OpenLLM-France/wikimedia huggingface dataset:
# Gelfand–Mazur theorem

In operator theory, the Gelfand–Mazur theorem is a theorem named after Israel Gelfand and Stanisław Mazur which states that a Banach algebra with unit over the complex numbers in which every nonzero element is invertible is isometrically isomorphic to the complex numbers, i. e., the only complex Banach algebra that is a division algebra is the complex numbers C.
The theorem follows from the fact that the spectrum of any element of a complex Banach algebra is nonempty: for every element a of a complex Banach algebra A there is some complex number λ such that λ1 − a is not invertible. This is a consequence of the complex-analyticity of the resolvent function. By assumption, λ1 − a = 0. So a = λ · 1. This gives an isomorphism from A to C.
The theorem can be strengthened to the claim that there are (up to isomorphism) exactly three real Banach division algebras: the field of reals R, the field of complex numbers C, and the division algebra of quaternions H. This result was proved first by Stanisław Mazur alone, but it was published in France without a proof, when the author refused the editor's request to shorten his proof. Gelfand (independently) published a proof of the complex case a few years later.
# Russell Sutor

Russell Allan "Russ" Sutor (April 24, 1951 – September 23, 1995) was a businessman and political figure in Saskatchewan. He represented Regina North East from 1982 to 1985 in the Legislative Assembly of Saskatchewan as a Progressive Conservative.
He was born in Mossbank, Saskatchewan, the son of Steve Sutor and Anetta Atkinson. Sutor operated a travel agency, a delivery service and a Regina motel. He served as legislative secretary to the Minister of Economic Development and Trade. Sutor resigned his seat in the Saskatchewan assembly in 1985 citing personal business reasons. He died in Fort Lauderdale, Florida at the age of 44.
# Catajana

Catajana is a monotypic moth genus in the family Eupterotidae described by Embrik Strand in 1910. Its only species, Catajana bimaculata, described by Hermann Dewitz in 1879, is found in Angola and the Democratic Republic of the Congo.
# BO2

BO2 may refer to:

## Arts, entertainment, and media

* Blackout! 2, rap album by Method Man & Redman
** BO2, first song of the Blackout! 2 album
* BO*2, MusiquePlus TV series by the Sckoropad Twins
* Call of Duty: Black Ops II

## Other uses

* Bo.2, see List_of_aircraft_(B)#Borel
* Borate
# Live at Montreux 2000

Live at Montreux 2000 is a concert DVD by Lou Reed, released in 2005 by Eagle Vision. It was recorded at the 2000 Montreux Jazz Festival in Montreux, Switzerland. Reed performed eight songs from his Ecstasy album plus a few older ones.

## Track listing

All tracks composed by Lou Reed; except where indicated
* "Paranoia Key of E" Ecstasy, 2000
* "Turn to Me" New Sensations, 1984
* "Modern Dance" Ecstasy, 2000
* "Ecstasy" Ecstasy, 2000
* "Smalltown" (Reed, John Cale), Songs for Drella, 1990
* "Future Farmers of America" Ecstasy, 2000
* "Turning Around Time" Ecstasy, 2000
* "Romeo Had Juliette" New York, 1989
* "Riptide" Set the Twilight Reeling, 1996
* "Rock Minuet Ecstasy, 2000
* "Mystic Child" Ecstasy, 2000
* "Tatters" Ecstasy, 2000
* "Set the Twilight Reeling" Set the Twilight Reeling, 1996
* "Dirty Blvd." New York, 1989
* "Dime Store Mystery" New York, 1989
* "Perfect Day" Transformer, 1972

## Personnel

* Lou Reed - guitar, vocals
* Fernando Saunders - bass guitar, backing vocals
* Mike Rathke - guitar
* Tony Thunder Smith - drums
# Safety Bay Road

