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FC St. Pauli

Fußball-Club St. Pauli von 1910 e.V., commonly known as simply FC St. Pauli, is a German professional football club based in the St. Pauli district of Hamburg. The team will compete in the Bundesliga in the 2024–25 season following promotion.

The football department is part of a larger sports club that also has departments in rugby (FC St. Pauli Rugby), baseball, bowling, boxing (FC St. Pauli Boxen), chess, cycling, handball, roller derby (Harbor Girls Hamburg), skittles, softball, and table tennis and since 2011 Marathon. Until the end of 2013, the club also had a department in American football, but it was dissolved because it lacked the youth team required in order to hold a men's team. As of April 2023, FC St. Pauli has 30,400 members.

The men's professional football team dropped down to the Regionalliga in 2003, at that time the third highest football division in Germany and remained there for four years. In 2007, they won promotion back to the 2. Bundesliga, the second highest division in Germany and in 2010, they were promoted to the Bundesliga, the highest division. After relegation, since the 2011–12 season they have played in 2. Bundesliga until the 2023–24 season when they were promoted back to the Bundesliga.

FC St. Pauli has a cross-city rivalry with Hamburger SV; the matches between the two are known as the Hamburger Stadtderby or simply Derby. The club also has a more recent rivalry with Hansa Rostock.

Although the club has been only modestly successful, it is widely recognised for its distinctive social culture and has a large popular following as one of the country's "Kult" clubs. FC St. Pauli supporters are strongly identified with their support of left wing politics.

Early years
The club began its existence in 1899 as a loose, informal group of football enthusiasts within the Hamburg-St.Pauli Turn-Verein 1862. This group did not play its first match until 1907, when they faced a similar side assembled from the local Aegir swimming club. Officially established on 15 May 1910, the club played as St. Pauli TV in the Kreisliga Groß-Hamburg (Alsterkreis) until 1924, when a separate football side called St. Pauli was formed. The team played as an undistinguished lower-to-mid table side until making their first appearance in 1934 in the top-flight Gauliga Nordmark, 1 of 16 premier level divisions created in the re-organization of German football that took place under the Third Reich. They were immediately relegated, but returned to the top flight in 1936. Relegated again in 1940, St. Pauli re-appeared in the Gauliga Hamburg in 1942, and played there until the end of World War II.

Post-war football
After the war, the club resumed play in the Oberliga Nord in 1947. A second-place finish in the 1947–48 season led St. Pauli to its first appearance in the national championship rounds. They advanced as far as the semi-finals, where they were knocked out 2–3 by eventual champions 1. FC Nürnberg. The club continued to play well throughout the early 1950s, but were unable to overtake rivals Hamburger SV, finishing in second place in five of the next seven seasons, and going out in the early rounds in each of their championship-round appearances from 1949 to 1951. In the late 1950s and into the early 1960s, St. Pauli were overtaken by rivals such as Werder Bremen and VfL Osnabrück, but finished fourth a number of times.

Promotion to the Bundesliga
In 1963, the Bundesliga – West Germany's new top-flight professional league – was formed. Hamburger SV, Werder Bremen, and Eintracht Braunschweig joined the new circuit as the top-finishers from the Oberliga Nord, while FC St. Pauli found themselves in the second-tier Regionalliga Nord. That year, the club signed Guy Acolatse, who became the first Black professional footballer to play in Germany.

Nearly a decade-and-a-half of frustration followed. St. Pauli won their division in 1964, but finished bottom of their group in the promotion play-off round. They won their next Regionalliga Nord title in 1966, but, while they performed far better in the play-offs, still could not advance to the top-flight, losing to Rot-Weiss Essen on goal difference, having conceded two more goals. Division championships in 1972 and 1973, and runner-up finishes in 1971 and 1974, were each followed by promotion-round play-off disappointment.

The success of the Bundesliga, and the growth of professional football in West Germany, led to the formation of the 2. Bundesliga in 1974. St. Pauli was part of the new second-tier professional circuit in the 2. Bundesliga Nord and, in 1977, they advanced to the top flight as winners of their division. The team survived for one season at the highest level in the Bundesliga.

The club's return to the 2. Bundesliga Nord was also short-lived. On the verge on bankruptcy in 1979, they were denied a license for the following season and were sent down to the Oberliga Nord (III). Strong performances that set the team atop that division in 1981 and 1983 were marred by poor financial health. By 1984, the club had recovered sufficiently to return to the 2. Bundesliga, overtaking Werder Bremen's amateur side, who, despite finishing two points ahead of St. Pauli, were ineligible for promotion.

"Kult" phenomenon
It was in the mid-1980s that St. Pauli's transition from a standard traditional club into a "Kult" club began. The club was also able to turn the location of its ground in the dock area part of town, near Hamburg's famous Reeperbahn – centre of the city's night life and its red-light district – to its advantage. An alternative fan scene slowly emerged, built around left-leaning politics, social activism and the event and party atmosphere of the club's matches. St. Pauli became the first team in Germany to officially ban right-wing nationalist activities and displays in its stadium during a period of fascist-inspired football hooliganism across Europe. In 1981, the team was averaging small crowds of only 1,600 spectators, but by the late 1990s they were frequently selling out their entire 20,000-capacity ground.

Supporters adopted the skull and crossbones as their own unofficial emblem in the 1980s. Although precise details are uncertain, the story goes that named "Doc Mabuse", a singer in a Hamburg punk band, nailed a Jolly Roger flag to a broomstick and brought it to the Millerntor-Stadion. The original flag featured a skull with pirate eyepatch. Inspired, other fans began to bring similar flags to matches. In 1989, Hamburg screenprinter Steph Braun created an image combining a detailed representation of a skull (taken from an anatomy textbook) with the words "ST. PAULI" underneath. Intended to represent the area itself, and sold in various record shops around the district, Braun's graphic was adopted by St. Pauli fans and came to be seen as specifically associated with the club.

In the early 1990s, the media in Germany began to recognize the Kult-image of the club, focusing on the punk part of the fan-base in TV broadcasts of the matches. By this time, the media also started to establish nicknames like "Freibeuter der Liga" ("Buccaneers of the League") as well as the satirical "das Freudenhaus der Liga" ("Brothel of the League", literally "House of Joy"). The club itself realized the potential and in September 1999 bought the rights to Steph Braun's skull and crossbones graphic, making it an official club logo.

St. Pauli moved in and out of the Bundesliga over the course of the next dozen years: the club was narrowly relegated to the Oberliga in the 1984–85 season, but won the 1985–86 championship and returned to 2. Bundesliga. Two increasingly strong years followed, resulting in promotion and three seasons in the Bundesliga, from 1988 to 1991. Four seasons followed in 2. Bundesliga, and then another two in the Bundesliga in 1995 to 1997, before another return to the 2. Bundesliga.

Into the new millennium
Until 2010, the club's most recent appearance in the top-flight had been a single-season cameo in 2001–02. A win against Bayern Munich, the reigning Intercontinental Cup winners, led to the popular "Weltpokalsiegerbesieger" ("World Club Champion beaters") shirts. However, the team finished last in the league, partly because the management did not trust the team which surprisingly won the promotion in 2001, but rather spent the additional money from Bundesliga TV contracts and advertisements on expensive but disappointing players. After the relegation to the 2. Bundesliga, only a skeleton of the successful 2001 team remained. The 2002–03 season ended up in chaos, with the team fighting relegation (ultimately in vain) from the very beginning, various coaches departing and other problems internal to the club.

With the club almost bankrupt again and the less-lucrative Regionaliga Nord (III) looming, the club began its fund-raising activities, the so-called "Retteraktion". They printed t-shirts with the club's crest surrounded by the word Retter ("rescuer/saviour") and more than 140,000 were sold within six weeks. They also organized a lucrative benefit game, against Bayern Munich, to raise funds to save the club.

The club has also been active in terms of charity and in 2005 the club, the team and the fans initiated the Viva con Agua de Sankt Pauli campaign, which collects money for water-dispensers for schools in Cuba, for clean water in Rwanda et cetera.

During the 2005–06 season, the team enjoyed unprecedented success in the DFB-Pokal, with wins over Burghausen, VfL Bochum and, significantly, Bundesliga sides Hertha BSC and, in the quarter-finals on 25 January 2006, Werder Bremen. Their 3–1 victory in front of a sell-out Millerntor crowd, and their subsequent place in the DFB Cup semi-final, netted the club approximately €1 million in TV and sponsorship money, going a long way to saving the club from immediate financial ruin.

St. Pauli finally went out of the cup to Bayern Munich on 12 April, going down 3–0 with a goal from Owen Hargreaves and two from Claudio Pizarro. Coincidentally, Bayern were also St. Pauli's opponents and dispatchers in the first round of the following season's cup.

After success in the 2006–07 season, the team was promoted to the 2. Bundesliga. After defeating SpVgg Greuther Fürth in the 2009–10 season, the team secured promotion back to the Bundesliga for the 2010–11 season. On 16 February 2011, during the 2010–11 season and for the first time since 1977, St. Pauli defeated their bitter cross-city rivals Hamburger SV away at the Volksparkstadion courtesy of a Gerald Asamoah goal. The team, however, finished the domestic season in last place, resulting in their relegation to the 2. Bundesliga for the 2011–12 season. Since then, the club remained in the 2. Bundesliga, finishing fourth in 2011–12 but declining in results in the years to come, until they earned promotion back to the Bundesliga in the 2023–24 season.

