OpenLLM-France/wikimedia huggingface dataset:
# Sphere packing in a sphere

Sphere packing in a sphere is a three-dimensional packing problem with the objective of packing a given number of equal spheres inside a unit sphere. It is the three-dimensional equivalent of the circle packing in a circle problem in two dimensions.
| Number of inner spheres | Maximum radius of inner spheres | Maximum radius of inner spheres | Packing density | Optimality | Arrangement | Diagram |
| Number of inner spheres | Exact form | Approximate | Packing density | Optimality | Arrangement | Diagram |
| 1 | $1$ | 1.0000 | 1 | Trivially optimal. | Point | |
| 2 | ${\dfrac {1}{2}}$ | 0.5000 | 0.25 | Trivially optimal. | Line segment | |
| 3 | $2{\sqrt {3}}-3$ | 0.4641... | 0.29988... | Trivially optimal. | Triangle | |
| 4 | ${\sqrt {6}}-2$ | 0.4494... | 0.36326... | Proven optimal. | Tetrahedron | |
| 5 | ${\sqrt {2}}-1$ | 0.4142... | 0.35533... | Proven optimal. | Trigonal bipyramid | |
| 6 | ${\sqrt {2}}-1$ | 0.4142... | 0.42640... | Proven optimal. | Octahedron | |
| 7 | ${\frac {1}{{\frac {{\sqrt {3}}+2\cos \left({\frac {\pi }{18}}\right)}{\sqrt {2+2{\sqrt {3}}\cos \left({\frac {\pi }{18}}\right)}}}+1}}$ | 0.3859... | 0.40231... | Proven optimal. | Capped octahedron | |
| 8 | ${\frac {1}{{\sqrt {2+{\frac {1}{\sqrt {2}}}}}+1}}$ | 0.3780... | 0.43217... | Proven optimal. | Square antiprism | |
| 9 | ${\frac {{\sqrt {3}}-1}{2}}$ | 0.3660... | 0.44134... | Proven optimal. | Tricapped trigonal prism | |
| 10 | | 0.3530... | 0.44005... | Proven optimal. | | |
| 11 | ${\dfrac {{\sqrt {5}}-3}{2}}+{\sqrt {5-2{\sqrt {5}}}}$ | 0.3445... | 0.45003... | Proven optimal. | Diminished icosahedron | |
| 12 | ${\dfrac {{\sqrt {5}}-3}{2}}+{\sqrt {5-2{\sqrt {5}}}}$ | 0.3445... | 0.49095... | Proven optimal. | Icosahedron | |
# Speedline

Speedline may refer to:
* Speed line, artistic lines indicating speed and direction of travel
* PATCO Speedline, a rapid transit system
* Speedline Corse and Speedline Truck, brands of magnesium wheels produced by Ronal
* SPEEDLINE, the call sign for the former Airspeed Aviation; see Abbotsford International Airport
* SpeedLine, a rifle manufactured by Verney-Carron
# Sphire Croid

Sphire-Croid is the first studio album of the Japanese rock band Rentrer en Soi. It was released on 26 January 2005 in Japan and produced by Yukari, the vocalist of Baiser. On their debut full-length album, Rentrer en Soi take a much more mellow approach to their music compared to the band's later adapted, heavy metal influenced style.

## Track listing

All lyrics are written by Satsuki
# Spherium

The "spherium" model consists of two electrons trapped on the surface of a sphere of radius $R$. It has been used by Berry and collaborators to understand both weakly and strongly correlated systems and to suggest an "alternating" version of Hund's rule. Seidl studies this system in the context of density functional theory (DFT) to develop new correlation functionals within the adiabatic connection.

