matrices depending on parameters to wavefronts. In singularity theory the general phenomenon of points and sets of singularities is studied, as part of the concept that manifolds may acquire special, singular points by a number of routes. Projection is one way obvious in visual terms when three-dimensional objects are projected into two dimensions. Singularities of this kind include caustics familiar as the light patterns at the bottom of a swimming pool. Other ways in which singularities occur is by degeneration of manifold structure; the presence of symmetry can be good cause to consider orbifolds, which are manifolds that have acquired "corners" in a process of folding up, resembling the creasing of a table napkin. Singularities were first noticed in the study of algebraic curves; the double point at of the curve y 2 = x 2 + x 3 and the cusp there of y 2 = x 3 are qualitatively different, as is seen just by sketching. Isaac Newton carried out a detailed study of all cubic curves, the general family to which these examples belong.

It was noticed in the formulation of Bézout's theorem that such singular points must be counted with multiplicity, in accounting for intersections of curves. It was a short step to define the general notion of a singular point of an algebraic variety; such singularities in algebraic geometry are the easiest in principle to study, since they are defined by polynomial equations and therefore in terms of a coordinate system. One can say. Intensive studies of such singularities led in the end to Heisuke Hironaka's fundamental theorem on resolution of singularities; this means that the simple process of "lifting" a piece of string off itself, by the "obvious" use of the cross-over at a double point, is not misleading: all the singularities of algebraic geometry can be recovered as some sort of general collapse. This result is implicitly used to extend affine geometry to projective geometry: it is typical for an affine variety to acquire singular points on the hyperplane at infinity, when its closure in projective space is taken.

Resolution says that such singularities can be handled rather as a sort of compactification, ending up with a compact manifold. At about the same time as Hironaka's work, the catastrophe theory of René Thom was receiving a great deal of attention; this is another branch of singularity theory, based on earlier work of Hassler Whitney on critical points. Speaking, a critical point of a smooth function is where the level set develops a singular point in the geometric sense; this theory deals with differentiable functions in general, rather than just polynomials. To compensate, only the stable phenomena are considered. One can argue. Whitney had shown that in low numbers of variables the stable structure of critical points is restricted, in local terms. Thom built on this, his own earlier work, to create a catastrophe theory supposed to account for discontinuous change in nature. While Thom was an eminent mathematician, the subsequent fashionable nature of elementary catastrophe theory as propagated by Christopher Zeeman caused a reaction, in particular on the part of Vladimir Arnold.

He may have been responsible for applying the term singularity theory to the area including the input from algebraic geometry, as well as that flowing from the work of Whitney and other authors. He wrote in terms making clear his distaste for the too-publicised emphasis on a small part of the territory; the foundational work on smooth singularities is formulated as the construction of equivalence relations on singular points, germs. Technically this involves group actions of Lie groups on

The Program Exchange

The Program Exchange was a syndicator of television programs. It was founded as Program Syndication Services Inc. in 1973 and launched the DFS Program Exchange in 1979, which became the DFS-Dorland Program Exchange from 1986 to 1987. From 1987 to 2008, it was a division of Saatchi & Saatchi, an advertising agency, would be acquired by Publicis in 2000. In January 2008, Publicis transferred The Program Exchange from the Saatchi & Saatchi subsidiary to its ZenithOptimedia subsidiary, the logo was changed to reflect this move. In early 2016, the programexchange.com website was shut down. The Program Exchange was a "barter syndicator," distributing programming on behalf of the shows' producers, many of them having their own cash distribution services. Instead of paying a cash fee, television stations who ran those programs agreed to a barter exchange, wherein the station agreed to air a certain number of commercials for various General Mills products per program; this arrangement allowed for the programs to air on stations that may not have large budgets to acquire them.

