OpenLLM-France/wikimedia huggingface dataset:
# Routh–Hurwitz theorem

In mathematics, the Routh–Hurwitz theorem gives a test to determine whether all roots of a given polynomial lie in the left-half complex plane. Polynomials with this property are called Hurwitz stable polynomials. The Routh–Hurwitz theorem is important in dynamical systems and control theory, because the characteristic polynomial of the differential equations of a stable, linear system has roots limited to the left half plane (negative eigenvalues). Thus the theorem provides a mathematical test, the Routh–Hurwitz stability criterion, to determine whether a linear dynamical system is stable without solving the system. The Routh–Hurwitz theorem was proved in 1895, and it was named after Edward John Routh and Adolf Hurwitz.

## Notations

Let f(z) be a polynomial (with complex coefficients) of degree n with no roots on the imaginary axis (i.e. the line z = ic where i is the imaginary unit and c is a real number). Let us define real polynomials P$_0$(y) and P$_1$(y) by f(iy) = P$_0$(y) + iP$_1$(y), respectively the real and imaginary parts of f on the imaginary line.
Furthermore, let us denote by:
* p the number of roots of f in the left half-plane (taking into account multiplicities);
* q the number of roots of f in the right half-plane (taking into account multiplicities);
* Δ arg f(iy) the variation of the argument of f(iy) when y runs from −∞ to +∞;
* w(x) is the number of variations of the generalized Sturm chain obtained from P$_0$(y) and P$_1$(y) by applying the Euclidean algorithm;
* I$^{+∞}$ $_{−∞}$ r is the Cauchy index of the rational function r over the real line.

## Statement

With the notations introduced above, the Routh–Hurwitz theorem states that:
    $p-q={\frac {1}{\pi }}\Delta \arg f(iy)=\left.{\begin{cases}+I_{-\infty }^{+\infty }{\frac {P_{0}(y)}{P_{1}(y)}}&{\text{for odd degree}}\\[10pt]-I_{-\infty }^{+\infty }{\frac {P_{1}(y)}{P_{0}(y)}}&{\text{for even degree}}\end{cases}}\right\$
From the first equality we can for instance conclude that when the variation of the argument of f(iy) is positive, then f(z) will have more roots to the left of the imaginary axis than to its right. The equality p − q = w(+∞) − w(−∞) can be viewed as the complex counterpart of Sturm's theorem. Note the differences: in Sturm's theorem, the left member is p + q and the w from the right member is the number of variations of a Sturm chain (while w refers to a generalized Sturm chain in the present theorem).

## Routh–Hurwitz stability criterion

We can easily determine a stability criterion using this theorem as it is trivial that f(z) is Hurwitz-stable if and only if p − q = n. We thus obtain conditions on the coefficients of f(z) by imposing w(+∞) = n and w(−∞) = 0.
# Mołoczki

Mołoczki is a village in the administrative district of Gmina Boćki, within Bielsk County, Podlaskie Voivodeship, in north-eastern Poland. It lies approximately 13 kilometres (8 mi) south-east of Boćki, 19 km (12 mi) south of Bielsk Podlaski, and 58 km (36 mi) south of the regional capital Białystok.
# List of rulers of the Gcaleka

This is a list of the paramounts of the Xhosa of the Eastern Cape province in modern South Africa.
(Reigned-From:1648 Till 1681)
(Reigned-From:1681 Till 1702)
(Held-Power-From:1702 Till 1728)
(Reigned-From:1728 Till 1755)
{=Main-House-Branch=}
(Reigned-From:1755 Till 1778)
(Reigned-From:1778 Till 1804)
(Held-Power-From:1804 Till 1817)
(Reigned-From:1817 Till 1835)
(Reigned-From:1835 Till 1892)
(Reigned-From:1892 Till 1902)
(Reigned-From:1902 Till 1921)
(Held-Power-From:1921 Till 1923)
(Reigned-From:1923 Till 1933)
(Reigned-From:1933 Till 1965)
(Reigned-From:1965 Till 2005)
(Reigned-From:2005 Till 2019)
(Held-Power-From:2019 Till 2020)
(Reigned-From:2020 Till Present-Date)
# Mościska, Podlaskie Voivodeship

