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R-12 Dvina

The R-12 Dvina was a theatre ballistic missile developed and deployed by the Soviet Union during the Cold War. Its GRAU designation was 8K63 (8K63U or 8K63У in Cyrillic for silo-launched version), and it was given the NATO reporting name of SS-4 Sandal. The R-12 rocket provided the Soviet Union with the capability to attack targets at medium ranges with a megaton-class thermonuclear warhead and constituted the bulk of the Soviet offensive missile threat to Western Europe. Deployments of the R-12 missile in Cuba caused the Cuban Missile Crisis in 1962. A total of 2335 missiles were produced; all were destroyed in 1993 under the START II treaty.

As well as the single-stage ballistic technology, the R-12 Dvina had a two-stage capability that allowed payloads to be placed into low Earth orbit.

The Iranian Shahab-4 missile is likely an offshoot of the R-12 Dvina.

Beginning
OKB-586 formed from a spin-off of portions of Sergei Korolev's OKB-1 production infrastructure under the direction of Mikhail Yangel in the early 1950s. Soon after, he started the development of an improved strategic missile that would outperform the R-5, that Korolev was in the process of bringing into production. Yangel's design was based on combining the basic airframe from the R-5 with an engine developed from the R-11 Zemlya. The R-11 was a short-range missile that used nitric acid as an oxidizer and kerosene as a fuel and could be stored for extended periods of time.

Valentin Glushko had long advocated using storable propellants, and proposed developing a new engine for the project. Earlier designs like the R-5 and R-7 used liquid oxygen as the oxidizer, and therefore had to be fueled immediately before launch, as the oxygen would "boil off" over time. He developed the RD-214 for the R-12, which consisted of four combustion chambers sharing a common turbopump assembly. The pumps were powered by decomposing hydrogen peroxide, like earlier designs, to generate an exhaust. The new engine was too large to fit in the existing R-5 airframe, so a conical tail section was added to hold the engine.

Nikolay Pilyugin, head of the leading control system bureau, convinced Yangel to introduce a fully autonomous control system in the R-12 instead of the traditional radio control that had been used on earlier missiles. The R-5, for instance, used an inertial guidance system that had to be "fine tuned" by commands from ground radio stations that it passed over during its flight. Pilyugin felt that newer inertial systems would have the accuracy needed to hit targets at 2,000 km without the mid-course updates.

According to the official NPO Yuzhnoye history, Yangel's design was approved on 13 February 1953 by the Council of Ministers of the USSR. However, another source reports that the approval was granted on 13 August 1955. The first test was conducted at Kapustin Yar on 22 June 1957. In September 1958, Nikita Khrushchev personally visited Kapustin Yar to witness the launch of R-12, as well as its competitor, the R-5M. The latter had already been accepted into deployment at the time. The R-12 launch was a success and the next month, mass production of the vehicle started in Dnepropetrovsk. Test launches continued until December and demonstrated a maximum error of 2.3 km.

For the work on R-12, on 1 July 1959, OKB-586 received the Order of Lenin, while the Hero of Socialist Labor (the highest industrial award) was awarded to Yangel, Smirnov and Budnik.

Deployment
The R-12 missile was introduced into the inventory on 4 March 1959 according to Russian sources, though Western intelligence believed that an initial operational capability was reached in late 1958.

The first public display of this system was in November 1960, and they were deployed to Cuba in October 1962 during the Cuban Missile Crisis. The first five regiments with surface-based R-12 missiles were put on alert in May 1960, while the first regiment of silo-based missiles was placed on alert in January 1963. Their reaction time was assessed by the West at one to three hours in the normal soft-site readiness condition, and five to fifteen minutes in the normal hard-site readiness condition. The allowable hold time in a highly alert condition (reaction time equals three to five minutes) was long—many hours for soft sites, and days for hard sites.

The R-12 and R-12U missiles reached their maximum operational launcher inventory of 608 in 1964–66. Some soft-site phase-out began in 1968, with some hard-site phase-out beginning in 1972. In 1978 their phase out and replacement with mobile ground-launched RSD-10 Pioneer missiles began.

Further development

Efforts to create a railway based version of the R-12 missile were suspended, but work then started on a silo-launched version. An underground launch complex, code-named Mayak-2 (Beacon-2), was constructed in Kapustin Yar. In September 1959 the R-12 took off from the silo complex for the first time. In May 1960 the development of a new R-12 missile designated as R-12U was begun. The R-12U was designed to be used with both surface launchers and silos. The silo-launch complex of the R-12U missile comprised four launchers and was designated as "Dvina" (8П763 «Двина»; Dvina)". The testing phase of the missile and the launch complex lasted from December 1961 until December 1963.

The R-12 was also used during the development of the V-1000 anti-ballistic missile, serving as a target. During a series of tests two R-12s detonated their warheads in the upper atmosphere in order to test radar systems. A follow-on test planned to launch an R-12 from Kapustin Yar while two R-9s from Tyuratam would fly into the area, but only the R-12 launched successfully.

Elimination
The Intermediate-Range Nuclear Forces Treaty was signed in December 1987 and entered into force in June 1988. The fundamental purpose of the INF Treaty was to eliminate and ban US and Soviet ground-launched ballistic and cruise missiles, as well as associated support equipment, with ranges between 500 and 5500 kilometers. Elimination of R-12 and R-14 Chusovaya missiles and components took place at the Lesnaya Missile Elimination Facility. The last of the 149 Soviet R-12 missiles was eliminated at Lesnaya in May 1990.

Rockets with new booster
In 1961, an upper stage using LOX and UDMH propellants was added to the R-12 to create the Kosmos 63S1 booster. Since there were no surface pads for the R-12, all launches took place from the Mayak silo at Kapustin Yar. However, as silos were not designed for repeated use, this arrangement proved impractical and necessitated their refurbishment after every few launches. The first two launch attempts of the 63S1 took place in October and December 1961 and both failed. On March 16, 1962, Kosmos 1, a navigation test satellite, was successfully orbited, marking the first Soviet space launch to be performed with a booster other than the R-7. Finally, a dedicated launch complex was constructed at Kapustin Yar and first used in December 1964.

An enhanced R-12 booster was flown in 1965–67 from the Dvina silo at Kapustin Yar on suborbital tests, eventually giving way to the 11K63, a modernized, improved launch vehicle. In 1967, a second launch complex was opened at Plesetsk and from there on, 11K63 flights alternated between Kapustin Yar and Plesetsk, mostly for orbiting lightweight scientific and military payloads. A total of 123 were flown, of which eight failed to attain orbit. In 1977, the R-12 and 11K63 were retired from use.

Overview
The R-12 is a single-stage rocket with a separable single reentry vehicle. In the integrated fuel tanks the oxidizer was put forward of the fuel tank, separated by an intermediate plate. During flight this allowed the oxidizer from the lower unit to be spent first, improving in-flight stabilization. The propulsion system consists of four liquid propellant rocket motors with a common turbo pump unit. The flight control was carried out with the help of four carbon jet vanes, located in the nozzles of the rocket motors. The autonomous guidance and control system used center of mass normal and lateral stabilization devices, a velocity control system and a computer-assisted automatic range control system. The R-12 was deployed at both soft launch pads and hard silos.

The standard yield was 2.3 megatons. Conventional explosives or chemical weapons could have been used as well.

R-12 steps of readiness
Readiness nr. 4 (constant). The missile was in the hangar. The gyroscopes (control devices) and warhead were not installed, the missile was not fueled. The missile could stay so for seven years (factory-guaranteed service time). It would take 3 hours and 25 minutes to launch.

Readiness nr. 3 (elevated). The missile was in the hangar. The gyroscopes and warhead were installed. The missile could stay so for three years. It would take 2 hours and 20 minutes to launch.

Readiness nr. 2 (first step elevated). The missile was transported to the launch site, the gyroscopes were started, and initial data inserted. Propellant tankers stood next to the missile. The missile could stay so for three months. It would take 1 hour to launch.

Readiness nr. 1 (total). The missile was fueled and targeted, but the starting mixture gas was not loaded. The missile could stay so for one month. It would take 30 minutes to launch.

Operators

 * Strategic Rocket Forces − Scrapped
 * 58th Rocket Division
 * other rocket divisions
 * other rocket divisions

title: R-12 Dvina


text:
Battle of Cixi

The Battle of Cixi or Battle of Tzeki (慈溪之戰) was an armed engagement in the Taiping Rebellion fought between the Ever Victorious Army of the Qing dynasty and forces of the Taiping Heavenly Kingdom on September 21, 1862, at Cixi. The battle, which was won by the Ever Victorious Army, resulted in the mortal wounding of Frederick Townsend Ward, the American mercenary who founded and commanded the force. Ward's death after the battle led to the succession of Henry Andres Burgevine as commander of the Ever Victorious Army and initiated a period of decline for the force.

Background
When Shanghai was successively attacked by Taiping Rebels in 1862, foreign inhabitants favored removing the potential threat and cooperating with imperial forces; as a result, combined British and French naval troops under the command of Adm. James Hope were involved in military conflict with the Taiping Rebellion. One of the communities inhabited by the rebels was Ningbo, a port and walled city located south of Hangzhou Bay.

The imperial army laid siege to Ningbo's occupiers on 6 May. After a false flag attack on the British ships docked outside Ningbo, the western ships began bombarding the Taiping. They then sent their crews into the city, overpowering rebel forces and turning over Ningbo to the imperial army. With Ningbo secure, Ward's soldiers and the Qing forces began launching attacks in the surrounding areas against the rebels. During this time Cixi was one of the encircling cities ravaged by violence.

Battle
The Ever Victorious Army attacked Cixi on 21 September. As well as being trained in artillery and rifle usage, they were accompanied by the gunboats H.M.S. Hardy and Confucius. Ward led from the front and was hit in the stomach by a musket ball. However, he remained on the battlefield until victory was certain.

Aftermath
Ward died from his wound the day after the battle. The death of Ward started a period of decline for the Ever Victorious Army. Henry Andres Burgevine, another American mercenary and Ward's second-in-command, succeeded Ward as commander, despite initial objections from the British army officer Charles Staveley and the Huai Army commander Li Hongzhang. As commander, Burgevine allowed the soldiers under his command to become unruly, mismanaged the army's finances, and frequently quarreled with his superiors. The resulting disagreements between Burgevine, British officials, Li Hongzhang, and the army's sponsors led to his betrayal of the Qing Dynasty.

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

title: Battle of Cixi


text:
Deuce Bigalow: Male Gigolo

Deuce Bigalow: Male Gigolo is a 1999 American sex comedy film directed by Mike Mitchell (in his directorial debut) and written by Harris Goldberg and Rob Schneider. The film stars Schneider (in the title role), William Forsythe, Eddie Griffin, and Arija Bareikis, with supporting roles by Oded Fehr, Gail O'Grady, Richard Riehle, Jacqueline Obradors, Big Boy, Amy Poehler, and Dina Platias. The film tells the story of a hapless fishtank cleaner who goes into business as a male prostitute in an attempt to earn enough money to repair damage he caused while house-sitting. It was the first film produced by Adam Sandler's production company Happy Madison Productions.

Deuce Bigalow: Male Gigolo was released in the United States on December 10, 1999, by Buena Vista Pictures. While the film received generally negative reviews from critics, it was a box office success, grossing over $92 million worldwide against a $17 million budget.

A sequel, titled Deuce Bigalow: European Gigolo, was released in August 2005 by Sony Pictures Releasing.

Plot
Deuce Bigalow is a lonely and insecure aquarist living in Los Angeles. He meets a gigolo, Antoine, who asks Deuce to care for his sick lionfish and luxury beachfront apartment while he is away on business in Europe. Deuce accidentally sets Antoine's kitchen on fire and breaks his custom aquarium.

