OpenLLM-France/wikimedia huggingface dataset:
# Kolmogorov backward equations (diffusion)

The Kolmogorov backward equation (KBE) (diffusion) and its adjoint sometimes known as the Kolmogorov forward equation (diffusion) are partial differential equations (PDE) that arise in the theory of continuous-time continuous-state Markov processes. Both were published by Andrey Kolmogorov in 1931. Later it was realized that the forward equation was already known to physicists under the name Fokker–Planck equation; the KBE on the other hand was new.
Informally, the Kolmogorov forward equation addresses the following problem. We have information about the state x of the system at time t (namely a probability distribution $p_{t}(x)$); we want to know the probability distribution of the state at a later time $s>t$. The adjective 'forward' refers to the fact that $p_{t}(x)$ serves as the initial condition and the PDE is integrated forward in time (in the common case where the initial state is known exactly, $p_{t}(x)$ is a Dirac delta function centered on the known initial state).
The Kolmogorov backward equation on the other hand is useful when we are interested at time t in whether at a future time s the system will be in a given subset of states B, sometimes called the target set. The target is described by a given function $u_{s}(x)$ which is equal to 1 if state x is in the target set at time s, and zero otherwise. In other words, $u_{s}(x)=1_{B}$, the indicator function for the set B. We want to know for every state x at time $t,\ (t<s)$ what is the probability of ending up in the target set at time s (sometimes called the hit probability). In this case $u_{s}(x)$ serves as the final condition of the PDE, which is integrated backward in time, from s to t.

## Formulating the Kolmogorov backward equation

Assume that the system state $X_{t}$ evolves according to the stochastic differential equation
    $dX_{t}=\mu (X_{t},t)\,dt+\sigma (X_{t},t)\,dW_{t}\,,$
then the Kolmogorov backward equation is
    $-{\frac {\partial }{\partial t}}p(x,t)=\mu (x,t){\frac {\partial }{\partial x}}p(x,t)+{\frac {1}{2}}\sigma ^{2}(x,t){\frac {\partial ^{2}}{\partial x^{2}}}p(x,t),$
for $t\leq s$, subject to the final condition $p(x,s)=u_{s}(x)$. This can be derived using Itō's lemma on $p(x,t)$ and setting the $dt$ term equal to zero.
This equation can also be derived from the Feynman–Kac formula by noting that the hit probability is the same as the expected value of the indicator function $u_{s}(x)=\mathbf {1} _{B}(x)$ over all paths that originate from state $x$ at time $t$:
    $\Pr(X_{s}\in B\mid X_{t}=x)=E[\mathbf {1} _{B}(X_{s})\mid X_{t}=x].$
Historically, the KBE was developed before the Feynman–Kac formula (1949).

## Formulating the Kolmogorov forward equation

With the same notation as before, the corresponding Kolmogorov forward equation is
    ${\frac {\partial }{\partial s}}p(x,s)=-{\frac {\partial }{\partial x}}[\mu (x,s)p(x,s)]+{\frac {1}{2}}{\frac {\partial ^{2}}{\partial x^{2}}}[\sigma ^{2}(x,s)p(x,s)],$
for $s\geq t$, with initial condition $p(x,t)=p_{t}(x)$. For more on this equation see Fokker–Planck equation.
# Phillip Austin

Phillip Austin (born 14 February, 1969 in Northampton, England) is a British convicted triple murderer. During the course of a day in July 2000, Austin killed his wife Claire Quinn (aged 31), their two children, Kieren (aged 8) and Jade (aged 7), and two dogs. In March 2001, Austin was sentenced to three concurrent life sentences. The presiding judge described Austin's family annihilation as "beyond the bounds of belief."

## Background

Claire and Phillip Austin married in 1993, after the births of their children. Austin worked the night shift as a forklift operator, and Claire worked for Northamptonshire County Council as a part-time home help. Phillip Austin was 31 years old when he murdered his family.

## Murders

On 10 July 2000, Austin and Claire were at the house they shared on the Standens Barn housing estate in Northampton. Austin hit his wife over the head with a mallet. After a struggle, Austin strangled her with her bra, and then stabbed her with two carving knives. Using the same mallet, Austin battered the family's poodles, Dandy and Sooty, to death. Austin proceeded to pick up his children from school, and took them out for a meal of fish and chips on the way home. Once home, Austin sedated both children and strangled them in their bedrooms.

