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In mathematics, a super vector space is a Z 2 -graded vector space, that is, a vector space over a field K with a given decomposition of subspaces of grade 0 and grade 1. The study of super vector spaces and their generalizations is sometimes called super linear algebra; these objects find their principal application in theoretical physics where they are used to describe the various algebraic aspects of supersymmetry. A super vector space is a Z 2 -graded vector space with decomposition V = V 0 + V 1, 0, 1 ∈ Z 2 = Z / 2 Z. Vectors that are elements of either V 0 or V 1 are said to be homogeneous; the parity of a nonzero homogeneous element, denoted by | x |, is 0 or 1 according to whether it is in V 0 or V 1, | x | = { 0 x ∈ V 0 1 x ∈ V 1 Vectors of parity 0 are called and those of parity 1 are called odd. In theoretical physics, the elements are sometimes called Bose elements or bosonic, the odd elements Fermi elements or fermionic. Definitions for super vector spaces are given only in terms of homogeneous elements and extended to nonhomogeneous elements by linearity.

If V is finite-dimensional and the dimensions of V 0 and V 1 are p and q then V is said to have dimension p | q. The standard super coordinate space, denoted K p | q, is the ordinary coordinate space K p + q where the subspace is spanned by the first p coordinate basis vectors and the odd space is spanned by the last q. A homogeneous subspace of a super vector space is a linear subspace, spanned by homogeneous elements. Homogeneous subspaces are super vector spaces in their own right. For any super vector space V, one can define the parity reversed space Π V to be the super vector space with the and odd subspaces interchanged; that is, 0 = V 1 1 = V 0. A homomorphism, a morphism in the category of super vector spaces, from one super vector space to another is a grade-preserving linear transformation. A linear transformation f: V → W between super vector spaces is grade preserving if f ⊂ W i, i = 0, 1; that is, it maps the elements of V to elements of W and odd elements of V to odd elements of W.

An isomorphism of super vector spaces is a bijective homomorphism. The set of all homomorphisms V → W is denoted H o m; every linear transformation, not grade-preserving, from one super vector space to another can be written uniquely as the sum of a grade-preserving transformation and a grade-reversing one—that is, a transformation f: V → W such that f ⊂ W 1 − i, i = 0, 1. Declaring the grade-preserving transformations to be and the grade-reversing ones to be odd gives the space of all linear transformations from V to W, denoted H o m

John Cronin is a repeat-offence Scottish convict. Imprisoned for running up a 140,000 kronor bill in one of Sweden's top restaurants and refusing to pay, Cronin is infamous for a string of sex offences against women, most notably against "Judy X", a Conservative Party worker, in May 1992. On 20 March 2013 at Antrim Crown Court, Cronin pleaded guilty to the burglary of Drumalis House on 15 February 2012 and the theft of money belonging to the Church. Cronin is the centre of current debate in Scotland over the reporting and handling of sex offenders and how they are dealt with once out of prison. Cronin was born in the son of Michael Cronin and Jeanette Cronin. Cronin's early years were marked with frequent moves between East Lothian and the U. S.. In 1978, the Cronins moved back to East Lothian to care for Jeanette's father, ill, it was about this time. By the age of three, he was difficult for his parents to control, smashing light bulbs and breaking various things in the home. At age five, he was enrolled in a private school, but was expelled shortly thereafter for disruptive behaviour, including overturning desks, urinating on the floor and attacking teachers.

The remainder of his school years were said by Cronin to be filled with repeated difficulties. He went through several schools, where he built up a record for repeat offences at the schools, from theft and assault to urinating and defecating on school property. Cronin obtained four O-grades at a boarding school in Newton Stewart in 1989. Shortly after leaving the school he committed his first criminal act, sexually assaulting a 14-year-old female classmate, for which he served a three-month sentence. Around this time Cronin discussed with a social worker his plans to take his father's military records and alter them so that he could join the IRA. There was a period between 1990 and 1992 that he served short prison sentences in Ireland for various crimes. Sometime in the early 1990s, he began to pass himself off as a visiting Irish Catholic priest, his skill was competent enough that he was able to celebrate Mass with and to exploit genuine priests stealing from them after being given hospitality.

