OpenLLM-France/wikimedia huggingface dataset:
# Hilbert's twentieth problem

Hilbert's twentieth problem is one of the 23 Hilbert problems set out in a celebrated list compiled in 1900 by David Hilbert. It asks whether all boundary value problems can be solved (that is, do variational problems with certain boundary conditions have solutions).

## Introduction

Hilbert noted that there existed methods for solving partial differential equations where the function's values were given at the boundary, but the problem asked for methods for solving partial differential equations with more complicated conditions on the boundary (e.g., involving derivatives of the function), or for solving calculus of variation problems in more than 1 dimension (for example, minimal surface problems or minimal curvature problems)

## Problem statement

The original problem statement in its entirety is as follows:
   An important problem closely connected with the foregoing [referring to Hilbert's nineteenth problem] is the question concerning the existence of solutions of partial differential equations when the values on the boundary of the region are prescribed. This problem is solved in the main by the keen methods of H. A. Schwarz, C. Neumann, and Poincaré for the differential equation of the potential. These methods, however, seem to be generally not capable of direct extension to the case where along the boundary there are prescribed either the differential coefficients or any relations between these and the values of the function. Nor can they be extended immediately to the case where the inquiry is not for potential surfaces but, say, for surfaces of least area, or surfaces of constant positive gaussian curvature, which are to pass through a prescribed twisted curve or to stretch over a given ring surface. It is my conviction that it will be possible to prove these existence theorems by means of a general principle whose nature is indicated by Dirichlet's principle. This general principle will then perhaps enable us to approach the question: Has not every regular variation problem a solution, provided certain assumptions regarding the given boundary conditions are satisfied (say that the functions concerned in these boundary conditions are continuous and have in sections one or more derivatives), and provided also if need be that the notion of a solution shall be suitably extended?

## Boundary value problems

In the field of differential equations, a boundary value problem is a differential equation together with a set of additional constraints, called the boundary conditions. A solution to a boundary value problem is a solution to the differential equation which also satisfies the boundary conditions.
To be useful in applications, a boundary value problem should be well posed. This means that given the input to the problem there exists a unique solution, which depends continuously on the input. Much theoretical work in the field of partial differential equations is devoted to proving that boundary value problems arising from scientific and engineering applications are in fact well-posed.
# Swimming at the 1987 Pan American Games – Men's 200 metre freestyle

The men's 200 metre freestyle competition of the swimming events at the 1987 Pan American Games took place on 9 August at the Indiana University Natatorium. The last Pan American Games champion was Bruce Hayes of US.
This race consisted of four lengths of the pool, all in freestyle.

## Results

All times are in minutes and seconds.
| KEY: | q | Fastest non-qualifiers | Q | Qualified | GR | Games record | NR | National record | PB | Personal best | SB | Seasonal best |

### Final

The final was held on August 9.
| Rank | Name | Nationality | Time |
| | John Witchel | United States | 1:50.90 |
| | Carlos Scanavino | Uruguay | 1:51.21 |
| | Brian Jones | United States | 1:52.11 |
| 4 | Júlio César Rebolal | Brazil | 1:52.15 |
| 5 | Gary Vandermeulen | Canada | 1:52.44 |
| 6 | Cristiano Michelena | Brazil | 1:52.89 |
| 7 | Darren Ward | Canada | 1:53.38 |
| 8 | Luis Moreli | Puerto Rico | 1:53.57 |
# Hirth 2702

The Hirth 2702 and 2703 are a family of in-line twin cylinder, two stroke, carburetted aircraft engines designed for use on ultralight aircraft and especially two seat ultralight trainers, single seat gyrocopters, and small homebuilts. It is manufactured by Hirth of Germany.

## Development

The 2703 was developed as a competitor to the 50 hp (37 kW) Rotax 503 and is similar to the Rotax powerplant in being a two-cylinder in-line engine, with dual capacitor discharge ignition. The 2702 was developed from the 2703 as a de-rated version.
Both the 2702 and 2703 use free air or fan cooling, with Bing 34mm slide carburetors. The cylinder walls are electrochemically coated with Nikasil. Standard starting is recoil start. Reduction drive systems available are the G-50 gearbox with reduction ratios of 2.16:1, 2.29:1, 2.59:1, 3.16:1, or 3.65:1, or a multi-element cog belt drive. A tuned exhaust and electric start are optional.
The engines runs on a 50:1 pre-mix of unleaded 93 octane auto fuel and oil.

