Samantha912/NLP_A2_WTH huggingface dataset:
In mathematics, a partial order or total order < on a set  is said to be dense if, for all  and  in  for which , there is a  in  such that . That is, for any two elements, one less than the other, there is another element between them. For total orders this can be simplified to "for any two distinct elements, there is another element between them", since all elements of a total order are comparable.

Example
The rational numbers as a linearly ordered set are a densely ordered set in this sense, as are the algebraic numbers, the real numbers, the dyadic rationals and the decimal fractions. In fact, every Archimedean ordered ring extension of the integers  is a densely ordered set. 

On the other hand, the linear ordering on the integers is not dense.

Uniqueness for total dense orders without endpoints 

Georg Cantor proved that every two non-empty dense totally ordered countable sets without lower or upper bounds are order-isomorphic. This makes the theory of dense linear orders without bounds an example of an ω-categorical theory where ω is the smallest limit ordinal. For example, there exists an order-isomorphism between the rational numbers and other densely ordered countable sets including the dyadic rationals and the algebraic numbers. The proofs of these results use the back-and-forth method.

Minkowski's question mark function can be used to determine the order isomorphisms between the quadratic algebraic numbers and the rational numbers, and between the rationals and the dyadic rationals.

Generalizations
Any binary relation R is said to be dense if, for all R-related x and y, there is a z such that x and  z and also z and  y are R-related. Formally:
  Alternatively, in terms of composition of R with itself, the dense condition may be expressed as R ⊆ R ; R.

Sufficient conditions for a binary relation R on a set X to be dense are:
 R is reflexive;
 R is coreflexive;
 R is quasireflexive;
 R is left or right Euclidean; or
 R is symmetric and semi-connex and X has at least 3 elements.
None of them are necessary. For instance, there is a relation R that is not reflexive but dense.
A non-empty and dense relation cannot be antitransitive.

A strict partial order < is a dense order if and only if < is a dense relation. A dense relation that is also transitive is said to be idempotent.

See also
Dense set — a subset of a topological space whose closure is the whole space
Dense-in-itself — a subset  of a topological space such that  does not contain an isolated point 
Kripke semantics — a dense accessibility relation corresponds to the axiom

References

Further reading

 David Harel, Dexter Kozen, Jerzy Tiuryn, Dynamic logic, MIT Press, 2000, , p. 6ff

Binary relations
Order theory
Queenie Williams (November 17, 1896 – June 9, 1962), also billed as Little Queenie Williams and later as Ina Williams, was an Australian child actress, singer, comedian, and dancer.

Early life 
Alfreda Ina Williams was born in Footscray, near Melbourne, in 1896, the daughter of Frank Williams and Annie Armstrong Williams. She trained as a dancer with Mrs. William Green and Florrie Green in Melbourne.

Career 
Williams appeared in The Fatal Wedding (1906), touring Australia and New Zealand with the Meynell & Gunn show. She also performed in Meynell & Gunn's The Rake's Wife (1906–1907), The Grey Kimona (1907), The Little Breadwinner (1908), and The Old Folks at Home (1909), as well as revivals of The Fatal Wedding.

Beginning in 1912, she toured with Pollard's Juvenile Opera Company in the United States and Canada in the years before and during World War I. She also became a solo act with a short musical comedy sketch called "Married via Wireless". She was noted for her slight stature and skills as a dancer; her singing voice was "of ample range, adequate volume and quality that is tenderly sympathetic." In 1914 she joined other actresses "who have agreed never to wear a bird's body or wing on their hats or to wear animal skins as furs."

After the war, as a young woman, she used the name "Ina Williams" on the vaudeville stage in the North America. Some of her other partners in vaudeville acts were Hal Skelly, Teddy MacNamara (in "The Guide of Monte Carlo"), Dick Keene, Johnny Dooley, and Jere Delaney. She retired from the stage in 1932.

Personal life 
Queenie Williams married theatrical manager Ernest Chester in 1914. They were separated by the end of 1919. She married again in 1923, to engineer Charles Stecher. They had a daughter and lived in New Jersey. Ina "Queenie" Williams died in 1962, in Los Angeles, aged 65 years.

References 

1896 births
1962 deaths
Vaudeville performers
Australian child actresses
Actresses from Melbourne
People from Footscray, Victoria
Teresa Weißbach (born 26 April 1981 in Zwickau, Bezirk Karl-Marx-Stadt, East Germany) is a German actress best known for her role as Miriam in the 1999 film Sonnenallee.

Biography

She grew up in Stollberg, and at 10 years old joined the Youth Theater.