League

 * 2. Bundesliga (II)
 * Champions: 1977(Nord), 2023–24
 * Runners-up : 1987–88, 1994–95, 2009–10
 * Regionalliga Nord (II)
 * Champions : 1963–64, 1965–66, 1971–72, 1972–73
 * Regionalliga Nord (III)
 * Champions : 2007
 * Oberliga Nord (III)
 * Champions : 1981, 1983, 1986
 * Stadtliga Hamburg (I)
 * Champions : 1947

Cup

 * Hamburger Pokal
 * Winners: 1986, 2004, 2005, 2006

Reserve team

 * Oberliga Hamburg/Schleswig-Holstein (IV)
 * Champions: 1995, 1999, 2003
 * Oberliga Hamburg (V)
 * Champions: 2011
 * Hamburger Pokal
 * Winners: 1998, 2001, 2008, 2009, 2010

Colours and kit
The colours of FC St. Pauli are brown and white, and to a lesser extent red. Black is also common among fans and on third kits.

The club has worn brown and white since 1910, when it joined the Northern German Football Association (Norddeutscher Fußball-Verband). These early uniforms were made up of brown shirts and socks with white shorts. Some time between the 1920s and 30s, the club took on what would become its traditional look, namely a white shirt, brown shorts and brown socks with a white turnover. From early on in the club's history until the 1990s, the club readily wore its brown change shirts at home, even during such games as those against rivals HSV, who also wear white shirts.

During the 1960s, the club introduced white socks which regularly alternated with plain brown socks. A motif was used on the club shirt for the first time in 1968, when the club donned stripes, and, in the 1970s, various other motifs adorned the club's first and second-choice shirts. In the 1976–77 season, St. Pauli began wearing Adidas kits, marking the end of a period of often experimental shirts, and this traditional look continued when the club started wearing Puma kits in the 1980s. For the 1985–86 season, the club sported an all-white Puma kit, which would be worn for four consecutive seasons before some brown details returned to the shirt. However, the Kiezkicker would continue to wear these predominantly white kits until 1993.

At this point, the club would return to a kit based on a white-brown-white scheme, but in a more contemporary style, often incorporating patterns. The Reusch kits of 1994–96 and 1996–97 had hoops and stripes respectively, while Kappa would also produce a striped kit in 2000–01. The Italian brand would provide a set of kits for the 2001–02 and 2002–03 seasons in which the shirt, shorts, and socks were all available in white and brown, meaning that the team would wear a different combination each game, reminiscent of the club's look between the 1960s and 1980s. During the 2001–02 season, the team would frequently make recourse to the previous year's all-black away kit.

In 2003–04, the club would once again sport a white shirt with brown sleeves, manufactured by Stanno. However this is, as of the 2022–23 season, the last time the club has donned its traditional kit. While the club's uniform for the 2005–06 season would combine a light shirt and brown shorts, St. Pauli would wear an all-black kit during the following campaign (marking the first time that neither of the club's colours were present on the home kit). From the 2007–08 season, St. Pauli has worn an all-brown home kit on all but three occasions, one of which saw the team return to a striped shirt, while in the two other instances the team wore white shorts.

Between 2019–20 and 2021–22, LGBT details were integrated into the third shirt. In 2020, having sought a kit supplier who would meet their ecological and ethical requirements since 2018, St. Pauli founded their own brand, Di!Y ("Do it. Improve Yourself"). From the 2021–22 season, St. Pauli have worn kits made in-house by Di!Y.

Recent seasons
The club's recent seasons:

Supporters
St. Pauli enjoys a certain fame for the left-leaning character of its supporters: most of the team's fans regard themselves as anti-racist, anti-fascist, anti-homophobic and anti-sexist, and this has, on occasion, brought them into conflict with neo-Nazis and hooligans at away games. The organization has adopted an outspoken stance against racism, fascism, sexism, and homophobia and has embodied this position in its constitution. Team supporters traditionally participate in demonstrations in the St. Pauli district of Hamburg, including those over squatting or low-income housing, such as the Hafenstraße and Bambule. The centre of fan activity is the Fanladen St. Pauli. St. Pauli has a supporters group in England, Yorkshire St. Pauli.

Partly because of shared leftist political views, St. Pauli fans have strong relationships with supporters of Bayern Munich (Schickeria), Werder Bremen, Ternana, Club Universidad Nacional, Unione Calcio Sampdoria, Rayo Vallecano, SV Babelsberg 03, Hapoel Tel Aviv, AEK Athens (Original 21), Olympique Marseille, Celtic,    Venezia, Cosenza, Standard Liège and Clapton CFC In the past they also had a friendship with the fans of Bohemians 1905, Partizan Minsk and F.C. United of Manchester, the latter of whom were invited to the Millerntor for a friendly game to celebrate St. Pauli's centenary. The group Ultrá Sankt Pauli also has a special friendship with the group Schickeria München, from the ultras scene of Bayern Munich. A banner of the Schickeria München is occasionally displayed at the Millerntor-Stadion, and a flag of the Ultrá Sankt Pauli – sporting a picture of Che Guevara – has been displayed at the Allianz Arena. Both Ultrá Sankt Pauli and Schickeria München are members of Alerta Network, an international anti-fascist network of supporter groups.

The club prides itself on having the largest number of female fans in all of German football. In 2002, advertisements for the men's magazine Maxim were removed from the Millerntor-Stadion in response to fans' protests over the adverts' sexist depictions of women. In 2011, the club banned lap dancers from performing during match before guests at a corporate suite, following fans' complaints. The suite belonged to local lap dance club Susies Show Bar.

St. Pauli is also a worldwide symbol for punk and related subcultures. The skull and crossbones logo and the team's brown and white football jerseys have often been worn by international artists such as the bands Asian Dub Foundation, Gaslight Anthem and Panteon Rococo. The KMFDM frontman and Hamburg native Sascha Konietzko is a recognisable St. Pauli fan, at one point placing a huge picture of a fist smashing a swastika on his band's main page, with the caption "St. Pauli Fans gegen Rechts!" ("St. Pauli fans against the Right") underneath it. American punk band Anti-Flag can be seen wearing St. Pauli shirts in numerous music videos for their album American Fall. Another notable supporter and sponsor is Andrew Eldritch, lead singer of band The Sisters of Mercy. On his 2006 "Sisters Bite The Silver Bullet"- tour, Eldritch wore the famous skull and crossbones shirt. Georg Holm, the bassist of the Icelandic post rock band Sigur Rós, has performed at several festivals wearing a St. Pauli shirt. Alex Rosamilia, the guitarist for The Gaslight Anthem, frequently wears a St. Pauli hat and hoodie and displays a flag of the club's logo in front of the speakers of his guitar amp. Editors guitarist and synthesiser player Chris Urbanowicz frequently wears the skull and crossbones t-shirt. Dave Doughman, the singer for Dayton, Ohio's Swearing at Motorists, who has been spotted in concert with the skull and crossbones on his guitar and amplifier, moved to St. Pauli in 2010. Bad Religion played a charity match against St. Pauli's third team in 2000. German musicians who are fans include: Fettes Brot, Die Ärzte singer/drummer/songwriter Bela B., Kettcar, Tomte, and many other bands, most of them underground.

Several bands have also made music directly related to St. Pauli: The Norwegian punk rock band Turbonegro recorded a special version of their song "I Got Erection" with re-worked German lyrics for St. Pauli. In 2009, Italian ska combat-folk punk band Talco from Marghera, Venice, wrote the song "St. Pauli". The team has since used the song as an anthem and Talco has played a number of concerts at Millerntor-Stadion. Glasgow band The Wakes have also played the Millerntor, having written "The Pirates of the League" about the club. Also, British band Art Brut has written a song about the club called "St Pauli" which is featured on their album It's a Bit Complicated. In 2010, FC St. Pauli celebrated its 100th anniversary. For the occasion, the fan club 18auf12 recorded the song "Happy Birthday St Pauli, One Hundred Beers for You", with words and music by Henning Knorr and Christoph Brüx.

The Canadian punk rock band The Pagans of Northumberland recorded a song in 2014 called simply "St Pauli" for their first 7-inch detailing their love of the club and its supporters around the world.

In January 2017, FC St. Pauli announced an extensive co-operation with Irish-American Celtic punk band Dropkick Murphys. The co-operation includes a strictly limited seven-inch picture disc of the song "You’ll Never Walk Alone" recorded by the band, and new club merchandise labeled "You’ll Never Walk Alone", sporting both the club and the band.

When the team played in Germany's 2. Bundesliga, their home fixtures at the Millerntor used to average greater attendances than any other team and often exceeded turnouts for second division teams. As of the 2011–12 season, St. Pauli was the only team that has close to 100% in average home attendance.

In 2006, St. Pauli had more season ticket holders than many Bundesliga teams. One study estimated that the team had roughly 11 million fans throughout Germany, making the club one of the most widely recognised German sides. The number of official fan clubs in 2011 passed 500, which was an increase of 300 over three years.

In January 2020, the club's famous skull and crossbones flag was listed by the United Kingdom's counter-terrorism police in a guide sent to public sector workers, to notice potential extremism, prompting a backlash from St. Pauli's Welsh defender James Lawrence.

Club culture
St. Pauli opens its home matches with "Hells Bells" by AC/DC, and after every home goal "Song 2" by Blur is played.

The former club president Corny Littmann, long active in German theatre and head of the Schmidt Theater on the Reeperbahn, is openly gay.

St. Pauli have made pre-season appearances at Wacken Open Air, a heavy metal festival, several times.