## Variants
### 2702

    Twin-cylinder in-line, two stroke, aircraft engine with a single Bing 34mm slide carburetor. Produces 40 hp (30 kW) at 5500 rpm and has a factory rated TBO of 1200 hours. Still in production.

### 2703

    Twin-cylinder in-line, two stroke, aircraft engine with dual or optionally a single Bing 34mm slide carburetor. Produces 55 hp (41 kW) at 6200 rpm and has a factory rated TBO of 1000 hours. The 2703 has been largely supplanted in production by the Hirth 3202, but in 2009 was still available as a special order from the factory.

## Applications
### 2702

* Airfer Transan
* Brutsche Freedom 40
* Flightstar
* Hy-Tek Hurricane 103
* ISON Airbike
* Preceptor N3 Pup
* Spacek SD-1 Minisport

### 2703

* Airfer Transan
* Airmotive EOS 001
* American Sportscopter Ultrasport 254
* CGS Hawk
* Exkluziv Joker
* Falconar Golden Hawk
* Kolb Firestar
* RemSchetMash Robust
* US Light Aircraft Hornet

## Specifications (2702)

Data from Recreational Power Engineering

### General characteristics

* Type: Twin cylinder, two-stroke, in-line, aircraft engine
* Bore: 72 mm (2.8 in)
* Stroke: 64 mm (2.5 in)
* Displacement: 521 cc (31.8 cu in)
* Length: 413 mm (16.3 in)
* Width: 450 mm (17.7 in)
* Height: 376 mm (14.8 in)
* Dry weight: 70 lb (31.8 kg) with free air cooling, 76 lb (34.5 kg) with fan cooling, including recoil starter and exhaust. G-50 gearbox adds an additional 19 lb (8.6 kg)

### Components

* Fuel system: 1 X Bing 34mm slide type carburetor
* Fuel type: unleaded 93 octane auto fuel
* Oil system: 50:1 fuel/oil premix
* Cooling system: free air or fan
* Reduction gear: G-50 gearbox with reduction ratios of 2.16:1, 2.29:1, 2.59:1, 3.16:1, or 3.65:1, or a multi-element cog belt drive

### Performance

* Power output: 40 hp (30 kW) at 5500 rpm
* Compression ratio: 9.5:1
# Hirth 3002

The Hirth 3002 is a German aircraft engine, that was designed and produced by Hirth of Benningen for use in ultralight aircraft.
By March 2018, the engine was no longer advertised on the company website and seems to be out of production.

## Design and development

The Hirth 3002 is a four-cylinder, two-stroke, horizontally-opposed, 1,042 cc (63.6 cu in) displacement, fan-forced air-cooled, petrol engine design, with a mechanical gearbox reduction drive with reduction ratios from 2.03 to 3.79:1. It employs dual capacitor discharge ignition and produces 83 hp (62 kW) at 6000 rpm.

## Specifications (Hirth 3002 E)

Data from Tacke

### General characteristics

* Type: Four cylinder, two stroke aircraft engine
* Bore: 72 mm (2.8 in)
* Stroke: 64 mm (2.5 in)
* Displacement: 1,042 cc (63.6 cu in)
* Length: 380 mm (15.0 in)
* Width: 570 mm (22.4 in)
* Height: 338 mm (13.3 in)
* Dry weight: 42 kg (92.6 lb)

### Components

* Fuel type: petrol
* Cooling system: fan-forced air
* Reduction gear: mechanical gearbox

### Performance

* Power output: 83 hp (62 kW)
# Hirth F-23

The Hirth F-23 is a twin cylinder, horizontally-opposed, two stroke, carburetted or optionally fuel injected aircraft engine designed for use on ultralight aircraft. It is manufactured by Hirth of Germany.

