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 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 first four rolls turn up heads, the probability that the next toss is a head is in fact,

Given its limitations, however, NAALC has not produced ( and in fact was not intended to achieve ) convergence in employment, productivity and salary trend in North America.

Given infinite space, there would, in fact, be an infinite number of Hubble volumes identical to ours in the universe.

Given the above fact, one can ask:

Given that assumption, the evidence for the one-seed theory is the fact that a woman can conceive without coming to orgasm ( though this was still a matter of dispute in the ancient world and the Middle Ages ).

Given the fact that many of the royal depictions of Akhenaten often featured such an elongated head, it is likely an exaggeration of a family trait, rather than a distinct abnormality.

Given any vector space V over K we can construct the tensor algebra T ( V ) of V. The tensor algebra is characterized by the fact:

Given the fact that the period P of an object in circular orbit around a spherical object obeys

Given the symmetry of circularly polarized light, we could have in fact selected any other two orthogonal components and found the same phase relationship between them.

" Given the fact that it's the third film in the series, you couldn't just end with them obtaining the object.

Given Switzerland's particularly strong opinions on who is " Swiss " and who is " other ", it is easy to see that groups such as Stoffunita make use of the fact that hip hop " is still considered a voice for the oppressed " as hip hop scholar and author Jeff Chang notes.

Given on 16 October 1732, they amounted only to recreating his first expedition, but with the added task of heading east and finding North America ( a feat which had in fact just been completed by Mikhail Gvozdev, though this was not known at the time ).

Given parallel morphisms f and g, the equaliser of f and g is just the kernel of g − f, if either exists, and the analogous fact is true for coequalisers.

Given the fact that it was an election year, whose outcome might have changed as a result of a pre-election-day economic downturn, the Bank of Mexico decided to buy Mexican Treasury Securities in order to maintain the monetary base, and thus prevent the interest rates from rising.

Given the fact that the Lakeport area has an economy that is based somewhat on agricultural activities occurring in the Big Valley and Scotts Valley area which involve the growing and harvesting of food and nut crops as well as the increasing wine industry, there are a significant number of transient and seasonal farm workers.

Given the extent and central location of his original holding from the Mill Seat Tract, and the fact that most of the town's pre-1944 building lots are to, Bare's ability to shape the size and extent of development in Roaring Spring was substantial.

Given the fact that the following Popes John, from John XV ( 985 – 996 ) until John XIX ( 1024 – 1034 ), seemed to have neglected the existence of John XIV " bis ", Petrus Hispanus meant to correct this error by electing for himself the name John XXI.

Dr. Tennison states: " Given the account of Elliot Paul, and given that Lead Belly witnessed boogie-woogie in 1899 in the Arklatex ; and given the North to South migration of the Thomas family ; and given the Texas & Pacific headquarters in Marshall in the early 1870s ; and given that Harrison County had the largest slave population in the state of Texas ; and given the fact that the best-documented and largest-scale turpentine camps in Texas did not occur until after 1900 in Southeast Texas, it is most probable that boogie-woogie spread from Northeast to Southeast Texas, rather than from Southeast to Northeast Texas, or by having developed diffusely with an even density over all of the Piney Woods of East Texas.

Given the character's unprecedented popularity and the fact that his name was partially derived from the Latin word for " lucky ", some rather notable individuals and organizations adopted Felix as a mascot.

Given the morphological distinctness of the Cape Verde birds and the fact that the Cape Verde population was isolated from other populations of Red Kites, it cannot be conclusively resolved at this time whether the Cape Verde population was not a distinct subspecies ( as M. migrans fasciicauda ) or even species that frequently absorbed stragglers from the migrating European populations into its gene pool.

Given Juwayni's polemical aims, and the fact that he burned the Ismaili libraries which may have offered much more reliable testimony about the history, scholars have been dubious about his narrative but are forced to rely on it given the absence of alternative sources.

Given the epidemic proportions of obesity in the Western world, and the fact that it is increasing rapidly in some poorer countries, observers expect developments in this area to snowball in the near future.

Given the fact that Puerto Rico has 78 municipalities, there was enough material to show and research over the program's six-year run.