The club hosted the 2006 FIFI Wild Cup, a tournament made up of unrecognised national football teams like Greenland, Tibet and Zanzibar. They participated as the "Republic of St Pauli".

In 2008, Nike commemorated the club with two exclusive Dunk shoes, both released in limited quantities. The High Dunk (featuring a black colorway, and the skull and crossbones symbol) was released to all countries throughout Europe, with only 500 pairs produced. The Low Dunk (featuring a smooth white colorway, and holding the team's logo impregnated in the side panel leather) was released only to shops in Germany, Switzerland and Austria, with only 150 pairs produced.

Fundamental Principles
St. Pauli were the first club in Germany to integrate a set of Fundamental Principles (Leitlinien) to dictate how the club is run, passed by an overwhelming majority at the club's annual general meeting in 2009.

The first five Principles states that:

– "In its totality, consisting of members, staff, fans and honorary officers, St Pauli FC is a part of the society by which it is surrounded and so is affected both directly and indirectly by social changes in the political, cultural and social spheres."

– "St Pauli FC is conscious of the social responsibility this implies, and represents the interests of its members, staff, fans and honorary officers in matters not just restricted to the sphere of sport."

– "St Pauli FC is the club of a particular city district, and it is to this that it owes its identity. This gives it a social and political responsibility in relation to the district and the people who live there."

– "St Pauli FC aims to put across a certain feeling for life and symbolises sporting authenticity. This makes it possible for people to identify with the club independently of any sporting successes it may achieve. Essential features of the club that encourage this sense of identification are to be honoured, promoted and preserved."

– "Tolerance and respect in mutual human relations are important pillars of the St Pauli philosophy."

Stadium
The home venue of the FC St. Pauli is the Millerntor-Stadion. Work on the stadium began in 1961, but its completion was delayed until 1963 as there was initially no drainage system in place, making the pitch unplayable after rain. It originally held 32,000 supporters, but the capacity was later reduced for safety reasons.

In 1970, the stadium was renamed the Wilhelm Koch-Stadium in honour of a former club president. However, this name became highly controversial when it was discovered by historian René Martens that Wilhelm Koch had been a member of the Nazi Party from 1937 to 1945, as stated in his 1997 book "FC St. Pauli - You'll never walk alone". After protests by fans, the name was changed back to Millerntor-Stadion in 1999.

A total redevelopment began in 2006. The final phase of the redevelopment work ended with the completion of the new north stand in July 2015. The stadium is since then permitted for a capacity of 29,546 spectators of which 16,940 are standing and 12,606 are seated.

The stadium is located next to the Heiligengeistfeld, and is overlooked by the infamous Flak Tower IV to the north and a building of the Deutsche Telekom to the south. It can easily be reached with the Hamburg U-Bahn line U3 (St. Pauli Station and Feldstraße Station).

International players
The following international players have also played for St. Pauli:

 * 🇳🇬 Yakubu Adamu
 * 🇧🇯 Moudachirou Amadou
 * 🇩🇪 Gerald Asamoah
 * 🇧🇦 Zlatan Bajramović
 * 🇹🇷 Deniz Barış
 * 🇨🇦 Jonathan Beaulieu-Bourgault
 * 🇩🇪 Alfred Beck
 * 🇳🇴 Morten Berre
 * 🇲🇦 Mourad Bounoua
 * 🇺🇸 Paul Caligiuri
 * 🇵🇦 Armando Cooper
 * 🇺🇸 Cory Gibbs
 * 🇨🇲 Marc Gouiffe à Goufan
 * 🇺🇸 Joe Gyau
 * Heino Hansen
 * 🇫🇮 Ari Hjelm
 * 🇨🇦 Junior Hoilett
 * 🇹🇷 Uğur İnceman
 * 🇳🇬 Henry Isaac
 * Ivan Klasnić
 * Ante Budimir
 * Ivo Knoflíček
 * Ján Kocian
 * 🇩🇪 Max Kruse
 * 🏴 James Lawrence
 * 🇮🇷 Alireza Mansourian
 * 🇺🇸 Michael Mason
 * Frantz Mathieu
 * 🇦🇱 Artur Maxhuni
 * 🇨🇩 Michél Mazingu-Dinzey
 * 🇩🇪 Karl Miller
 * 🇯🇵 Kazuo Ozaki
 * 🇳🇴 Tore Pedersen
 * Miguel Francisco Pereira
 * 🇦🇹 Michael Gregoritsch
 * Fafà Picault
 * 🇷🇺 Nikolai Pisarev
 * 🇺🇦 Andriy Polunin
 * 🇩🇪 Ingo Porges
 * 🇩🇪 Christian Rahn
 * 🇷🇺 Yuri Savichev
 * 🇩🇪 Helmut Schön
 * Feiz Shamsin
 * 🇨🇼 Rocky Siberie
 * 🇵🇱 Waldemar Sobota
 * 🇨🇦 Ive Sulentic
 * 🇬🇭 Charles Takyi
 * 🇨🇬 Jean-Clotaire Tsoumou-Madza
 * Niels Tune-Hansen
 * 🇨🇳 Yang Chen
 * 🇵🇪 Carlos Zambrano
 * 🇯🇵 Ryo Miyaichi
 * Sáu Dũng

Greatest ever team
In 2010, as part of the club's celebration of its 100th anniversary, fans voted the following players as the best in the club's history:

 * 🇩🇪 Klaus Thomforde
 * 🇩🇪 André Trulsen
 * 🇩🇪 Walter Frosch
 * 🇩🇪 Karl Miller
 * 🇩🇪 Dirk Dammann
 * 🇨🇩 Michél Mazingu-Dinzey
 * 🇩🇪 Thomas Meggle
 * 🇩🇪 Jürgen Gronau
 * 🇩🇪 Harald Stender
 * 🇩🇪 Peter Osterhoff
 * 🇩🇪 Franz Gerber

Player records
Note: FC St. Pauli did not play in the Bundesliga or the 2. Bundesliga until 1974, 1979–1984, 1985–86 and 2003–2007. Statistics are correct as of 22 June 2022.

Most appearances overall
BL = Bundesliga, 2.BL = 2. Bundesliga, OLN = Oberliga Nord (1947–1963), RLN = Regionalliga Nord (1963–1974) OtL = Other leagues: Oberliga Nord (1974–1994), Regionalliga Nord (since 1994) Cup = DFB-Pokal, OtC = Other competitions: German championship (1947–1951), Relegation play-offs, Hamburg Cup

Top goalscorers in Bundesliga and 2. Bundesliga
Numbers in brackets indicate appearances made.

Managerial history

 * 🇩🇪 Walter Risse (1950–52)
 * 🇩🇪 Hans Appel (1952)
 * 🇩🇪 Otto Westphal (1963–64)
 * 🇩🇪 Kurt Krause (1964–65)
 * 🇩🇪 Erwin Türk (1970–71)
 * 🇩🇪 Edgar Preuß (1971–72)
 * 🇩🇪 Karl-Heinz Mülhausen (1972–74)
 * 🇩🇪 Kurt Krause (1974–76)
 * 🇩🇪 Diethelm Ferner (1976–78)
 * 🇩🇪 Sepp Piontek (1978–79)
 * 🇩🇪 Michael Lorkowski (1982–86)
 * 🇩🇪 Willi Reimann (1986–87)
 * 🇩🇪 Helmut Schulte (1987–91)
 * 🇩🇪 Horst Wohlers (1991–92)
 * 🇩🇪 Josef Eichkorn (1992)
 * 🇩🇪 Michael Lorkowski (1992)
 * 🇩🇪 Josef Eichkorn (1992–94)
 * 🇩🇪 Uli Maslo (1994–97)
 * 🇩🇪 Klaus-Peter Nemet (1997)
 * 🇩🇪 Eckhard Krautzun (1997)
 * 🇩🇪 Gerhard Kleppinger (1997–99)
 * 🇩🇪 Willi Reimann (1999–00)
 * 🇩🇪 Dietmar Demuth (2000–02)
 * 🇩🇪 Joachim Philipkowski (2002)
 * 🇩🇪 Franz Gerber (2002–04)
 * 🇩🇪 Andreas Bergmann (2004–06)
 * 🇩🇪 Holger Stanislawski (2006–07)
 * 🇩🇪 André Trulsen (2007–08)
 * 🇩🇪 Holger Stanislawski (2008–11)
 * 🇩🇪 André Schubert (2011–12)
 * 🇩🇪 Michael Frontzeck (2012–13)
 * 🇩🇪 Roland Vrabec (2013–14)
 * 🇩🇪 Thomas Meggle (2014)
 * 🇩🇪 Ewald Lienen (2014–2017)
 * 🇩🇪 Olaf Janßen (2017)
 * 🇩🇪 Markus Kauczinski (2017–19)
 * 🇳🇱 Jos Luhukay (2019–20)
 * 🇩🇪 Timo Schultz (2020–22)
 * 🇩🇪 Fabian Hürzeler (2022–24)

Other sports
The St. Pauli rugby section has several teams, both in the men's and women's leagues.

The men's rugby department has not been as successful as its female counterpart, reaching the German final only once, in 1964. In 2008–09, St. Pauli was the only club to have a team in both the rugby and football 2nd Bundesliga. In 2008–09, the men's team finished fourth in the second division.

The women's team have won the German rugby union championship eight times (1995, 2000, 2001, 2003, 2005–08) and the sevens championship 3 times (2000, 2001 and 2002). Several of their players play in the national squad.

St. Pauli has a blind football team which plays in the Blindenfussball Bundesliga.

