OpenLLM-France/wikimedia huggingface dataset:
# Riemann Xi function

In mathematics, the Riemann Xi function is a variant of the Riemann zeta function, and is defined so as to have a particularly simple functional equation. The function is named in honour of Bernhard Riemann.

## Definition

Riemann's original lower-case "xi"-function, $\xi$ was renamed with an upper-case $~\Xi ~$ (Greek letter "Xi") by Edmund Landau. Landau's lower-case $~\xi ~$ ("xi") is defined as
    $\xi (s)={\frac {1}{2}}s(s-1)\pi ^{-s/2}\Gamma \left({\frac {s}{2}}\right)\zeta (s)$
for $s\in \mathbb {C}$. Here $\zeta (s)$ denotes the Riemann zeta function and $\Gamma (s)$ is the Gamma function.
The functional equation (or reflection formula) for Landau's $~\xi ~$ is
    $\xi (1-s)=\xi (s)~.$
Riemann's original function, rebaptised upper-case $~\Xi ~$ by Landau, satisfies
    $\Xi (z)=\xi \left({\tfrac {1}{2}}+zi\right)$,
and obeys the functional equation
    $\Xi (-z)=\Xi (z)~.$
Both functions are entire and purely real for real arguments.

## Values

The general form for positive even integers is
    $\xi (2n)=(-1)^{n+1}{\frac {n!}{(2n)!}}B_{2n}2^{2n-1}\pi ^{n}(2n-1)$
where B$_n$ denotes the n-th Bernoulli number. For example:
    $\xi (2)={\frac {\pi }{6}}$

## Series representations

The $\xi$ function has the series expansion
    ${\frac {d}{dz}}\ln \xi \left({\frac {-z}{1-z}}\right)=\sum _{n=0}^{\infty }\lambda _{n+1}z^{n},$
where
    $\lambda _{n}={\frac {1}{(n-1)!}}\left.{\frac {d^{n}}{ds^{n}}}\left[s^{n-1}\log \xi (s)\right]\right|_{s=1}=\sum _{\rho }\left[1-\left(1-{\frac {1}{\rho }}\right)^{n}\right],$
where the sum extends over ρ, the non-trivial zeros of the zeta function, in order of $|\Im (\rho )|$.
This expansion plays a particularly important role in Li's criterion, which states that the Riemann hypothesis is equivalent to having λ$_n$ > 0 for all positive n.

## Hadamard product

A simple infinite product expansion is
    $\xi (s)={\frac {1}{2}}\prod _{\rho }\left(1-{\frac {s}{\rho }}\right),\!$
where ρ ranges over the roots of ξ.
To ensure convergence in the expansion, the product should be taken over "matching pairs" of zeroes, i.e., the factors for a pair of zeroes of the form ρ and 1−ρ should be grouped together.
# Kalinić

Kalinić (Serbian Cyrillic: Калинић, pronounced) is a surname found in Croatia and Serbia. It may refer to:

## People

* Ivica Kalinić (b. 1956), former Croatian football player and manager
* Lovre Kalinić (b. 1990), Croatian footballer
* Nikola Kalinić (footballer) (b. 1988), Croatian footballer
* Nikola Kalinić (basketball) (b. 1991), Serbian basketballer
* Pavle Kalinić (b. 1959), Croatian politician and writer
* Sretko Kalinić, (b. 1974), Serbian gangster
* Zoran Kalinić (b. 1958), former Yugoslav table tennis player
# Gatine, Alberta

Gatine is a locality in Alberta, Canada.
The locality has the name of one Mrs. Gatine, a railroad employee.
# Gondwana (Murail)