Mościska is a village in the administrative district of Gmina Michałowo, within Białystok County, Podlaskie Voivodeship, in north-eastern Poland, close to the border with Belarus. It lies approximately 3 kilometres (2 mi) west of Michałowo and 29 km (18 mi) east of the regional capital Białystok.
# Muły, Augustów County

Muły is a village in the administrative district of Gmina Płaska, within Augustów County, Podlaskie Voivodeship, in north-eastern Poland, close to the border with Belarus. It lies approximately 16 kilometres (10 mi) east of Płaska, 35 km (22 mi) east of Augustów, and 90 km (56 mi) north of the regional capital Białystok.
# Młynisk

Młynisk is a settlement in the administrative district of Gmina Boćki, within Bielsk County, Podlaskie Voivodeship, in north-eastern Poland.
# Nadbory

Nadbory is a village in the administrative district of Gmina Jedwabne, within Łomża County, Podlaskie Voivodeship, in north-eastern Poland. It lies approximately 12 kilometres (7 mi) north-east of Jedwabne, 31 km (19 mi) north-east of Łomża, and 54 km (34 mi) north-west of the regional capital Białystok.
# Duet for Four

Duet for Four is a 1982 film directed by Tim Burstall.

## Plot

A middle aged man, Ray Martin, faces a series of problems – his wife is cheating on him, his mistress wants to get married and Americans want to take over his toy business.

## Cast

* Mike Preston as Ray Martin
* Wendy Hughes as Barbara Dunstan
* Michael Pate as Al Geisman
* Diane Cilento as Margot Martin
* Gary Day as Terry Byrne
* Vanessa Leigh as Dianne Sanders
* Warwick Comber as Cliff Ingersoll
* Sigrid Thornton as Carline Martin
* Rod Mullinar as Ken Overland
* Clare Binney as Jacki Nesbitt

## Production

The script by David Williamson was originally commissioned by Hexagon Productions in the wake of the success of Petersen (1974). Tim Burstall asked Williamson to write a script on a mid life crisis even though he was young at the time. Williamson wrote the script in eight days under the title The Toy Man but Hexagon decided not to make it, even though at one stage it was announced as a vehicle for Jack Thompson.
In the 1980s Williamson's reputation remained high and Burstall decided to make it. Burstall:
   I was going through a mid-life crisis of some sort and thought – 'What is the nature of work? Have I wasted my time? Am I doing the right thing?' That sort of thing. And toys was the industry we decided to use because it was being taken over by the Yanks. It was a sort of image of what was happening in film at the time. I don't think the picture works very well.
The title during shooting was Partners. The film was shot in Melbourne and Queenscliff. According to David Stratton the movie features some in jokes about the Australian film industry of the early 1970s.
Finance was partly provided by the Australian Film Commission and Victorian Film Corporation.
Wendy Hughes later described making the film as "one of my most enjoyable experiences" but thought "the role I was playing... seemed more a part of the early 1970s, when in fact it was written".
# Niebrzydy

Niebrzydy is a village in the administrative district of Gmina Wąsosz, within Grajewo County, Podlaskie Voivodeship, in north-eastern Poland.
# Niewodnica Korycka

Niewodnica Korycka is a village in the administrative district of Gmina Turośń Kościelna, within Białystok County, Podlaskie Voivodeship, in north-eastern Poland. It lies approximately 8 kilometres (5 mi) north of Turośń Kościelna and 7 km (4 mi) south-west of the regional capital Białystok.
# Niewodnica Nargilewska-Kolonia

Niewodnica Nargilewska-Kolonia [[Help:IPA/Polish|[ɲɛvɔdˈnit͡sa narɡiˈlɛfska kɔˈl]]ɔɲa] is a village in the administrative district of Gmina Juchnowiec Kościelny, within Białystok County, Podlaskie Voivodeship, in north-eastern Poland.
# Thayé

