OpenLLM-France/wikimedia huggingface dataset:
# Ermakov–Lewis invariant

Many quantum mechanical Hamiltonians are time dependent. Methods to solve problems where there is an explicit time dependence is an open subject nowadays. It is important to look for constants of motion or invariants for problems of this kind. For the (time dependent) harmonic oscillator it is possible to write several invariants, among them, the Ermakov–Lewis invariant which is developed below.
The time dependent harmonic oscillator Hamiltonian reads
    ${\hat {H}}={\frac {1}{2}}\left[{\hat {p}}^{2}+\Omega ^{2}(t){\hat {q}}^{2}\right].$
It is well known that an invariant for this type of interaction has the form
    ${\hat {I}}={\frac {1}{2}}\left[\left({\frac {\hat {q}}{\rho }}\right)^{2}+(\rho {\hat {p}}-{\dot {\rho }}{\hat {q}})^{2}\right],$
where $\rho$ obeys the Ermakov equation
    ${\ddot {\rho }}+\Omega ^{2}\rho =\rho ^{-3}.$
The above invariant is the so-called Ermakov–Lewis invariant. It is easy to show that ${\hat {I}}$ may be related to the time independent harmonic oscillator Hamiltonian via a unitary transformation of the form
    ${\hat {T}}=e^{i{\frac {\ln \rho }{2}}({\hat {q}}{\hat {p}}+{\hat {p}}{\hat {q}})}e^{-i{\frac {\dot {\rho }}{2\rho }}{\hat {q}}^{2}}=e^{i{\frac {\ln \rho }{2}}{\frac {d{\hat {q}}^{2}}{dt}}}e^{-i{\frac {{\hat {q}}^{2}}{2}}{\frac {d\ln \rho }{dt}}},$
as
    ${\frac {1}{2}}\left[{\hat {p}}^{2}+{\hat {q}}^{2}\right]={\hat {T}}{\hat {I}}{\hat {T}}^{\dagger }.$
This allows an easy form to express the solution of the Schrödinger equation for the time dependent Hamiltonian.
The first exponential in the transformation is the so-called squeeze operator.
This approach may allow to simplify problems such as the Quadrupole ion trap, where an ion is trapped in a harmonic potential with time dependent frequency. The transformation presented here is then useful to take into account such effects.
The geometric meaning of this invariant can be realized within the quantum phase space.

## History

It was proposed in 1880 by Vasilij Petrovich Ermakov (1845-1922). The paper is translated in.
In 1966, Ralph Lewis rediscovered the invariant using Kruskal's asymptotic method. He published the solution in 1967.
# Douliu railway station

Douliu (Chinese: 斗六; pinyin: Dòuliù) is a railway station in Yunlin County, Taiwan served by Taiwan Railways. Yunlin HSR station can be accessed here by bus.

## Overview

The station has two island platforms. Ticketing and customer service are located in the main concourse on the second floor, while tracks are located in front of and behind the station. The station has an accessibility elevator.

### History

* 1904-02-01: The station opened as Toroku-eki (斗六驛).
* 1940: After an earthquake, the station was closed for three months for reconstruction.
* November 1958: The second-generation station (with reinforced concrete) was completed.
* 2006-11-03: The second-generation station was demolished.
* 2008-12-19: The current cross-platform station opened for service.

## Platform layout

| 1 | 1A | ■ West Coast line (southbound departure) | Toward Chiayi, Tainan, Kaohsiung |
| 1 | 1A | ■ West Coast line (southbound through service) | Toward Chiayi, Tainan, Kaohsiung |
| 2 | 1B | ■ West Coast line (southbound) | Toward Tainan, Kaohsiung, Pingtung |
| 2 | 1B | ■ South-link line (southbound) | Toward Fangliao, Taitung |
| 3 | 2A | ■ West Coast line (northbound) | Toward Changhua, Taichung, Taipei |
| 3 | 2A | ■ Eastern line (southbound, cross-line) | Toward Yilan, Suao, Hualien |
| 4 | 2B | ■ West Coast line (northbound departure) | Toward Changhua, Taichung, Taipei |
| 4 | 2B | ■ West Coast line (northbound through service) | Toward Changhua, Taichung, Taipei |

