Samantha912/NLP_A2_WTH huggingface dataset:
In homological algebra, a branch of mathematics, a matrix factorization is a tool used to study infinitely long resolutions, generally over commutative rings.

Motivation 
One of the problems with non-smooth algebras, such as Artin algebras, are their derived categories are poorly behaved due to infinite projective resolutions. For example, in the ring  there is an infinite resolution of the -module  whereInstead of looking at only the derived category of the module category, David Eisenbud studied such resolutions by looking at their periodicity. In general, such resolutions are periodic with period  after finitely many objects in the resolution.

Definition 
For a commutative ring  and an element , a matrix factorization of  is a pair of  square matrices  such that . This can be encoded more generally as a  graded -module  with an endomorphism such that .

Examples 
(1) For  and  there is a matrix factorization  where  for .

(2) If  and , then there is a matrix factorization  where

Periodicity 
definition

Main theorem 
Given a regular local ring  and an ideal  generated by an -sequence, set  and let

be a minimal -free resolution of the ground field. Then  becomes periodic after at most  steps. https://www.youtube.com/watch?v=2Jo5eCv9ZVY

Maximal Cohen-Macaulay modules 
page 18 of eisenbud article

Categorical structure

Support of matrix factorizations

See also 

 Derived noncommutative algebraic geometry
 Derived category
 Homological algebra
 Triangulated category

References

Further reading 

 Homological Algebra on a Complete Intersection with an Application to Group Representations
 Geometric Study of the Category of Matrix Factorizations
 https://web.math.princeton.edu/~takumim/takumim_Spr13_JP.pdf
 https://arxiv.org/abs/1110.2918

Homological algebra
OMF may refer to:

 Object Module Format, an object-file format of the  VME operating system or of the IBM personal computer
 Open Media Framework, a file format that aids in exchange of digital media across applications and platforms
 Relocatable Object Module Format, an object-file format used primarily on Intel 80x86 microprocessors or Apple IIGS
 Offshoring Management Framework
 Ohmefentanyl, a potent piperidine narcotic
 One Must Fall, a fighting computer-game
 Open Source Metadata Framework, a Document Type Definition based on Dublin Core used for describing document metadata
 Opposing Military Force
 Oracle-managed files, a feature controlling datafiles in Oracle databases
 Ostmecklenburgische Flugzeugbau, a former (1998–2003) manufacturer of light aircraft
 OMF International, formerly Overseas Missionary Fellowship, a Christian missionary-society
 Organisation de la microfrancophonie, a micronational oorganisation
 Omnipresent Music Festival, an American music festival based in New York City.
 Options Market France a regulated stock index futures and options market with integrated clearing
 Gerry Wright Operations and Maintenance Facility, a light rail transit maintenance facility in Edmonton, Alberta, Canada
Cassyma is a genus of moths in the family Geometridae first described by Achille Guenée in 1857. Its species are found primarily in South and Southeast Asia.

Species
Cassyma amplexaria (Walker, 1862)
Cassyma chrotadelpha Sommerer & Stuning, 1992
Cassyma chrotodon (Prout, 1925)
Cassyma deletaria (Moore, 1888)
Cassyma electrodes Sommerer & Stuning, 1992
Cassyma erythrodon Sommerer & Stuning, 1992
Cassyma indistincta (Moore, 1887)
Cassyma lucifera (Warren, 1903)
Cassyma pallidula Warren, 1896
Cassyma quadrinata Guenée, 1857
Cassyma sciticincta (Walker, 1863)
Cassyma undifasciata (Butler, 1892)

References

Kandasamy, Gunathilagaraj (2016). "Checklist of Indian Geometridae with FBI number". Tamil Nadu Agricultural University.

Abraxini
Geometridae
Metridia pacifica is a copepod found in the north Pacific and surrounding waters.

Taxonomy
M. pacifica is most closely related to M. lucens; before being split by Brodsky based on morphological differences, these were considered to be the same species.

Description
M. pacifica has a clear body with a whitish tint. In terms of length, females are range from about , and males are usually between about .

Distribution
M. pacifica is found in the north Pacific and sub-Arctic waters. It can be found north as far as the southern Chukchi Sea. It is reported to be an expatriate in the Arctic Ocean.

Ecology

Life cycle and reproduction
M. pacifica has multiple broods. At Station P, for example, there are three cohorts: one in March, one in late June and July, and one in September to early October. The nauplii are generally found above depths of  (and mostly above , and their distribution in these surface waters varies seasonally. It is likely that this is influenced by temperature; in one study, over 85% of nauplii were found below the thermocline from 14 June until 22 September, when it is warmer at the surface.