Gondwana (1980) is a defining musical composition of spectral music for large orchestra composed by Tristan Murail using simulated synthesis to create a harmonic interpolation between an orchestrally synthesized chord derived from a simulated bell sound (inharmonic) and a chord derived from a trombone sound (harmonic). This process is meant to evoke the shifting of continents and thus the piece is named after the former supercontinent Gondwana.
The piece uses interpolation to make a smooth transformation on all musical parameters including spectral profile, envelope, and instrumental attacks. The bell sounds were created through a Frequency Modulation (FM) synthesis with a single modulator affecting five carriers to create five different harmonies, these being connected by interpolated chords. The components of the trombone's frequency spectrum was derived through a Fourier transform.
The piece's long quiet or silent moments are shaped in "long, seamlessly evolving paragraphs" evoking the geological processes which created the continent. The first opening slowly transforms a chord before turning to trills. The opening chord has been compared to the work of Messiaen. The piece, "incorporates a substantial passage directly modelled upon," Sibelius's Lemminkäinen in Tuonela from the Four Lemminkäinen Legends op.22 (1896).

## Sources

* 1 2 Staines, Joes (2010). The Rough Guide to Classical Music, p.372. ISBN 978-1-4053-8321-9. "The locus classicus of early spectral music".
* 1 2 Fineberg, Joshua (2000). Spectral Music: History and Techniques, p.69. (Overseas Publishers Association, published by license under the Harwood Academic Publishers imprint, ©2000) OCLC: 48862556. ISBN 978-90-5755-131-4.
* ↑ Sanderson, Blaire. "Tristan Murail: Gondwana; Désintégrations; Time and Again". Retrieved 3 March 2022.
* ↑ Fineberg (2000), p.108
* ↑ Fineberg (2000), p.128-129.
* ↑ "Murail Gondwana & Désintégrations", CompositionToday.com.
* ↑ Griffiths, Paul (2011). Modern Music and After, p.344. ISBN 978-0-19-974050-5.
* ↑ Grimley, Daniel M., ed. (2004). The Cambridge Companion to Sibelius, p.200. ISBN 978-0-521-89460-9.
* This article about a classical composition is a stub. You can help Wikipedia by expanding it.
* v
* t
* e
# Keith Robson

Keith Robson (born 15 November 1953 in Hetton-le-Hole, County Durham) is an English former professional footballer.
Robson, who was usually used as a winger or Utility player, played for Newcastle United youth teams before signing with the first team in 1971. He played only fourteen games over three seasons before signing for West Ham United for £60,000 in 1974. He made his Hammers debut in a League Cup game against Tranmere Rovers on 18 September 1974.
Robson was a member of the team that finished runners-up of the European Cup Winners' Cup in 1976, scoring in the semi-final second leg game against Eintracht Frankfurt and in the final against Anderlecht. He spent time on loan with North American Soccer League team Team Hawaii for the franchise's single season under the moniker, playing with former Hammer Yılmaz Orhan. He played his last game for the east London club on 5 March 1977 against Sunderland.
Robson moved to Cardiff City in August 1977, having scored 19 goals in 87 league games for West Ham. However, his time in South Wales was plagued by disciplinary problems and, in December, he was heavily fined by the club and placed on the transfer list with manager Jimmy Andrews commenting he "had problems with the player since he came here". He went on to play for Norwich City, where he teamed up with ex-West Ham players Alan Taylor, Graham Paddon, Martin Peters and John McDowell. The £25,000 signing scored 13 goals in 65 games for the Carrow Road club before moving to Leicester City. He spent time on loan to Carlisle United where he played with another former Hammer, Pop Robson.
After a short spell in Hong Kong playing with the South China Athletic Association, Robson worked at Impress Metal Packing Co. and played for Norwich Busmen, Corinthian-Casuals and Wroxham, where he became assistant manager in 1993–94.
# Cooronga mcalpinei

Cooronga mcalpinei is a species of tephritid or fruit flies in the genus Cooronga of the family Tephritidae.

## Distribution

Australia.
# Black Market Activities

Black Market Activities (BMA) is an American independent record label that was founded in 2003 by Guy Kozowyk, the frontman of the Boston, Massachusetts-based extreme metal band the Red Chord.

