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Nonlinear programming

In mathematics, nonlinear programming is the process of solving an optimization problem where some of the constraints or the objective function are nonlinear. An optimization problem is one of calculation of the extrema of an objective function over a set of unknown real variables and conditional to the satisfaction of a system of equalities and inequalities, collectively termed constraints, it is the sub-field of mathematical optimization. A typical non-convex problem is that of optimizing transportation costs by selection from a set of transportation methods, one or more of which exhibit economies of scale, with various connectivities and capacity constraints. An example would be petroleum product transport given a selection or combination of pipeline, rail tanker, road tanker, river barge, or coastal tankship. Owing to economic batch size the cost functions may have discontinuities in addition to smooth changes. In experimental science, some simple data analysis can be done with linear methods, but in general these problems are nonlinear.

One has a theoretical model of the system under study with variable parameters in it and a model the experiment or experiments, which may have unknown parameters. One tries to find a best fit numerically. In this case one wants a measure of the precision of the result, as well as the best fit itself. Let n, m, p be positive integers. Let X be a subset of Rn, let f, gi, hj be real-valued functions on X for each i in and each j in, with at least one of f, gi, hj being nonlinear. A nonlinear minimization problem is an optimization problem of the form minimize f subject to g i ≤ 0 for each i ∈ h j = 0 for each j ∈ x ∈ X. A nonlinear maximization problem is defined in a similar way. There are several possibilities for the nature of the constraint set known as the feasible set or feasible region. An infeasible problem is one for which no set of values for the choice variables satisfies all the constraints; that is, the constraints are mutually contradictory, no solution exists. A feasible problem is one for which there exists at least one set of values for the choice variables satisfying all the constraints.

An unbounded problem is a feasible problem for which the objective function can be made to be better than any given finite value. Thus there is no optimal solution, because there is always a feasible solution that gives a better objective function value than does any given proposed solution. If the objective function f is linear and the constrained space is a polytope, the problem is a linear programming problem, which may be solved using well-known linear programming techniques such as the simplex method. If the objective function is concave, or convex and the constraint set is convex the program is called convex and general methods from convex optimization can be used in most cases. If the objective function is quadratic and the constraints are linear, quadratic programming techniques are used. If the objective function is a ratio of a concave and a convex function and the constraints are convex the problem can be transformed to a convex optimization problem using fractional programming techniques.

Several methods are available for solving nonconvex problems. One approach is to use special formulations of linear programming problems. Another method involves the use of branch and bound techniques, where the program is divided into subclasses to be solved with convex or linear approximations that form a lower bound on the overall cost within the subdivision. With subsequent divisions, at some point an actual solution will be obtained whose cost is equal to the best lower bound obtained for any of the approximate solutions; this solution is optimal, although not unique. The algorithm may be stopped early, with the assurance that the best possible solution is within a tolerance from the best point found. Terminating to ε-optimal points is necessary to ensure finite termination; this is useful for large, difficult problems and problems with uncertain costs or values where the uncertainty can be estimated with an appropriate reliability estimation. Under differentiability and constraint qualifications, the Karush–Kuhn–Tucker conditions provide necessary conditions for a solution to be optimal.

Under convexity, these conditions are sufficient. If some of the functions are non-differentiable, subdifferential versions of Karush–Kuhn–Tucker conditions are available. A simple problem

Thai temple art and architecture

Thai temple art and architecture is the art and architecture of Buddhist temples in Thailand. Temples are known as wat’s, from the Pāḷi vāṭa, meaning "enclosure." A temple has an enclosing wall. Wat architecture adheres to consistent principles. A wat, with few exceptions, consists of two parts: the Sangkhawat; the Phutthawat is the area, dedicated to Buddha. It contains several buildings: Chedi – known as a Stupa it is in the form of a bell-shaped tower accessible and covered with gold leaf, containing a relic chamber. Prang – the Thai version of Khmer temple towers in temples from the Sukhothai and the Ayutthaya period. Ubosot or Bot – the ordination hall and most sacred area of a wat. Eight Sema stones mark the consecrated area. Wihan – a shrine hall that contains the principal Buddha images, it is the assembly hall. Mondop - specific square- or cruciform-based building or shrine, sometimes with a spired roof, it is a ceremonial form. It can act as a shrine. Unlike the Mandapa of Khmer or Indian temple, which are part of a larger structure, the Thai Mondop is free-standing.

