OpenLLM-France/wikimedia huggingface dataset:
# Titchmarsh convolution theorem

The Titchmarsh convolution theorem describes the properties of the support of the convolution of two functions. It was proven by Edward Charles Titchmarsh in 1926.

## Titchmarsh convolution theorem

If φ(t){\textstyle \varphi (t)\, } and ψ(t){\textstyle \psi (t)} are integrable functions, such that
    $\varphi *\psi =\int _{0}^{x}\varphi (t)\psi (x-t)\,dt=0$
almost everywhere in the interval $0<x<\kappa \,$, then there exist $\lambda \geq 0$ and $\mu \geq 0$ satisfying $\lambda +\mu \geq \kappa$ such that $\varphi (t)=0\,$ almost everywhere in $0<t<\lambda$ and $\psi (t)=0\,$ almost everywhere in $0<t<\mu .$
As a corollary, if the integral above is 0 for all x>0, {\textstyle x>0, } then either φ{\textstyle \varphi \, } or ψ{\textstyle \psi } is almost everywhere 0 in the interval [0, +∞).{\textstyle [0, +\infty ).} Thus the convolution of two functions on [0, +∞){\textstyle [0, +\infty )} cannot be identically zero unless at least one of the two functions is identically zero.
As another corollary, if $\varphi *\psi (x)=0$ for all $x\in [0,\kappa ]$ and one of the function $\varphi$ or $\psi$ is almost everywhere not null in this interval, then the other function must be null almost everywhere in $[0,\kappa ]$.
The theorem can be restated in the following form:
    Let $\varphi ,\psi \in L^{1}(\mathbb {R} )$. Then $\inf \operatorname {supp} \varphi \ast \psi =\inf \operatorname {supp} \varphi +\inf \operatorname {supp} \psi$ if the left-hand side is finite. Similarly, $\sup \operatorname {supp} \varphi \ast \psi =\sup \operatorname {supp} \varphi +\sup \operatorname {supp} \psi$ if the right-hand side is finite.
Above, $\operatorname {supp}$ denotes the support of a function f (i.e., the closure of the complement of f$^{−1}$(0)) and $\inf$ and $\sup$ denote the infimum and supremum. This theorem essentially states that the well-known inclusion $\operatorname {supp} \varphi \ast \psi \subset \operatorname {supp} \varphi +\operatorname {supp} \psi$ is sharp at the boundary.
The higher-dimensional generalization in terms of the convex hull of the supports was proven by Jacques-Louis Lions in 1951:
    If $\varphi ,\psi \in {\mathcal {E}}'(\mathbb {R} ^{n})$, then $\operatorname {c.h.} \operatorname {supp} \varphi \ast \psi =\operatorname {c.h.} \operatorname {supp} \varphi +\operatorname {c.h.} \operatorname {supp} \psi$
Above, $\operatorname {c.h.}$ denotes the convex hull of the set and ${\mathcal {E}}'(\mathbb {R} ^{n})$ denotes the space of distributions with compact support.
The original proof by Titchmarsh uses complex-variable techniques, and is based on the Phragmén–Lindelöf principle, Jensen's inequality, Carleman's theorem, and Valiron's theorem. The theorem has since been proven several more times, typically using either real-variable or complex-variable methods. Gian-Carlo Rota has stated that no proof yet addresses the theorem's underlying combinatorial structure, which he believes is necessary for complete understanding.
# Koldo Fernández

Koldo Fernández de Larrea (born 13 September 1981) is a Spanish former professional road racing cyclist, who rode professionally between 2004 and 2014 for the Euskaltel–Euskadi and Garmin–Sharp teams. He now works as a transfer agent within the sport.
Born in Vitoria-Gasteiz, Basque Country, Fernández currently resides in Zurbano, Basque Country, Spain.

