Samantha912/NLP_A2_WTH huggingface dataset:
In abstract algebra, multiplicity theory concerns the multiplicity of a module M at an ideal I (often a maximal ideal)

The notion of the multiplicity of a module is a generalization of the degree of a projective variety. By Serre's intersection formula, it is linked to an intersection multiplicity in the intersection theory.

The main focus of the theory is to detect and measure a singular point of an algebraic variety (cf. resolution of singularities). Because of this aspect, valuation theory, Rees algebras and integral closure are intimately connected to multiplicity theory.

Multiplicity of a module 
Let R be a positively graded ring such that R is finitely generated as an R0-algebra and R0 is Artinian. Note that R has finite Krull dimension d. Let M be a finitely generated R-module and FM(t) its Hilbert–Poincaré series. This series is a rational function of the form

where  is a polynomial. By definition, the multiplicity of M is 

The series may be rewritten 

where r(t) is a polynomial. Note that  are the coefficients of the Hilbert polynomial of M expanded in binomial coefficients. We have

As Hilbert–Poincaré series are additive on exact sequences, the multiplicity is additive on exact sequences of modules of the same dimension.

The following theorem, due to Christer Lech, gives a priori bounds for multiplicity.

See also 
Dimension theory (algebra)
j-multiplicity
Hilbert–Samuel multiplicity
Hilbert–Kunz function
Normally flat ring

References

Theorems in ring theory
James Pulliam (1925−2005) was a noted Modernist architect in the Greater Los Angeles Area of Southern California.

Works
Pulliam was known for a "cut into box" style exhibited by the All-State Savings and Loan building in Glendale, California, and original Bronco Student Union Building at Cal Poly Pomona in 1976, and the interior remodeling of the San Pedro Municipal Ferry Building to house the Los Angeles Maritime Museum.  Noted architectural historian David Gebhard cited a house he designed in Beverly Hills as "monumental," and the Bronco Student Center at Cal Poly Pomona as the best building on campus.

He worked in the offices of Richard Neutra and Welton Beckett. He was later a partner in the architectural firm Pulliam Zimmerman Matthews. As president of the Los Angeles chapter of the AIA, he advocated for preserving the integrity of the Los Angeles Central Library.

He served as the campus architect at Cal Poly Pomona where he also served as an instructor at the College of Environmental Design.

Death
James Pulliam died in 2005, at his home in La Cañada Flintridge, California.

In his obituary, the Los Angeles Times said:
"Jim Pulliam, FAIA was a gentleman Los Angeles modernist architect, known for his highly detailed custom modernist residential and commercial commissions. Jim's mid career works were celebrated in a major Los Angeles area architectural exhibit identified as The Los Angeles 12 Architects, of which Jim Pulliam was one of the distinguished twelve architects. Pulliam's works were included in the Los Angeles Twelve Architects exhibit and conferences at the Pacific Design Center, Los Angeles; Cal Poly Pomona Bookstore and Student Center Building (which he designed) and the Aspen Design Conference, Aspen Co.."

References

Modernist architects
1925 births
2005 deaths
Architects from Los Angeles
California State Polytechnic University, Pomona faculty
Dartmouth College alumni
People from Lyons, Kansas
20th-century American architects
People from La Cañada Flintridge, California
Asterius of Cappadocia (Ἀστέριος; died c. 341) was an Arian Christian theologian from Cappadocia.  Few of his writings have been recovered in their entirety; the latest edition is by Markus Vinzent). He is said to have been a pupil of Lucian of Antioch, but it is unclear to what extent this was the case. He is said to have relapsed into paganism during the persecution under Maximian in 304 and thus, though received again into the church by Lucian and supported by the Eusebian party, never attained to ecclesiastical office. He was present at the synod of Antioch in 341.

Fragments of his Syntagmation are preserved by Athanasius of Alexandria and Marcellus of Ancyra.
His extant works include a commentary on the Psalms, a letter to Eusebius, the Syntagmation, and a few fragments.