St. Pauli also has a Roller Derby team known as Harbor Girls Hamburg.

Notable presidents

 * 1990–00: Heinz Weisener
 * 2002–10: Corny Littmann

title: FC St. Pauli


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Operation Iron Hammer (Iraq 2003)

Operation Iron Hammer was a joint operation between the US Army, US Air Force and Iraqi Civil Defense Corps with the objective of preventing the staging of weapons by anti-coalition forces, and preemptively destroy enemy operating bases and fighters in Baghdad.

Launch
The operation was launched on the night of 12 November 2003 by elements of the US Army's 1st Armored Division who performed cordon-and-search actions in several Baghdad neighborhoods. The operation's first salvo came when 1st Armored Division soldiers saw mortar rounds being fired from a van and gave chase, noting stops it made. An AH-64 Apache helicopter followed the van and attacked it, killing two suspected anti-coalition fighters and wounding three others. Five others were captured. Soldiers found an 82 mm mortar launch tube at one of the van's stops.

Strikes
In Operation Iron Hammer the military began preemptively destroying buildings suspected to be bases of operations for anti-coalition forces. The buildings included the former Republican Guard building, in the western part of the capital near Baghdad International Airport, and a warehouse in southern Baghdad. Both buildings had been used to conduct attacks on U.S. troops and were destroyed by AC-130 Spectre gunships and M2 Bradley fighting vehicles. U.S. forces also fired artillery rounds at two suspected mortar and rocket launch sites, one in western Baghdad and one in eastern Baghdad.

Conclusion
At the conclusion of Operation Iron Hammer Coalition forces has conducted 609 patrols in and around Baghdad capturing 33 enemy personnel. Combat actions included two cordon-and-search operations in Baghdad, detaining six people with suspected ties to the Fedayeen Saddam paramilitary organization and other anti-coalition elements. Another cordon-and-search operation in Baghdad's Azamiyah section netted 25 enemy personnel, including a former Republican Guard general, and significant quantities of weapons and ammunition. A joint cordon-and-search operation was also conducted in the Abu Ghuraib area with the Iraqi Civil Defense Corps.

Military Units Involved

 * US forces reported to be involved were
 * 1st Armored Division
 * USS Enterprise (CVN 65)

 * Iraqi forces reported to be involved were
 * Iraqi Civil Defense Corps

Casualties
No casualty figures are available. Please see Wikipage "Casualties of Iraq War" for information on casualty figures for the war in general.

Next Operations
Followed Operation OK Corral, followed by Operation Eagle Curtain.

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

title: Operation Iron Hammer (Iraq 2003)


text:
Eat Drink Man Woman

Eat Drink Man Woman is a 1994 comedy-drama film directed by Ang Lee, from a script co-written with James Schamus and Hui-Ling Wang. It stars Sihung Lung, Wang Yu-wen, Wu Chien-lien, and Yang Kuei-mei. as members of the Zhu family navigate the challenges of love, life, tradition and family. Part of Lee's "Father Knows Best" trilogy and similar to Lee's other works, this film deals with the transition from tradition to modernity. It is Lee's only film, to date, to be shot entirely in his native Taiwan.

The film premiered in Taiwan on July 2, 1994, and it was both a critical and box office success. It won several accolades including an Academy Award nomination for Best Foreign Language Film. It was also nominated for both a Golden Globe and BAFTA Award, as well as three Golden Horse Awards and six Independent Spirit Awards. It would inspire films like Tortilla Soup and Joyful Reunion and has an eponymous musical rendition. A BBC Culture poll of film critics ranked the film at number 54 of the 100 Greatest Non-English Language Films.

The title is a quote from the Book of Rites, one of the Confucian classics, referring to the basic human desires and accepting them as natural. The beginning of the quote reads as follows: “The things which men greatly desire are comprehended in food and drink and sexual pleasure.”

Plot
On a Sunday evening in Taipei, semi-retired chef and widower Zhu prepares a feast for his three daughters. Jia-Jen, the eldest, is a chemistry teacher who devotes herself to Christianity after facing heartbreak from her college ex-boyfriend. The second daughter, Jia-Chien, is an executive at an airline company. She wanted to become a head chef like her father but he claimed that it was not for a woman. Jia-Ning, the youngest, is a college student who works part-time at a Wendy's fast food restaurant.

At dinner, Jia-Chien announces that she has invested in a new apartment and will be moving out once construction is complete. Surprisingly, Mr. Zhu approves. Jia-Chien criticizes the flavor, claiming Mr. Zhu's taste is deteriorating. Mr. Zhu dismisses the idea before suddenly rushing off to help his (and Jia-Chien's) long-time friend and "taster", Old Wen, at a banquet. Afterwards, Mr. Zhu wonders with Old Wen if there is anything more to life than eating, drinking, man, and woman. Meanwhile, family friend Jin-Rong stops by the Zhu residence with her daughter Shan-Shan. Jin-Rong vocalizes her difficulties with a messy divorce while being responsible for work, Shan-Shan, and her opinionated mother, Madame Liang, as she returns to Taipei from America. Jia-Jen comforts her while Shan-Shan colors a caricature of Mr. Zhu.

The next morning, Mr. Zhu meets Shan-Shan, learns that the lunches Jin-Rong provides her are suboptimal, and decides to cook for her. Shan-Shan agrees, letting Mr. Zhu eat the lunches her mom made to prevent her from discovering their secret. At school, Jia-Jen meets the new volleyball coach Ming-Dao and they take interest in one another. Jia-Chien meets the chief negotiator Li Kai during a meeting at work and they flirt with one another. She has a chance to relocate to Amsterdam due to a potential promotion. Jia-Ning meets up with Guo-Lun, her friend Rachel's on-and-off boyfriend. As Guo-Lun mopes about his unrequited love, Jia-Ning comforts him, telling him that true love is being with someone he can express his feelings to comfortably, leading Guo-Lun to realize his love for Jia-Ning.

Meanwhile, Old Wen becomes hospitalized. Jia-Jen is fooled by love letters she believes are from Ming-Dao, falling for a prank by her students. Jia-Chien's apartment investment falls through as she discovers that the apartment company went bankrupt and ran away with her savings. She also learns that it was Li Kai who broke Jia-Jen's heart in college and confronts him about it. Li Kai says he never dated Jia-Jen. Jia-Ning faces a dilemma when she begins dating Guo-Lun even after Rachel confesses that she loves him. Mr. Zhu's health deteriorates and secretly visits the hospital, unaware that Jia-Chien saw him while visiting Old Wen. Eventually, Old Wen passes away and Mr. Zhu concludes that his sense of taste has officially departed.

At another Sunday feast, Jia-Chien announces that she will no longer be moving out; Mr. Zhu tells her not to worry. Later, Jia-Ning reveals her relationship with Guo-Lun and her pregnancy. The next dinner, Jia-Jen divulges that she and Ming-Dao have eloped. Jia-Jen and Jia-Ning move out of the residence, leaving Mr. Zhu with Jia-Chien. Troubled, Mr. Zhu begins to confide in and meet Madame Liang, leading the daughters to believe that the two are romantically involved.

Worried about her father's health, Jia-Chien rejects her promotion. Soon, the sisters, their partners, and Jin-Rong's family gather for a large Sunday feast. Mr. Zhu announces his engagement, not to Madame Liang, but to Jin-Rong, also revealing that his visit to the hospital was to show good health to gain Madame Liang's blessing. Madame Liang goes into shock, abruptly ending the dinner. Later, Jia-Ning and Guo-Lun have their baby, Jia-Jen converts Ming-Dao to Christianity, and Mr. Zhu sells the family home and buys a condo with Jin-Rong and Shan-Shan. Jia-Chien, no longer needing to take care of her father, accepts the job in Amsterdam. Before she leaves she prepares a final feast for the family in the family home, but only Mr. Zhu arrives. When Mr. Zhu tastes her cooking he suddenly realizes that his sense of taste has returned. The two hold each other’s hands in the dining room, and call each other “Father” and “Daughter”.

Cast

 * Lung Sihung as Zhu, an aging master Chinese chef who works at Grand Hotel in Taipei and the widower father of three adult daughters.
 * Yang Kuei-mei as Zhu Jia-Jen, the eldest daughter, who works as a high school Chemistry teacher. Jia-Chien believes that Li Kai broke the heart of her older sister Jia-Jen, and Dariotis and Fung wrote that the event seems to have caused Jia-Jen to turn away from the world. Later in film it is revealed that Jia-Jen fabricated the story, in order to "create a barrier against intimacy—even with her family" according to Dariotis and Fung. Ultimately she marries a new boyfriend after being abstinent for nine years. Her family members seem puzzled when they realize he is not a Christian but Jia-Jen says "He will be."
 * Wu Chien-lien as Zhu Jia-Chien, the second daughter, an executive at an airline company. Unlike her elder sister, Jia-Chien is sexually liberated, and suspects she disapproves of her moral system.
 * Chien-lien Wu, who plays Jia-Chien, also portrays Mr. Chu's dead wife. Lizzie Francke wrote that Jia-Chien taking the role of the cook "makes manifest the various needs that bind a family by setting a mother back at the heart of it". Dariotis and Fung wrote that therefore the phrase from Francke has multiple meanings since Jia-Chien takes her father's role of being a chef and therefore "is trying to be the son her father never had" and she takes the role of the mother.
 * Wang Yu-wen as Zhu Jia-Ning, the youngest daughter, who works at Wendy’s fast food restaurant. She becomes involved with an on-and-off boyfriend of her friend Rachel and gets into a love triangle.
 * Winston Chao as Li Kai, Jia-Chien’s co-worker and love interest. She believes Li Kai broke the heart of her older sister Jia-Jen, and Dariotis and Fung wrote that the event seems to have caused Jia-Jen to turn away from the world. Later in film it is revealed that Jia-Jen fabricated the story, in order to "create a barrier against intimacy—even with her family" according to Dariotis and Fung.
 * Sylvia Chang as Liang Jin-Rong, a single mother and neighbour of Chu’s, going through a messy divorce.
 * Gua Ah-leh as Madame Liang, Jin-Rong’s mother who’s recently moved back to Taiwan from the United States.
 * Chen Chao-jung as Guo Lun, Rachel’s ex-boyfriend and eventually Jia-Ning’s love interest.
 * Lu Chin-cheng as Ming-Dao, the high school volleyball coach whom Jia-Jen falls in love with.
 * Lester Chit-Man Chan as Raymond, Jia-Chien’s ex-boyfriend.
 * Yu Chen as Rachel, Jia-Ning’s friend and co-worker.
 * Tang Yu-Chien as Shan-Shan, Jin-Rong’s six-year old daughter.
 * Wang Jui as Old Wen, Chu’s longtime friend and fellow chef.
 * Hsu Gin-Ming as Coach Chai
 * Lin Huel-Yi as Sister Chang