## Major results

Sources:

### 1999

    1st Road race, National Junior Road Championships

### 2006

    5th Trofeo Mallorca
    10th Grand Prix Pino Cerami

### 2007

    1st Stage 7 Tirreno–Adriatico
    Vuelta a Mallorca
       4th Trofeo Mallorca
       6th Trofeo Calvia
    5th Overall Vuelta a Andalucía

### 2008

    1st Tour de Vendée
    Vuelta a Murcia
       1st Points classification
       1st Stage 5
    1st Stage 5 Vuelta a Castilla y León
    1st Stage 2 Euskal Bizikleta
    1st Stage 3 Vuelta a Burgos
    2nd Circuito de Getxo
    4th Clásica de Almería
    4th Gran Premio de Llodio

### 2009

    1st Circuito de Getxo
    1st Stage 1 Vuelta a Burgos
    1st Stage 2 Volta ao Algarve
    5th Trofeo Cala Millor
    5th Vattenfall Cyclassics
    6th Gent–Wevelgem

### 2010

    1st Tour de Vendée
    1st Stage 1 Vuelta a Burgos
    2nd Overall Tour de Picardie
    Vuelta a Mallorca
       2nd Trofeo Palma de Mallorca
       2nd Trofeo Magaluf-Palmanova
       5th Trofeo Cala Millor
    3rd Road race, National Road Championships
    9th Circuito de Getxo

### 2011

    2nd Road race, National Road Championships
    8th Trofeo Magaluf-Palmanova

### 2012

    2nd Road race, National Road Championships

### Grand Tour general classification results timeline

| Grand Tour | 2006 | 2007 | 2008 | 2009 | 2010 | 2011 | 2012 | 2013 | 2014 |
| Giro d'Italia | DNF | 135 | DNF | — | — | — | — | — | DNF |
| Tour de France | — | — | — | DSQ | — | — | — | — | — |
| Vuelta a España | — | 134 | 94 | — | 139 | — | 134 | DNF | 86 |
Legend :
| — | Did not compete |
| DNF | Did not finish |
# Saeed-Al-Saffar

Saeed-al-Saffar (born 31 July 1968) is an Emirati cricketer who has represented the UAE at international level, most notably in the One Day International the Emirates side played against the Netherlands in Lahore in the 1996 Cricket World Cup. He also competed for the UAE in the 1996–97 and 2001 versions of the ICC Trophy, which is the qualifying competition for the World Cup played between non-Test nations.
He has the distinction of scoring a double hundred against Thailand in the acc trophy, scoring 209 not out, which by itself is a huge feat in the one day form of the game.
He also carries the record for the third wicket for the domestic competition in Sharjah Cricket stadium in Ramadhan Night Tournament, where he along with Qais Farooq put up 217 runs for the 3rd wicket.
His only ODI was where he did not bat and bowled 3 overs conceding 25 runs without taking a wicket.
# Irfan Sajid

Irfan Sajid (born 1 January 1983) is a Pakistani-born cricketer who played for the United Arab Emirates national cricket team. He made his One Day International debut for the United Arab Emirates against Afghanistan in the 2014 ACC Premier League on 2 May 2014.
# Ruby Pipeline

The Ruby Pipeline is a 680-mile, 42-in. diameter natural gas pipeline running from Opal, Wyoming, to Malin, Oregon. The route crosses Northern Utah, and Northern Nevada. Ruby Pipeline, L.L.C. filed an application with the Federal Energy Regulatory Commission (FERC) on January 27, 2009, authorizing the construction and operation of the Ruby Pipeline Project. On April 5, 2010, the FERC approved the application. Construction began on July 31, 2010, and the pipeline was placed in service on July 28, 2011. The pipe is 680 miles (1,090 km) long with an expected capacity of 1.5 billion cubic feet per day (42×10^$^6$ m$^3$/d).