Ho trai – the temple library or scriptures depository houses the sacred Tipiṭaka scriptures. Sometimes they are built in the form of a Mondop, a cubical-shaped building where the pyramidal roof is carried by columns. Sala – an open pavilion providing shade and a place to rest. Sala kan parian – a large, open hall where laity can hear sermons or receive religious education, it means "hall, in which monks study for their Parian exam" and is used for chanting afternoon prayers. Ho rakhang – bell tower, used for waking the monks and to announce the morning and evening ceremonies. Phra rabiang – a peristyle sometimes built around the sacred inner area as a cloister. Ancillary buildings such as a crematorium or a school; the buildings are adorned with elements such as chofas. In temples of the Rattanakosin era, such as Wat Pho and Wat Ratchabophit, the ubosot can be contained within a inner wall called a Kamphaeng Kaeo, which translates to "crystal wall"; the sangkhawat contains the monks' living quarters.

It lies within the wall surrounding the temple compound. The sangkhawat can have the following buildings: Kuti – a small structure, built on stilts, designed to house a monk, with its proper size defined in the Sangkhathiset, rule 6, to be 12 by 7 kheup. Modern kutis take the shape of an apartment building with small rooms; the sangkhawat can contain the'Ho rakhang' and the'Sala Kan Parian'. Houses most of the functional buildings such as the kitchen. Temples display multiple roof tiers; the use of ornamented tiers is reserved for roofs on temples and important public buildings. Two or three tiers are most used, but some royal temples have four; the practice is more aesthetic than functional. Temple halls and their roofs are large. To lighten the roof's appearance, the lowest tier is the largest with a smaller middle layer and the smallest tier on top. Multiple breaks in each roof lighten it further – a double-tiered roof might have 2-4 breaks in each tier; the tiers and tier patterns create dynamic visual rhythms.

In northern temples, the roof area is sweeping low to cover more of the wall. The lower tiers telescope toward the entrance. In a central Thai temple, the lower tiers reach a short distance beyond the top roof at the gable ends. Most decorations are attached to the bargeboard, the long, thin panel on the edge of the roof at the gable ends; the decorative structure is called the lamyong. The lamyong is sculpted in an undulating, serpentine nag sadung shape evoking the Nāga, its blade-like projection called bai raka suggest the feathers of Garuda. Its lower finial is called a hang hong, which takes the form of a Nāga's head turned up and facing away from the roof; the Nāga head may have multiple heads. A roof with multiple breaks or tiers has identical hang hong finials at the bottom of each section. Perched on the peak of the lamyong is the large curving ornament called a Chofah, which resembles the beak of a bird representing Garuda. Thai Theravada Buddhism and Hindu cultures merged, Hindu elements were introduced into Thai iconography.

Popular figures include the four-armed figure of Vishnu. Development of the Buddha image in Thailand Iconography of Gautama Buddha in Laos and Thailand Characteristics of a Thai Buddha Apsara Erawan Ganesh Garuda Hanuman Indra Kinnara Kirtimukha Makara Nāga Rama Ravana Shiva Vishnu Yaksha Chofa Buddhism in Thailand List of Buddhist temples in Thailand Thai art Ramakien Sumeru Himavanta Discovery Channel by Scott Rutherford, "Insight Guides: Thailand.", APA Publications GmbH & Co. 2004. Discovery Channel by Steve Van Beek, "Insight Pocket Guide: Thailand.", APA Publications GmbH & Co. 2004. Maria Grazia Casella and Paola Piacco, "Thailand: Nature and Wonders.", Asia Books Co. Ltd. 2004. John Hoskin and Gerald Cubitt, "This is Thailand.", Asia Books Co. Ltd. 2003 Karl Döhring, Buddhist Temples of Thailand: an Architectonic Introduction, White Lotus, 2000. ISBN 974-7534-40-1 Wat Thai: Dhammathai Thai Ar

The Members

The Members are a British punk band that originated in Camberley, England. In the UK, they are best known for their single "The Sound of the Suburbs", reaching No. 12 in 1979, in Australia, "Radio" which reached No. 5 in 1982. The Members were formed by lyricist Nicky Tesco in 1976, through an invited audition at a recording studio at Tooley Street, London; the original personnel, with Tesco, was Gary Baker, Steve Morley with Steve Maycock Clive Parker. Morley and Parker were replaced by Chris Payne and Adrian Lillywhite. In 1976, the band performed for its first engagements at The Red Cow, The Windsor Castle and The Nashville Rooms. In that year composer Jean Marie Carroll joined the band to complement Tesco's lyrics; the Members had recorded a number of songs, but the first released recording was "Fear on the Streets", produced by Lillywhite's brother Steve Lillywhite. This song was included on the first record released by the Beggars Banquet label, the punk compilation Streets; the song-writing collaboration between Tesco and Carroll moved The Members' sound towards an incorporation of reggae, shown in the first single released for Stiff Records, "Solitary Confinement", produced by Larry Wallis.