Themes
Wei Ming Dariotis and Eileen Fung, authors of "Breaking the Soy Sauce Jar: Diaspora and Displacement in the Films of Ang Lee", wrote that Jia-Jen's story is that of a "spinster turned sensual woman". They wrote that her Christianity was there "perhaps to match her role as a mother-figure". She suspects Jia-Chien of disapproving of her moral system. Dariotis and Fung wrote that after Jia-Chien states that she needs not a mother but sister, Jia-Jen "is able to become who she really is with all the complexity that entails" rather than being someone she believed her family needed, with "who she really is" being "a modern, conservative, Christian, sexually aggressive Taiwanese woman". Desson Howe of The Washington Post wrote that of the actresses, Yang was the "most memorable".

Dariotis and Fung wrote that Jia-Ning's story is of "naïveté and immature love" and that the love triangle involving her, Guo Lun, and Rachel "is in many ways a parody of comic book romance." Dariotis and Fung argue that Jia-Ning's story, along with Jia-Jen's, is "not only flat but also dangerously uncomplicated." They further state that "[t]he lack of inquiry is endemic of this storyline" and that its "superficial treatment" is "quite disturbing."

“Due to love and traditional matters, they have to obey, they have to care well. They’re not really level with each other. I think that’s the biggest problem in that family, so the food and that banquet in the movie has become a ritual,” said Ang Lee. The banquet becomes a burden on the family.

The authors Hong Zhao and Haixin Jin argue in their article 破坏中的重建与传承——《饮食男女》解读 that in the film Eat Drink Man Woman, Zhu’s family first maintains a semblance of calm when everyone represses their desires, then, the family is destructed when members throw off the shackles of their family roles to pursue their own desires. The family structure is eventually reconstructed when everyone’s desire for eat, drink and sex is well balanced. At the beginning of the film, Zhu’s family struggles between maintaining the banquet (eat and drink) and their sexual desire (man and woman). Food is the bond that holds the family together. However, though they dine together every week, they are afraid to confide in each other. When they focus on “eat drink” but suppress sexual desire, the family is unhappy. No one enjoys the meal and Zhu even loses his sense of taste. When Zhu, Jia Jen, and Jia Ning chase after their sexual desires (man and woman), the original family structure disintegrates, but the family becomes happier since everyone gets what they want. The desire for food and sex eventually reach a balance and Zhu’s sense of taste is back at this moment.

Each character in this film has their own desire but at the beginning of the film, due to the concern with their family roles, they cannot express themselves.

Production
Eat Drink Man Woman was filmed on-location in director Ang Lee's hometown Taipei. As of 2022, it is Lee's only film to be shot entirely in Taiwan.

The opening sequence - in which a Sunday lunch is lovingly prepared - took over a week to film and was accomplished with the use of an actual master chef, who doubled for actor Sihung Lung.

Music
The musical score was composed by French musician Thierry Schollhammer, credited under the mononym "Mader", and arranged by Sarah Plant. The soundtrack was released by Varèse Sarabande.

Track listing
Included in the film but not on the soundtrack, are several Mandopop tracks and classical excerpts from "Israel in Egypt", "All Creatures of Our God and King", and "Quattro pezzi sacri."

Box office
The film grossed $24.2 million worldwide generating the third biggest percentage return on cost of films released in the year, behind Four Weddings and a Funeral and The Lion King. It was the highest-grossing foreign-language film in the United States and Canada for the year with a gross of $7.3 million.

Critical response
In her review in The New York Times, Janet Maslin praised Ang Lee as "a warmly engaging storyteller". She wrote, "Wonderfully seductive, and nicely knowing about all of its characters' appetites, Eat Drink Man Woman makes for an uncomplicatedly pleasant experience".

In his review in The Washington Post, Hal Hinson called the film a "beautiful balance of elements ... mellow, harmonious and poignantly funny". Hinson concluded: "As the relationships evolve and deepen, there seems to be a surprise around every corner—for both the characters and the audience. But what is most surprising, perhaps, is how involved we become with these people. As satisfying as food can be, the fullness we feel at the end here is far richer and more complex than that offered by the most extravagant meal. “ Eat Drink Man Woman” is a delicacy but also something more—something like food for the heart."

According to the review aggregator website Rotten Tomatoes, 91% of critics have given the film a positive review based on 46 reviews, with an average rating of 7.6/10. The site's critics consensus reads, "A richly layered look at the complex interactions between a widowed chef and his daughters, Ang Lee's generational comedy Eat Drink Man Woman offers filmgoers a tasty cinematic treat."

Legacy
Tortilla Soup, a 2001 American comedy-drama film directed by Maria Ripoll, is based on Eat Drink Man Woman. A semi-sequel, Eat Drink Man Woman 2012 [饮食男女2012] (billed as Joyful Reunion in English) was released, with Jui-Yuan Tsao, producer for the original film, serving as director, and a new set of characters exploring similar themes.

The film was adapted off-screen as well. In 2019, produced by PerfectMatch Theatre co., LTD, the National Kaohsiung Centre for the Arts put on a musical production titled, Eat Drink Man Woman: The Musical. The musical is a direct adaptation of the film. With a total runtime of 160 minutes, the production strived to showcase as many iconic aspects from Ang Lee's film, such as the character's unique qualities and the beauty of food, through song and dance as possible. Unfortunately, the musical only ran for a recorded three days in September 2019; the production had a total of one night showing and two matinees.

Father Knows Best trilogy
Eat Drink Man Woman is Ang Lee’s third feature film and forms the final part of his ‘Father Knows Best’ Trilogy, following Pushing Hands (1991) and The Wedding Banquet (1993). All three films depict a clash between cultures like youth and old age, tradition and progress, east and west, and investigate the freedoms and constraints inherent in family structures particularly those between fathers, daughters and sons. Si-hung Lung takes the place of a father in all three films - here as Mr. Zhu, a retired master chef - and He had used it as the motif (idealization of the household's head) to resolve all the contradictions and conflict that happened within the family members. The trilogy also takes the repression of individual desire in the face of social pressure as one of its central themes.

title: Eat Drink Man Woman


text:
Talk:Reproducing kernel Hilbert space

Problem with section on connection between RKHS and ReLu and Neural Networks
The first part of this section is very disconnected from the last sentence which reads

"Using this formulation, we can apply the Representer theorem to the RKHS, letting one prove the optimality of using ReLU activations in neural network settings. "

The first part of the section just shows that the ReLu is a reproducing kernel when a Hilber space is considered. The Representer theorem shows that when optimizing a sum of two functionals, one just depending on a few points of a function and the second being monotonic on the norm of its input, that we only really need to optimize the objective on the function on the points that the first functional depends on.

When one rights "letting one prove the optimally of using Relu activation' what kind of optimallity is the text referring too? Is there some citation to go with this ? Typically, when using NN, one does not optimize the activaiton functions, but the weights. How is the Representer theorem then used in this context? — Preceding unsigned comment added by 136.167.52.51 (talk) 21:39, 11 July 2020 (UTC)

This sesquilinearity convention
What is this sesquilinearity convention of which you speak? Do you mean linear in the second variable and conjucate-linear in the first? If so, it seems a strange convention to me. Lupin 08:39, 6 Aug 2004 (UTC)

The definition requires two spaces, X and H!
A lot of the article (e.g. examples) is currently written as if an RKHS (as the name implies) is a special kind of Hilbert Space. This is quite misleading. Every Hilbert Space, H, is an RKHS for X := H.