The Program Exchange distributed older programming, no longer distributed in syndication, as well as programming designed to meet federal educational/information mandates. The Program Exchange continued to hold distribution rights to the Jay Ward Productions and Total Television archives throughout the exchange's existence; the Program Exchange handled distribution for all titles listed below. The dates listed are the dates that they were distributed, not the dates they aired. All-New Dennis the Menace Around the World in 80 Days Beakman's World The Berenstain Bears The Biskitts Buford and the Galloping Ghost The Bullwinkle Show and Rocky and His Friends Dennis the Menace Devlin Dino Babies Dive Olly Dive Dudley Do Right and Friends The Flintstones Garfield and Friends Go Go Gophers Goober and the Ghost Chasers The Harveytoons Show Inch High, Private Eye Inspector Gadget's Field Trip Jana of the Jungle Jakers! The Adventures of Piggley Winks The Jetsons Jonny Quest King Leonardo and His Short Subjects Knights of the Zodiac Korg: 70,000 B.

C. The Mr. Magoo Show Picture Pages The Real Adventures of Jonny Quest The Roman Holidays Sailor Moon Sealab 2020 Scooby-Doo Space Kidettes and Young Samson Sport Billy The Super Mario Bros. Super Show! Tennessee Tuxedo and His Tales Uncle Waldo's Cartoon Show The Underdog Show Valley of the Dinosaurs The Wacky World of Tex Avery Wheelie and the Chopper Bunch Where on Earth Is Carmen Sandiego? Where's Huddles The Woody Woodpecker Show Zoo Clues 227 3rd Rock from the Sun The Addams Family The Abbott and Costello Show Alfred Hitchcock Presents Amen Benson Bewitched Bosom Buddies The Brady Bunch Charles in Charge Coach The Cosby Show Dear John A Different World Fantasy Island Gimme a Break! I Dream of Jeannie The Jeffersons Just Shoot Me! Laverne and Shirley Leave It to Beaver Mork & Mindy The Munsters NewsRadio The Odd Couple The Partridge Family Taxi Three's Company Too Close for Comfort Webster What's Happening!! What's Happening Now!! Who's the Boss? Ironside Kojak B. Smith: Simply Style Funniest Pets & People That Teen Show The Greats of the Game Sale of the Century B. Smith Cooking Vignettes Cartoon Network Short Cartoons Dr. Bob Arnot: Eat Better America Healthy Break by Jake Medical Minute Nutrition Minute Archive of The Program Exchange's website The Program Exchange on IMDb DFS Program Exchange on IMDb

Save the Children (film)

Save the Children is a 1973 American documentary film directed by Stan Lathan and written by Matt Robinson. The concert documentary film chronicles performers that appeared during Jesse Jackson's Operation PUSH exposition held in 1972 in Chicago; the film was released on September 1973, by Paramount Pictures. Cannonball Adderley Jerry Butler Sammy Davis Jr. Dennis Edwards Roberta Flack Melvin Franklin Marvin Gaye Cuba Gooding, Sr. Damon Harris Isaac Hayes Jackson 5 Jackie Jackson Jermaine Jackson Jesse Jackson Marlon Jackson Michael Jackson Tito Jackson Gladys Knight Merald Knight Ramsey Lewis Curtis Mayfield Wilson Pickett Richard Street Otis Williams Nancy Wilson Bill Withers List of American films of 1973 Save the Children on IMDb

Oikophobia

In psychiatry, oikophobia is an aversion to home surroundings. The term is used to indicate an abnormal fear of one's home, or more narrowly to the contents of a house; the term derives from the Greek words oikos, meaning household, house, or family, phobos, meaning "fear". In 1808, the poet and essayist Robert Southey used the word to describe a desire to leave home and travel. Southey's usage as a synonym for wanderlust was picked up by other nineteenth century writers; the term has been used in political contexts to refer critically to political ideologies that repudiate one's own culture and laud others. One prominent usage was by Roger Scruton in a 2004 book. In psychiatric usage, oikophobia may narrowly refer to fear of the physical space of the home interior, where it is linked to the fear of household appliances, electrical equipment and other aspects of the home perceived to be dangerous. In this psychiatric context, the term is properly applied to fear of the objects within the house, whereas the fear of the house itself is referred to as domatophobia.