## Definition and solution

The electronic Hamiltonian in atomic units is
    ${\hat {H}}=-{\frac {\nabla _{1}^{2}}{2}}-{\frac {\nabla _{2}^{2}}{2}}+{\frac {1}{u}}$
where $u$ is the interelectronic distance. For the singlet S states, it can be then shown that the wave function $S(u)$ satisfies the Schrödinger equation
    $\left({\frac {u^{2}}{4R^{2}}}-1\right){\frac {d^{2}S(u)}{du^{2}}}+\left({\frac {3u}{4R^{2}}}-{\frac {1}{u}}\right){\frac {dS(u)}{du}}+{\frac {1}{u}}S(u)=ES(u)$
By introducing the dimensionless variable $x=u/2R$, this becomes a Heun equation with singular points at $x=-1,0,+1$. Based on the known solutions of the Heun equation, we seek wave functions of the form
    $S(u)=\sum _{k=0}^{\infty }s_{k}\,u^{k}$
and substitution into the previous equation yields the recurrence relation
    $s_{k+2}={\frac {s_{k+1}+\left[k(k+2){\frac {1}{4R^{2}}}-E\right]s_{k}}{(k+2)^{2}}}$
with the starting values $s_{0}=s_{1}=1$. Thus, the Kato cusp condition is
    ${\frac {S'(0)}{S(0)}}=1$.
The wave function reduces to the polynomial
    $S_{n,m}(u)=\sum _{k=0}^{n}s_{k}\,u^{k}$
(where $m$ the number of roots between $0$ and $2R$) if, and only if, $s_{n+1}=s_{n+2}=0$. Thus, the energy $E_{n,m}$ is a root of the polynomial equation $s_{n+1}=0$ (where $\deg s_{n+1}=\lfloor (n+1)/2\rfloor$) and the corresponding radius $R_{n,m}$ is found from the previous equation which yields
    $R_{n,m}^{2}E_{n,m}={\frac {n}{2}}\left({\frac {n}{2}}+1\right)$
$S_{n,m}(u)$ is the exact wave function of the $m$-th excited state of singlet S symmetry for the radius $R_{n,m}$.
We know from the work of Loos and Gill that the HF energy of the lowest singlet S state is $E_{\rm {HF}}=1/R$. It follows that the exact correlation energy for $R={\sqrt {3}}/2$ is $E_{\rm {corr}}=1-2/{\sqrt {3}}\approx -0.1547$ which is much larger than the limiting correlation energies of the helium-like ions ($-0.0467$) or Hooke's atoms ($-0.0497$). This confirms the view that electron correlation on the surface of a sphere is qualitatively different from that in three-dimensional physical space.

## Spherium on a 3-sphere

Loos and Gill considered the case of two electrons confined to a 3-sphere repelling Coulombically. They report a ground state energy of ($-.0476$).
# Sporting Clube de Pombal

Sporting Clube de Pombal (also known as Sporting de Pombal, SC Pombal or Sp. Pombal) is a Portuguese sports club from Pombal. It was established on 20 October 1922 as the branch number 10 of Sporting Clube de Portugal (Sporting CP). The sports club has 1,200 affiliated paying members (sócios) and is dedicated to the following sports: football (seniors, juniors, youths, beginners, children U-11 and U-12, and schools); camping; swimming; acrobatic gymnastics; and karate.
# Sphingobacterium daejeonense

Sphingobacterium daejeonense is a Gram-negative, strictly aerobic, non-spore-forming and non-motile bacterium from the genus of Sphingobacterium which has been isolated from compost.
# Spiralix

Spiralix is a genus of very small aquatic snails, operculate gastropod mollusks in the family Moitessieriidae.