Norm-continuous
The article states that H is a reproducing kernel Hilbert space iff the linear map f→f(x) is norm-continuous for any element x of X. -- what does norm-continuous mean in this context? linas 15:06, 25 Jun 2005 (UTC)

 * H is a Hilbert space, thus carries a norm. This f → f(x) has a well-defined topology on both source and target.--CSTAR 15:38, 25 Jun 2005 (UTC)

Examples, too
Some examples would be handy too. Reading this article naively, one has the Dirac delta function playing the role of K, so that $$f(x)=\int \delta(x-y) f(y) dy$$ and δ is usually naively understood to be the "identity operator" on the Hilbert space in question (that is, its the sum over all states, e.g. the sum over all orthogonal polynomials on an interval). Is this naive reading correct? Can I correctly say that an example is

 * $$K(x,y)=\sum_{n=0}^\infty T_n(x) T_n(y) $$

where T_n ar the Chebyshev polynomials (and the norm/volume elt/weight is taken appropriately)? It seems to fulfill the requirements described in this article, I think ... linas 15:21, 25 Jun 2005 (UTC)

 * That's just it, the delta function is not in the space.--CSTAR 15:38, 25 Jun 2005 (UTC)

 * Would you object if I added the above as an example to the article? linas 18:31, 25 Jun 2005 (UTC)

Counter-examples, too
Assuming the example given above is correct, then, naively, every hilbert space encountered by a naive physicist is a reproducing kernel hilbert space. So it now becomes hard to imagine a Hilbert space that doesn't have such a beast associated with it. (Since K seems to be defined as "the identity operator", and these are always easily constructed as a sum over states). linas 15:27, 25 Jun 2005 (UTC)

 * What's relevant here is the realization of the Hilbert space as a space of functions on a set X.--CSTAR 15:38, 25 Jun 2005 (UTC)

 * Well, then, for the record, are there any hilbert spaces that are not realized as a space of functions on a set? Alternately, are there any hilbert spaces that are realized as a space of functions on a set, but do not have the norm-continuous property? I'm one of these people who don't feel comfortable with a topic until I have understood both an example and a counter-example.  I'll try to think of something, but if you have something up your sleeve, that's certainly better than whatever I might dream up.  linas 18:31, 25 Jun 2005 (UTC)

 * Yes: any L2μ for a non-atomic measure μ. These are realized as equivalence classes of functions.--CSTAR 18:41, 25 Jun 2005 (UTC)

 * late late comment: i think linas's original post is right. every Hilbert space H is isomorphic to a reproducing kernel Hilbert space, meaning there exist a set X, and a positive kernel K: X × X → C such that the resulting Hilbert space is isomorphic H, and, yes, K can be taken as, essentially, the identity operator.Mct mht 19:38, 30 March 2007 (UTC)

 * Late late late comment. Whilst it is true that every Hilbert space is isomorphic to a RKHS, that's not the same as saying it is a RKHS. For example, L2[0,1] is isomorphic to $$l^2 (\mathbb{Z})$$, which is a RKHS. However, the reproducting kernel here is $$K(x,y)=\delta_{xy}$$ for $$x,y\in \mathbb{Z}$$. The key thing is, that this does not lead to a reproducting kernel for L2[0,1], as it takes x and y in $$\mathbb{Z}$$, not [0,1]. In fact, L2[0,1] is not a RKHS, as point evaluation is not a continuous function. The message here is that being a RKHS is not preserved by isomorphism. Also, I should point out that the delta function is not a function in the conventional sense. It's a common shorthand to regard it as one, but it isn't a function in the conventional sense, and it certainly isn't in L2[0,1]. James pic 13:37, 9 October 2007 (UTC)

 * P.s, the delta function I use in the example above as $$\delta_{xy}$$ is the Kronecker delta, not the Dirac delta. The Kronecker delta is in $$l^2 (\mathbb{Z})$$, whereas the Dirac delta is not in L2[0,1].

 * Incidentally, in response to the request for examples, L2(X) is not a RKHS for X any open subset of $$\mathbb{C}^n$$. On the other hand, Hardy spaces usually are RKHSs, using various variants of the Szego kernel.

 * For example $$L^2(\mathbb{T})$$, the Hilbert space of L2 functions on the circle is not a RKHS. On the other hand, $$H^2(\mathbb{T})$$, the space of L2 functions on the circle which are radial limits of holomorphic functions on the disc, is. James pic 14:18, 9 October 2007 (UTC)

Edit
User:Oleg Alexandrov states that the sentence I edited was wrong, e.g. Hoever, several sentences were modified. Which sentence are you referring to here?--CSTAR 17:34, 25 Jun 2005 (UTC)
 * Well, I modified there only one sentence, everything else is just link insertion. I was referring to the sentence:

 * H is a reproducing kernel Hilbert space iff the linear map

 * $$ f \mapsto f(x) $$

 * is norm-continuous for any element x of X.

I thought that the part "for any element x of X" is wrong, but then I realized I was wrong, so I put it back in the next edit. Does that make more sence now? Oleg Alexandrov 17:43, 25 Jun 2005 (UTC)

 * Seems to. I'll give this more thought later tonight. linas 18:35, 25 Jun 2005 (UTC)
 * So, basically x is fixed, and then you get a linear map with input f and output f(x). I understand that this is weird, because usually the function f is fixed and input is x while output is f(x). Oleg Alexandrov 19:29, 25 Jun 2005 (UTC)

 * An important class of examples are Hilbert spaces of analytic functions.--CSTAR 05:59, 26 Jun 2005 (UTC)

Article is not consistent
what is meant by "reproducing kernel Hilbert space" here? sections of the article disagree.

 * 1) one can say that a Hilbert space of functions on X is a RKHS if it admits a positive definite kernel K on X × X. this is the approach in the first section. with this definition, as CSTAR said above, any L2μ for a non-atomic measure μ would not be a RKHS. (BTW, the positivity of the kernel is really the central theme whether one adopts this formulation or the one below, but that's not pointed out at all in the intro.)
 * 2) one can start with a positive kernel K on X × X. then there exists a Hilbert space H for which K is a reproducing kernel. this is alluded to in the Moore-Aronszajn theorem section. but then "is a reproducing kernel for" now means something slightly different. it is no longer insisted that H consists of functions on X. after quotiening out the degenrate subspace and taking the completion, we'd end up with equivalence classes in general. in this formulation, any Hilbert space is a RKHS, because the existence of orthonormal basis.

this should be resolved. if it's ok, i am going to attach clean-up tag to the article. Mct mht 01:40, 31 March 2007 (UTC)

 * I don't think your second point is correct. The phrase "is a reproducing kernel" implies that H consists of functions. This is because a reproducing kernel implies a continuous point-evaluation functional. Unless you are dealing with functions, point-evaluation makes no sense. Also, not every Hilbert space is an RKHS (which has been discussed above) although it may be isomorphic to one.150.203.33.77 02:27, 13 August 2007 (UTC)

 * i did not make a claim regarding what "is a reproducing kernel" means. i just pointed out that article seems to imply two inconsistent meanings. merely choosing one and label the other one incorrect, as you did, doesn't address the issue. in the intro, article states, as you say, "is a reproducing kernel" means H consists of functions and pointwise evaluations are bounded functionals. on the other hand, in the Moore-Aronszajn theorem section, it seems pretty clear to me that, if one carries out the construction as intended, the resulting Hilbert space would not in general be a spaces of functions, unless the ≥ is changed to >. Mct mht 03:04, 13 August 2007 (UTC)

 * Ah, I see. You are talking about the construction that you removed, right? I'll add in a correct construction.203.173.5.212 10:38, 13 August 2007 (UTC)

 * you've changed the section completely and i doubt it's right. do you have a reference? i think the point is that one considers here spaces of functions, not equivalence classes of functions. by starting with L2, this is already violated (contradicting what you said yourself above). furthermore, your inner product does not converge in general. TK is compact, so its eigenvalues λi goes to zero. if they do so, say, exponentially, then your inner product is not well-defined. assuming the inner product is valid, even then you may not have a Hilbert space. i don't think it is true in general that the range of TK is closed.

 * For a reference, see (for example) "On the Mathematical Foundations of Learning" by Cucker&Smale (bulletin of the AMS). They define an RKHS on page 11. Also, "On the Performance of Kernel classes" by Mendelson (Journal of Machine Learning Research) has a slightly different way of defining it. I'll add these to the references list.

 * The fact that I started with L2 is irrelevant. Two functions that belong to the same equivalence class will be mapped by the kernel operator to the same function so my RKHS is indeed a space of functions. I'll make a point of this.

 * The inner product I defined may not (in fact, will not) converge in L2. Note, however, that I only defined it in the image of LK. Then $$L_K^{-1}g$$ is in L2 and so the inner product is defined. The fact that the inner product doesn't converge in L2 in important; it means that the RKHS is a proper subset of L2. For a start, functions in the RKHS are continuous and have the same number of derivatives as the kernel does.

