* Given any topological space X, the continuous real-or complex-valued functions on X form a real or complex unitary associative algebra ; here the functions are added and multiplied pointwise.

Given the complexity of the calculations involved and the convoluted structure that a convertible bond can have, an arbitrageur often relies on sophisticated quantitative models in order to identify bonds that are trading cheap versus their theoretical value.

Given this, the bidding is said to start at the one-level when contracting for a total of seven tricks, at the two-level for eight tricks and so on to the seven-level to contract to take all thirteen tricks.

Given the federal nature of the holiday, celebrating Canada Day can be a cause of friction in the province of Quebec, where the holiday is overshadowed by Quebec's National Holiday, on June 24.

Given the rugged terrain of Ngazidja and Nzwani, and the dedication of extensive tracts to agriculture on all three islands, population pressures on Comoros are becoming increasingly critical.

Given an asymmetric subunit on a triangular face of a regular isosahedron, with three subunits per face 60 such subunits can be placed in an equivalent manner.

Given this kind of data, the estimated coefficient on Years of Education in the equation above reflects both the effect of education on wages and the effect of other variables on wages, if those other variables were correlated with education.

* Frederick Douglass lecture on Haiti – Given at the World's Fair in Chicago, January 1893.

Given also a measure on set, then, sometimes also denoted or, has as its vectors equivalence classes of measurable functions whose absolute value's-th power has finite integral, that is, functions for which one has

Given both Einstein's equations and suitable equations for the properties of matter, such a solution consists of a specific semi-Riemannian manifold ( usually defined by giving the metric in specific coordinates ), and specific matter fields defined on that manifold.

Given the difficulty of finding exact solutions, Einstein's field equations are also solved frequently by numerical integration on a computer, or by considering small perturbations of exact solutions.

Given an equilateral triangle, the counterclockwise rotation by 120 ° around the center of the triangle " acts " on the set of vertices of the triangle by mapping every vertex to another one.

Given these, a new term Anthropocene, is specifically proposed and used informally for the latest part of this epoch since approximately synchronous lithospheric evidence, or more recently atmospheric evidence, of human impacts have been found on the Earth and its ecosystems ; these impacts may be considered of global significance for future evolution of living species.

Given that this etymology does not appear in the usual scholarly works on etymology, this claim is usually dismissed as a false etymology.

Given the dual status of science as objective knowledge and as a human construct, good historiography of science draws on the historical methods of both intellectual history and social history.

Given a binary operation ★ on a set S, an element x is said to be idempotent ( with respect to ★) if

Given its heavy dependence on imported energy, Japan has aimed to diversify its sources.

Along with a hand-picked escort led by Given Campbell, Davis and his wife were captured on May 10, 1865, at Irwinville in Irwin County, Georgia.

Given the repeated failures and frustrations of workers ' revolutions and movements, Marx also sought to understand capitalism, and spent a great deal of time in the reading room of the British Museum studying and reflecting on the works of political economists and on economic data.

Given that estimation is undertaken on the basis of a least squares analysis, estimates of the unknown parameters β < sub > j </ sub > are determined by minimising a sum of squares function

Given that spinning a Dyson Sphere would result in the atmosphere pooling around the equator, the Ringworld removes all the extraneous parts of the structure, leaving a spinning band landscaped on the sun-facing side, with the atmosphere and inhabitants kept in place through centrifugal force and 1000 mile high perimeter walls ( rim walls ).

Given Poseidon's connection with horses as well as the sea, and the landlocked situation of the likely Indo-European homeland, Nobuo Komita has proposed that Poseidon was originally an aristocratic Indo-European horse-god who was then assimilated to Near Eastern aquatic deities when the basis of the Greek livelihood shifted from the land to the sea, or a god of fresh waters who was assigned a secondary role as god of the sea, where he overwhelmed the original Aegean sea deities such as Proteus and Nereus.

