OpenLLM-France/wikimedia huggingface dataset:
# Thue's lemma

In modular arithmetic, Thue's lemma roughly states that every modular integer may be represented by a "modular fraction" such that the numerator and the denominator have absolute values not greater than the square root of the modulus.
More precisely, for every pair of integers (a, m) with m > 1, given two positive integers X and Y such that X ≤ m < XY, there are two integers x and y such that
    $ay\equiv x{\pmod {m}}$
and
    $|x|<X,\quad 0<y<Y.$
Usually, one takes X and Y equal to the smallest integer greater than the square root of m, but the general form is sometimes useful, and makes the uniqueness theorem (below) easier to state.
The first known proof is attributed to Axel Thue (1902) who used a pigeonhole argument. It can be used to prove Fermat's theorem on sums of two squares by taking m to be a prime p that is congruent to 1 modulo 4 and taking a to satisfy a$^2$ + 1 ≡ 0 mod p. (Such an "a" is guaranteed for "p" by Wilson's theorem.)

## Uniqueness

In general, the solution whose existence is asserted by Thue's lemma is not unique. For example, when a = 1 there are usually several solutions (x, y) = (1, 1), (2, 2), (3, 3), ..., provided that X and Y are not too small. Therefore, one may only hope for uniqueness for the rational number ⁠x/y⁠, to which a is congruent modulo m if y and m are coprime. Nevertheless, this rational number need not be unique; for example, if m = 5, a = 2 and X = Y = 3, one has the two solutions
    $2a+1\equiv -a+2\equiv 0{\pmod {5}}$.
However, for X and Y small enough, if a solution exists, it is unique. More precisely, with above notation, if
    $2XY<m,$
and
    $ay_{1}-x_{1}\equiv ay_{2}-x_{2}\equiv 0{\pmod {m}}$,
with
    $\left|x_{1}\right|<X,\quad \left|y_{1}\right|<Y,$
and
    $\left|x_{2}\right|<X,\quad \left|y_{2}\right|<Y,$
then
    ${\frac {x_{1}}{y_{1}}}={\frac {x_{2}}{y_{2}}}.$
This result is the basis for rational reconstruction, which allows using modular arithmetic for computing rational numbers for which one knows bounds for numerators and denominators.
The proof is rather easy: by multiplying each congruence by the other y$_i$ and subtracting, one gets
    $y_{2}x_{1}-y_{1}x_{2}\equiv 0{\pmod {m}}.$
The hypotheses imply that each term has an absolute value lower than XY < ⁠m/2⁠, and thus that the absolute value of their difference is lower than m. This implies that $y_{2}x_{1}-y_{1}x_{2}=0$, hence the result.

## Computing solutions

The original proof of Thue's lemma is not efficient, in the sense that it does not provide any fast method for computing the solution.
The extended Euclidean algorithm, allows us to provide a proof that leads to an efficient algorithm that has the same computational complexity of the Euclidean algorithm.
More precisely, given the two integers m and a appearing in Thue's lemma, the extended Euclidean algorithm computes three sequences of integers (t$_i$), (x$_i$) and (y$_i$) such that
    $t_{i}m+y_{i}a=x_{i}\quad {\text{for }}i=0,1,...,$
where the x$_i$ are non-negative and strictly decreasing. The desired solution is, up to the sign, the first pair (x$_i$, y$_i$) such that x$_i$ < X.
# Thudiyalur railway station

Thudiyalur railway station is a suburban railway station of Coimbatore. It is a station in between Coimbatore Junction and Mettupalayam. The station was reopened by Railway minister Suresh Prabhu. Recently Thudiyalur railway station building was refurbished and the station started functioning from July 3, 2017 onwards. Thudiyalur railway station is just 800 meter from Thudiyalur bus stand.
There is huge acres of land available for railways here, earlier CRPF Goodshed is planned near the railway station.

## Administration

The station is operated by the Southern Railway zone of the Indian Railways and comes under the Salem railway division.

## Lines

The station has one platform and a line connecting Mettupalayam and Coimbatore.