 * Are there any more issues with that section, or can I reinstate it? (I'm the same person that made the changes before -- I finally got around to making an account) Jneem 00:18, 19 August 2007 (UTC)

 * Sorry, I forgot to address the point of the space being complete. Let E be the closed (in L2) span of the eigenfunctions of LK. This, with the standard L2 inner product, is a Hilbert space. Also, LK1/2 is an isomorphism between E (with the L2 inner product) and the RKHS (with the RKHS inner product). Therefore the RKHS is also complete. Jneem 00:24, 19 August 2007 (UTC)

 * i think the assumption of the previous version was probably correct and it just needed some elaboration. Mct mht 06:38, 17 August 2007 (UTC)

 * The previous version may have been correct, but it doesn't directly follow from any construction I am aware of. In addition, the construction I give says explicitly what the inner product is. It doesn't seem to be mentioned elsewhere on the page that the inner product on a RKHS will, except in finite-dimensional situations, be completely different from the normal L2 inner product. Reading the talk page, there seems to be some confusion on this point (with people thinking of the point-evaluation functional as being a dirac function) so I think it's worth having.Jneem 00:18, 19 August 2007 (UTC)

 * hi, Jneem, good to have you contributing. is there a pdf file for the Cucker & Smale paper? some questions/replies:
 * Re "Two functions that belong to the same equivalence class will be mapped by the kernel operator to the same function": ok, that is true.
 * Re "The inner product I defined may not (in fact, will not) converge in L2. Note, however, that I only defined it in the image of LK. Then $$L_K^{-1}g$$ is in L2 and so the inner product is defined.": ok, that is also true.
 * Re "Let E be the closed (in L2) span of the eigenfunctions of LK. This, with the standard L2 inner product, is a Hilbert space.": by adjoining elements of L2 to get completeness, are you not ending up with a space of equivalence classes? in the line where you verified that this is a RKHS: $$\langle K_x, f \rangle_H = \langle K_x, T_K^{-1} f \rangle_2 = (T_K (T_K^{-1} f)) (x) = f(x) $$, you only did it for f in the image of TK. what if f is not in the image of TK but in its completion?
 * Re the original (in the article right now) version: it is more general and fundamental than the construction you gave, which seems to me constructs a Hilbert space (of either functions or equivalence classes of them) using a positive, in your case unbounded, operator in a pretty standard way. it's clear that a positive definite kernel on a set X (with no extra structure, such as a measure) gives an inner product on functions from X to C with finite support. the issue is completion. if we take the usual Cauchy completion, then it will not be a space of functions. but i think it can be bypassed. Mct mht 01:28, 19 August 2007 (UTC)

 * OK, you make a good point about completion. What if I define the RKHS by the set of functions $$\{f(x) = \sum_{i=1}^\infty a_i \sqrt{\lambda_i} \phi_i (x):\ \sum a_i^2 < \infty\}$$. Then f is defined pointwise because, by Mercer's theorem, $$\infty > K(x, x) = \sum \lambda_i \phi_i (x)^2$$ and so f(x) < ∞ by Cauchy-Shwartz. Then this is obviously a family of functions and the fact that it is complete under the RKHS inner product follows from a diagonalisation argument. Basically, I'm forgetting about the kernel operator and following Mendelson's second definition more closely. By the way, there is a pdf of Cucker&Smale at the same address as the ps -- just change the ".ps" to ".pdf". Jneem 03:36, 19 August 2007 (UTC)

 * besides some details, i think that does it. that the positive operator has purely discrete spectrum seems to me essential here. this is really a kernel K on the natural numbers N given by K(i,j) = λi δi j in disguise (one can substitute the natural basis {ei(j) = δi j} with any set of orthonormal functions and you did it here with the eigenvectors of TK). i for one am not going to object if you wanna add it back. in any case let's keep the Moore-Aronszajn theorem section, as that is the most general formulation. Mct mht 17:56, 19 August 2007 (UTC)

 * Sorry, I'm still missing something. The Moore-Aroszajn theorem says that the RKHS is unique. Therefore, any construction we give must result in the same RKHS. So why is one thing more general than another? Jneem 22:57, 19 August 2007 (UTC)

 * well, the assumptions of the Moore-Aroszajn theorem are different than those for your construction so i don't think you can apply their uniqueness statement. if i understand correctly, the Moore-Aroszajn theorem says that for any set X and any positive definite kernel K: X × X → C, there is a unique RKHS consisting of functions on X. so no structure such as a measure is assumed on X and no passing through an integral operator. Mct mht 01:50, 20 August 2007 (UTC)

 * you're right, so I've done a proof of Moore-Aroszajn in the general case. I'll add the stuff about Mercer kernels when I have time.Jneem 08:17, 20 August 2007 (UTC)

also, the the Moore-Aronszajn theorem section contains some unusual notation and language ("first class citizens"?), and the very brief outline of the construction doesn't look quite right. Mct mht 02:04, 31 March 2007 (UTC)

 * I agree; the previous version by the anon contributor made a mishmash of Carleman operators, Hilbert Schmidt operators and Kernels. --CSTAR 15:21, 17 August 2007 (UTC)

It is a Hilbert space
The most recent edit claims that the inner product given in the proof of Moore-Aronszajn may be degenerate but doesn't say why. I think that it cannot be degenerate: suppose it is. Then there exists a point x such that $$\langle K_x, K_x \rangle = 0$$ and Kx is not the zero function. Then we can find y such that Kx(y) is not zero. Then the kernel matrix determined by x and y is

\begin{bmatrix} 0 & a \\ \overline a & b \\ \end{bmatrix} $$ for some non-zero a and some real number b. One can check that the eigenvalues are

\frac{b \pm \sqrt {b^2 + 4|a|^2}}{2} $$ and so one eigenvalue is negative, contradicting the fact that the kernel was positive definite. Unless someone can poke a hole in my argument, I'll reinstate the claim that the construction produces a genuine Hilbert space. Jneem 12:14, 27 September 2007 (UTC)

 * I see no flaw in your argument. I'll undo my edit. Memming 13:08, 27 September 2007 (UTC)

 * You were right to require symmetry of the kernel, though, so I'll put that back in. Jneem 00:17, 28 September 2007 (UTC)

i don't know if one is interested in real RKHS's but in the complex case, positivity implies Hermiticity, i.e. K(x,y) and K(y,x,) are mutual conjugates. Mct mht 05:06, 9 October 2007 (UTC)

Informal description
an anon contributor recently added the following passage:

 * "Informally, a reproducing kernel Hilbert space is a function space on which the concept of a Dirac delta function makes sense, despite possibly being technically absent from the Hilbert space."

i think that can be misleading, unless one introduces some concrete examples of RKHS (necessarily one that is not a space of analytic functions). does the anon have some such e.g.'s at hand?

even then, one might still argue that the statement is misleading. talking about δ-functions implicitly assumes that some kinda analytic structure is present, while the generic RKHS does not. take for instance the trivial kernel on R, K(x,y) = δxy. apply the Moore-Aronszajn construction given in the article. the resulting space of functions on R has no obvious analytic description. it would be a big stretch for fit δ-function into the picture, if that is possible. neither does it make sense to speak of δ-functions in the context of spaces of analytic functions. something that is closer to what anon describes is perhaps a rigged Hilbert space. although in that case, the δ-functions do reside in the space IIRC. Mct mht 05:50, 30 September 2007 (UTC)

Hi, I'm anon. My original statement was wrong. I changed it to

 * "Informally, a reproducing kernel Hilbert space is a function space which contains a Dirac delta-like function at every point of the underlying set."

Anyways, let me explain the rationale. There are only two important things about a dirac delta function: it has a mass (integral) of one concentrated entirely on a single point of the underlying set. The concept of analyticity and taking limits, while important in its construction and interpretation on R^n, is irrelevant to its purpose. It's more of a measure theoretic object (dirac measure) than an analytic object. Perhaps I should have said dirac measure instead of dirac delta function, but since the article was talking about function spaces I thought I'd use the latter to avoid confusion.

Since the rkhs abstracts those two essential properties from the Dirac delta into the definition of the reproducing kernel, I thought it appropriate to make that informal connection. In the article as it stood, it was not clear why anyone would care about rkhs. I couldn't figure out why until I read it carefully and made the connection above, so I thought it was worth sharing.

Your concerns are certainly legitimate (the dirac delta is technically an object with analytic structure, although I'm downplaying that to make the connection) and if you can think of a way to make it more accurate, please do. But let's try to make the article more readable, it's too formalistic right now.--141.211.61.254 18:50, 7 October 2007 (UTC)

 * I agree with Mct mht and I think the reference to a dirac function should be removed. It might make sense to think of a dirac "function" if the inner product on an RKHS were the usual L2 inner product -- but it isn't and that is a very important point (I already removed a sentence that made the same mistake, so this probably needs to be emphasised somewhere). The inner product on an RKHS is given in the proof of Moore-Aronszajn and it is definitely not the usual one. In fact, as Mct mht pointed out on this talk page, an RKHS does not need a measure.

 * I think the term "point-evaluation functional" is less misleading than the term "Dirac delta function." I do agree, however that the article needs some motivation. However, I think that the motivation must not be misleading.Jneem 02:07, 9 October 2007 (UTC)

the connection between pointwise evaluations and delta-functions is rather forced in this setting. given a positive operator A on a Hilbert space H, it induces an inner product on its domain: . in particular, a positive semifinite n × n matrix allows one to renorm Cn. a RKHS is really a very natural generalization of this. if X is the integers, then one can think of positive kernel as an infinite positive matrix. the definition of positivity copies verbatim from the matrix case: we require that every principal minor (of finite size) is positive. so naturally we have an inner product on the space of functions f: X → C with finite support. to get a Hilbert space, two possible obstacles: degeneracy and completeness. if a positive semifinite n × n matrix A is not strictly positive, the induced inner product would be degenerate on Cn. but it one restricts to the range of A, spanned by its columns, degeneracy is removed. this is essentially what is done also for the kernel case. for completeness, we include all functions of finite norm (the abstract Cauchy completion would not do here). Mct mht 05:02, 9 October 2007 (UTC)

Sesquilinearity
Should we be following the convention for inner product spaces of $$\langle \cdot, \ \cdot \rangle$$ being linear in the first variable, or the convention for more general sesquilinear forms of being linear in the second variable? My feeling is that since we're dealing solely with Hilbert spaces here, so we're only dealing with inner products, we should use the inner product space convention, which also seems to be more common in the literature. What say you? James pic 11:35, 18 October 2007 (UTC)

 * matter of consensus. i personally don't have a preference. article just needs to be consistent. Mct mht 19:19, 18 October 2007 (UTC)

 * I don't mind terribly -- I used linearity in the second variable for consistency with the page on sesquilinear forms (the page on inner product spaces is inconsistent: first, it says that an inner product is a sesquilinear form. Then it says that an inner product is linear in the first variable. Then it gives an example of an inner product (the third example) that is linear in the second variable). Anyway, if you want to make it linear in the first variable, you should also change the proof of the Moore-Aronszajn theorem. Jneem 01:47, 20 October 2007 (UTC)

 * Like I said, my preference is to use linearity in the first variable, as this seems to be most consistent with the literature, at least for Hilbert spaces. However, even this could be contentious, as physics literature generally uses the opposite convention. As you said, it should be a matter of consensus, so I thought I'd call for a vote.