Fearing Antoine will kill him, Deuce is forced to find a way to pay $6,000 for the damage. After attempting gigolo work, Deuce is approached by a pimp, T.J., who offers to help him.

T.J. sets Deuce up on various dates: Fluisa, a mannish morbidly obese woman; narcoleptic Carol; Ruth, who has Tourette syndrome with coprolalia; and Tina, who is extremely tall. Each of Deuce's clients is satisfied by his attention and support, and he does not have sex with any of them. However, Deuce becomes enamored with Kate, who has a prosthetic leg. Deuce introduces Kate to his dad Bob who is a bathroom attendant. Initially embarrassed, Kate reassures Deuce and the pair fall in love. However, when she learns that Deuce is a gigolo, she breaks up with him.

Meanwhile, Deuce is stalked by police detective Chuck Fowler, who demands Antoine's black book of clients and threatens to arrest Deuce if he does not comply. Deuce learns Fowler's wife was one of Antoine's clients; he helps Fowler excite his wife when they perform an erotic dance for her. However, Deuce is still arrested for prostitution when he refuses to betray T.J.

In court, Deuce's clients testify and reveal that he never had sex with any of them, but rather he made them feel good about themselves. Deuce only had sex with Kate, and because he returned the money he was given to sleep with her, is cleared of all charges. Deuce and Kate reconcile.

Learning that Antoine is returning home, Deuce and his friends work quickly to restore the damaged apartment; he is warned that the custom aquarium glass may not be installed properly. Kate's blind roommate Bergita accidentally kills the lionfish, so Deuce buys a replacement and returns to Antoine's just as he arrives. Antoine taps on the glass and it shatters. Deuce reveals his gigolo venture to the furious Antoine, who tries to kill Deuce using a medieval crossbow. Fluisa saves Deuce when the bolt hits a roast chicken she had hidden in her bra. Antoine is arrested by Fowler.

The postscript at a beach-side reception reveals the fates of the characters: Bob became a gigolo and earns $7.00. Ruth opened up an all-girls school for those with Tourette's. Carol fulfilled her dream trip to the Eiffel Tower, "she will be missed". Fluisa underwent liposuction and became a Victoria's Secret model named Naomi. Antoine and Tina had tall and hairy children. T.J. starred in a hit sitcom called "Hanging with Mr. Man-Pimp". Deuce and Kate married and formed an anti-sushi movement, living happily ever after.

Cast

 * Rob Schneider as Deuce Bigalow, an insecure fishtank cleaner turned gigolo.
 * William Forsythe as Detective Charles "Chuck" Fowler, an LAPD detective.
 * Eddie Griffin as Tiberius Jefferson "T.J." Hicks, a crazy low-rent pimp and Deuce's friend.
 * Arija Bareikis as Kate, a woman with a prosthetic leg, one of Deuce's clients and later his wife.
 * Oded Fehr as Antoine Laconte, a famous gigolo from Argentina and Chuck's nemesis.
 * Gail O'Grady as Claire, a woman who is Deuce's first client.
 * Richard Riehle as Robert "Bob" Bigalow, a restroom attendant who is Deuce's dad.
 * Jacqueline Obradors as Elaine Fowler, Chuck's wife.
 * Big Boy as Fluisa aka Jabba, an obese woman weighing close to 750 pounds and one of Deuce's clients.
 * Amy Poehler as Ruth, a woman who has Tourette syndrome with coprolalia and is one of Deuce's clients.
 * Dina Platias as Bergita, Kate's blind roommate.
 * Deborah Lemen as Carol, a woman with narcolepsy who is one of Deuce's clients and is seeking to go on a trip to France.
 * Torsten Voges as Tina, a woman that has a pituitary gland disorder and is extremely tall enough that her face isn't seen. She is also one of Deuce's clients.
 * Bree Turner as Allison
 * Andrew Shaifer as Neil, a fish tank repairman.
 * Allen Covert as Vic
 * Elle King as a girl scout who Deuce buys cookies from
 * Jackie Sandler as Sally
 * Pilar Schneider as Old Lady at Restaurant
 * Barry Cutler as Dr. Rosenblatt, a doctor who Kate works for
 * John Harrington Bland as Dr. Rosenblatt's Patient
 * Ron Soble as Judge Addison, a judge who presided over Deuce's trial
 * Robb Skyler as the district attorney who prosecuted Deuce
 * Norm Macdonald as the bartender who Deuce interacts with (uncredited). The postscript stated that Norm Macdonald only worked on this movie for one day.
 * Adam Sandler as the voice of Robert Justin (uncredited), an offscreen passerby who insults Tina.
 * Wes Takahashi as a sushi chef (uncredited)
 * Marlo Thomas as Margaret (uncredited)

Production
Deuce Bigalow: Male Gigolo was the first film released by the Happy Madison Productions film production company. Adam Sandler served as the film's executive producer. Sandler can be heard yelling the infamous "Freak!' line and other various lines in the background.

Soundtrack

 * 1) "Call Me" – Blondie
 * 2) "Spill the Wine" – Eric Burdon and War
 * 3) "You Sexy Thing" – Hot Chocolate
 * 4) "Get Down Tonight" – KC and the Sunshine Band
 * 5) "Let's Get It On" – Marvin Gaye
 * 6) "I'm Not in Love" – 10cc
 * 7) "Magnet and Steel" – Walter Egan
 * 8) "No Worries" - Hepcat
 * 9) "Can't Smile Without You" – Sean Beal
 * 10) "Lift Me Up" – Jeff Lynne
 * 11) "Call Me" – Emilia Maiello

Box office
Deuce Bigalow: Male Gigolo opened theatrically on December 10, 1999 in 2,154 venues and earned $12,224,016 in its opening weekend, ranking third in the North American box office behind Toy Story 2 fourth weekend and fellow newcomer The Green Mile. The film ended its run, having grossed $65,538,755 in the United States and Canada, and $27,400,000 overseas for a worldwide total of $92,938,755. Based on a $17 million budget, the film was a box office success.

Critical reception
Deuce Bigalow: Male Gigolo received negative reviews from critics. On Rotten Tomatoes, it has an approval rating of 22% based on 76 reviews, with an average rating of 4.01/10. The site's consensus states: "According to critics, Deuce Bigalow is just too dumb and filled with old, tired gags." On Metacritic it has a score of 30 out of 100 based on reviews from 26 critics, indicating "generally unfavorable reviews". Audiences surveyed by CinemaScore gave the film a grade B.

Roger Ebert of the Chicago Sun-Times gave the film one-and-a-half out of four stars, stating "It's the kind of picture those View n' Brew theaters were made for, as long as you don't View." Kendall Morgan from The Dallas Morning News writes in her review, "Deuce Bigalow: Male Gigolo makes There's Something About Mary look like Masterpiece Theatre."

Sequel
In 2005, a sequel, Deuce Bigalow: European Gigolo, was released by Sony Pictures Releasing.

title: Deuce Bigalow: Male Gigolo


text:
Maudlin of the Well

Maudlin of the Well (stylized as maudlin of the Well; commonly abbreviated as motW) is an avant-garde metal band from Boston, Massachusetts. Their music contains elements from many different genres including jazz, progressive rock, psychedelic rock, post rock, art rock, progressive metal, doom metal, death metal, and gothic metal, as well as chamber music, ambient music and electronic music. After a five-year hiatus, the band re-united to record their latest album, Part the Second, which was funded by fan donations and released online May 14, 2009 for free.

Biography
Maudlin of the Well released three full-length albums before disbanding in 2003. These albums included 1999's My Fruit PsychoBells...A Seed Combustible and 2001's Bath and Leaving Your Body Map, these last two made as complementary companion albums. The band had a consistent core membership, which consisted of Jason Byron, Greg Massi, and Toby Driver. Throughout its career a sort of "revolving door" of members and session musicians participated as needed.

Maudlin's music, lyrics, and atmosphere dealt predominantly with the subject of astral projection. The band described their approach as trying to find music rather than compose it. This was done through practicing astral projection and lucid dreams, from which they were purportedly able to "bring back" pre-existing music from the astral plane (as stated by Toby Driver in the liner notes included with the reissued Bath and Leaving Your Body Map).

In late 2001, the band began working on a fourth studio album. During this time, the band lost several longtime members, changed labels, and ultimately renamed themselves to Kayo Dot. This fourth album was later released in 2003 as Kayo Dot's Choirs of the Eye.

The Dark Symphonies label re-issued Bath and Leaving Your Body Map in 2006 and My Fruit PsychoBells...A Seed Combustible in 2008, all with bonus tracks consisting of early demos.

On June 20, 2008, Toby Driver published a blog post explaining that he had unreleased motW material on his mind and was considering giving community-funding a try in order to have it materialize as a free to download, digital-only release. Driver questioned whether this could be done considering the high cost of production and mastering and the band's relatively small following. A fan of the band, Etienne Dubé, later announced his project of playing online poker throughout the following month in an attempt to finance the new material. Dubé documented his progress on his blog, successfully raising $6000 for the project by the end of July 2008. On the band's MySpace page on July 27, 2008, as well as Driver's blog, it was announced that Dubé's donation allowed them to record a new full-length album, while further fan donations would be going towards hiring orchestral musicians and a possible physical release. According to Driver, only two songs at the time could be considered "100% old motW material", but he would work with "a dozen worthwhile fragments" and expand upon them, with the end result being, in Driver's words, "a hybrid of two different eras of my compositional mind".

Recording for the new album started on February 10, 2009, and the album, titled Part the Second was finally released in May 2009. It is available for free download in various file formats (MP3, FLAC and WAV) on motW's website, torrent networks, or alternatively, it can be streamed directly from the site. An amalgam of many different musical styles, the new songs share an ethereal quality with previous motW recordings, but are distinctly more mellow than the group's prior releases and contain no death growls.

The Finnish label Blood Music later ran a limited CD pressing of Part the Second, as well as further small runs of the band's previous albums, in 2012. The project has remained inactive since then with the exception of a reunion show in August 2015 at The Stone in New York City, announced by Greg Massi in his podcast on January 2, 2015, as part of a several day celebration of Toby Driver's career.

Demos

 * Through Languid Veins - 1996
 * Sacred Spaces: Second demo, January 1997 - 1997
 * Begat of the Haunted Oak: An Acorn - 1997
 * Odes to Darksome Spring - 1997
 * For My Wife - 1998

Albums

 * My Fruit Psychobells...A Seed Combustible (1999)
 * Bath (2001)
 * Leaving Your Body Map (2001)
 * Part the Second (2009)

Compilations

 * The Complete Works (2012)

title: Maudlin of the Well


text:
Dichlorodifluoromethane

Dichlorodifluoromethane (R-12) is a colorless gas usually sold under the brand name Freon-12, and a chlorofluorocarbon halomethane (CFC) used as a refrigerant and aerosol spray propellant. In compliance with the Montreal Protocol, its manufacture was banned in developed countries (non-article 5 countries) in 1996, and in developing countries (Article 5 countries) in 2010 out of concerns about its damaging effect on the ozone layer. Its only allowed usage is as a fire retardant in submarines and aircraft. It is soluble in many organic solvents. R-12 cylinders are colored white.

Preparation
It can be prepared by reacting carbon tetrachloride with hydrogen fluoride in the presence of a catalytic amount of antimony pentachloride:

 * CCl4 + 2HF → CCl2F2 + 2HCl

This reaction can also produce trichlorofluoromethane (CCl3F), chlorotrifluoromethane (CClF3) and tetrafluoromethane (CF4).

History
Charles F. Kettering, vice president of General Motors Research Corporation, was seeking a refrigerant replacement that would be colorless, odorless, tasteless, nontoxic, and nonflammable. He assembled a team that included Thomas Midgley Jr., Albert Leon Henne, and Robert McNary. From 1930 to 1935, they developed dichlorodifluoromethane (CCl2F2 or R12), trichlorofluoromethane (CCl3F or R11), chlorodifluoromethane (CHClF2 or R22), trichlorotrifluoroethane (CCl2FCClF2 or R113), and dichlorotetrafluoroethane (CClF2CClF2 or R114), through Kinetic Chemicals which was a joint venture between DuPont and General Motors.