## Development

The F-23 is intended to compete with the 50 hp (37 kW) Rotax 503 and is differentiated from the Rotax powerplant by offering a horizontally-opposed cylinder layout. The F-23 uses free air cooling and piston-ported induction, with dual Bing 34mm slide or optional diaphragm type carburetors. The cylinder walls are electrochemically coated with Nikasil. Standard starting is recoil start. A belt reduction drive system, fuel injection, tuned exhaust and electric start are optional.
The engine runs on a 50:1 pre-mix of unleaded 93 octane auto fuel and oil. Recommended time between overhauls is 1000 hours.
The F-23 produces 50 hp (37 kW) at 6150 rpm and 40 hp (30 kW) at 5500 rpm.

## Applications

* Aeronix Airelle
* Air Sports AIRector 120
* Aurore MB 02-2 Mini Bulle
* DAR-23
* Fisher FP-303
* Monnett Moni - motorglider
* Rotorschmiede VA115
* Sadler Vampire
* Solid Air Diamant LP
* Spacek SD-1 Minisport
* TechProAviation Merlin 100
* Team Mini-Max AeroMax
* TeST TST-1 Alpin
* Wings of Freedom Phoenix 103

## Specifications (F-23)

Data from Recreational Power Engineering

### General characteristics

* Type: Twin cylinder, two-stroke, aircraft engine
* Bore: 72 mm (2.8 in)
* Stroke: 64 mm (2.5 in)
* Displacement: 521 cc (31.8 cu in)
* Length: 247 mm (9.7 in)
* Width: 570 mm (22.4 in)
* Height: 338 mm (13.3 in)
* Dry weight: 84 lb (38.1 kg) including reduction unit, full exhaust system and electric start

### Components

* Valvetrain: piston-ported
* Fuel system: 2 X Bing 34mm slide or optional diaphragm type carburetor or fuel injection
* Fuel type: unleaded 93 octane auto fuel
* Oil system: 50:1 fuel/oil premix
* Cooling system: free air
* Reduction gear: cog belt with 1.8:1, 2.2:1 and 2.5:1 ratios optional

### Performance

* Power output: 50 hp (37 kW) at 6150 rpm
* Compression ratio: 9.5:1
# Hinjal

Hinjal is a town and union council in the Bannu District of Khyber-Pakhtunkhwa, Pakistan.
# Hino

Hino may refer to:

## Places
### Estonia

* Hino, Põlva County
* Hino, Võru County
** Lake Hino

### Japan

* Hino, Shiga
* Hino, Tokyo
* Hino, Tottori
** Hino District, Tottori
** Hino River

## Transportation

* Hino Motors, a Japanese truck manufacturer owned by Toyota
** Hino Pakistan
* Hino Station (disambiguation), railway stations in Japan:
** Hino Station (Nagano), a railway station Susuka, Nagano, operated by Nagano Electric Railway
** Hino Station (Shiga), a railway station operated by Ohmi Railway
** Hino Station (Tokyo), a railway station operated by East Japan Railway Company

## Other uses

* Hino (surname), a Japanese surname
* Hé-no, also called Hino, an Iroquois thunder spirit
# Swimming at the 2015 Parapan American Games – Men's 50 metre freestyle S5

The men's S5 50 metres freestyle competition of the swimming events at the 2015 Parapan American Games was held on August 12, 2015 at the Toronto Pan Am Sports Centre.

## Schedule

All times are Eastern Standard Time (UTC-5).
| Date | Time | Round |
| 12 August | 9:31 | Heats |
| 12 August | 17:59 | Final |

## Results
### Heats
#### Heat 1

| Rank | Lane | Name | Nationality | Time |
| 1 | 4 | Clodoaldo Da Silva | Brazil | 35.02 |
| 2 | 5 | Edgar Pineda | Mexico | 39.66 |
| 3 | 3 | Danial Murphy | Canada | 43.22 |
| 4 | 6 | Gerardo Castro | Mexico | 48.61 |
| 5 | 2 | Sebastian Ortiz | Puerto Rico | 1:12.24 |