In Burmese mythology, the thayé (Burmese: သရဲ), also spelled 'tasei' (တစ္ဆေ), are deceased evil people condemned to be disembodied spirits. They often appear as tall, dark people with huge ears, long tongues, and tusk-like teeth. Thayé enter towns at noon or at night, and usually cause minor illnesses.
The thayé is said have many faces and bodies; e.g., one might be a pregnant ghost with a fat white body and big ears. Others may be tall and slim, male, or with other varying characteristics.
# Nowa Wieś, Gmina Bakałarzewo

Nowa Wieś is a village in the administrative district of Gmina Bakałarzewo, within Suwałki County, Podlaskie Voivodeship, in north-eastern Poland. It lies approximately 2 kilometres (1 mi) south-west of Bakałarzewo, 21 km (13 mi) west of Suwałki, and 113 km (70 mi) north of the regional capital Białystok.
# Nowa Łupianka

Nowa Łupianka is a village in the administrative district of Gmina Łapy, within Białystok County, Podlaskie Voivodeship, in north-eastern Poland.
# Nowe Kalinowo

Nowe Kalinowo is a village in the administrative district of Gmina Kulesze Kościelne, within Wysokie Mazowieckie County, Podlaskie Voivodeship, in north-eastern Poland.
# Nowe Osipy

Nowe Osipy is a village in the administrative district of Gmina Wysokie Mazowieckie, within Wysokie Mazowieckie County, Podlaskie Voivodeship, in north-eastern Poland.
From 1975-1998, the village belonged administratively to Łomża Voivideship.
The faithful of the Roman Catholic Church belong to the parish of St John the Baptist in Wysokie Mazowieckie.

## History

At the time of the enfranchisement of the manorial land in Russia, in 1864 9 independent farms were established here on 128 morgens of land.
At the end of the 19th century, the village was in Wysokie Mazowieckie County, municipality and parish of Wysokie. It comprised 9 settlements with arable land of 128 morgens.
In 1921, the village 10 residential buildings and 77 inhabitants were counted. All declared Polish nationality and to be faithful in the Roman Catholic religion.
From 1954 the village belonged to the Osipy-Kolonia district, then to the Wysokie Mazowieckie district and finally to the Wysokie Mazowieckie municipality.
# Nowe Piekuty

Nowe Piekuty is a village in Wysokie Mazowieckie County, Podlaskie Voivodeship, in north-eastern Poland. It is the seat of the gmina (administrative district) called Gmina Nowe Piekuty. It lies approximately 15 kilometres (9 mi) south-east of Wysokie Mazowieckie and 43 km (27 mi) south-west of the regional capital Białystok.
# Nowe Wiechy

Nowe Wiechy is a settlement in the administrative district of Gmina Kulesze Kościelne, within Wysokie Mazowieckie County, Podlaskie Voivodeship, in north-eastern Poland.
# Nowe Zalesie, Zambrów County

Nowe Zalesie is a village in the administrative district of Gmina Rutki, within Zambrów County, Podlaskie Voivodeship, in north-eastern Poland.
# Nowinka, Gmina Dąbrowa Białostocka

Nowinka is a village in northeast Poland in the gmina of Dąbrowa Białostocka, Sokółka County, Podlaskie Voivodeship. As of 2021, it had a population of 41.
# Nowinka, Gmina Sokółka

Nowinka is a village in the administrative district of Gmina Sokółka, within Sokółka County, Podlaskie Voivodeship, in north-eastern Poland, close to the border with Belarus. The population in January 2022 was approximately 350.
# Nowiny Bargłowskie

Nowiny Bargłowskie is a village in the administrative district of Gmina Bargłów Kościelny, within Augustów County, Podlaskie Voivodeship, in north-eastern Poland. It lies approximately 5 kilometres (3 mi) north-east of Bargłów Kościelny, 10 km (6 mi) south-west of Augustów, and 79 km (49 mi) north of the regional capital Białystok.
# Los Blanquitos Formation

The Los Blanquitos Formation is a geological formation in Salta Province, Argentina whose strata date back to the late Campanian to early Maastrichtian age of the Late Cretaceous Period. Dinosaur remains are among the fossils that have been recovered from the formation. The formation consists of friable, micaceous, grayish-red sandstones with quartz pebbles containing small carbonate veins. In the base of this layer the remains of a titanosaurid dinosaur were discovered. Above the layer with bones appears a lens of thick, greenish-gray, calcareous, very hard sandstone with pebbles and gravel. The bones were covered by a "halo" of the same rock but of greenish or grayish color, especially visible because the normal sediment is red. The bed thickness is 1.5 metres (4.9 ft).