Given the definition of morpheme as " the smallest meaningful unit " Nanosyntax aims to account for idioms where it is often an entire syntactic tree which contributes " the smallest meaningful unit.

Given a sample of wood, the variation of the tree ring growths provides not only a match by year, it can also match location because the climate across a continent is not consistent.

Given a connected, undirected graph, a spanning tree of that graph is a subgraph that is a tree and connects all the vertices together.

Given an embedding of a rooted tree in the plane, if one fixes a direction of children ( starting from root, then first child, second child, etc.

Given the rules of any two-person game with a finite number of positions, one can always trivially construct a minimax algorithm that would exhaustively traverse the game tree.

Given that humanity cannot exist except within a covenantal relationship with God, and all covenants use symbols to give us " the attestation of his grace ", he gives the tree, " not because it could confer on man that life with which he had been previously endued, but in order that it might be a symbol and memorial of the life which he had received from God.

Given before her thirteenth birthday to a man who makes her a slave, she sheds her tears on the tree she planted, which bears the best fruit in the world.

The original problem was stated in the form that has become known as the Euclidean Steiner tree problem or geometric Steiner tree problem: Given N points in the plane, the goal is to connect them by lines of minimum total length in such a way that any two points may be interconnected by line segments either directly or via other points and line segments.

The realization problem for Euclidean minimum spanning trees is stated as follows: Given a tree T = ( V, E ), find a location D ( u ) for each vertex u ∈ V so that T is a minimum spanning tree of D ( u ): u ∈ V, or determine that no such locations exist.

Given a square of 2 < sup > 2k </ sup > cells, 2 < sup > k </ sup > on a side, at the kth level of the tree, the hash table stores the 2 < sup > k-1 </ sup >- by-2 < sup > k-1 </ sup > square of cells in the center, 2 < sup > k-2 </ sup > generations in the future.

Given the environmental impact of the brown tree snake, studies have attempted to provide a capturing methodology to alleviate the detrimental effects of the tree snake.

Given a list of n points, the following algorithm uses a median-finding sort to construct a balanced k-d tree containing those points.

Given BASIC's straightforward nature, it was a simple matter to type in the code from the magazine and execute the program.

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 the cosmological principle, Hubble's law suggested that the universe was expanding.

Given the large number of U. S. military personnel and their dependents residing in Europe, it was expected that over 7 % of donors would be deferred due to the policy.

Given more time to prepare for trial, Kidd likely would have been able to find the deposition Palmer gave when he was captured in Rhode Island two years earlier.

The question concerned the educational value of pre-Christian classical thought: " Given that the body of knowledge of the pre-Christian Romans was heathen in origin, was it safe to teach it to Christian children?

Given away at theatrical showings was a comic herald that told a simplified version of the film.

" Given that there's a gulf of 100, 000, 000 light years, he checks his diary to find out what he had been doing that day, and finds out that it was something he wished to hide.

Given the toleration of Hinduism, such imperial leeway was not shocking.

Given that Fine Gael normally received 25 % of the election result, and were reduced to third place this was an achievement in itself.

Given high fixed costs, the new price was below average total cost, resulting in a loss.

Given the ideals of Juche, North Korea chose to default on its loans and by the late 1980s its industrial output was declining.

Given a year to complete the work, Gibson undertook the actual writing out of " blind animal terror " at the obligation to write an entire novel – a feat which he felt he was " four or five years away from ".

Given these issues, Microsoft started to work in parallel on a version of Windows which was more future-oriented and more portable.

Given the task of overhauling the Cardinals by owner Gussie Busch, Herzog was looking to trade Templeton when he was approached by Padres General Manager Jack McKeon at the 1981 baseball winter meetings.

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 this and other evidence, many scholars agree that Peter was martyred in Rome under Nero, although some scholars argue that he may have been martyred in Palestine.

Without doubt, the single most significant paper concerning the distribution of prime numbers was Riemann's 1859 memoir On the Number of Primes Less Than a Given Magnitude, the only paper he ever wrote on the subject.

Given that most French supporters of phrenology were liberal, left-wing or socialist, it was an objective of the social elite of France who held a restrained vision of social change that phrenology remain on the fringes.