## History

Black Market Activities was started with the stated goal of releasing records by bands that are pushing the boundaries of extreme music while keeping a friendly artist-centered attitude that steers clear of a lot of the "major label" business-like dealings that tend to hurt and exploit bands. The founder of the label being an extreme musician himself, he can more easily relate to the issues that are important to the bands on the label, and attempts to balance the business and art aspects of the music world. BMA is a tight-knit group of bands and friends who share similar ideas and musical tastes.
In the years since its creation, BMA has grown quickly and gained much recognition. Black Market Activities teamed up with long-running metal record label Metal Blade Records on a production and distribution deal which allows all BMA releases to reach the same major stores as Metal Blade releases. This has propelled BMA and all its bands forward quite a bit. It has also, however, lead to some confusion as to which bands are on BMA and which bands are on Metal Blade, as both record labels' logos now appear on the backs of all BMA recordings.

## Artists
### Current artists

* The Abominable Iron Sloth
* Architect
* Behold... The Arctopus
* Bird Eater
* Dance Club Massacre
* Destroy Destroy Destroy
* Ed Gein
* Engineer
* Fit for an Autopsy
* Khann
* Lords
* Lye By Mistake
* the_Network
* Romans
* Stomach Earth
* Sweet Cobra
* Today Is the Day

### Past artists

* Animosity (disbanded in 2009)
* Backstabbers Incorporated (inactive since 2008)
* Beyond the Sixth Seal (now on Metal Blade)
* Born From Pain (now on Metal Blade)
* Cancer Bats (now on Distort Entertainment)
* Deadwater Drowning (disbanded in 2004)
* Found Dead Hanging (changed name to Architect)
* From A Second Story Window (disbanded in 2008)
* Gaza (disbanded in 2013)
* Lamb Of God (now on Epic and Roadrunner)
* Paria (disbanded in 2010)
* Premonitions of War (now on Victory)
* Psyopus (disbanded in 2012)
* The Red Chord (now on Metal Blade)
* Sleep Terror (inactive)
* The Tony Danza Tapdance Extravaganza (disbanded in 2012)
# Bizkarreta-Gerendiain

Bizkarreta-Gerendiain (Spanish: Viscarret-Guerendiáin) is a village located in the Erro municipality of Navarre, The French Way of the Camino de Santiago passes through the town.
# Biên Sơn

Biên Sơn is a commune (xã) and village in Lục Ngạn District, Bắc Giang Province, in northeastern Vietnam.
# Birthright Unplugged

Birthright Unplugged is an educational organization, designed as a response to the Birthright Israel trips. The name "Birthright Unplugged" is a spin on the "Birthright Israel" program.

## History and organization

According to Birthright Unplugged, it was founded in 2003 by Dunya Alwan and Hannah Mermelstein. Alwan, an Iraqi-American of Muslim and Jewish descent, serves as the organization's current director.
In 2005, Birthright Israel filed a "cease and desist" complaint against Birthright Unplugged for trademark infringement, alleging "unfair competition".

## Activities

The Unplugged trip sought to expose mostly North American people to the Palestinian side of the Israeli–Palestinian conflict through travel and conversations with a range of Palestinian activists. In six days, they visited Palestinian cities, villages, and refugee camps in the West Bank and spend time with Palestinian refugees living inside Israel.
The organization ran a second program, Birthright Re-Plugged, which took Palestinian children living in Palestinian refugee camps on field trips in Israel to see the villages left by their families in the 1948 Palestinian expulsion and flight. In two days, they visit Jerusalem, the Mediterranean Sea, and the children's ancestral villages.
# Bismoclite

Bismoclite is a bismuth oxohalide mineral with formula BiOCl. It is the naturally occurring form of bismuth oxychloride. The name was derived from its chemical constituents. It is a secondary bismuth mineral first thought to be composed of bismuthyl ions (BiO$^+$) and chloride anions, however, the existence of the diatomic bismuthyl ion is doubtful.
It is a member of the matlockite group.
It was first described in 1935 from alluvium near bismuth-bearing pegmatites in South Africa. It has been found in association with granite pegmatite and in greisen. Associated minerals include bismutite, mica, jarosite, alunite, cerussite, atacamite, connellite. Occurrences include the type locality at Jackals Water, SW of Prieska, South Africa; Bygoo, Australia; the Tintic district in the East Tintic Mountains of Utah; and from Dalbeattie, Scotland.