## Around the station

* Douliou City area
* Huwei River
* Yunlin River
* Yunlin County Government
* House of Citizen-Memorial Hall of Attendance
* Douliu City Office
* National Yunlin University of Science and Technology
* TransWorld University
* Douliu High School
* Yunlin County Stadium
# El diablito

El Diablito (The Little Devil, which was originally to be called Volumen 2) is the second studio album by Mexican rock band Caifanes, released on June 19, 1990. Original members Saúl Hernández, Alfonso André, Sabo Romo, and Diego Herrera returned, along with a new guitar player, Alejandro Marcovich, who joined in September 1989.

## Track listing

All songs written by Saúl Hernández except where noted.
* Detrás de ti (Behind You) (Saúl Hernández, Diego Herrera, Alfonso André) – 3:36
* Antes de que nos olviden (Before We're Forgotten) – 4:45
* La vida no es eterna (Life Isn't Eternal) (Bonus Track) – 3:54
* De noche todos los gatos son pardos (At Night All Cats Are Brown) – 4:13
* Sombras en tiempos perdidos (Shadows in Lost Times) – 5:52
* El negro cósmico (The Cosmic Blackness) – 3:42
* La célula que explota (The Exploding Cell) – 3:33
* Aquí no pasa nada (Nothing Happens Here) (Bonus Track) – 4:37
* Los dioses ocultos (The Hidden Gods) – 4:39
* El elefante (The Elephant) – 3:00
* Amárrate a una escoba y vuela lejos (Tie Yourself to a Broom and Fly Far Away) – 3:52

## Personnel

* Diego Herrera – saxophone, keyboards
* Sabo Romo – bass
* Saúl Hernández – vocals, guitar
* Alfonso André – drums
* Alejandro Marcovich – guitar

## Certifications

| Region | Certification | Certified units/sales |
| Mexico (AMPROFON) | Platinum | 250,000$^‡$ |
| $^‡$ Sales+streaming figures based on certification alone. |||
# Koroinen (ward)

Koroinen (Finnish; Korois in Swedish) is a ward (suuralue, storområde) of Turku, Finland, also known as Ward 5. The ward is located to the northeast of the city centre and named after Koroinen, a district in the centre of the ward.
The ward has a population of 10,419 (as of 2004) and an annual population increase of 1.42%. 14.76% of the ward's population are under 15 years old, while 6.25% are over 65. It is one of the most multicultural of the city's wards, and this is reflected in the linguistic makeup, which is 83.01% Finnish, 5.42% Swedish, and 11.57% other.

## Districts

The ward consists of five districts. One of them is divided with another ward.
* Koroinen (Korois)
* Halinen (Hallis)
* Nummi (Nummis)
* Oriketo
* Räntämäki
# Elrod

Elrod may refer to:
* Elrod (surname), including a list of people with the name
* Elrod, Indiana, an unincorporated community
* Elrod, South Dakota, an unincorporated community
* Elrod, North Carolina, a census-designated place
# Wanarn Community

Wanarn is a medium-sized Aboriginal community, located in the Goldfields–Esperance region of Western Australia, within the Shire of Ngaanyatjarraku.

## Native title

The community is located within the determined Ngaanyatjarra Lands (Part A) (WAD6004/04) native title claim area.

## Governance

The community is managed through its incorporated body, Wanarn (Aboriginal Corporation) (formally Wannan Community (Aboriginal Corporation)), incorporated under the Aboriginal Councils and Associations Act 1976 on 27 June 1989.