## Species

* Spiralix affinitatis Boeters, 2003
* Spiralix asturica Quiñonero-Salgado, Ruiz-Cobo & Rolán, 2017
* Spiralix burgensis Boeters, 2003
* Spiralix burgundina (Locard, 1883)
* Spiralix calida Corbella, Guillén, Prats, Tarruella & Alba, 2014
* Spiralix clarae Quiñonero-Salgado, Ruiz-Cobo & Rolán, 2017
* Spiralix collieri (Nicolas, 1891)
* Spiralix cubelli Quiñonero-Salgado, López-Soriano, Á. Alonso & Rolán, 2020
* Spiralix gloriae (Rolán & Martínez-Ortí, 2003)
* Spiralix gusii Quiñonero-Salgado, López-Soriano, Á. Alonso & Rolán, 2020
* Spiralix heisenbergi Quiñonero-Salgado, Á. Alonso & Rolán, 2021
* Spiralix hofmanni Boeters & Falkner, 2003
* Spiralix kuiperi Boeters & Falkner, 2009
* Spiralix mieraensis Quiñonero-Salgado, Ruiz-Cobo & Rolán, 2017
* Spiralix ovidiensis Girardi & Bertrand, 2009
* Spiralix pequenoensis Boeters, 2003
* Spiralix puteana (Coutagne, 1883)
* Spiralix rayi (Bourguignat, 1883)
* Spiralix thaisensis Girardi, 2009
* Spiralix tuba Quiñonero-Salgado, Á. Alonso & Rolán, 2019
* Spiralix valenciana Boeters, 2003
* Spiralix vetusta Quiñonero-Salgado, Á. Alonso & Rolán, 2018
* Spiralix vitrea (Draparnaud, 1801)

### Synonyms

* Spiralix corsica (R. Bernasconi, 1994) : synonym of Corseria corsica (R. Bernasconi, 1994) (new combination)
# Spiralizoros

Spiralizoros is a genus of zorapterans in the family Spiralizoridae. There are about eight described species in Spiralizoros. The species of this genus were transferred from the genus Zorotypus as a result of research published in 2020.

## Species

These species belong to the genus Spiralizoros:
* Spiralizoros buxtoni (Karny, 1932)
* Spiralizoros caudelli (Karny, 1923)
* Spiralizoros cervicornis (Mashimo, Yoshizawa & Engel, 2013)
* Spiralizoros ceylonicus (Silvestri, 1913)
* Spiralizoros hainanensis (Yin & Li, 2015)
* Spiralizoros magnicaudelli (Mashimo, Engel, Dallai, Beutel & Machida, 2013)
* Spiralizoros philippinensis (Gurney, 1938)
* Spiralizoros silvestrii (Karny, 1927)
# Spulerina isonoma

Spulerina isonoma is a moth of the family Gracillariidae. It is known from India (Bihar), Malaysia and Thailand.
The larvae feed on Mangifera indica. They probably mine the leaves or stems of their host plant.
# Squatting in Bangladesh

Squatting in Bangladesh occurs when squatters make informal settlements known as "bastees" on the periphery of cities such as Chittagong, Dhaka and Khulna. As of 2013, almost 35 per cent of Bangladesh's urban population lived in informal settlements.

## History

Squatting in the territory which would become Bangladesh has a long history, reaching back to the Mughal Empire. After the Partition of Bengal in 1947, Muslims migrated to what became East Pakistan. In contemporary times, squatting since the 1971 Bangladesh Liberation War has resulted from factors such as migration from rural areas to urban ones, the lack of affordable housing, bad governance and natural disasters.$^{:17–18}$ As well as informal settlements on the ground, there are rooftop slums and boat squatters. There are also rural squatters who make land grabs.
During the Bangladesh famine of 1974, flooding affected 80 per cent of the country and almost 100,000 people were displaced to 183 camps in Dhaka. After the flooding subsided, many refugees decided to live in informal settlements on the periphery of Dhaka rather than going home.$^{:25–26}$ These are known as "bastees". At the time this was the only available option since there was already a housing deficit of 47,195 units and little option to rent, except in the innercity slums. Thus ten per cent of Dhaka's population were squatters in 1974.$^{:31–36}$ The following year, the government began a forcible resettlement program which moved 200,000 squatters either back to their villages or into camps at Demra, Mirpur and Tongi. Whilst most resettled people stayed in the camps, this did not stop informal settlements growing in Dhaka.
In the early 1990s, the city of Chittagong had a population of just over 1.5 million, of which there were an estimated 66,676 squatters living in 69 areas. As of 2013, almost 35 per cent of Bangladesh's urban population lived in informal settlements. In Khulna, the largest squatted area was Supraghat, with 15,875 residents.
# St. Gerard's Roman Catholic Church

Saint Gerard's Roman Catholic Church is located at 1190 E Delavan Avenue, in the East Side of Buffalo, New York. The Roman Basilica-style church previously served as a Catholic parish of the Roman Catholic Diocese of Buffalo. The church held its final full mass on January 1, 2008, and currently sits secured but deteriorating.