## Crystal structure

The crystal structure of bismoclite was found to be composed of linked decahedrons, specifically a square antiprism. These decahedrons consist of 2 squares with sides of 3.487 Å (O-O-O-O and Cl-Cl-Cl-Cl) connected by 8 isosceles triangles (O-Cl-O and Cl-O-Cl), with a bismuth atom at the centre. The Bi-O distances and Bi-Cl distances are 2.316 Å and 3.059 Å, respectively. The O-Cl distances in the triangles are 3.249 Å. The decahedrons are linked to each other through shared O-Cl sides.

## Practical significance

Bismoclite is a rare secondary mineral, a product of the oxidation of basic bismuth ores in the presence of active chlorine ions. In addition, bismoclite does not represent the final oxidation product. For example, during the oxidation of native bismuth under hypergenesis conditions, the intermediate product is bismuth chloride, and the final product is a sparingly soluble carbonate.$^{:96}$ For this reason, bismoclite is found in deposits of bismuthinite and native bismuth in much smaller volumes than the similar minerals bismite and bismuthinite, in which it is often present as an impurity. With the same success as these latter, it can be used to obtain bismuth and its compounds. However, the main significance of bismoclite is purely scientific, allowing more accurate monitoring and determination of geochemical processes in zones of oxidation and weathering of the main bismuth ores.
* In medical diagnostics, bismoclite (in the form of purified bismuth oxychloride) is used as a local radiocontrast agent.
* In addition, in the production of cosmetics, bismoclite is used as an enhancing agent; it gives a pearlescent shine to lipstick, nail polish and eye shadow.
* In the chemical industry, in the process of cracking hydrocarbons, bismuth oxochloride is used as a catalyst.
# Bismo

Bismo is a town in and the administrative centre of Skjåk municipality in Innlandet county, Norway. The village is located along the river Otta in the Ottadalen valley, about 40 kilometres (25 mi) east of Grotli and about 17 kilometres (11 mi) west of Fossbergom.
The 1.2-square-kilometre (300-acre) village has a population (2021) of 634 and a population density of 526 inhabitants per square kilometre (1,360/sq mi).
The Norwegian National Road 15 runs through the village. The lake Aursjoen lies on the mountain plateau just north of the village and the mountain Tverrfjellet lies just south of the village. Skjåk Church lies just east of the village.

## Climate

Data for nearby Bråtå weather station. Bismo has a dry summer subarctic climate (Dsc). Spring and early summer are the driest time of year and fall and winter are the wettest. The coldest month, January, averages −8.8 °C (16.2 °F) while the warmest month, July, averages 11.7 °C (53.1 °F).
Climate data for Bråtå 1961-1990, extremes 1968-2010 :
| Month | Jan | Feb | Mar | Apr | May | Jun | Jul | Aug | Sep | Oct | Nov | Dec | Year |
| Record high °C (°F) | 8.2 (46.8) | 7.7 (45.9) | 10.0 (50.0) | 15.5 (59.9) | 21.6 (70.9) | 27.0 (80.6) | 27.0 (80.6) | 27.0 (80.6) | 23.2 (73.8) | 17.4 (63.3) | 10.0 (50.0) | 7.3 (45.1) | 27.0 (80.6) |
| Mean daily maximum °C (°F) | −5.7 (21.7) | −4.0 (24.8) | −0.1 (31.8) | 3.7 (38.7) | 10.1 (50.2) | 14.8 (58.6) | 16.3 (61.3) | 15.4 (59.7) | 10.0 (50.0) | 4.9 (40.8) | −1.2 (29.8) | −3.7 (25.3) | 5.0 (41.1) |
| Mean daily minimum °C (°F) | −11.8 (10.8) | −11.1 (12.0) | −7.7 (18.1) | −4.1 (24.6) | 1.5 (34.7) | 5.5 (41.9) | 7.1 (44.8) | 6.7 (44.1) | 3.0 (37.4) | −0.6 (30.9) | −6.7 (19.9) | −9.9 (14.2) | −2.3 (27.8) |
| Record low °C (°F) | −35.0 (−31.0) | −28.0 (−18.4) | −23.5 (−10.3) | −17.8 (0.0) | −11.0 (12.2) | −2.6 (27.3) | −4.6 (23.7) | −1.6 (29.1) | −8.7 (16.3) | −16.0 (3.2) | −24.0 (−11.2) | −35.8 (−32.4) | −35.8 (−32.4) |
| Average precipitation mm (inches) | 62 (2.4) | 37 (1.5) | 43 (1.7) | 15 (0.6) | 21 (0.8) | 33 (1.3) | 43 (1.7) | 45 (1.8) | 55 (2.2) | 62 (2.4) | 61 (2.4) | 71 (2.8) | 548 (21.6) |
| Average precipitation days | 10.6 | 7.3 | 7.6 | 3.5 | 5.0 | 7.2 | 8.7 | 8.7 | 10.5 | 10.6 | 10.7 | 11.6 | 102 |
| Source: Met Norway Eklima ||||||||||||||
# Pierre Réal

