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Princess Maria Antonia of Naples and Sicily

Maria Antonia of Naples and Sicily (14 December 1784 – 21 May 1806) was the youngest surviving daughter of Ferdinand, King of Naples and Sicily, and Maria Carolina of Austria. As the wife of the future Ferdinand VII of Spain, then heir apparent to the Spanish throne, she held the title of Princess of Asturias. It is alleged that her mother-in-law, Maria Luisa of Parma, poisoned her, causing her death, but there is no evidence to prove this.

Early life
Born at the Caserta Palace in Caserta, Italy, Maria Antonia was the youngest daughter of King Ferdinand IV/III of Naples and Sicily and his first wife, Maria Carolina of Austria. Named after her mother's favorite sister, her maternal aunt Queen Marie Antoinette of France, she was an intelligent girl, having learned several languages by the age of seventeen.

Marriage
In a series of dynastic alliances, Maria Antonia became engaged to her first cousin, Infante Ferdinand, Prince of Asturias (who later became King Ferdinand VII of Spain), while her eldest brother, Francis, became engaged to Infante Ferdinand's sister, Infanta Maria Isabella of Spain. On 6 October 1802, Maria Antonia married Infante Ferdinand in Barcelona, Spain.

Princess of Asturias
The princess failed to provide the expected heir to the throne: her two pregnancies, in 1804 and 1805, ended in miscarriages. Her mother, Maria Carolina, was highly anti-French after the execution of her sister and brother-in-law during the French Revolution. She was also strongly opposed to the military expansion of the French republic. As Spain became more easily dominated by Napoleon Bonaparte, there were rumours that Maria Carolina wanted her daughter to poison the Queen of Spain and Manuel Godoy, Spain's prime minister. However, as with most poison rumours of the period, it is unlikely to be true, not least because both women were devout Roman Catholics and secondly because the Spanish court's ties to France were in no way greater or lesser than most in Europe's after Napoleon’s early victories. Maria Antonia's mother-in-law, Queen Maria Luisa, disliked her daughter-in-law and she encouraged rumours of a Habsburg poisoning plot, even subjecting her books and clothes to scrutiny in order to discredit her daughter-in-law further. In spite of all of this campaign of character assassination, Maria Antonia managed to gain considerable influence over her husband and created an opposition party against Queen Maria Luisa and Godoy.

Death
Maria Antonia died of tuberculosis on 21 May 1806 at the Royal Palace of Aranjuez in Aranjuez, Spain, at the age of 21. It was rumoured that Maria Antonia had been poisoned by Queen Maria Luisa and Manuel Godoy but there is no evidence to support this claim. However, Queen Maria Carolina, who was devastated, truly believed this. Maria Antonia's father, King Ferdinand, consolidated Naples and Sicily into the Kingdom of the Two Sicilies a decade after her death.

The Neapolitan princess was buried at El Escorial in Spain. Her husband was to marry three more times: –

 * Infanta Maria Isabel of Portugal in Madrid on 29 September 1816; the couple had a daughter who died young.
 * Maria Josepha Amalia of Saxony on 20 October 1819, who bore him no children.
 * Maria Antonia's niece (born a month before her death), Princess Maria Christina of Naples and Sicily (more often known as of the Two Sicilies) with whom Ferdinand had the future Isabella II of Spain.


text: Category:Egyptian mythology

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

title: Category:Egyptian mythology


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User:Gyrospire

Gyrospire

A personification of the balance of light and dark. From the Greek "gyros". In Greek mythology, the Gyrospire was a being which faded from dark black on the left to almost pure white on the right. Often, the Gyrospire had the ability to levitate and to fade into nothing but a shadow.

title: User:Gyrospire


text: Category:Chess

title: Category:Chess


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Ali Larter

Alison Elizabeth Larter (born February 28, 1976) is an American actress. She portrayed fictional model Allegra Coleman in a 1996 Esquire magazine hoax and took on guest roles on several television shows in the 1990s. She made her film debut in Varsity Blues (1999), which was followed by the horror film House on Haunted Hill (1999). Her role as Clear Rivers in the first two films of the Final Destination horror franchise earned her a reputation as a scream queen.

Larter played supporting roles in the comedy Legally Blonde (2001) and the romantic comedy A Lot Like Love (2005), and led the Bollywood movie Marigold (2007) and the thriller Obsessed (2009). She played the dual roles of Niki Sanders and Tracy Strauss on the NBC science fiction drama Heroes (2006–2010), and achieved wider recognition for her portrayal of video game heroine Claire Redfield in Resident Evil: Extinction (2007), Resident Evil: Afterlife (2010), and Resident Evil: The Final Chapter (2016).

As of April 2017, Larter's films have grossed over US$1.31 billion worldwide. Her presence in the media is reinforced by her appearances in lists compiled by Maxim, FHM, and Stuff, as well as People magazine's "Best Dressed List" in 2007. She released her cookbook, Kitchen Revelry: A Year of Festive Menus from My Home to Yours, in September 2013.

Early life
Larter was born in Cherry Hill, New Jersey, the daughter of Margaret, a realtor, and Danforth Larter, a trucking executive. She attended Carusi Middle School and later graduated from Cherry Hill High School West during her time as a model, but she didn't finish her senior year of high school because of modeling. Her mom accompanied her everywhere until she turned 18. Her parents have since moved to Allentown, Pennsylvania. Larter said she was a tomboy until she turned 13.

Early modeling work (1990–1998)
She began her modeling career at the age of 14 when a modeling scout discovered her on the street and was asked to star in a Phillies commercial; this led to a modeling contract with the prestigious Ford Modeling Agency in New York. Larter subsequently skipped her senior year to model in Australia, Italy, and Japan, the latter a country she would temporarily settle in at the age of seventeen. While modeling in Italy, Larter met fellow model and aspiring actress Amy Smart and the two "became instant friends", according to Larter.

In November 1996, Larter portrayed fictional actress Allegra Coleman in an Esquire magazine hoax. When speaking about the cover and her subsequent fame, Larter said, "When the door opens for you in Hollywood, you need to run with it. You know?" Larter is currently signed to IMG Models. She landed her first professional acting roles in 1997 when she appeared in several television programs. She appeared in an episode of the Brooke Shields television series Suddenly Susan, and the short-lived series Chicago Sons. These roles were followed by a number of other appearances on Dawson's Creek, Chicago Hope, and Just Shoot Me!

Acting debut and breakthrough (1999–2005)
In 1999, Larter made her film debut in the coming-of-age dramedy Varsity Blues, which re-united her with Dawson's Creek star James Van Der Beek and close friend Amy Smart. Smart had persuaded Larter to audition for the movie, in which she played Darcy Sears, a love interest for one of the main characters. Varsity Blues drew a domestic box office gross of US$53 million. Also in 1999, she made supporting appearances in the teen comedies Giving It Up and Drive Me Crazy, and starred in the remake House on Haunted Hill which was made for around US$20 million. The horror film, following a group of strangers invited to a party at an abandoned asylum, was panned by critics, but grossed US$15 million on its opening weekend and went on to earn over US$40 million overall.

Larter starred as Clear Rivers, one of the main characters in the teen supernatural horror film Final Destination (2000). Also starring Devon Sawa and Kerr Smith, the movie's premise followed several teenagers who survive a plane crash but are stalked and killed by Death itself. Final Destination made US$112 million by the end of its theatrical run. In 2001, she appeared in the comedy Legally Blonde with Reese Witherspoon. She played Brooke Taylor Windham, a widow accused of her husband's murder. The film earned the top spot with US$20 million in its opening weekend and ended up grossing $141 million worldwide. With US$96 million of its total gross deriving from domestic markets, Legally Blonde is Larter's highest-grossing film domestically.

Larter next appeared as Zerelda Mimms in the western comedy American Outlaws. Directed by Les Mayfield and co-starring Colin Farrell and Scott Caan, the film was poorly received by critics and at the box office, garnering US$13 million at the end of its theatrical run. She also starred in Kevin Smith's Jay and Silent Bob Strike Back. That year, Larter appeared on the cover of Maxim magazine and performed in the stage play The Vagina Monologues in New York City. In Spring 2002, Larter moved from Los Angeles to New York. "I was too young and impressionable to handle the pressures of L.A." Larter recalled in an interview: "I'm a woman now. I am no longer the little girl who could be easily influenced."

Her first project there was to reprise her role as Clear Rivers in the sequel to Final Destination entitled Final Destination 2. In an interview with IGN, Larter explained her return to the franchise: "When New Line asked me to come back, I thought it was great. They showed me the script and let me have some input, and it was really terrific." The film made US$90 million worldwide, to a mixed critical reception. A year later, Larter served as an associate producer of and starred in the thriller Three Way. After doing so, Larter commented about future producing endeavors during an interview for Resident Evil: Extinction: "I definitely have many ideas and different avenues that I want to take as my career goes on." In 2005, she appeared in the independent political thriller Confess, and had a role in the romantic comedy A Lot Like Love, starring Amanda Peet and Ashton Kutcher.

Rise to prominence and subsequent hiatus (2006–2011)
Larter moved back to Los Angeles in 2005. Her first audition was for the NBC science fiction drama television series Heroes. Larter played the characters of Niki Sanders, who suffered from DID, and Tracy Strauss on the show created by Tim Kring. Larter's initial character Niki Sanders, was a wife, mother, and a former internet stripper from Las Vegas who exhibits superhuman strength and alternate personalities who go by the names of Jessica and Niki. "Ali read for the part and just owned it from the second she walked in," Kring said to the Chicago Tribune, "It was a very impressive audition." As of the third season, Larter began to play the new character of Tracy Strauss, who possessed the ability to freeze objects; and later, turn her body into water.

Larter took on the title role in Marigold (2007), alongside Salman Khan. The film was released in August 2007 and revolved around an American actress (Larter) who goes to India and gets caught up in the exotic world of Bollywood. Filming took place in North India and London, commencing in June 2004. In an interview with the BBC, Larter remarked this role was "an opportunity to overcome my fear of singing and dancing because I have no professional training [...] I really focused on the character and loved this journey she went on and the experiences she had." She was paid a seven-figure salary for her part in the film.

In 2007, she appeared opposite Milla Jovovich in Resident Evil: Extinction, portraying the character of Claire Redfield, who in the film, is the leader of a convoy of zombie apocalypse survivors who go to Alaska in search of a safe haven. Her role sent her to Mexicali, Mexico for filming from May to late July, and required her hair to be dyed a light red. Larter explained her character Claire: "She became the leader of this convoy. She's incredibly strong, patient. I think she serves a role for everyone within this convoy, let it be a mother to someone, a buddy, a best friend." Despite negative reviews, the film made a total of US$147 million worldwide. Also in the same year, she appeared with Hayes McArthur in the comedy Homo Erectus and appeared as Evelyn Garland in the biographical drama Crazy, based on guitarist Hank Garland.