## Controversy

There is concern that the project crosses more than 1000 rivers and streams and, according to the Center for Biological Diversity, threatens some endangered fish species.
The Center for Biological Diversity and Summit Lake Paiute Tribe of Nevada petitioned the Ninth Circuit Court of Appeals for an emergency action blocking the pipeline. Despite not winning the injunction requests, the Court ultimately ruled in their favor, finding that environmental reviews for the pipeline's impacts to endangered fish species and sagebrush habitats did not comply with environmental laws.
On April 1, 2022, Ruby Pipeline filed for Chapter 11 bankruptcy.
# Tawfik Khatib

Tawfik Khatib (Arabic: توفيق خطيب, Hebrew: תאופיק ח'טיב; born 21 April 1954) is an Israeli Arab former politician who served as a member of the Knesset for the United Arab List and the Arab National Party between 1996 and 2003.

## Biography

Born in Jaljulia, Khatib studied political science at Bar-Ilan University, gaining a BA. He went on to study Islamic culture, writing his MA thesis on ancient taxation.
In 1989 he became head of Jaljulia's local council. A member of the Islamic Movement, He was elected to the Knesset on the United Arab List list in the 1996 elections. After winning fifth place on the party's list for the 1999 elections he retained his seat, but on 19 February 2001, left the party to establish the Arab National Party along with Muhamad Kanan. Prior to the 2003 elections media reports suggested that Khatib would join Meretz, but nothing came of them, and he lost his seat.
Khatib is married with five children. He current teaches Arabic at Beit Berl College.
# Alessandro Raimo

Alessandro Raimo (born 8 March 1999) is an Italian professional footballer who plays as a right back for Serie C Group C club Catania.

## Club career

Born in Piombino, Raimo started his footballer career in Fiorentina youth sector.
He joined to Livorno U-19 in 2016. On 24 August 2017, he was loaned to Serie D club Massese. He was loaned again the next season, on 17 July 2019 to Pontedera.
On 3 December 2019, he signed with Grosseto.
On 26 August 2022, Raimo joined Siena on a multi-year contract.
On 28 August 2024, Raimo signed a two-season contract with Catania.
# The Curiosity of Chance

The Curiosity of Chance is a 2006 comedy film directed by Russell P. Marleau, produced by Bigfoot Entertainment and starring Tad Hilgenbrink.

## Plot

In 1980s Europe, flamboyant and gay 16-year-old Chance Marquis shows up at an international high school in a top hat and tails, immediately attracting the attention of the "queer-hating" resident bully, among others. Through his involvement in the school newspaper, he meets an introverted photographer with a mysterious briefcase, and while practicing tennis, he befriends a catty fashionista, both of whom act as his wingmen in his new high school. He also meets the jock-next-door, with whom he forms a tentative friendship, despite the jock's cacophonous group of friends. The film follows Chance through a year of high school, with its attendant drama, successes, and hijinks—including sneaking into a drag bar, where Chance begins to explore his true self.
Themes underscored throughout the film include facing one's fears as one grows into adulthood, and the barriers that people put up in order to cope with life. Chance claims to be strong with his nonchalant attitude, but when photos of him in drag show up all over school, Chance must face his own preachings of staying true to oneself.

## Cast

* Tad Hilgenbrink as Chance Marquis
* Brett Chukerman as Levi Sparks
* Aldevina Da Silva as Twyla Tiller
* Pieter Van Nieuwenhuyze as Hank Hudson
* Chris Mulkey as Sir
* Maxim Maes as Brad Harden
* Colleen Cameron as Sienna Marquis
* Magali Uytterhaegen as Vice Principal Ophelia Smelker

## Accolades

* Winner "Best Narrative Feature" at The Chicago LGBT International Film Festival - Chicago, IL 2007
* Winner "Best New Director" at Seattle Lesbian & Gay Film Festival - Seattle, WA 2006
* Honorable Mention "Best Music in a Feature Film" at Nashville Film Festival - Nashville, TN 2007
* Chosen as one of the Audience's and Critic's "Best of the Fest" at the Palm Springs International Film Festival - Palm Springs, CA 2007
# Newton Blackmour State Trail

The Newton Blackmour State Trail is a crushed limestone trail in northern Outagamie County in Wisconsin, United States. The trail spans 24 miles (39 km) on a former rail corridor. Its name is derived from the four communities the trail passes through: New London, Shiocton, Black Creek and Seymour. The trail's eastern end in Seymour connects to the Duck Creek Trail, which travels east through the Oneida Nation of Wisconsin and ends in the Village of Oneida.
With the connection to the Duck Creek Trail, the combined trails are over 30 miles (48 km) long. The combined trails extend from the Village of Oneida to New London.