## Vertebrate paleofauna

* Guemesia ochoai - an abelisaurid theropod dinosaur, known from a nearly complete braincase
* Unquillosaurus ceiballi - a theropod dinosaur (possibly carcharodontosaurian or Maniraptoran), known from a pubis
* ?Titanosaurus sp. - a sauropod dinosaur
# Nowosady, Gmina Zabłudów

Nowosady is a village in the administrative district of Gmina Zabłudów, within Białystok County, Podlaskie Voivodeship, in north-eastern Poland.
# Nowosady, Sejny County

Nowosady is a village in the administrative district of Gmina Sejny, within Sejny County, Podlaskie Voivodeship, in north-eastern Poland, close to the border with Lithuania. It lies approximately 6 kilometres (4 mi) north of Sejny and 118 km (73 mi) north of the regional capital Białystok.
# Nowosiółki, Gmina Gródek

Nowosiółki is a village in the administrative district of Gmina Gródek, within Białystok County, Podlaskie Voivodeship, in north-eastern Poland, close to the border with Belarus.
# Nowy Cydzyn

Nowy Cydzyn is a village in the administrative district of Gmina Piątnica, within Łomża County, Podlaskie Voivodeship, in north-eastern Poland.
# Nowy Dwór, Suwałki County

Nowy Dwór is a village in the administrative district of Gmina Bakałarzewo, within Suwałki County, Podlaskie Voivodeship, in north-eastern Poland.
# Nowy Janów, Podlaskie Voivodeship

Nowy Janów is a village in the administrative district of Gmina Janów, within Sokółka County, Podlaskie Voivodeship, in north-eastern Poland. It lies approximately 2 kilometres (1 mi) east of Janów, 20 km (12 mi) north-west of Sokółka, and 40 km (25 mi) north of the regional capital Białystok.
# The Olympic Hero

The Olympic Hero is a 1928 American silent comedy sports film directed by Roy William Neill and starring Charles Paddock, Julanne Johnston and Crauford Kent. It incorporated some real footage from the 1924 Olympic Games.

## Cast

* Charles Paddock as Charlie Patterson
* Julanne Johnston as Mary Brown
* Donald Stuart as Assistant Coach
* Harvey Clark as Coach Regan
* Crauford Kent as Man-About-Town
* Jack Selwyn as Harold Fellows
* Emile Chautard as Grandpa Brown
* R.O. Pennell as Professor
* Aileen Manning as Physical Instructress
* Bob Maxwell as Balfor Champ
* Raoul Paoli as French Champ
# Ogrodniki, Sokółka County

Ogrodniki is a village in the administrative district of Gmina Sidra, within Sokółka County, Podlaskie Voivodeship, in north-eastern Poland. It lies approximately 4 kilometres (2 mi) east of Sidra, 17 km (11 mi) north of Sokółka, and 53 km (33 mi) north-east of the regional capital Białystok.
# Bob Brooks (Pennsylvania politician)

Robert "Bob" Brooks is an American politician. He is a former Republican member of the Pennsylvania House of Representatives, representing the 54th district from 2018 to 2023. Previously, he served as a city councillor and mayor in Murrysville, Pennsylvania.

## Political career

Brooks was a member of the City Council in Murrysville, Pennsylvania, and was Mayor of Murrysville from 2010 to 2018. In 2015, he was named Pennsylvania's Mayor of the Year by the Pennsylvania State Mayors Association.
In 2018, he ran for election to represent the 54th district in the Pennsylvania House of Representatives. The Republican primary was a four-way race, which Brooks won with 35% of the vote. He went on to win the general election with 59.8% of the vote.
He currently sits on the following House committees:
* Commerce
* Finance
* Local Government
* Urban Affairs (Subcommittee Chair on Cities, Third Class)