Larter starred opposite Beyoncé and Idris Elba in the Screen Gems-produced thriller Obsessed (2009). The film follows an office executive (Elba) whose marriage to Knowles' character is threatened by the aggressive interests of a co-worker, portrayed by Larter. In an interview with Glam, Larter said that she "was excited to get the chance to play a femme fatale. I love playing women that are dark and vulnerable and sort of filled with a little bit of crazy emotion." While the film was released to mixed reviews, Larter was critically praised for her performance. Derek Malcolm of The London Evening Standard felt that the movie was a "dim reworking of Fatal Attraction" and noted: "Larter as the pathological minx is the best thing about it." Obsessed opened at top spot in its opening weekend with US$28 million, and made a total domestic gross of US$68 million, becoming Larter's second highest-grossing film in North-America. It resulted in Larter's third Teen Choice Award nomination and an MTV Movie Award for Best Fight with Beyonce.

Larter reprised her role of Claire Redfield in Resident Evil: Afterlife (2010), which was filmed in 3D and saw her character ambushed and mentally manipulated by the fictional Umbrella Corporation, before she is rescued by Alice (Milla Jovovich). Like the previous Resident Evil entries, the film received negative reviews but became a major commercial success, earning US$296 million worldwide. On returning to the role of Claire, she stated in an interview with JoBlo.com: "I guess people liked me as her [...] I'm excited that they brought me back [...] To work with the man [Paul W. S. Anderson] who really created this world and this vision was what excited me about joining this next installment". In 2010, Larter appeared as the title character in a short film for Absolut Vodka entitled "Lemon Drop". Following the release of Afterlife, Larter took a career hiatus to focus on her family.

Return to acting (2014–present)
Larter returned to the big screen playing the love interest of a successful but psychotic man (Matt LeBlanc) in the comedy Lovesick (2014). The film screened at the 15th annual Newport Beach Film Festival and was released for VOD and selected theaters. She portrayed the "fair-weather" friend of a woman with ALS in the independent drama You're Not You (2014), directed by George C. Wolfe and starring Hilary Swank, Emmy Rossum and Josh Duhamel.

In 2014, Larter obtained a regular part in the first season of TNT's drama series Legends, appearing as Crystal McGuire, an operative with the FBI's Deep Cover Operations. Larter starred in the supernatural thriller The Diabolical as Madison, a single mother who battles evil forces in her house. Released the following year at South by Southwest, it was distributed for a VOD and limited release in certain parts of United States only. The film received largely mixed reviews; Gary Goldstein of Los Angeles Times felt that her "fraught, more seemingly complex [character] remains underdeveloped" in what he described as a "weak horror-thriller".

Larter starred in Resident Evil: The Final Chapter (2016), where her role of Claire teams up with Alice (Jovovich) and the Red Queen to save the remnants of humanity. Despite a largely mixed critical response, with a worldwide gross of over US$312 million, the film emerged as her biggest box office success. She played the role of Amelia Slater in the Fox series Pitch, about a young black woman who makes history by becoming the first woman to play Major League Baseball. The series ran for one season, which was released in 2016. From 2019 to 2020, Larter played the recurring role of Grace Sawyer in the police procedural series The Rookie.

She starred in the thriller The Man in the White Van, which premiered at the 2023 Newport Beach Film Festival to positive reviews.

In the media
Larter first appeared in the media when she portrayed the fictional character of Allegra Coleman in the November 1996 issue of Esquire. The magazine, which billed Coleman as the movies' next dream girl, told of Allegra's relationship with David Schwimmer, how Quentin Tarantino broke up with Mira Sorvino to date her, and how Woody Allen overhauled a film to give her a starring role. When the magazine was published, Esquire received hundreds of phone calls about the non-existent Coleman and various talent agencies sought to represent her, even after the hoax was revealed. Larter herself received a considerable amount of attention after the cover; she received phone calls from morning TV shows and others for interviews.

The Esquire cover led Larter to a role on Varsity Blues. One particular scene where Larter's character, Darcy Sears, wears nothing but whipped cream to cover herself has become a media favorite. It has been referenced a number of times in the media including on MTV's Jersey Shore, where one character refers to it as the "Varsity Blues outfit". Larter has been acknowledged as a Scream queen by MSN due to her appearances in horror/thriller films. After the success of Heroes, Larter appeared on People "Ten Best Dressed List" as "The Newcomer" in 2007. In 2009, Larter was named Cosmopolitan magazine's Fun Fearless Female of the year at a ceremony held in Beverly Hills.

Larter has appeared on the cover of numerous magazines, including Cosmopolitan (France, Indonesia, Ecuador, Germany, Greece, Turkey and U.S.), Glamour, Health, Seventeen, Self, Shape, Maxim, Esquire, Lucky, Allure and Philadelphia Style. She has appeared in print ads and commercials throughout her career. In 2004, she appeared in print ads for Estee Lauder cosmetics. She has appeared in commercials for Parfums de Coeur Designer Imposter Body Sprays and Stolichnaya vodka.

In June 2010, Larter was one of thousands of delegates from 130 countries who participated in a United Nations conference, 'Women Deliver' in Washington, D.C. Larter, along with her husband Hayes MacArthur, hosted The Art of Elysium Gala in 2013 and are to be recipients of the Spirit of Elysium Award at the January 2014 ceremony. She has appeared on the covers of Shape, Cosmopolitan, Allure, Glamour, Lucky, InStyle, Maxim, and Entertainment Weekly.

Personal life
During her time as a model, Larter moved to Los Angeles to pursue acting. In 2002, she moved to New York for a period of three years. In an interview with Phillymag, Larter gave reason for the move: I took some time off to define myself outside the pressures of the industry. Part of me really needed to know if this is what I wanted to do with the rest of my life. In January 2005, she moved back to Los Angeles for a role in Heroes. In December 2007, Larter and her then longtime boyfriend, Hayes MacArthur, were engaged to marry. They had met on the set of National Lampoon's Homo Erectus. In a 2007 interview with Cosmo, Larter said: "I told my boyfriend after three weeks that I wanted to marry him and that we could do it tomorrow." On August 1, 2009, Larter married MacArthur at MacArthur's parents' estate in Kennebunkport, Maine; among the invited was Larter's close friend Amy Smart. The couple later purchased a three-story home in the Hollywood Hills for $2.9 million.

On July 20, 2010, Larter announced that she and MacArthur were expecting their first child and later, on the September 10 episode of Late Night with Jimmy Fallon, announced that she was expecting a boy. Larter gave birth to the couple's son in 2010. In August 2014, Larter confirmed that she and MacArthur were expecting their second child that winter. She gave birth to a girl in 2015. As of 2013, Larter had two dogs, Jackpot and Ella.

title: Ali Larter


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Gene Wood

Eugene Edward Wood  (October 20, 1925 – May 21, 2004) was an American television personality, known primarily for his work as an announcer on various game shows. From the 1950s to the 1990s, he announced many game shows, primarily Mark Goodson–Bill Todman productions such as Family Feud, Classic Concentration, Card Sharks, Password, and Beat the Clock. Wood also served a brief stint as a host on this last show, and on another show, Anything You Can Do. After retiring from game shows in 1996, Wood worked as an announcer for the Game Show Network until his retirement in 1998.

Early life
Wood was born in Quincy, Massachusetts. He majored in speech and theater at Emerson College.

Career
His early career included stand-up comedy, television commercials, and writing for Bob Keeshan of Captain Kangaroo fame. This work included a Terrytoons-produced cartoon series, The Adventures of Lariat Sam, which aired on the Captain Kangaroo show. Wood also supplied voices and sang the theme song. Wood also had a comedy career, often pairing with partner Bill Dana, performing their comedy act at nightclubs.

His first role as a game show announcer came as a substitute on the ABC version of Supermarket Sweep in 1966; three years later, he began a long association with Mark Goodson-Bill Todman Productions, where he worked on Beat the Clock as its announcer from 1969 to 1972; after the departure of the show's host, Jack Narz, Wood then took over as host of Beat the Clock, with Nick Holenreich serving as announcer. Wood hosted the 1971–72 season of the short-lived game show Anything You Can Do, which featured teams of men competing against teams of women in stunts similar to Beat the Clock. He also appeared as a celebrity panelist on one week of Match Game in 1974.

By 1976, Wood had become a regular announcer for Goodson–Todman, working as voice-over for many of the company's game shows. In addition to his role as announcer, Wood regularly served as a warm-up act for the audiences on these shows, and often performed a series of comedy skits. Among his most popular jobs was as announcer on the original version of Family Feud. The original version, hosted by Richard Dawson, ran on ABC from 1976 to 1985, and when Family Feud was revived in 1988 with Ray Combs as host, Wood announced on that version as well through the 1994–1995 season, during which Dawson returned as host. Another show for which he announced on both the original version and a revival was Card Sharks. The show's first incarnation, starring Jim Perry, ran from 1978 to 1981 on NBC, while two concurrent revivals (one on CBS and another in syndication, hosted by Bob Eubanks and Bill Rafferty, respectively) ran from 1986 to 1989. Wood announced the first few weeks of Bruce Forsyth's Hot Streak on ABC, before being replaced by Marc Summers.

After the 1985 death of the original announcer Johnny Olson on the Bob Barker version of The Price Is Right, Wood was one of four interim announcers on that show, until Rod Roddy was chosen as Olson's successor. At that same time, Wood also announced on the nightly syndicated version hosted by Tom Kennedy that ran for the season. According to former producer Roger Dobkowitz, between Barker, Goodson & Dobkowitz, himself, felt that his voice was a little on the harsh side and was unsuitable for the show, despite his experience.

Wood returned to Price briefly in 1998 to read the summer rerun fee plugs. He also filled in for Olson, during the final weeks of the Tom Kennedy-hosted version of Body Language. Other shows on which Wood served as a regular announcer were Tattletales (CBS, 1974–78), Double Dare (CBS, 1976–77), Match Game-Hollywood Squares Hour (NBC, 1983–84), Password Plus (NBC, 1979–82), Super Password (NBC, 1984–89), Love Connection (Syndication, 1985–1988), Classic Concentration (NBC, 1987–91), Win, Lose or Draw (Syndicated, 1987–90), the Ross Shafer-hosted Match Game (1990–91) and Family Challenge (1995–96). Prior to his retirement in the late 1990s, he also did voiceovers for the Game Show Network.