## Services

This station handles local passenger MEMU trains between Mettupalayam railway station and Coimbatore Junction. It just takes 10 to 15 minutes to reach Coimbatore Junction and 25 minutes to reach Mettupalayam railway station from Thudiyalur railway station and fare is also just Rs.10 in both directions. And"monthly pass" is just Rs.100 per person for both up and down trips to Coimbatore.
Train timings at Thudiyalur station
| Train No. | Towards | Time | Stops | Service |
| 06009 | Coimbatore Junction | 08.45 AM | Coimbatore North Junction | Monday to Sunday |
| 06813 | Coimbatore Junction | 11.15 AM | Coimbatore North Junction | Monday to Saturday (Sunday not available) |
| 06815 | Coimbatore Junction | 13.20 PM | Coimbatore North Junction | Monday to Sunday |
| 06817 | Coimbatore Junction | 17.10 PM | Coimbatore North Junction | Monday to Sunday |
| 06823 | Coimbatore Junction | 19.38 PM | Coimbatore North Junction | Monday to Saturday (Sunday not available) |
| Train No. | Towards | Time | Stops | Service |
| 06812 | Mettupalayam railway station | 09.50 AM | Periyanaickenpalayam, Karamadai | Monday to Sunday |
| 06814 | Mettupalayam railway station | 12.00 PM | Periyanaickenpalayam, Karamadai | Monday to Saturday (Sunday not available) |
| 06816 | Mettupalayam railway station | 15.55 PM | Periyanaickenpalayam, Karamadai | Monday to Sunday |
| 06010 | Mettupalayam railway station | 18.05 PM | Periyanaickenpalayam, Karamadai | Monday to Sunday |
| 06822 | Mettupalayam railway station | 20.40 PM | Periyanaickenpalayam, Karamadai | Monday to Saturday(Sunday not available) |
# Ludmila Červinková

Ludmila Červinková (29 April 1908 – 16 September 1980) was a Czech operatic soprano who had a celebrated international career during the 1930s through the 1960s. She notably had a long and fruitful association with the National Theatre in Prague from 1942 until 1966. Her voice is preserved on a number of recordings on the Supraphon label.

## Biography

Born in Prague, Červinková studied singing privately with Jarmila Pěničková, while attending a girl's college in Prague. From 1928 to 1934 she studied singing at the Prague Conservatory with Doubravka Branbergerová née Černochová (1885–1945). In 1936, she went to Vienna to study with Cecílie Steinbrücková. She continued studying with Pěničková after 1942. She began her career as a principal soprano at the opera house in Olomouc in 1934. She remained at that house for the next six years, after which she was involved with the Zdeněk Nejedlý Theatre in Ostrava from 1940 to 1942. Vaclav Talich attended some of her performances in Ostrava and was impressed by her beautiful voice and dramatic skills. Under his recommendation she was engaged as a member of the National Theatre in Prague in 1942.
Červinková spent the rest of her career at the National Theatre and was one of the house's most important artists during the 1940s through the 1960s. Her repertoire in Prague constituted mainly dramatic soprano and spinto roles, including Donna Anna in Don Giovanni, Julie in The Jacobin, Kostelnička Buryjovka in Jenůfa, Mařenka in The Bartered Bride, Tatyana in Eugene Onegin, Venus in Tannhäuser, and the title roles in Aida, Káťa Kabanová, Libuše, and Tosca among others.
Červinková was also active as a concert singer and was particularly admired for her interpretations of the concert works of Antonín Dvořák. She gave numerous guest performances with the orchestras and opera houses in Moscow and Sofia, and made several appearances at the Berlin State Opera. She made numerous recordings on the Supraphon label, including complete opera recordings of the roles of Vendulka in Bedřich Smetana's The Kiss and the title heroine in Dvořák's Rusalka.
She taught singing, from 1958 at the Music Faculty of the Academy of Performing Arts in Prague (HAMU) and from 1960 at the Prague Conservatory. Červinková retired from the stage in 1966, shortly after being honored with the title of People's Artist of the USSR. She then devoted herself to teaching
# Tillandsia caulescens

Tillandsia caulescens is a species in the genus Tillandsia. This species is native to Bolivia.

## Cultivars

* Tillandsia 'Pink Surprise'
# Lopezia

Lopezia is a genus of plants of the family Onagraceae, largely restricted to Mexico and Central America.