Use as an aerosol
The use of chlorofluorocarbons as aerosols in medicine, such as USP-approved salbutamol, has been phased out by the U.S. Food and Drug Administration. A different propellant known as hydrofluoroalkane, or HFA, which was not known to harm the environment, was chosen to replace it.

Retrofitting
R-12 was used in most refrigeration and vehicle air conditioning applications prior to 1994 before being replaced by 1,1,1,2-tetrafluoroethane (R-134a), which has an insignificant ozone depletion potential. Automobile manufacturers started using R-134a instead of R-12 in 1992–1994. When older units leak or require repair involving removal of the refrigerant, retrofitment to a refrigerant other than R-12 (most commonly R-134a) is required in some jurisdictions. The United States does not require automobile owners to retrofit their systems; however, taxes on ozone-depleting chemicals coupled with the relative scarcity of the original refrigerants on the open market make retrofitting the only economical option. Retrofitment requires a system flush and a new filter/dryer or accumulator, and may also involve the installation of new seals and/or hoses made of materials compatible with the refrigerant being installed. Mineral oil used with R-12 is not compatible with R-134a. Some oils designed for conversion to R-134a are advertised as compatible with residual R-12 mineral oil. Another replacement for R-12 is the highly flammable, but truly drop-in HC-12a, whose flammability has led to injuries and deaths in a bus fire in 2006.

Dangers
Aside from its environmental impacts, R12, like most chlorofluoroalkanes, forms phosgene gas when exposed to a naked flame.

Properties
Table of thermal and physical properties of saturated liquid refrigerant 12:

title: Dichlorodifluoromethane


text:
R12

R12 may refer to:

Automobiles

 * BMW R12, a motorcycle
 * Renault 12, a French family car

Aviation

 * Bell R-12, an American utility helicopter
 * Caudron R.12, a French experimental biplane
 * Republic XR-12 Rainbow, an American experimental reconnaissance aircraft
 * R-12 Kassel/Rothwesten, a former United States Army Air Corps airfield in Germany
 * Rubik R-12 Kevély, a Hungarian training glider
 * Yakovlev R-12, a Soviet prototype reconnaissance aircraft

Roads

 * R12 road (Belgium)
 * R12 road (Ghana)
 * R-12 regional road (Montenegro)
 * R12 road (Russia)

Public transport

 * R12 (New York City Subway car)
 * R12 (Rodalies de Catalunya), a regional rail line in Catalonia, Spain
 * Kenilworth Avenue Line of the Washington Metropolitan Area Transit Authority

Vessels

 * HMS Contest (R12), a destroyer of the Royal Navy
 * HMS Hermes (R12), an aircraft carrier of the Royal Navy
 * HMS R12, a submarine of the Royal Navy
 * USS R-12 (SS-89), a submarine of the United States Navy

Other uses

 * R12 (cemetery), a Neolithic cemetery in Sudan
 * Dichlorodifluoromethane, a refrigerant
 * Ndombe language
 * R-12 Dvina, a Soviet ballistic missile
 * R12: Extremely flammable, a risk phrase
 * Small nucleolar RNA R12

title: R12


text:
User:Shane Smith

Please do not edit this page. Feel free to post anything at all on my talk page.

My name is Shane Smith. I am still working on this page.

My PT user page is here. My ES user page is here.

Recently I have begun working on translating Portuguese- and Spanish-language pages into English, and cleaning up English-language pages after translation from Portuguese and Spanish.

I used to be known as Joshays. You can see my contributions as Joshays here.

title: User:Shane Smith


text:
Monorail camera

Monorail cameras are view cameras with lens mount, bellows, and interchangeable viewing and film backs all fitted along a rigid rail along which they can slide until locked into position. They can take sheet film in large sizes, and since the advent of digital photography can take a digital back. They are used to take very high-quality photographs of static subjects on large film, or at high digital image resolution, and capable of much enlargement with good quality. They have many camera movements for image control. The image is usually viewed on a ground-glass screen in the film plane; after the scene has been composed, the ground glass is replaced by the film, and the exposure made. Monorail cameras rarely have any other viewfinder than the ground glass.

Details
Virtually any lens can be fitted, and backs for sheet film, rollfilm, digital back and Polaroid backs. For some uses with long exposures, or flash lighting; a shutter is unnecessary; removing a lens cap to expose the film is sufficient. Extremely small apertures such as 64 can be used without issues of diffraction on the lenses, of much larger focal length than those used for smaller images (a small relative aperture is still a fairly large hole, reducing diffraction).

The trade-off for their versatility is their large weight and bulk, and use limited to slow photographs of static subjects. Some models, such as the Arca Swiss F-Line, are more compact and designed for field use, still retaining generous movements; however the F-Line cameras still weigh about 3 kg.

Monorail cameras have capabilities that most other cameras do not. Both the lens and the film planes are separate and can be moved independently. By moving the front of the camera, the lens plane, independently of the rear which houses the film, the photographer can alter the depth-of-field (actually, the plane of sharp focus) without changing the perspective of the image. The converse is also true. The rear of the camera, which holds the film, can be moved to alter or improve the perspective of the image without changing the depth-of-field.

Film is typically loaded one sheet at a time into a special holder. Each film holder can hold two sheets of film - one on each side of the holder. Different holders can be loaded with different film; the type of film can be changed from one photograph to the next. Typical film sizes are 4 inch by 5 inch (4"×5") and 8 inch by 10 inch (8"×10"). There are other formats, including 5×7 inch and 11×14 inch.

Monorail cameras are among the simplest cameras possible according to their operating principles, consisting of the front standard (holding the lens) and rear standard (holding the ground glass viewing and focussing screen, then replaced by the film) sliding on a single rail, with a light-tight bellows stretched between. They are built to a high standard of precision and smoothness of operation, and sell in low volume, which makes prices higher than most smaller cameras.

In addition to high-quality general images, monorails can be used for high-precision technical applications. For a general subject it does not matter if the geometry of the image is imperceptibly different from the subject; the measurable, though very small, optical aberrations of even good quality lenses do not cause problems. When photographing subjects which must be very accurately represented, for example in making a mask for integrated circuit manufacture, apochromatic lenses of very high geometric accuracy and minimal color aberration (traded off against a small maximum aperture) and high price, are used.

Unlike with most other cameras, lenses used with view cameras (including monorails) are rarely manufactured by the body manufacturer. The body will be bought with lens panels and a film back; the owner will then choose lenses (in shutters) made by specialist manufacturers. A digital back from yet another manufacturer may be used.

Several companies produce monorail camera bodies, including Arca-Swiss, Ebony, Horseman, Linhof, Cambo, Sinar, and Toyo. Older monorail cameras are available second-hand; unlike most other cameras they are relatively immune to obsolescence, so long as parts and accessories are available. Many parts which would be difficult to replace are unlikely to fail on these large, rugged, and basically simple devices.

title: Monorail camera


text:
User talk:Lookoii-las-iju

Wangish
I can find absolutely no proof this language exists. Please cite your sources, or it's likely going to get deleted again.

title: User talk:Lookoii-las-iju


text:
Cross-entropy

In information theory, the cross-entropy between two probability distributions $$p$$ and $$q$$, over the same underlying set of events, measures the average number of bits needed to identify an event drawn from the set when the coding scheme used for the set is optimized for an estimated probability distribution $$q$$, rather than the true distribution $$p$$.

Definition
The cross-entropy of the distribution $$q$$ relative to a distribution $$p$$ over a given set is defined as follows:

 * $$H(p, q) = -\operatorname{E}_p[\log q]$$,

where $$E_p[\cdot]$$ is the expected value operator with respect to the distribution $$p$$.

The definition may be formulated using the Kullback–Leibler divergence $$D_{\mathrm{KL}}(p \parallel q)$$, divergence of $$p$$ from $$q$$ (also known as the relative entropy of $$p$$ with respect to $$q$$).

 * $$H(p, q) = H(p) + D_{\mathrm{KL}}(p \parallel q),$$

where $$H(p)$$ is the entropy of $$p$$.

For discrete probability distributions $$p$$ and $$q$$ with the same support $$\mathcal{X}$$, this means

The situation for continuous distributions is analogous. We have to assume that $$p$$ and $$q$$ are absolutely continuous with respect to some reference measure $$r$$ (usually $$r$$ is a Lebesgue measure on a Borel σ-algebra). Let $$P$$ and $$Q$$ be probability density functions of $$p$$ and $$q$$ with respect to $$r$$. Then

 * $$-\int_\mathcal{X} P(x)\, \log Q(x)\, \mathrm{d}\ \!x = \operatorname{E}_p[-\log Q],$$

and therefore

NB: The notation $$H(p,q)$$ is also used for a different concept, the joint entropy of $$p$$ and $$q$$.

Motivation
In information theory, the Kraft–McMillan theorem establishes that any directly decodable coding scheme for coding a message to identify one value $$x_i$$ out of a set of possibilities $$\{x_1,\ldots,x_n\}$$ can be seen as representing an implicit probability distribution $$q(x_i) = \left(\frac{1}{2}\right)^{\ell_i}$$ over $$\{x_1, \ldots, x_n\}$$, where $$\ell_i$$ is the length of the code for $$x_i$$ in bits. Therefore, cross-entropy can be interpreted as the expected message-length per datum when a wrong distribution $$q$$ is assumed while the data actually follows a distribution $$p$$. That is why the expectation is taken over the true probability distribution $$p$$ and not $$q.$$ Indeed the expected message-length under the true distribution $$p$$ is

 * $$ \operatorname{E}_p[\ell] = - \operatorname{E}_p\left[\frac{\ln{q(x)}}{\ln(2)}\right] = - \operatorname{E}_p\left[\log_2 {q(x)}\right] = - \sum_{x_i} p(x_i)\, \log_2 q(x_i) = -\sum_x p(x)\, \log_2 q(x) = H(p, q). $$

Estimation
There are many situations where cross-entropy needs to be measured but the distribution of $$p$$ is unknown. An example is language modeling, where a model is created based on a training set $$T$$, and then its cross-entropy is measured on a test set to assess how accurate the model is in predicting the test data. In this example, $$p$$ is the true distribution of words in any corpus, and $$q$$ is the distribution of words as predicted by the model. Since the true distribution is unknown, cross-entropy cannot be directly calculated. In these cases, an estimate of cross-entropy is calculated using the following formula:

 * $$H(T,q) = -\sum_{i=1}^N \frac{1}{N} \log_2 q(x_i)$$

where $$N$$ is the size of the test set, and $$q(x)$$ is the probability of event $$x$$ estimated from the training set. In other words, $$q(x_i)$$ is the probability estimate of the model that the i-th word of the text is $$x_i$$. The sum is averaged over the $$N$$ words of the test. This is a Monte Carlo estimate of the true cross-entropy, where the test set is treated as samples from $$p(x)$$.

Relation to maximum likelihood
The cross entropy arises in classification problems when introducing a logarithm in the guise of the log-likelihood function.