Asterius was a firm defender of Arianism and Eusebius of Caesarea's theology, emphasising the derivative nature of the Son as a spontaneous manifestation and generation of the Father's will.

Notes

341 deaths
4th-century Christian theologians
Arian Christians
4th-century Romans
4th-century writers
4th-century Arian Christians
Cappadocia (Roman province)
Year of birth unknown
People from Cappadocia
Fairy Tale Killer (追凶, Pupil in Chinese) is a 2012 Hong Kong horror film directed by Danny Pang Phat. The film was released on 11 May 2012, and stars Sean Lau, Wang Baoqiang, and Elanne Kong. The Fairy Tale Killer follows police detective Wong Wai-han as he investigates a series of brutal murders.

Plot
When a bloodied and incoherent Wu Zaijun confesses to five murders that have not occurred, the police assume that he's mentally unstable and ignore his claims. Police detective Wong Wai-han is investigating a series of gruesome murders, but soon discovers that all is not as it seems and that not only are the murders connected, but that Jun is tied to them in some way.

Cast
Sean Lau as Wong Wai-han
Wang Baoqiang as Wu Zaijun
Elanne Kong as Wong Yue-yee
Joey Meng as Wai
Ken Lo as Old Guy
Lam Suet as Cheung Fai
Felix Lok as Commander Chan
Elena Kong as Chiu Lan
James Ho as Simon
Gary Chiu as Sai
Anson Leung as pathologist
Kelly Fu as Cindy
Ciwi Lam
Rex Ho
Lam Ying-yuen
Carolyn Chan
Yip Wan-keung
Kunpimook Bhuwakul as Wong Wai-han's son

Reception
The movie review site Twitch panned the film, expressing disappointment in the acting range of Wang Baoqiang in the film. The Xinhua News Agency praised the film's acting, but criticized the film's ending as too bizarre and not always coherent.

References

External links

2012 horror films
2012 films
Hong Kong horror films
Police detective films
2010s Cantonese-language films
2010s crime thriller films
2010s police films
Hong Kong serial killer films
Films directed by Danny Pang
Films set in Hong Kong
Films shot in Hong Kong
Hong Kong police films
Hong Kong crime thriller films
Le Vision Pictures films
2010s Hong Kong films
The men's marathon swimming at the 2016 Summer Olympics in Rio de Janeiro took place on 16 August at Fort Copacabana, over a distance of 10 kilometres.

Summary
A photo finish saw Spyridon Gianniotis of Greece narrowly loses to dutchman Ferry Weertman for the gold, with both record time of 1:52:59.8 and 1:53:00.5. In the final race of his career, Gianniotis, who was also the oldest competitor at the age of 36, won the first medal for Greece in swimming since the inaugural 1896 Summer Olympics in Athens.

The battle for bronze also saw a photo finish, with France's Marc-Antoine Olivier pipping Zu Lijun and Jack Burnell on the line to finish in 1:53:02.0. Burnell was subsequently disqualified for a second yellow card for a tussle with defending champion Oussama Mellouli just before the line.

Qualification

The men's 10 km open water marathon at the 2016 Olympics featured a field of 25 swimmers:

10: the top-10 finishers in the 10 km races at the 2015 World Championships
9: the top-9 finishers at the 2016 Olympic Marathon Swim Qualifier (June 11–12, 2016 in Setúbal, Portugal)
5: one representative from each FINA continent (Africa, Americas, Asia, Europe and Oceania). (These have been selected based on the finishes at the qualifying race in Setúbal.)
1: from the host nation (Brazil) if not qualified by other means. If Brazil already contained a qualifier in the race, this spot had been allocated back into the general pool from the 2016 Olympic qualifier race.