## Description

Herbs or shrubs, mostly freely branched. Leaves petioled, alternate, or the lower opposite, simple. Flowers -solitary, small, pedicelled, in upper axils of sometimes much reduced leaves. Floral tube inconspicuous. Sepals 4, mostly red, narrow. Petals 4, dissimilar, white to rose, the 2 upper unguiculate, with none, one, or two glands at apex of claw; the 2 lower clawed and curved upward, glandless. Stamens 2, adnate to the style and connate with each other at the base, the posterior fertile, the anterior sterile, petaloid. Ovary 4-loculed; style short, filiform, with slightly enlarged and barely lobed stigma; ovules multiseriate, many. Capsule globose to clavate, coriaceous, 4-loculed and -valved. Seeds many, obovoid, granulate.

## Taxonomy

The genus name of Lopezia is in honour of Manuel López-Figueiras (1915-2012), who was a (Spanish-) Venezuelan botanist (Mycology and Lichenology), from the University of Havana (in Cuba).

## Distribution

It is found in Costa Rica, El Salvador, Guatemala, Honduras, Mexico and Panamá.

## Species

According to Kew, there are 28 species are recognized in the genus Lopezia in 2022:
* Lopezia ciliatula Plitmann, P.H.Raven & Breedlove
* Lopezia clavata Brandegee
* Lopezia concinna P.H. Raven
* Lopezia conjugans Brandegee
* Lopezia cornuta S. Watson
* Lopezia coronata Andrews
* Lopezia galeottii Planch.
* Lopezia gentryi (Munz) Plitmann, P.H. Raven & Breedlove
* Lopezia gracilis S. Watson
* Lopezia grandiflora Zucc.
* Lopezia hirsuta Jacq.
* Lopezia integrifolia DC.
* Lopezia laciniata (Rose) M.E. Jones
* Lopezia langmaniae Miranda. The species name langmaniae was given in honor of Ida Kaplan Langman.
* Lopezia longiflora Decne.
* Lopezia lopezioides (Hook. & Arn.) Plitmann, P.H. Raven & Breedlove
* Lopezia miniata Lag. ex DC.
** Lopezia miniata subsp. paniculata (Seem.) Plitmann, P.H. Raven & Breedlove
* Lopezia oaxacana Rose
* Lopezia ovata (Plitmann, P.H. Raven & Breedlove) Plitmann
* Lopezia pringlei Rose
* Lopezia racemosa Cav.
* Lopezia riesenbachia Plitmann, P.H. Raven & Breedlove
* Lopezia semeiandra Plitmann, P.H. Raven & Breedlove
* Lopezia sinaloensis Munz
* Lopezia smithii Rose
* Lopezia suffrutescens Munz
* Lopezia trichota Schltdl.
* Lopezia violacea Rose

## Gallery

* L. coronata
* L. longiflora
* L. miniata
* L. paniculata
* L. racemosa
# Long Duckmanton

Long Duckmanton is a village in the civil parish of Sutton cum Duckmanton between Bolsover and Chesterfield, in North East Derbyshire, England. It is located 3 km west of Bolsover and about 18 km south-east of the city of Sheffield.
# Jake's Corner (film)

Jake's Corner is a 2008 American independent drama film starring Richard Tyson and Danny Trejo. The title of the film refers to the census-designated place of the same name.

## Cast

* Colton Rodgers as Spence
* Richard Tyson as Johnny Dunn
* Diane Ladd as Fran
* Danny Trejo as Clint
* B. J. Thomas as Doc

## Production

The film was shot in three weeks in Jakes Corner, Arizona.

## Reception

Laurie Jayne Frost of White Mountain Independent gave the film a positive review and wrote, "go see this movie." Randy Cordova of The Arizona Republic gave the film a negative review and wrote: "The lunkheaded logic isn't made any more palatable by the script, in which all of Dunn's pals are given silly quirks and blah back stories."
# Whiteville Tobs

The Whiteville Tobs were a minor league baseball team based in Whiteville, North Carolina. In 1950, the Tobs played a partial season as members of the Class D level Tobacco State League in the final season of the league, hosting home games at Legion Memorial Field.