Wood wrote the narration for the 1965 film The World of Abbott and Costello.

Death
Wood retired to Adamsville, Rhode Island in the 1990s. He died of lung cancer in Boston, Massachusetts on May 21, 2004 at the age of 78. He was survived by his wife of 44 years, Carleen Anderson Wood; two daughters, Sasha and Mia Wood, both of Los Angeles; a son from a previous marriage, Timothy E. Wood of San Francisco; and two grandchildren. Wood's body was cremated, and his ashes were given to his family.

title: Gene Wood


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Category:Composers

Composers are those individuals who write/wrote music in notation, usually for but not limited to classical instruments such as orchestra and piano, or for jazz.

Composers may be subcategorized according to:
 * Composers by century
 * Composers by city
 * Composers by genre
 * Composers by instrument
 * Composers by nationality

title: Category:Composers


text: Category:Computer chess

title: Category:Computer chess


text: Category:Mythology

title: Category:Mythology


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Category:Chess players

This category and its subcategories include people notable as chess players.
 * All players will be found in the appropriate subcategory of chess players by nationality. Female players by nationality will be found in both the unrestricted chess player category (e.g., Category:Argentine chess players) and the respective female chess player category (e.g., Category:Argentine female chess players) per WP:DIFFUSE.
 * Players who have been awarded the Grandmaster title will be found in the subcategory chess Grandmasters. (The Grandmaster title was first awarded by FIDE in 1950 so most strong players from the middle of the 20th century on will be in the chess grandmaster category.)
 * Female players who hold the Woman Grandmaster title will be found in the subcategory chess Woman Grandmasters. Some women hold both the Woman Grandmaster and the unrestricted Grandmaster title and will be found in both categories.
 * Players who are grandmasters of correspondence chess will be found in the subcategory correspondence chess grandmasters. A small number of players are grandmasters of both over-the-board and correspondence chess and will be found in both categories.
 * Players of the Persian precursor to modern chess will be in Shatranj players.

title: Category:Chess players


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Category:Chess games

These are famous individual games in the history of chess. See List of famous chess games for an annotated list. Articles on chess matches and tournaments are in the category Chess competitions.

For descriptions of chess variants (games similar to chess but played with different rules, pieces, or boards), see Category:Chess variants.

title: Category:Chess games


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Category:Swedish monarchs

Swedish monarchs includes three queens regnant also to be found under Swedish queens and one duchess regent also found under Swedish princesses. The list of articles below is complete (as of July 15, 2009) with all legitimate monarchs included.

Regarding alphabetical (and chronological) name sorting, note:
 * Kings are always listed by official first name.
 * Coal or Cole is listed here as Kol.
 * Edmund is listed here as Emund.
 * Filip is listed in English as Philip.
 * Gustaf (legal spelling after 1901) and Gustavus are alphabetized here as Gustav.
 * Håkan and Haakon are alphabetized here in English as Hacon.
 * Halsten is listed here in English as Alstan.
 * Hans is listed in English as John.
 * Karl is listed here under C as Carl, with Charles also alphabetized as Carl.
 * Kristian is listed here under C as Christian.
 * Kristoffer is listed here under C as Christopher.
 * Waldemar is listed here as Valdemar.
 * Other Swedish name forms below do not affect the alphabet.

title: Category:Swedish monarchs


text: Category:Sweden

title: Category:Sweden


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Diamond principle

In mathematics, and particularly in axiomatic set theory, the diamond principle $◊$ is a combinatorial principle introduced by Ronald Jensen in that holds in the constructible universe ($L$) and that implies the continuum hypothesis. Jensen extracted the diamond principle from his proof that the axiom of constructibility ($V = L$) implies the existence of a Suslin tree.

Definitions
The diamond principle $◊$ says that there exists a ◊-sequence, a family of sets $A_{α} ⊆ α$ for $α < ω_{1}$ such that for any subset $A$ of ω1 the set of $α$ with $A ∩ α = A_{α}$ is stationary in $ω_{1}$.

There are several equivalent forms of the diamond principle. One states that there is a countable collection $A_{α}$ of subsets of $α$ for each countable ordinal $α$ such that for any subset $A$ of $ω_{1}$ there is a stationary subset $C$ of $ω_{1}$ such that for all $α$ in $C$ we have $A ∩ α ∈ A_{α}$ and $C ∩ α ∈ A_{α}$. Another equivalent form states that there exist sets $A_{α} ⊆ α$ for $α < ω_{1}$ such that for any subset $A$ of $ω_{1}$ there is at least one infinite $α$ with $A ∩ α = A_{α}$.

More generally, for a given cardinal number $κ$ and a stationary set $S ⊆ κ$, the statement $◊_{S}$ (sometimes written $◊(S)$ or $◊_{κ}(S)$) is the statement that there is a sequence $⟨A_{α} : α ∈ S⟩$ such that

 * each $A_{α} ⊆ α$
 * for every $A ⊆ κ$, ${α ∈ S : A ∩ α = A_{α} }$ is stationary in $κ$

The principle $◊_{ω_{1}}|undefined$ is the same as $◊$.

The diamond-plus principle $◊^{+}$ states that there exists a $◊^{+}$-sequence, in other words a countable collection $A_{α}$ of subsets of $α$ for each countable ordinal α such that for any subset $A$ of $ω_{1}$ there is a closed unbounded subset $C$ of $ω_{1}$ such that for all $α$ in $C$ we have $A ∩ α ∈ A_{α}$ and $C ∩ α ∈ A_{α}$.

Properties and use
showed that the diamond principle $◊$ implies the existence of Suslin trees. He also showed that $V = L$ implies the diamond-plus principle, which implies the diamond principle, which implies CH. In particular the diamond principle and the diamond-plus principle are both independent of the axioms of ZFC. Also $♣ + CH$ implies $◊$, but Shelah gave models of $♣ + ¬ CH$, so $◊$ and $♣$ are not equivalent (rather, $♣$ is weaker than $◊$).

Matet proved the principle $$\diamondsuit_\kappa$$ equivalent to a property of partitions of $$\kappa$$ with diagonal intersection of initial segments of the partitions stationary in $$\kappa$$.

The diamond principle $◊$ does not imply the existence of a Kurepa tree, but the stronger $◊^{+}$ principle implies both the $◊$ principle and the existence of a Kurepa tree.

used $◊$ to construct a $C*$-algebra serving as a counterexample to Naimark's problem.

For all cardinals $κ$ and stationary subsets $S ⊆ κ^{+}$, $◊_{S}$ holds in the constructible universe. proved that for $κ > ℵ_{0}$, $◊_{κ^{+}}(S)|undefined$ follows from $2^{κ} = κ^{+}$ for stationary $S$ that do not contain ordinals of cofinality $κ$.

Shelah showed that the diamond principle solves the Whitehead problem by implying that every Whitehead group is free.

title: Diamond principle


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Desert Eagle

The Desert Eagle  is a single-action, gas-operated, semi-automatic pistol known for chambering the .50 Action Express, the largest centerfire cartridge of any magazine-fed, self-loading pistol.

Magnum Research Inc. (MRI) designed and developed the Desert Eagle. The design was further refined by (and was also manufactured by) Israel Military Industries (IMI), until 1995, when MRI shifted the manufacturing contract to Saco Defense, in Saco, Maine. In 1998, MRI moved manufacturing back to IMI, which later commercialized its small arms branch under the name Israel Weapon Industries. Since December 2009, the Desert Eagle pistol has been produced in the United States at MRI's Pillager, Minnesota, facility. Kahr Arms acquired Magnum Research in 2010.

Magnum Research has marketed various versions of the short recoil Jericho 941 pistol under the Baby Eagle and Desert Eagle pistol names; these weapons are not directly related to the Desert Eagle, but share a similar visual design.

Design

The design for the Desert Eagle was initiated by Bernard C. White of Magnum Research and Arnolds Streinbergs of Riga Arms Institute, who filed a US patent application for a mechanism for a gas-actuated pistol in January 1983. This established the basic layout of the Desert Eagle. A second patent application was filed in December 1985, after the basic design had been refined by IMI Systems (Israel Military Industries) for production, and this is the form that went into production.

The pistol is fired by a single-action hammer and has a manual safety switch on the slide. The ambidextrous safety switch rotates a drum mechanism that sits over the firing pin, causing the firing pin to lock in, which prevents it from moving forward and reduces the possibility of the gun discharging accidentally. With the safety off, pulling the trigger releases, allowing the hammer to fall downward, hitting the firing pin, and causing the chambered round to discharge.

The Desert Eagle uses a gas-operated ejection and chambering mechanism normally found in rifles, as opposed to the short recoil or blowback designs most commonly seen in semi-automatic pistols. When a round is fired, gases are ported out through a small hole in the barrel in front of the chamber. These travel forward through a small tube under the barrel, to a cylinder underneath the front of the barrel. The slide, which acts as the bolt carrier, has a small piston on the front that fits into this cylinder. When the gases reach the cylinder, the piston pushes the slide rearward, with a large pin inside the camming surface in the rear of the bolt causing the bolt to rotate and unlock. A mechanism on the left side of the bolt prevents the bolt from rotating freely as the slide moves, forcing it to remain aligned correctly with the barrel while the breech is open. The spring-loaded ejector is continually being depressed by the case, until the case is free of the chamber and the tension from the ejector is released, causing the case to eject, breaking free of the extractor in the process. The slide reaches its rearmost position, and then moves forward again under the tension of the recoil springs. The bottom lug of the bolt pushes a new round into the chamber, then the bolt locks up and the gun can be fired again.

The rotating bolt has three radial locking lugs (the fourth lug is only for pushing the next round in the chamber), with the extractor on the right-hand side fitting where the fifth lug would be, and strongly resembles the seven-lug bolt of the M16 series of rifles, while the fixed gas cylinder and moving piston resemble those of the Ruger Mini-14 carbine (the original patent used a captive piston similar to the M14 rifle).

The advantage of the gas operation is that it allows the use of far more powerful cartridges than traditional semi-automatic pistol designs. Thus, it allows the Desert Eagle to compete in an area that had previously been dominated by magnum revolvers. Downsides of the gas-operated mechanism are the large size of the Desert Eagle, and the fact that it discourages the use of unjacketed lead bullets, as lead particles sheared off during firing can clog the gas release tap, preventing proper function.

