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James Stirling (mathematician)
James Stirling (11 May Old Style and New Style dates, O.S. 1692, Garden, Stirlingshire – 5 December 1770, Edinburgh) was a Scotland, 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 cubic plane curves. Biography Stirling was born on 11 May 1692 Old Style and New Style dates, O.S. at Garden House near Stirling, the third son of Archibald Stirling (1651-1715) and Anna Hamilton, and grandson of Archibald Stirling, Lord Garden, (1617-1668). At 18 years of age he went to Balliol College, Oxford, where, chiefly through the influence of the John Erskine, Earl of Mar (1675–1732), 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 fami ... [...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, they refer to the change from the Julian calendar to the Gregorian calendar as enacted in various Europe, European countries between 1582 and 1923. In England, Wales, Ireland and British America, Britain's American colonies, there were two calendar changes, both in 1752. The first adjusted the start of a new year from 25 March (Lady Day, the Feast of the Annunciation) to 1 January, a change which Scotland had made in 1600. The second discarded the Julian calendar in favour of the Gregorian calendar, skipping 11 days in the month of September to do so.. "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 until 24th March. ... We as h ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
John Erskine, Earl Of Mar (1675–1732)
John Erskine, 23rd and 6th Earl of Mar and 1st Duke of Mar Order of the Thistle, KT (1675 – May 1732), was a Scotland, Scottish nobleman and a key figure in the Jacobitism, Jacobite movement. He held the title of the 23rd Earl of Mar from the earldom's first creation and was the sixth earl in its seventh creation (of 1565). Erskine, often remembered for his political adaptability, navigated the complex and shifting landscape of early 18th-century British politics. As the eldest son of Charles Erskine, Earl of Mar, Charles, the 22nd and 5th Earl of Mar, Erskine inherited estates that were facing financial challenges. In 1714, following the ascension of George I of Great Britain, George I, he found himself without official office and subsequently championed the Jacobite cause. He raised an army to contest the Hanoverian rule, leading his forces at the Battle of Sheriffmuir in November 1715. Despite having a numerical advantage, the battle concluded inconclusively. After the sub ... [...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, which is the number of partitions of a set of size n into k parts. This is a linear sequence transformation. The inverse transform is :a_n=\sum_^n (-1)^ \leftrightb_k, where (-1)^ \leftright/math> is a signed Stirling number of the first kind, where the unsigned \leftright/math> can be defined as the number of permutations on n elements with k cycles. 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( ... [...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 ar ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pound Sterling
Sterling (symbol: £; currency code: GBP) is the currency of the United Kingdom and nine of its associated territories. The pound is the main 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 in continuous use since its inception. In 2022, it was 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 the renminbi, it forms the basket of currencies that calculate the value of IMF special drawing rights. As of late 2022, sterling is also the fourth most-held reserve currency in global reserves. The Bank of England is the central bank for sterling, issuing its own banknotes and regulating issuance of banknotes by private banks in Scotland and Northern Ireland. Sterling banknotes issu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Glasgow
Glasgow is the Cities of Scotland, most populous city in Scotland, located on the banks of the River Clyde in Strathclyde, west central Scotland. It is the List of cities in the United Kingdom, third-most-populous city in the United Kingdom and the 27th-most-populous city in Europe, and comprises Wards of Glasgow, 23 wards which represent the areas of the city within Glasgow City Council. Glasgow is a leading city in Scotland for finance, shopping, industry, culture and fashion, and was commonly referred to as the "second city of the British Empire" for much of the Victorian era, Victorian and Edwardian eras. In , it had an estimated population as a defined locality of . More than 1,000,000 people live in the Greater Glasgow contiguous urban area, while the wider Glasgow City Region is home to more than 1,800,000 people (its defined functional urban area total was almost the same in 2020), around a third of Scotland's population. The city has a population density of 3,562 p ... [...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 United States. 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: a ''water-supply pipe'' or ''shaft'' with an ''air-inlet'' inside it, a ''water ...[...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 ... [...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 (poet), 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 (physician, born 1810), John Brown (author of ''Rab and his Friends'') and James Braid (surgeon), James Braid, were also full members — houses an extensive antiquarian book collection, loca ... [...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 production involves two main methods – the float glass process that produces sheet glass, and glassblowing that produces bottles and other containers. It has been done in a variety of ways during the history of glass. Glass container production Broadly, modern glass container factories are three-part operations: the "batch house", the "hot end", and the "cold end". The batch house handles the raw materials; the hot end handles the manufacture proper—the forehearth, forming machines, and annealing (glass), annealing ovens; and the cold end handles the product-inspection and packaging equipment. Batch processing system (batch house) Batch processing is one of the initial steps of the glass-making process. The batch house simply houses the raw materials in large silos (fed by truck or railcar), and holds anywhere from 1–5 days of material. Some batch systems include material processing such as raw material screening/sieve, drying, or pre-heating (i.e. cullet). Whethe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Royal Society
The Royal Society, formally The Royal Society of London for Improving Natural Knowledge, is a learned society and the United Kingdom's national academy of sciences. The society fulfils a number of roles: promoting science and its benefits, recognising excellence in science, supporting outstanding science, providing scientific advice for policy, education and public engagement and fostering international and global co-operation. Founded on 28 November 1660, it was granted a royal charter by Charles II of England, King Charles II and is the oldest continuously existing scientific academy in the world. The society is governed by its Council, which is chaired by the society's president, according to a set of statutes and standing orders. The members of Council and the president are elected from and by its Fellows, the basic members of the society, who are themselves elected by existing Fellows. , there are about 1,700 fellows, allowed to use the postnominal title FRS (Fellow ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