The section is concerned with the subject of estimation of the probability of different possible discrete outcomes. To this end, denote a parametrized family of distributions by $$q_{\theta}$$, with $$\theta$$ subject to the optimization effort. Consider a given finite sequence of $$N$$ values $$x_i$$ from a training set, obtained from conditionally independent sampling. The likelihood assigned to any considered parameter $$\theta$$ of the model is then given by the product over all probabilities $$q_{\theta}(X=x_i)$$. Repeated occurrences are possible, leading to equal factors in the product. If the count of occurrences of the value equal to $$x_i$$ (for some index $$i$$) is denoted by $$\#x_i$$, then the frequency of that value equals $$\#x_i/N$$. Denote the latter by $$p(X=x_i)$$, as it may be understood as empirical approximation to the probability distribution underlying the scenario. Further denote by $$PP := {\mathrm e}^{ H(p, q_\theta) }$$ the perplexity, which can be seen to equal $$ {\textstyle \prod_{x_i}} q_{\theta}(X=x_i)^{-p(X=x_i)}$$ by the calculation rules for the logarithm, and where the product is over the values without double counting. So
 * $$\mathcal{L}(\theta; {\mathbf x}) = \prod_{i} q_{\theta}(X=x_i) = \prod_{x_i} q_{\theta}(X=x_i)^{\#x_i} = PP^{-N} = {\mathrm e}^{ - N\cdot H(p, q_\theta) }$$

or
 * $$\log \mathcal{L}(\theta; {\mathbf x}) = -N\cdot H(p, q_\theta).$$

Since the logarithm is a monotonically increasing function, it does not affect extremization. So observe that the likelihood maximization amounts to minimization of the cross-entropy.

Cross-entropy minimization
Cross-entropy minimization is frequently used in optimization and rare-event probability estimation. When comparing a distribution $$q$$ against a fixed reference distribution $$p$$, cross-entropy and KL divergence are identical up to an additive constant (since $$p$$ is fixed): According to the Gibbs' inequality, both take on their minimal values when $$p = q$$, which is $$0$$ for KL divergence, and $$\mathrm{H}(p)$$ for cross-entropy. In the engineering literature, the principle of minimizing KL divergence (Kullback's "Principle of Minimum Discrimination Information") is often called the Principle of Minimum Cross-Entropy (MCE), or Minxent.

However, as discussed in the article Kullback–Leibler divergence, sometimes the distribution $$q$$ is the fixed prior reference distribution, and the distribution $$p$$ is optimized to be as close to $$q$$ as possible, subject to some constraint. In this case the two minimizations are not equivalent. This has led to some ambiguity in the literature, with some authors attempting to resolve the inconsistency by restating cross-entropy to be $$D_{\mathrm{KL}}(p \parallel q)$$, rather than $$H(p, q)$$. In fact, cross-entropy is another name for relative entropy; see Cover and Thomas and Good. On the other hand, $$H(p, q)$$ does not agree with the literature and can be misleading.

Cross-entropy loss function and logistic regression
Cross-entropy can be used to define a loss function in machine learning and optimization. Mao, Mohri, and Zhong (2023) give an extensive analysis of the properties of the family of cross-entropy loss functions in machine learning, including theoretical learning guarantees and extensions to adversarial learning. The true probability $$p_i$$ is the true label, and the given distribution $$q_i$$ is the predicted value of the current model. This is also known as the log loss (or logarithmic loss or logistic loss); the terms "log loss" and "cross-entropy loss" are used interchangeably.

More specifically, consider a binary regression model which can be used to classify observations into two possible classes (often simply labelled $$0$$ and $$1$$). The output of the model for a given observation, given a vector of input features $$ x $$, can be interpreted as a probability, which serves as the basis for classifying the observation. In logistic regression, the probability is modeled using the logistic function $$g(z) = 1/(1+e^{-z})$$ where $$ z $$ is some function of the input vector $$x$$, commonly just a linear function. The probability of the output $$y=1$$ is given by
 * $$q_{y=1} = \hat{y} \equiv g(\mathbf{w}\cdot\mathbf{x}) = \frac 1 {1+e^{-\mathbf{w}\cdot\mathbf{x}}},$$

where the vector of weights $$\mathbf{w}$$ is optimized through some appropriate algorithm such as gradient descent. Similarly, the complementary probability of finding the output $$y=0$$ is simply given by
 * $$q_{y=0} = 1-\hat{y}.$$

Having set up our notation, $$p\in\{y,1-y\}$$ and $$q\in\{\hat{y},1-\hat{y}\}$$, we can use cross-entropy to get a measure of dissimilarity between $$p$$ and $$q$$:
 * $$H(p,q)\ =\ -\sum_i p_i\log q_i\ =\ -y\log\hat{y} - (1-y)\log(1-\hat{y}).$$
 * Comparison of Loss functions for binary classification.png

Logistic regression typically optimizes the log loss for all the observations on which it is trained, which is the same as optimizing the average cross-entropy in the sample. Other loss functions that penalize errors differently can be also used for training, resulting in models with different final test accuracy. For example, suppose we have $$N$$ samples with each sample indexed by $$n=1,\dots,N$$. The average of the loss function is then given by:

 * $$\begin{align}

J(\mathbf{w})\ &=\ \frac1N\sum_{n=1}^N H(p_n,q_n)\ =\ -\frac1N\sum_{n=1}^N\ \bigg[y_n \log \hat y_n + (1 - y_n)  \log (1 - \hat y_n)\bigg]\,, \end{align}$$

where $$\hat{y}_n\equiv g(\mathbf{w}\cdot\mathbf{x}_n) = 1/(1+e^{-\mathbf{w}\cdot\mathbf{x}_n}) $$, with $$g(z)$$ the logistic function as before.

(In this case, the binary label is often denoted by {−1,+1}. )

Remark: The gradient of the cross-entropy loss for logistic regression is the same as the gradient of the squared-error loss for linear regression. That is, define

 * $$X^T=\begin{pmatrix}

1&x_{11}&\dots&x_{1p}\\ 1&x_{21}&\cdots&x_{2p}\\ \vdots & \vdots && \vdots \\ 1&x_{n1}&\cdots&x_{np}\\ \end{pmatrix}\in \mathbb{R}^{n\times(p+1)},$$
 * $$\hat{y_i} = \hat{f}(x_{i1},\dots,x_{ip}) = \frac{1}{1+\exp(-\beta_0-\beta_1x_{i1}-\dots-\beta_px_{ip})},$$
 * $$L(\boldsymbol{\beta}) = -\sum_{i=1}^N \left[y_i\log \hat{y}_i+(1-y_i)\log(1-\hat{y}_i)\right].$$

Then we have the result

 * $$\frac{\partial}{\partial\boldsymbol{\beta}}L(\boldsymbol{\beta})=X^T(\hat{Y}-Y).$$

The proof is as follows. For any $$\hat{y}_i$$, we have

 * $$\frac{\partial}{\partial\beta_0}\ln\frac{1}{1+e^{-\beta_0+k_0}} = \frac{e^{-\beta_0+k_0}}{1+e^{-\beta_0+k_0}},$$
 * $$\frac{\partial}{\partial \beta_0}\ln \left(1-\frac{1}{1+e^{-\beta_0+k_0}}\right)=\frac{-1}{1+e^{-\beta_0+k_0}},$$
 * $$\begin{align}

\frac{\partial}{\partial\beta_0}L(\boldsymbol{\beta}) &= -\sum_{i=1}^{N}\left[\frac{y_i \cdot e^{-\beta_0+k_0}}{1+e^{-\beta_0+k_0}}-(1-y_i)\frac{1}{1+e^{-\beta_0+k_0}}\right] \\ &= - \sum_{i=1}^{N} \left[y_i-\hat{y}_i\right] = \sum_{i=1}^{N}(\hat{y}_i-y_i), \end{align}$$
 * $$\frac{\partial}{\partial \beta_1}\ln \frac{1}{1+e^{-\beta_1x_{i1}+k_1}} = \frac{x_{i1}e^{k_1}}{e^{\beta_1x_{i1}}+e^{k_1}},$$
 * $$\frac{\partial}{\partial \beta_1}\ln\left[1-\frac{1}{1+e^{-\beta_1x_{i1}+k_1}}\right] = \frac{-x_{i1}e^{\beta_1x_{i1}}}{e^{\beta_1x_{i1}}+e^{k_1}},$$
 * $$\frac{\partial}{\partial\beta_1}L(\boldsymbol{\beta}) = -\sum_{i=1}^N x_{i1}(y_i-\hat{y}_i) = \sum_{i=1}^N x_{i1}(\hat{y}_i-y_i).$$

In a similar way, we eventually obtain the desired result.

Amended cross-entropy
It may be beneficial to train an ensemble of models that have diversity, such that when they are combined, their predictive accuracy is augmented. Assuming a simple ensemble of $$ K $$ classifiers is assembled via averaging the outputs, then the amended cross-entropy is given by

e^k = H(p,q^k)-\frac{\lambda}{K}\sum_{j\neq k}H(q^j,q^k) $$ where $$ e^k $$ is the cost function of the $$ k^{th} $$ classifier, $$ q^k $$ is the output probability of the $$ k^{ th} $$ classifier, $$ p $$ is the true probability to be estimated, and $$ \lambda $$ is a parameter between 0 and 1 that defines the 'diversity' that we would like to establish among the ensemble. When $$ \lambda=0 $$ we want each classifier to do its best regardless of the ensemble and when $$ \lambda=1 $$ we would like the classifier to be as diverse as possible.

title: Cross-entropy


text:
Talk:Maudlin of the Well

Redirect
I deleted the original article text, which clearly had NPOV and copyright issues and was neither informative nor encyclopedic, and for the time being the article redirects to Kayo Dot, the newer incarnation of this band.Onlyemarie 20:07, 13 Apr 2005 (UTC)

Major Cleanup
I reverted the text on this page to the previous version while maintaining some of the header changes made by Avador. I made this revision because Avador's overhaul had contained numerous instances of misspelling, incorrect information, or presumption on the author's part. 12:11, 27 Feb 2006 (EST)
 * As far as I know, I have fully conferred the article to the MoS, I have reinstated most of my text, while correcting some of the issues you mentioned. Much of what I have placed is information I have gathered, in my own word, from various website with information about the band (from both wikipedia and other places.  The purpose of my edits was to make the articles easier to read for someone who was not familiar with the band or wikipedia in general.  I recently reverted to my last version, because two of the last anonymous users had deleted much of sections & information, which is a crucial part of nearly all of wikipedia articles (i.e., deleting the headline text, and making it show nothing but some of the bands genres). Avador 01:10, 2 March 2006 (UTC)

 * I felt that stating that "longtime members lost interest" was presumptive, so I reverted that sentence to the previous version's. 1:49, 14 Mar 2006 (EST)

Template
I added the template and cleaned the article text up a bit. --86.13.227.234 17:52, 31 March 2007 (UTC)

Influences
I see a couple of influential genres are mentioned in the article. I agree on doom metal, indie rock, progressive metal but I don't understand why new age is mentioned. New age to me is keyboard laden music made for meditating/relaxing. With artist like Enya or maybe Vangelis or even the nameless CD's that can be bought at The Body Shop etc. with crappy titles like "The Sounds of the Sea" and other CD's chockfull of keyboards, singing birds and flowing rivulets. motW were not doing that, were they?

When listening to motW I hear more notable influences. Like death and black metal (songs like "They Aren't All Beautiful" (Bath) or "Riseth He.." (Leaving Your Body Map)). Sometimes I hear jazz and classical music listening to the chord progressions and arrangements/use of instruments (songs like Interlude 4 (Leaving Your Body Map)). Emmaneul 09:40, 23 April 2007 (UTC)

Changed genre
Because of these:

http://www.bnrmetal.com/groups/motw.htm Progressive Metal

http://www.rockdetector.com/artist,31014.sm Avant-garde

http://www.metal-archives.com/band.php?id=16 Avant-garde Progressive Metal

http://www.metal-observer.com/articles.php?lid=1&sid=1&id=268 Avantgarde Metal Emmaneul (Talk) 22:51, 13 September 2007 (UTC)

Is this a notable band?
I have heard about them, and they are awesome, actually, but are they notable? The article doesn't contain any reliable sources, same goes for the interwiki links as well. During a search I couldn't find anything reliable, just the usual databases, retail sites, blogs, forums and lots and lots of trivial mentions and sites where the words are separated. They don't seem to be notable, but if reliable sources would be presented, I change my mind. (And I know this is not an Afd, but still...) GhostDestroyer100 (talk) 19:34, 29 May 2021 (UTC)

title: Talk:Maudlin of the Well


text:
Deuce Bigalow

Deuce Bigalow is a fictional character played by Rob Schneider in the following movies:

 * Deuce Bigalow: Male Gigolo (1999)
 * Deuce Bigalow: European Gigolo (2005)

title: Deuce Bigalow


text:
Diabolical Masquerade

Diabolical Masquerade was a Swedish one-man black metal band with progressive influences. The band was formed in 1993 in Stockholm as side project of Anders Nyström (aka Blakkheim), known for his work as the guitarist of Katatonia.