Switching a Desert Eagle to another chambering requires only that the correct barrel, bolt assembly, and magazine be installed. Thus, a conversion to fire other cartridges can be quickly accomplished. The rim diameter of the .50 AE (Action Express) is the same as the .44 Remington Magnum cartridge, consequently, only a barrel and magazine change is required to convert a .44 Desert Eagle to the larger, more powerful, .50 AE round. The most popular barrel length is 6 in (152 mm), although a 10 in (254 mm) barrel is available. The Mark XIX barrels are machined with integral scope mounting bases, simplifying the process of adding a pistol scope.

The Desert Eagle is fed with a detachable magazine. Magazine capacity is nine rounds in .357 Magnum, eight rounds in .44 Magnum, and seven rounds in .50 Action Express. The Desert Eagle's barrel features polygonal rifling. The pistol is primarily used for hunting, target shooting, and silhouette shooting.

Marks I and VII
The Mark I, which is no longer produced, was offered with a steel, stainless steel, or aluminum alloy frame and differs primarily in the size and shape of the safety levers and slide catch. The Mark VII includes an adjustable trigger (retrofittable to Mark I pistols). The Mark I and VII are both available in .357 Magnum and .44 Magnum; the Mark VII has been chambered for .41 Magnum. The barrels have a $3/8$ in dovetail, to which an accessory mount can be attached. Later Mark VII models were offered in .50 Action Express with a $7/8$ in Weaver-pattern rail on the barrel; the .50 Mark VII later became the Mark XIX. Barrel lengths are 6, 10, and 14 inches for .357 Magnum and .44 Magnum, but only 6 or 10 inches for .41 Magnum.

Mark XIX

The most recent model, the Mark XIX, is available in .357 Magnum, .44 Magnum, .429 DE (introduced in 2018) and .50 Action Express. This model comes in a variety of different finishes, such as brushed chrome or titanium gold. Magnum Research offered this model in .440 Cor-Bon caliber, a .50 AE derived case. There were fewer than 500 original .440 Cor-Bon Desert Eagles imported into U.S. in December 2000. These are marked by the number 440 on the left lower side of the barrel, in numerals twice the size of other calibers, and without the preceding period. A number of .44 Magnum barrels were re-chambered to produce .440 Corbon barrels, but these can be identified by the off-centered ".440" (with period) produced by adding the final 0 to the original barrel mark.

Mark XIX barrels are available in 6 in and 10 in lengths only. All .357 Magnum barrels have exterior barrel flutes on the left, right and top sides of the barrel. All .44 Magnum barrels have flutes on the left and right side only, not on the top. The .50 AE barrels have no flutes.

All current-production Mark XIX models except for the CA approved models have Weaver rails along the top of the barrels, as opposed to the Dovetail rails on previous models. Selected Mark XIX models have ported barrels or under-barrel picatinny rails.

The DE44CA (Desert Eagle .44 Magnum California) is the only Mark XIX model approved for dealer sales to the public in the State of California. The CA approved version differs from the regular XIX models in that it has an automatic firing pin block and a two-slot Weaver-style rail for mounting optics.

In popular culture
The Desert Eagle has been featured in more than 600 films, television shows and video games, making it well known in popular culture. The commercial success of the pistol is due in part to its use in films, according to Magnum Research chairman and CEO John Risdall. According to a 1994 newspaper article, the company actively solicited prop houses to use the gun. By 2000, it had been used in over 40 films, including The Matrix, Eraser, Red Heat, Last Action Hero, Cliffhanger, Demolition Man, Assassins, The Last Boy Scout, Double Impact, and Austin Powers.

Users

 * 🇵🇱 Poland: GROM
 * 🇵🇹 Portugal: GOE

title: Desert Eagle


text:
Benet's Reader's Encyclopedia of American Literature

Benet's Reader's Encyclopedia of American Literature was published in 1991 by Harper Collins Publishers. The book contains facts on American authors' major and lesser works, summarizes the critical consensus, gives biographical information and often lists secondary biographical and critical works.

Publication information

 * ISBN 0-06-270110-X


text:
Character theory

In mathematics, more specifically in group theory, the character of a group representation is a function on the group that associates to each group element the trace of the corresponding matrix. The character carries the essential information about the representation in a more condensed form. Georg Frobenius initially developed representation theory of finite groups entirely based on the characters, and without any explicit matrix realization of representations themselves. This is possible because a complex representation of a finite group is determined (up to isomorphism) by its character. The situation with representations over a field of positive characteristic, so-called "modular representations", is more delicate, but Richard Brauer developed a powerful theory of characters in this case as well. Many deep theorems on the structure of finite groups use characters of modular representations.

Applications
Characters of irreducible representations encode many important properties of a group and can thus be used to study its structure. Character theory is an essential tool in the classification of finite simple groups. Close to half of the proof of the Feit–Thompson theorem involves intricate calculations with character values. Easier, but still essential, results that use character theory include Burnside's theorem (a purely group-theoretic proof of Burnside's theorem has since been found, but that proof came over half a century after Burnside's original proof), and a theorem of Richard Brauer and Michio Suzuki stating that a finite simple group cannot have a generalized quaternion group as its Sylow $2$-subgroup.

Definitions
Let $V$ be a finite-dimensional vector space over a field $F$ and let $ρ : G → GL(V)$ be a representation of a group $G$ on $V$. The character of $ρ$ is the function $χ_{ρ} : G → F$ given by

 * $$\chi_{\rho}(g) = \operatorname{Tr}(\rho(g))$$

where $Tr$ is the trace.

A character $χ_{ρ}$ is called irreducible or simple if $ρ$ is an irreducible representation. The degree of the character $χ$ is the dimension of $ρ$; in characteristic zero this is equal to the value $χ(1)$. A character of degree 1 is called linear. When $G$ is finite and $F$ has characteristic zero, the kernel of the character $χ_{ρ}$ is the normal subgroup:

 * $$\ker \chi_\rho := \left \lbrace g \in G \mid \chi_{\rho}(g) = \chi_{\rho}(1) \right \rbrace, $$

which is precisely the kernel of the representation $ρ$. However, the character is not a group homomorphism in general.

Properties

 * Characters are class functions, that is, they each take a constant value on a given conjugacy class. More precisely, the set of irreducible characters of a given group $G$ into a field $F$ form a basis of the $F$-vector space of all class functions $G → F$.
 * Isomorphic representations have the same characters. Over a field of characteristic $0$, two representations are isomorphic if and only if they have the same character.
 * If a representation is the direct sum of subrepresentations, then the corresponding character is the sum of the characters of those subrepresentations.
 * If a character of the finite group $G$ is restricted to a subgroup $H$, then the result is also a character of $H$.
 * Every character value $χ(g)$ is a sum of $n$ $m$-th roots of unity, where $n$ is the degree (that is, the dimension of the associated vector space) of the representation with character $χ$ and $m$ is the order of $g$. In particular, when $F = C$, every such character value is an algebraic integer.
 * If $F = C$ and $χ$ is irreducible, then $$[G:C_G(x)]\frac{\chi(x)}{\chi(1)}$$ is an algebraic integer for all $x$ in $G$.
 * If $F$ is algebraically closed and $char(F)$ does not divide the order of $G$, then the number of irreducible characters of $G$ is equal to the number of conjugacy classes of $G$. Furthermore, in this case, the degrees of the irreducible characters are divisors of the order of $G$ (and they even divide $[G : Z(G)]$ if $F = C$).

Arithmetic properties
Let ρ and σ be representations of $G$. Then the following identities hold: where $ρ⊕σ$ is the direct sum, $ρ⊗σ$ is the tensor product, $ρ^{∗}$ denotes the conjugate transpose of $ρ$, and $Alt^{2}$ is the alternating product $Alt^{2}ρ = ρ ∧ ρ$ and $Sym^{2}$ is the symmetric square, which is determined by $$\rho \otimes \rho = \left(\rho \wedge \rho \right) \oplus \textrm{Sym}^2 \rho.$$
 * $$\chi_{\rho \oplus \sigma} = \chi_\rho + \chi_\sigma$$
 * $$\chi_{\rho \otimes \sigma} = \chi_\rho \cdot \chi_\sigma$$
 * $$\chi_{\rho^*} = \overline {\chi_\rho}$$
 * $$\chi_{{\scriptscriptstyle \rm{Alt}^2} \rho}(g) = \tfrac{1}{2}\! \left[ \left(\chi_\rho (g) \right)^2 - \chi_\rho (g^2) \right]$$
 * $$\chi_{{\scriptscriptstyle \rm{Sym}^2} \rho}(g) = \tfrac{1}{2}\! \left[ \left(\chi_\rho (g) \right)^2 + \chi_\rho (g^2) \right]$$

Character tables
The irreducible complex characters of a finite group form a character table which encodes much useful information about the group $G$ in a compact form. Each row is labelled by an irreducible representation and the entries in the row are the characters of the representation on the respective conjugacy class of $G$. The columns are labelled by (representatives of) the conjugacy classes of $G$. It is customary to label the first row by the character of the trivial representation, which is the trivial action of $G$ on a 1-dimensional vector space by $$ \rho(g)=1$$ for all $$ g\in G $$. Each entry in the first row is therefore 1. Similarly, it is customary to label the first column by the identity. Therefore, the first column contains the degree of each irreducible character.

Here is the character table of

 * $$C_3 = \langle u \mid u^{3} = 1 \rangle,$$

the cyclic group with three elements and generator u:

where $ω$ is a primitive third root of unity.

The character table is always square, because the number of irreducible representations is equal to the number of conjugacy classes.

Orthogonality relations
The space of complex-valued class functions of a finite group $ω$ has a natural inner product:

 * $$\left \langle \alpha, \beta\right \rangle := \frac{1}{|G|}\sum_{g \in G} \alpha(g) \overline{\beta(g)}$$

where $(1)$ is the complex conjugate of $(u)$. With respect to this inner product, the irreducible characters form an orthonormal basis for the space of class-functions, and this yields the orthogonality relation for the rows of the character table:

 * $$\left \langle \chi_i, \chi_j \right \rangle = \begin{cases} 0 & \mbox{ if } i \ne j, \\ 1 & \mbox{ if } i = j. \end{cases}$$

For $(u^{2})$ in $ω$, applying the same inner product to the columns of the character table yields:

 * $$\sum_{\chi_i} \chi_i(g) \overline{\chi_i(h)} = \begin{cases} \left | C_G(g) \right |, & \mbox{ if } g, h \mbox{ are conjugate } \\ 0 & \mbox{ otherwise.}\end{cases}$$

where the sum is over all of the irreducible characters $1$ of $G$ and the symbol $1$ denotes the order of the centralizer of $G$. Note that since $G$ and $g$ are conjugate iff they are in the same column of the character table, this implies that the columns of the character table are orthogonal.