## Town planning

Wanarn Layout Plan No.1 has been prepared in accordance with State Planning Policy 3.2 Aboriginal Settlements. Layout Plan No.1 was endorsed by the community on 1 December 2003 and the Western Australian Planning Commission on 4 May 2004.
# La Poupée (film)

La Poupée ("The Doll") is a 1962 French-Italian science fiction film directed by Jacques Baratier. It was entered into the 12th Berlin International Film Festival. It was Baratier's final film. La Poupée is a surrealistic work, "part theater of the absurd, part musical with Greek chorus". Grand Guignol
In La Poupée, a rebel impersonates the leader of a fictional country, loosely modeled off Latin American dictators. His "wife" Marion (played by the crossdressing actor Sonne Teal) is in fact also a robot imposter, the Poupée.

## Cast

* Zbigniew Cybulski - Col. Prado Roth / The Rebel
* Sonne Teal - Marion / La Poupée
* Claudio Gora - Moren, the Banker
* Catherine Milinaire - Mirt
* Jean Aron - Prof. Palmas
* Sacha Pitoëff - Sayas
* Daniel Emilfork - Gant de Crin
* Jacques Dufilho - The Indian
* Gabriel Jabbour - Joachim
* Michel de Ré - Gervasio
* László Szabó - Pascuel
* Roger Karl - Terremoche
* Jean Galland - Gonziano
* Max Montavon - Scientist
# Vicolungo

Vicolungo is a comune (municipality) in the Province of Novara in the Italian region Piedmont, located about 80 kilometres (50 mi) northeast of Turin and about 12 kilometres (7 mi) northwest of Novara. As of 31 December 2004, it had a population of 857 and an area of 13.4 square kilometres (5.2 sq mi).
Vicolungo borders the following municipalities: Arborio, Biandrate, Casaleggio Novara, Landiona, Mandello Vitta, Recetto, and San Pietro Mosezzo.
# Ester Helenius

Ester Emmy Maria Helenius (16 May 1875 – 12 October 1955) was a Finnish artist known for the vibrant use of color in her paintings. This vibrancy was so notable that art historian Tutta Palin described her as a "worshipper of ecstasy." While mainly a painter, Helenius was also trained in printmaking.

## Background and work

Helenius was an artist in residence at the famous Lallukka Artists’ Home in the Etu-Töölö district of Helsinki. Her art from this period was on display in 2020–2021 at the Helsinki Art Museum in the exhibition Lallukka – Life in the Home of Artists, alongside other well-known Finnish visual artists of the mid 20th century.
Helenius' work has gained posthumous notoriety after being written on by Finnish art historian Tutta Palin in the book Ester Helenius: Värihurmion palvoja, a popular reference for tracing the evolution of Helenius' work.
Her sales records have been donated to the Hämeenlinna Art Museum as part of her legacy.
Helenius is known to have had love affairs with women. Popular Finnish author and illustrator Tove Jansson has written of her interactions with Helenius during her time in Paris, France in her book Letters From Tove. Both artists lived at the Lallukka Artists’ Home.
Helenius' art can be found at auction on sites such as Hagelstam & Co. and Bukowskis for estimated values of up to 2,000 euros
Her work also remains in the collections of the Finnish National Gallery, the Helsinki Art Museum, and the Hämeenlinna Art Museum, among others.
# Cephalopod fin

| Standard measurements for squid, showing the location of the fins and tail in different configurations | Measurement of fin angle in a squid with sagittate fins |
Cephalopod fins, sometimes known as wings, are paired flap-like locomotory appendages. They are found in ten-limbed cephalopods (including squid, bobtail squid, cuttlefish, and Spirula) as well as in the eight-limbed cirrate octopuses and vampire squid. Many extinct cephalopod groups also possessed fins. Nautiluses and the more familiar incirrate octopuses lack swimming fins. An extreme development of the cephalopod fin is seen in the bigfin squid of the family Magnapinnidae.
Fins project from the mantle and are often positioned dorsally. In most cephalopods, the fins are restricted to the posterior end of the mantle, but in cuttlefish and some squid they span the mantle's entire length.
Fin attachment varies greatly among cephalopods, though in all cases it involves specialised fin cartilage (which reaches its greatest development in Octopodiformes). A fin may be attached to the internal shell or shell remnant (such as the gladius), to the opposite fin, to the mantle, or a combination of these.