In the post-World War II era some commentators used the term to refer to a supposed "fear and loathing of housework" experienced by women who worked outside the home and who were attracted to a consumerist lifestyle. Southey used the term in Letters from England, stating that it is a product of "a certain state of civilisation or luxury", referring to habit of wealthy people to visit spa towns and seaside resorts in the summer months, he mentions the fashion for picturesque travel to wild landscapes, such as the highlands of Scotland. Southey's link of oikophobia to wealth and the search for new experiences was taken up by other writers, cited in dictionaries. A writer in 1829 published an essay about his experience witnessing the aftermath of the Battle of Waterloo, saying "the love of locomotion is so natural to an Englishman that nothing can chain him home, but the absolute impossibility of living abroad. No such imperious necessity acting upon me, I gave away to my oiko-phobia and the summer of 1815 found me in Brussels."

In 1959 the Anglo-Egyptian author Bothaina Abd el-Hamid Mohamed used Southey's concept in his book Oikophobia: or, A literary craze for education through travel. In his 2004 book England and the Need for Nations, British conservative philosopher Roger Scruton adapted the word to mean "the repudiation of inheritance and home." He argued that it is "a stage through which the adolescent mind passes", but that it is a feature of some leftist, political impulses and ideologies which espouse xenophilia, i.e. preference for alien cultures. Scruton uses the term as the antithesis of xenophobia. In his book, Roger Scruton: Philosopher on Dover Beach, Mark Dooley describes oikophobia as centered within the Western academic establishment on "both the common culture of the West, the old educational curriculum that sought to transmit its humane values." This disposition has grown out of, for example, the writings of Jacques Derrida and of Michel Foucault's "assault on'bourgeois' society result in an'anti-culture' that took direct aim at holy and sacred things and repudiating them as oppressive and power-ridden."

Derrida is a classic oikophobe in so far as he repudiates the longing for home that the Western theological and literary traditions satisfy.... Derrida's deconstruction seeks to block the path to this'core experience' of membership, preferring instead a rootless existence founded'upon nothing.' An extreme aversion to the sacred and the thwarting of the connection of the sacred to the culture of the West is described as the underlying motif of oikophobia. The paradox of the oikophobe seems to be that any opposition directed at the theological and cultural tradition of the West is to be encouraged if it is "significantly more parochial, exclusivist and ethnocentric." Scruton described "a chronic form of oikophobia has spread through the American universities, in the guise of political correctness." Scruton's usage has been taken up by some American political commentators to refer to what they see as a rejection of traditional American culture by the liberal elite. In August 2010 James Taranto wrote a column in the Wall Street Journal entitled "Oikophobia: Why the liberal elite finds Americans revolting", in which he criticized supporters of the proposed Islamic center in New York as oikophobes who were defending Muslims who aimed, in his words, to "exploit the 9/11 atrocity".

In the Netherlands, the term oikophobia has been adopted by politician and writer Thierry Baudet, which he describes in his book, Oikophobia: The fear of home. Nostophobia – fear of returning home Allophilia Clientitis Wanderlust Xenocentrism Xenophily List of phobias

Vancouver Whitecaps (1986–2010)

Vancouver Whitecaps was a Canadian professional soccer club based in Vancouver, British Columbia. Founded in 1986, the team played its final year in the second tier of the United States soccer pyramid in the NASL Conference of the USSF Division 2 Professional League coached by Teitur Thordarson; the team played its home games at Swangard Stadium in British Columbia. The team's colours were white. On March 19, 2009, an ownership group led by principal Greg Kerfoot was granted a Major League Soccer expansion franchise which began play in 2011 under the name Vancouver Whitecaps FC. In addition to its men's side the Whitecaps field a women's team in the USL W-League, two developmental teams, four youth teams in the USL Super Y-League ranging in age from U13 to U17 for both boys and girls; the team was known as the Vancouver 86ers of both the Canadian Soccer League, American Professional Soccer League, the A-League. The club played in two versions of the second tier A-League known as the USL-1 and USSF Division 2 Professional League in North America.

In 1986, a professional soccer team was again launched in Vancouver, the Vancouver 86ers—so named because of both the year of the team's founding and to commemorate the year Vancouver was founded. Eighty-six people originally put up $500 each to fund the new team as the West Coast Soccer Society. Led by player/head coach Bob Lenarduzzi and his assistant Alan Errington, the 86ers were triumphant in their inaugural CSL match, as they defeated Edmonton Brickmen 4–2 in front of 7,646 fans at Swangard Stadium in Burnaby, BC, on June 7, 1987; the 86ers went on to finish second in the Western Division standings that year before bowing out to inaugural league champions Calgary Kickers in the playoff semifinals. The 86ers played in the Canadian Soccer League winning four straight CSL Championships and five consecutive CSL regular-season first-place finishes. In 1988–1989, the team, coached by Bob Lenarduzzi, set a North American professional sports record by playing 46 consecutive games without a loss.

