OpenLLM-France/wikimedia huggingface dataset:
# Symmetric set

In mathematics, a nonempty subset S of a group G is said to be symmetric if it contains the inverses of all of its elements.

## Definition

In set notation a subset $S$ of a group $G$ is called symmetric if whenever $s\in S$ then the inverse of $s$ also belongs to $S.$ So if $G$ is written multiplicatively then $S$ is symmetric if and only if $S=S^{-1}$ where $S^{-1}:=\left\{s^{-1}:s\in S\right\}.$ If $G$ is written additively then $S$ is symmetric if and only if $S=-S$ where $-S:=\{-s:s\in S\}.$
If $S$ is a subset of a vector space then $S$ is said to be a symmetric set if it is symmetric with respect to the additive group structure of the vector space; that is, if $S=-S,$ which happens if and only if $-S\subseteq S.$ The symmetric hull of a subset $S$ is the smallest symmetric set containing $S,$ and it is equal to $S\cup -S.$ The largest symmetric set contained in $S$ is $S\cap -S.$

## Sufficient conditions

Arbitrary unions and intersections of symmetric sets are symmetric.
Any vector subspace in a vector space is a symmetric set.

## Examples

In $\mathbb {R} ,$ examples of symmetric sets are intervals of the type $(-k,k)$ with $k>0,$ and the sets $\mathbb {Z}$ and $(-1,1).$
If $S$ is any subset of a group, then $S\cup S^{-1}$ and $S\cap S^{-1}$ are symmetric sets.
Any balanced subset of a real or complex vector space is symmetric.
# Swenoda Township, Swift County, Minnesota

Swenoda Township is a township in Swift County, Minnesota, United States. The population was 159 at the 2000 census.

## History

Swenoda Township was organized in 1873. Swenoda is a portmanteau of Swedish, Norwegian, and Danish, commemorating the nationalities of the pioneers who first settled in the area.

## Geography

According to the United States Census Bureau, the township has a total area of 35.8 square miles (92.7 km$^2$), all land.

## Demographics

As of the census of 2000, there were 159 people, 53 households, and 44 families residing in the township. The population density was 4.4 people per square mile (1.7/km$^2$). There were 58 housing units at an average density of 1.6/sq mi (0.6/km$^2$). The racial makeup of the township was 100.00% White.
There were 53 households, out of which 41.5% had children under the age of 18 living with them, 73.6% were married couples living together, 7.5% had a female householder with no husband present, and 15.1% were non-families. 15.1% of all households were made up of individuals, and 5.7% had someone living alone who was 65 years of age or older. The average household size was 3.00 and the average family size was 3.31.
In the township the population was spread out, with 32.1% under the age of 18, 9.4% from 18 to 24, 25.8% from 25 to 44, 20.8% from 45 to 64, and 11.9% who were 65 years of age or older. The median age was 34 years. For every 100 females, there were 123.9 males. For every 100 females age 18 and over, there were 120.4 males.
The median income for a household in the township was $50,179, and the median income for a family was $51,607. Males had a median income of $36,458 versus $16,607 for females. The per capita income for the township was $32,557. None of the families and 1.4% of the population were living below the poverty line, including no under eighteens and 10.5% of those over 64.
# Synaphe predotalis

Synaphe predotalis is a species of moth of the family Pyralidae described by Hans Zerny in 1927. It is found in Spain and Tunisia.

## Taxonomy

Synaphe predotalis is sometimes treated as a subspecies of Synaphe chellalalis.
# Synaphe interjunctalis

Synaphe interjunctalis is a species of moth of the family Pyralidae described by Achille Guenée in 1849. It is found in Portugal and Algeria.
# Mala Krupska Rujiška

Mala Krupska Rujiška (Serbian Cyrillic: Мала Крупска Рујишка) is a village in the municipality of Novi Grad, Republika Srpska, Bosnia and Herzegovina.
# System partition and boot partition

The system partition and the boot partition (also known as the system volume and the boot volume) are computing terms for disk partitions of a hard disk drive or solid-state drive that must exist and be properly configured for a computer to operate. There are two different definitions for these terms: the common definition and the Microsoft definition.