## Tail and secondary fins

Certain squid species possess a tail, which is an extension of the body past the fins. The tail may be said to start at "the point where a hypothetical line, continuous with the broad posterior edge of the fin, crosses the midline of the body". This tail may be lost with age (as in most paralarval chiroteuthids) or remain through sexual maturity (as in Grimalditeuthis). Grimalditeuthis and larval Chiroteuthis are unusual in that they possess a pair of flotation devices or "secondary fins" attached to the tail. The vampire squid (Vampyroteuthis infernalis) also has two pairs of fins during a brief period of its ontogeny, and secondary fins have been reported in the extinct Trachyteuthis.

## Fin morphology and placement

Cephalopod fin morphology is highly variable. The fins may be large and muscular, extending for the entire length of the mantle, or greatly reduced (sometimes less than 10% ML) and restricted to the mantle's posterior end. Fin placement in cephalopods is often termed normal, terminal, or subterminal, depending on their position with respect to the muscular mantle.
Eight major fin shapes can be distinguished among the Decapodiformes: sagittate (the most common shape in squid), rhomboid, circular/elliptical, lanceolate, ear-shaped, ribbed, lobate, and skirt-like.
* Ventral (left) and dorsal aspects of Onychoteuthis banksii, showing classic sagittate fins
* The diamondback squid, Thysanoteuthis rhombus, has full-length rhomboid fins
* Mastigoteuthis magna has very large circular fins, characteristic of its family, Mastigoteuthidae
* Galiteuthis phyllura in dorsal (top) and ventral views, showing its lanceolate fins
* Spirula spirula has small ear-shaped fins on either side of a terminal photophore
* The highly distinctive ribbed fins of Chtenopteryx sicula
* Skirt-like fins spanning the length of the mantle are characteristic of sepiids, such as this Sepia officinalis
# Dren, Kostel

Dren (pronounced) is a small settlement in the hills above the left bank of the Kolpa River southwest of Kostel in southern Slovenia. The area is part of the traditional region of Lower Carniola and is now included in the Southeast Slovenia Statistical Region.
# Leptura aethiops

Leptura aethiops is a species of beetle in the family Cerambycidae. It was described by Poda in 1761.
# Komšići

Komšići is a village in the municipality of Žepče, Bosnia and Herzegovina.

## Demographics

According to the 2013 census, its population was 147.
Ethnicity in 2013 :
| Ethnicity | Number | Percentage |
| Croats | 146 | 99.3% |
| other/undeclared | 1 | 0.7% |
| Total | 147 | 100% |
# Elli Pappa

Elli Pappa (formerly Ioannidou; 1920–2009) was a Greek writer and activist. She was the sister of Greek author Dido Sotiriou and the partner of Nikos Beloyannis, with whom she had a son in 1951. As a member of the Communist Party of Greece, Pappa worked in the newspaper Rizospastis during the years of the Greek Resistance, and continued contributing articles during and after the Greek Civil War until her arrest in December 1950.

## Career

Pappa became known internationally in 1952 when a campaign for clemency against the death sentence given to her by the military tribunal in Athens saw a letter from her prison cell published across the world. Her account of these events and consequent imprisonment was published in the book Martyries mias diadromis (2010). It contains two parts, which were the two large files she had deposited with a museum archive in the 1990s to be published after her death. It narrates her life after the end of the Second World War until her release from prison in 1964, concentrating on conveying her own experience of these events while detailing historical facts.
Her writings on political theory include the book The Ancient Greek Philosophers in Karl Marx's 'Capital' (1983), in which ancient Greek philosophical texts and their use by Karl Marx in his book Capital are examined, and the journal article 'Machiavelli versus Marx' (1992), which was based on an earlier conference paper.