Pierre Réal (1922 – 13 December 2009) was a French entomologist. He specialised in Lepidoptera.
He was a professor at the Faculty of Besançon.

## Works

His best known work is the book he wrote with Le Moult on the genus Morpho, published as a supplement to the journal Novitates Entomologicae.
A list of 29 of his works is given by J. C. Robert.

## Genera and species he described

1953
* Anoplocnephasia
* Brachycnephasia
* Cnephasia alternella interjunctana
* Cnephasia alternella parvana
* Cnephasia alternella peyerimhoffi
* Cnephasia alternella pseudochrysantheana
* Cnephasia alternella rectilinea
* Cnephasia alternella siennicolor
* Cnephasia alternella vulgaris
* Cnephasia alticola decaryi
* Cnephasia alticola juncta
* Cnephasia bizensis
* Cnephasia canescana griseana
* Cnephasia canescana grisescana
* Cnephasia canescana montserrati
* Cnephasia canescana venansoni
* Cnephasia communana caprionica
* Cnephasia communana lucia
* Cnephasia communana pseudorthoxyana
* Cnephasia communana seminigra
* Cnephasia conspersana albicans
* Cnephasia conspersana gallicana
* Cnephasia conspersana pseudoalternella
* Cnephasia cottiana buvati
* Cnephasia cottiana pyrenaea
* Cnephasia incanana infuscata
* Cnephasia interjecta mediocris
* Cnephasia joannisis dumonti
* Cnephasia legrandi
* Cnephasia longana minor
* Cnephasia obsoletana algerana
* Cnephasia osseana alpicola
* Cnephasia osseana alpicolana
* Cnephasia osseana borreoni
* Cnephasia osseana pratana
* Cnephasia osseana pseudolongana
* Cnephasia osseana solfatarana
* Cnephasia pascuana pseudocommuana
* Cnephasia penziana alpestris
* Cnephasia penziana clarana
* Cnephasia penziana livonica
* Cnephasia sedana mediterranea
* Cnephasia wilkinsoni directana
* Eana cyanescana
* Eana filipjevi
* Eana viardi
1951
* Cnephasia ecullyana
* Cnephasia orthoxyana
* Cnephasia orthoxyana confluentana
* Cnephasia orthoxyana reducta
* Cnephasia orthoxyana styx
* Cnephasia rielana
* Hypostephanuncia
1952
* Cnephasia interjecta confluens
* Cnephasia obsoletana cleuana
* Cnephasia obsoletana pseudotypica
* Cnephasia sedana meridionalis
* Cnephasia wilkinsoni
1988
* Coccidiphila charlierella
* Leptidea lorkovicci, becoming Leptidea reali Reissinger, 1989
* Micopterix liogierella
* Micopterix vallebonella