## Common definition

In context of every operating system, except those developed by Microsoft, the system partition and the boot partition are defined as follows:
* The boot partition is a primary partition that contains the boot loader, a piece of software responsible for booting the operating system. For example, in the standard Linux directory layout (Filesystem Hierarchy Standard), boot files (such as the kernel, initrd, and boot loader GRUB) are mounted at /boot/. Despite Microsoft's radically different definition (see below), System Information, a utility app included in Windows NT family of operating systems, refers to it as "boot device".
* The system partition is the disk partition that contains the operating system folder, known as the system root. By default, in Linux, operating system files are mounted at / (the root directory).
In Linux, a single partition can be both a boot and a system partition if both /boot/ and the root directory are in the same partition.

## Microsoft definition

Since Windows NT 3.1 (the first version of Windows NT), Microsoft has defined the terms as follows:
* The system partition (or system volume) is a primary partition that contains the boot loader, a piece of software responsible for booting the operating system.$^{:1087}$ This partition holds the boot sector and is marked active.$^{:970}$
* The boot partition (or boot volume) is the disk partition that contains the operating system folder, known as the system root or %systemroot% in Windows NT.$^{:174}$
Before Windows 7, the system and boot partitions were, by default, the same and were given the "C:" drive letter.$^{:971}$ Since Windows 7, however, Windows Setup creates, by default, a separate system partition that is not given an identifier and therefore is hidden. The boot partition is still given "C:" as its identifier. This configuration is suitable for running BitLocker, which requires a separate unencrypted system partition for booting. As of Windows 11, this nomenclature is still used by the "Disk Management" utility.
# Sybropraonetha minuta

Sybropraonetha minuta is a species of beetle in the family Cerambycidae, and the only species in the genus Sybropraonetha. It was described by Stephan von Breuning in 1960.
# Malikâne

Malikâne was a form of tax farming introduced in the Ottoman empire in 1695. It was intended as an improvement on the Iltizam system, in which a tax-farmer was responsible for a single year. Malikâne contracts were for life; this provided more security for the tax farmer (malikaneci) and a less exploitative relationship with the peasants; malikanecis might even make investments to improve productivity. However, vested interests - from existing mültezims who benefited from the Iltizam system - prevented wider adoption of malikâne. Also, malikâne could not be converted into vakf - an important distinction from mülk.
A malikâne tax-farm, typically for a village or district, would be auctioned to the highest bidder; in return for collecting all state taxes (rüsüm) from that area, the winner of the auction would make a large downpayment called muaccele, and then annual payments called mâl. The auction determined the initial payment - subject to a minimum price set by the treasury. A malikaneci might finance their initial payment by borrowing from a moneylender or sarraf - who would expect to take a cut of the tax revenue; this could even become a second layer of tax-farming.
The winner of the auction was given a document called "berat", as proof of their right to the tax-farm. In theory, when the tenant died their tax farm would revert to the state, but a tenant could give the tax-farm to an heir if the treasury agreed (and officials would expect to be paid for their agreement).
As the tax-farming market became more competitive, the treasury collected bigger payments, but profitability for tax-farmers decreased.
The malikâne system may have been modelled on an earlier system of "double rent" paid by waqfs.
From the treasury's perspective, malikâne was a more reliable source of revenue. Auctions of local tax-farming rights had the effect of integrating diverse provincial tax-farmers into the Ottoman state, and also helped build a more modern concept of private landownership.
# Södra Vi

Södra Vi is a locality situated in Vimmerby Municipality, Kalmar County, Sweden with 1,182 inhabitants in 2010. According to Svenskt ortnamnslexikon the name of the locality loosely mean "southern place of worship". Tens of kilometers to the northwest lies Norra Vi.
# Syzygium spathulatum

Syzygium spathulatum is a species of plant in the family Myrtaceae. It is endemic to Sri Lanka.
# Malaysia at the 2007 Asian Indoor Games

Malaysia participated in the 2007 Asian Indoor Games in Macau, China from 26 October to 3 November 2007.