The orthogonality relations can aid many computations including:
 * Decomposing an unknown character as a linear combination of irreducible characters.
 * Constructing the complete character table when only some of the irreducible characters are known.
 * Finding the orders of the centralizers of representatives of the conjugacy classes of a group.
 * Finding the order of the group.

Character table properties
Certain properties of the group $g$ can be deduced from its character table:

 * The order of $h$ is given by the sum of the squares of the entries of the first column (the degrees of the irreducible characters). More generally, the sum of the squares of the absolute values of the entries in any column gives the order of the centralizer of an element of the corresponding conjugacy class.
 * All normal subgroups of $G$ (and thus whether or not $G$ is simple) can be recognised from its character table. The kernel of a character $G$ is the set of elements $G$ in $χ$ for which $1$; this is a normal subgroup of $g$. Each normal subgroup of $G$ is the intersection of the kernels of some of the irreducible characters of $G$.
 * The commutator subgroup of $G$ is the intersection of the kernels of the linear characters of $G$.
 * If $G$ is finite, then since the character table is square and has as many rows as conjugacy classes, it follows that $G$ is abelian iff each conjugacy class is a singleton iff the character table of $G$ is $$|G| \!\times\! |G|$$ iff each irreducible character is linear.
 * It follows, using some results of Richard Brauer from modular representation theory, that the prime divisors of the orders of the elements of each conjugacy class of a finite group can be deduced from its character table (an observation of Graham Higman).

The character table does not in general determine the group up to isomorphism: for example, the quaternion group $G$ and the dihedral group of $1$ elements, $χ_{1}$, have the same character table. Brauer asked whether the character table, together with the knowledge of how the powers of elements of its conjugacy classes are distributed, determines a finite group up to isomorphism. In 1964, this was answered in the negative by E. C. Dade.

The linear representations of $G$ are themselves a group under the tensor product, since the tensor product of 1-dimensional vector spaces is again 1-dimensional. That is, if $$\rho_1:G\to V_1$$ and $$ \rho_2:G\to V_2$$ are linear representations, then $$ \rho_1\otimes\rho_2 (g)=(\rho_1(g)\otimes\rho_2(g))$$ defines a new linear representation. This gives rise to a group of linear characters, called the character group under the operation $$ [\chi_1*\chi_2](g)=\chi_1(g)\chi_2(g)$$. This group is connected to Dirichlet characters and Fourier analysis.

Induced characters and Frobenius reciprocity
The characters discussed in this section are assumed to be complex-valued. Let $Q$ be a subgroup of the finite group $G$. Given a character $H$ of $G$, let $1$ denote its restriction to $χ$. Let $G$ be a character of $H$. Ferdinand Georg Frobenius showed how to construct a character of $θ$ from $H$, using what is now known as Frobenius reciprocity. Since the irreducible characters of $G$ form an orthonormal basis for the space of complex-valued class functions of $θ$, there is a unique class function $ω^{2}$ of $G$ with the property that

 * $$ \langle \theta^{G}, \chi \rangle_G = \langle \theta,\chi_H \rangle_H $$

for each irreducible character $G$ of $G$ (the leftmost inner product is for class functions of $χ$ and the rightmost inner product is for class functions of $G$). Since the restriction of a character of $G$ to the subgroup $H$ is again a character of $G$, this definition makes it clear that $χ_{2}$ is a non-negative integer combination of irreducible characters of $H$, so is indeed a character of $H$. It is known as the character of $G$ induced from $G$. The defining formula of Frobenius reciprocity can be extended to general complex-valued class functions.

Given a matrix representation $G$ of $θ$, Frobenius later gave an explicit way to construct a matrix representation of $ρ$, known as the representation induced from $H$, and written analogously as $1$. This led to an alternative description of the induced character $ω^{2}$. This induced character vanishes on all elements of $G$ which are not conjugate to any element of $ρ$. Since the induced character is a class function of $G$, it is only now necessary to describe its values on elements of $H$. If one writes $G$ as a disjoint union of right cosets of $H$, say

 * $$G = Ht_1 \cup \ldots \cup Ht_n,$$

then, given an element $G$ of $H$, we have:

 * $$ \theta^G(h) = \sum_{i \ : \ t_iht_i^{-1} \in H} \theta \left (t_iht_i^{-1} \right ).$$

Because $h$ is a class function of $H$, this value does not depend on the particular choice of coset representatives.

This alternative description of the induced character sometimes allows explicit computation from relatively little information about the embedding of $θ$ in $H$, and is often useful for calculation of particular character tables. When $H$ is the trivial character of $G$, the induced character obtained is known as the permutation character of $θ$ (on the cosets of $H$).

The general technique of character induction and later refinements found numerous applications in finite group theory and elsewhere in mathematics, in the hands of mathematicians such as Emil Artin, Richard Brauer, Walter Feit and Michio Suzuki, as well as Frobenius himself.

Mackey decomposition
The Mackey decomposition was defined and explored by George Mackey in the context of Lie groups, but is a powerful tool in the character theory and representation theory of finite groups. Its basic form concerns the way a character (or module) induced from a subgroup $G$ of a finite group $H$ behaves on restriction back to a (possibly different) subgroup $H$ of $G$, and makes use of the decomposition of $K$ into $\overline{β(g)}$-double cosets.

If $ G = \bigcup_{t \in T} HtK $ is a disjoint union, and $G$ is a complex class function of $G$, then Mackey's formula states that

 * $$\left( \theta^{G}\right)_K = \sum_{ t \in T} \left(\left [\theta^{t} \right ]_{t^{-1}Ht \cap K}\right)^{K},$$

where $β(g)$ is the class function of $g, h$ defined by $χ_{i}$ for all $θ$ in $H$. There is a similar formula for the restriction of an induced module to a subgroup, which holds for representations over any ring, and has applications in a wide variety of algebraic and topological contexts.

Mackey decomposition, in conjunction with Frobenius reciprocity, yields a well-known and useful formula for the inner product of two class functions $h$ and $H$ induced from respective subgroups $θ$ and $ψ$, whose utility lies in the fact that it only depends on how conjugates of $H$ and $K$ intersect each other. The formula (with its derivation) is:

 * $$\begin{align}

\left \langle \theta^{G},\psi^{G} \right \rangle &= \left \langle \left(\theta^{G}\right)_{K},\psi \right \rangle \\ &= \sum_{ t \in T} \left \langle \left( \left [\theta^{t} \right ]_{t^{-1}Ht \cap K}\right)^{K}, \psi \right \rangle \\ &= \sum_{t \in T} \left \langle \left(\theta^{t} \right)_{t^{-1}Ht \cap K},\psi_{t^{-1}Ht \cap K} \right \rangle, \end{align}$$

(where $H$ is a full set of $$-double coset representatives, as before). This formula is often used when $K$ and $T$ are linear characters, in which case all the inner products appearing in the right hand sum are either $χ(g) = χ(1)$ or $8$, depending on whether or not the linear characters $D_{4}$ and $θ$ have the same restriction to $χ_{H}$. If $ψ$ and $ψ$ are both trivial characters, then the inner product simplifies to $θ^{G}$.

"Twisted" dimension
One may interpret the character of a representation as the "twisted" dimension of a vector space. Treating the character as a function of the elements of the group $θ^{G}$, its value at the identity is the dimension of the space, since $ρ^{G}$. Accordingly, one can view the other values of the character as "twisted" dimensions.

One can find analogs or generalizations of statements about dimensions to statements about characters or representations. A sophisticated example of this occurs in the theory of monstrous moonshine: the $θ$-invariant is the graded dimension of an infinite-dimensional graded representation of the Monster group, and replacing the dimension with the character gives the McKay–Thompson series for each element of the Monster group.

Characters of Lie groups and Lie algebras
If $$G$$ is a Lie group and $$\rho$$ a finite-dimensional representation of $$G$$, the character $$\chi_\rho$$ of $$\rho$$ is defined precisely as for any group as
 * $$\chi_\rho(g)=\operatorname{Tr}(\rho(g))$$.

Meanwhile, if $$\mathfrak g$$ is a Lie algebra and $$\rho$$ a finite-dimensional representation of $$\mathfrak g$$, we can define the character $$\chi_\rho$$ by
 * $$\chi_\rho(X)=\operatorname{Tr}(e^{\rho(X)})$$.

The character will satisfy $$\chi_\rho(\operatorname{Ad}_g(X))=\chi_\rho(X)$$ for all $$g$$ in the associated Lie group $$ G$$ and all $$X\in\mathfrak g$$. If we have a Lie group representation and an associated Lie algebra representation, the character $$\chi_\rho$$ of the Lie algebra representation is related to the character $$\Chi_\rho$$ of the group representation by the formula
 * $$\chi_\rho(X)=\Chi_\rho(e^X)$$.

Suppose now that $$\mathfrak g$$ is a complex semisimple Lie algebra with Cartan subalgebra $$\mathfrak h$$. The value of the character $$\chi_\rho$$ of an irreducible representation $$\rho$$ of $$\mathfrak g$$ is determined by its values on $$\mathfrak h$$. The restriction of the character to $$\mathfrak h$$ can easily be computed in terms of the weight spaces, as follows:
 * $$\chi_\rho(H) = \sum_\lambda m_\lambda e^{\lambda(H)},\quad H\in\mathfrak h$$,

where the sum is over all weights $$\lambda$$ of $$\rho$$ and where $$m_\lambda$$ is the multiplicity of $$\lambda$$.

The (restriction to $$\mathfrak h$$ of the) character can be computed more explicitly by the Weyl character formula.

title: Character theory


text:
Domo (NHK)

Domo (どーも くん) is the official mascot of Japan's public broadcaster NHK, appearing in several 30-second stop-motion interstitial sketches, which are shown as station identification in between the channel's programming.

DOMO
Domo-kun first appeared in short stop-motion sketches on December 22, 1998, to mark the 10th anniversary of NHK's satellite broadcasting. The name "Domo" was acquired during the second episode of his show, in which a TV announcer said "dōmo, konnichiwa" (どーも、こんにちは), which is a greeting that can be translated as "Well, hello there!", but which can also be interpreted as "Hello, Domo", and thus is a convenient pun (dajare). The kun suffix on "Domo-kun", the name used to describe the character in the Japanese versions, is a Japanese honorific often used with young males.

Development
Tsuneo Gōda, a stop motion animator and character designer, created Domo for NHK in 1998 and directed a stop motion animated TV series based on the character in 2008. Gōda says that by using stop motion one can "create a work filled with feeling".