M. pacifica has an average generation time of three to four months at Station P.

References

Calanoida
Tennō Sekkan Daijin Eizukan (天皇摂関大臣影図巻) is a Japanese emakimono in three scrolls. It is in the holdings of the Archives and Mausolea Department of the Imperial Household Agency. It is traditionally attributed to  and . It is also known as Tenshi Sekkan Miei (天子摂関御影). It dates to the late Kamakura period. It is a series of picture scrolls of portraits of emperors, regents and ministers of state arranged in roughly chronological order.

Content 
Tennō Sekkan Daijin Eizukan, also known as Tenshi Sekkan Miei, is an emakimono in three scrolls. It includes portraits of emperors, regents and ministers of state arranged in roughly chronological order.

Authorship and date 
Tennō Sekkan Daijin Eizukan is traditionally attributed to Fujiwara no Tamenobu (藤原為信) and Fujiwara no Gōshin (藤原豪信). It dates to the late Kamakura period.

Textual tradition 
It is in the holdings of the Archives and Mausolea Department of the Imperial Household Agency. According to , in his article on the work for the Nihon Koten Bungaku Daijiten, another work, the two-volume Tennō Sekkan Miei (天皇摂関御影) in the holdings of the , has many similarities to it, but the relationship remains unclear.

References

Citations

Works cited 

 

Emakimono
Kamakura-period works
The 1922 North Dakota gubernatorial election was held on November 7, 1922. Incumbent Republican Ragnvald Nestos defeated Nonpartisan League nominee William Lemke with 57.65% of the vote.

Primary elections
Primary elections were held on June 28, 1922.

Republican primary

Candidates
Ragnvald Nestos, incumbent Governor
Bert F. Baker, State Senator
Harvey L. Stegner

Results

General election

Candidates
Ragnvald Nestos, Republican
William Lemke, Democratic

Results

References

1922
North Dakota
Gubernatorial
Gaizka Campos Bahillo (born 16 May 1997) is a Spanish footballer who plays as a goalkeeper for CF Intercity.

Club career
Campos was born in Barakaldo, Biscay, Basque Country, and joined Barakaldo CF's youth setup in 2015, from neighbouring SD Retuerto Sport. On 23 July 2016, he was promoted to the main squad in Segunda División B, signing a two-year deal.

Initially a backup to Txusta, Campos made his senior debut on 19 February 2017, starting in a 2–1 home win against Arenas Club de Getxo. He finished the season as a starter, contributing with ten appearances.

On 4 July 2017, Campos signed a three-year contract with CD Numancia, as a third-choice behind Aitor Fernández and Munir and being assigned to the reserves in Tercera División. After both departed the club, he was definitely promoted to the main squad and acted as a backup to new signing Juan Carlos.

Campos made his professional debut on 13 September 2018, starting in a 1–2 home loss against Sporting de Gijón, for the season's Copa del Rey. He made his Segunda División debut the following 26 April, playing the full 90 minutes in a home defeat to Deportivo de La Coruña for the same scoreline, as Juan Carlos was suspended.

On 5 July 2019, Campos signed a two-year contract with Real Valladolid B after terminating his previous deal with the Soria club. On 7 July 2021, he moved to another reserve team, Celta de Vigo B in Primera División RFEF.

On 6 July 2022, Campos agreed to a two-year contract with Real Zaragoza in the second division, but the move was declared void just hours later, after the discovery of offensive tweets about the club made in 2013. Thirteen days later, he signed for CF Intercity in the third tier.

References

External links

1997 births
Living people
Spanish men's footballers
Footballers from Barakaldo
Men's association football goalkeepers
Segunda División players
Primera Federación players
Segunda División B players
Tercera División players
Barakaldo CF footballers
CD Numancia B players
CD Numancia players
Real Valladolid Promesas players
RC Celta Fortuna players
CF Intercity players
Alfred Herbert Amos (9 February 1893 – 27 October 1959) was an English professional footballer who played as a wing half in the Football League for Brentford and Millwall. He is a member of the Millwall Hall of Fame.

Career 
A wing half, Amos began his career as an amateur with Old Kingstonians and joined Southern League Second Division club Brentford in 1913. He remained with Brentford during the First World War and was still a regular in the team when the club was admitted to the new Football League Third Division for the 1920–21 season. By the time Amos transferred to Millwall in 1922, he had made 139 appearances and scored five goals for Brentford. He remained with Millwall for seven seasons and was an ever-present in the team which finished the 1927–28 season as Third Division South champions, which secured promotion to the Second Division for the first time in the club's history. Amos' achievements were recognised posthumously with a place in the Millwall Hall of Fame. He finished his career with non-league club Hitchin Town and had a successful spell as the club's manager.