At 17 she made her debut as Miriam Sommer in the film Sonnenallee. Her parents own a bakery in Stollberg, and made special pastry in celebration of the success of Sonnenallee in cinemas.

From 1999 to 2003 she studied at the University for Music and Theater in Rostock and was awarded a degree in acting. During her studies, she performed at the Volkstheater in Rostock, and at the Mecklenburg State Theatre in Schwerin, playing, among other roles, Ismene in the tragedy Antigone by Sophocles.

In 2002 she performed in the ARD television series Berlin, Berlin. In summer 2004 she trod the boards at the Bayreuth Festival, and in February 2005 she began an engagement at the Burgtheater in Vienna.

Filmography 
 Sonnenallee (dir Leander Haußmann, 1999)
 Barbecue Ladies (dir. Tini Tüllmann, 2002, Short)
 About a Girl (dir. Catharina Deus, 2004)
  (dir. Jakob Schäuffelen, 2004)
 Sonst ist alles so groß (dir. Nic Niemann, 2005, Short)
 Sommerwald (dir. Christoph Lehmann, 2006, Short)
 Armee der Stille – La Isla Bonita (dir. Roland Lang, 2009)
  (dir. , 2009)

External links 
  (in German)
 

1981 births
Living people
People from Zwickau
German film actresses
Rostock University of Music and Theatre alumni
German stage actresses
German television actresses
20th-century German actresses
21st-century German actresses
Hin Stuttligi Flokkurin (English: The Funny Party) was a joke political party in the Faroe Islands. It was founded in 2004 by the current party leader, Johan Dalsgaard, also known as Johan í Kollafirði and later as Johan í Fámará. The party is based upon political satire. Dalsgaard was mainly inspired by Jacob Haugaard, who pulled a similar prank in the Danish parliament. Johan Dalsgaard was not the only candidate on the list. Rubek Lilaa was the candidate for Eysturoyar Valdømi. At that time the Faroe Islands had 7 districts, so people could only vote for a candidate from their own district (valdømi). Hin stuttliga Flokkurin had two candidates, Johan Dalsgaard was candidate for the South Streymoy district (Suðurstreymoyar valdømi) and Rubek Lilaa was candidate in Eysturoy. The party had no other candidates.

The party got 747 votes in the Faroese parliament election in 2004. Hin Stuttligi Flokkurin is currently not represented in any Faroese local governments.

See also 

 Monster Raving Looney Party 
 List of frivolous political parties

References 

Joke political parties
Defunct political parties in the Faroe Islands
The  New York Giants season was the franchise's 24th season in the National Football League.

Regular season

Schedule

Standings

See also
List of New York Giants seasons

References

New York Giants seasons
New York Giants
1948 in sports in New York City
1940s in Manhattan
Washington Heights, Manhattan
Pyhäsalmi Airfield is an airfield in Pyhäjärvi, Finland. It is located along the main road 4 (E75), about  north-northwest of Pyhäsalmi, the centre of Pyhäjärvi.

See also
List of airports in Finland

References

External links
 VFR Suomi/Finland – Pyhäsalmi Airfield
 Lentopaikat.net – Pyhäsalmi Airfield 

Airports in Finland
Airfield
Buildings and structures in North Ostrobothnia
The Frank E. Heller Dam is an embankment dam that impounds Hagerman's Run and creates the Hagerman Reservoir that supplies water for Lycoming County, Pennsylvania. It is owned by the Williamsport Municipal Water Authority and Pennsylvania-American Water Company. Opened in 1975 it is located in Armstrong Township in southern Lycoming County.

History 
Construction of the dam began in 1972 and was completed in 1975. With population of Williamsport and the county rising the Williamsport Municipal Water Authority was in need of expansion. The expansion added 530 million gallons to the storage capacity.

Danger of breach 
In August 2019 engineers found signs of fatigue in the dams base and had failed its inspection. A water authority spokesperson said the dam is "highly likely to have a complete failure in the next five to ten years". Its estimated over 2,600 people as well as hundreds of homes and businesses would be at risk if the dam were to fail. Economic costs are could to be at over $22 million. The Williamsport Municipal Water Authority has submitted an emergency grant request of $221,357 in preliminary engineering funds to the Federal Emergency Management Agency and hopes to receive approval by Sept. 30.

References 

Dams in Pennsylvania
Bodies of water of Lycoming County, Pennsylvania
1975 establishments in Pennsylvania
Embankment dams
Dams completed in 1975
The Elabared Estate is a Government operated cooperative immediately outside the small town of Elabored, Eritrea.