## History

This church is the second to the parish, and was built in response to demand for a larger place of worship. The building, a Roman Basilica style, is based on the design of Basilica of Saint Paul Outside the Walls in Rome, being one-third as large. The interior of the church contains 12 granite columns, a coffered ceiling, 15 murals, 26 rondos, and a fresco. In 1930 the nave was raised to 60 ft. and a three-stage, 110 ft. bell tower was added.

## Moving the Church

In October 2008, "Mary Our Queen" parish in Norcross, Georgia expressed interest in moving the church 900 miles south to serve as their new house of worship. Their $16 million plans call for the church to be completely deconstructed, packed, and trucked south for reassembly for continued use as a Catholic church. During the summer of 2010, "Mary Our Queen" arranged the removal of a 7 ft, 1600 lb statue of St. Gerard. The statue was broken in two while being transported to their Georgia parish. In July 2016 the 47 beautiful stained glass windows were removed from the church. The windows will be restored by Lynchburg Stained Glass and re-installed at the new "Mary Our Queen" parish in Georgia. Eventually the deal to move the church fell through and the building was sold to an Islamic group to be used as a mosque.

## Gallery

* Front outside View
* Adjacent school house
* The church as it appeared in a 1914 publication
# Sprint Cup (trophy)

The Sprint Cup Trophy is the trophy that was presented to the championship winner of the premier series of the National Association for Stock Car Auto Racing (NASCAR) from 2004 to 2016.
It is made of sterling silver with a wood base and it depicts two checkered flags in flight, and was created by silversmiths Tiffany & Co., whose other major championship trophies in sports have included the World Series (Major League Baseball) Commissioner's Trophy, the NFL's Vince Lombardi Trophy, given to the champions of the Super Bowl, the Larry O'Brien Trophy, handed to the playoff champions of the NBA following the NBA Finals, and the Philip F. Anschutz Trophy, given to the champions of Major League Soccer.
The trophy is 24 inches (61 cm) tall and weighs 27 pounds (12 kg). It was designed in 2003 by Bruce Newman and was first awarded in 2004 to series champion Kurt Busch and the last one being awarded to Jimmie Johnson in 2016.
The Sprint Cup was awarded to the driver who scores the most points after the Chase for the Sprint Cup at a post season awards banquet in Las Vegas (formerly New York City) in December and is crowned the champion for that season. The winner maintains permanent possession of the trophy, but some teams display the trophy in their race shop. Also teams who had not won a Sprint Cup usually had a reserved display case located in their race shop for the trophy.
Traditionally, there were three Sprint Cup trophies handed out; one each to the championship driver, team, and primary sponsor.
There was a permanent Sprint Cup trophy at the Daytona 500 Experience next to Daytona International Speedway that featured all of the past champions into perpetuity. Another Sprint Cup was located within NASCAR's New York City offices that is put on display during "Championship Week", when the annual awards ceremony and banquet honoring that year's champion is held and another one travels from track-to-track as part of the Sprint Experience tour.
# Sprint Cup

Sprint Cup may refer to:
* Sprint Cup Series, an auto racing series in the United States
** Sprint Cup (trophy), the trophy awarded to the winner of the Sprint Cup Series driver's championship
* Haydock Sprint Cup, a horse race in the United Kingdom
* Sprint Cup (Hong Kong), a horse race in Hong Kong
# St. Paul's Presbyterian Church