## Species named after him

* Leptidea reali Reissinger, 1989
# Black robe

Black robe, blackrobe or variant may refer to:
* Black Robes, the Jesuits (Society of Jesus)
* Black Robe, a 1985 historical novel by Brian Moore
* Black Robe (film), a 1991 historical film based on the Brian Moore novel
* The Black Robe, an 1881 epistolary novel by Wilkie Collins
* The Black Robe (film), a 1944 German film
* The Black Robe (TV series), a 1949 American television program
* Blackrobe, a book by Maurice Kenny
* Black Robe Regiment
# Blackburn Royal Infirmary

The Blackburn Royal Infirmary was an acute District General Hospital in Blackburn, Lancashire. It was managed by East Lancashire Hospitals NHS Trust.

## History

Although the foundation stone was laid on 24 May 1858, because of the depressed state of the local cotton industry, the Blackburn Infirmary did not open until 1864. The Victoria Wing was added to commemorate the diamond jubilee of Queen Victoria in 1897. The facility became known as the Blackburn and East Lancashire Royal Infirmary from 1914.
A War Memorial Wing, built to commemorate soldiers who died in the First World War, would not have been completed but for a large donation from Elma Yerburgh, Chairman of Thwaites Brewery: the wing opened in June 1928. Further extensions were completed in 1965 and 1980.
As part of a plan to rationalise acute and tertiary healthcare in the local area, most of the services transferred to the Royal Blackburn Teaching Hospital in July 2006, and the infirmary site was sold to Barratt Developments. The War Memorial Wing was demolished in February 2015.
# Blair Williams (disambiguation)

Blair Williams (born 1992) is an Australian television personality working in South Korea.
Blair Williams may also refer to:
* Blair Williams, a fictional character played by Moon Bloodgood in the 2009 American military science fiction action film Terminator Salvation
* Blair Williams, a performer in the animated television series The Adventures of Chuck and Friends
# Black Rocks (Kauri Bay)

Black Rocks is an island in the Kauri Bay of Northland, New Zealand.
# Pigfish

Pigfish may refer to:
* Fishes in the family Congiopodidae
* Redmouth grunt, Orthopristis chrysoptera (Linnaeus)
* Golden-spot hogfish, Bodianus perditio
* Red pigfish, Bodianus unimaculatus
# Pigface Island Conservation Park

Pigface Island Conservation Park is a protected area in the Australian state of South Australia associated with Pigface Island located in Streaky Bay on the west coast of Eyre Peninsula about 13 kilometres (8.1 miles) north north-east west of the town of Streaky Bay.
It was proclaimed under the National Parks and Wildlife Act 1972 in 1972 for the purpose of conserving a ‘sea bird roosting habitat’. The land under protection had previously been dedicated as a Fauna Conservation Reserve on 2 May 1968. A statement of significance published in 1980 advises: ‘a small island utilised by silvergulls and black-faced cormorants as a breeding area and by other seabirds as a roosting and feeding habitat.’
The conservation park is classified as an IUCN Category Ia protected area. In 1980, the conservation park was listed on the former Register of the National Estate.
# Geoffroy le Rat

Geoffroy le Rat (died 1207) was the thirteenth grand master of the Knights Hospitaller, serving between 1206–1207. He succeeded the Grand Master Fernando Afonso after his resignation in 1206, and was succeeded by Guérin de Montaigu.

## Biography

Geoffroy le Rat did not occupy the position of Grand Master until mid–1206 and the beginning of the second half of 1207. He was of French origin, attached to a family of Touraine.
He had been a commander in the Principality of Antioch and lord of the Krak des Chevaliers before being elected as master.
As the Fourth Crusade was diverted to Constantinople, the Hospitallers did not have a military role at the beginning of the thirteenth century.
# Strong confinement limit

In physics, the strong confinement limit, or "festina lente" limit, is a mode of an atom laser in which the frequency of emission of the Bose–Einstein condensate is less than the confinement frequency of the trap.