History
In 1908 Pietro Casciani, an Italian colonial immigrant was granted a plot of 10 km2 and planted grains. In 1958 Fratelli De Nadai purchased Pietro Casciani's land and replanted with citrus for export. During the ownership of De Nadai there was a great expansion of goods produced at the plantation, with the addition of a canning plant, dairy factory and winery.

Production fluctuated during the Eritrean War of Independence, specifically after the massacre of the elders in the nearby village.  The Estate was nationalized by the Derg in 1975 but was liberated by the Eritrean People's Liberation Front (EPLF) in 1977.  In that same year however, the EPLF withdrew in what was called the Strategic Withdrawal.

After Independence the EPLF (later the People's Front for Democracy and Justice) offered the plantation to private capital however, no buyers availed themselves of the opportunity.

References

Agriculture in Eritrea
Food and drink companies of Eritrea
Anseba Region
1908 establishments in the Italian Empire
The Coleman's station was a former New York Central Railroad station that served the residents of North East, New York.

History
When the New York and Harlem Railroad began building their line through the Taconic Mountains towards Chatham in 1851, Coleman's was recommended as a freight only station by local entrepreneur Amasa Coleman, and landowner Oliver Barrett in order to take up a service overflow from Sharon and Millerton Stations. The station which was established in 1852 operated primarily as a freight stop throughout the 19th and early 20th centuries, but began accepting passengers by the late 1950s. As with the rest of the Harlem Line it became a Penn Central station when NYC merged with their longtime rival Pennsylvania Railroad in 1968. Penn Central ended all passenger service north of Dover Plains on March 20, 1972 and the station resumed its freight only status until March 27, 1980 when Conrail abandoned service on that segment of the line.

Today it is located along the Harlem Valley Rail Trail in the middle of the Coleman Station Historic District.

References

Former New York Central Railroad stations
North East, New York
Railway stations in Dutchess County, New York
Former railway stations in New York (state)
Railway stations in the United States opened in 1852
Railway stations closed in 1972
Historic district contributing properties in New York (state)
1852 establishments in New York (state)
National Register of Historic Places in Dutchess County, New York
Railway stations on the National Register of Historic Places in New York (state)
Transportation in Dutchess County, New York
The 1988 Virginia Slims of San Diego was a women's tennis tournament played on outdoor hard courts at the San Diego Tennis & Racquet Club in San Diego, California in the United States and was part of the Category 2 tier of the 1988 WTA Tour. The tournament ran from August 1 through August 7, 1988. Second-seeded Stephanie Rehe won the singles title and earned $17,000 first-prize money.

Finals

Singles

 Stephanie Rehe defeated  Ann Grossman 6–1, 6–1
 It was Rehe's 2nd singles title of the year and the 5th of her career.

Doubles

 Patty Fendick /  Jill Hetherington defeated  Betsy Nagelsen /  Dianne van Rensburg 7–6(12–10), 6–4
 It was Fendick's 6th title of the year and the 6th of her career. It was Hetherington's 4th title of the year and the 5th of her career.

References

External links
 ITF tournament edition details
 Tournament draws

Virginia Slims of San Diego
Southern California Open
Virg
Virg
Bernadette Marie Thérèse Menu (née Mangin, 8 May 1938 – 29 May 2023) was a French archaeologist and Egyptologist, whose research work on ancient Egypt is widely known. She was mother of the writer Jean-Christophe Menu.

Life and career 
Bernadette Menu was Honorary Director of Research at the French National Centre for Scientific Research (Paul Valéry University, Montpellier III), president of the  (“International Association for the Study of the Law of Ancient Egypt”) and a professor of Ancient Egyptian at Charles de Gaulle University – Lille III and Institut Catholique de Paris. Her illustrated pocket book about Ramesses II, , from the collection “Découvertes Gallimard”, has been translated into eight languages, including English.

Menu died in Aubenas on 29 May 2023, at the age of 85.

Publications 
 Le régime juridique des terres et du personnel attaché à la terre dans le Papyrus Wilbour, Publications de la faculté des lettres et sciences humaines, N° XVII, Institut de papyrologie et d’égyptologie, 1970
 L’Obélisque de la Concorde, Éditions du Lunx, 1987
 Ramsès II : Souverain des souverains, collection « Découvertes Gallimard » (nº 344), série Histoire. Éditions Gallimard, 1998
 US edition – Ramesses II: Greatest of the Pharaohs, “Abrams Discoveries” series. Harry N. Abrams, 1999
 UK edition – Ramesses the Great: Warrior and Builder, ‘New Horizons’ series. Thames & Hudson, 1999
 Vivre en Égypte ancienne, collection « Découvertes Gallimard Texto » (nº 1). Éditions Gallimard, 1998
 Exercices corrigés de la petite grammaire de l’égyptien hiéroglyphique à l’usage des débutants, Librairie orientaliste Paul Geuthner, 1998
 Recherches sur l’histoire juridique, économique et sociale de l’ancienne Égypte. II, Institut français d’archéologie orientale, 1998
 Égypte pharaonique : Nouvelles recherches sur l’histoire juridique, économique et sociale de l’ancienne Égypte, collection « Droit et cultures » (nº 4). Éditions L’Harmattan, 2004