History
Diabolical Masquerade was a Swedish one-man black metal band. All music is written and played by Katatonia guitarist Anders "Blakkheim" Nyström, who wanted to have a band where he could compose more extreme music while Katatonia was exploring more mellow moods. The music leans heavily on avant-garde melodic black metal with some death metal and thrash metal influences. Blakkheim wanted to experiment more with song structure, theme and composition. This is most notably seen on the last Diabolical Masquerade album, Death's Design. This album is conceived as the soundtrack to a nonexistent Swedish horror movie, with 61 tracks broken up into 20 movements, each with a unique feel and theme. Death's Design includes many passages featuring various genres and styles, experimenting with progressive rock, progressive metal, ambient, classical music, and rhythmic percussion-based passages. Nyström worked together on the album with Dan Swanö. In early September 2004, Nyström announced that he had put the project to rest, after not having found the necessary inspiration while working on a fifth album.

Discography

 * Promo 1993 (1993) (demo)
 * Ravendusk in My Heart (1996)
 * The Phantom Lodge (1997)
 * Nightwork (1998)
 * Death's Design (2001)

Band members

 * Diabolical Masquerade
 * Anders "Blakkheim" Nyström – vocals, guitar (1993–2004), bass, keyboards (1993–1998)
 * Dan Swanö – keyboards (1996, 1998–2001), drums (1996, 1998), guest vocals (1997), backing vocals (1998), guitar (2001)

title: Diabolical Masquerade


text:
Wikipedia:Articles for deletion/Wangish

 This page is an archive of the discussion about the proposed deletion of the article below. This page is no longer live. Further comments should be made on the article's talk page rather than here so that this page is preserved as an historic record. The result of the debate was delete. – ABCD 21:17, 19 Apr 2005 (UTC)

Wangish
Previously deleted as nonsense. Can some verify this exists? If no evidence shows up I vote delete strong delete. Also see attached talk page. Mgm|(talk) 20:08, Apr 13, 2005 (UTC)
 * Additional research with clusty shows no relevant hits for Ganish, Kwiarizian, or Wangish. Mgm|(talk) 20:18, Apr 13, 2005 (UTC)
 * They want an apology? Hold your breath, fellas.  Delete. - Lucky 6.9 20:45, 13 Apr 2005 (UTC)
 * Please don't, unless you want to suffocate. Patent nonsense, not good enough for BJAODN. Delete. - Mike Rosoft 06:55, 14 Apr 2005 (UTC)
 * Delete MGM's research was convincing enough without having to see that rediculous demand. --InShaneee 20:48, 13 Apr 2005 (UTC)
 * The deletion log, in particular the article content, makes for interesting reading:
 * 18:20, 2005 Apr 13 Mikkalai deleted "Talk:Elections in Kwiarizia" (content was: 'I plead with you not to delete article this because even though there is no such place, we are an unrepresented people who actually do have an electio...')
 * 18:19, 2005 Apr 13 Mikkalai deleted "Wangish" (nonsense)
 * Admitted hoax. And I concur about the research. Delete. Uncle G 20:53, 2005 Apr 13 (UTC)
 * Delete. No credible third party sources. Zzyzx11 | Talk 23:52, 13 Apr 2005 (UTC)
 * Delete, patent nonsense. No relevant google results: . Also, those characters look dodgy - the first one is pi with a couple of squiggles, the second is 'J' and '3' stuck together. --bainer 23:55, 13 Apr 2005 (UTC)
 * Delete, not notable, possible hoax. Megan1967 07:15, 14 Apr 2005 (UTC)
 * Delete as an obvious hoax.   — J I P | Talk 10:00, 14 Apr 2005 (UTC)

 * This page is now preserved as an archive of the debate and, like some other VfD subpages, is no longer 'live'. Subsequent comments on the issue, the deletion, or the decision-making process should be placed on the relevant 'live' pages. Please do not edit this page.

title: Wikipedia:Articles for deletion/Wangish


text:
User talk:Samweis

Messages
Hello, use this site to leave me a message. Please put new messages at the top.

Hallo, benutze diese Seite, um mir Nachrichten zu hinterlassen. Bitte platziere neue Nachrichten oben.

title: User talk:Samweis


text:
User:Talrias/Templates/Box free/press

This article has been cited in the press. The source is:

 * "" . . [].

title: User:Talrias/Templates/Box free/press


text:
Talk:Diabolical Masquerade

Untitled
Attention needed - the article as it is consists of copyvio and a brief discography. Can someone flesh it out? Onlyemarie 20:10, 13 Apr 2005 (UTC)

External links modified
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title: Talk:Diabolical Masquerade


text: Talk:Clifford Chance

title: Talk:Clifford Chance


text: Category:Battles of the Taiping Rebellion


text:
Betsukai, Hokkaido

Betsukai (別海町) is a town located in Nemuro Subprefecture, Hokkaido, Japan. As of April 30, 2017, the town has an estimated population of 15,179, and an area of 1,320.15 km2 (the second largest in Hokkaido). The town is primarily agricultural, with numerous dairy farms. It comprises a part of the agricultural region referred to as "Milk Land Hokkaido".

History

 * 1923 - 6 villages combine, forming the village of Betsukai.
 * 1971 - Betsukai Village becomes Betsukai Town.

Mascot
Betsukai's mascot is Ryoushi-kun (りょウシくん) whose real name is Ryoushi Betsukai (別海りょウシ). He is a bull that looks like a cow. He is a fisherman, and a milk farmer. His friends are Hotatetchi (ホタテっち) (who is a Yesso scallop), Ebumaru (エビまる) (who is a shrimp), Milkchi (みるちー) (who is a milk bottle), Sakezo (サケゾー) (who is a salmon), Asarin (あさりん) (who is a Japanese littleneck clam), Hocki (ホッキー) (who is a Sakhalin surf clam) and Shiratori-san (シラトリさん) (who is a white swan). He was unveiled on 30 June 2013.

title: Betsukai, Hokkaido


text:
Talk:Declaration of Indulgence (1687)

Comment
I don't know how to do a redirect, but someone should do so - there is a somewhat more detailed article at Royal Declaration of Indulgence. Sturgeonslawyer (13 April 05 1.12 PDST)

 * They are not the same thing. One was issued in 1672, the other in 1688. --Valentinian 17:53, 13 February 2006 (UTC)

Untitled
why is the full text not reproduced here? presumably it is in the public domain. 70.187.18.116 20:24, 23 February 2007 (UTC)

Untitled
James II not Charles II in opening para. —Preceding unsigned comment added by 96.255.6.82 (talk) 21:41, 19 October 2008 (UTC)

Untitled
The description of the Covenanters as "extremist" is biased and has no place in an encyclopedia. I propose that it be removed Acorn897 (talk) 17:13, 24 July 2015 (UTC)

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title: Talk:Declaration of Indulgence (1687)


text:
Jerry Slocum

Jerry Slocum (born July 5, 1931) is an American historian, collector and author specializing on the field of mechanical puzzles. He worked as an engineer at Hughes Aircraft prior to retiring and dedicating his life to puzzles.

His personal puzzle collection, numbering over 40,000 mechanical puzzles and 4,500 books, is believed to be the world's largest. In 2006, the Association of Game & Puzzle Collectors awarded Slocum with the Sam Loyd Award.

In 2006, Slocum donated over 30,000 puzzles to the Lilly Library at Indiana University: marking the first time a major collection of puzzles was made available in an academic setting.

Slocum's first book, Puzzles Old and New, published in 1986, was the first comprehensive book to include all types of mechanical puzzles with hundreds of color illustrations of antique puzzles. In the introduction Martin Gardner predicted that the book would "remain a classic for decades."

Slocum has appeared on The Tonight Show Starring Johnny Carson, Martha Stewart Living, and eight other nationwide TV shows.

Slocum Puzzle Foundation
In 1993, Slocum founded the Slocum Puzzle Foundation, a non-profit organization dedicated to educating the public on puzzles through puzzle collecting, exhibitions, publications, and communications.

International Puzzle Party
Slocum also founded the International Puzzle Party in 1978. The first eight International Puzzle Parties (an event dedicated to discussing, showing, and trading mechanical puzzles) were held in Slocum's Beverly Hills living room and evolved into an annual by-invitation-only event rotating between North America, Europe, and Asia.

Works
Slocum has authored or co-authored more than a dozen books on the topic of puzzles.

 * Puzzles Old and New, with Jack Botermans (1986) ISBN 0295965797
 * The Puzzle Arcade (1996) ISBN 157054056X
 * The Tangram Book, with Dieter Gebhardt, Jack Botermans, Monica Ma, Xiaohe Ma 2003 ISBN 1-4027-0413-5 Sterling Publishing Company (Comprehensive, illustrated history, 1,756 problem figures) beautiful photos of historic Tangrams from Asia, Europe and America
 * The 15 Puzzle, with Dic Sonneveld, 2006 ISBN 1-890980-15-3 Slocum Puzzle Foundation.
 * The Cube: The Ultimate Guide to the World's Bestselling Puzzle, with David Singmaster, Wei-Hwa Huang, Dieter Gebhardt, Geert Hellings, and an introduction by Ernő Rubik, 2006 ISBN 978-1-57912-805-0, Black Dog & Leventhal Publishers, Inc. Covers the history of the Rubik's Cube, with solutions to the 2x2 and 3x3 puzzles.

title: Jerry Slocum


text: User talk:68.236.19.100

title: User talk:68.236.19.100


text:
User:Talrias/Templates/Box free/peerreview

  is currently being reviewed by the community.

Please add your comments to help others improve this article.


text:
Talk:Midwestcon

deVore...From Demon Prince Vore, D. Vore? From Piers Anthony? 64.198.97.66 20:14, 13 Apr 2005 (UTC)
 * No. DeVore has always been Howard's last name, since about nine years before Piers Anthony was born.

Longest running?
A bit puzzled by the opening statetement about being longest continuously running con. Worldcon has run longer continuously even accounting for the gap for WWII, since Worldcon ran without break from 1946 till now. Perhaps a better opening text would be something like: "Midwestcon is an annual science fiction convention held in the Cincinnati, Ohio area. The first Midwestcon was held in 1950 and it has taken place every year since, making it the longest running annual SF con occuring in the same location. (Worldcon has run since 1946 continuously, but it moves to a new location each year.) VJDocherty 17:23, 6 March 2007 (UTC)

 * And Westercon has been running since 1948, and Philcon's history goes back so far they are having trouble documenting it. Avt tor 14:42, 13 March 2007 (UTC)

 * Thanks. I've updated the opening text to make this clearer. VJDocherty 15:12, 13 March 2007 (UTC)

title: Talk:Midwestcon


text:
Aubrey Menen

Salvator Aubrey Clarence Menen (22 April 1912 – 13 March 1989) was a British writer, novelist, satirist and theatre critic. Born in London, his essays and novels explore the nature of nationalism and the cultural contrast between his own Irish-Indian ancestry and his traditional British upbringing. The first sentence of Dead Man in the Silver Market offers an example of his good-humoured approach to this contentious topic: "Men of all races have always sought for a convincing explanation of their own astonishing excellence and they have frequently found what they were looking for."