Personal life 
Amos served in the British Armed Forces during the First World War.

Career statistics

Honours

Player 
Brentford
 London Combination (1): 1918–19
Millwall
 Football League Third Division South (1): 1927–28

Manager 
Hitchin Town
 Spartan League Premier Division (1): 1934–35
 Spartan League First Division second-place promotion (1): 1930–31
 Spartan League Challenge Cup (1): 1935
 AFA Senior Cup (1): 1931–32
 Herts Senior Cup (3): 1930–31, 1931–32, 1933–34

Individual 

 Millwall Hall of Fame

References 

English men's footballers
Brentford F.C. players
Millwall F.C. players
English Football League players
1893 births
1959 deaths
Kingstonian F.C. players
Southern Football League players
Hitchin Town F.C. players
Hitchin Town F.C. managers
Men's association football wing halves
British military personnel of World War I
English football managers
Footballers from the London Borough of Lewisham
Sir Peter Stanley Harper  (28 April 1939 – 23 January 2021) was a British physician and academic who was University Research Professor (Emeritus) in Human Genetics at Cardiff University. His work focused on researching neurogenetics and has resulted in discoveries concerning muscular dystrophies and Huntington's disease. He was knighted in 2004 for services to medicine.

Work
Until 2004, Sir Peter was Professor of Medical Genetics at the University of Wales College of Medicine, Cardiff. He helped to develop the All Wales Medical Genomics Service (AWMGS) and has been a member of the UK Human Genetics Commission and Advisory Committee on Genetic testing. He was a member of the Nuffield Council on Bioethics 2004-2010. As a consultant to the History of Modern Biomedicine Research Group, he has contributed to several oral histories which address recent developments in clinical genetics in the UK.

Honours and awards
He delivered the Lumleian Lecture to the Royal College of Physicians in 1995. He was appointed a Commanders of the Order of the British Empire (CBE) in the 1995 Birthday Honours for services to Medical Genetics and was knighted in the 2004 Birthday Honours, for services to Medicine.

Books
 Practical Genetic Counselling, 1998 Hodder Arnold
 Myotonic Dystrophy: The Facts, 2002
 Landmarks in Medical Genetics, 2004 OUP
 First Years of Human Chromosomes, 2006 Scion Press
 A Short History of Medical Genetics, 2008. OUP

References

External links
 Genetics and Medicine Historical Network
 Peter Harper's personal archive and library are held at Special Collections and Archives, Cardiff University.
 

People from Barnstaple
20th-century English medical doctors
Commanders of the Order of the British Empire
Knights Bachelor
Harper
Fellows of the Linnean Society of London
Fellows of the Royal College of Physicians
1939 births
2021 deaths
Prior to 2000 a local government officer or councillor in the United Kingdom, who had unlawfully spent public funds, or caused loss to a local authority through misconduct could be surcharged to recover public money. The surcharge was applied, after referral to a court by the Audit Commission.

In the case of an illegal corporate decision by an elected body, all the councillors could be surcharged. Councillors from Lambeth London Borough Council and Liverpool City Council who were involved in the rate-capping rebellion in 1985 were surcharged. Councillors in the 1973 Clay Cross Urban District Council Housing Finance Act dispute were surcharged £685 (this is equivalent to £ today) for refusing to increase housing rent.

The Committee on Standards in Public Life recommended repealing surcharge because it was unfair for local government officers and councillors, and "bore no relation to people's ability to pay or their culpability". The Local Government Act 2000 amended the Audit Commission Act 1998 to remove the ability of the Audit Commission or Secretary or State to recover financial losses from individuals. Instead they would be subject to normal sanctions determined by the Standards Board and Adjudication Panel. Following the Tribunal Review such sanctions are now dealt with by the General Regulatory Chamber of the First-tier Tribunal.

See also
 Disgorgement (law)

References

External links
 Audit Commission website

Commission
Miantso  is a town in Analamanga Region, in the  Central Highlands of Madagascar, located north-west from the capital of Antananarivo.

The town is linked by the  RNT 36 in bad state of conservation to Antananarivo, via Ampanotokana and  Mahitsy.