## Access

The trail is open to bicyclists, walkers, joggers, horseback riders, and pets on leashes. In the winter the trail is open to cross-country skiing, snowshoeing, and snowmobiling.

## Amenities

In the west end of the trail in New London there are hotels, campgrounds, and bike shops. Twenty minutes east of the trail in Ashwaubenon, there are also hotels and bike shops. In each of the communities the trail goes through, there are various restaurants, grocery stores, and gas stations very close to the path.

## Trailheads

On the west end, the trail begins at House Road in New London (44°24′17″N 88°43′05″W﻿ / ﻿44.40471°N 88.71805°W﻿ / 44.40471; -88.71805﻿ (Newton Blackmour State Trail, western end)). Eventually the trail will continue to Pfeifer Park near downtown New London. In the east, the trail doesn't seem to end at all, as it becomes the Duck Creek Trail east of Vandenhueval Road in Seymour (44°30′35″N 88°18′37″W﻿ / ﻿44.50974°N 88.31027°W﻿ / 44.50974; -88.31027﻿ (Newton Blackmour State Trail, eastern end)). However, if a hiker begins in Seymour, the downtown area at Nagel Park makes a good trail head. Nagel Park is located at Main and Depot Streets in downtown Seymour. The trail runs right through the park. The park has a community museum, a train museum located in an old depot, and an old general store. There is plenty of public parking. Nearby are a grocery store, gas station, and several restaurants.
# Reidar Andersen

Reidar Andersen (20 April 1911 – 15 December 1991) was a Norwegian ski jumper who competed in the 1930s.

## Career

He won a ski jumping bronze at the 1936 Winter Olympics in Garmisch-Partenkirchen. In addition, he won ski jumping silver medals at the 1930, 1935, and 1937 FIS Nordic World Ski Championships.
On 14 and 15 March 1935 he set a total of three world records (93, 98 and 99 metres) on Bloudkova velikanka hill in Planica, Kingdom of Yugoslavia.
Andersen won the Holmenkollen ski festival's men's ski jumping competition in 1936, 1937, and 1938, the only person to ever win this event three straight years.
In 1938, Andersen shared the Holmenkollen medal with fellow Norwegian Johan R. Henriksen.

## Ski jumping world records

| Date | Hill | Location | Metres | Feet |
| 14 March 1935 | Bloudkova velikanka K106 | Planica, Kingdom of Yugoslavia | 93 | 305 |
| 15 March 1935 | Bloudkova velikanka K106 | Planica, Kingdom of Yugoslavia | 98 | 322 |
| 15 March 1935 | Bloudkova velikanka K106 | Planica, Kingdom of Yugoslavia | 99 | 325 |
# Transition metal thioether complex

Transition metal thioether complexes comprise coordination complexes of thioether (R$_2$S) ligands. The inventory is extensive.

## Dimethylsulfide complexes

As the simplest thioether, dimethyl sulfide forms complexes that are illustrative of the class. Well characterized derivatives include cis-[TiCl$_4$L$_2$], VCl$_3$L$_2$, NbCl$_5$L, NbCl$_4$L$_2$, Cr(CO)$_5$L, CrCl$_3$L$_3$, RuCl$_2$L$_4$, RuCl$_3$L$_3$, RhCl$_3$L$_3$, cis- and trans-[IrCl$_4$L$_3$]$^−$, cis-MCl$_2$L$_2$ (M = Pd, Pt), [PtCl$_3$L]$^−$, cis- and trans-[PtCl$_4$L$_2$] (L = SMe$_2$). With respect to donor properties, dimethyl sulfide is a soft ligand with donor properties weaker than phosphine ligands. Such complexes are generally prepared by treating the metal halide with the thioether. Chloro(dimethyl sulfide)gold(I) can however be prepared by redox reaction of elemental gold and DMSO in the presence of hydrochloric acid.