## Medallists

| Medal | Name | Sport | Event | Date |
| Silver | Zatil Iman Abdul Ghani | Bowling | Women's singles | 28 October |
| Silver | Fariq Mohamed Esa | Extreme sports | Inline skate big air | 28 October |
| Silver | Chong Kok Fu Er Chong Yen Lwee Wee Chien Pang Pee Wei Si Tiam Yong Te Hwa Chong Tiong Chun Khai Wong Lian Khai | Dragon and lion dance | Southern lion optional exercise | 2 November |
| Bronze | Mas Hafizulhelmi | Chess | Men's classical individual | 30 October |
| Bronze | Siti Zulaikha | Chess | Women's classical individual | 30 October |
| Bronze | Norhanizah Abu Bakar Sin Li Jane Trish Khoo Zatil Iman Abdul Ghani | Bowling | Women's team | 2 November |
| Bronze | Ahmad Shaiful Aziz | Extreme sports | BMX freestyle flatland | 2 November |
| Bronze | Ahmad Fadzil Musa | Extreme sports | Skateboard park best technical | 27 October |
| Bronze | Boo Chen Loong Cher Chin Yong Chua Khai Ping Hoo Jenn Shyang Lau Chin Chuen Lau Yong Meng Lim Chap Yeong Ng Chi Chang Ng Chi Khai Ng Per Yuean Own Yen Ming Sia Chee Hong Tan Jiunn Siong Tan Teck Sien | Dragon and lion dance | Dragon dance optional exercise | 2 November |
* This article about sports in Malaysia is a stub. You can help Wikipedia by expanding it.
* v
* t
* e
* This Asian Games article is a stub. You can help Wikipedia by expanding it.
* v
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* e
# Makelesi Bulikiobo-Batimala

Makelesi Bulikiobo Batimala (born 23 October 1977) is a Fijian sprinter.

## Biography

Nicknamed the "Sprint Queen" by the Fiji Times and Fiji Village, she has represented her country in several international competitions, including the 2004 Summer Olympics in Athens. She won four gold medals at the 2003 South Pacific Games, in the 100m, 200m, 400m and 4 × 100 m relay events. She also won the women's 200m sprint at the Australian Athletics Championships in 2008.
While taking part in the 2007 World Athletics Championships, she qualified to represent Fiji at the 2008 Summer Olympics in Beijing. She was Fiji's flag bearer at the Games' opening ceremony.
As of 2007, she held the Fiji national record for the women's 100-metre sprint, at 11.66 seconds.

## Achievements

| Year | Competition | Venue | Position | Event | Notes |
| Representing Fiji ||||||
| 1993 | Oceania Youth Championships | Canberra, Australia | 1st | 400 m | 60.94 |
| 2001 | South Pacific Mini Games | Middlegate, Norfolk Island | 1st | 100 m | 12.26 s (wind: +0.3 m/s) |
| 2001 | South Pacific Mini Games | Middlegate, Norfolk Island | 1st | 200 m | 25.29 s (wind: -2.2 m/s) |
| 2001 | South Pacific Mini Games | Middlegate, Norfolk Island | 1st | 400 m | 58.17 s |
| 2001 | South Pacific Mini Games | Middlegate, Norfolk Island | 1st | 4 × 100 m relay | 47.84 s |
| 2001 | South Pacific Mini Games | Middlegate, Norfolk Island | 1st | 4 × 400 m relay | 3:49.24 min |
| 2002 | Oceania Championships | Christchurch, New Zealand | 1st | 100 m | 12.22 s (wind: -2.6 m/s) |
| 2002 | Oceania Championships | Christchurch, New Zealand | 1st | 200 m | 24.21 s (wind: +1.5 m/s) |
| 2002 | Oceania Championships | Christchurch, New Zealand | 1st | 400 m | 56.67 s |
| 2002 | Oceania Championships | Christchurch, New Zealand | 1st | 800 m medley relay | 1:45.09 min |
| 2003 | South Pacific Games | Suva, Fiji | 1st | 100 m | 11.9 s (ht) |
| 2003 | South Pacific Games | Suva, Fiji | 1st | 200 m | 23.68 s (wind: -2.1 m/s) GR |
| 2003 | South Pacific Games | Suva, Fiji | 1st | 400 m | 52.66 s GR |
| 2003 | South Pacific Games | Suva, Fiji | 1st | 4 × 100 m relay | 44.86 s GR |
| 2007 | Pacific Games | Apia, Samoa | 1st | 100 m | 11.55 s (wind: +0.1 m/s) GR |
| 2007 | Pacific Games | Apia, Samoa | 1st | 200 m | 23.40 s (wind: +0.3 m/s) GR |
| 2007 | Pacific Games | Apia, Samoa | 1st | 400 m | 52.96 s |
| 2007 | Pacific Games | Apia, Samoa | 2nd | 4 × 100 m relay | 46.01 s |
| 2007 | Pacific Games | Apia, Samoa | 2nd | 4 × 400 m relay | 3:41.03 min |
| 2009 | Pacific Mini Games | Rarotonga, Cook Islands | 1st | 100 m | 11.97 s (wind: +0.1 m/s) |
| 2009 | Pacific Mini Games | Rarotonga, Cook Islands | 1st | 200 m | 24.52 s (wind: +0.4 m/s) |
| 2009 | Pacific Mini Games | Rarotonga, Cook Islands | 1st | 400 m | 55.71 s |
# Malla, Estonia