In one case, he stole the purse of a janitor at St. Mary's Cathedral in Edinburgh after having fooled the monsignor present, it was this guise he used when entering the home of Judy X, a Conservative Party activist on 21 May 1992. Posing as a priest who wished to donate money to the party, he came in and sexually assaulted her as well as beating her with a fireplace poker. Arrested shortly afterwards, his trial was brief, in August 1992, having been called by the Scottish High Court a "Walter Mitty gone mad", Cronin was sentenced to life in prison for the crime. A December 1992 appeal resulted in a six-year prison sentence. Shortly after release from prison in 1997, he was jailed again, this time for making harassing phone calls and threats to various female politicians. By May 2005, he had been jailed on various charges from petty theft to fraud to bank robbery in 2001. Cronin was bullied by other prisoners whilst serving a two-year sentence in Ireland's Cork Prison for the bank robbery, spending much of the time in voluntary solitary confinement.

He was arrested for petty theft only hours after his release. In August 2007 he ran up a \$20,500 bill at the exclusive Operakällaren restaurant in Stockholm, Sweden, he ordered a three course meal, with a different bottle of wine for each course. When presented with the bill, he told waiters that he could not pay it, asked them to call the police, he was sentenced to four months jail to be served in Sweden, after which he was deported, banned from re-entering Sweden for 5 years. He was considered enough of a threat that the East Lothian Police set up a special unit to deal with tracking Cronin. From the earliest points of childhood, Cronin had been involved with mental health specialists. At the age of four, he was sent to a child psychologist who wrote that from the beginning, "it was clear he was not one of us." Two years at age five, he was referred to the family psychiatry department of the Royal Hospital for Sick Children, where he was considered to be aggressive and mercurial. Cronin's school years expanded his psychiatric profile, with numerous instances of disruptive behaviour, most notably a 1987 incident when he was interned for a night at a psychiatric hospital in Edinburgh, after threatening to burn down a homeless shelter.

In the case of the hospital stay, he became agitated and threw faeces at a nurse. Robert Waite, a psychiatrist who assessed Cronin in the wake of his first offence, found marked discrepancies in Cronin's intellectual abilities. Cronin had revealed to Waite that he had felt suicidal while serving his sentence for the initial assault. Waite concluded: "It is clear he has a severe disorder of his personality, which has grossly interfered with his social adjustment and might be expected to do so for some considerable time." During his discussions with the social worker, Cronin was said to be defiant and arrogant, interested in politics and expressing admiration for Nazism and dictatorship

Beth Cullen-Kerridge is an English sculptor. Cullen-Kerridge was born in Stoke on Trent to Judith Vincent, a businesswoman, James Cullen, a painter, she attended the Royal College of Art. In 1994, she became the first artist to be presented with the commission for the Napoleon Garden Sculpture exhibition in Holland Park, her work was subsequently shown in two of the London Parks. Her work has been shown in exhibitions England including specifically-made sculptures for her home town of Stoke on Trent, she has worked as an assistant in foundries producing works for Eduardo Paolozzi, Elisabeth Frink, Alberto Giacometti and Sir Anthony Caro. In 2004 Cullen-Kerridge moved to Norfolk to work on property renovation. A year she moved to Marlow in Buckinghamshire to develop and open a gastropub, The Hand and Flowers with her husband, chef Tom Kerridge, they were able to purchase the pub with the help of money she had received for a sculpture commission for a roundabout in Stoke. She subsequently gave up producing sculpture for a number of years.

Cullen-Kerridge travelled to Carrara in 2010. She had an exhibition at Hoxton Arches, East London, in 2014. Works included a formal shirt on a crucifix called "Hung out to Dry", her sculptures include a shirt torso with a shark fin protruding from the back. She exhibited at Gallery Different in Percy Street, London in Oct 2015. Official website

There are many institutions and fellowships in the Philippines that hands out awards and recognitions to outstanding film achievements for a certain calendar year. The Maria Clara Awards was established in 1950 by The Manila Times. However, it was criticized for being judged only by movie outsiders. In response, a group of writers established the Filipino Academy of Movie Arts and Sciences Awards in 1952. In 1975, the first Metropolitan Film Festival was held in commemoration of the third anniversary of the continuation of Martial Law. From 1952 to 1976, the FAMAS was the sole award-giving body for film in the Philippines. On May 1, 1976, a group of nine film critics and writers formed the Manunuri ng Pelikulang Pilipino, an organization aiming at giving recognition to Filipino film achievements through the eyes of a film critic; the MPP formed the Gawad Urian Awards, the first award-giving body to contest the long-reigning FAMAS Awards. The Gawad Urian gave a Philippine equivalent to the New York Film Critics Circle Awards.