## Stereochemistry

Thioether complexes feature pyramidal sulfur centers. Typical C-S-C angles are near 99° in both free thioethers and their complexes. The C-S distance in dimethylsulfide is 1.81 Å, which is also unaffected in its complexes. The stereochemistry of thioether complexes have been extensively studied. Unsymmetrical thioethers, e.g., SMeEt, are prochiral ligands, and their complexes are chiral. One example is [Ru(NH$_3$)$_5$(SMeEt)]$^{2+}$. The complex cis-VOCl$_2$(SMeEt)$_2$ exists as meso- and a pair of enantiomers. In complexes of thioethers of the type S(CH$_2$R)$_2$ (R ≠ H), the methylene protons are diastereotopic. Examination of the NMR spectra of such complexes reveal that they undergo inversion at sulfur, without dissociation of the M-S bond.

## Thioether as a bridging ligand

Unlike ethers, thioethers occasionally serve as bridging ligands. The complexes Nb$_2$Cl$_6$(SMe$_2$)$_3$ is one such example. It adopts a face-sharing bioctahedral structure with a Nb(III)=Nb(III) bond, spanned by two chloride and one dimethylsulfide ligands. The complex Pt$_2$Me$_4$(μ-SMe$_2$)$_2$ is a source of "PtMe$_2$".

## Complexes chelating thioether ligands

* Structure of [Ag(18-ane-S6)]$^{2+}$. The Ag-S distances are 2.62 Å.
* Structure of [Ru(15-ane-S5)Cl]$^+$.
* Structure of (DTCO)PdCl$_2$.
Thiacrown ligands are analogous to crown ethers. The best studied thiacrown ligands have the formula (SCH$_2$CH$_2$)$_n$ (n = 3,4,5,6). The tridentate tri-thioether 9-ane-S3 forms extensive families of complexes of the type M(9-ane-S3)L$_3$ and [M(9-ane-S3)$_2$]$^{2+}$. Examples of Cu(II)-thioether complexes were prepared from 14-ane-S4 and 15-ane-S5. The hexadentate ligand 18-ane-6 also forms extensive family of complexes, including unusual examples of Pd(III) and Ag(II). Examples of homoleptic complexes [M(SR$_2$)$_6$]$^{n+}$ are otherwise rare.

## Occurrence

Thioether complexes in nature arise from coordination of the sulfur substituent found in the amino acid methionine. One of the axial ligands in cytochrome c is illustrative. Methionine sulfur weakly binds to copper in azurin.
# Harriet Lundgren

Harriet M. Lundgren (November 20, 1907 – January 1996) was prima ballerina for the Chicago Civic Opera Company from 1922 until 1932. She was also a ballet teacher.

## Early life and education

Lundgren was born in Chicago, the daughter of Martin Lundgren and Ida Lundgren. Both of her parents were born in Sweden. As a teenager, she trained with several prominent ballet companies, including the Hazel Wallack Studio, the Pavley-Oukrainsky Ballet, and the Adolph Bolm Company.

## Career

In 1925, Lundgren was in the production of The Legend of the Nile with the Civic Opera. She toured in production called A Bird Fantasy in 1926, including at the Palace Theatre in Dallas, Texas and in Kansas City's Newman Theater. She made an appearance as a bird of paradise in the final number of the silent film A Social Celebrity (1926) with Vivian Gonchar, with whom she had toured. In 1927, she joined the faculty of the Bush Conservatory of Music in Chicago.
In 1936, she was announced as the principal dancer with the new Coe Glade touring company. She and her dancers performed in the Glade productions of Rigoletto and Carmen in Duluth, Madison, Sioux City, Minneapolis, and other midwestern cities. Lundgren was one of the principal dancers in the Outdoor Opera of Soldier Field productions of Aida and Il Trovatore in Chicago in 1936.
After her tenure at the opera, Lundgren taught Russian and Italian ballet at the Bush Conservatory, eventually opening her own school in the Edgewater Beach Apartments, which remained open until the 1960s.