#### Heat 2

| Rank | Lane | Name | Nationality | Time |
| 1 | 4 | Daniel Dias | Brazil | 34.97 |
| 2 | 5 | Diego Lopez | Mexico | 39.94 |
| 3 | 3 | Andrew Cooke | Canada | 42.82 |
| 4 | 6 | Francisco Avelino | Brazil | 43.99 |
| 5 | 2 | Jonathan Dielman | Canada | 1:06.01 |

### Final

| Rank | Lane | Name | Nationality | Time | Notes |
| | 4 | Daniel Dias | Brazil | 32.41 | PR |
| | 5 | Clodoaldo Da Silva | Brazil | 34.94 | |
| | 3 | Edgar Pineda | Mexico | 38.52 | |
| 4 | 6 | Diego Lopez | Mexico | 39.57 | |
| 5 | 7 | Danial Murphy | Canada | 42.15 | |
| 6 | 2 | Andrew Cooke | Canada | 42.30 | |
| 7 | 1 | Francisco Avelino | Brazil | 44.08 | |
| 8 | 8 | Gerardo Castro | Mexico | 46.15 | |
# Swimming at the 1998 World Aquatics Championships – Women's 400 metre individual medley

The finals and the qualifying heats of the women's 400 metre individual medley event at the 1998 World Aquatics Championships were held on Monday 12 January 1998 in Perth, Western Australia.

## A Final

| Rank | Name | Time |
| | Chen Yan (CHN) | 4:36.66 |
| | Yana Klochkova (UKR) | 4:38.60 |
| | Yasuko Tajima (JPN) | 4:39.45 |
| 4 | Wu Yanyan (CHN) | 4:40.16 |
| 5 | Kristine Quance (USA) | 4:42.01 |
| 6 | Maddy Crippen (USA) | 4:43.45 |
| 7 | Joanne Malar (CAN) | 4:46.91 |
| 8 | Nadine Neumann (AUS) | 4:48.84 |

## B Final

| Rank | Name | Time |
| 9 | Beatrice Câșlaru (ROM) | 4:46.91 |
| 10 | Nicole Hetzer (GER) | 4:46.93 |
| 11 | Lourdes Becerra (ESP) | 4:47.52 |
| 12 | Hana Černá (CZE) | 4:48.86 |
| 13 | Emma Johnson (AUS) | 4:50.99 |
| 14 | Simona Păduraru (ROM) | 4:52.09 |
| 15 | Mirjana Boševska (MKD) | 4:53.43 |
| 16 | Carolyn Adel (SUR) | 4:55.33 |

## Qualifying heats

| Rank | Name | Time |
| 1 | Chen Yan (CHN) | 4:40.72 |
| 2 | Yasuko Tajima (JPN) | 4:41.45 |
| 3 | Maddy Crippen (USA) | 4:42.13 |
| 4 | Joanne Malar (CAN) | 4:44.85 |
| 5 | Kristine Quance (USA) | 4:44.95 |
| 6 | Nadine Neumann (AUS) | 4:45.83 |
| 7 | Yana Klochkova (UKR) | 4:45.94 |
| 8 | Wu Yanyan (CHN) | 4:46.00 |
| 9 | Beatrice Câșlaru (ROM) | 4:46.80 |
| 10 | Nicole Hetzer (GER) | 4:48.64 |
| 11 | Hana Černá (CZE) | 4:48.64 |
| 12 | Emma Johnson (AUS) | 4:49.94 |
| 13 | Simona Păduraru (ROM) | 4:50.11 |
| 14 | Lourdes Becerra (ESP) | 4:50.46 |
| 15 | Carolyn Adel (SUR) | 4:54.30 |
| 16 | Mirjana Boševska (MKD) | 4:55.56 |
| 17 | Ravee Intporn-Udom (THA) | 4:55.92 |
| 18 | Yseult Gervy (BEL) | 4:56.25 |
| 19 | Sabine Herbst (GER) | 4:57.16 |
| 20 | Oxana Verevka (RUS) | 4:57.59 |
| 21 | Karine Chevrier (CAN) | 4:59.22 |
| 22 | Aikaterini Sarakatsani (GRE) | 4:59.88 |
# Hippotion moorei