Competition format

Unlike all of the other swimming events in the pool, the men's and women's marathon 10 kilometre races are held in open water. No preliminary heats are held, with only the single mass-start race being contested. This race is held using freestyle swimming, with a lack of stroke regulations.

Results

References

External links

Men's 10000 metre marathon
Olympics
Men's events at the 2016 Summer Olympics
Wayne Anderson may refer to:

 Wayne D. Anderson (1930–2013), American college basketball coach
 Wayne Anderson (politician) (born 1953 or 1954), Canadian politician in Alberta
 Wayne Anderson (racing driver) (born 1968), American race car driver
 Wayne Anderson (swimmer) (born 1945), American former swimmer

See also
 Wayne Andersen (born 1945), former United States federal judge
En Todo Estaré (English: I'll Be In Everything) is the 15th studio album by Puerto Rican performer Chayanne. This album was released on August 25, 2014.

Track list

Reception

The album was well received by critics on AllMusic where it got a 3.5 star rating. It also received gold and platinum certifications in several countries in America such as Mexico and Chile.

Charts

Weekly charts

Year-end charts

Sales and certifications

See also
List of number-one Billboard Latin Albums from the 2010s
List of number-one albums of 2014 (Spain)

References

2014 albums
Chayanne albums
Sony Music Latin albums
Birthplace of Country Music Museum is a museum celebrating the historic 1927 Bristol Sessions, which recorded some of the earliest country music in America when the Carter Family and Jimmie Rodgers and several other musicians recorded for the first time before gaining prominence.  The museum is located at 520 Birthplace of Country Music Way in Bristol, Virginia. A live radio station WBCM-LP broadcasts from within the museum. The original site of the Bristol recordings is marked by a plaque several blocks from the museum.

See also
 List of music museums
 WBCM-LP

References

External links
Birthplace of Country Music Museum

Buildings and structures in Bristol, Virginia
American country music
American music awards
Museums established in 2014
Music museums in Virginia
Music of East Tennessee
2014 establishments in Virginia
Country music museums
Uwe Hesse (born 16 December 1987) is a German footballer who plays for KSG Georgenhausen.

References

External links
 
 Uwe Hesse at FuPa

1987 births
Living people
German men's footballers
SV Darmstadt 98 players
SSV Jahn Regensburg players
SC Hessen Dreieich players
2. Bundesliga players
3. Liga players
Regionalliga players
Men's association football midfielders
People from Rüsselsheim
Footballers from Darmstadt (region)
Ius privatum is Latin for private law. Contrasted with ius publicum (the laws relating to the state), ius privatum regulated the relations between individuals. In Roman law this included personal, property and civil law. Judicial proceeding was a private process (iudicium privatum). Criminal law was also considered private matters, except where the crimes were particularly severe.

Lex Aquilia

The lex Aquilia was a plebiscite which codified the law on damage to person and property through a particular fault. It is a forerunner of the modern law of tort.

Stipulatio

Stipulatio was the basic form of contract in Roman law. It was made in the format of question and answer. The precise nature of the contract was disputed, as can be seen below.

Vindicatio

Rei vindicatio is a legal action by which the plaintiff demands that the defendant return a thing that belongs to the plaintiff. It may only be used when plaintiff owns the thing, and the defendant is somehow impeding the plaintiff's possession of the thing. The plaintiff could also institute an actio furti (a personal action) in order to punish the defendant. If the thing could not be recovered, the plaintiff could claim damages from the defendant with the aid of the condictio furtiva (a personal action). With the aid of the actio legis Aquiliae (a personal action), the plaintiff could claim damages from the defendant. Rei vindicatio was derived from the ius civile, therefore was only available to Roman citizens.

See also
Privatus

Roman law
Latin legal terminology
John Boswell, 4th Laird of Auchinleck (1532?–1609), was a Scottish gentleman.  He is considered by some scholars to be the first recorded non-operative Freemason.

