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For and given
For the moment there was no woman in his life, and it was this vacuum that had given Claire her opportunity.
For readjustment to the U.S., volunteers should be given some separation allowance at the end of their overseas service, based on the length of time served.
For purposes of sample selection only ( individual tests were given later ) we obtained group test scores of reading achievement and intelligence from school records of the entire third-grade population in each school system.
For the industry of this model, the effect of such public pressures in the past has been to hold the price well below the short-run profit-maximizing price ( given the wage rate and the level of GNP ), and even below the entry-limited price ( but not below average cost ).
For some substances, auxiliary properties such as the melting point are given.
For circular fibers in a closely packed hexagonal array, the packing efficiency is given by: Af where Af, and 0.906 is the ratio of the area of a circle to that of the circumscribed hexagon.
For any choice of admissible policy Af in the first stage, the state of the stream leaving this stage is given by Af.
For Mrs. Shaefer -- who had been given a clean bill of health by her own physician at the time she visited Lee -- and her friend were agents for the California Pure Food and Drug Inspection Bureau.
On the clock given him was the inscription, `` For Outstanding Contribution to Billiken Basketball, 1960-61 ''.
For nearly a year, they have been receiving counseling, separately and together, in an effort to understand and overcome the antagonisms which had given rise to the possibility of divorce.
A Sonata For Violin And Piano, called `` Bella Bella '', by Robert Fleming, was given its first United States performance.
For this reason the examples given below are grouped by voltage level.
" For some people, a program is only an algorithm if it stops eventually ; for others, a program is only an algorithm if it stops before a given number of calculation steps.
Algorithm versus function computable by an algorithm: For a given function multiple algorithms may exist.
For Altaicists, the version of Altaic they favor is given at the end of the entry, if other than the prevailing one of Turkic – Mongolic – Tungusic – Korean – Japanese.
For each element a of a group G, conjugation by a is the operation φ < sub > a </ sub >: G → G given by ( or a < sup >− 1 </ sup > ga ; usage varies ).
For example, one can say for a given transition that it corresponds to the excitation of an electron from an occupied orbital to a given unoccupied orbital.
For an ideal gas the internal energy is given by
For example, given two image elements A and B, the most common compositing operation is to combine the images such that A appears in the foreground and B appears in the background.
For example, if for a given problem size a parallelized implementation of an algorithm can run 12 % of the algorithm's operations arbitrarily quickly ( while the remaining 88 % of the operations are not parallelizable ), Amdahl's law states that the maximum speedup of the parallelized version is times as fast as the non-parallelized implementation.
For example, some see the World Bank and the IMF as corrupt bureaucracies which have given repeated loans to dictators who never do any reforms.
For a first order predicate calculus, with no (" proper ") axioms, Gödel's completeness theorem states that the theorems ( provable statements ) are exactly the logically valid well-formed formulas, so identifying valid formulas is recursively enumerable: given unbounded resources, any valid formula can eventually be proven.
For cross-referencing, they are given with list indices from Andreini ( 1-22 ), Williams ( 1-2, 9-19 ), Johnson ( 11-19, 21-25, 31-34, 41-49, 51-52, 61-65 ), and Grünbaum ( 1-28 ).
For curves given by the graph of a function, horizontal asymptotes are horizontal lines that the graph of the function approaches as x tends to Vertical asymptotes are vertical lines near which the function grows without bound.

For and nonzero
*( EF2 ) For all nonzero a and b in R,.
* K, the ring of polynomials over a field K. For each nonzero polynomial P, define f ( P ) to be the degree of P.
* K < nowiki ></ nowiki > X < nowiki ></ nowiki >, the ring of formal power series over the field K. For each nonzero power series P, define f ( P ) as the degree of the smallest power of X occurring in P. In particular, for two nonzero power series P and Q, f ( P )≤ f ( Q ) iff P divides Q.
For another example, the nonzero complex numbers form a group under the operation of multiplication, as do the nonzero real numbers.
For instance, Fermat's little theorem for the nonzero integers modulo a prime generalizes to Euler's theorem for the invertible numbers modulo any nonzero integer, which generalizes to Lagrange's theorem for finite groups.
For example, if an apple is sitting in a glass elevator that is descending, an outside observer looking into the elevator sees the apple moving, so to that observer the apple has a nonzero momentum.
For a nonzero vector of finite norm in, one can assume that is nonzero, or to fix ideas.
For example, suppose ( generalizing to nonzero is straightforward ).
For nonzero Q there exists a canonical linear isomorphism between Λ ( V ) and Cℓ ( V, Q ) whenever the ground field K does not have characteristic two.
# Structures such as fields have some axioms that hold only for nonzero members of S. For an algebraic structure to be a variety, its operations must be defined for all members of S ; there can be no partial operations.
For a general n × n invertible matrix A, i. e., one with nonzero determinant, A < sup >− 1 </ sup > can thus be written as an ( n − 1 )- th order polynomial expression in A: As indicated, the Cayley – Hamilton theorem amounts to the identity
For exactly the same reasons as before, the conjugation operator yields a norm and a multiplicative inverse of any nonzero element.
For instance, it is possible to attempt to " repair " the proof by supposing that a and b have a definite nonzero value to begin with, for instance, at the outset one can suppose that a and b are both equal to one:
For functions of a single variable, the theorem states that if ƒ is a continuously differentiable function with nonzero derivative at the point a, then ƒ is invertible in a neighborhood of a, the inverse is continuously differentiable, and
For a curve of degree d, the weight of any control point is only nonzero in d + 1 intervals of the parameter space.
For each nonzero countable ordinal α there are classes,, and.
For a slower than light particle, a particle with a nonzero rest mass, the formula becomes
For example, when one is subtracting ten thousand minus 4, 679, the leftmost three digits of 4, 679 — 4, 6 and 7 -- are subtracted from 9, and the rightmost nonzero digit — that is, 9 -- is subtracted from 10, yielding the solution: 5, 321.
For real nonzero values of x, the exponential integral Ei ( x ) is defined as

0.130 seconds.