## Arrest and sentencing

During the week in which the murders remained undiscovered, Austin spent the week on the run, in Blackpool and Scarborough. On 20 July, Austin was arrested in the Lake District, as he sat in his car with his wrists slashed.
When asked what caused him to attack his wife, Austin told detectives, "She started hassling me and arguing and that. I just turned on her." When asked his reasons for murdering his children, he stated, "It sort of came to me that I had killed her so I went upstairs and killed my children."
Austin initially pleaded not guilty to the murders on the grounds of diminished responsibility. Austin then changed his plea and was given three concurrent life sentences. Austin will have to serve a minimum of 20 years, after which time he will be eligible to apply for parole. After applying for parole in 2021, his move to an open prison was refused by the Parole Board for England and Wales. In 2023, the justice secretary again overruled the parole board's recommendation for a move to an open prison. His case is next up for review in 2025.
# Macracantha

Macracantha is a genus of Asian orb-weaver spiders recognized as containing the species, Macracantha arcuata., although some schemes also recognise inclusion of Gasteracantha hasselti in this genus. Macracantha is notable for the extremely long, curved spines on the abdomens of female members of the genus; Eugène Simon created the taxon name from the Greek words μακρός (large, long) and ἄκανθα (spine). It occurs from India and China through Southeast Asia to Indonesia.

## Description

The females of this genus have tough, shell-like abdomens armed with three pairs of spines. The spectacular middle (median) spines project upward and outward, curving in toward each other along their length. They are up to three times as long (20–26 mm) as the abdomen is wide (8–9 mm). The front (anterior) and rear (posterior) spines are short, relatively inconspicuous, and roughly equal in length.
The upper surface of the female abdomen ranges from yellow to red or even white or black and is marked with black sigilla. The ventral surface of the abdomen bears yellow or orange marks, and the median spines can show a bluish iridescence.
The male of the species measures only 1.5 mm, with stout, conical spines.

## Taxonomy

The taxon was first described by Eugène Simon in 1864 as a subgenus of Gasteracantha, and was raised to genus status in 1974 by Michel Emerit.
M. arcuata was historically included in the genus Gasteracantha. A 2019 study examining three mitochondrial and two nuclear genes found that M. arcuata is allied with Gasteracantha hasselti and Actinacantha globulata and that Gasteracantha is paraphyletic with respect to Macracantha, Actinacantha, and Thelacantha. The authors, however, did not propose generic reassignments based on their data.

## Ecology

Female M. arcuata build orb webs three or four feet wide in forested areas. These webs have hollow hubs and white silk beads on the radial threads. Siliwal and Molur report that females were more often observed on the underside of leaves near their webs than hanging in the center of the web.
Based on a study in Singapore, the species appears to depend heavily on primary tropical forest.
# Ecclesiastical confiscations of Mendizábal

The ecclesiastical confiscations of Mendizábal (Spanish: desamortización eclesiástica de Mendizábal), more often referred to simply as la Desamortización in Spanish, were a set of decrees that resulted in the expropriation and privatisation of monastic properties in Spain from 1835 to 1837.
The legislation was promulgated by Juan Álvarez Mendizábal, who was briefly prime minister under Queen regent Maria Christina during the reign of the two-year-old Queen Isabel II of Spain. The aims of the legislation were varied. Some of its impulses were fostered by the anticlerical liberal factions engaged in a civil war with Carlist and other reactionary forces. The government wished to use the land to encourage the enterprises of small-land owning middle class, since much of the land was thought of as underused by monastic orders. The government, which refused to compensate the church for the properties, saw this as a source of income. Finally, wealthy noble and other families took advantage of the legislation to increase their holdings.
Ultimately, the desamortización led to the vacating of most of the ancient monasteries in Spain, which had been occupied by the various convent orders for centuries. Some of the expropriations were reversed in subsequent decades, as happened at Santo Domingo de Silos, but these re-establishments were relatively few. Some of the secularised monasteries are in a reasonably good state of preservation, for example the Valldemossa Charterhouse; others are ruined, such as San Pedro de Arlanza.
# T. Raja (social worker)

Thomas Raja, popularly known as Auto Raja (born 1967) is an Indian humanitarian, social worker and the founder of the New Ark Mission of India (NAMI), a non governmental organization engaged in helping the destitutes of Bengaluru, a south Indian metropolitan city. The organization houses around 750 inmates, providing them food, shelter and healthcare. Raja is a recipient of a number of awards including the NDTV Man of The Year Award, the CNN-IBN Real Heroes Award and the Namma Bengaluru Award.