References 

1938 births
2023 deaths
20th-century French archaeologists
21st-century French archaeologists
French Egyptologists
French women archaeologists
French National Centre for Scientific Research scientists
People from Amiens
Events of 2022 in Zimbabwe.

Incumbents 

 President: Emmerson Mnangagwa
 Vice President
 Constantino Chiwenga

Events 
Ongoing: COVID-19 pandemic in Zimbabwe

 March 26 - 2022 Zimbabwean by-elections.
 April 15 - At least 35 people are killed and 71 others are injured when a bus carrying churchgoers to an Easter gathering crashes in Chipinge.
 May 26 - Zimbabwean courts rule that the age of consent in Zimbabwe must be raised to 18.
 May 31 - Six African countries, on Zimbabwe's initiative, agree to restart trade in ivory as the population of elephants soars beyond sustainable levels.

Scheduled events

Deaths 

 January 27 – Gwinyai Chingoka, tennis player (b. 1982)
 January 31 – Phyllis Ndlovu, politician
 February 14 - Charles Yohane, footballer (b. 1973)
 April 7 - Elvis Nyathi, refugee (b. 1979)
 April 24 - Collin Williams, cricket player (b. 1961)
 April 27 - John Gwitira, political activist (b. 1949)
 May 15 - Martin Munyanyi, Roman Catholic prelate (b. 1956)
 May 26 - Aldiglade Bhamu, footballer (b. 1987)
 May 28 - Christopher Kuruneri, politician (b. 1949)
 June 5 - Stanley Goreraza, military officer
 June 5 - Alex Magaisa, political advisor (b. 1975)
 May 27 - Mildred Reason Dube, politician
 May 27 - Giles Mutsekwa, politician (b. 1948)
 July 17 - Watson Khupe, politician (b. 1962)
 August 1 - Cont Mhlanga, actor (b. 1957)

See also 

COVID-19 pandemic in Africa
African Continental Free Trade Area

References 

 
2020s in Zimbabwe
Years of the 21st century in Zimbabwe
Zimbabwe
John C. Boyle Reservoir is an artificial impoundment behind John C. Boyle Dam on the Klamath River in the U.S. state of Oregon. The lake is  west-southwest of Klamath Falls along Oregon Route 66.

The dam is at about river mile (RM) 225 or river kilometer (RK) 362, about  by river downstream of the community of Keno. Spencer Bridge carries the highway over the lake at about its midpoint.

Water from the reservoir is diverted through a sluice to the Boyle Powerhouse, about  downstream of the dam. Fluctuations of up to  daily in the reservoir level occur as water is added for storage or diverted for power generation.

History
The California–Oregon Power Company (COPCO), which later merged with Pacific Power, a future subsidiary of PacifiCorp, built the dam in the mid-1950s as part of the multi-dam Klamath River Hydroelectric Project. Meant primarily to generate hydroelectricity, the reservoir can hold up to  of water. Originally called Big Bend Reservoir, it was renamed in 1962 for John C. Boyle, COPCO's vice president, general manager, and chief engineer.

The Boyle dam is one of four Klamath River dams that may be removed as early as 2020 if the United States Congress eventually agrees. The other three, all owned by PacifiCorp and all in California, are Iron Gate, Copco 2, and Copco 1. A tentative agreement reached in 2009 by major stakeholders, including PacifiCorp, would remove the dams to restore salmon runs blocked below Iron Gate for about a century.As of February 25, 2022, the FERC released their final Environmental Impact Statement (EIS) on the dam's removal. The dam is expected to be removed sometime in 2023 or 2024.

It is named after John C. Boyle (1899-1979), who was vice president, general manager, and long-time chief engineer of the California Oregon Power Company (COPCO), a privately held utility that served southern Oregon and portions of northern California.

Recreation
The reservoir supports largemouth bass ranging from , which can be fished for by boat or from the bank. Other fish found in the lake include black crappie, white crappie, yellow perch, brown bullhead, and pumpkinseed sunfish.