Malla is a village in Viru-Nigula Parish, Lääne-Viru County, in northeastern Estonia. It is located about 3 km east of the town of Kunda. On 1 January 2011 Malla had a population of 82.

## Malla manor

Malla manor traces its history back to 1443, when it is first recorded in written sources. During that time, there was a small castle at the site. Around 1620, the estate became the property of Swedish field marshal Gustav Horn. In 1651–1654, he commissioned architect Zakarias Hoffmann to erect a new manor house on the site. The house burnt down during the Great Northern War, and the current building received its appearance in the 1880s.
# Asakawa

Asakawa (written: 朝河 or 浅川) is a Japanese surname. Notable people with the surname include:
* Asakawa brothers, Japanese academics
** Noritaka Asakawa (浅川 伯教, 1884–1964)
** Takumi Asakawa (浅川 巧, 1891–1931)
* Kan'ichi Asakawa (朝河 貫一, 1873–1948), Japanese academic and historian
* Maki Asakawa (浅川 マキ, 1942–2010), Japanese jazz singer and composer
* Masatsugu Asakawa (浅川 雅嗣, born 1958), Japanese civil servant
* Nana Asakawa (浅川 梨奈, born 1999), Japanese actress and former singer
* Yū Asakawa (浅川 悠, born 1975), Japanese voice actress
# Sternarchella schotti

Sternarchella schotti is a species of weakly electric knifefish in the family Apteronotidae. This species is endemic to Brazil where it is found in the Amazon River basin, and is sometimes kept in aquaria. The species grows to approximately 20 cm in length, and has a pale pink color in life with brown speckling along the dorsal surface of the head and body. As with many other ghost knifefishes (Apteronotidae) this species is aggressive with other electric fish species (Gymnotiformes), but is often compatible in captivity with species in other orders, such as catfish and angelfish. A recommended diet for S. schotti is frozen or live blood worms and insect larva, and diced meat.
# Buno

Buno may refer to:

## People

* Conrad Buno (1613–1671), German copperplate engraver, cartographer and publisher
* Buno Ramnath (fl. 18th century), Hindu philosopher

## Places

* Buno-Bonnevaux, France
* Buño, Spain

## Other

* Buno (era), in Japan
* Buno (wrestling)
* BuNo, a US military aircraft numbering system
* Buno people
# Tapellaria intermedia

Tapellaria intermedia is a little-known species of foliicolous (leaf-dwelling) crustose lichen in the family Pilocarpaceae. It occurs in Bolivia.