St. Paul's Presbyterian Church may refer to:
* St Paul's Presbyterian Church, Spring Hill, a heritage-listed Presbyterian church in Brisbane, Queensland, Australia
* St Paul's Uniting Church, Mackay or St Paul's Presbyterian Church, Queensland, Australia
* St. Paul's Presbyterian Church Merigomish, a Presbyterian congregation in Nova Scotia, Canada
* St. Paul's Presbyterian Church, Glace Bay, a Presbyterian congregation in Nova Scotia, Canada
* St. Paul's Presbyterian Church (Hamilton, Ontario), a congregation of the Presbyterian Church in Canada
* St. Paul's Presbyterian Church (Leaskdale), a Presbyterian Church in Canada congregation in Uxbridge Township, Ontario, Canada
* St. Paul's Presbyterian Church (Peterborough, Ontario), a Presbyterian Church in Canada congregation
* Central Presbyterian Church (Saint Paul, Minnesota), US
* St. Paul's German Presbyterian Church and Cemetery, a historic place in Elmont, New York, US
* St. Paul's Presbyterian Church (Somerset, Pennsylvania), US, a NRHP historic district contributing property
* St. Paul Presbyterian Church (Lowland, Tennessee), US
# St. Columba's High School

St Columba's High School may refer to: is a school
* St Columba's High School, Gourock in Inverclyde, Scotland, United Kingdom
* St Columba's Catholic College in Australia
# St. Columba Church (Saint Paul, Minnesota)

The Church of St. Columba is a Roman Catholic church in Saint Paul, Minnesota, United States. The parish was formed in the Hamline-Midway neighborhood in 1915. After the mid-twentieth century baby boom, the church was expanding and needed a new building. Then-pastor Michael Casey contracted with architect Barry Byrne to design and construct the building. Byrne was based in Chicago and his formal schooling ended in the Ninth Grade. Byrne worked under Frank Lloyd Wright and was involved with the Prairie School of architecture before later turned towards Expressionist architecture. Byrne designed the building later in his career.
The 1949 church is very similar in design to St. Francis Xavier Church in Kansas City, Missouri, that was also designed by Byrne. The pastor Michael Casey had the bell tower built to look like an Irish round tower. The interior of the church is built from two overlapping circles. This creates an elliptical interior and an overhead profile that resembles a fish. The fish is one of the earliest symbols of Christianity and the construction of the shape of the church was undoubtedly intentional. The amount of light available on the inside of the building is worth mentioning. There are more than 24 slit like clerestory windows that let natural light in. The interior lightness contrasts with the heavy concrete exterior. The interior of the church features an under lit cove close to the ceiling. Twin Cities architecture critic Larry Millett views the altar as being small for the large interior of the building. Vincent Michael also believes that the altar is undersized compared to the size of the nave.
Unlike St. Francis Xavier the entrance doors are made of metal instead of polished glass. Michael Vincent believes it still leaves the impression of emptiness underneath the bell tower. To create the internal shape the external walls are curved. They are constructed of limestone. There is a large amount of concrete and has been described as a "tour de force" of concrete. Several elements of the church are viewed as unique due to their combination. Millett sees the slots in the bell tower, the granite crosses embedded in the exterior walls and the metal on the entrance doors as a special grouping.
Millett describes the building as a "high point in modern church architecture in the Twin Cities" and notes it as being removed from many religious and architectural norms. Other critiques note it as having shapes and orders that defy orthodox expectations.

## School

The parish had an elementary school for 82 years until it was closed in 2004 due to a decline in enrollment and a large amount of debt.
# St Andrews (New) railway station

St Andrews railway station was the second station to be built in the town of St Andrews, Fife, Scotland. The station, which was in service from 1887 to 1969, was built by the St Andrews Railway and the Anstruther and St Andrews Railway.