Biographical details

John Boswell, 3rd laird of Auchinleck was the son of David Boswell and Janet Hamilton. In 1562 he married Christian Dalzell, and his marriage contract was signed by Thomas McCalzean of Clifton Hall, Gavin Hamilton, Commendator of Kilwinning, and others. His son, also John Boswell, married secondly, Christian Stewart, a sister of James Stewart, Earl of Arran.

On 5 March 1591 John Boswell, younger, was accused in the Privy Council of practising witchcraft, sorcery and enchantments, consulting with witches and taking part in other devilish activities. Boswell's response to these allegations was to flee the country. The Privy Council heard that he had, "not only has oft and diverse times consulted with witches, but also by himself practised witchcraft, sourcery, enchantment, and other devilish practices, to the dishonour of God, slander of his word, and great contempt of his Highness, his authority and laws."

Freemasonry

Boswell's signature and mark are found on the records of a meeting of the Lodge of Edinburgh held at Holyrood on 8 June 1600.  According to many masonic historians, this is the earliest authentic record of a non-operative (or accepted) Mason attending a Masonic Lodge.  There are others, however, who disagree.  It is not clear in what capacity Boswell was in attendance at this meeting. It was not an ordinary masonic meeting of the lodge, but a trial of its Warden 'Jhone Broune'. While it is possible that he was there as a member (or an honorary member) of the lodge, it is also possible that he was there only as counsel for prosecution or defence (or for some other reason), and was not a member of the lodge at all. There is no evidence of his initiation in the lodge on that occasion or any other occasion, and the meeting of 8 June 1600 was the only occasion to which Boswell’s connection with the masonic Craft can be traced.

References

1532 births
1609 deaths
Clan Boswell
Scottish Freemasons
Witchcraft in Scotland
Jeris Jerome White (born September 3, 1952) is a former professional American football cornerback in the National Football League (NFL) for nine seasons for the Miami Dolphins, Tampa Bay Buccaneers, and Washington Redskins. He played football at Radford High School, Honolulu, Hawaii, and at the University of Hawaii. He was drafted by Miami in the second round of the 1974 NFL Draft. He is the first person from a Hawaii high and collegiate school to ever play in a Super Bowl. White was a holdout when the Redskins opened the 1983 season, so Washington replaced him with its first-round draft pick Darrell Green.

References

1952 births
Living people
American football cornerbacks
Hawaii Rainbow Warriors football players
Miami Dolphins players
Players of American football from Honolulu
Tampa Bay Buccaneers players
Washington Redskins players
Admiral Arthur W. Radford High School alumni
The Keynes effect is the effect that changes in the price level have upon goods market spending via changes in interest rates. As prices fall, a given nominal money supply will be associated with a larger real money supply, causing interest rates to fall and in turn causing investment spending on physical capital to increase.

This implies that insufficient demand in the product market cannot exist forever, because insufficient demand will cause a lower price level, resulting in increased demand.

There are two cases in which the Keynes effect does not occur: in the liquidity trap (when the LM curve is horizontal and thus changes in the real money supply do not affect interest rates), and when expenditure is inelastic with respect to (unresponsive to) interest rates (when the IS curve is vertical). The Patinkin-Pigou real balance effect suggests that due to wealth effects of changes in the price level upon spending itself, insufficient demand cannot persist even in the two cases in which the Keynes effect does not operate.

See also
Pigou effect
John Maynard Keynes

References 

Keynesian economics
Economics effects
The Hyp-Doctor was an 18th-century weekly paper edited and produced by John 'Orator Henley'. It was a pro-Walpole newspaper established in opposition to another periodical of the period, entitled the Craftsman.

The first number of The Hyp-Doctor appeared on 15 December 1730, and it ceased publication in 1741.

References

Defunct newspapers published in the United Kingdom
Publications established in 1730
Year of disestablishment missing
1730 establishments in Great Britain
George Herbert (23 January 1892 – 16 June 1982) was a British Conservative Party politician. He was elected as the Member of Parliament (MP) for Rotherham at the 1931 general election, and resigned on 6 February 1933 by appointment as Steward of the Chiltern Hundreds.