Following these releases, band personnel became Tesco, Nigel Bennett and Lillywhite. In 1978/79 The Members continued to play the London pub and club circuit, became a feature in the music press and were championed by John Peel, they signed to Virgin Records in 1978, for which label they recorded "The Sound of the Suburbs", again produced by Steve Lillywhite. This became The Members' biggest chart success and their best-known song in the UK; the follow-up single, "Offshore Banking Business", a reggae tune written by Carroll based on his experiences working in offshore banking at the private bank Coutts, did not achieve the same popularity. A version of "Offshore Banking Business" was recorded for the early 1980s film Urgh! A Music War, produced by Michael White, distributed by Lorimar Productions; the Members' first album, At the Chelsea Nightclub, was followed by a second for Virgin, 1980 – The Choice Is Yours. Augmented by saxophonists Steve Thomson and Simon Lloyd, the group recorded what would turn out to be their final album.

This last album was first issued in the US as Uprhythm, Downbeat in 1982, it surfaced in the UK a year retitled Going West. The album featured the singles "Radio," which made the Top 10 in parts of Australia, "Working Girl," the music video for which gave the band exposure in North America via MTV; the band broke up in 1983, when Tesco left the band after the last tour of the US. Lillywhite went on to join the band King in the mid-1980s in time for their second album. Lloyd soon joined the Australian band Icehouse, remaining with them for their international smash hits "Electric Blue" and "Crazy." In 1989, Tesco appeared in Leningrad Cowboys Go America and directed by Aki Kaurismäki, a film about a fictional Russian rock band touring the US. This fictional band toured as an actual band, recorded the Tesco song "Thru the Wire". Kaurismäki directed a video for "Thru the Wire"; as well as working as a music journalist for the magazine Music Week, Tesco has been a commentator on new releases for BBC 6 Music's "Roundtable".

In 2007, The Members were reunited at The Inn on Ladbroke Grove, London. In 2008, a line up of Carroll and Nick Cash resumed touring, In 2009 a new single "International Financial Crisis" was released, recorded by Tesco, Carroll and Bennett, with artwork by the original Members' album sleeve designer, Malcolm Garrett; this line up played Isle of Wight festivals. The Members line-up of Carroll and Rat Scabies performed from 2010 to 2013, playing over 90 Shows including 3 European Tours and New Zealand and Australian Tours, Nick Cash rejoined the Band in 2014. In March 2012, the Members released their fourth studio album, InGrrLand, featuring Carroll, Bennett and Rat Scabies. in December 2013 Nigel Bennett rejoined the Members. In 2014 The Members mounted a coast-to-coast tour of the US, without Payne's temporary replacement Calle Engelmarc who had injured his hand. Instead, JC Carroll played bass; this was the band's first tour of the US for 32 years. In 2015, the band began work on their fifth studio album in studios in London and West Byfleet featuring a nucleus of Carroll, Cash and Bennett together with guest appearances from Guy Pratt and former Jam guitarist Steve Brookes.

One Law, released in early 2016, was produced by Carroll, received reviews in Record Collector, Vive Le Rock, Louder Than War, The Aberdeen Voice. Streets The Moonlight Tapes The Sound of the Suburbs The Members Official YouTube Channel The Members web site Nick Tesco music review blog. Review of The Members in Sacramento 2014 Record Collector Article September 2015 J C Carroll Official Site Nicky Tesco filmography Nick Cash: a bio Nick Tesco biographical videos

Jacksons Fencing

Jacksons fencing is a British fencing manufacturing company based in Stowting Common near Ashford in Kent. The company employs over 250 staff, was established in 1947 by Harold Sands Jackson and his son Ian Jackson who began selling chestnut stakes and agricultural fencing to local farmers. In April 2010, the company became the first to have a timber security fence system certified by Loss Prevention Certification Board when its Jakoustic Class 3 system was certified to LPS 1175 Security Rating 3, it went onto develop security fencing systems in steel and novel timber and steel combinations with LPCB LPS 1175 security ratings covering SR1 to SR5. LPCB LPS 1175 SR5 is the highest security rating attained by a fencing system and is held by Jacksons Trident 5 system. In 2016 the company reported an increase in pre-tax profits following the win of the Eurotunnel contract to supply and install security fencing and gate upgrades around the terminal's perimeter in Coquelles, France. In June 2017 The Sunday Times featured the organisation in their International Track 200 League Table for its involvement in the Eurotunnel project and projects in Russia.