## History

Whiteville, North Carolina first hosted minor league play in 1950, when the Whiteville "Tobs" became members of the eight–team Class D level Tobacco State League during the last season of the league. The "Tobs" nickname is a shortened version of "tobacconists," common in the region in the era.
After beginning play mid-season, the Angier–Fuquay Springs Bulls, Clinton Sampson Blues, Lumberton Auctioneers, Red Springs Red Robins, Rockingham Eagles, Sanford Spinners, Smithfield–Selma Leafs and Wilmington Pirates teams joined Whiteville in Tobacco State League play.
During the 1950, season, the Dunn–Erwin Twins team relocated to Whiteville and finished last in the Tobacco State League standings. On June 16, 1950, the Dunn-Erwin Twins moved to Whiteville, North Carolina, with a record of 11–34. Finishing the season as the Whiteville Tobs, the team compiled a record of 28–48 based in Whiteville. Overall, the team finished with a record of 39–92, to place eighth, missing the Tobacco State League playoffs. Playing under manager Jim Staton, the Twins/Tobs finished 51.0 games behind the first place Lumberton Auctioneers. Granville Denning led the Tobacco State League in batting average, hitting .374 with 174 hits. The Twins/Tobs team failed to qualify for the playoffs, won by the Rockingham Eagles. The Tobacco State League permanently folded following the 1950 season.
Whiteville, North Carolina has not hosted another minor league team.

## The ballpark

The Whiteville Tobs hosted home minor league games at Legion Memorial Field. Still in use today by Whiteville High School sports teams, Legion Memorial Stadium is located at 413 North Lee Street, Whiteville, North Carolina.

## Year–by–year record

| Year | Record | Finish | Manager | Playoffs/Notes |
| 1950 | 39–92 | 8th | Jim Staton | Dunn-Erwin (11–34) moved to Whiteville June 16 |
# Anglican Diocese of Ogbia

The Anglican Diocese of Ogbia is one of ten within the Anglican Province of the Niger Delta, itself one of 14 provinces within the Church of Nigeria.
The diocese was created in 2008. James Oruwori is the incumbent bishop.
# Łódź Ring Road

Łódź Ring Road (Obwodnica Łodzi in Polish) is a complex of motorways (A1 and A2) and expressways (S8 and S14) in Poland, built in order to decrease the traffic in the city of Łódź and neighboring regions of Zgierz, Pabianice and Rzgów.

## Sections
### Eastern section: A1

This section is 37 km (23 mi) long and it is a part of E75 European route. It has been opened on July 1, 2016.

#### Junctions

| Name | Location | Roads |
| Łódź Północ | Stryków | A 2 ( E30) |
| Brzeziny | Łódź (Nowosolna) | DK 72 |
| Łódź Wschód | Łódź (Widzew) | DW 713 |
| Łódź Górna | Wola Rakowa | DW 714 |
| Łódź Południe | Tuszyn | S 8 ( E67) |

### Northern section: A2

This section is 20 km (12 mi) long and it is a part of E30 European route. The section between Emilia and Stryków junctions has been opened on July 26, 2006. Following section between Stryków and Łódź Północ junctions has been opened on December 22, 2008.

#### Junctions

| Name | Location | Roads |
| Emilia | Emilia | DK 91 / S 14 |
| Zgierz | Stefanów | DW 702 |
| Stryków $_{formerlyStrykówI}$ | Stryków | DK 14 |
| Łódź Północ $_{formerlyStrykówII}$ | Stryków | A 1 ( E75) |

### Southern section: S8

This section is 19.3 km (12.0 mi) long and it is a part of E67 European route and DK12 Polish national road. The first section between Róża and Rzgów has been opened on April 11, 2014. The second section between Rzgów and Łódź Południe junction has been opened on July 1, 2016.

