* 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.

Idealists are skeptics about the physical world, maintaining either: 1 ) that nothing exists outside the mind, or 2 ) that we would have no access to a mind-independent reality even if it may exist ; the latter case often takes the form of a denial of the idea that we can have unconceptualised experiences ( see Myth of the Given ).

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 that Bozizé accuses Sudan of supporting the UFDR rebels who are actively fighting the Central African Government, the relation between the two countries has remained good.

Given this popular understanding of the term, it can also be used illegitimately and inappropriately, as a means to dismiss what are in fact substantial and well-evidenced accusations.

Given that many journeys are for relatively short distances, there is considerable scope to replace car use with walking or cycling, though in many settings this may require some infrastructure modification, particularly to attract the less experienced and confident.

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 this basic definition, further criteria are needed to establish a dividing line between postlexical clitics and morphological affixes, since both are characterized by a lack of prosodic autonomy.

Given that a father's age is 1 less than twice that of his son, and that the digits AB making up the father's age are reversed in the son's age ( i. e. BA ), leads to the equation 19B-8A

Given its different forms, there are various ways of representing uncertainty and modelling economic agents ' responses to it.

* Given a partition of A, G is a transformation group under composition, whose orbits are the cells of the partition ‡;

* Given a transformation group G over A, there exists an equivalence relation ~ over A, whose equivalence classes are the orbits of G.

Raymond also coined an aphorism he dubbed " Linus ' Law ", inspired by Linus Torvalds: " Given enough eyeballs, all bugs are shallow ", that first appeared in The Cathedral and the Bazaar.

Given the great historical link between Persian and Jewish history, modern day Persian Jews are called " Esther's Children ".

Given that the vast majority of all emeralds are treated as described above, and the fact that two stones that appear visually similar may actually be quite far apart in treatment level and therefore in value, a consumer considering a purchase of an expensive emerald is well advised to insist upon a treatment report from a reputable gemological laboratory.

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 a trigonometric series f ( x ) with S as its set of zeros, Cantor had discovered a procedure that produced another trigonometric series that had S ' as its set of zeros, where S ' is the set of limit points of S. If p ( 1 ) is the set of limit points of S, then he could construct a trigonometric series whose zeros are p ( 1 ).

Given that genes are universal to living organisms, genetics can be applied to the study of all living systems, from viruses and bacteria, through plants and domestic animals, to humans ( as in medical genetics ).

Given a groupoid G, the vertex groups or isotropy groups or object groups in G are the subsets of the form G ( x, x ), where x is any object of G. It follows easily from the axioms above that these are indeed groups, as every pair of elements is composable and inverses are in the same vertex group.

On poverty, Hoover said that " Given the chance to go forward with the policies of the last eight years, we shall soon with the help of God, be in sight of the day when poverty will be banished from this nation ", and promised, " We in America today are nearer to the final triumph over poverty than ever before in the history of any land ," but within months, the Stock Market Crash of 1929 occurred, and the world's economy spiraled downward into the Great Depression.

Given that the coiled texture is the natural state of some African Americans ' hair, or perceived as being more " African ", this simple style is now often seen as a sign of self-acceptance and an affirmation that the beauty norms of the ( eurocentric ) dominant culture are not absolute.

Given these two assumptions, the coordinates of the same event ( a point in space and time ) described in two inertial reference frames are related by a Galilean transformation.

Given the preponderance of men among the colonists in the early years, generally European men married American Indian women.

* Relationship extraction: Given a chunk of text, identify the relationships among named entities ( e. g. who is the wife of whom ).

Given this sense of caution among key members of the British cabinet and of the army, it is even harder to understand why the British government went against the advice of its generals ( such as Wolsely ) to send substantial reinforcements to South Africa before war broke out.

Given an initial allocation of goods among a set of individuals, a change to a different allocation that makes at least one individual better off without making any other individual worse off is called a Pareto improvement.

Given the ensuing decline in world commodity prices, countries heavily dependent on the export of raw materials such as oil were among those most severely hit.

Given that any frame in the space can be described by a rotation matrix, the displacement among them can also be described by a rotation matrix.

Given that male authors had limited knowledge of her rites and attributes, ancient speculations about her identity abound, among them that she was an aspect of Terra, Ops, the Magna Mater, or Ceres, or a Latin form of Damia.

Given that Earl Ferchar heads the list of those named, it is presumed that Donnchad II, Mormaer of Fife, was not among the rebels.

Given the opposition to the mission when it began, the primary U. S. concern was to do its limited job and avoid casualties among its forces.

Given the subsequent emergence of organized fandom for comic books among adults who grew up reading them during Comics ' Golden Age, it is ironic Wertham at one point in Seduction ( pp. 89 – 90 ) asserts " I have known many adults who have treasured throughout their lives some of the books they read as children.

Given the Nazi predilection for “ racial purity ”, the Roma were among their first victims.

Given that economic geoscientists had the lowest percentage of all Earth scientists surveyed, critic and author John Cook has claimed that " climate scepticism seems strongest among geologists closely linked to the mining and fossil fuel industries " and that this is due to the influence of their funding.

Given that gated communities are spatially a type of enclave, Setha M. Low, among other anthropologists, has argued that they have a negative effect on the overall social capital of the broader community outside the gated community.

Given similar doses of the same neuroleptic, differences among individuals still exist in the likelihood of developing tardive dyskinesia.

Given that they are paying to be there, some clubs allow as many dancers as possible to appear on any given night, increasing competition among the dancers.

Given the University of Georgia School of Law's low in-state tuition of $ 14, 448, the New York Times recently completed a survey comparing starting salaries and degree costs of law schools and found " Georgia Law graduates earning some of the highest salaries in the country while their educational costs were reported among the very lowest, speaking to the quality of the education as well as the excellent return on investment provided at Georgia Law.

Given the varied ideologies among the parties, there have been many cases of disagreement and split voting among the allies.

Given this, the eagles would not have been among the spirits summoned by Yavanna in that paragraph, suggesting that Tolkien didn ’ t change from the view that the eagles are animals, and have no fëar.

Given the ethnic diversity of the city, Marbella's newspapers and magazines are published in several European languages, among which are La Tribuna de Marbella ( Spanish ), Sydkusten ( in Swedish ) and Costa del Sol Nachrichten ( in German ).

Given the resulting linguistic fragmentation, French became the lingua franca among the slaves.

Given their relatively competitive fares to the mainstream Greyhound Lines, it has become popular among non-Chinese customers as well, especially students.

" ( from Yield ), and " Given to Fly ", among others.

The coincidence of the goalscorer's name quickly led to the popular word game among football fans that Given " is the only Irishman who doesn't know where Dublin is " and the goal itself is still regularly featured on lists compiled of bizarre goals.

Given Ialá's sharp hostility to Vieira in previous years, this endorsement was viewed as surprising by many, and there was reportedly significant dissatisfaction with the decision among Ialá's supporters.