References

External links 
 

1892 births
1982 deaths
Conservative Party (UK) MPs for English constituencies
UK MPs 1931–1935
Eupithecia convallata is a moth in the family Geometridae. It is found in Afghanistan and Iran.

Subspecies
Eupithecia convallata convallata (Iran)
Eupithecia convallata terricolor Vojnits, 1988 (Afghanistan)

References

Moths described in 1938
convallata
Moths of the Middle East
Mecloqualone (Nubarene, Casfen) is a Quinazolinone-class GABAergic and is an analogue of methaqualone that was first made in 1960 and marketed mainly in France and some other European countries. It has sedative, hypnotic, and anxiolytic properties caused by its agonist activity at the β subtype of the GABAa receptor, and was used for the treatment of insomnia.  Mecloqualone is faster-acting but shorter-lasting than methaqualone and so was used only as a sleeping pill, in contrast to methaqualone, which was used as a general-purpose anxiolytic as well. Mecloqualone was never as widely used as methaqualone and is no longer prescribed because of concerns about its potential for abuse and overdose. In the United States it is a Schedule I non-narcotic (depressant) controlled substance with an ACSCN of 2572 and 30 g annual aggregate manufacturing quota.

See also 
 Methaqualone 
 Afloqualone
 Etaqualone
 Methylmethaqualone
 Mebroqualone
 Cloroqualone
 Diproqualone
 Gamma-Aminobutyric acid

References 

Sedatives
Chlorobenzenes
Designer drugs
Quinazolinones
GABAA receptor positive allosteric modulators
The Galula Formation is a geological formation located south of Lake Rukwa in Tanzania, part of the Red Sandstone Group of the Rukwa Rift Basin. Along with the unconformably overlying Oligocene Nsungwe Formation. It is divided into two members, the lower Mtuka Member and the upper Namba Member.

The age of the deposit is poorly constrained, with the Mtuka Member likely being Aptian to Cenomanian in age, while the Namba Member being Cenomanian to Campanian in age based on Geomagnetic reversals. It is correlated with the Dinosaur Beds of Malawi.

The formation is fossiliferous, with Dinosaurs and Crocodyliformes being known from the formation.

Geology

Lithology 
The Lithology of the formation is a sequence of red, pink, purple and occasionally white colored sandstones, conglomerates and mudstones. The Mtuka member is 160–180 m thick in the type section, and is typified by coarser sandstone, a higher frequency of conglomerates, higher proportions of extraformational clasts, thicker and a greater frequency of overbank siltstone and mudstone lenses and a higher proportion of paleosols. While the Namba member is between 340–360 m in the type section, and is less variable in facies, predominated by very fine-to medium-grained sandstones with less overbank mudstone and siltstone lenses.

Vertebrate paleofauna

Fish

Crocodyliformes

Dinosaurs

Turtles

Mammals

References 

Geologic formations of Tanzania
Albian Stage
Aptian Stage
Lower Cretaceous Series of Africa
Cenomanian Stage
Turonian Stage
Coniacian Stage
Santonian Stage
Campanian Stage
Upper Cretaceous Series of Africa
Cretaceous Tanzania
Sandstone formations
Fluvial deposits
Paleontology in Tanzania
Khmer(s) may refer to:

Cambodia
Srok Khmer (lit. "Khmer land" or "Land of the Khmer(s)"), a colloquial exonym used to refer to Cambodia by Cambodians; see 

