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 example, consider the quadratic polynomial

For quadratic forms of any signature, an orthogonal basis

For r =-1, 1 and 2 we have the harmonic, the arithmetic and the quadratic means respectively.

Thus Legendre's contribution lay in introducing a convenient notation that recorded quadratic residuosity of a mod p. For the sake of comparison, Gauss used the notation, according to whether a is a residue or a non-residue modulo p.

For example, prime ideals in the ring of integers of quadratic number fields can be used in proving quadratic reciprocity, a statement that concerns the solvability of quadratic equations

For instance, one could define a general quadratic function by defining

For example, the discriminant of the quadratic polynomial

For example, in the quadratic polynomial

For example, consider the venerable quadratic equation:

For example, in a pseudo-Euclidean space one has the use of a quadratic form:

Much attention has been given to the special case that the function f is a polynomial ; there exist root-finding algorithms exploiting the polynomial nature of f. For a univariate polynomial of degree less than five, there are closed form solutions such as the quadratic formula which produce all roots.

For a free particle, the dispersion relation is a quadratic, and so the effective mass would be constant ( and equal to the real mass ).

For a given n a list of the quadratic residues modulo n may be obtained by simply squaring the numbers 0, 1, …, n − 1.

For this reason some authors add to the definition that a quadratic residue q must not only be a square but must also be relatively prime to the modulus n.

For example, if p ≡ 1 ( mod 8 ), ( mod 12 ), ( mod 5 ) and ( mod 28 ), then by the law of quadratic reciprocity 2, 3, 5, and 7 will all be residues modulo p, and thus all numbers 1 – 10 will be.

For such a function, a smooth quadratic interpolant like the one used in Simpson's rule will give good results.

We can use this fact to prove part of a famous result: for any prime p such that p ≡ 1 ( mod 4 ) the number (− 1 ) is a square ( quadratic residue ) mod p. For suppose p = 4k + 1 for some integer k. Then we can take m = 2k above, and we conclude that

For some small fields, such as the field of rational numbers or its quadratic imaginary extensions there is a more detailed theory which provides more information.

For instance, a coherent state describes the oscillating motion of the particle in a quadratic potential well ( for an early reference, see e. g.

For an equation involving a non-monic quadratic, the first step to solving them is to divide through by the coefficient of x < sup > 2 </ sup >.

For the case of the quadratic kernel, we have:

For example, quadratic fields K of degree 2 over Q are either real ( and then totally real ), or complex, depending on whether the square root of a positive or negative number is adjoined to Q.