## Biography

Thomas Raja was born in 1967 in Vaniyambadi, a village in Tirupattur district in the south Indian state of Tamil Nadu. His father, who worked as a lineman with Bharat Sanchar Nigam Limited, moved to Bengaluru with family when Raja was young. He dropped out of school at third standard and when his father kicked him out from home, went to Chennai with the money obtained by selling some goods stolen from his own home. He started drinking and gambling, slept on pavements and had to spend time in Chennai Central Prison after getting caught by the police. There, he fell ill and after recovering from the illness, he was released from jail and was taken back to Bengaluru by his family.
The life in the prison is said to have changed Raja's life who started driving an auto-rickshaw for a living. However, he continued his ruffian ways and even worked as a henchman to the secretary of the auto-rickshaw drivers' union. It was during his several trips along the Bengaluru streets that he came across the people who lived in the streets. He brought one such person, a destitute woman, home and sheltered her in the parking space of his auto-rickshaw. Later, he rented a small house and started looking after destitute people, initially with 13 inmates. Subsequently, with funds collected from the public, he bought a half-acre plot of land in Doddagubbi Village near the city, where he constructed a 2000 sq. ft building which served as the base for New Ark Mission of India, a non-governmental organization when he started it in 1997. The home, named Home of Hope, has since grown to manage one centre in Chikkagubbi village for men and two centres for women in Doddagubbi, housing around 750 inmates and also runs an ambulance service.
Raja is married and the couple has three children.

## Awards and honors

CNN-IBN selected Raja for the Real Heroes Award in 2010. He received the NDTV Man of The Year the next year; the same he was chosen for the Namma Bengaluru Award. A recipient of the Individual H. Honnaiah Samaja Seva Prashasti Award in 2001, Raja delivered a speech at TEDx Talks in 2012.
# Mobarakeh

Mobarakeh (Persian: مباركه) is a city in the Central District of Mobarakeh County, Isfahan province, Iran, serving as capital of both the county and the district.

## Demographics
### Population

At the time of the 2006 National Census, the city's population was 62,454 in 16,583 households. The following census in 2011 counted 66,092 people in 19,545 households. The 2016 census measured the population of the city as 69,449 people in 21,676 households.

## Industry

Mobarakeh Steel Company (MSC, Persian: فولاد مبارکه, Foolad Mobarakeh) is an Iranian steel company, located 65 km south west of Esfahan, near the city of Mobarakeh. It is Iran's largest steel maker, and one of the largest industrial complexes operating in Iran. It was first commissioned after the Iranian Revolution in 1979 by the Saririans and officially initiated operations during 1993. Underwent major revamping during year 2000, and was scheduled for a second and third revamping in 2009–2010, bringing the total steel output to 7,200,000 metric tons per year. The company owns the successful football club, F.C. Sepahan.

## Natural and cultural attractions

The natural attractions of this city are: Tang Dozan Spring, Hoz Mahi Spring, Nekoabad Dam, Pir Hajat Tomb, Bazi Castle, Bazi Castle Historical Caves, Serarud Coastal Park Groves, Sanjadi Spring, Laila Spring and Hassan Abad Bidgan Qanat, Amin Abad Qanat, Tank Bidkan Spring, Kerkund Spring, Daulat Abad Water Mill and 500 year old tree in Diziche city.
More than 800 works of history have been identified in Mobarakeh city, of which 35 have been registered in the list of National works of Iran. In the investigations carried out on the old structure of Mobarakeh city, after knowing the old existing neighborhoods and determining its limits, it has been determined that the most modern urban structure in the world today was founded in this city many years ago.
# Devilstep Hollow Cave

Devilstep Hollow Cave is a natural limestone cave located within Justin P. Wilson Cumberland Trail State Park. The cave, part of the Mill Cave System, drains Grassy Cove, which is the largest sinkhole in North America. It contains numerous instances of Mississippian era Native American cave art. The entrance is 125 feet by 150 feet. The cave stream forms the nearby Head of Sequatchie spring, the source of the Sequatchie River.

## Artwork

The artwork within Devilstep Hollow Cave was created by the Mississippian culture, and contains 22 known images. These include woodpeckers, fish, and an image of the falcon man. The glyphs are thought to be around 1,100 years years old.
# Juhani Salakka

Juhani Salakka (13 September 1950 – 17 February 2015) was a Finnish weightlifter. He competed in the men's lightweight event at the 1980 Summer Olympics.
# Clarence A. Reid

Clarence A. Reid (December 11, 1892 – January 1978) was the 50th lieutenant governor of Michigan, from 1953 to 1955.