Early life and education
Aubrey Menen was born in London in 1912 to Kali Narain Menon (also Kalipurayath Narayana Menon), "scion of a prominent Nayar family" of Indian Malayali origin, and Alice Villet, an Englishwoman of Irish descent. Aubrey chose to change his surname's spelling, allegedly to avoid confusion with his friend V. K. Krishna Menon. Menen was raised at Islington and Forest Hill in London. He was brought up Roman Catholic. His mixed heritage was central to his career, and he often drew heavily on it in his writing.

He took a BA in Philosophy from University College London (UCL) in 1932. Whilst at UCL, he founded a drama group, the London Student Players, writing, directing, and performing in their productions; he befriended Duncan Grant, and commissioned him to design sets. Through Grant, Menen became acquainted with members of the Bloomsbury Group including Virginia Woolf and John Maynard Keynes.

Career
In 1932, having graduated from UCL, Menen became drama critic for The Bookman magazine, until, in 1934, serving as director of the Experimental Theatre in London until 1936. In 1933, H. G. Wells had granted Menen permission to produce an adaptation of his novel The Shape of Things to Come, which generated "considerable publicity". Menen's unconventional, boundary-pushing performances included production of politically-charged drama, his "radical plays... often fraught with controversy". He was sued for blasphemy and obscenity in 1934 in response to his play Genesis II, based on an incident when UCL had rejected Menen for a bursary due to his Indian heritage. In 1939, he went to India, where he became a "leading personality" in radio; from 1948 to 1980, he lived in Italy, where he "flourished as a writer of both fiction and non-fiction" until returning to India, settling at Kerala, where he spent the rest of his life.

Menen's 1954 retelling of the classic Hindu epic Ramayana – meant as a funny and readable version of the work – was banned in India for some years, as devout Hindus were horrified by the liberties Menen took with a sacred text. Menen stated that his goal was to, "aim at reviving [Valmiki's] attitude of mind." Menen's humor did not undercut his love for India, however, as can be seen in his book on Hindu mystics and his text to Roloff Beny's great book of photographs of India (India, 1969).

Novels

 * The Prevalence of Witches (1947)
 * The Stumbling-Stone (1949)
 * The Backward Bride: A Sicilian Scherzo (1950)
 * The Duke of Gallodoro (1952)
 * The Ramayana, As Told by Aubrey Menen (1954)
 * The Abode of Love: The Conception, Financing and Daily Routine of an English Harem in the Middle of the 19th Century (1956)
 * The Fig Tree (1959)
 * SheLa: A Satire (1962)
 * A Conspiracy of Women (1965)
 * Fonthill: A Comedy (1974)

Travel

 * Rome Revealed (1960)
 * Speaking the Language Like a Native (1962)
 * India, with Roloff Beny (1969)
 * Upon This Rock (1972)
 * Cities in the Sand (1973), about Leptis Magna, Timgad, etc.
 * London (1976)
 * Venice (1976)

Other non-fiction

 * Dead Man in the Silver Market (1953)
 * The Space within the Heart (1970)
 * Cities in the Sand (1972)
 * The New Mystics and the True Indian Tradition (1974)
 * Four Days of Naples (1979)
 * Art and Money (1980)

title: Aubrey Menen


text:
Talk:QR decomposition

No time to fix this but there seem to be errors
I only had a look at the section "Using for solution to linear inverse problems" because I was going to point students to something for further reading on economy/deluxe decomposition, but that section seems to be full of mistake. I'm about to catch a flight but maybe I'll come back to this article later, but since that part looks so weird, I am suspicious of everything. Maybe someone else can look at it if I get distracted and don't come back. Loisel (talk) 18:06, 21 February 2020 (UTC)

translation question
I'm trying to translate this article in french. I'm wondering about the example of Householder reflections method and especially, the calcul for the length of the vector $$a_1$$. I see that $$\| a_1 \| = 12+6+(-4) = 14 $$, I would prefer $$\| a_1 \|  = 12+6+|-4| = 22$$ or $$\| a_1 \|  = \sqrt{12^2+6^2+(-4)^2} $$. PierreLM April 13th 2005
 * You know you can just use that in your French version. Dysprosia 13:30, 14 Apr 2005 (UTC)

I'm so sorry, $$\| a_1 \|_2 = \sqrt{12^2+6^2+(-4)^2} = 14$$. So there is no problem. PierreLM April 15th 2005

Sign of $$\alpha$$ in Householder
The section on the Householder method says that $$\alpha$$ should take its sign from the first element in $$\mathbf{x}$$. In the example which follows, however, the second matrix generated appears not to use the sign operation. Am I missing something, or should this be fixed?--rlhatton 16:11, 25 January 2006 (UTC)

 * Using the other sign does not matter if you use exact computations, as in the example. I tried to clarify this. However, perhaps it is better to change the example to match the sign convention, or at least make a remark at that point. -- Jitse Niesen (talk) 13:44, 27 January 2006 (UTC)

 * He's right though. When you do it correctly, the signs change in the second Q matrix.  The correct answer has signs flipped.  — Preceding unsigned comment added by 50.40.70.99 (talk) 16:37, 30 November 2016 (UTC)

QR decomposition with rank deficiency
Is there somebody to editorialize the definition without assuming the full rank? S. Jo 14:03, 7 May 2006 (UTC)

 * Aha, I didn't notice that this was the point behind the edit I reverted. Better now? -- Jitse Niesen (talk) 01:45, 8 May 2006 (UTC)

 * Somehow, I don't think that we need to start with a square matrix. When we solve an over-determined system of equations in order to minimize the unitarily invariant norm of residuals, we sometimes use the QR-factorization to reduce a computational complexity. That kind of application reveals one of the essential properties among which the QR-factorization has. Also, except for the uniqueness, QR factorization has good features even in non-square matrices, I guess. For example, we can recognize that an orthonormal basis of the column space of A (=QR) consists of the columns of Q associated with non-zero diagonal entries of R. S. Jo 02:21, 8 May 2006 (UTC)

 * I agree that it's possible to give only the general definition (complex rectangular matrices), and that the general definition is useful, but I think that it's better from an educational point of view to start with the simpler definition (real square matrices). However, I do not feel strongly about this.
 * I do not understand your last sentence. If we take
 * $$ A = \begin{bmatrix} 1 & 1 & 1 \\ 0 & 0 & 1 \\ 0 & 0 & 1 \end{bmatrix} $$
 * then A = QR where Q is the 3-by-3 identity matrix and R = A, but the column space of A is not spanned by the first and third columns of Q. -- Jitse Niesen (talk) 05:00, 8 May 2006 (UTC)

 * You are right. My claim was true only if A is full rank, I guess. S. Jo 21:38, 8 May 2006 (UTC)

Householder-Example: QR=A ?
Hello there,

I'm just wondering why (in the householder-example) the resulting Q- and R-matrices don't multiply to A. Futhermore, the given Q and Q^t are not equal to I. Is the example correct?

 * When I calculate the products, I get QR = A and QQT = I. Could you please be more specific? What value do you take for Q, and what do you get for QQT? -- Jitse Niesen (talk) 12:59, 8 June 2006 (UTC)

Oh, you're right. I'm sorry, math is too hard for me :-)

$$QR=\begin{pmatrix} 6/7 & -69/175 & 58/175\\ 3/7 & 158/175 & -6/175 \\ -2/7 & 6/35 & 33/35 \end{pmatrix} \cdot \begin{pmatrix} 14 & 21 & -14 \\ 0 & 175 & -70 \\ 0 & 0 & -35 \end{pmatrix} = \begin{pmatrix} 12 & -51 & 4 \\ 6 & 167 & -68 \\ -4 & 24 & -41 \end{pmatrix} =A

$$

 * No worries, happens to me all the time ;) -- Jitse Niesen (talk) 13:54, 9 June 2006 (UTC)

 * Why isn't there a more simple example (easier numbers, these n/175 scares me ;-) )? 84.72.103.163 (talk) 22:35, 11 August 2009 (UTC)

I do not understand the example. The first step is still clear: $$u = x - sgn(x_1) * ||x|| * e_1 = (12, 6, -4)^T - (+1) * 14 * (1, 0, 0)^T = (12, 6, -4)^T - (14, 0, 0)^T = (-2, 6, -4)^T $$

In the next step, $$ v = u / ||u||$$ with the Euklidian norm $$||u|| = \sqrt(56) \approx 7.48 $$. Apparently, $$||(-1, 3, -2)^T|| = \sqrt{14}$$ is used instead. The reason should be made explicit. Then the text gives the equation for the Householder Matrix as $$Q = I - 2vv^T$$, but in the example the term $$2/||v||^2$$ suddenly appears. Textbooks give $$\frac{2}{v^T \odot v}$$, with $$\odot$$ the dot-product, which is 2/14 (arguably, this can be written as $$2/\sqrt{14}^2$$).

typo ?
"We can similarly form Givens matrices G2 and G3, which will zero the sub-diagonal elements a21 and a32, forming a rectangular matrix" should this actually say triangular instead of rectangular? -- User:Richard Giuly

 * Yes, indeed. Now fixed. -- Jitse Niesen (talk) 12:43, 22 October 2006 (UTC)

A more stable version of Householder?
Hi, I am new to the Wikipedia community, as far as editing goes... this is my first so please let me know if this is against protocol. After studying numerical linear algebra using the textbook by Trefethen and Bau, I noticed that there is a crucial step in the Householder implementation of the QR decomposition in this article that makes this article less than optimal in numerical stability. The operation that I would like to verify is the last one in the following snippet of pseudo code from "Numerical Linear Algebra":

for k = 1 to n
 * x = Ak:m,k
 * vk = sign(x1)||x||2e1 + x
 * vk = vk / ||vk||2
 * Ak:m,k:n = Ak:m,k:n - 2vk(vk*Ak:m,k:n)

//-

Notation:
 * * = complex conjugate
 * Ak:m,k:n = sub-matrix of A starting at the k-th row and k-th column
 * sign = sign of

The reason that I say this is more accurate is because the one presented in this page requires that A be multiplied with the successive new Qn every iteration of the loop, which adds to the numerical instability of the algorithm. The pseudo code proposed by Trefethen and Bau reduces that by having a fresh copy of the original A every iteration. --Jasper 06:58, 23 January 2007 (UTC)

 * I'm afraid that I don't quite understand what you mean. What is the difference between the statement
 * Ak:m,k:n = Ak:m,k:n - 2vk(vk*Ak:m,k:n)
 * in Trefethen and Bau's code, and the operation
 * $$ A = Q_k A $$
 * in the article?
 * I readily agree that the pseudocode is much easier to understand than the explanation in the article. Indeed, I've never been happy how the recursion is explained in the article (I think I am myself to blame for this), so please do go ahead and improve the text. -- Jitse Niesen (talk) 12:06, 24 January 2007 (UTC)

 * The reason that say that is because the operation you had was:
 * Qn = I - ...
 * after trying to implement that I noticed that you have to do tempA = tempA*Qn after initializing it to A with every iteration of Q. Whereas the technique I had you can get a fresh copy of A every time. —The preceding unsigned comment was added by 144.118.52.106 (talk) 17:36, 31 January 2007 (UTC).

QR decomposition for complex matrices?
hi. it seems that the algorithms that are discussed in this page are only compatible with matrices that have real elements and it seems that they can't be modified easily to be compatible with complex matrices.please guide me. —The preceding unsigned comment was added by Sina kh (talk • contribs) 11:59, 14 February 2007 (UTC).