## Electoral record

2018 Republican primary election: Pennsylvania House of Representatives, District 54 :
| Party | Candidate | Votes | % |
| Republican | Robert Brooks | 1,755 | 35.0% |
| Republican | Michael Korns Jr. | 1,333 | 26.6% |
| Republican | Maryalice Newborn | 1,319 | 26.3% |
| Republican | Bryan Kline | 612 | 12.2% |
2018 general election: Pennsylvania House of Representatives, District 54 :
| Party | Party | Candidate | Votes | % |
| | Republican | Robert Brooks | 16,301 | 59.8% |
| | Democratic | Jonathan McCabe | 10,944 | 40.2% |
# Andy Halter

André "Andy" Halter (born 21 April 1966) is a Swiss former footballer who played as a forward and made nine appearances for the Switzerland national team.

## Career

Halter made his debut for Switzerland on 9 April 1986 in a friendly match against West Germany, which finished as a 0–1 loss. He went on to make nine appearances, scoring one goal, before making his last appearance on 7 June 1989 in a 1990 FIFA World Cup qualification match against Czechoslovakia, which finished as a 0–1 loss.

## Career statistics
### International

Switzerland :
| Year | Apps | Goals |
| 1986 | 6 | 0 |
| 1987 | 2 | 1 |
| 1989 | 1 | 0 |
| Total | 9 | 1 |

### International goals

| No. | Date | Venue | Opponent | Score | Result | Competition |
| 1 | 17 June 1987 | Stade olympique de la Pontaise, Lausanne, Switzerland | Sweden | 1–0 | 1–1 | UEFA Euro 1988 qualifying |
# Saphobius inflatipes

Saphobius inflatipes is one of several species of dung beetle that are endemic to New Zealand. It belongs to the tribe Deltochilini of the family Scarabaeidae. It was first described by Thomas Broun in 1893. In the Auckland region, it is most abundant during the summer and autumn seasons.
# HMS Snapper (1895)

HMS Snapper was a Salmon-class destroyer which served with the Royal Navy. She was launched in 1895, and served in home waters.
She served as part of the Medway Instructional Flotilla in 1901. Lieutenant John Foster Grant-Dalton was appointed in command on 14 February 1902. She docked for repairs to her stem in late May 1902, but was back in the North Sea by early June, and took part in the fleet review held at Spithead on 16 August 1902 for the coronation of King Edward VII. Lieutenant Charles Montagu Foot was appointed in command on 17 October 1902.
She was sold off in 1911.
# Italian submarine Carlo Feccia di Cossato (S 519)

Carlo Fecia di Cossato (S 519) was aSauro-class submarine of the Italian Navy.

## Construction and career

Carlo Fecia di Cossato was laid down at Fincantieri Monfalcone Shipyard on 15 November 1975 and launched on 16 November 1977. She was commissioned on 5 November 1979.
She was decommissioned on 30 April 2002. From 1 April 2005, she began disarmament while moored at La Spezia and she is expected to undergo restoration where she will be transferred to Trieste serve as a museum ship in their old port. The sister submarine, Nazario Sauro was destined for a similar role and was transferred on 18 September 2009 to be exhibited at the Galata - Museum of the sea in Genoa as an integral part of the museum. Carlo Fecia di Cossato was sold for scrap 2023.

## Citations

* ↑ "Smg. " DI COSSATO "". www.sommergibili.com. Retrieved 18 May 2021.
# HMS Orby (1918)

HMS Orby was a 24-class sloop of the British Royal Navy.
# Goniothalamus tortilipetalus

Goniothalamus tortilipetalus is a species of plant in the family Annonaceae. It is native to Peninsular Malaysia and Thailand. Murray Ross Henderson, the Scottish botanist who first formally described the species, named it after its twisted (tortilis in Latin) petals.

