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, the prime number theorem states that the number of prime numbers less than or equal to N is asymptotically equal to N / ln N. Therefore the proportion of prime integers is roughly 1 / ln N, which tends to 0.

* For a finite field of prime order p, the algebraic closure is a countably infinite field which contains a copy of the field of order p < sup > n </ sup > for each positive integer n ( and is in fact the union of these copies ).

For example, the set with elements 2, 3, and 5 is equal to the set of all prime numbers less than 6.

For example, the Riemann hypothesis is a conjecture from number theory that ( amongst other things ) makes predictions about the distribution of prime numbers.

For 50 years, Coronation Street has remained at the centre of ITV's prime time schedule.

For example, primality testing is the problem of determining whether a given number is prime or not.

For a prime p, the p-adic numbers arise by completing the rational numbers with respect to a different metric.

For each of the prime fields, one elliptic curve is recommended.

For example, neither 6 nor 35 is a prime number, since they both have two prime factors: 6 = 2 × 3 and 35 = 5 × 7.

The GCD of two numbers a and b is the product of the prime factors shared by the two numbers, where a same prime factor can be used multiple times, but only as long as the product of these factors divides both a and b. For example, since 1386 can be factored into 2 × 3 × 3 × 7 × 11, and 3213 can be factored into 3 × 3 × 3 × 7 × 17, the greatest common divisor of 1386 and 3213 equals 63 = 3 × 3 × 7, the product of their shared prime factors.

* For every prime number p and positive integer n, there exists a finite field with p < sup > n </ sup > elements.

For example, 9 and 28 are relatively prime.

For example, Campbell states that, " There have been systems of religion where the mother is the prime parent, the source ... We talk of Mother Earth.

For prime minister, he selected Odilon Barrot, an unobjectionable middle-road parliamentarian, who had led the " loyal opposition " under Louis-Philippe.

For most of Nehru's term as prime minister, India would continue to face serious food shortages despite progress and increases in agricultural production.

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 instance, Goldbach's conjecture is the assertion that every even number ( greater than 2 ) is the sum of two prime numbers.

For example, a non-identity finite group is simple if and only if it is isomorphic to all of its non-identity homomorphic images, a finite group is perfect if and only if it has no normal subgroups of prime index, and a group is imperfect if and only if the derived subgroup is not supplemented by any proper normal subgroup.

For many people choosing an office suite, prime considerations include how valuable having learned that office suite will prove to potential employers, and how well the software interoperates with other users.

For example, 5 is prime, as only 1 and 5 divide it, whereas 6 is composite, since it has the divisors 2 and 3 in addition to 1 and 6.