 * Actually, I think that the algorithms all work for complex matrices if you replace the transpose with the conjugate transpose. For the first algorithm (Gram-Schmidt), this is mentioned in the section listed in the references. -- Jitse Niesen (talk) 04:44, 15 February 2007 (UTC)

 * Hi everyone.i had checked converting tranpose to transpose conjugate before and it doesn't work in householder reflectors algorithm(Q will be unitary but R won't be upper triangular).In Gram-Schmidt the algorithm have a constraint that "A" must be square(the author have mentioned it in the "definition" section).Sina kh 13:25, 27 February 2007 (UTC)

 * I'm afraid I don't understand you. I guess the A you're considering is not square. Why do you think R is not upper triangular when doing QR via Householder reflections? Where does it say that A has to be square for Gram-Schmidt? Did you check whether that is in fact true? -- Jitse Niesen (talk) 13:59, 28 February 2007 (UTC)

hi there.I have performed QR decomposition via householder reflection algorithm for a non-square small-sized complex matrix.I tried to follow the algorithm exactly:

A= -10+4i   4-5i 2-i      8+6i 6        7i

a1=A(:,1)= -10+4i 2-i 6 alfa=norm(a1)=sqrt(a1'*a1)        ("'" means transpose conjugate)

alfa=12.53

u1=a1-(alfa*e)              e=(1,0,0)undefinedt u1= -22.53+4i 2-i 6

v1=u1/norm(u1)= -0.9482+0.1683i 0.0842-0.0421i 0.2525

q1=I(3*3)-2*v1*v1'= -0.8548            0.1738 + 0.0515i   0.4789 - 0.0850i 0.1738 - 0.0515i   0.9823            -0.0425 + 0.0213i 0.4789 + 0.0850i  -0.0425 - 0.0213i   0.8725

q1*a= 11.8198 - 4.0000i  -1.7425 + 9.0803i 0.1775 + 0.3551i   8.1473 + 4.5214i -0.0000 + 1.0652i  2.1279 + 3.6281i

as it is clear,the elements (2,1) and (3,1) of the matrix "q1*a" are not zero.(against the algorithm).I continued the algorithm but i don't want to take your time more than this.finally:

Q= -0.8548           -0.2307 + 0.4265i   0.0231 - 0.1837i 0.1738 - 0.0515i  -0.1566 - 0.0464i    -0.5619 - 0.7904i 0.4789 + 0.0850i  -0.4857 + 0.7088i   0.1520 + 0.0464i

and

R= 11.8198 - 4.0000i -1.7425 + 9.0803i 0.8315 - 0.6607i  0.3750 - 4.5215i -0.3873 + 0.1202i -7.9021 + 4.6355i

I also performed QR decomposition in MATLAB and the result was:

Q= -0.7981 + 0.3192i -0.3036 - 0.2224i   0.3220 - 0.1260i 0.1596 - 0.0798i -0.7472 - 0.4151i  -0.4190 + 0.2490i 0.4789 - 0.0000i -0.1779 - 0.3101i   0.8017 - 0.0085i

and

R= 12.5300           -3.9904 + 7.6616i 0              -10.7413                  0               0

PS:I apologize if the text has some mistakes gramatically or in vocabulary.I'm not a native speaker and i am not fluent and i am not familiar with the other languages of the the article. thank you.Sina kh 17:07, 5 March 2007 (UTC)

 * It took me a while before I had time to go through it; sorry. It also was more complicated than I'd expected. Householder reflections behave a bit differently in complex spaces.
 * You are right, the algorithm does not work for complex matrices. However, it's possible to fix it. Instead of
 * $$ Q = I - 2vv^\top, $$
 * you have to take
 * $$ Q = I - (1+\omega) vv^* \quad\text{with}\quad \omega = \frac{\overline{v^*x}}{v^*x}. $$
 * Of course, if v and x are real vectors then ω = 1 and we get the same algorithm as before.
 * In your Matlab code, you write  instead of   and it should work.
 * This formulation of the method is taken from Dirk Laurie's post to NA Digest. Apparently, this is somewhere in Golub and Van Loan; I'll look it up and add to the Wikipedia article. Let me know if you need some more help.
 * PS: Your English is fine. -- Jitse Niesen (talk) 06:45, 10 March 2007 (UTC)
 * The link to Dirk Laurie's post above is dead. I found Dirk's post at netlib.org. I am not sure whether I have the privilege to change Jitse's note above, so I am appending this one. If it is acceptable under Wikipedia guidelines to change Jitse's note, I hope someone will please do so, and then delete this note. Thanks. Mike Mannon (talk) 01:37, 8 September 2014 (UTC)

 * In fact, Golub & Van Loan and Stoer & Bulirsch use a slightly different (but equivalent) approach. I added a sentence about it to the article. -- Jitse Niesen (talk) 07:19, 14 March 2007 (UTC)

 * The $$(1+w)$$ referred to above in Dirk Laurie's post is only necessary if $$\mathbf{v}^H\mathbf{x}$$ (or its conjugate $$\mathbf{x}^H\mathbf{v}$$) is potentially not real (as stated in the same post). However, in this case it is always real:
 * $$\mathbf{v}^H\mathbf{x} = ({\mathbf{u}\over\|\mathbf{u}\|})^H\mathbf{x}

= {\mathbf{u}^H\mathbf{x}\over\|\mathbf{u}\|} = {({\mathbf{x} - \alpha\mathbf{e}_1})^H\mathbf{x}\over\|\mathbf{u}\|} = {{\mathbf{x}^H\mathbf{x} - \alpha^*\mathbf{e}_1^T\mathbf{x}}\over\|\mathbf{u}\|} $$
 * $$\mathbf{x}^H\mathbf{x}$$ and $$|\mathbf{u}|$$ are always real, and the remaining term $$\alpha^*\mathbf{e}_1^T\mathbf{x}$$ has only one non-zero element $$\alpha^* x_k$$:
 * $$\alpha^* x_k

= (-e^{-i \arg x_k} \|\mathbf{x}\|) (|x_k|e^{i \arg x_k}) = -\|\mathbf{x}\| |x_k| $$
 * which is also real. In which case, the top and bottom of $$w = {{\mathbf{x}^H\mathbf{v}}\over{\mathbf{v}^H\mathbf{x}}}$$ are always the same.  So I think the $$(1+w)$$ can be replaced with 2. -- Rogueigor (talk) 19:07, 7 September 2017 (UTC)

Apparently the way sign of alpha is computed is also different. Even with these 2 changes I didn't get the correct answer. Can anyone please add a example for complex matrix too? thanks. — Preceding unsigned comment added by 192.54.222.11 (talk) 11:43, 30 December 2013 (UTC)

FULL QR decomposition
Hello everyone. Is anyone interested in adding some information for FULL QR decomposition? Since currently, everything seem to be in reduced form. —The preceding unsigned comment was added by Yongke (talk • contribs) 22:11, 6 March 2007 (UTC).

QR alorithm
There is a page on the same topic on QR algorithm, which I think should be merged in this page, and then the QR algorithm should link to this page.

--Fbianco 22:12, 15 April 2007 (UTC)

 * I don't think they should be merged. This page explains the QR decomposition and algorithms for computing it. The QR algorithm describes an algorithm for computing the eigenvalues of a matrix, which uses the QR decomposition. Those are different topics. -- Jitse Niesen (talk) 03:35, 16 April 2007 (UTC)

Suggested fix for number of iterations using Householder reflections
The text has- "After $$t$$ iterations of this process, $$t = \min(m, n)-1$$" I think it should be $$t = \min(m-1, n)$$. Consider $$A = \begin{pmatrix} 12 & -51 & 4 \end{pmatrix}$$. It neads no iterations and correctly $$ t = \min(1, 2)-1 = 0 $$.
 * But

$$ A = \begin{pmatrix} 12 \\ 6 \end{pmatrix}$$ needs one iteration. Incorrectly $$ t = \min(2, 1)-1 = 0 $$

 * If the #rows > #columns every column needs to be "triangularized" in turn
 * If the #columns >= #rows then every row except the first needs to be "triangularized".

 * Thanks for all the work ( I stumbled on this while implementing)

I am making the change-chad

Householder Problem
In the Householder section, since R = Qm...Q2Q1A, shouldn't it follow that the QR decomp is given by Q = Q1TQ2T... QmT instead of just Q = Q1Q2...Qm? -- anonymous

 * Yep, you're right. Thanks for bringing this to our attention. -- Jitse Niesen (talk) 16:58, 27 October 2007 (UTC)

Mention Octave instead of Matlab
I guess Wikipedia doesn't have a specific policy on using non-free software for mathematics, but I thought it would be nice to mention GNU Octave instead of Octave in the section where it mentions the numerical QR factorisation. I note that Octave's result is -Q and -R of Matlab's result.

I know lots of people have vociferous opposition to free software in mathematics, so this is why I ask before I go ahead and do it. I don't want to start an edit war. Swap 17:39, 26 October 2007 (UTC)

 * I'm not sure why Matlab is mentioned at all. It doesn't seem to add anything, so I removed that sentence.
 * On my computer, the R matrix returned by Matlab has minus signs on the diagonal just like Octave. That's not so surprising because both of them use the same routines (LAPACK) to do the factorization. I guess different versions of Matlab yield different results and that's why the article had R with the opposite sign. -- Jitse Niesen (talk) 16:58, 27 October 2007 (UTC)

total flop counts
Does someone know the total flop counts for the various QR algorithms (in particular, for a general m x n matrix, not necessarily square)?

Also, this link at the bottom of the page is bad -- maybe someone knows the new URL? The failed URL is http://www.cs.ut.ee/~toomas_l/linalg/lin2/node5.html Lavaka (talk) 16:18, 4 April 2008 (UTC)

 * I'll answer my own question, thanks to Golub and Van Loan's "Matrix Computations". The setup is: A is a m x n matrix, with m >= n.  I assume that if m < n, then everything still holds if you swap m and n.  The flop counts for various algorithms are:
 * "Householder QR": $$2n^2(m-n/2)$$
 * "Givens QR": $$3n^2(m-n/3)$$
 * "Hessenberg QR via Givens" (i.e. A is in Hessenberg form): $$2n^2$$
 * "Fast Givens QR": $$2n^2(m-n/3)$$
 * "Modified Gram-Schmidt": $$2mn^2$$

 * So, if m << n, then it looks like Modified Gram-Schmidt is the winner. 131.215.105.118 (talk) 19:10, 4 April 2008 (UTC)

Why writing transposed Qi instead of Qi?
Why in the
 * $$ Q = Q_1^T Q_2^T \cdots Q_t^T, $$

there is: $$ Q_i^T $$ instead of simply: $$ Q_i $$? After all $$ Q_i^T = Q_i $$ because it's symmetric, isn't it?! —Preceding unsigned comment added by Milimetr88 (talk • contribs) 16:27, 6 December 2009 (UTC)

No... $$ Q_i^T = Q_i^{-1} $$ — Preceding unsigned comment added by 131.211.53.159 (talk) 14:05, 13 December 2016 (UTC)

Using Householder reflections O(n^3) incorect
If using the trick (and not explicitly forming Q) $$A_{k+1} = A_k - 2 \cdot v_k \cdot v_k^T$$ Then the algorithm is $$O(n^3)$$

However, the current explanation loops over an n-by-n matrixm multiplication n times, making the given algorithm $$O(n^4)$$ ($$O(n^3) \cdot n = O(n^2)$$, yes you can do matrix multiplication faster than $$O(n^3)$$, but its still > $$O(n^2)$$ making the algorithm still > $$O(n^3)$$).