Characters
Domo, the main character, is a brown, furry monster with a large, sawtoothed mouth that is locked wide open. His favorite food is nikujaga, a Japanese meat and potato stew. According to a Tokyopop press release of the Domo comic book, Domo "communicates sotto voce with a verve that only his friends can understand." Clint Bickham, the writer of the Domo comic book, said that to him Domo's expression is "a sort of cheery wonderment. Like when a kid wakes to a room full of presents on Christmas day." While Domo's face has variants, to Bickham most of his expressions have "an underlying sense of fascination." Domo is known to pass gas repeatedly when nervous or upset. He also sweats when nervous.

Domo lives in a cave with Mr. Usaji, known in Japanese-language versions as Usajii (うさじい), a portmanteau of the words usagi (うさぎ), (rabbit), and jii (じい) (old man, grandpa). Mr. Usaji is a wise old rabbit who has lived in a cave for decades, loves to watch television and drink astringent green tea. Mr. Usaji is not into any "new" materials, and does not own a telephone. In terms of fashion, Mr. Usaji focuses on materials instead of shapes. Mr. Usaji's favorite food is carrots, and his least favorite food is "something that is meaningless."

Also in the cave live two bats, a mother named Maya (Shinobu (しのぶ) in the Japanese version) and her child Mario (Morio (もりお) in the Japanese version). Maya suffers from alcoholism; her favorite foods are seasonal while her least favorite food is alcohol. Mario's favorite food is Japanese-style tomato spaghetti, while his least favorite food is shiitake mushrooms.

The other main character in the shorts is a weasel girl named Tashanna (Tā-chan (たーちゃん) in the Japanese version). Tashanna, 17 years old, is a weasel who aspires to be a fashion stylist or model in Tokyo and is always using technology (televisions, mobile phones, and cameras). In English Tashanna has a "weaselly accent" (いたちなまり) (bear in mind weasels in Japan are not associated with underhandedness) and ends her sentences with "y"s. In the Japanese version, she ends her sentences with "chi" (ち). She has not had a boyfriend in ten years and she is seeking a platonic boyfriend. She has a passion for bidding in auctions, but she gives up by the end. Tashanna's favorite food is apricot and mint tarts, and her least favorite food is sea urchin. The Japanese name originates from the word "multichannel" (多チャンネル) of digital broadcasting.

Bear Boy (Kogumagorō (こぐまゴロー)), also known as A Little Bear (くまのこ), is a Moon Bear and one of Domo's friends from the neighborhood; the timid cub enjoys playing baseball.

Hee (Flower One (花一)) and Haw (Flower Two (花二)) are pixie twins from a flower. Domo is the only individual who can see them.

The Fox Trio consists of Esther (Esuko (エスコ)), Brother Fox (あにきち), and Fox Boy (Konjirō (コンジロー)). Esther, the youngest member, enjoys producing crocodile tears, plotting schemes, and causing havoc. Brother Fox, the eldest member, dutifully cares for his youngest siblings and feels upset when referred to as "short-legged" (短足). Fox Boy, having a quiet demeanor, converses with Domo and Bear Boy and prefers to read.

Hungry Bear (はらぺこぐま), a large and powerful bear, feels too hungry to take advantage of his strength.

The Ghost (Hyūtarou (ヒュ～たろう)) randomly appears and disappears.

In other media

 * A stop-motion children's television series based on the character, titled Domo TV, was co-produced by Nickelodeon and NHK. It was first announced in 2006 and premiered in October 2008 on Nicktoons Network. It continued to air until February 2009. Later that year, Nickelodeon also aired a series of 7-Eleven advertisements featuring Domo. Domo TV was released to DVD on July 1, 2009, along with every Domo commercial that had been produced to that date.
 * Tokyopop published an original English-language manga based on the character titled Domo: The Manga in the United States and Canada. Clint Bickham created the stories and crafted the dialog; Bickham said that he did "pretty much everything short of drawing it." The stories were drawn by Priscilla Hamby (aka Rem), Lindsay Cibos, Jared Hodges, Sonia Leong, Maximo V. Lorenzo (in the special 7-11 edition only) and Erie Horita.  Bickham decided to use a series of short stories instead of one long story to "recreate the feel of the original series," "so hopefully, reading a story from the manga will feel the same as watching an episode of the show." Bickham said that writing the stories became entertaining when he "got into the Domo mindset." The writer said that Domo's thoughts do not need to be expressed in words as they are "always very simple and innocent." Bickham added that sometimes other characters speak for him. Bickham said that the Domo: the Manga stories "are driven by situations instead of dialogue." To prepare for writing the series, Bickham watched each episode multiple times; Bickham intended to "get a feel for the characters so that the jump from stop-motion to manga would be as seamless as possible." He added that "more than anything, I had to have fun doing it. I don't think you can create a good Domo story without fun."
 * On February 5, 2014, Domo celebrated its 15th anniversary with Domo Hollywood e Iku! (Domo Goes to Hollywood!), a television special which was premiered on March 28, 2014.
 * In September 2015, the first music compilation based on Domo, Domo Loves Chiptune, was released on iTunes, Amazon, and all major music streaming services. The compilation features top artists in the Chiptune genre such Anamanaguchi and Disasterpeace. A Domo Loves Christmas compilation was released in November 2015.
 * Domo became well known outside Japan through a mock public service announcement that circulated on the Internet depicting Domos chasing a kitten with the words stating: "Every time you masturbate... God kills a kitten." An article from ICv2 stated: "This phony PSA is quite out of character with Domo's image in Japan."
 * Domo has 5 video games on the DSiWare on the Nintendo DSi Shop application for the Nintendo DSi. The 5 games are Crash-Course Domo, Hard-Hat Domo, Rock-n-Roll Domo, Pro-Putt Domo and White-Water Domo. The Game Boy Advance game Domo-kun no Fushigi Terebi also features Domo-kun. On Facebook, Domo is featured in the social game Planet Domo.

title: Domo (NHK)


text:
Phil de Glanville

Philip Ranulph de Glanville (born 1 October 1968 in Loughborough) is a former English rugby union player who played at centre for Bath and England.

Rugby career
de Glanville played for Durham University while an Economics and Politics student, then at Oxford University won a Blue with Oxford University RFC and also represented England U21s and England Students.

de Glanville joined Bath in 1989 and captained them to a league and cup double in 1996, partnering Jeremy Guscott in the centre for this club that season, as well as many others. He played 201 times for Bath over a 12-year career, scoring 53 tries. He started for Bath in the victorious 1998 Heineken Cup Final as they defeated Brive.

He made his England debut as a replacement in the match against the Springboks in 1992. Many of de Glanville's international caps were earned in a replacement role, as the incumbent centres were Will Carling (long-serving England captain) and Jeremy Guscott. De Glanville is seen as likely to have won many more caps if it weren't for this firmly entrenched Carling-Guscott combination, a pairing solidified by early Carling-Guscott successes like the 1991 Rugby World Cup.

In the Autumn of 1996 coach Jack Rowell appointed him as England captain following Will Carling's decision to step-down, following England's 1996 Five Nations Championship win. However, there was criticism of his inclusion in the starting XV for the 1997 Five Nations as it wasn't felt that he was in good enough form to be guaranteed a place in the team. He was not selected for that summer's Lions tour to South Africa losing his place to uncapped Will Greenwood. Under new coach Clive Woodward in autumn 1997 he lost both the captaincy to Lawrence Dallaglio and his starting position to Greenwood, though he remained a valued squad member. He showed some very good form in the 1999 world cup, particularly in the pool game against New Zealand. In total he won 38 caps for England and started in the centre throughout the 1994/1995 season, including an outstanding performance in the first tour to South Africa after apartheid, where he played in both test matches. He was involved in over 60 England match day squads

After rugby
Chiding his renowned good-looks, teammates often referred to de Glanville as "Hollywood"; a trait seemingly incongruous with his hard, committed playing style.

In 2003 he competed in the BBC's Superstars television show, winning the kayaking and golf events but eventually coming last in the final. He was a regional member of Sport England and from 2012 to 2015 was the Director of Elite Sport at Hartpury College. He went into executive search with Hanover Fox UK in 2015 and is one of the three current owners of the business having bought it in 2019.

De Glanville lives in Bath, UK.

He is the father of rugby player Tom de Glanville.

title: Phil de Glanville


text:
La Marche

La Marche may refer to:

 * La Marche (cave), an archaeological cave site in Vienne, France
 * La Marche, Nièvre, France
 * La Marche, Cavaellon, Haiti, a village in the Cavaellon commune of Haiti
 * March (territory), or La Marche in French
 * County of La Marche, a medieval French county
 * La Marche (film), a 2013 French film

title: La Marche


text:
Marian Chace

Marian Chace (31 October 1896 – 19 July 1970) is one of the founders of modern dance therapy.

Marian Chace was born 31 October 1896 in Providence, Rhode Island, the daughter of Daniel Champlin Chace, a journalist and editor, and Harriet Edgaretta (Northrop) Chace. Her younger siblings were Marjorie (1899–1991), Olive (1905–1977), and Edgar Northrop Chace (1908–1983).

She studied modern dance and choreography with Ted Shawn and Ruth St. Denis at the Denishawn School of Dance and started work as a dance performer. She later moved to Washington, D.C., and opened her own studio. As she developed her teaching she believed that the body and mind are interrelated, and was influenced by the work of Harry Stack Sullivan.

She began to teach in Washington D.C. and Wondered why people who were not wanting to be performers continued to take dance classes. She began to change her teaching methods as she observed her students closely. Her students reported feelings of well being which intrigued local doctors, some of the National Institutes of Health, who began to send some of their patients to her classes. Her approach developed into the use of body action, symbolism, therapeutic movement relationship, and rhythmic group activity when she eventually joined the staff at St. Elizabeths hospital in southeast Washington D.C. and studied at the Washington School of Psychiatry. Chace taught in schools and hospitals advocating and lecturing on the therapeutic benefits of dance/body movement.

She worked for number of years with patients at Chestnut Lodge in Rockville Maryland. She taught a course at Turtle Bay Music school in New York City for a number of years. With others in the field she enabled the founding of the American Dance Therapy Association in 1966 and became its first president.

title: Marian Chace


text:
Category:Norwegian monarchs

See List of Norwegian monarchs for a chronological list.

title: Category:Norwegian monarchs


text:
Talk:Dance therapy

Wiki Education Foundation-supported course assignment
This article was the subject of a Wiki Education Foundation-supported course assignment, between 27 August 2018 and 19 December 2018. Further details are available on the course page. Student editor(s): Gjose3.