## Early life

Reid was born in a log cabin in Circleville, Ohio on December 11, 1892.

## Education

Reid graduated Circleville High School. Reid attended the University of Michigan Law School. His education was interrupted by his enlistment into the United States Army, but was continued afterward. Reid was admitted to the bar in 1920.

## Military career

Reid enlisted into the United States Army in 1917 during World War I. Reid was first assigned to the 85th Infantry Division, then later to the 14th Infantry Division.

## Career

After World War I, Reid opened a law office in Detroit, Michigan in 1920. Reid was a failed candidate in the 1932 Republican primary for the position of the United States representative from Michigan's 15th district. Reid ran for the position of member of the Michigan Senate from the 18th district in 1934 and 1938. Reid was elected to this position in 1940, and served in this position from 1941 to 1948. In 1948, he would not win re-election, being defeated by James P. Hannan. He would be elected to this position again on 1950, and served his last term in the Michigan Senate from 1951 to 1952. In 1953, Reid served as the lieutenant governor under Governor G. Mennen Williams. Reid failed to gain re-election to this position in 1954, 1956, 1960, and 1962.

## Personal life

Reid married Grace Mapes on March 26, 1921. Together they had three children. Reid was a member of a number of groups including the Lions Club, the Elks, the Eagles, the Forty and Eight, the American Legion, and the American Bar Association. Reid was a Freemason.

## Death

Reid died in the January of 1978.
# Mats Nyberg (sailor)

Mats Nyberg (13 December 1959 – 13 February 1999) was a Swedish sailor. He competed at the 1988 Summer Olympics, the 1992 Summer Olympics, and the 1996 Summer Olympics.
# Saint Monica Preparatory

Saint Monica Preparatory is a parochial, co-educational Catholic school in Santa Monica, California, consisting of students in grades Transitional kindergarten to grade 12. It is located in the Archdiocese of Los Angeles and serves the parish of St. Monica Catholic Church.
The school in its current organizational structure was formed by the merging of the parish elementary and high schools into a single TK–12 school, but the elementary and high schools remain on their respective separate campuses.

## Background

Saint Monica was established in 1899 by the Sisters of the Holy Names of Jesus and Mary. The academy housed both an elementary school and a high school until 1930, when the elementary school became the "Saint Monica Parish Elementary School" and was transferred to its present site on Seventh Street. The school was sold in 1935, and Saint Monica High School was opened in 1939. The women's high school and the men's high schools were operated separately until the fall of 1968, when classroom instruction became co-educational.
The elementary and high schools had long been affiliated with one another as parish schools serving the St. Monica Catholic Church but were administered separately. In the spring of 2022, the school board announced that the two schools would merge into one legal entity under a single administration beginning in the 2022–23 academic year. The TK-12 school would be rebranded as Saint Monica Preparatory.

## Notable alumni

* Donna Corcoran, actress
* Bison Dele, formerly Brian Williams, basketball player
* Steven M. Hilton, businessman and philanthropist. His mother Marilyn is also an alumnus
* Adrian Klemm, football player
* Bob Klein, football player for USC, LA Rams and San Diego Chargers
* Michael Klesic, actor
* Daniel "Danny" Moder, cameraman, husband of Julia Roberts
* Jason Patric, actor
* Terry Schofield, basketball player on three NCAA Championship teams at UCLA under legendary coach John Wooden. German Professional Basketball League player and coach
* Leon Wood, NBA Basketball player and referee
* The Lennon Sisters, singing family
* Randy Pedersen (1980), professional bowler, color analyst for ESPN coverage of PBA Tour
* Robert Wagner, actor
* Marcellus Wiley, National Football League Pro Bowl defensive lineman, Columbia University Hall of Fame, former ESPN TV and Radio Host, now co-host on Speak for Yourself
* C.J. Wallace, actor, musician, son of The Notorious B.I.G. and Faith Evans
# Michael Heatley

Michael Heatley (born 29 October 1955) is the author or editor of over thirty biographies, including Backstreet Boys: The Unofficial Book, Bon Jovi: In Their Own Words and Rolf Harris: The Most Talented Man In The World. In 1995, he wrote the liner notes to Rolf's best-selling album Rolf Rules OK!
Since 1977 he has written more than a hundred music, sport and TV books.
He has written for magazines including Privileged View (for viewers of UK Gold and UK Living), 442 and Fultime (Fulham FC), Music Week, Billboard, Goldmine (US record collecting magazine), Radio Times, Daily Record and the Mail on Sunday colour supplement.
In addition, Michael runs a fanzine in honour of legendary Welsh psychedelic rock band Man called The Welsh Connection which is circulated to a small but fervent fanbase on a bi-monthly basis.
Michael Heatley co-wrote the Encyclopedia of Singles with Philip Dodd, Eithne Farry and Martin Noble.