## Cultural references

Nikos Tzimas's film The Man with the Carnation (1980) tells the story of Beloyannis (played by Foivos Gikopoulos) in the post-Civil War period. It includes many scenes with Pappa (played by Mirka Papakonstantinou), who worked with him when he arrived in Athens in June 1950 and remained close to him during their trials and the consequent execution of Beloyannis and his associates.
# North Berwick Coastal (ward)

North Berwick Coastal is one of the six wards used to elect members of the East Lothian Council. It elects three Councillors.

## Councillors

| Election | Councillors | Councillors | Councillors | Councillors | Councillors |
| 2007 | | Stuart MacKinnon (Liberal Democrats) | | Neil Rankin (Conservative) | David Berry (SNP) |
| 2012 | | Jim Goodfellow (Labour) | Tim Day (Conservative) | | David Berry (SNP) |
| 2017 | Jeremy Douglas Findlay (Conservative) | Jim Goodfellow (Labour) | | Jane Henderson (Conservative) |
| 2022 | Jeremy Douglas Findlay (Conservative) | Carol McFarlane (Labour) | | Liz Allan (SNP) |

## Election Results
### 2017 Election

2017 East Lothian Council election
North Berwick Coastal - 3 seats :
| Party | Party | Candidate | FPv% | Count | Count | Count | Count | Count |
| Party | Party | Candidate | FPv% | 1 | 2 | 3 | 4 | 5 |
| | Conservative | Jeremy Douglas Findlay | 27.16 | 1,703 | | | | |
| | Labour | Jim Goodfellow (incumbent) | 23.73 | 1,488 | 1,497 | 1,573 | | |
| | Conservative | Jane Henderson | 21.38 | 1,341 | 1,454 | 1,474 | 1,475 | 1,589 |
| | SNP | Laura Lowe Forrest | 17.97 | 1,127 | 1,128 | 1,233 | 1,234 | 1,335 |
| | Liberal Democrats | Robert O'Riordan | 5.07 | 318 | 323 | 388 | 389 | |
| | Scottish Green | Eurig Scandrett | 4.67 | 293 | 294 | | | |
| Electorate: 10,752 Valid: 6,270 Spoilt: 114 Quota: 1,568 Turnout: 59.4 |||||||||

### 2012 Election

2012 East Lothian Council election
North Berwick Coastal - 3 seats :
| Party | Party | Candidate | FPv% | Count | Count | Count | Count |
| Party | Party | Candidate | FPv% | 1 | 2 | 3 | 4 |
| | Conservative | Tim Day | 30.65 | 1,465 | | | |
| | Labour | Jim Goodfellow | 27.08 | 1,294 | | | |
| | SNP | David Stuart Berry (incumbent)† | 21.30 | 1,018 | 1,043.8 | 1,059 | 1,253.9 |
| | Liberal Democrats | Stuart Leitch MacKinnon (incumbent) | 8.47 | 405 | 485.2 | 510.6 | 526.3 |
| | Independent | Jeremy Douglas Findlay | 7.32 | 350 | 426.8 | 444.4 | 464.9 |
| | SNP | Ronnie Gurr | 5.17 | 247 | 250.1 | 255.1 | |
| Electorate: 9,811 Valid: 4,779 Spoilt: 42 Quota: 1,195 Turnout: 4,821 (48.71%) ||||||||

### 2007 Election

2007 East Lothian Council election
North Berwick Coastal :
| Party | Candidate | 1st Pref | % | Seat | Count |
| Conservative | Neil Rankin | 1,837 | 29.7 | 1 | 1 |
| SNP | David Berry | 1,670 | 27.0 | 2 | 1 |
| Labour | Pat Hanson | 980 | 15.8 | | |
| Liberal Democrats | Stuart MacKinnon | 747 | 12.1 | 3 | 5 |
| Conservative | Kathryn Smith | 565 | 9.1 | | |
| Scottish Green | Susan Moffat | 393 | 6.3 | | |
# Ester Graff

