George Stubbs

George Stubbs was an English painter, best known for his paintings of horses. Self-trained, Stubbs learnt his skills independently from other great artists of the eighteenth century such as Reynolds or Gainsborough. Stubbs' output includes history paintings, but his greatest skill was in painting animals influenced by his love and study of anatomy, his most famous painting, hangs in the National Gallery, London. Stubbs was born in Liverpool, the son of a currier, or leather-dresser, John Stubbs, his wife Mary. Information on his life until the age of 35 or so is sparse, relying entirely on notes made by Ozias Humphry, a fellow artist and friend. Stubbs worked at his father's trade until the age of 15 or 16, at which point he told his father that he wished to become a painter. While resistant, Stubbs's father acquiesced in his son's choice of a career path, on the condition that he could find an appropriate mentor. Stubbs subsequently approached the Lancashire painter and engraver Hamlet Winstanley, was engaged by him in a sort of apprenticeship relationship not more than several weeks in duration.

Having demonstrated his abilities and agreed to do some copying work, Stubbs had access to and opportunity to study the collection at Knowsley Hall near Liverpool, the estate where Winstanley was residing. Thereafter as an artist he was self-taught, he had had a passion for anatomy from his childhood, in or around 1744, he moved to York, in the North of England, to pursue his ambition to study the subject under experts. In York, from 1745 to 1753, he worked as a portrait painter, studied human anatomy under the surgeon Charles Atkinson, at York County Hospital, One of his earliest surviving works is a set of illustrations for a textbook on midwifery by John Burton, Essay towards a Complete New System of Midwifery, published in 1751. In 1754 Stubbs visited Italy. Forty years he told Ozias Humphry that his motive for going to Italy was, "to convince himself that nature was and is always superior to art whether Greek or Roman, having renewed this conviction he resolved upon returning home". In 1756 he rented a farmhouse in the village of Horkstow and spent 18 months dissecting horses, assisted by his common-law wife, Mary Spencer.

He moved in 1766 published The anatomy of the Horse. The original drawings are now in the collection of the Royal Academy. Before his book was published, Stubbs's drawings were seen by leading aristocratic patrons, who recognised that his work was more accurate than that of earlier horse painters such as James Seymour, Peter Tillemans and John Wootton. In 1759 the 3rd Duke of Richmond commissioned three large pictures from him, his career was soon secure. By 1763 he had produced works for several more dukes and other lords and was able to buy a house in Marylebone, a fashionable part of London, where he lived for the rest of his life, his most famous work is Whistlejacket, a painting of the thoroughbred race horse rising on his hind legs, commissioned by the 2nd Marquess of Rockingham, now in the National Gallery in London. This and two other paintings carried out for Rockingham break with convention in having plain backgrounds. Throughout the 1760s he produced a wide range of individual and group portraits of horses, sometimes accompanied by hounds.

He painted horses with their grooms, whom he always painted as individuals. Meanwhile, he continued to accept commissions for portraits of people, including some group portraits. From 1761 to 1776 he exhibited at the Society of Artists of Great Britain, but in 1775 he switched his allegiance to the founded but more prestigious Royal Academy of Arts. Stubbs painted more exotic animals including lions, giraffes and rhinoceroses, which he was able to observe in private menageries, his painting of a kangaroo was the first glimpse of this animal for many 18th-century Britons. He became preoccupied with the theme of a wild horse threatened by a lion and produced several variations on this theme; these and other works became well known at the time through engravings of Stubbs's work, which appeared in increasing numbers in the 1770s and 1780s. Stubbs painted historical pictures, but these are much less well regarded. From the late 1760s he produced some work on enamel. In the 1770s Josiah Wedgwood developed a new and larger type of enamel panel at Stubbs's request.

Stubbs hoped to achieve commercial success with his paintings in enamel, but the venture left him in debt. In the 1770s he painted single portraits of dogs for the first time, while receiving an increasing number of commissions to paint hunts with their packs of hounds, he remained active into his old age. In the 1780s he produced a pastoral series called Haymakers and Reapers, in the early 1790s he enjoyed the patronage of the Prince of Wales, whom he painted on horseback in 1791, his last project, begun in 1795, was A comparative anatomical exposition of the structure of the human body with that of a tiger and a common fowl, fifteen engravings from which appeared between 1804 and 1806. The project was left unfinished in London, he was buried in the graveyard of Marylebone Church, now a public garden. Stubbs's son George Townly Stubbs was an printmaker. Stubbs remained

De Morgan algebra

In mathematics, a De Morgan algebra is a structure A = such that: is a bounded distributive lattice, ¬ is a De Morgan involution: ¬ = ¬x ∨ ¬y and ¬¬x = x. In a De Morgan algebra, the laws ¬x ∨ x = 1, ¬x ∧ x = 0 do not always hold. In the presence of the De Morgan laws, either law implies the other, an algebra which satisfies them becomes a Boolean algebra. Remark: It follows that ¬ = ¬x ∧ ¬y, ¬1 = 0 and ¬0 = 1, thus ¬ is a dual automorphism. If the lattice is defined in terms of the order instead, i.e. is a bounded partial order with a least upper bound and greatest lower bound for every pair of elements, the meet and join operations so defined satisfy the distributive law the complementation can be defined as an involutive anti-automorphism, that is, a structure A = such that: is a bounded distributive lattice, ¬¬x = x, x ≤ y → ¬y ≤ ¬x. De Morgan algebras were introduced by Grigore Moisil around 1935. Although without the restriction of having a 0 and a 1, they were variously called quasi-boolean algebras in the Polish school, e.g. by Rasiowa and distributive i-lattices by J. A. Kalman.