Above undated message substituted from Template:Dashboard.wikiedu.org assignment by PrimeBOT (talk) 19:01, 16 January 2022 (UTC)

Correction
The sentence, "In contrast to artistic dance, which is usually concerned with the aesthetic appearance of movement, dance therapy explores the nature all movement." does not sound correct to me. I think it should be, "dance therapy explores the nature of all movement."--71.194.247.36 (talk) 20:12, 23 January 2008 (UTC)

 * before claiming that something is incorrect I suggest you to do some research first. Google is your friend. Mikkalai 16:50, 30 May 2004 (UTC)

 * "dance/movement therapy": titles with slashes are generally not allowed in wikipedia. You may want dance and movement therapy or a separate movement therapy instead. Mikkalai 16:52, 30 May 2004 (UTC)

 * my wiki convention may be wrong but my information is correct, not from Google but 8 years of dance study with a MA and current phd research to back it up. go to the library and find yourself some good dance books

 * choreotherapy does not exist, all the web entries you see are from wiki, choreotherapy would be choreographic therapy, go top the library and you will find it is dance therapy

 * Ohka- 17:28, 30 May 2004 (UTC)

 * The word was in google BEFORE any articles in wikipedia. Unfortunately wikipedia and its mirrors litter the web heavily with their content, so it is difficult indeed to find other references, especially on rare subjects. Mikkalai 18:01, 30 May 2004 (UTC)

Linkspam
I deleted most of the external links on this page because Wikipedia is neither a repository of links nor a directory. Links designed to call attention to a provider of dance therapy are not appropriate even if the page also contains information about dance therapy.--FreeKresge 04:21, 6 February 2007 (UTC)

Integrated/mixed ability dance
See my quesiton here

Matt (talk) 00:45, 11 March 2008 (UTC)

Hello, I'm doing a project for my psychology program consisting of contributing to a relative wiki page. I would like to be able to provide a few sentences to the Dance Therapy page. My contributions would be posted after thorough research on the subject, all edits will be factual. Would it be possible to add a sentence on developmental movement therapy identifying with dance therapy? I'm also new to editing wikipedia and would appreciate any suggestions or guidance. Thank you! — Preceding unsigned comment added by Rachellondon (talk • contribs) 01:58, 4 November 2011 (UTC)

Ya you can add a new section, just remember to provide a few references, just paste the citations into these brackets at the end and it will make a reference. Meatsgains (talk) 02:08, 4 November 2011 (UTC)

Why is the second wave referred to as the first wave?
How can the introduction of the idea of DMT to the US by Marian Chace represent "inspiring the first wave of DMT" when the development and use of dance therapy in the UK in the 19th century must, surely, be the first wave (according to this same Wikipedia entry)? Clearly, the first wave was "dance being used as a form of therapy... as far back as the 19th century in the UK". Marian Chace's introduction of DMT to the US can surely only be considered to have "inspired" the SECOND wave!

This article states "The development of DMT can be split into two waves throughout history", then makes a mockery of that claim by then stating that the development and use of dance therapy first occurred in the UK in the 19th century, implying that this wasn't one of the stages or "waves" of its development. Mmm. 86.157.141.30 (talk) 13:31, 20 December 2012 (UTC)

Editing Dance Therapy Page
I'm editing this article as part of my History & Systems of Psychology course at Shenandoah University, in conjunction with the APS Wikipedia Initiative. Any suggestions or comments are welcome. Thanks! 3faith.hope.love (talk) 20:05, 14 February 2013 (UTC)

Bibliography- all resources below have been deemed secondary sources by my Professor for this project.

 * [21] Payne, Helen. "Dance Movement Therapy: Theory and Practice". Taylor & Francis. Retrieved 11 February 2013

 * A Systematic Review of the Evidence for the Effectiveness of Dance Therapy|journal=ALTERNATIVE THERAPIES|year=2011|month=May/june|volume=17|pages=50-59|url=http://www.achancetodancelj.org/A_Systematic_Review_of_the_Evidence_for_the_Effectiveness_of_Dance_Therapy.pdf|accessdate=21 February 2013}}

Despite literature on Dance Therapy dating back to the 1940s, there remains no scientific evidence for the therapeutic efficacy of DMT. This section needs to be deleted or updated because there is scientific evidence for efficiency. — Preceding unsigned comment added by 3faith.hope.love (talk • contribs) 14:08, 8 March 2013 (UTC)

Delete or update this information
Despite literature on Dance Therapy dating back to the 1940s, there remains no scientific evidence for the therapeutic efficacy of DMT.

This section needs to be deleted or updated because there is scientific evidence for efficiency and there is now a whole section on effectiveness. — Preceding unsigned comment added by 3faith.hope.love (talk • contribs) 14:14, 8 March 2013 (UTC)

Clemson Student Editor
Hi all! My name is Meredith Harper, and I am a senior Psychology major from Clemson University. I will be editing this article as part of an assignment for my senior Psychology lab. I would appreciate any input, corrections, or advice that you all would be willing to give! — Preceding unsigned comment added by Harper5 (talk • contribs) 00:54, 4 April 2013 (UTC)

So, I've added some things to this article. I added an entire section on the use of DT for anxiety, depression, and severe stress. From the research I found, that seems to be what it is most commonly used to treat. I also added a paragraph or two to the Education and Principles section. Lastly, I added the last two sentences to the Effectiveness section. Just wanted to make you all aware of the changes I've made! I appreciate any constructive criticism you may offer. — Preceding unsigned comment added by Harper5 (talk • contribs) 14:30, 23 April 2013 (UTC)

Hello Meredith I would also be willing to put some work into this. I am a Somatic Movement Therapist and work alongside various people who are DMPs (I’m in the UK), so I am quite up to date with current practice, at least in the UK. SebastianBechinger (talk) 00:52, 3 January 2018 (UTC)

Movement Therapy is not the same as Dance Movement Therapy
Movement therapy shouldn't redirect here. "Dance/Movement Therapy" as it is being called here is a branch of movement therapy, and not the otherway around. To refer movement therapy here is to imply all movement therapy comes from dance, ignoring the wide range of methodologies evolved from yoga therapy, tai chi, feldenkrais, somatic and physical therapy techniques et cetera. It's like having the word 'bird' take you the page about bluejays. This page is giving an overly narrow definition to movement therapy which should either be a different page, or "DMT" should be a subheader for the parent topic of movement therapy.Iṣṭa Devatā (talk) 16:11, 17 August 2015 (UTC)

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History
About the removal by an anonymous of my adition to History, I find the source correct, one might add Penny Lewis Bernstein's:A mythologic quest, American Journal of Dance Therapy September 1980, Volume 3, Issue 2, pp 44–55.--Neworsy (talk) 20:07, 4 November 2017 (UTC)

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History More Inclusive?!
The history section of this page could do with some serious work. Citing Marion Chase and Mary Stark-Whitehouse is a good start but development of DMP/DMT as a field has had a complex and pluralistic history and I think it would be good to have at least reference to some of the major influences including Somatics, psychoanalytically based Art Therapy etc. Also perhaps to mention that the field did not start with some consensus about what DMT is and what it includes - to this day there is debate about whether, for example, developmental movement therapy belongs to an aspect of DMT or not.

Additionally, since almost every DMT that I know works pretty heavily with Laban Movement Analysis in some way, I think the influence of Irmgard Bartinieff (one of Laban’s students) and Judith Kestenberg (one of Bartinieff’s students) needs some more reference. SebastianBechinger (talk) 00:45, 3 January 2018 (UTC)

Wiki Education assignment: SSC199 Hon
— Assignment last updated by Ctysick (talk) 13:25, 6 December 2022 (UTC)

Wiki Education assignment: ENGW3307 Adv Writing for the Sciences 11520
— Assignment last updated by Vennan (talk) 18:04, 8 November 2023 (UTC)

Therapist Qualifications
Seeing as the European Association of Dance Movement Therapy and the Association for Dance Movement Psychotherapy, United Kingdom are included in the Organizations sections, I would like to add the therapist qualifications for these organizations. Vennan (talk) 18:12, 17 November 2023 (UTC)

Efficacy
I would like to add evidence on the efficacy of Dance Therapy as a treatment for anxiety disorders. There is only one sentence on efficacy, claiming that there is not enough evidence on the efficacy of Dance Therapy for those with dementia. Vennan (talk) 18:14, 17 November 2023 (UTC)

title: Talk:Dance therapy


text: Category:Norway

title: Category:Norway


text:
Talk:Jim Coplien

Untitled
I attended Coplien's lecture for his Vloeberghs Leerstoel at the Vrije Universiteit Brussel. To the unknown contributer who added the fact: did you?

Agile, a pattern language?
I am analyzing Agile software development and came to conclussion that it is an organisational pattern language. It came to me because I heard Coplien's lecture in Belgrade back in 2004. He was also talking about difference in nature between patterns and methodologys. Now I understand it.

I have difficulties convicing people that XP, or Agile isn't methodology but pattern lenguages. Am I right? You can see the discussion here on wikipedia. Littlesal 16:15, 20 November 2006 (UTC)

Of course it's a pattern language
Some of Scrum and most of the structural components of XP came out of organizational patterns research at Bell Laboratories. See the Wikipedia page: Organizational patterns

Beedle, Devos, Schwaber, Sutherland and others recognized early on that Scrum was a pattern language, and they published some supplementary patterns to the Organizational Patterns of Agile Software Development book, which Beedle recognizes as the standing comprehensive representation of what Agile development is. (You can find citations in the Organizational Patterns Wikipedia article.)

The Scrum community has been going forward with this notion of Organizational patterns. See http://www.scrumorgpatterns.com as an example. Jcoplien (talk) 10:39, 19 January 2009 (UTC)

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Nationality
Jim Coplien writes in the foreword to the book Clean Code by Robert C. Martin: "One of our favorite candies here in Denmark is Ga-Jol, whose strong licorice vapors are a perfect complement to our damp and often chilly weather. Part of the charm of Ga-Jol to us Danes is the wise or witty sayings printed on the ﬂap of every box top.". The category on this article says British computer scientists. Since he write himself that he is Dane, that must be true, but is he also British or is the category on the article wrong? Kinamand (talk) 12:07, 3 July 2019 (UTC)

title: Talk:Jim Coplien


text:
Campo Grande

Campo Grande (, lit. '"Great Field"') is the capital and largest city of the Brazilian state of Mato Grosso do Sul in the Center-West region of the country. The city is nicknamed Cidade Morena ("Swarthy City" in Portuguese) because of the reddish-brown colour of the region's soil. It has a population of 898,100, according to a 2022 IBGE census.