## Taxonomy

Tapellaria intermedia was formally described as new to science in 2008 by the lichenologists Adam Flakus and Robert Lücking. The type specimen was collected by Flakus by lake Copaiba near Reyes village in José Ballivián Province (Beni Department, Bolivia), where it was found growing on the plant leaves in the Amazon rainforest at an elevation of 189 m (620 ft). The species epithet alludes to morphology of its ascospores, which are intermediate (in terms of size and septation) between two similar species, Tapellaria nigrata and T. molleri.

## Description

Tapellaria intermedia forms a thin layer (the thallus) on the surface of leaves. This layer appears as small, scattered patches, each measuring 0.1–0.6 mm in diameter. These patches often merge in the centre of the lichen. The thallus is smooth and pale greyish-green in colour, with a faint whitish hypothallus. The lichen's algal partner is a type of green alga with round cells, measuring 4–7 μm in diameter. The fungal partner produces small, disc-shaped reproductive structures called apothecia. These are 0.15–0.4 mm in diameter, sit directly on the leaf surface, and are slightly constricted at the base. The apothecia are black, with a persistent rim (margin) that becomes less noticeable as the structure ages. Beneath the apothecium, there is a layer with a blue-green (aerugineous) tinge.
Inside the apothecia are structures called asci, which produce the lichen's spores. Each ascus contains eight spores. The spores are colourless and have a complex structure with multiple cross-walls (septa) and occasional lengthwise walls, measuring 35–65 by 5–8 μm. Various other microscopic features are important for identifying this species, including the structure of the apothecium rim (excipulum), the hypothecium, and the branching threads (paraphyses) that grow between the asci.

## Habitat and distribution

As of its initial description, Tapellaria intermedia had only been found in one location: near Reyes village in the Beni Department of Bolivia. This area is part of the lowland southwest Amazon rainforest. The lichen was discovered in an "island" of rainforest surrounded by savanna vegetation. It was found growing on the leaves of an unspecified vascular plant, which is typical for foliicolous lichens. These organisms are specially adapted to live on the surface of leaves in humid, tropical environments.
The lichen has since been recorded from two locations in the Manuripi-Heath Amazonian Wildlife National Reserve in the Manuripi Province.
# Ševica

Ševica is a village in the municipality of Kučevo, Serbia. According to the 2002 census, the village has a population of 809 people.
# 1999 NCAA Division III baseball tournament

The 1999 NCAA Division III baseball tournament was played at the end of the 1999 NCAA Division III baseball season to determine the 24th national champion of college baseball at the NCAA Division III level.
The tournament concluded with eight teams competing at Salem Memorial Ballpark in Salem, Virginia, for the championship.
The tournament champion was N.C. Wesleyan, who defeated St. Thomas for the championship.
Eight regional tournaments were held to determine the participants in the World Series. Regional tournaments were contested in double-elimination format, with four regions consisting of six teams and four regions consisting of four teams, for a total of 40 teams participating in the tournament.
# Bangladesh–Sudan relations

Bangladesh–Sudan relations refers to the bilateral relations between Bangladesh and Sudan. Colleges in Bangladesh, like the Sher-e-Bangla Medical College, have hosted students from Sudan.

## High level visits

Mir Shawkat Ali was previously the Bangladeshi High Commissioner to Sudan. In 2008, former chairman of Joint Chiefs of Staff of Sudanese Armed Forces, General Muhammad Abdul Qadir Nasruddin paid an official visit to Dhaka.

## Military relations

A number of Sudanese soldiers have been participating in several training programmes in Bangladesh, specially in UN Peacekeeping training in Bangladesh Institute of Peace Support Operation Training.

## Economic relations

Both Bangladesh and Sudan have expressed mutual interest in expanding their bilateral trade and investment. Bangladeshi pharmaceuticals, ready made garments and ceramics have been identified as potential products in the Sudanese market. In 2008, Bangladesh and Sudan signed an agreement related to the importation of manpower. Prime Minister of Bangladesh Sheikh Hasina has taken the initiative of opening labour wing in the Bangladeshi Mission of Sudan. Bangladesh exports tea to Sudan.
# Dichomeris syringota