Safety Bay Road is an east-west metropolitan road located in the City of Rockingham, about 50 kilometres (31 mi) south of Perth, Western Australia. The road starts in Rockingham's coastal suburbs and heads south from Peron past Lake Richmond. The road then turns left at the coast with a roundabout with Arcadia Drive which is a coastal road in Shoalwater. Safety Bay Road takes a left turn and extends past Ennis Avenue and Warnbro railway station to the newer suburban estates at Baldivis, before ending just past the Kwinana Freeway. As such, it forms a key link between Rockingham, Perth and Mandurah. Until 2009, the end of the road marked the start of the Kwinana Freeway.
Safety Bay Road was gazetted in 1949, having first existed as two roads – Road No.10168, and a coastal road in Safety Bay known as "The Esplanade".

## Major intersections

The entire road's length is in the City of Rockingham, with all intersections listed below controlled by roundabouts unless otherwise indicated.
| Location | km | mi | Destinations | Notes |
| Rockingham–Peron boundary | 0 | 0.0 | Parkin Street (State Route 18) eastbound/Hymus Street northbound – Rockingham, Kwinana Beach, Fremantle, Garden Island | Northern terminus at T junction. Road continues north as Hymus Street with turnoff to Cape Peron and Garden Island just north of the intersection. |
| Rockingham–Shoalwater–Peron tripoint | 1.0 | 0.62 | Frederick Street – Peron | |
| Safety Bay–Shoalwater boundary | 2.2 | 1.4 | Rae Road – Cooloongup | Access to Rockingham railway station. Uncontrolled T junction |
| Safety Bay | 3.0 | 1.9 | Arcadia Drive (Tourist Drive 202) | Tourist Drive 202's (Rockingham Coastal Drive) northern concurrency terminus. |
| Safety Bay | 5.0 | 3.1 | Malibu Road | |
| Waikiki–Warnbro boundary | 8.3 | 5.2 | Read Street northbound / Warnbro Sound Avenue southbound – Rockingham, Port Kennedy, Secret Harbour, Golden Bay | |
| Waikiki–Warnbro boundary | 9.0– 9.3 | 5.6– 5.8 | Ennis Avenue (National Route 1) – Rockingham, Perth, Mandurah | Dumbbell–Dogbone interchange hybrid, northbound exit ramp looped. Tourist Drive 202's (Rockingham Coastal Drive) southern terminus. |
| Waikiki–Warnbro boundary | 9.5 | 5.9 | Warnbro railway station access road | Signalised intersection |
| Baldivis–Warnbro–Waikiki tripoint | 11.5 | 7.1 | Mandurah Road – Kwinana Beach, Leda, Hillman, Karnup | |
| Baldivis | 13.8 | 8.6 | Nairn Drive | |
| Baldivis | 14.0 | 8.7 | Settlers Avenue | Access to Stockland Baldivis Shopping Centre. Signalised intersection |
| Baldivis | 14.4 | 8.9 | Norseman Approach northbound / Burlington Drive southbound | Signalised intersection |
| Baldivis | 14.9 | 9.3 | Baldivis Road – Wellard, Karnup | |
| Baldivis | 15.4– 15.6 | 9.6– 9.7 | Kwinana Freeway (State Route 2) north and southbound / Folly Road eastbound – Joondalup, Perth, Mandurah, Bunbury | Southern terminus at signalised diamond interchange favouring Kwinana Freeway. Road continues as Folly Road eastbound. |
| 1.000 mi = 1.609 km; 1.000 km = 0.621 mi Concurrency terminus |||||
# Botticelli (crater)

Botticelli is a crater on Mercury. It has a diameter of 136.35 kilometres (84.72 mi). Its name was adopted by the International Astronomical Union (IAU) in 1979. Botticelli is named for the Italian painter Sandro Botticelli, who lived from 1445 to 1510.
Botticelli is one of 110 peak ring basins on Mercury, although its ring is nearly eroded away or flooded by lava.
# Gelfand–Raikov theorem