## Description

It is a tree reaching 6 meters in height. Its small, hairless, grey to black branches have longitudinal wrinkles. Its black, wrinkled petioles are 0.7-1.6 centimeters with a channel on their upper surfaces. It leathery, hairless, oblong to oval leaves are 20-39 by 6.5-11.5 centimeters with wedge-shaped bases and abruptly tapering tips. The leaves are covered with minutes dots; their upper surface is shiny and pale brown to olive-colored while the undersides are dull and pale brown. Its leaves have 14-22 secondary veins that arch and connect with one another about 6 millimeters from leaf edge. The leaves have prominent tertiary veins. Its solitary (sometimes in pairs) flowers are born on hairless, wrinkled pedicels that are 2-3.7 centimeters long. The pedicels emerge from warty tubercles on the main trunk. Its leathery to membranous, triangular to oval sepals are 1.9-3.1 by 1.5-2.6 centimeters with fused bases and short blunt-pointed tips. The sepals are hairless except their tips which have minute red hairs. The outside of the sepals are shiny while the insides are dull and covered in minute dots. Its flowers have 6 petals in two rows of three. The chartreuse, leathery, lance-shaped, twisted outer petals are 3.5-10 by 1-3.2 centimeters with tips that taper to a blunt point. The outer petals are covered on both surfaces with minute hairs. The outer petals are sometimes fused at their base to the inner petals. The thick, fleshy, oblong to lance-shaped inner petals are 1.2-2 by 0.5-0.8 centimeters. The upper 2/3 of the inner petals are fused at their margins. The inside of the inner petals is covered in velvety hairs. Its flowers have 170-260 hairless stamen that are 4 millimeters long and curve inwards. The connective tissue between the lobes of the anther extends upward for 0.6-0.7 millimeters to form a tapering tip. Its flowers have 50-100 carpels with oblong, flattened ovaries that are 2-2.2 millimeters long and covered in dense, matted, silky, golden hairs. Each ovary has 1-2 ovules. Its flattened styles are 4.5-5 millimeters long and come to a tapering tip that exudes sticky mucilage. Its fruit are on pedicels that are 1.9-3.6 centimeters long. The elliptical fruit are 0.9-1.2 centimeters wide. The hairless seeds are 1.2-1.7 by 0.8-1.1 centimeters.

### Reproductive biology

The pollen of G. tortilipetalus is shed as permanent tetrads.

## Habitat and distribution

It has been observed growing in lowland forests with soil rich in calcium carbonate at elevations of 60 to 300 meters.

## Uses

Bioactive molecules extracted from its bark have been reported to have vasoconstrictive activity in tests with rat arteries.
# USS Nettle (1862)

USS Nettle was a steamer acquired by the Union Navy from the Union Army during the American Civil War.
She served the Navy primarily as a tugboat on the Mississippi River.

## Service history

Wonder, a side-wheel steamer, purchased by the Union Army early in the Civil War for service in the Western Flotilla, was transferred to the Navy 30 September 1862 and renamed Nettle 19 October 1862. Nettle, commanded by Acting Ens. Perry C. Wright, served as a tug on the Mississippi River above Vicksburg, Mississippi, until after the Confederate river fortress fell 4 July 1863. Then, based at Vicksburg, she continued supporting operations of the Mississippi Squadron maintaining Union lines of supply and communication along the inland waters of the Mississippi and its tributaries. She was sunk in a collision with an ironclad 20 October 1865.
# HMS Milford (1690)

HMS Milford was a fifth rate built under the 1689 programme built at Deptford Dockyard. Her guns were listed under old terms for guns as demi-culverines, sakers and minions. After commissioning she spent her short career in Newfoundland and Home Waters. She was taken by the French in 1693.
Milford was the second name vessel since it was used for a 22-gun ship launched by Page of Wivenhoe in 1654, renamed Milford in 1660 and burnt by accident at Leghorn on 7 July 1673.

## Construction

She was ordered on 28 June 1689 from Woolwich Dockyard to be built under the guidance of Master Shipwright Joseph Lawrence. She was launched on 18 March 1690.

## Commissioned service

She was commissioned on 10 March 1690 under the command of Captain Charles Hawkins, RN for service on the Newfoundland fisheries. In 1692 she came under command of Captain Rodger Vaughan for service in the North Sea,

## Loss

HMS Milford was taken by a squadron of four French ships off Oxfordness losing 16 members of her crew killed on 1 December 1693. She served in the French Navy as Le Milford or Le Milfort until 1702.