Topsy Recreation Site, maintained by the Bureau of Land Management, has a campground, a boat launch, a dock, and a fishing pier at J. C. Boyle Reservoir. Swimming, picnicking, and bird-watching are among recreational activities in addition to camping and fishing.

See also
 List of lakes in Oregon

References

Lakes of Klamath County, Oregon
Reservoirs in Oregon
1950s establishments in Oregon
Per-Gunnar "Peggen" Andersson (born 15 August 1957) is a race car driver from Falkenberg, Sweden.

He started his career in Sweden in 1980. In 1988 he won the Thai Touring Car Championship and the Swedish Touring Car Championship. He won the Swedish championship again in 1989, 1991 and 1992. In the 1980s Andersson also competed in DTM and the British Touring Car Championship.

In 1993 and 1995 he won the Nordic Touring Car Championship. Since then he has returned to Swedish touring cars, finishing his career at the end of 2001 after driving for Carly BMW in the European Touring Car Championship.

Today, Andersson works as a commentator in the Swedish broadcast of DTM for Canal+.

Racing record

Complete European Touring Car Championship results
(key) (Races in bold indicate pole position) (Races in italics indicate fastest lap)

Complete Deutsche Tourenwagen Meisterschaft results
(key) (Races in bold indicate pole position) (Races in italics indicate fastest lap)

Complete British Touring Car Championship results
(key) (Races in bold indicate pole position) (Races in italics indicate fastest lap)

‡ Endurance driver (Ineligible for points in 1990)

Complete Swedish Touring Car Championship results
(key) (Races in bold indicate pole position) (Races in italics indicate fastest lap)

Complete European Super Production Championship results
(key) (Races in bold indicate pole position) (Races in italics indicate fastest lap)

References

External links
https://web.archive.org/web/20111003162607/http://www.pgandersson.se/

1957 births
Swedish Touring Car Championship drivers
Swedish racing drivers
British Touring Car Championship drivers
People from Falkenberg
Living people
European Touring Car Championship drivers
Sportspeople from Halland County
Ken McKenzie (1923–2003) was a Canadian newspaper publisher and sports journalist.

Ken McKenzie or Ken MacKenzie may also refer to:
 Ken MacKenzie (baseball) (born 1934), Canadian Major League Baseball pitcher
 Ken MacKenzie (businessman) (born 1964), Canadian-born businessman and Chairman of BHP
 Ken McKenzie (footballer, born 1865) (1865–1917), Australian rules footballer for Port Adelaide
 Ken McKenzie (footballer, born 1887) (1887–1958), Australian rules footballer for St Kilda
 Ken McKenzie (rugby league) (1926–1998), Australian rugby league player

See also 
 Kenneth Mackenzie (disambiguation)
Backfire is a 1988 mystery-thriller film about a murderous love triangle which forms between an affluent Vietnam War veteran, his wife, and another man. The film was directed by Gilbert Cates, and stars Karen Allen, Keith Carradine, Dean Paul Martin and Jeff Fahey. The film is dedicated to Martin, who died in a plane crash before the film was released.

Plot
Mara is married to Vietnam veteran Donny, who has horrible visions and nightmares of his combat experiences. Mara is having an affair with Jake, and the lives of all are disrupted when she meets a mysterious stranger, Reed.

Cast
 Keith Carradine as Reed
 Karen Allen as Mara
 Jeff Fahey as Donny
 Dean Paul Martin as Jake
 Bernie Casey as Clinton
 Dinah Manoff as Jill Tyson

References

External links
 
 
 
 

1988 films
1988 crime thriller films
American crime thriller films
Canadian crime thriller films
English-language Canadian films
Films directed by Gilbert Cates
Films scored by David Shire
ITC Entertainment films
1980s English-language films
1980s American films
1980s Canadian films
English-language crime thriller films
Su Po-ya (, born 17 September 1998) is a Taiwanese taekwondo practitioner. She represented Chinese Taipei at the 2018 Asian Games and claimed a gold medal in the women's 53kg bantamweight event.

References

External links
 

1998 births
Living people
Taiwanese female taekwondo practitioners
Taekwondo practitioners at the 2018 Asian Games
Medalists at the 2018 Asian Games
Asian Games gold medalists for Chinese Taipei
Asian Games medalists in taekwondo
Medalists at the 2019 Summer Universiade
Medalists at the 2021 Summer Universiade
FISU World University Games gold medalists for Chinese Taipei
Universiade silver medalists for Chinese Taipei
Universiade medalists in taekwondo
Taekwondo practitioners at the 2020 Summer Olympics
Olympic taekwondo practitioners for Taiwan
21st-century Taiwanese women