Hippotion moorei is a moth of the family Sphingidae. It is known from dry areas from northern Tanzania to Ethiopia and Somalia.
# Superfriend

Super Friends is an animated television show based on DC Comics superheroes. The term or others like it may also refer to:
* "Superfriend", a song by Audio Adrenaline from the 1997 album Some Kind of Zombie
* "Superfriend", a song by Rivers Cuomo from the 2007 album Alone: The Home Recordings of Rivers Cuomo
# Hospital de la Caridad

Hospital de la Caridad may refer to:
* Hospital de la Caridad (Algeciras), a former charity hospital in Algeciras, Spain
* Hospital de la Caridad (Seville), a baroque charity hospital building in Seville, Spain
# Heroic Expeditions

Heroic Expeditions is a 1981 fantasy role-playing game adventure published by Judges Guild.

## Contents

Heroic Expeditions is an adventure supplement which consists of three separate scenarios with each intended for a specific set of character types: "Spear of Darkness," "Quest for the Book of Ancestry," and "Cave of Despair".

## Reception

J. David George reviewed Heroic Expeditions in The Space Gamer No. 50. George commented that "Any of these three quests could have been interesting, were they given more background and published separately in a more complete form. "Cave," the best of the three, can only be described as almost clever. For the most part, even novice referees would be better off designing their own quests than using those presented in Heroic Expeditions."
# Henry Paget, 3rd Marquess of Anglesey

Henry William George Paget, 3rd Marquess of Anglesey (9 December 1821 – 30 January 1880), styled Lord Paget until 1854 and Earl of Uxbridge between 1854 and 1869, was a British peer and Liberal politician.

## Background

Anglesey was the only son of Henry Paget, 2nd Marquess of Anglesey, by his first wife Eleanora, daughter of Colonel John Campbell.

## Military career

He was appointed as Captain of the Burton-on-Trent Troop of the part-time Staffordshire Yeomanry on 26 March 1839. The following year he obtained permission for the troop to be renamed the Anglesey Troop. On 21 May 1841 he purchased a commission in the Grenadier Guards as Ensign & Lieutenant. He sold his commission and retired on 23 May 1845.

## Political career

Anglesey was returned to Parliament as one of two representatives for Staffordshire South in 1854, a seat he held until 1857. In 1869 he succeeded his father in the marquessate and entered the House of Lords.

## Personal life

On 7 June 1845 in her home parish of Horsham, he married Sophia Eversfield, born 24 June 1819, the daughter of James Eversfield, of Denne Park, and his wife Mary Crew, daughter of Robert Hawgood Crew. There were no children from the marriage. He died in Westminster on 30 January 1880, aged 58, and was succeeded by his half-brother, Lord Henry Paget. His widow moved to Fordingbridge and later to Tunbridge Wells, where she died on 7 December 1901.
# Jamuniya, Sarlahi

Jamuniya is a village development committee in Sarlahi District in the Janakpur Zone of south-eastern Nepal. At the time of the 1991 Nepal census it had a population of 5,399 people living in 914 individual households.
Though there is no any documented evidence, but as per the villagers, the village was settled around 18th century by group of Gwalas (Yadav) migrated from Bansghatgonra ( a village, whchich has become a part of today's Patna). The group was led by Chhitnu Ray Yadav, who became the first landlord of the village. The village was settled by clearing the Jungle area predominant with the trees of Jamun, hence named Jamuniya.
The last Landlord of Jamuniya was Nandipat Ray. Late Mr. Ramdhyaan Ray (ex-minister of state HMG-Nepal) is the most famous personality in Sarlahi District. Though the majority of population in the VDC is poor and farmers like in other villages of Nepal, it has also produced some eminent personalities like:-
* Late Mr. Sanjay Yadav ( Martyr- Madheshi Pepoples' Movement)
* Prof.Dr. Ramswarth Ray (ex-campus chief RRM Campus Janakpur)
* Prof. Krishna Deo Yadav (ex-campus chief Sarlahi Campus Malangwa) * Mr Tarun Yadav (social worker,social actievist and political analyser)
* Honourable Khobhari Ray (minister of state Nepal)
* Mr. Brahmadeo Ray (Social worker) *Ram Deo Ray (ex Mukhiya & social worker)
Gadhi Mai Temple, Deval Baba Temple and Madanpur Math are some important landmark of Sarlahi district, which are located in Jamuniya VDC.
# Nasiruddin Mahmud

