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 a subset X of a manifold M and a subset Y of a manifold N, a function f: X → Y is said to be smooth if for all p in X there is a neighborhood of p and a smooth function g: U → N such that the restrictions agree ( note that g is an extension of f ).

Given concerns about the previous programs using nuclear-tipped interceptors, in the 1980s the U. S. Army began studies about the feasibility of hit-to-kill vehicles, i. e. interceptor missiles that would destroy incoming ballistic missiles just by colliding with them head-on.

Given a functor U and an object X as above, there may or may not exist an initial morphism from X to U. If, however, an initial morphism ( A, φ ) does exist then it is essentially unique.

Given current trends in the UMC — with overseas churches growing, especially in Africa, and U. S. churches collectively losing about 1, 000 members a week — it has been estimated that Africans will make up at least 30 % of the delegates at the 2012 General Conference, and it is also possible that 40 % of the delegates will be from outside the U. S. One Congolese bishop has estimated that typical Sunday attendance of the UMC is higher in his country than in the entire United States.

Given control by the U. N. to Magneto until the E Is for Extinction story.

Given Rickover's single-minded focus on naval nuclear propulsion, design and operations, it came as a surprise to many when in 1982, near the end of his career, he testified before the U. S. Congress that, were it up to him, he " would sink them all.

A conceptually very simple method for generating exponential variates is based on inverse transform sampling: Given a random variate U drawn from the uniform distribution on the unit interval ( 0, 1 ), the variate

Given subspaces U and W of a vector space V, then their intersection U ∩ W :=

Given Binet's stance that intelligence testing was subject to variability and was not generalizable, it is important to look at the metamorphosis that mental testing took on as it made its way to the U. S.

The American Library Association issued a recommendation to libraries still holding Alms for Jihad: " Given the intense interest in the book, and the desire of readers to learn about the controversy first hand, we recommend that U. S. libraries keep the book available for their users.

Kendall West is home to a large concentration of Colombians and Colombian Americans in the U. S. Given the local name " Little Bogota ".

* Given two complex vectors x and y, multiplication by U preserves their inner product ; that is,

* Given that Historic U. S. Route 66 runs through Elk City, a sprawling museum complex has developed, which includes the National Route 66 Museum, the Old Town Museum, the Transportation Museum, the Farm and Ranch Museum, and the Blacksmith Museum.

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 importance of the seasonal gift-giving to the U. S. economy, one driven largely by consumer spending, and with the music industry making at least 40 percent of its annual revenue in the fourth quarter culminating at Christmas, demands for increased revenues motivates the shift.

Given a concrete category ( C, U ) and a cardinal number N, let U < sup > N </ sup > be the functor C → Set determined by U < sup > N </ sup >( c ) = ( U ( c ))< sup > N </ sup >.

Given a Hermitian form Ψ on a complex vector space V, the unitary group U ( Ψ ) is the group of transforms that preserve the form: the transform M such that Ψ ( Mv, Mw ) = Ψ ( v, w ) for all v, w ∈ V. In terms of matrices, representing the form by a matrix denoted, this says that.

Given a theological lead, I asked what he thinks about those who find a religious significance to his plays.

Given a small ball or marbles, he would invent games and play by himself for hours.

: Given any family of nonempty sets, their Cartesian product is a nonempty set.

: Given any set X of pairwise disjoint non-empty sets, there exists at least one set C that contains exactly one element in common with each of the sets in X.

Given the similarities in the two characters ' names, professions, written works and generally dark subject matter, it is likely that Lovecraft's Alhazred provided the main inspiration for al-Hazir.

* Given an algebraic number, there is a unique monic polynomial ( with rational coefficients ) of least degree that has the number as a root.

Given two subspaces with, this leads to a definition of angles called canonical or principal angles between subspaces.

" Given that Thomas Aquinas died six years before Albertus Magnus ' death, this legend as stated is unlikely.

Given that John of Worcester wrote his chronicle after the eruption of the Canterbury – York supremacy struggle, the story of Ealdred renouncing any claims to Worcester needs to be considered suspect.

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

Given the ongoing Danish invasion and the youth of his nephews, Alfred's succession probably went uncontested.

) Given the exclusionary and ancestral conception of citizenship held by Greek city-states, a relatively large portion of the population took part in the government of Athens and of other radical democracies like it.

* Given any Banach space X, the continuous linear operators A: X → X form a unitary associative algebra ( using composition of operators as multiplication ); this is a Banach algebra.

* 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 other ZF axioms, the axiom of regularity is equivalent to the axiom of induction.

Given the United States ' large size it has numerous regional variations.

After Christians in Ephesus first wrote to their counterparts recommending Apollos to them, he went to Achaia where Paul names him as an apostle ( 1 Cor 4: 6, 9-13 ) Given that Paul only saw himself as an apostle ' untimely born ' ( 1 Cor 15: 8 ) it is certain that Apollos became an apostle in the regular way ( as a witness to the risen Lord and commissioned by Jesus-1 Cor 15: 5-9 ; 1 Cor 9: 1 ).< ref > So the Alexandrian recension ; the text in < sup > 38 </ sup > and Codex Bezae indicate that Apollos went to Corinth.

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 its " blue-water " bias, the navy is even less inclined to become involved in counterdrug operations than the army or air force.

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 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 any expression involving complex numbers, bras, kets, inner products, outer products, and / or linear operators ( but not addition ), written in bra-ket notation, the parenthetical groupings do not matter ( i. e., the associative property holds ).

* Given any combination of complex numbers, bras, kets, inner products, outer products, and / or linear operators, written in bra-ket notation, its Hermitian conjugate can be computed by reversing the order of the components, and taking the Hermitian conjugate of each.