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James Stirling (mathematician)
James Stirling (11 May O.S. 1692, Garden, Stirlingshire – 5 December 1770, Edinburgh) was a Scottish mathematician. He was nicknamed "The Venetian". The Stirling numbers, Stirling permutations, and Stirling's approximation are named after him. He also proved the correctness of Isaac Newton's classification of cubics. Biography Stirling was born on 11 May 1692 O.S. at Garden House near Stirling, the third son of Archibald Stirling, Lord Garden. At 18 years of age he went to Balliol College, Oxford, where, chiefly through the influence of the Earl of Mar, he was nominated in 1711 to be one of Bishop Warner's exhibitioners (or Snell exhibitioner) at Balliol. In 1715 he was expelled on account of his correspondence with his cousins, who were members of the Keir and Garden families, who were noted Jacobites, and had been accessory to the " Gathering of the Brig o' Turk" in 1708. From Oxford he made his way to Venice, where he occupied himself as a professor of mathematics. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Old Style And New Style Dates
Old Style (O.S.) and New Style (N.S.) indicate dating systems before and after a calendar change, respectively. Usually, this is the change from the Julian calendar to the Gregorian calendar as enacted in various European countries between 1582 and 1923. In England, Wales, Ireland and Britain's American colonies, there were two calendar changes, both in 1752. The first adjusted the start of a new year from Lady Day (25 March) to 1 January (which Scotland had done from 1600), while the second discarded the Julian calendar in favour of the Gregorian calendar, removing 11 days from the September 1752 calendar to do so.Spathaky, MikOld Style and New Style Dates and the change to the Gregorian Calendar "Before 1752, parish registers, in addition to a new year heading after 24th March showing, for example '1733', had another heading at the end of the following December indicating '1733/4'. This showed where the Historical Year 1734 started even though the Civil Year 1733 continued ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Snell Exhibitioner
The Snell Exhibition is an annual scholarship awarded to students of the University of Glasgow to allow them to undertake postgraduate study at Balliol College, Oxford. The award was founded by the bequest of Sir John Snell in a will made in 1677, although the original stipulation referred to the University of Oxford, rather than Balliol in particular. Snell died on 6 August 1679, but wrangling over the will meant that it was nearly twenty years before the first scholarships were awarded; the first four Snell Exhibitioners were admitted to Balliol in mid-1699. Snell had been a Royalist in the Civil War, and was later secretary to the Duke of Monmouth and had the management of his Scottish estates. He intended the bequest to be used to educate Scottish clergymen for the then-established Scottish Episcopal Church. By Adam Smith's day, the bequest was mostly regarded as an educational charity, though its exact status was not settled until later. "By the will of John Snell his ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stirling - Methodus Differentialis, Sive Tractatus De Summatione Et Interpolatione Serierum Infinitarum, 1764 - 739821
Stirling (; sco, Stirlin; gd, Sruighlea ) is a city in central Scotland, northeast of Glasgow and north-west of Edinburgh. The market town, surrounded by rich farmland, grew up connecting the royal citadel, the medieval old town with its merchants and tradesmen, the Old Bridge and the port. Located on the River Forth, Stirling is the administrative centre for the Stirling council area, and is traditionally the county town of Stirlingshire. Proverbially it is the strategically important "Gateway to the Highlands". It has been said that "Stirling, like a huge brooch clasps Highlands and Lowlands together". Similarly "he who holds Stirling, holds Scotland" is often quoted. Stirling's key position as the lowest bridging point of the River Forth before it broadens towards the Firth of Forth made it a focal point for travel north or south. When Stirling was temporarily under Anglo-Saxon sway, according to a 9th-century legend, it was attacked by Danish invaders. The sound of a w ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stirling Transform
In combinatorial mathematics, the Stirling transform of a sequence of numbers is the sequence given by :b_n=\sum_^n \left\ a_k, where \left\ is the Stirling number of the second kind, also denoted ''S''(''n'',''k'') (with a capital ''S''), which is the number of partitions of a set of size ''n'' into ''k'' parts. The inverse transform is :a_n=\sum_^n s(n,k) b_k, where ''s''(''n'',''k'') (with a lower-case ''s'') is a Stirling number of the first kind. Berstein and Sloane (cited below) state "If ''a''''n'' is the number of objects in some class with points labeled 1, 2, ..., ''n'' (with all labels distinct, i.e. ordinary labeled structures), then ''b''''n'' is the number of objects with points labeled 1, 2, ..., ''n'' (with repetitions allowed)." If :f(x) = \sum_^\infty x^n is a formal power series, and :g(x) = \sum_^\infty x^n with ''a''''n'' and ''b''''n'' as above, then :g(x) = f(e^x-1).\, Likewise, the inverse transform leads to the generating function identity ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stirling Polynomials
In mathematics, the Stirling polynomials are a family of polynomials that generalize important sequences of numbers appearing in combinatorics and analysis, which are closely related to the Stirling numbers, the Bernoulli numbers, and the generalized Bernoulli polynomials. There are multiple variants of the ''Stirling polynomial'' sequence considered below most notably including the Sheffer sequence form of the sequence, S_k(x), defined characteristically through the special form of its exponential generating function, and the ''Stirling (convolution) polynomials'', \sigma_n(x), which also satisfy a characteristic ''ordinary'' generating function and that are of use in generalizing the Stirling numbers (of both kinds) to arbitrary complex-valued inputs. We consider the "''convolution polynomial''" variant of this sequence and its properties second in the last subsection of the article. Still other variants of the Stirling polynomials are studied in the supplementary links to the art ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pound Sterling