The Gel'fand–Raikov (Гельфанд–Райков) theorem is a theorem in the mathematics of locally compact topological groups. It states that a locally compact group is completely determined by its (possibly infinite dimensional) unitary representations. The theorem was first published in 1943.
A unitary representation $\rho :G\to U(H)$ of a locally compact group $G$ on a Hilbert space $H=(H,\langle \,,\rangle )$ defines for each pair of vectors $h,k\in H$ a continuous function on $G$, the matrix coefficient, by
    $g\mapsto \langle h,\rho (g)k\rangle$.
The set of all matrix coefficientsts for all unitary representations is closed under scalar multiplication (because we can replace $k\to \lambda k$), addition (because of direct sum representations), multiplication (because of tensor representations) and complex conjugation (because of the complex conjugate representations).
The Gel'fand–Raikov theorem now states that the points of $G$ are separated by its irreducible unitary representations, i.e. for any two group elements $g,h\in G$ there exist a Hilbert space $H$ and an irreducible unitary representation $\rho :G\to U(H)$ such that $\rho (g)\neq \rho (h)$. The matrix elements thus separate points, and it then follows from the Stone–Weierstrass theorem that on every compact subset of the group, the matrix elements are dense in the space of continuous functions, which determine the group completely.
# Libby Wilkinson

Elizabeth Mary "Libby" Wilkinson (born 1965) is an Anglican priest. Since 2020, she has been Archdeacon of Durham in the Church of England's Diocese of Durham
Wilkinson was educated at st Edmund Hall, Oxford. Before ordination she worked for Norwich Union. Her first post was a curacy in Gateshead. She was then priest in charge at Burnmoor. She was the area dean for Houghton-le-Spring. She was Vicar of Bishopswearmouth from 2016 to 2020, since when she has been the archdeacon of Durham.
# Boulder County Poor Farm

Boulder County Poor Farm is the site of a poor farm in the Valmont area of Boulder County, Colorado, where long-term care for the county's indigent was provided from 1902 to 1918. The site operated as a farm from 1897, and many of the original farm buildings are still present, including a main house built in Queen Anne style. It was listed on the National Register of Historic Places in 2011.
Starting in 1875, Boulder County leased a series of properties to serve as the county poorhouse. In 1902, the 120-acre (49 ha) farm on today's 63rd Street was purchased to house the Boulder County Poor Farm and Hospital; many modifications were made to the farm house, including the construction of a two-story dormitory annex. By 1918, a larger building was needed, and the institution was moved to another location. The farm was sold and returned to private operation. In 2018, a century after the county left the property, the city of Boulder purchased the combined Poor Farm / Fort Chambers (a/k/a Fort Valmont) property for Open Space Mountain Parks (OSMP) use.
# Saxifraga globulifera

Saxifraga globulifera is a flowering plant of the genus Saxifraga and the family Saxifragaceae.

## Habitat

The plant grows in southern Spain on limestone rocks and cliffs. The Gibraltar Saxifrage, a variety, is an endemic plant in the Upper Rock Nature Reserve in Gibraltar. An 1838 survey of plants in the region said that the plants found in Spain did not differ in any respect from plants found in the Atlas mountains across the strait of Gibraltar. Sir William Jackson Hooker wrote of the plants he found in 1844 on the Sierra de Mijas, to the north of the road from Málaga to Gibraltar. He found Saxifraga globulifera in the clefts of rock on the south side of the mountain, as well as other plants that grow on Mount Atlas.

## Description

In 1827 the plant was described as follows:
   Stem bulbiferous; leaves nerved, the lower ones spatulate, quite entire, the upper ones palmate three of five-cleft, in the flowering branch remote, linear.—This has the appearance of the preceding [Saxifraga hypnoides, mossy saxifrage], and is scarcely distinct from it.—Found on the top of Mount Atlas.
The leaves are glandular-hairy, 5 to 15 millimetres (0.20 to 0.59 in) long. They have semi-circular outlines with three or more lobes. Stems 7 to 12 centimetres (2.8 to 4.7 in) tall bear from three to seven small, white-petaled flowers.
# Franz Goeschke

Franz Goeschke (German spelling, Göschke); (1844 – 1912) was a German horticulturist who was director of horticulture and head of the Royal Prussian Pomological Institute in Proskau. His father, Gottlieb Göschke (1818-1898), was also a noted horticulturalist.
Franz Göschke was a leading authority of strawberry cultivation. He is credited with creating around thirty new varieties of strawberry, including the once popular Erdbeere Königin Luise (Queen Luise strawberry), a variety he first introduced in 1905.