## Selected bibliography

* Michael Heatley Rolf Harris: The Most Talented Man in the World , (Twisterella Books), (1997) ISBN 1-901483-01-0
* Michael Heatley The Immortal John Lennon, 1940-1980
* Michael Heatley The Complete Deep Purple
* Michael Heatley John Peel - A Life In Music
* Heatley, Michael (1997). Neil Young: in his own words. London, New York: Omnibus Press. ISBN 978-0-7119-6161-6. OCLC 38727767.
* Heatley, Michael (17 July 2009). Michael Jackson: Life of a Legend. Headline. p. 192. ISBN 978-0-7553-6053-6.
# Baku City Executive Committee

Baku City Executive Committee (Russian: Бакинский городской исполнительный комитет [Bakinskiy gorodskoy ispolnitel'nyi komitet], commonly known as Bakgorispolkom (Бакгорисполком)) was the main administrative institution of Baku during the Soviet period. Bakgorispolkom was headed by the presidium and consisted of the Chief Architecture Department and Town-planning Council. The head of BCEC was actually the city mayor.

## Heads of BCEC

| Name | Term of office |
| Levon Mirzoyan | ?-1925 |
| Ruben Rubenov | January 1933-December 1933 |
| Gurban Khalilov | 1942–1945 |
| Mir Dzhafar Bagirov | 1933–1953 |
| Mamed Iskenderov | 1953–1954 |
| Nasrulla Nasrullayev | 1961–1966 |
| Alish Lemberanskiy | 1958–1966 |
| Ali Kerimov | 1970–1980 |
| Vagif Huseynov | 1980–1983 |
| Muslim Mamedov | 1988–1990 |
| Rufat Agayev | February 1990–1991 |
# Robert Kendall (actor)

Robert Kendall (June 26, 1927 – November 12, 2009) was an American actor, writer and teacher.
Kendall was born Arthur Robert Kendall in Stephenson, Michigan in 1927, and moved to Battle Creek as a child. In 1945, he won a "Hollywood at Your Door" talent contest at the W.K. Kellogg Auditorium, and headed to Hollywood to take up the prize of a screen test. Upon his arrival, Kendall was told the company who had sponsored the contest had gone bankrupt and was asked for a loan. He returned to the YMCA where he was staying to discover that his clothes had been stolen. Undeterred, he took work as a waiter in a drive-in restaurant until he was noticed by Sylvia Sidney's talent agent Christopher Hofeld, and invited to try out for some roles at the Universal Studios lot.
Kendall auditioned for Universal and was given the small role of Hassan in the 1947 musical Song of Scheherazade starring Yvonne De Carlo and Jean-Pierre Aumont, and the next year appeared in Casbah, also starring De Carlo, alongside Tony Martin. During the 1950s, he played gangster Baby Face Nelson in several installments of the Gang Busters TV serial. He also played him in the 1960 film Ma Barker's Killer Brood.

## Selected filmography

* The Women of Pitcairn Island (1956)
# Jukka Rauhala

Jukka Matti Rauhala (born March 1, 1959, in Muurame) is a former wrestler from Finland, who claimed the bronze medal in the Men's Freestyle Lightweight Division (– 68 kg) at the 1984 Summer Olympics in Los Angeles.
He's married to Jaana, with whom he has son Jaakko and daughter Johanna.
On 18 March 2013 he was chosen to European Council of Associated Wrestling board of directors.

## Results

* 1980 European Championship — 62.0 kg Freestyle (11th)
* 1981 European Championship — 68.0 kg Freestyle (4th)
* 1982 European Championship — 68.0 kg Freestyle (5th)
* 1983 World Championship — 68.0 kg Freestyle (10th)
* 1986 European Championship — 68.0 kg Freestyle (4th)
* 1986 World Championship — 68.0 kg Freestyle (5th)
* 1987 European Championship — 68.0 kg Freestyle (4th)
* 1987 World Championship — 68.0 kg Freestyle (11th)
* 1988 European Championship — 68.0 kg Freestyle (14th)