#### Junctions

| Name | Location | Roads |
| Róża | Róża | S 14 |
| Pabianice Południe | Pawlikowice | DW 485 |
| Rzgów | Rzgów | DK 12 / DK 91 |
| Łódź Południe | Tuszyn | A 1 ( E75) |

### Western section: S14

This section is 42 km (26 mi) long. The first section between Dobroń and Łódź Lublinek junctions was opened on May 16, 2012 (400 m (1,300 ft) long section between planned Łódź Lublinek junction and Szynkielew III temporary junction, along with a section of DK14 national road between Pabianicka St. in Łódź and Łódź Lublinek junction) and July 13, 2012 (following Dobroń - Szynkielew III section). The second section, between Róża and Dobroń junctions, has been opened on April 11, 2014. The construction of third section, between Emilia and Łódź Lublinek junctions, has begun in 2019 and opened in July 2023, thus making Łódź the first city in Poland with a complete beltway.

#### Junctions

| Name | Location | Roads |
| Emilia | Emilia | DK 91 / A 2 ( E30) |
| Zgierz Lućmierz | Lućmierz | DK 91 |
| Aleksandrów Łódzki | Aleksandrów Łódzki | DK 71 |
| Łódź Teofilów | Łódź (Teofilów) | DK 72 |
| Konstantynów Łódzki | Konstantynów Łódzki | DK 71 |
| Łódź Retkinia | Łódź (Nowy Józefów) | local road |
| Łódź Lublinek | Łódź (Lublinek) | DK 14 |
| Pabianice Północ | Szynkielew | DK 71 |
| Dobroń | Chechło Drugie | DW 482 |
| Róża | Róża | DK 12 / S 8 ( E67) |
# Örencik

Örencik can refer to the following villages in Turkey:
* Örencik, Bolu
* Örencik, Bozdoğan
* Örencik, Çorum
* Örencik, Daday
* Örencik, Gerede
* Örencik, Gölbaşı
* Örencik, Göynük
* Örencik, Hocalar
* Örencik, Karacabey
* Örencik, Kargı
* Örencik, Kastamonu
* Örencik, Kazan
* Örencik, Kızılcahamam
* Örencik, Mudurnu
* Örencik, Palu
* Örencik, Şanlıurfa
* Örencik, Vezirköprü
* Örencik, Yenice
* Örencik, Yeşilova
* Örencik, Zonguldak
# Mosagallaku Mosagadu

Mosagallaku Mosagadu (transl. gaming the system) may refer to these Indian Telugu-language films:
* Mosagallaku Mosagadu (1971 film)
* Mosagallaku Mosagadu (2015 film)
# Speak (Hungarian rapper)

Tamás Deák (born 31 May 1976), better known by his stage name Speak, is a rap artist, model and actor based in Hungary. The music video for his 2003 anti-war song, "Stop the War", became popularized through video sharing websites and was satirized by the US comedy TV show Saturday Night Live. Speak lives in London, England.

## "Stop the War"

Speak is known primarily for his 2003 rap single "Stop the War". A video for this single appeared on YouTube, and featured other semi-famous musicians. Various commentators called the song unintentionally humorous.
The song and music video were parodied on Saturday Night Live in a sketch starring Beck Bennett titled "World Peace Rap", broadcast 7 May 2017.

## Notable collaborations

On 20 June 2012, Speak announced on his website that he would be supporting Australian rap duet Hilltop Hoods and DJ Debris on their upcoming UK tour.
# MIIS

MIIS is an acronym that could refer to a number of things.
* Middlebury Institute of International Studies at Monterey, a graduate school in California
* MIIS (programming language), a computer programming language
* Microsoft Identity Integration Server, Microsoft server software for identity and access management solutions
* Mii, a simulated avatar created on the Wii, DS, Wii U, 3DS, and Switch consoles
* Seat Mii, a car that is a rebadge of the Volkswagen Up
* Multiple Intelligence International School, an international school in Metro Manila, Philippines
# MLS All-Time Best XI

The Major League Soccer All-Time Best XI was selected In 2005 as part of the league's tenth anniversary celebrations. Major League Soccer, the top soccer league in the United States, named its All-Time Best XI, a selection of the best eleven players in the history of the league. The winners were chosen by a combination of voting that included online voting on the league's official website, media votes, and MLS coaches and general managers.
The All-Time Best XI team was chosen from a pool of 78 players who were previous "Best XI" yearly selections or who were named to at least three All-Star Games since the inaugural season in 1996. D.C. United had four players selected who were with the team from 1996–2000, when D.C. United was the dominant team in MLS. Nine of the eleven players selected played with the league in the 1996 inaugural season; only Nowak (joined 1998) and Donovan (joined 2001) did not.