## Selected publications

* Die rationelle Spargelzucht (Rational asparagus cultivation), 1882.
* Die Haselnuss, ihre Arten und ihre Kultur (Hazelnuts, types and cultivars), 1885.
* Das Buch der Erdbeeren (The book of strawberries), 2nd edition 1888.
* Der Hausgarten auf dem Lande (The garden in the countryside), 1899.
* Einfassungspflanzen (Edging plants), 1900.
* Einträgliche Spargelzucht (Lucrative asparagus cultivation), 1904.
* The hazel, 1922; English translation of works by Göschke and Karl Koch.
# Carl Greenidge

Carl Gary Greenidge (born 20 April 1978) is an English cricketer. He is a right-handed batsman and a right-arm medium-fast bowler. He was born in Basingstoke, Hampshire, the son of Gordon Greenidge.
Greenidge played for Gloucestershire and has in the past represented both Northamptonshire and Surrey. He has played Twenty20 cricket since 2004. In 2000, he was a candidate for Cricket Writers' Young Cricketer Of The Year.
Following his playing career, Greenidge has worked as Head of Cricket at Bancroft's School coaching alongside John Lever until the latter's retirement in 2019.
Carl Greenidge played the role of his father, Gordon, in the bollywood film 83.
# Barratry

Barratry is a legal term with several meanings. It can refer to:
* Simony, its original meaning in English, along with the sale of public offices.
* Barratry (common law), litigation for the purpose of harassment or profit
* Ambulance chasing, when a lawyer seeks clients at a disaster site
* Barratry (admiralty law), misconduct by crew of a ship resulting in its damage
* Barratry, an old name for graft (politics)
# Black (crater)

Black is a small lunar impact crater that lies just to the southeast of the walled basin Kästner. To the south-southwest is the crater Ansgarius, and to the east is the small Dale. It is located near the eastern limb of the Moon, just to the southwest of the Mare Smythii.
Black is circular with a well-defined edge, and inner walls that slope down to a small interior floor. It is not notably marked by erosion or impacts. The northwest wall is separated from the rim of Kästner by less than one crater diameter. This crater was formerly designated Kästner F before it was named by the IAU.
# Avatar Reality

Avatar Reality is a Honolulu-based game studio founded by Henk B. Rogers and Kazuyuki Hashimoto in December 2006. They develop an advanced virtual realm platform aimed at bringing together individuals worldwide on a grandiose level. Rogers with Alexy Pajitnov is known for creating Tetris and introducing it to the world and especially to US markets, and Kazuyuki is best known for developing the game Final Fantasy VII and the film Final Fantasy: The Spirits Within. Avatar Reality is one of FiReStarter companies at the 2009 Future In Review Conference. Minoru Arakawa, former CEO of Nintendo of America, is an advisor to the company. The company is led by CEO Jim Sink.
In 2010 the company announced a 4.2 million dollar investment.
Currently the company is working on Crytek's middleware CryEngine 2-based game Blue Mars. Avatar Reality's goal is to create a next-generation platform for high definition interactive 3D content. Similar to other 3D worlds like EVE Online, the Blue Mars platform will be able to support thousands of simultaneous users per region by using shared servers, capable of handling 10,000 users each.
In March 2009, the firm released the SDK for its game content developers. It also added partners for the 3D party content developing program – Virtual Space Entertainment (VSE) and e Frontier, which will create homes and 3D models.
# King Si