The region where the city is located was in the past a waypoint for travellers who wanted to go from São Paulo or Minas Gerais to northern Mato Grosso by land. In the early 1900s, a railway was completed, connecting Campo Grande to Corumbá on the Bolivian border and to Bauru, São Paulo. Also in the beginning of the 20th century, the Western Brazilian Army Headquarters was established in Campo Grande, making it an important military center.

With a population growth from 140,000 people in 1970 to 750,000 people in 2008, Campo Grande is the third largest urban center of the Center-West region, and the 17rd largest city in the country. In 1977, the State of Mato Grosso was split into two, and Campo Grande became the capital of the new state of Mato Grosso do Sul, comprising the southern portion of the former state. By that time, Campo Grande had long surpassed the latter's capital city of Cuiabá in population, which is unusual in Brazil, where most capitals are also the states' largest cities.

Today, the city has its own culture, which is a mixture of several ethnic groups, most notably immigrants from the Japanese prefecture of Okinawa, Middle Easterners, Armenians, Portuguese people, Germans, Italians, Spaniards, and Paraguayans, finally mixed with Asian and European Brazilians from the Brazilian Southern and Southeast regions, its native Amerindian peoples and Afro-Brazilians.

History
Campo Grande started as a small village founded in 1877 by farmers José Antônio Pereira and Manoel Vieira de Sousa (a.k.a. Manoel Olivério), who came from Minas Gerais just after the end of the Paraguayan War. They founded the village, known at that time as Santo Antônio de Campo Grande, near the Serra de Maracaju cliffs, at the confluence of two streams named Prosa and Segredo (Portuguese for "conversation" and "secret," respectively), whose courses now coincide with two of the city's most important avenues. In the end of 1877, the founder built the village's first church. The roughly aligned houses formed the first street, known as Rua Velha (Old Street), today Rua 26 de Agosto (26 August Street). This street ended where today one finds a square in honor of the immigrants that later came to the city.

The city started to develop relatively fast because of its privileged climate and location. These factors drew people from other regions of the country, especially the South, the Southeast and the Northeast regions. The settlement was officially recognized as a municipality by the State Government on August 26, 1899, and renamed Campo Grande.

Vegetation
The vegetation in Campo Grande and Central Brazil is a tropical savanna called "Cerrado" that varies from pure grassland to a nearly closed canopy of medium height trees overlying grass. Since forest is the expected climax vegetation there, several theories have been given to explain the types of grassland present.

The most promising of these involve differences in soil properties, but only a few sites have been used for evaluation. The 1960s marked the beginning of the expansion of large-scale agriculture across the Cerrado. The state is one of the largest producers of soybeans in the world.

The municipality contains the 178 ha Matas do Segredo State Park, created in 2000 to protect an area of cerrado forest. and the 135 ha Prosa State Park, created in 2002.

Climate
Campo Grande has a tropical savanna climate (Köppen: Aw), just slightly drier than a tropical monsoon climate, with a mild appearance of cold air masses on the southern edge of the tropics. It has semi-humid, hot summers, and notably seasonal, with a dry winter season from June through September, but without major irregularities in the precipitation. Its altitude a few hundred meters higher than in the surrounding swamps and its location in the interior of South America, gives a much more extreme climate than several Brazilian cities, although still moderate. In addition, the flood is one of the problems seen in the city, the result of intense rains that occur in a short period. Annual rainfall averages 1465 mm. January is the warmest and rainiest month, with mean highs of 29 °C (84.2 °F) and lows of 20 °C (68.0 °F).

July brings on sunny days but cooler temperatures, with mean highs of 25 °C (77.0 °F) and lows of 14 °C (57.2 °F). Occasional near-freezing temperatures can occur on winter's coldest nights.

Economy
Most of the city's active economic labor is absorbed by the tertiary sector (commerce and services). In spite of that, the primary and secondary sectors, especially agribusiness, still play an important role in the local economy. The farming of bovine livestock supplies local slaughterhouses, which in turn allows Campo Grande to export meat to other states in Brazil and abroad. In addition to food processing and agribusiness, construction and non-metallic mineral processing are important. The area's most important crops are soy, rice and manioc. Recently, sugar cane is becoming important as well. According to IBGE, Campo Grande has a total of 11,657 commercial and 1,300 industrial enterprises.

The city's GDP was R$ 20,7 billion (about US$ 9,59 billions) in 2013, ranks as the richest city in the state, the third in the Central-West region of the country, and the 33rd richest in Brazil (2013).

Per capita income was R$24.839 in 2013 (about US$11,511).

Education
Portuguese is the official national language, and thus the primary language taught in schools. But English and Spanish are part of the official high school curriculum.

Educational institutions
The city has several universities. The most notable ones are:
 * Universidade Federal de Mato Grosso do Sul (UFMS) (Federal University of Mato Grosso do Sul);
 * Universidade Estadual de Mato Grosso do Sul (UEMS) (State University of Mato Grosso do Sul);
 * Universidade Católica Dom Bosco (UCDB) (Dom Bosco Catholic University);
 * Faculdade Campo Grande (FCG) (Campo Grande College);
 * Centro Universitário de Campo Grande (UNAES) (Academic Center of Campo Grande).
 * Universidade para Desenvolvimento do Estado e da Regiao do Pantanal (UNIDERP) (Academic Center of Campo Grande).

International Airport
The operation of Campo Grande International Airport is shared with Campo Grande Air Force Base. The airport has two runways. The airport can receive medium-sized jets such as the Boeing 737 and the Airbus A320, but occasional operations of larger jets have occurred. Operations are mostly domestic, but there are also a few flights to Bolivia and Paraguay.

Campo Grande Air Force Base - ALA5, one of their most important bases of the Brazilian Air Force, is located in Campo Grande.

Railroad
Campo Grande is served by a system of railway transport under administration of the Novoeste company, interconnecting with other cities in the state, in a line that goes from Bauru and São Paulo state through Campo Grande all the way to Corumbá and on to Bolivia. This mode of transport has had significant effects on the transport infrastructure, allowing the export of products to other centres of production and consumption. Currently, no passenger services are operated, only freight trains.

Highways
Three main federal highways intersect at Campo Grande. BR-262 links Campo Grande to Corumbá and Bolivia to the west, and the Brazilian State of São Paulo to the east. BR-163 connects Campo Grande to Cuiabá and the Amazon region to the north, and to Dourados (which is 120 km from the Paraguayan border) to the south. BR-060 links Campo Grande to the state of Goiás and the national capital city of Brasília to the northeast. There are also several state highways converging there.

Culture
Festas Juninas were introduced to Northeastern Brazil by the Portuguese and the custom spread to the rest of the country, including Campo-Grande, where festivities take place with the usual fare of typical foods and decoration, rural costumes, music, dancing, a bonfire, and fireworks.

The Campo Grande Film Festival is held annually in the months of January and February since 2004. It focuses on independent cinema, presenting Brazilian and foreign films alike, as well as regional and short films.

Car racing
The city has a car racing and a kart racing track. Orlando Moura International Autodrome has a 3,433-metre (11,263 ft.) runway, and Kartódromo Ayrton Senna a 930-metre (3,051 ft.) runway.

Football
As in all of Brazil, the most popular sport in Campo Grande is football. The city has a major football stadium, Estádio Universitário Pedro Pedrossian, popularly known as "Morenão" ("the big brown" in Portuguese, after the city's nickname and the Brazilian custom of often giving names derived of augmentatives to football stadiums). The stadium was opened in 1971 and accommodates up to 45,000 people. There are five other minor stadiums in the city, which occasionally host competition games. The city's main teams are Esporte Clube Comercial and Operário Futebol Clube.

Additionally, there are 45 multisport playing fields in the city, in clubs, cultural associations and public squares.

Volta das Nações
"Volta das nações" is a mini-marathon of 21 km that takes place at Parque das Nações Indígenas every October, where around 26.4 thousand people participate, including professional athletes from Kenya and other parts of the world.

Consular representation
Paraguay has a Consulate in Campo Grande.

Notable people

 * Rafael Silva, judoka
 * Leonardo de Deus, swimmer
 * Müller, footballer
 * Hoover Orsi (born 1978), racing driver

Twin towns – Sister cities
Campo Grande is twinned with:

 * Pedro Juan Caballero, Amambay Department, Paraguay
 * 🇮🇹 Turin, Piedmont, Italy

title: Campo Grande


text:
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Polyform

In recreational mathematics, a polyform is a plane figure or solid compound constructed by joining together identical basic polygons. The basic polygon is often (but not necessarily) a convex plane-filling polygon, such as a square or a triangle. More specific names have been given to polyforms resulting from specific basic polygons, as detailed in the table below. For example, a square basic polygon results in the well-known polyominoes.

Construction rules
The rules for joining the polygons together may vary, and must therefore be stated for each distinct type of polyform. Generally, however, the following rules apply:
 * 1) Two basic polygons may be joined only along a common edge, and must share the entirety of that edge.
 * 2) No two basic polygons may overlap.
 * 3) A polyform must be connected (that is, all one piece; see connected graph, connected space). Configurations of disconnected basic polygons do not qualify as polyforms.
 * 4) The mirror image of an asymmetric polyform is not considered a distinct polyform (polyforms are "double sided").

Generalizations
Polyforms can also be considered in higher dimensions. In 3-dimensional space, basic polyhedra can be joined along congruent faces. Joining cubes in this way produces the polycubes, and joining tetrahedrons in this way produces the polytetrahedrons. 2-dimensional polyforms can also be folded out of the plane along their edges, in similar fashion to a net; in the case of polyominoes, this results in polyominoids.

One can allow more than one basic polygon. The possibilities are so numerous that the exercise seems pointless, unless extra requirements are brought in. For example, the Penrose tiles define extra rules for joining edges, resulting in interesting polyforms with a kind of pentagonal symmetry.

When the base form is a polygon that tiles the plane, rule 1 may be broken. For instance, squares may be joined orthogonally at vertices, as well as at edges, to form hinged/pseudo-polyominos, also known as polyplets or polykings.

Types and applications
Polyforms are a rich source of problems, puzzles and games. The basic combinatorial problem is counting the number of different polyforms, given the basic polygon and the construction rules, as a function of n, the number of basic polygons in the polyform.

title: Polyform


text: Category:Science fiction films

title: Category:Science fiction films


text: Category:The Beatles

title: Category:The Beatles