## All-Time Best XI

| Pos | Player | Teams | MLS accolades |
| GK | Tony Meola | MetroStars/New York (1996–98, 2005–06) Kansas City (1999–2004) | 62 shutouts |
| DF | Jeff Agoos | D.C. United (1996–2000), San Jose (2001–04), MetroStars (2005) | 3 times MLS Best XI |
| DF | Marcelo Balboa | Colorado (1996–2001), MetroStars (2002) | — |
| DF | Eddie Pope | D.C. United (1996–2002), MetroStars (2003-04), Salt Lake (2005–07) | 4 times MLS Best XI |
| MF | Piotr Nowak | Chicago (1998–2002) | 48 assists |
| MF | Preki | Kansas City (1996–2000, 2002–05), Miami (2001) | 112 assists 4 times MLS Best XI |
| MF | Marco Etcheverry | D.C. United (1996–2003) | 101 assists, 4 times MLS Best XI |
| MF | Carlos Valderrama | Tampa Bay (1996–97, 2000–01), Miami (1998–99), Colorado (2001-02) | 114 assists |
| MF | Landon Donovan | San Jose (2001–04), Los Angeles (2005–2014, 2016) | 144 goals, 136 assists 7 times MLS Best XI |
| FW | Jaime Moreno | D.C. United (1996–2002, 2004–10), MetroStars (2003) | 133 goals, 102 assists 5 times MLS Best XI |
| FW | Brian McBride | Columbus Crew (1996–2003), Chicago Fire (2008–10) | 80 goals |
# Jennie Wade

Mary Virginia Wade (May 21, 1843 – July 3, 1863), also known as Jennie Wade or Ginnie Wade, was a resident of Gettysburg, Pennsylvania during the Battle of Gettysburg. At the age of 20, she was the only direct civilian casualty of the battle, when she was killed by a stray bullet on July 3, 1863.
The house where she was killed is now a popular tourist attraction and museum called the "Jennie Wade House".

## Early life

Wade was born in Gettysburg, and worked as a seamstress with her mother in their house on Breckenridge Street while her father was in a mental asylum. She may have been engaged to Johnston Hastings "Jack" Skelly, a corporal in the 87th Pennsylvania, who had been wounded two weeks earlier in the Battle of Winchester. He died from his injuries on July 12, 1863, unaware that Wade had died days earlier.

## Casualty of war

Wade, her mother, and two younger brothers left their home in central Gettysburg and traveled to the house of her sister, Georgia Anna Wade McClellan at 548 Baltimore Street to assist her and her newborn child. It was July 1, 1863, during the first day's fighting of the Battle of Gettysburg. More than 150 bullets hit the McClellan house during the fighting.
About 8:00 a.m. on July 3, Wade was kneading dough for bread when a Minié ball traveled through the kitchen door and the parlor door of her sister's house and hit her. It pierced her left shoulder blade, went through her heart, and ended up in her corset. She was killed instantly. While it is uncertain which side fired the fatal shot, some authors have attributed it to an unknown Confederate sharpshooter.
Wade's mother heard her fall to the floor and went to tell her sister Georgia in the other room that her sister had been shot dead; two Union soldiers came from upstairs when they heard the screams of the women. They temporarily buried Wade's body in the back yard of the McClellan house, in a coffin originally intended for the Confederate General William Barksdale. In January 1864, her body was relocated to the cemetery of the German Reformed Church on Stratton Street. Her final resting place is located in the Evergreen Cemetery in Gettysburg. On July 4, her mother baked 15 loaves of bread with the dough Wade had kneaded.
In 1882, the United States Senate voted to grant Wade's mother a pension, citing that her daughter had been killed serving the Union cause – baking bread for the soldiers.

## Monument

In November 1865, Wade's remains were reburied in the Evergreen Cemetery near Jack Skelly. A monument to her, designed by Gettysburg resident Anna M. Miller, was erected in 1900 that includes an American flag that flies around the clock. (The Betsy Ross House in Philadelphia is the only other site devoted to a woman to share this distinction of the perpetual flag. The Evergreen Cemetery grave of John L. Burns also flies the perpetual flag.)