For instance, can hold an unboxed integer in a range supported by the hardware and implementation, permitting more efficient arithmetic than on big integers or arbitrary precision types.

For instance, there is no instruction to load an arbitrary “ immediate ” value into an accumulator ( although memory reference instructions do encode such a value to form an effective address ).

For arbitrary n ≥ 2 we may generalize this formula, as noted above, by interpreting the third equation for the harmonic mean differently.

For who durst set himself in opposition to the crown and ministry, or aspire to the character of being a patron of freedom, while exposed to so arbitrary a jurisdiction?

For that reason it is beneficial to include keyframes at arbitrary intervals while encoding video.

Note: For any arbitrary number of propositional constants, we can form a finite number of cases which list their possible truth-values.

For a boost in an arbitrary direction with velocity v, it is convenient to decompose the spatial vector r into components perpendicular and parallel to v:

For an arbitrary n there exists a monotone formula for majority of size O ( n < sup > 5. 3 </ sup >).

For a number of years after the passing of the first Quarantine Act ( 1710 ) the protective practices in England were of the most haphazard and arbitrary kind.

For an arbitrary ring, let be the underlying additive group.

For intersexual selection to work, one sex must evolve a feature alluring to the opposite sex, sometimes resulting in a " fashion fad " of intense selection in an arbitrary direction.

For example, many theories of quantum gravity can create universes with arbitrary numbers of dimensions or with arbitrary cosmological constants.

It is important to realize that the word problem is in fact solvable for many groups G. For example, polycyclic groups have solvable word problems since the normal form of an arbitrary word in a polycyclic presentation is readily computable ; other algorithms for groups may, in suitable circumstances, also solve the word problem, see the Todd – Coxeter algorithm and the Knuth – Bendix completion algorithm.

For an initial value problem, the arbitrary functions and can be determined to satisfy initial conditions:

For arbitrary square matrices M, N we write M ≥ N if M − N ≥ 0 ; i. e., M − N is positive semi-definite.

For example, in the IEEE 754-2008 standard it means the number of bits in the significand, so it is used as a measure for the relative accuracy with which an arbitrary number can be represented.

For any two arbitrary integers, m and n, form the equimultiples

For triclinic, orthorhombic, and cubic crystal systems the axis designation is arbitrary and there is no principle axis.

For example, in computer graphics rendering, the scene is divided until each node of the BSP tree contains only polygons that can render in arbitrary order.

For a flat spatial geometry, the scale of any properties of the topology is arbitrary and may or may not be directly detectable.

For an arbitrary heat engine, the efficiency is:

For example, with radiographic equipment such as a CT scanner, one would reasonably require the operator to have competence in radiological safety ; but for consumer electronics, the goal ( distant as it often may be ) is to shield the user from having to possess any arbitrary threshold of skill.

For trips into largely arbitrary Earth orbits, almost any time will do.

For example, it is not possible to obtain a filter which has both an arbitrary impulse response and arbitrary frequency function.

For it includes the emotional ties that bind men to their homeland and the complex motivations that hold a large group of people together as a unit.

For ten years a small group of European and U.S. critics has been calling attention to the half-forgotten Austrian expressionist Egon Schiele, who died 42 years ago at the age of 28.

For example, the steering committee might announce that the group felt a topic under study should not be dropped for an additional week as there was still too much of it untouched.

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 if the small group notion involves the implicit claim that the phenomena of sociological investigations are of atomic or subatomic proportions, the philosopher needs to know the extent to which such entities are valid.

** For every non-empty set S there is a binary operation defined on S that makes it a group.

For example, in some groups, the group operation is commutative, and this can be asserted with the introduction of an additional axiom, but without this axiom we can do quite well developing ( the more general ) group theory, and we can even take its negation as an axiom for the study of non-commutative groups.

For every group G there is a natural group homomorphism G → Aut ( G ) whose image is the group Inn ( G ) of inner automorphisms and whose kernel is the center of G. Thus, if G has trivial center it can be embedded into its own automorphism group.

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, three isomers exist for cresol because the methyl group and the hydroxyl group can be placed next to each other ( ortho ), one position removed from each other ( meta ), or two positions removed from each other ( para ).

For the bottom, only the group of higher priority need be considered.

For the U. S. Government's scientific enterprise, a significant impact of NAPAP were lessons learned in the assessment process and in environmental research management to a relatively large group of scientists, program managers and the public.

For the case of a non-commutative base ring R and a right module M < sub > R </ sub > and a left module < sub > R </ sub > N, we can define a bilinear map, where T is an abelian group, such that for any n in N, is a group homomorphism, and for any m in M, is a group homomorphism too, and which also satisfies

For a few years, this group of animals was regarded as a subfamily, called the Callitrichinae, of the family Cebidae.

For example, it is thought that ammonites were the principal food of mosasaurs, a group of giant marine reptiles that became extinct at the boundary .< ref name =" Kauffman ">

For example, an " X " is used to indicate a variable group amongst a class of compounds ( though usually a halogen ), while " R " is used for a radical, meaning a compound structure such as a hydrocarbon chain.

For example, it is thought that ammonites were the principal food of mosasaurs, a group of giant marine reptiles that became extinct at the boundary .< ref name =" Kauffman ">

For example, it is immediately proven from the axioms that the identity element of a group is unique.