Given the controversy over the struggle over territory, a vocal minority of Cherokee and a generation of political leaders in Washington considered Ross to be dictatorial, greedy, and an " aristocratic leader sought to defraud " the Cherokee Nation.

Given that his support in the Reichstag relied heavily on this conservative aristocratic support, his position was tenuous.

Given Ealdred's known support of Godwin's family, John of Worcester is probably correct.

While tests have been done to support this with fixed pieces of flat metal, the result is inconclusive with respect to the curved armour of the period. Given the following actions of the archers, it seems likely Froissart was correct.

Given that the Qur ' an is vague regarding the punishment of homosexual sodomy, Islamic jurists turned to the collections of the hadith and seerah ( accounts of Muhammad's life ) to support their argument for Hudud punishment ; these are perfectly clear but particularly harsh.

Given prevailing views on homosexuality at the time, circulation of the diaries helped undermine support for clemency for Casement.

Given that the decree was issued at Memphis, the ancient capital of Egypt, rather than Alexandria, the centre of government of the ruling Ptolemies, it is evident that the young king was anxious to gain their active support.

Given the same set of resources, IS-IS can support more routers in an area than OSPF.

Given that many businessmen and bankers were terrified of Bryan's populist rhetoric and support for ending the gold standard, Hanna had few problems in raising record amounts of money.

Given that many open source projects fail due to lack of developer support, exposure to such a large community of developers can continually breathe new life into a project.

Given that all Jews had been expelled from the province of Styria ( which includes Graz ) in the 15th century and were not allowed to return until the 1860s, scholars such as Ian Kershaw and Brigitte Hamann dismiss as baseless the Frankenberger hypothesis, which before had only Frank's speculation to support it.

Given the high level of support within the party for her leadership, MacPhail surprised many by choosing not to seek the party leadership in 2003.

Given postwar urban erosion of support, Lenin designed propaganda campaigns as a supplement to the New Economic Policy to further increase backing of the Bolsheviks.

Given Ríos Montt's staunch anticommunism and ties to the United States, the Reagan administration continued to support the general and his regime, paying a visit to Guatemala City in December 1982.

Given the inter-tribal style of powwow music it may be viewed as less traditional or valuable though the music is also used to support tribal identity and display the value of a living culture.

Given this, few alternative programs support the format.

Given its harbors and fortifications, Saint Thomas still retained a strategic importance, and thus, in the 1860s, during the American Civil War and its aftermath, the United States government considered buying the island and its neighbors from Denmark for $ 7. 5 million, but at the time failed to find domestic legislative support for the bid.

Given the dwindling support for the NDP reflected in all the public opinion polls, the formation of a new party on the left could not be ignored.

Given that his reign lasted for, at best, only a few weeks after his acclamation and he does not seem to have secured significant military or political support Domitianus is more properly categorized as a Roman Usurper rather than an Emperor.

Given this lengthy support it was reasonable for Tyrconnell and Tyrone to try to solicit help from Philip III, but Spanish policy was to maintain its recent ( 1604 ) peace with England, and its European fleet had anyway been destroyed by the Dutch over four months earlier.

Given the military-industrial requirements of the Cold War, the authors of the then secret National Security Council Report 68 ( NSC-68 ) proposed the US government undertake a massive permanent national economic expansion that would let it “ siphon off ” a part of the economic activity produced to support an ongoing military buildup to contain the Soviet Union.

Given this rapid rate of construction, the GVN was unable to fully support or protect the hamlets or its residents, despite the immense funding by the United States government.

Given the size of the CAW with the Canadian labour movement, the CAW's support for the Liberals has caused significant problems for the CLC leadership in continuing to follow the Congress ' policy of NDP support.

The Government believes that it must remain so .” Given the prospect of " incineration without representation ", Canadians seemed to feel that the doctrine which most encouraged restraint was the strategically soundest one to support.

Given this additional support the scheme has expanded its reach to cover most children in primary schools in India.