Ester Graff (3 May 1897 – 23 January 1991) was a Danish businesswoman and feminist. She worked for what later became Unilever from 1922, and after World War II became CEO of the Danish branch of the marketing bureau Lintas. From 1952 to 1958, she served as the 4th President of the International Alliance of Women.
# Dren (name)

Dren, also spelled Drin, is a given name.
It is used as a masculine given name in Albanian culture. The origin of this name comes from the Albanian word dren (Gheg Albanian); dre (Standard Albanian), which means deer. The feminine form is Drenusha (female deer).
The word "Dren" (Дрен) means dogwood or specifically European Cornel (Cornus mas) in Serbian.

## People

* Dren Abazi (born 1985), Kosovar Albanian singer and songwriter
* Dren Feka (born 1997), Kosovo Albanian footballer
* Dren Hodja (born 1994), Albanian footballer
* Dren Mandić, Serbian climber, one of the fatalities of the 2008 K2 disaster.
* Dren McDonald, American musician
* Dren Terrnava (born 2005), Finnish footballer

## Fictional characters

* Dren, the name of the character Kish in the English adaptation (Mew Mew Power) of the anime series Tokyo Mew Mew
* Dren, a human hybrid creature in the 2010 movie Splice
# Elachista nobilella

Elachista nobilella is a moth of the family Elachistidae found in Europe.

## Description

The wingspan is 6–8 millimetres (0.24–0.31 in). Adults are on wing from May to July.
The larvae feed on grasses, including Agrostis, Arrhenatherum, Bromus, Carex, Dactylis, Festuca, Yorkshire fog (Holcus lanatus) and hairy wood-rush (Luzula pilosa).

## Distribution

It is found from Scandinavia and Finland to the Iberian Peninsula and Italy and from France to Romania.
# Digital Garbage

Digital Garbage is the tenth studio album by American rock band Mudhoney. It was released on September 28, 2018. This is their seventh studio album release on Sub Pop.

## Critical reception

Professional ratings :
| Review scores ||
| Source | Rating |
| AllMusic | |
| ClashMusic | 8/10 |
| Exclaim! | 9/10 |
| MusicOMH | |
| Pitchfork | 7.1/10 |
| PopMatters | 7/10 |
| The Quietus | |
| Rolling Stone | |
Digital Garbage received generally positive reviews from most music critics. At Metacritic, they assign a "weighted average" score out of 100 to reviews and ratings from mainstream critics, and the album received a score of 75, based on 17 reviews. AllMusic's Mark Deming affirmed that "Digital Garbage isn't quite Mudhoney's great protest album, but as a reaction to a chaotic and divisive time, it's powerfully eloquent in its own grimy way, and it shows they can still sound like nothing but themselves without being tethered to the past. Come for the rage on Digital Garbage and stay for the rock. Both feel intense and purifying."
AllMusic chose it as one of their favorite rock albums of 2018, and Mojo listed it No. 55 on its list of top 75 albums of 2018.

## Track listing

All tracks written by Mark Arm, Steve Turner, Dan Peters, and Guy Maddison.

## Personnel

Adapted from the album liner notes.

### Mudhoney

* Mark Arm – vocals, guitar, organ
* Steve Turner – guitar, vocals
* Dan Peters – drums, percussion, guitar
* Guy Maddison – bass, synthesizer, vocals

### Additional musicians

* Johnny Sangster – piano, vocals
* Kelly Van Kamp – harmonica

### Technical

* Johnny Sangster – producer, engineer, mixing
* Jon Roberts – engineer
* Bob Weston – mastering
* Dusty Summers – art direction, design
* Ed Fotheringham – illustrations
* Emily Rieman – photography

## Charts

| Chart (2018) | Peak position |
| Scottish Albums (OCC) | 83 |
| US Vinyl Albums (Billboard) | 24 |
| US Independent Albums (Billboard) | 31 |
| US Heatseekers Albums (Billboard) | 16 |