Can you even form the Q matrix of qr factorization by householder reflections in $$O(n^3)$$ time? —Preceding unsigned comment added by 139.222.243.106 (talk) 22:51, 1 November 2010 (UTC)

Example is grossly incorrect
The example given is just wrong. Using R, I get this:

> x      V1  V2  V3    1 12 -51   4 2 6 167 -68    3 -4  24 -41

> qr.R(qr(x)) V1  V2  V3    [1,] -14  -21  14 [2,]  0 -175  70    [3,]   0    0 -35

Testing the result given in the example gives this:

> as.matrix(q) %*% as.matrix(r) V1       V2         V3    [1,] 11.99996 -50.98650   4.002192 [2,] 5.99998 166.97736  24.000335    [3,]  3.99994 -67.98786 -40.998769    > q            V1      V2      V3    1 -0.85714  0.3110 -0.4106 2 -0.42857 -0.8728 0.2335    3 -0.28571  0.3761  0.8814    > r       V1        V2       V3    1 -14   -8.4286  -2.0000 2  0 -187.1736 -35.1241    3   0    0.0000 -32.1761

Clearly the example is screwed up just after the first step (the first column of Q is correct as is the first element of R). — Preceding unsigned comment added by 67.160.196.149 (talk) 08:23, 19 January 2012 (UTC)

 * The example is correct. The QR decomposition is not unique.  Q is orthogonal, R is upper triangular, and Q*R = A. What part worries you?  You even used a calculator to prove the example was correct. JackSchmidt (talk) 19:24, 19 January 2012 (UTC)

I and others prefer forcing the R factor diagonal to be positive real which reduces range of different solutions. — Preceding unsigned comment added by 149.199.62.254 (talk) 15:57, 17 May 2016 (UTC)

Inconsistencies in matrix dimension for rectangular matrices
The given dimensions of the matrices in the "Rectangular matrix" paragraph seem inconsistent to me. If, e.g., R is n by n as stated in the first sentence, then its bottom (m-n) rows are not zero. If "Q1 is m×n, Q2 is m×(m−n)", then Q should be m by m and not "an m×n unitary matrix Q". Am I wrong? — Preceding unsigned comment added by 195.176.179.210 (talk) 12:54, 15 February 2012 (UTC)
 * Well spotted. That was the result of this edit of 5 February, so not long ago. I've just undone it. Hope that section makes more sense now. Qwfp (talk) 15:28, 15 February 2012 (UTC)

Origin of the name?
It would be interesting from a historical point of view (of just for curiosity's sake) to know who first used the letters "QR", and why (if any special reason exists). — Preceding unsigned comment added by Boriaj (talk • contribs) 07:57, 27 July 2012 (UTC)
 * The QR algorithm article has some history in its lead and its history section. It appears that QR decomposition hadn't been invented prior to its use in the QR algorithm, though I could be wrong. The Francis (1961) paper referenced there says (bottom left of first page): "... the QR transformation, as I have (somewhat arbitrarily) named this modification of Rutishauer's algorithm...", so it appears that John G.F. Francis is responsible for naming the orthogonal/unitary matrix Q. The R is an obvious name for a right triangular matrix (more often referred to as an upper triangular matrix these days, it seems). Qwfp (talk) 12:22, 27 July 2012 (UTC)

Stability of inverse using QR decomposition
In the section "Using for solution to linear inverse problems", there is the sentence Compared to the direct matrix inverse, inverse solutions using QR decomposition are more numerically stable as evidenced by their reduced condition numbers [Parker, Geophysical Inverse Theory, Ch1.13].

That particular referenced book is not available to me, so I don't know what's written there. The argument by itself however is clearly wrong, as if $A = QR$, then $\cond(A) = \cond(R)$ (at least in the 2-norm). Hence, the condition number of the linear system one must solve (now involving R) has not changed. There might be still advantages due to more subtle issues (though I doubt that the advantage would be big).

Can anybody say more about the statement? I'd actually be in favor of removing it completely, rather than having it here in its current form

Wmmrmchl (talk) 14:10, 10 December 2012 (UTC)

 * The referenced text discusses this in terms of the condition numbers of $$R_1$$ versus $$\Gamma = A^T A$$ (in this article's notation; the original uses $$G$$ instead of $$A$$). Specifically, $$\text{cond}(R_1) = \|R_1\|_2 \|R_1^{-1}\|_2 = \sqrt{\lambda_{max}(\Gamma) \lambda_{max}(\Gamma^{-1})} = c$$, where $$\lambda_{max}(M)$$ indicates the largest eigenvalue of a matrix $$M$$. Contrast this with $$\text{cond}(\Gamma) = \sqrt{\lambda_{max}(\Gamma^2) \lambda_{max}(\Gamma^-2)} = c^2$$. Therefore, least-squares solutions computed using the QR transform, requiring solving $$R_1 X = B$$ can potentially be more accurate than those relying on solving $$(A^T A) X = B'$$ (for some $$B$$ and $$B'$$). The sentence in question really should be reworded. Aldebrn (talk) 12:45, 18 June 2013 (UTC)

Sign of alpha in householder example
The part about householder says: u = x - alpha * e1. In the example below, alpha is -14 and x is [12,6,-4]^T. 12 - (-14) is 26. So according to the above, u should be [26,6,-4]^T. However, it's [-2,6,-4]^T in the rest of the example, so alpha was added rather than subtracted. It still seems to work though, it seems to work with both. Still, why is the example inconsistent with the article? Might be worth explaining. Thanks! 85.2.5.221 (talk) 00:42, 6 January 2014 (UTC)

Is QR decomposition basis-dependent?
QR decomposition is basis-dependent, yes? --VictorPorton (talk) 23:07, 25 April 2014 (UTC)

Remark about "Using for solution to linear inverse problems"
The first paragraph states that QR decomposition has a lower condition number than direct matrix inverse. However, "condition number" is a property of the problem (solving a linear system) and not of the method. So AFAIK, this sentence has no sense. Somebody knows what is the actual reason why QR decomposition is more "numerically stable"? — Preceding unsigned comment added by Alexshtf (talk • contribs) 12:02, 17 August 2014 (UTC)

This statement should be made in reference to another method of solving Ax=b such as LU decomposition. If you are solving linear equations Ax=b with LUx = b versus QRx=b then the condition number of L and Q are relevant to the accuracy of the solution. L can have a large condition number; however, Q is orthogonal and thus has condition number 1. — Preceding unsigned comment added by 128.61.55.207 (talk) 19:36, 16 February 2016 (UTC)

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Alternative QR decomposition for rectangular matrix
In our linear algebra course we used the term QR decomposition of a m×n matrix to mean Q (of dimensions m×n) with orthonormal columns and upper triangular R (of dimensions n×n). This would be A=Q₁R₁ in the article's section Rectangular matrix. However, I don't know how to edit the section to mention that QR decomposition can sometimes mean Q₁R₁. If I should edit it at all. Michal Grňo (talk) 03:53, 17 June 2019 (UTC)

Q is not always orthogonal
At the very beginning of the page, there is a mistake: "In linear algebra, a QR decomposition, also known as a QR factorization or QU factorization, is a decomposition of a matrix A into a product A = QR of an orthogonal matrix Q and an upper triangular matrix R." I think it's worth noting that Q is only orthogonal if it's square. Also it can be changed to "matrix with orthonormal columns Q" — Preceding unsigned comment added by Astadnik (talk • contribs) 16:30, 18 October 2021 (UTC)

Is Someone Willing to Include a Year of Publication for a paper on QR Factorization?
It would be useful to know how old $$QR$$ factorization is.

For example, when studying algorithms for the maximum flow problem, we could say that...

 * 1) first came the Ford–Fulkerson algorithm (1956)
 * 2) second came the Edmonds–Karp algorithm (1970)
 * 3) third came the Preflow–push algorithm (1974)
 * 4) fourth came the Chen, Kyng, Liu, Peng, Gutenberg and Sachdeva's algorithm (2022)

The Maximum Flow problem is not related to $$QR$$ factorization of matrices.

However, I was hoping that the article on $$QR$$ factorization could be edited to say when QR factorization was first published. If someone published it even earlier, that is good, the Wikipedia page is openly editable by anyone, and we can amend the official date of publication and name of the author.

The year of publication is useful for determining what method was popular before $$QR$$ factorization and what method of solving linear systems computationally was popular after $$QR$$ factorization.

People are always publishing faster, more efficient approaches to solving these problems.

At the time of my writing, the this article on $$QR$$ factorization does not say anything about when the method was first published. In lieu of date of first publication, we could cite the older method or approach (the proceeding popular technique) and maybe also cite one of the newer techniques. That way, the position of $$QR$$ factorization in time is available to the reader.

Usually, the old approaches were easy to understand, but take a long time to computer.

The old techniques for matrix decomposition are good for undergraduate students.

The newer techniques run quickly on GPUs (graphics processing units), but are too complicated for most undergraduate students to understand.

We must guide people through the progression of different techniques for solving linear systems through time, so that students see the easy-to-understand stuff first, and they see the complicated cutting-edge research sometime later. 174.215.16.174 (talk) 16:50, 6 June 2023 (UTC)

Clarification needed on assumptions in ‘Cases and definitions’ Section
At the end of the subsection "square matrix" there is the following statement: “If A has n linearly independent columns,[...] More generally, the first k columns of Q form an orthonormal basis for the span of the first k columns of A for any 1 ≤ k ≤ n”. However, this is not generally true. It assumes that the first k columns of A are linearly independent. Shouldn't this be stated explicitly? Simonedl (talk) 02:54, 12 January 2024 (UTC)

title: Talk:QR decomposition


text:
Category talk:Operation Overlord

There seems to be some inconsistency here. The articles on the beaches are under Category:Operation Neptune while the contemporaneous aiborne operations are under Operation Overlord. I'm going to try some moves to make things at least consistent. DJ Clayworth 20:15, 13 Apr 2005 (UTC)

See the codenames section of Operation Overlord for an explanation of the operation names. DJ Clayworth 20:17, 13 Apr 2005 (UTC)

title: Category talk:Operation Overlord


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Licensing
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text:
William Whittingham Lyman Jr.

William Whittingham Lyman Jr. (January 3, 1885 – November 8, 1983), also known as Jack Lyman, was an American writer and academic, primarily in the field of Celtic studies.

Life and work
Lyman was born at Napa County, California, the son of William Whittingham Lyman and Mrs Sarah A. Nowland, and the grandson of Theodore Benedict Lyman. His father built the Lyman winery, now known as the El Molino winery. In 1905, while an undergraduate at University of California, Berkeley, he was convinced by Charles Mills Gayley to achieve an academic major in English literature. Upon completion of his Master's degree, Gayley arranged for him to receive a university fellowship to travel to the University of Oxford to study Celtic languages with Sir John Rhys. After a year at Oxford, Lyman spent two years at Harvard University studying the Irish language. He returned to the University of California, Berkeley to take up a post as Instructor in Celtic (then a tenure-track position) within the English department in 1911-1912. In the same year, Celtic appears on the list of approved majors in the College of Letters and Science and in the following year Lyman is named also as "Graduate Adviser" in Celtic. There he remained until 1922, whereupon he moved to Southern California and taught English at Los Angeles City College until his retirement. After retirement he and his family moved back to the family home near the Bale Grist Mill north of St. Helena.

Commenting on his long life, Ruth Witt-Diamant declared him to be the "oldest living poet".

He was a poet of some renown, as mentioned by Josephine Miles: "In a legendary time in the Greek Theater in Berkeley at the end of the first world war, poets gathered around the visitor Witter Bynner with a great sense of inventiveness and praise. Names I have heard from that time were Genevieve Taggard, Hidegarde Flanner, Eda Lou Walton, David Greenhood, Jack Lyman."

On January 1, 1921, he married the poet Helen Hoyt.

As editor

 * (With Dudley Chadwick Gordon and Vernon Rupert King). Today's Literature: An Omnibus of Short Stories, Novelettes, Poems, Plays, Profiles, and Essays. New York: American Book Company. 1935. ISBN 0-8486-6628-3

Unpublished memoirs
His typescript memoirs are held at the University of California, Berkeley, Bancroft Library and contain comments on many of his faculty colleagues as well as the circumstances of his departure from the university.

title: William Whittingham Lyman Jr.


text: Category:New Jersey State Legislators

title: Category:New Jersey State Legislators