First Variable: I've seen it most often in the literature. James pic 16:20, 22 October 2007 (UTC)

 * looks like there won't be any objection if you wanna switch conventions. Mct mht 20:38, 24 October 2007 (UTC)

It all depends on whether you prefer Forward Polish Notation, fx to denote the application of f to x, or Reverse Polish Notation, xf. The usual convention is that the vector space V consists of column vectors v, which transform covariantly as Mv when multiplied on the left by a matrix M representing a linear transformation from V to some vector space. Its dual V* consists of row vectors, which transform contravariantly when multiplied on the right by the adjoint (as distinct from the adjugate) of M. Dot product has the row vector on the left representing a functional from V to the one-dimensional space. So if dot product is your basic example of an inner product then the second variable should be the linear one. Physicists got that one right, see e.g. Blank et al, Hilbert Space Operators in Quantum Physics where the bra is applied to the ket. The other way round corresponds to Reverse Polish Notation as popularized by HP calculators, no inconsistency there as long as you stick to RPN throughout. Switching everything in the article to RPN looks like more work than RPN warrants. --Vaughan Pratt (talk) 09:16, 1 February 2013 (UTC)

Is the proof correct?
I do not think that your proof on the fact that given a kernel K, there exists a unique RKHS associared with it is correct. Or, at leats, it is incomplete. After introducing G as another Hilbert space of functions for which K is a reproducing kernel, to prove uniqueness it is assumed that G is the completion of the span of \{K_x:\ x \in E \}. But where does this fact come from? This has to be proved. Notice that in Cucker and Smale's paper "On the mathematical foundations of learning" this is a condition which is listed in the statement of theorem 2 on pag. 35. —Preceding unsigned comment added by Spline (talk • contribs) 17:34, 10 December 2008 (UTC)

 * I understand that H (or G as well) is a space of functions on E: if an element f ∈ H is orthogonal to all the $$\{K_x:\ x \in E \}$$, then f is the 0 function on E, thus $$f = 0_H$$, hence $$\{K_x:\ x \in E \}$$ is total. Does it make sense? Bdmy (talk) 11:38, 11 December 2008 (UTC)

Yes, it makes sense. span{K_x} must contain an orthonormal basis of H, hence must be dense in G, if G has to satisfy the reproducing property. I think that this point should be mentioned in the proof, because it would make it more clear. —Preceding unsigned comment added by 87.4.244.249 (talk) 21:38, 11 December 2008 (UTC)

Yes, it makes sense. span{K_x} must contain an orthonormal basis of G, i.e. must be dense in G if G has to satisfy the reproducing property. I think that this point should be mentioned in the proof, it would make it more complete. The conclusion without mentioning this point is not so clear. —Preceding unsigned comment added by 87.4.244.249 (talk) 21:41, 11 December 2008 (UTC)

Symmetric or "Hermitian symmetric"
I find the wording "the kernel K is symmetric" ambiguous or misleading. Clearly what is meant but never said is the "Hermitian symmetry"
 * $$K(y, x) = \overline {K(x, y)}$$

like the one for the Szegö kernel. I am right? Bdmy (talk) 11:43, 11 December 2008 (UTC)

Kernel as dot-product after non-linear map
I don't know a lot about this topic, but I ended up here by studying support vector machines. It seems the SVM world ended up using RKHS's by first mapping statistical data from a set X into a Hilbert Space H using a non-linear map f: X -> H, defining the kernel k: X x X -> IR: (x, y) -> . I can see to some extent how these definitions might be equivalent or at least related, but I think it might be enlightening for some people to mention this approach to RKHS's in the article as well.

Apologies for the clumsy notation, I couldn't find any way to get a tex-template here.

94.224.49.243 (talk) 15:04, 14 October 2012 (UTC)

 * Take a look at Sławomir Biały's edit here and see if you agree. He's also the main editor for Bergman kernel (Bergman 1922) which he wrote starting on the same day.  Note that kernel trick (what you're talking about in connection with SVM's) has been in the See Also section of this article ever since this 2006 edit.

 * Incidentally you can tex-ify your formulas as $$k: X\times X\to IR: (x,y)\to\langle f(x),f(y)\rangle$$ etc. --Vaughan Pratt (talk) 08:05, 1 February 2013 (UTC)

Contrast with L^2-spaces
Subsuming large parts of the discussion above, it seems that the article should be more precise and clearer right at the beginning about the fact that usual $$L^2$$-spaces on manifolds are not RKHS's. These aren't because they are not defined as Hilbert spaces of functions, but only of equivalence classes of functions; leading to evaluation at a point of the manifold being undefined. This point is just too likely to be confusing for readers unfamiliar with the subject but used to the usual $$L^2$$-spaces. Wurzel33 (talk) 19:36, 1 December 2013 (UTC)

 * I agree, made this point in the first paragraph, hope this reads well. Biker333 (talk) 11:27, 21 February 2016 (UTC)

Reproducing Kernels and Operators with a Cyclic Vector (V.N. Singh)
On the page Vashishtha Narayan Singh I have linked his PhD subject "Reproducing Kernels and Operators with a Cyclic Vector" to this page, but I am not sure if this is correct. Could someone please check this? Further, on Wiki Data he is described as "mathematician known for challenging Einstein Gauss theory". Is this correct too? If so, could this be added in the text as well, if possible with an explanation what this implies? I have no knowledge about this subject. Wiki-uk (talk) 11:53, 12 June 2015 (UTC)

Problems with the definition
-In (1), can M depend on f or not? If it can (as stated in the text), the "forall" notation in the formula is confusing.

- Last sentence in the definition: "From this definition it is easy to see that a function K: X \times X \to \mathbb{R} is a reproducing kernel if it is both symmetric and positive definite". Isn't this what Moore-Aronszajn Theorem proves below?

Expanding the examples
The examples are mostly a list of kernels, but this doesn't give a clue as to which functions are in the corresponding RKHS, and what the norm is. I added a sentence to partially complete this for the linear and Laplacian kernels, do others know more, e.g., is anything known about the double exponential case? Biker333 (talk) 00:26, 20 February 2016 (UTC)

This is a mess. For example, the first sentence of the definition,
Let {\displaystyle X}X be an arbitrary set and {\displaystyle H}H a Hilbert space of real-valued functions on {\displaystyle X}X, equipped with pointwise addition and pointwise scalar multiplication.

Hilbert space which is also a vector space??? Then further down the Hilbert space can be given an inner product. I'd suggest reviewing the definition of a Hilbert space before yammering on about RKHS.

A banach space with an inner product. Izmirlig (talk) 02:47, 5 July 2022 (UTC)

 * I think the point is that H is a Hilbert space of functions and not just some abstract vectors, because a function can be evaluated at a point, while a vector (i.e. an element of a linear space) does not have this property. One related remark is made in the article: L^2 is not a space of functions (but a space of classes of equivalence). Also, the discussion from 2005--2007 just above touches upon how the "evaluation at a point" property is not preserved under isomorphisms between Hilbert spaces, which (if my understanding is correct) is precisely because "evaluation at a point" is not in the structure of a Hilbert space. Thus, being specific that we consider Hilbert spaces of functions is not only correct but also necessary. AVM2019 (talk) 21:54, 9 September 2022 (UTC)

References and citations: more primary, less secondary
Parts of the article refer extensively to a single source, | Lorenzo Rosasco's MIT course 9.520. This includes references to: The latter is not publicly available (neither free nor for a fee). The former are lecture notes for one of the classes apparently put together by one of Prof Rosasco's students (and has misattributed authorship).
 * Durrett, Greg. 9.520 Course Notes, Massachusetts Institute of Technology, https://www.mit.edu/~9.520/scribe-notes/class03_gdurett.pdf, February 2010.
 * Rosasco, Lorenzo and Poggio, Thomas. "A Regularization Tour of Machine Learning – MIT 9.520 Lecture Notes" Manuscript, Dec. 2014.

I suggest to remove these references and replace them by more appropriate primary sources, such as endorsed books or peer-reviewed articles.

(Incidentally, on the course page, Prof. Rosasco encourages students to contribute to Wikipedia as part of assignments, which being a commendable thing, may explain some peculiarities of this article) AVM2019 (talk) 15:48, 10 September 2022 (UTC)

Kernel Examples and Kernel Type Query
Is the function f(x, y) = e^(x, y) a valid kernel function?

While there are some examples of kernels, would you like to expand upon the examples list? Inlin (talk) 11:26, 9 July 2023 (UTC)

title: Talk:Reproducing kernel Hilbert space


text:
Talk:De La Salle University, Manila

I think we should only put in information that has enduring interest into this article. No offense meant to the persons involved, but do we really need to know who the current student council president is? And what will happen to this article once the council president changes in the following year? This is supposed to be an encyclopedia, not a journal. --Ronaldo Guevara 08:41, 6 Aug 2004 (UTC)

title: Talk:De La Salle University, Manila