Nasiruddin Mahmud (ناصر الدين محمود) may refer to:
* Nasir ad-Din Mahmud I (r. 1092-1094), Sultan of the Seljuk Empire
* Nasir al-Din Mahmud (r. 1201-1222), Bey of the Artuqids
* Nasir ad-Din Mahmud (r. 1219-1234), Zengid emir of Mosul
* Nasiruddin Mahmud (eldest son of Iltutmish) (r. 1227–1229), a governor of Bengal under the Delhi Sultanate
* Nasiruddin Mahmud Shah, Sultan of Delhi (r. 1246–1265)
* Nasir-ud-Din Mahmud Shah Tughluq (r. 1394–1413), Sultan of Delhi
* Mahmud Shah (Sultan of Bengal) (r. 1435–1459)
# Jacques Leschassier

Jacques Leschassier (or Lechassier) (1550 – 1625) was a French jurist and magistrate, known for his erudition and Gallican views.

## Life

He was an avocat of the Parlement of Paris, and then procureur-général of the Parlement. He supported the Salic Law and in 1606 argued the case for Gallican ecclesiastical independence.
Leschassier put forward proposals around 1597, intended to help Henry IV of France get better control of royal officeholders, by designating the posts as fiefs.
At the time of the Venetian Interdict, the Venetian diplomat Pietro Priuli recruited Leschassier and Louis Servin to write in Venice's defence. These works argued that the position of the Church of Venice should be equated with that of the Gallican view of the situation of the Church of France. Leschassier then became an intimate correspondent of Paolo Sarpi.
# Psilogramma bartschereri

Psilogramma bartschereri is a moth of the family Sphingidae. It is known from Sri Lanka. This species is currently considered synonymous with Psilogramma menephron nebulosa.
# Puepahk Tugypahgyn Noomwevehchuh Psehdtuhneeyet

Puepahk Tugypahgyn Noomwevehchuh Psehdtuhneeyet (also known as Seasons of Our Story) is a 1993 glass and red sandstone sculpture by Janet Shapero, installed in Salt Lake City, Utah, United States.

## Description and history

Installed in the Triad Center, the abstract work was commissioned during 1992–1993, copyrighted in 1993, and dedicated on June 21 of that year. The central stone measures approximately 12 x 8 x 4 feet, and the glass prisms each weigh 400 pounds and measure approximately 6 feet x 18 inches x 6 inches. The artwork was surveyed by the Smithsonian Institution's "Save Outdoor Sculpture!" program in 1994.
# New York and Greenwood Lake Railway

New York and Greenwood Lake Railway may refer to:
* New York and Greenwood Lake Railway (1878–1943), a predecessor of the Erie Railroad in New Jersey
* New York and Greenwood Lake Railway (1996), an unrelated shortline railroad in Garfield and Passaic, New Jersey
# James Cooney

James, Jim or Jimmy Cooney may refer to:
* James Cooney (Missouri politician) (1848–1904), Irish-American lawyer and United States Congressman from Marshall, Missouri
* James C. Cooney, Sergeant of the U.S. Army in the 8th U.S. Cavalry who found large silver and gold reserves in the Mogollon Mountains of Catron County, New Mexico
* Jimmy Cooney (1890s shortstop) (1865–1903), MLB shortstop from 1890 to 1892
* Jimmy Cooney (1920s shortstop) (1894–1991), MLB shortstop from 1917 to 1928
* Jimmy Cooney (Galway hurler) (1955–2023), Irish hurler
* James Cooney (Medal of Honor) (1860–1903), American Medal of Honor recipient
* James Cooney (American football) (c. 1880–1964), All-American football player
* Jimmy Cooney (Tipperary hurler) (born 1914), Irish hurler