They have been further studied in the Argentinian algebraic logic school of Antonio Monteiro. De Morgan algebras are important for the study of the mathematical aspects of fuzzy logic; the standard fuzzy algebra F = is an example of a De Morgan algebra where the laws of excluded middle and noncontradiction do not hold. Another example is Dunn's 4-valued logic, in which false < neither-true-nor-false < true and false < both-true-and-false < true, while neither-true-nor-false and both-true-and-false are not comparable. If a De Morgan algebra additionally satisfies x ∧ ¬x ≤ y ∨ ¬y, it is called a Kleene algebra; this notion has been called a normal i-lattice by Kalman. Examples of Kleene algebras in the sense defined above include: lattice-ordered groups, Post algebras and Łukasiewicz algebras. Boolean algebras meet this definition of Kleene algebra; the simplest Kleene algebra, not Boolean is Kleene's three-valued logic K3. K3 made its first appearance in Kleene's On notation for ordinal numbers.

The algebra was named after Kleene by Monteiro. De Morgan algebras are not the only plausible way to generalize Boolean algebras. Another way is to keep ¬x ∧ x = 0 but to drop the law of the excluded middle and the law of double negation; this approach is well-defined for a semilattice. If the pseudocomplement satisfies the law of the excluded middle, the resulting algebra is Boolean. However, if only the weaker law ¬x ∨ ¬¬x = 1 is required, this results in Stone algebras. More both De Morgan and Stone algebras are proper subclasses of Ockham algebras. Orthocomplemented lattice Balbes, Raymond. "Chapter IX. De Morgan Algebras and Lukasiewicz Algebras". Distributive lattices. University of Missouri Press. ISBN 978-0-8262-0163-8. Birkhoff, G.. "Reviews: Moisil Gr. C.. Recherches sur l'algèbre de la logique. Annales scientifiques de l'Université de Jassy, vol. 22, pp. 1–118". The Journal of Symbolic Logic. 1: 63. Doi:10.2307/2268551. JSTOR 2268551. Batyrshin, I. Z.. "On fuzzinesstic measures of entropy on Kleene algebras".

Fuzzy Sets and Systems. 34: 47–60. Doi:10.1016/0165-011490126-Q. Kalman, J. A.. "Lattices with involution". Transactions of the American Mathematical Society. 87: 485–491. Doi:10.1090/S0002-9947-1958-0095135-X. JSTOR 1993112. Pagliani, Piero. A Geometry of Approximation: Rough Set Theory: Logic and Topology of Conceptual Patterns. Springer Science & Business Media. Part II. Chapter 6. Basic Logico-Algebraic Structures, pp. 193-210. ISBN 978-1-4020-8622-9. Cattaneo, G.. Lattices with Interior and Closure Operators and Abstract Approximation Spaces. Lecture Notes in Computer Science 67–116. Doi:10.1007/978-3-642-03281-3_3. Gehrke, M.. "Fuzzy Logics Arising From Strict De Morgan Systems". In Rodabaugh, S. E.. Topological and Algebraic Structures in Fuzzy Sets: A Handbook of Recent Developments in the Mathematics of Fuzzy Sets. Springer. ISBN 978-1-4020-1515-1. Dalla Chiara, Maria Luisa. Reasoning in Quantum Theory: Sharp and Unsharp Quantum Logics. Springer. ISBN 978-1-4020-1978-4

Limited-run series

In television programming, limited-run series is a program with an end date and limit to the number of episodes each stated by release of the first episode. For instance, The Academy of Television Arts & Sciences' definition specifies a "program with two or more episodes with a total running time of at least 150 program minutes that tells a complete, non-recurring story, does not have an on-going storyline and/or main characters in subsequent seasons." Limited-run series are represented in the form of telenovelas in Latin America, serials in the United Kingdom. The shortest forms of limited-run series have two- or three-part described as "made for television film" or miniseries. Limited-run series with greater than 5 episodes do not have main characters recurring between seasons or a storyline that spans seasons. Series with 5 episodes or fewer per season—such as the BBC/Masterpiece coproduction Sherlock—also are considered limited series due to their short run if main characters and story lines do travel across seasons.

Series with a limited eight-to-twelve episode run are ordered to fill television networks' gap in midseason. Limited series differ from miniseries as the production has the potential to be renewed without a required number of episodes as a typical order per season. Under the Dome, Killer Women, Luther were marketed as limited series. Individual season-length stories of anthology series such as American Horror Story and True Detective are described as "limited series," which the Primetime Emmys have changed to their miniseries/limited series category to accommodate. Actors may choose to take part in limited-run series because their set start and end dates make scheduling other projects easier. In 2015, The Academy of Television Arts & Sciences changed its guidelines on how Emmy nominees are classified, with shows with a limited run all referred to as "limited series" instead of "miniseries." This is a reversion back to 1974 when the category was named "outstanding limited series." It had been changed to "outstanding miniseries" in 1986, added to the "made for television films" category in 2011.

Miniseries were brought back out in 2014, accommodating such limited series as HBO’s Olive Kitteridge, History’s Texas Rising, IFC’s The Honorable Woman and PBS’ Wolf Hall, TV movies such as HBO’s Bessie and National Geographic’s Killing Jesus. Short term reality television like Bravo's Eat, Love, scripted dramas like Netflix's Black Mirror, individual seasons of anthology series are examples of limited-run series that appear on American television networks. In the 1950s, telenovelas emerged as Latin limited series; these low-budget Spanish and Portuguese shows were modeled after American soap operas in style and form. These programs follow a story arc that ends at the end of a season, with the possibility of renewal for subsequent seasons. In British television, the term "serial" is used instead of "miniseries." Like telenovelas, these programs are stand-alone dramas, with a conclusion at the last episode of the season. Miniseries Television film Serial Telenovela