King Si may refer to:
* King Si of Zhou (died 441 BC), king of the Eastern Zhou dynasty
* Shi Xie (137–226), honoured as King Si in Vietnam
# Licheng, Jinan

Licheng District (simplified Chinese: 历城区; traditional Chinese: 歷城區; pinyin: Lìchéng Qū) is one of 10 urban districts of the prefecture-level city of Jinan, the capital of Shandong Province, East China, covering part of the eastern suburbs. It has an area of 1,303.88 km$^2$ and has 1,124,306 permanent residents as of 2010. The Jinan Yaoqiang International Airport is located in the district's northern reaches. The largest county-level division of Jinan by permanent resident population, it borders Zhangqiu District to the east, Changqing District to the southwest, the districts of Shizhong, Lixia, and Tianqiao to the west, Jiyang District to the northwest, as well as the prefecture-level city of Tai'an to the southeast.

## Administrative divisions

As 2012, this district is divided to 6 subdistricts and 11 towns.

### Subdistricts

| Shandalu Subdistrict (山大路街道) Hongjialou Subdistrict]] (洪家楼街道) Dongfeng Subdistrict (东风街道) | Quanfu Subdistrict (全福街道) Suncun Subdistrict (孙村街道) Juyehe Subdistrict (巨野河街道) |

### Towns

| Zhonggong (仲宫镇) Ganggou (港沟镇) Liubu (柳埠镇) Guodian (郭店镇) Dongjia (董家镇) Tangwang (唐王镇) | Yaoqiang (遥墙镇) Wangsheren (王舍人镇) Huashan (华山镇) Xiying (西营镇) Caishi (彩石镇) |
# Boulder Climate Action Plan

The Climate Action Plan (CAP) in Boulder, Colorado, is a set of strategies intended to guide community efforts for reducing greenhouse gas emissions. These strategies have focused on improving energy efficiency and conservation in homes and businesses—the source of nearly three-fourths of local emissions. The plan also promotes strategies to reduce emissions from transportation, which account for over 20 percent of local greenhouse gas sources.

## General information

In November 2006, citizens of Boulder, Colorado, voted to approve Ballot Issue No. 202, authorizing the city council to levy and collect an excise tax from residential, commercial and industrial electricity customers for the purpose of funding a climate action plan to reduce greenhouse gas emissions. The plan outlines programs to increase energy efficiency, increase renewable energy use, reduce emissions from motor vehicles, and take other steps toward meeting the goals set in the Kyoto Protocol.
Beginning April 1, 2007, and expiring March 31, 2013, the initial tax rate was set at $0.0022/kWh for residential customers, $0.0004/kWh for commercial customers, and $0.0002/kWh for industrial customers. The city council has the authority to increase the tax after the first year up to a maximum permitted tax rate of $0.0049/kWh for residential customers; $0.0009/kWh for commercial customers; and $0.0003/kWh for industrial customers. Voluntary purchases of utility-provided wind power are exempt from the tax.

## Allocation and generation of fund

Charge: March 2010 rates for electricity customers:
| Electricity User Type | Tax Rate | Average Annual Tax |
| Residential | $0.0049/kWh | $21 |
| Commercial | $0.0009/kWh | $94 |
| Industrial | $0.0003/kWh | $9,600 |
Total Fund: $860,265 in the first year and up to $1,342,000/year thereafter through March 31, 2013 Purpose: Renewable energy, energy efficiency, transportation.