In May 2018, the company announced its successful transition to the most up to date international quality management standard ISO 9001:2015. Headed by Peter Jackson since October 2014, the company remains in private, family ownership and serves both consumers<ref>"Jacksons Fencing Venetian". Retrieved 12 August 2018

Theron Lyman

Theron Upson "Tule" Lyman was a college football player and coach. He was the chief examiners of claims of the Travelers Life Insurance Company of Hartford, Connecticut. Theron Upson Lyman was born September 1869 in Alden, Iowa, his father C. N. Lyman was a long-time reverend of Onawa, it is said. Lyman played for Iowa College, in Grinnell, Iowa from 1888 to 1891, he was the coach of the team as well in addition to coaching Nebraska. One account reads "Iowa had an eleven and had a coach, wanted to play the upstarts from across the Missouri River... So, with a magnanimity equaled in the game's history, Iowa lent its coach, T. U. Lyman, to tutor the Nebraskans." Lyman was a prominent quarterback for the Wisconsin Badgers football team. He was captain every year. Parke H. Davis was coach in 1893. Lyman transferred to Wisconsin in order to defeat Minnesota, which he did in 1894. *Lyman was coach for preparing Nebraska for the game against Iowa only. Minnesota–Wisconsin football rivalry Theron Lyman at Find a Grave

Sinope Gospels

The Sinope Gospels, designated by O or 023, ε 21 known as the Codex Sinopensis, is a fragment of a 6th-century illuminated Greek Gospel Book. Along with the Rossano Gospels, the Sinope Gospels has been dated, on the basis of the style of the miniatures, to the mid 6th-century; the Rossano Gospels, however are considered to be earlier. Like Rossanensis and the Vienna Genesis, the Sinope Gospels are written on purple dyed vellum. There are only 44 extant folios in the Sinope Gospels; these folios carry unframed miniatures at the bottom of the page which are similar in style to the miniatures in the Rossano Gospels. The folios measure 30 cm by 25 cm, it is written in one column per page, 15 lines per column, in silver gold. It is written in large uncial letters; the manuscript is lacunose. Contents Matthew 7:7-22, it contains five illuminated miniatures: the festival of Herod and death of John the Baptist five thousand fed four thousand fed the healing of a blind man from Jericho the cursing of the fig tree.

It was written in the 6th-century. The style of illustrations suggests Palestine as the place of its origin; the codex was purchased in 1899 by a French officer from an old Greek woman. Its text was published by Henri Omont in 1901. At least one authority has suggested this manuscript has an association with a church at Çiftlik, under archeological excavation in 1998. According to B. H. Streeter it is a tertiary witness of the Caesarean text-type; this opinion was supported by Bruce Metzger. Aland placed it in Category V, which means the Byzantine text-type.43 leaves of the codex now are located at the Bibliothèque Nationale of the Manuscrits occidentaux at Paris. List of New Testament uncials H. Omont, Notice sur un très ancien manuscrit grec de l'évangile de saint Matthieu... Notices et extraits des manuscrits de la bibliothèque nationale... vol. 36, pp. 599–676. H. S. Cronin, Codex Chrysopurpureus Sinopensis, JTS II, pp. 590–600. A. Munoz, Il codice purpureo di Rossano e il frammento sinopense C. R. Gregory, Textkritik des Neuen Testaments, vol.

3, pp. 1022–1023. Petra Sevrugian, Der Rossano-Codex und die Sinope-Fragmente: Miniaturen und Theologie Weitzmann, Kurt, ed. Age of spirituality: late antique and early Christian art, third to seventh century, no. 442, 1979, Metropolitan Museum of Art, New York, ISBN 9780870991790 BnF Archives et manuscrits: Supplément grec 1286 image from Bibliothèque Nationale L'aventure des écritures website