Sterling (abbreviation: stg; Other spelling styles, such as STG and Stg, are also seen. ISO 4217, ISO code: GBP) is the currency of the United Kingdom and nine of #Crown Dependencies and British Overseas Territories, its associated territories. The Pound (currency), pound (pound sign, sign: £) is the main unit of account, unit of sterling, and the word "pound" is also used to refer to the British currency generally, often qualified in international contexts as the British pound or the pound sterling. Sterling is the world's oldest currency that is still in use and that has been in continuous use since its inception. It is currently the fourth most-traded currency in the foreign exchange market, after the United States dollar, the euro, and the Japanese yen. Together with those three currencies and Renminbi, it forms the basket of currencies which special drawing rights#Value definition, calculate the value of International Monetary Fund, IMF special drawing rights. As of mid ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Glasgow
Glasgow ( ; sco, Glesca or ; gd, Glaschu ) is the most populous city in Scotland and the fourth-most populous city in the United Kingdom, as well as being the 27th largest city by population in Europe. In 2020, it had an estimated population of 635,640. Straddling the border between historic Lanarkshire and Renfrewshire, the city now forms the Glasgow City Council area, one of the 32 council areas of Scotland, and is governed by Glasgow City Council. It is situated on the River Clyde in the country's West Central Lowlands. Glasgow has the largest economy in Scotland and the third-highest GDP per capita of any city in the UK. Glasgow's major cultural institutions – the Burrell Collection, Kelvingrove Art Gallery and Museum, the Royal Conservatoire of Scotland, the Royal Scottish National Orchestra, Scottish Ballet and Scottish Opera – enjoy international reputations. The city was the European Capital of Culture in 1990 and is notable for its architectur ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Trompe
A trompe is a water-powered air compressor, commonly used before the advent of the electric-powered compressor. A trompe is somewhat like an airlift pump working in reverse. Trompes were used to provide compressed air for bloomery furnaces in Catalonia and the USA. The presence of a trompe is a signature attribute of a Catalan forge, a type of bloomery furnace. Trompes can be enormous. At Canadian Hydro Developers' Ragged Chute facility in New Liskeard, Ontario, water falls down a shaft deep and across to generate compressed air for mining equipment and ventilation.Ragged Chutes Operation Trompes are very simple devices. They consist of four main parts: ''water-supply pipe'' or ''shaft'' with an ''air-inlet'' inside it, ''water outflow pipe' ...[...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Scots Mining Company House
The Scots Mining Company House, also known as Woodlands Hall, is an early-18th-century mansion house in Leadhills, South Lanarkshire, Scotland. The house was built around 1736 for the manager of the Leadhills mines, which were owned by the Earl of Hopetoun. Its design has been attributed to the architect William Adam. The house is now a category A listed building. The garden, which is largely unchanged since it was laid out in the 18th century, is included on the Inventory of Gardens and Designed Landscapes in Scotland, the national listing of significant gardens. History Lead and silver have been mined at Leadhills in the Southern Uplands for centuries. In the 17th century, Sir James Hope (1614–1661) married Anne, daughter of Robert Foulis of Leadhills, and the mines subsequently passed to his descendants the Earls of Hopetoun. The Scots Mining Company, formally The Governor and Company for Working the Mines and Minerals in that part of North Britain called Scotland, was fo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Leadhills
Leadhills, originally settled for the accommodation of miners, is a village in South Lanarkshire, Scotland, WSW of Elvanfoot. The population in 1901 was 835. It was originally known as Waterhead. It is the second highest village in Scotland, the highest being neighbouring Wanlockhead, south. It is near the source of Glengonnar Water, a tributary of the River Clyde. Local attractions Library The Leadhills Miners' Library (also known as the Allan Ramsay Library or the Leadhills Reading Society), founded in 1741 by 21 miners, the local schoolteacher and the local minister, specifically to purchase a collection of books for its members’ mutual improvement — its membership was not restricted to the miners; several non-miners, such as William Symington, John Brown (author of ''Rab and his Friends'') and James Braid, were also full members — houses an extensive antiquarian book collection, local relics, mining records and minerals. The library is the oldest subscription ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Scots Mining Company
The Scots Mining Company, or Scotch Mines Company,Peter L. Payne (Ed.) (2013) ''Studies in Scottish Business History'page 119-134Routledge. Retrieved February 2015 was formed shortly after the Jacobite rising of 1715 by Sir John Erskine with the intention of better developing the mineral resources of Scotland.John Nichols (1853) ''The Gentleman's Magazine'', Volume 193''A Trip to the Gold Regions if Scotland''p589-597, Publisher R. Newton. Retrieved February 2015 Primary investors were largely garnered from expatriate Scots living in London. History Following its incorporation by royal charter in 1729, the Scots Mining Company procured leases for mines at Leadhills and elsewhere. The company was near bankrupt when, in 1734, the mathematician James Stirling was appointed manager.Colin Russell (2014) ''Who Made the Scottish Enlightenment?'page 391 Xlibris Corporation, Retrieved February 2015 The systems of mining, social organisation and living conditions of the workers that Stir ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Glassmaker
Glass is a non-crystalline, often transparent, amorphous solid that has widespread practical, technological, and decorative use in, for example, window panes, tableware, and optics. Glass is most often formed by rapid cooling (quenching) of the molten form; some glasses such as volcanic glass are naturally occurring. The most familiar, and historically the oldest, types of manufactured glass are "silicate glasses" based on the chemical compound silica (silicon dioxide, or quartz), the primary constituent of sand. Soda–lime glass, containing around 70% silica, accounts for around 90% of manufactured glass. The term ''glass'', in popular usage, is often used to refer only to this type of material, although silica-free glasses often have desirable properties for applications in modern communications technology. Some objects, such as drinking glasses and eyeglasses, are so commonly made of silicate-based glass that they are simply called by the name of the material. Despite bei ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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