Commune
12 villages belong to the Fokontany (village) of Miantso:

Fokontany (village)  Surface (km2)
ANTSAMPANIMAHAZO - 9,61 km2
TAFAINA - 23,78
FKT FENOSOA  - 23,00
MANDROSORASAHA - 14,87
TALATA AVARADRANO - 35,86
ANDRIATEIARA - 8,17
ANDRAISO - 5,33
MIANTSO - 10,56
MANDRIANKENIHENY - 20,91
SOAVINA - 22,53
AVARATRAMBATO - 10,69
ANDREFAMBATO - 10,06
TOTAL 195,37 km2

References

Populated places in Analamanga
The 21801 / 02 Jhansi–Indore Link Express is an Express train of the Express/Mail series belonging to Indian Railways – North Central Railway zone that runs between  and  in India.

It operates as train number 21801 from Jhansi Junction to Indore Junction and as train number 21802 in the reverse direction, serving the states of  Madhya Pradesh & Uttar Pradesh.

Coaches

The 21801 / 02 Jhansi–Indore Link Express' has 1 AC 3 tier, 2 Sleeper class & 2 end-on generator coaches. It doesn't carry a pantry car.

As is customary with most train services in India, coach composition may be amended at the discretion of Indian Railways depending on demand.

Service
The 21801 Jhansi–Indore Link Express covers the distance of  in 14 hours 30 mins () & in 14 hours 00 mins as 21802 Indore–Jhansi Link Express ().

As the average speed of the train is below , as per Indian Railways rules, its fare doesn't includes a Superfast surcharge.

Routing

The 21801 / 02 Jhansi–Indore Link Express runs from  via , , ,  , ,  to .

Traction

As the route is partially electrified, a WAG-7 electric loco from Jhansi Junction powers the train up to  and then WDM-3A of  based pulls the train up to its destination.

It also shares its rakes with 11125 / 11126 Indore–Gwalior Intercity Express & 11801 / 11802 Jhansi–Etawah Link Express

References

External links
 21801 Jhansi–Indore Link Express at India Rail Info
21802 Indore–Jhansi Link Express at India Rail Info

Express trains in India
Rail transport in Madhya Pradesh
Trains from Jhansi
Transport in Indore
Rush Green is a suburban area in Romford in East London, England. It straddles the boundary of the London Borough of Barking and Dagenham and the London Borough of Havering, and is located  east-northeast of Charing Cross.

Government
Rush Green is divided between the Eastbrook Ward in the London Borough of Barking and Dagenham and the Brooklands Ward in the London Borough of Havering, electing three councillors to Barking and Dagenham London Borough Council and three councillors to Havering London Borough Council. It is also divided between the Dagenham and Rainham and Romford parliamentary constituencies, each electing a member of parliament.

Geography
The central part of the district is at the crossroads of Rush Green Road and Dagenham Road (in Havering), approximately half a mile south of Romford town centre. Several shops and businesses are located around this junction. Other parts extend further south along Dagenham Road into Barking and Dagenham; this neighbourhood is the location of Barking and Dagenham College and Rush Green Library, and was the site of Rush Green Hospital (once the main maternity unit for this part of London), now replaced by a housing estate.

Nearest places are Romford, Dagenham, Elm Park and Becontree Heath. Rush Green is roughly 70% White British, 10% Asian and 10% Black (2011).

Transport
The nearest tube station is Dagenham East tube station and the nearest railway station is Romford railway station.

Education

Sport 
Since December 2015, Rush Green has been the site of the training ground for West Ham United F.C. after the club decided to move from their previous facility at Chadwell Heath. The women's team use Rush Green for home matches.

References

Areas of London
Districts of the London Borough of Barking and Dagenham
Districts of the London Borough of Havering
Eoxenopoides is an extinct genus of prehistoric frogs. It is known from Banke, a Maastrichtian/Selandian crater lake mudstone in South Africa.

See also
 Prehistoric amphibian
 List of prehistoric amphibians

References

Prehistoric frogs
Taxa named by Sidney H. Haughton
Fossil taxa described in 1931
The section of the Iliad that ancient editors called the Dios apate (the "Deception of Zeus") stands apart from the remainder of Book XIV. In this episode, Hera makes an excuse to leave her divine husband Zeus; in her deception speech she declares that she wishes to go to Oceanus, "origin of the gods", and Tethys the "mother". Instead Hera beautifies herself in preparation for seducing Zeus and obtains the help of Aphrodite. In the climax of the episode Zeus and Hera make love hidden within a golden cloud on the summit of Mount Ida. By distracting Zeus, Hera makes it possible for the Greeks to regain the upper hand in the Trojan War.

Literary issues 
The peculiarities of this episode were already being discussed in Antiquity. Even early commentators were shocked by the storyline and its implications for the morality of the gods. An expression of this moral criticism is found in Plato's Republic.