## Personal life

In 1928, Lundgren was engaged to Chase Baromeo, an American basso singer with the Chicago Civic Opera. Instead, Baromeo married pianist Delphie Lindstrom, in 1931. Lundgren died in 1996, at the age of 88, in Chicago.
# The Devil in Stitches

"The Devil in Stitches" is a song written by Brett Gurewitz and performed by Bad Religion. It was the first single from their fifteenth studio album, The Dissent of Man, which was released on September 28, 2010.

## Chart performance

The song impacted radio on August 24, 2010, reaching No. 39 on the Hot Modern Rock Tracks, while it reached No. 38 on the Rock Songs chart. It was also the 24th most played song on KROQ in 2010.

## Appearances

The song was among those that appeared on formerly popular apps Tap Tap Revenge 3 and Tap Tap Revenge 4. Though the apps have now been taken off the App Store due to Disney no longer supporting it, the game and song remain for those who downloaded it previously.
# Mohammad Amin Kazemian

Mohammad Amin Kazemian (Persian: محمدامین کاظمیان; born 22 July 1996) is an Iranian football midfielder who plays for Aluminium Arak in the Persian Gulf Pro League.

## Club career
### Mes Kerman

He started football with his hometown team, Mes Kerman, and after playing for the reserve team, he was promoted to the premier league with the main team and was one of the main members of the team in the 2022–23 Persian Gulf Pro League.
# Abbas Mohammadi

Abbas Mohammadi (Persian: عباس محمدی, born August 23, 1975) is a retired Iranian football goalkeeper who mostly played at Iran's Premier Football League.

## Club career

Abbas Mohammadi played for Mes Kerman F.C. before moving to Sepahan F.C. in 2007. With Sepahan he was able to play in the AFC Champions League and his ability and effort was the reason Sepahan made it to Final match before losing to Urawa Red Diamonds. Mohammadi was also able to play in the 2007 FIFA Club World Cup with Sepahan and was again one of their top players.

### Club career statistics

    As of 13 June 2012
| Club performance | Club performance | Club performance | League | League | Cup | Cup | Continental | Continental | Total | Total |
| Season | Club | League | Apps | Goals | Apps | Goals | Apps | Goals | Apps | Goals |
| Iran | Iran | Iran | League | League | Hazfi Cup | Hazfi Cup | Asia | Asia | Total | Total |
| 2006–07 | Mes | Division 1 | 26 | 0 | | 0 | - | - | | 0 |
| 2007–08 | Sepahan | Pro League | 18 | 0 | | 0 | 9 | 0 | | 0 |
| 2008–09 | Sepahan | Pro League | 13 | 0 | | 0 | 0 | 0 | | 0 |
| 2009–10 | Mes | Pro League | 22 | 0 | | 0 | 2 | 0 | | 0 |
| 2010–11 | Tractor Sazi | Pro League | 3 | 0 | 2 | 0 | - | - | 5 | 0 |
| 2011–12 | Tractor Sazi | Pro League | 10 | 0 | 1 | 0 | - | - | 11 | 0 |
| 2011–12 | Sanat Naft | Pro League | 8 | 0 | 0 | 0 | - | - | 8 | 0 |
| Total | Iran | Iran | 95 | 0 | | 0 | 11 | 0 | | 0 |
| Career total | Career total | Career total | 95 | 0 | | 0 | 11 | 0 | | 0 |

## International career

He made his debut for Iran in a friendly match against Costa Rica on January 30, 2008.
# Meysam Khayyam

Meysam Khayyam (Persian: میثم خیام; born 4 May 1992) is an Iranian professional futsal player. He is currently a member of Crop in the Iranian Futsal Super League.

## Honours
### Country

* Asian Indoor and Martial Arts Games
** Champion (1): 2013

### Club

* Iranian Futsal Super League
** Champion (1): 2019–20 (Mes Sungun)