This organization was created after the first tie in lead categories was recorded in 21st FAMAS Awards in 1973. It was in the Best Actress category, in which both Boots Vilma Santos won. In 1977, the Metropolitan Film Festival was changed to Metro Manila Film Festival. During the commercialist era of movies in the 1980s, more award-giving bodies have sprung up to honor film achievements. In 1981, President Ferdinand Marcos passed Executive Order 640-A, which established the Film Academy of the Philippines, the Philippines' official counterpart of the United States' Academy of Motion Picture Arts and Sciences; the FAP handed out the first Luna Awards in 1983 to honor film achievements in 1982. In addition, the Catholic Church established the Catholic Mass Media Awards. In 1985, the Philippine Movie Press Club initiated the Star Awards for Movies and Television, the Philippines' Golden Globes' counterpart. Under the auspices of First Lady Imelda Marcos, the first Filipino international film festival was held in 1982: the Manila International Film Festival.

This prestigious festival opened at the Manila Film Center. During the 1980s, the term grand slam became popular; the Philippine grand slam is an unofficial moniker given to an actor or actress who had won the following awards: FAMAS Awards, Gawad Urian, CMMA and FAP Awards in one year. CMMA though stopped giving acting awards by 1990 while Star Awards started giving their awards in 1985; the moniker was first earned by actress Vilma Santos in 1983 when she won the FAMAS, Gawad Urian, CMMA and FAP Awards for her performance in the Ishmael Bernal film Relasyon. The number of film award-giving bodies in the Philippines grew beginning in the 1990s. Several university scholars and teachers formed their own awards, beginning with the Young Critics Circle in 1990, with members coming from various disciplines of the country's top universities. Gawad Pasado and Gawad Tanglaw followed suit in 2002, respectively. In 2003, several members of the PMPC formed a breakaway group called the Entertainment Press Society and started handing out awards - the Golden Screen Awards - in 2004.

FAMAS Awards Gawad Urian Luna Awards PMPC Star Award for Movies Young Critics Circle Film Desk Awards Gawad PASADO Backronym meaning: To pass Gawad TANGLAW Backronym meaning: light Gawad Genio Awards The EDDYS or The Entertainment Editors' Choice Awards Metro Manila Film Festival Cinemalaya Philippine Independent Film Festival Cinema One Originals QCinema International Film Festival Sinag Maynila Film Festival Pista ng Pelikulang Pilipino Cinemanila International Film Festival Sineng Pambansa CineFilipino Film Festival ToFarm Film Festival Maria Clara Awards Catholic Mass Media Awards Manila International Film Festival Golden Screen Awards - breakaway group from PMPC Cinemalaya Philippine Independent Film Festival - official website Cinemanila International Film Festival - official website Filipino Academy of Movie Arts and Sciences - official website Film Academy of the Philippines - official website Manunuri ng Pelikulang Pilipino - official website Metro Manila Film Festival - official website Young Critics Circle Film Desk - official blog

Sarenput I was an ancient Egyptian official during the reign of pharaoh Senusret I of the 12th Dynasty. Sarenput held several titles such as nomarch of the 1st nomos of Upper Egypt, mayor of Elephantine, overseer of the priests of Satet, overseer of the foreign lands and many others. Like his distant predecessors Harkhuf and Heqaib, he was the king's personal trading agent for the goods from Nubia and had a role in one of Senusret I's military campaign in this country, when the king rewarded Sarenput as reported in the latter's autobiography from his tomb; the same king appointed Sarenput as nomarch the first one for this nomos. Many of Sarenput's attestations came from the sanctuary of Heqaib at Elephantine, where he ordered a shrine for the deified Heqaib and one for himself, provided by many stelae and a statue depicting him. Sarenput I was buried in a large rock-cut tomb at Qubbet el-Hawa, decorated in sunk reliefs at the outside, lively painted in the interior; the tomb is composed of three rooms connected by hallways.

The whole tomb suffered significant damage over time. The outer reliefs depicts Sarenput with some of his relatives and his dogs, while among the survived inner paintings there is a scene of the owner with the god Khnum, significant because in this period, a similar scene in a private tomb was still rare; the aforementioned autobiography is written in one inside the tomb. There is a significant artistic contrast between the reliefs carved on the outer doorjambs and the ones on the façade of the tomb, the former being far finer and made by some royal sculptor, while the latter being more crude and a local product. Sarenput II – His nephew a nomarch of the same nomos Labib Habachi, The Sanctuary of Heqaib. 2 voll, von Zabern, Mainz 1985, ISBN 3-8053-0496-X