Later, as it became fashionable to question whether certain passages of the known text of the Iliad were really composed by Homer (see Homeric scholarship), the genuineness of the "Deception of Zeus" was doubted. Albrecht Dihle listed the linguistic features unique to this section and "found so many deviations from the normal traditional use of Homeric formulas that he concluded that this section of the Iliad could not belong to the phase of oral tradition but was a written composition." Richard Janko, by contrast, describes the episode as "a bold, brilliant, graceful, sensuous, and above all amusing virtuoso performance, wherein Homer parades his mastery of the other types of epic composition in his repertoire". The debate on this issue is not yet settled.

Walter Burkert found that the passage "shows divinity in a naturalistic, cosmic setting which is not otherwise a feature of Homeric anthropomorphism", and linked it to the opening of the Babylonian Enuma Elish where Apsu and Tiamat, respectively the fresh and salt waters, are the primordial couple who "were mixing their waters."

Like Tethys and Oceanus, Apsu and Tiamat were superseded by a later generation of gods. However, Tethys does not otherwise appear in early Greek myth and she had no established cult.

References

Sources

Walter Burkert (1992). The Orientalizing Revolution: Near Eastern Influence on Greek Culture in the Early Archaic Period. Harvard University Press.
Albrecht Dihle (1970). Homer-Probleme.
Richard Janko (1994). The Iliad: A Commentary. Vol. 4: Books 13-16. Cambridge: Cambridge University Press.

Iliad
Hera
Zeus
Edward Higginson (9 January 1807 – 12 February 1880) was an English Unitarian minister and author.

Life
He was born at Heaton Norris, Lancashire, on 9 January 1807. His father, Edward Higginson the elder (b. 20 March 1781, d. 24 May 1832), was a Unitarian minister and schoolmaster at Stockport (1801–10) and Derby (1811–31), who married as his first wife Sarah Marshall (d. 10 August 1827, aged 45) of Loughborough, Leicestershire. He was educated in his father's school, and in September 1823 entered Manchester College, York, as a divinity student.

In August 1828 Higginson settled as minister of Bowl Alley Lane Chapel, Kingston upon Hull. From 1829 he also taught a school. He removed in 1846 to Westgate Chapel, Wakefield, West Riding, taking his school with him. In 1858 he became minister of High Street Chapel, Swansea, Glamorganshire, a position which he resigned because of failing health in 1876. While at Swansea he assisted in the tutorial work of Carmarthen College, and at the end of 1875 was offered the principalship. From 1877 to 1879 he was president of the Royal Institute of South Wales.

Higginson was a conservative among Unitarian scholars, his theological position being similar to that of Samuel Bache, who married his sister.  He died at Swansea on 12 February 1880.

Works
Higginson published, with sermons and tracts:

 Orthodoxy and Unbelief, &c., 1832.
 The Sacrifice of Christ, &c., Hull, 1833; 2nd edition, 1848.
 Christ Imitable, or, The Religious Value of Christ's Proper Humanity, 1837.
 The Spirit of the Bible, &c., 1853–5, 2 vols.; 2nd edition, 1863.
 Astro-Theology, &c., 1855. This was a contribution to the debate of the time on cosmic pluralism, involving also David Brewster, Baden Powell, Thomas Collins Simon, and William Whewell.
 Six Essays on Inspiration, &c., 1856.
 The Morals of Belief, &c., 1860.
 An English grammar, specially intended for classical schools, London: Longman, Green. 1864
 A Short Memoir of the Rev. R. B. Aspland, &c., 1869.
 A Catechism without Questions, &c. [1869?]. 
 Ecce Messias, 1871.
 With his wife he published The Fine Arts in Italy, 1859, a translation from the French of Athanase Josué Coquerel.

Higginson's preaching was not popular, but his Spirit of the Bible was widely read. He contributed theological and critical articles to the Christian Reformer, edited by his friend Robert Brook Aspland; in 1857 and 1858 he wrote anonymously there a series of semi-autobiographical sketches, under the title A Minister's Retrospect; from 1876 he contributed to the Christian Life edited by Robert Spears.

Family
Higginson married first, on 25 December 1839, Lydia (d. 8 Feb. 1856, aged 42), youngest daughter of Flower Humble of Newcastle upon Tyne, and adopted by Samuel Shore; secondly, on 5 July 1857, Emily, daughter of George Thomas of Carmarthen, and left children.

See also
Astrotheology

Notes

Attribution

1807 births
1880 deaths
English Unitarian ministers
Alumni of Harris Manchester College, Oxford