In 1988 the Vancouver 86ers and Calgary Kickers played six friendly matches each against the Western Soccer Alliance in the month of May. In 1990, the Vancouver 86ers captured the North American Club Championship after defeating the Maryland Bays 3–2 in the final played in Burnaby; the game was played between the champions of the Canadian Soccer League and the champions of the American Professional Soccer League. The 86ers however came up short in the first round of the 1992 Professional Cup North American Club Championship. Facing APSL champions Colorado Foxes over two legs, Vancouver suffered a heartbreaking 3–2 defeat in the first leg in Colorado on August 3, 1992, before the Foxes advanced to the final, as a 2–1 second-leg win at Swangard on August 11, 1992, secured a 5–3 aggregate victory for Colorado. Vancouver played in the CSL from its inception in 1987 until the league folded in 1992, moved over to the APSL in 1993, absorbed into the USL hierarchy of leagues in 1997 becoming the A-League renamed the USL.

In 2001, the team began to use the old Vancouver Whitecaps moniker. In 2003, the name was again changed, albeit only to Whitecaps FC, which encompasses the men's, women's, youth development teams within the organization. At this time, the Whitecaps logo changed in colour and the word "Vancouver" was dropped from the image. In 2006, the Whitecaps organization won an unprecedented double-championship, claiming both the United Soccer Leagues First Division championship trophy, defeating the host Rochester Rhinos 3–0 at PAETEC Park, winning the W-League women's trophy; the men's team won the Nation's Cup, a new tournament established by their club as a way to feature the Whitecaps playing against international competition. The 2006 Nation's Cup tournament featured the Chinese and Indian U-20 National teams and Championship Welsh club Cardiff City F. C.. The added the "Vancouver" back into their name, changing it to "Vancouver Whitecaps FC"; the following season, the Whitecaps signed a deal to play an exhibition match against the Los Angeles Galaxy, which featured international David Beckham, promoted Director of Soccer Operations Bob Lenarduzzi to team president.

October 12, 2008, they claimed their second United Soccer Leagues First Division championship with a 2–1 victory over the Puerto Rico Islanders. Charles Gbeke scored twice with his head in the second half to help secure the title. In 2009, they placed 7th in the league and were eliminated in the final by the Montreal Impact on a 6–3 aggregate. In November 2009 the Whitecaps, along with several other teams, announced their intent to leave the USL First Division to become the co-founders of a new North American Soccer League, to begin play in 2010. On January 7, 2010 the U. S. S. F. announced that neither the USL nor the NASL would be permitted to have a second division league, the USSF would administer a league where the NASL and USL are conferences within the league. On November 24, 2009 it was announced that Paul Barber, the former Executive Director of Tottenham Hotspur, will become the Chief Executive Operations director of the Caps. Whitecaps played a 30-match regular season, with 15 home games and a 15 games away in the United States Soccer Federation Division 2 Professional League.

On July 24, 2008, the MLS

2014 UFL FA League Cup

The 2014 United Football League FA League Cup is the first edition of the UFL FA League Cup. The competition started on September 20 and expected to end on November 6, 2014; the 14 clubs separated into two groups of seven, where the top four will advance to the quarterfinals. Separate draws will take place before the quarterfinals and semi-finals to determine which clubs will face off. All times are Philippine Standard Time – UTC+8. In the quarter-finals stage, matchups were made via random draw, they will play against one another in a single leg knockout basis. The draw for the quarter-finals round was held on October 23, 2014. After the quarterfinals, another random draw will determine semifinal pairings. Correct as of 11:30, November 6, 2014 The following were the competition’s top individual awardees. Golden Gloves: Patrick Deyto Golden Boot: Louis Max Clark Golden Ball: Jin Ho Kim