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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 geometric
For two geometric objects P and Q represented by the relations P ( x, y ) and Q ( x, y ) the intersection is the collection of all points ( x, y ) which are in both relations.
For instance, volume and Riemannian curvature are invariants that can distinguish different geometric structures on the same smooth manifold — that is, one can smoothly " flatten out " certain manifolds, but it might require distorting the space and affecting the curvature or volume.
For example, the geometric mean can give a meaningful " average " to compare two companies which are each rated at 0 to 5 for their environmental sustainability, and are rated at 0 to 100 for their financial viability.
For instance, the geometric mean of two numbers, say 2 and 8, is just the square root of their product ; that is.
For all positive data sets containing at least one pair of unequal values, the harmonic mean is always the least of the three means, while the arithmetic mean is always the greatest of the three and the geometric mean is always in between ( see Inequality of arithmetic and geometric means.
For example, the geometric mean of 2 and 8 can be calculated as:
For instance, if one graphs a set of solutions of an equation in some higher dimensional space, he may ask about the geometric properties of the graph.
For example, the geometric mean of five values: 4, 36, 45, 50, 75 is:
For example, a similar geometric system was published in 1987 by Kjell Gustafson, whose method represents a rhythm as a two-dimensional graph.
For instance, an infinite geometric sum is implicit in Zeno's paradox of the dichotomy .< ref name =" Stillwell Infinite Series Early Results "> Later, Greek mathematicians such as Eudoxus and Archimedes made more explicit, but informal, use of the concepts of limits and convergence when they used the method of exhaustion to compute the area and volume of regions and solids.
For example, visual hallucinations during occipital lobe seizures are typically visions of brightly colored, geometric shapes that may move across the visual field, multiply, or form concentric rings and generally persist from a few seconds to a few minutes.
For the geometric parameter of bicycles, see Bicycle and motorcycle geometry.
: For " outer product " in geometric algebra, see exterior product.
For example, quantum finite automaton, geometric automaton and metric automaton have probabilistic acceptance.
For instance, the substitution x → ax gives the generating function for the geometric sequence 1, a, a < sup > 2 </ sup >, a < sup > 3 </ sup >,... for any constant a:
For example, the primitive equations which weather forecast models solve are more easily expressed in terms of geopotential than geometric height.
For instance in face recognition those geometric constraints can be obtained using principal component analysis ( PCA ) on a database of depth-maps of faces, allowing only surface normals solutions which are found in a normal population.
For example, in his treatise on mineralogy, Kitab al-Jamahir ( Book of Precious Stones ), he is " the most exact of experimental scientists ", while in the introduction to his study of India, he declares that " to execute our project, it has not been possible to follow the geometric method " and develops comparative sociology as a scientific method in the field.
For an infinitesimal deformation the displacements and the displacement gradients are small compared to unity, i. e., and, allowing for the geometric linearisation of the Lagrangian finite strain tensor, and the Eulerian finite strain tensor, i. e. the non-linear or second-order terms of the finite strain tensor can be neglected.
For infinitesimal deformations of a continuum body, in which the displacements and the displacement gradients are small compared to unity, i. e., and, it is possible to perform a geometric linearisation of the Lagrangian finite strain tensor, and the Eulerian finite strain tensor.
For his part Archimedes was the first to calculate the value of π and a geometric series, and also the earliest known mathematical physicist discovering the law of buoyancy, as well as conceiving the irrigation device known as Archimedes ' screw.
For a vector to represent a geometric object, it must be possible to describe how it looks in any other coordinate system.

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