Dichomeris syringota is a moth in the family Gelechiidae. It was described by Edward Meyrick in 1926. It is found in Peru.
The wingspan is about 15 mm (0.59 in). The forewings are rather dark grey with a broad costal band at the base occupying half of the wing but attenuated to a point at three-fourths, grey whitish mottled with grey, the dorsal area towards the base is also similarly suffused and between these a streak of blackish-fuscous suffusion along the fold from about one-sixth to two-fifths, with some undefined dark fuscous suffusion extending from this beneath the costal band to beyond the middle. There is a whitish dot on the end of the cell followed by a transverse fascia of obscure whitish irroration (sprinkling) terminated by a more distinct rather curved shade. The hindwings are grey, thinly scaled towards the base.
# Bardo (surname)

Bardo is a surname. Notable people with the surname include:
* Clinton L. Bardo (1868–1937), American businessman
* John Bardo (1948–2019), American educator
* Natalia Bardo (born 1988), Russian actress, singer and TV host
* Robert John Bardo (born 1970), American criminal
* Stephen Bardo (born 1968), professional basketball player
# Bandrani

Bandrani is a village on the island of Anjouan in the Comoros. According to the 1991 census the village had a population of 760. The current estimate for 2009 is 1,339 people
# Barbican Press

Barbican Press is an independent publishing house launched in 2013 by Martin J. Goodman for "innovative novels that are just too edgy for the mainstream but allow people to break all bounds and find a unique voice."
Its titles include Kate Horsley's The Monster's Wife, shortlisted for Scottish First Book of the Year 2014., Brian W. Lavery's The Headscarf Revolutionaries, and DD Johnston's The Secret Baby Room.
# Bangin Westcoast

Professional ratings :
| Review scores ||
| Source | Rating |
| DubCNN | 3/5 |
Bangin West Coast is the second studio album by American rapper and record producer Soopafly. It was officially released on May 8, 2007, through Gangsta Advisory Recordingz, despite the advance leaked in 2006. Production was handled by Soopafly himself, who also served as executive producer together with Daz Dillinger, Mr. Porter, DEA, DJ Battlecat, DJ Sebb, E-Swift and Exile. It features guest appearances from Tha Dogg Pound, Snoop Dogg, B-Real, LaToyia Williams and Nate Dogg.

## Personnel

* Priest "Soopafly" Brooks – vocals, producer (tracks: 2-4, 7-10, 12, 16), executive producer
* Delmar "Daz Dillinger" Arnaud – vocals (tracks: 3, 5, 10), executive producer
* Ricardo "Kurupt" Brown – vocals (track 3)
* Louis "B-Real" Freese – vocals (track 8)
* Calvin "Snoop Dogg" Broadus – vocals (tracks: 10, 11)
* Nathaniel "Nate Dogg" Hale – vocals (track 10)
* LaToiya Williams – vocals (track 16)
* Aleksander "Exile" Manfredi – producer (track 1)
* Denaun "Kon Artis" Porter – producer (tracks: 5, 6)
* Eric "E-Swift" Brooks – producer (track 11)
* Kevin "DJ Battlecat" Gilliam – producer (track 13)
* Sébastien "DJ Sebb" Vuignier – producer (track 14)
* DEA – producer (track 15)
* Alex "Toon" Deligiannis – cover design
* Young Breezy – cover design
* Arnold "Bigg A" White – markerting, promotion
# Dichomeris acratopa

Dichomeris acratopa is a moth in the family Gelechiidae. It was described by Edward Meyrick in 1926. It is found in Cameroon.
The wingspan is about 17 mm (0.67 in). Adults are similar to Dichomeris fracticostella, but have the stigmata simple, dot like and dark grey, with the plical beneath the first discal.
# Yaroslav I

Yaroslav I is the name of:
* Yaroslav I the Wise (ca. 970–1054), prince of Kiev
* Yaroslav I of Halych (ca. 1135–1187)
# Dietzella

Dietzella is a genus of minute seed weevils in the beetle family Curculionidae. There are two described species in Dietzella. It was previously referred to as Coelogaster, but that name was found to be preoccupied by an extinct chanid fish.

## Species

* Dietzella sextuberculata (Boheman, 1845)
* Dietzella zimmermanni (Gyllenhal, 1837)