## History

The station opened on 1 June 1887 by the North British Railway replacing the first station (which became a goods yard and depot). Although built to a two-track standard, the railway only had one line. The station, which was built within a stone-walled cutting on the edge of the town, had a side and an island platforms on either side of the single track and a side bay with a siding in place of a second through line. Rail traffic was controlled by a signal box on the west side of the stone cutting.
In 1965, the line south of the town, which had been the Anstruther and St Andrews Railway, was closed making St Andrews the terminus of the line for services from Leuchars railway station on the Edinburgh–Dundee line. The signal box closed in 1967. The station, along with the entire line, closed on 6 January 1969. The site, which has retained the walls of the stone cutting, is now used for onroad parking.
# St Andrews Beach, Victoria

St Andrews Beach is a coastal village in the southern extremity of the Mornington Peninsula in Melbourne, Victoria, Australia, 68 km (42 mi) south of Melbourne's Central Business District, located within the Shire of Mornington Peninsula local government area. St Andrews Beach recorded a population of 974 at the 2021 census.
St Andrews Beach is located on the Bass Strait side of the Mornington Peninsula and it is south of Rye. It forms part of a 35-kilometre (22 mi) continuous stretch of beach that runs from Cape Schank to Portsea. It is a popular surf location with many good breaks that attracts surfers all year round.
The settlement was first subdivided in 1959 and the subdivision was originally marketed as "Capri Beach". In 1962 a golf course (since closed) was constructed and the subdivision was re-marketed as St. Andrews by the Sea. Originally the homes that were built were small holiday homes but later in the 20th century more substantial homes began to be built as its location became more appreciated. At this time the name St Andrews Beach was adopted by the Council as its official name. Along with much of the Mornington Peninsula, land prices increased dramatically in 2020 and 2021.
St Andrews Beach is in the local government area of the Shire of Mornington Peninsula. At the 2001 census, St Andrews Beach had a population of 664, at the 2007 Census the population was 769, at the 2011 Census the population was 1,138, and at the 2016 Census, the population was 889.
St Andrews Beach features a unique topography known as The Cups Country, which creates an ideal environment for golf courses. Golfers have a choice of several nearby golf courses including the St Andrews Beach Club on Sandy Road, Moonah Links off Truemans Road, and The Dunes on Browns Road.
It is known for its good surf and while popular with experienced surfers, the beach’s history of dangerous rips, fast changing conditions and lack of lifeguards means swimmers should instead choose to swim at one of the Peninsula’s ‘front beaches.’
# St. James Roman Catholic Church (Crosstown, Missouri)

St. James Catholic Church is a Catholic church in Crosstown, Missouri. It is operated as a mission church of the parish of St. Vincent de Paul in Perryville. It is under the jurisdiction of the Ste. Genevieve Deanery of the Archdiocese of St. Louis.

## History

The original mission church started in a private home in 1860s. The frame church was begun in 1884 and finished in 1889. The church was restored after the fire of 1926.
# St. Dominic Hospital

St. Dominic Catholic Hospital (SDCH) is a not-for-profit Catholic medical facility located in Akwatia in the Denkyembour District in the Eastern Region of Ghana. On 10 January 2024, the hospital received a magnetic resonance imaging (MRI) scanner to be the first in the Eastern Region to receive the device. The device was inaugurated by EASE Ghana.

## History

The hospital was established in 1960.
In 1998, the Chaplain at the hospital was Monsignor Alex Bobby-Benson.
As at 2008, Dr Mrs Constance Addo Yobo was a chief dental surgeon at the hospital. As at 2008, Dr Mrs Mercy Dawson was a medical superintendent at the hospital.
As at 2024, the manager and administrator of the hospital is Rev. Fr. Ebenezer Kenneth Abban PhD. As at 2024, Dr Maite Alfonso Romero is the medical director of the hospital.

## Facilities

* COVID-19 High Dependency Unit (HDU)
* Dental clinic
* Neo Natal Intensive-Care Unit (NICU)
* Solar plant

## Controversy

In 2016, it was alleged the head of finance of the hospital, Mr. Yaw Opoku Agyei spearheaded fraudulent activity at the hospital which caused the Government of Ghana to lose money.
In 2022, the hospital was accused by Madam Lydia Dagasu of neglecting her baby.