## Incentive authority

Authority 1: Ballot Issue 202 (Climate Action Plan Tax) Date Enacted:11/7/2006
Authority 2: Boulder Revised Code 3-12 Date Effective: 4/1/2007 Expiration Date: 3/31/2013
# Sili Province

Sili Province or Silizhou (司隸州), in the 5th century reconstituted as Si Province or Sizhou (司州), also known as the capital province or the imperial province, was a province of ancient China. It encompassed the two Han dynasty capitals of Chang'an and Luoyang, and was bordered in the west by Liang Province.
Sili Province was governed by Director of Retainers (司隸 Sī Lì). The province consisted of the commanderies of Henan (around Luoyang), Hedong, Henei, Hongnong, Jingzhao, Youfufeng and Zuopingyi (around Chang'an).
In the early 5th century, the former Sili Province was reconstituted as Si Province or Sizhou by Liu Yu, the future founder of the Liu Song dynasty.
# Seafarer 24

The Seafarer 24 is an American trailerable sailboat that was designed by McCurdy & Rhodes as a cruiser and first built in 1974.

## Production

The design was built by Seafarer Yachts in Huntington, New York, in the United States starting in 1974, but it is now out of production.
Boats were supplied complete and ready-to-sail, or as kits for amateur completion.

## Design

The Seafarer 24 is a recreational keelboat, built predominantly of fiberglass. It has a masthead sloop rig, a raked stem and a reverse transom. There were versions with a fixed keel and a retractable centerboard.
There were two different decks available, "Standard" and "Futura", plus four different cabin layouts. The Standard deck has 57 in (145 cm) of cabin headroom, while the Futura has 70 in (178 cm) in the aft portion.
The design has sleeping accommodation for five people. One typical layout has a double "V"-berth in the bow cabin, a straight settee berth to starboard in the main cabin and a drop-down dinette table to port that converts to a double berth. The galley is located on the starboard side amidships and is equipped with a two-burner stove and a sink. A navigation station is opposite the galley, on the starboard side. The enclosed head is located just aft of the bow cabin on the port side. The fresh water tank has a capacity of 20 U.S. gallons (76 L; 17 imp gal).
The boat is normally fitted with a small 3 to 6 hp (2 to 4 kW) outboard motor for docking and maneuvering.
The design has a hull speed of 6.1 kn (11.3 km/h).

## Variants
### Seafarer 24 K

    This keel-equipped model has a skeg-mounted rudder controlled by a tiller and a fixed fin keel. It displaces 3,910 lb (1,774 kg) and carries 1,400 lb (635 kg) of ballast. The boat has a draft of 3.75 ft (1.14 m) with the standard keel. The boat has a PHRF racing average handicap of 240.

### Seafarer 24 C

    Marketed as the "Seafarer Sail 'n Trail 24", this centerboard model has a kick-up, transom-hung rudder controlled by a tiller. It displaces 3,920 lb (1,778 kg) and carries 1,407 lb (638 kg) of ballast of which 207 lb (94 kg) of lead is in the centerboard. The boat has a draft of 3.75 ft (1.14 m) with the centerboard extended and 1.75 ft (0.53 m), with it retracted, allowing operation in shallow water, beaching or ground transportation on a trailer. The boat has a PHRF racing average handicap of 243.

## Operational history

In a 2010 review Steve Henkel wrote, "the centerboard version has virtually the same ballast and displacement as the fixed keel design, but with ballast weight centered higher up: the board has only 207 lbs. of lead, which makes her significantly more tender than the keel boat in heavy air. A Seafarer brochure mentions that this version 'has positive self-righting ability regardless of centerboard position.' Maybe so, but since 85 percent of the ballast is only a foot below the [waterline], righting moment is minimal. We'd not venture far out in heavy air."
# Knudsen force

Knudsen force is the force experienced by two surfaces at two different temperatures that are separated by a distance comparable to a mean free path of the molecules of the ambient medium.
# Błędowo

Błędowo may refer to the following places:
* Błędowo, Wąbrzeźno County in Kuyavian-Pomeranian Voivodeship (north-central Poland)
* Błędowo, Włocławek County in Kuyavian-Pomeranian Voivodeship (north-central Poland)
* Błędowo, Nowy Dwór Mazowiecki County in Masovian Voivodeship (east-central Poland)
* Błędowo, Ostrołęka County in Masovian Voivodeship (east-central Poland)
* Błędowo, Warmian-Masurian Voivodeship (north Poland)