Khmer people, the ethnic group to which the great majority of Cambodians belong
Khmer Americans, Americans of Khmer (Cambodian) ancestry
Khmer Krom, Khmer people living in the Mekong Delta and Southeast Vietnam
Khmer Loeu, the Mon-Khmer highland tribes in Cambodia
Northern Khmer people, ethnic Khmer people of Northeast Thailand
Khmer (Unicode block), a block of Unicode characters of the Khmer script
Khmer architecture, the architecture of Cambodia
Khmer cuisine, the dominant cuisine in Cambodia
Khmer Empire, which ruled much of Indochina from the 9th to the 13th centuries 
Khmer Issarak, anti-French, Khmer nationalist political movement formed in 1945
Khmer language, the language of the Khmers, also the official and national language of Cambodia
Khmer Khe dialect, a Khmeric language spoken in Stung Treng Province, Cambodia
Northern Khmer dialect, a dialect of the Khmer language spoken by the ethnic Khmers in Northeast Thailand
Western Khmer dialect, a dialect of the Khmer language spoken by the Khmers native to the Cardamom Mountains
Khmer nationalism, a form of nationalism founded in Cambodia
Khmer Republic, the official name of Cambodia from 1970 to 1975
Khmer Sâ (White Khmer), a pro-US force formed by the Khmer Republic's defence minister Sak Sutsakhan
Khmer script, the script used to write the Khmer and Khmer Loeu languages
Khmer Serei, anti-communist and anti-monarchist guerrilla force founded by Cambodian nationalist Son Ngoc Thanh
Political terms coined by Norodom Sihanouk based on the word 'Khmer':
Khmer Bleu, Sihanouk's domestic opponents on the right
Khmer Rouge, a Cambodian Communist political group and guerrilla movement
Khmer Việt Minh, Cambodian communists who lived in exile in North Vietnam after the 1954 Geneva Conference

Other uses
Khmer (album), a 1997 jazz album by Nils Petter Molvær
Khmer (food), traditional dish native to Jizan, Saudi Arabia
Khmer: The Lost Empire of Cambodia, a 1997 nonfiction book by Thierry Zéphir

See also
 
Khemara (disambiguation)

Language and nationality disambiguation pages
Chadsia is a genus of flowering plants in the family Fabaceae. It includes nine species native to Madagascar. It belongs to subfamily Faboideae.

Species 
Accepted species in the genus include.

References

Millettieae
Fabaceae genera
Taxa named by Wenceslas Bojer
Endemic flora of Madagascar
Phonology: An Introduction to Basic Concepts is a 1984 book by Roger Lass designed for an introductory course in phonology.

Reception
The book was reviewed by Richard Coates, Larry M. Hyman, John R. Rennison and Ellen Broselow.

References

External links
Phonology: An Introduction to Basic Concepts

1984 non-fiction books
Phonology books
Linguistics textbooks
Cambridge University Press books
The El Doctor Formation is a geologic formation in Mexico. It preserves fossils dating back to the Albian and Cenomanian stages of the Cretaceous period.

Description 
The light grey micritic limestone sequence with intercalated black chert lenses was deposited in an open marine basin with a hypersaline and/or poorly oxygenated bottom.

Fossil content 
The formation has provided the following fossils:
Fish
 Enchodus zipapanensis
Crustaceans
 Aeger hidalguensis
 Polzia eldoctorensis
 Victoriacaris muhiensis
 Palinurus sp.

See also 
 List of fossiliferous stratigraphic units in Mexico
 Sierra Madre Formation

References

Bibliography 
 
 
 

Geologic formations of Mexico
Cretaceous System of North America
Cretaceous Mexico
Albian Stage
Cenomanian Stage
Mudstone formations
Deep marine deposits
Paleontology in Mexico
The Waitahaia River is a river in the Waiapu Valley of the Gisborne Region of New Zealand's North Island. It flows northeast from the southern end of the Raukumara Range to reach the Mata River  west of Te Puia Springs. Brown trout, a European species of fish, was introduced into New Zealand for fishing in the late 1860s.

See also
List of rivers of New Zealand

References

Rivers of the Gisborne District
Rivers of New Zealand