Such a Galois closure should contain a splitting field for all the polynomials p over K that are minimal polynomials over K of elements a of K ′.

Such a sequence of basic polynomials is always of binomial type, and it can be shown that no other sequences of binomial type exist.

An important class of polynomials whose irreducibility can be established using Eisenstein's criterion is that of the cyclotomic polynomials for prime numbers p. Such a polynomial is obtained by dividing the polynomial by the linear factor corresponding to its obvious root 1 ( in fact its only rational root if ):

Such a homomorphism exists and is uniquely defined for every principal G-bundle P on M. If G is compact, then under the homomorphism, the cohomology ring of the classifying space for G-bundles B < sup > G </ sup > is isomorphic to the algebra of invariant polynomials:

Such problems are of extreme interest as well as importance and are so much like fighting in a rain forest or guerrilla warfare at night in tall grass that we might have to re-examine primitive conflicts for what they could teach.

Such manipulations are frequently encountered in his essay on the suppression of the monasteries during the English reformation.

Such support should not be difficult to come by if all the plans to be presented by the NCTA are as attractive as this outline of express buses coming into the downtown area.

Such measures are essential to its job of presenting business and Government with the facts required to meet the objective of expanding business and improving the operation of the economy.

Such additional daytime class 2, assignments are appropriate if optimum use is to be made of these frequencies, and the Commission has over the years made a large number of them.

Such locks are nearly always used where the switch points `` face '' oncoming traffic.

Such disks are very handy for cutting and shaping small parts.

Such modifications are all for the best but it takes something as different as a Deerstalker or a Jet to change arms-making concepts.

Such sweeping distractions are hardly conducive to `` Oscar '' winning performances.

Such ambiguous exercises compound confusion by making it worse compounded, and they are sometimes expanded until the cream of the jest sours.

Such high-resolution observations as these are needed at several wave lengths in order that the radio emission of the moon can be properly interpreted.

Such an instrument is expected to be especially useful if it could be used to measure the elasticity of heavy pastes such as printing inks, paints, adhesives, molten plastics, and bread dough, for the elasticity is related to those various properties termed `` length '', `` shortness '', `` spinnability '', etc., which are usually judged by subjective methods at present.

Such an indicator, or indicators, are needed as means of recognizing specific periods of delay in skeletal developmental progress.

Such specialized training institutions could be located near the most rapidly growing industries, where the equipment and job experience exist and where the future employment opportunities are located.

Such books are easy prey for critics.

Such systems are expensive and are oriented geographically.

Such projections, however, appear highly speculative and the capacities involved are far beyond those foreseen for food-preservation facilities.

Such cases are not considered here.

Such `` depletion allowances '', in the form of percentages of sales are authorized by tax law for specified raw materials producers using up their assets.

Such judgments are meaningful only in so far as persons are members of a world, let us say a community, that embraces Scarsdale or Yonkers, but is also infinitely richer since it is all-inclusive.

And new vistas of hairshirt asceticism are opened by scholarly monographs entitled: `` Friends, Romans, Countrymen, Lend Me Your Ear-Muffs '', `` Such a Phrase as Drifts Through Dream '', and `` The New Vocabularianism ''.

Such explanations do not imply that humans are always consciously calculating how to increase their inclusive fitness when they are doing altruistic acts.

Such methods are useful tools for biologists in many areas of research, including those who study the mechanisms of human and other diseases or fundamental biological processes in eukaryotic or prokaryotic cells.

Such an algorithm contradicts fundamental laws of mathematics because, if it existed, it could be applied repeatedly to losslessly reduce any file to length 0.

Such an assessment is known as a cost-benefit analysis, and is usually a fundamental piece of information for decision-makers, as it places a value on the net benefits ( or disbenefits ) of schemes and generates a ratio of benefits to costs which may be used to prioritise projects when funding is constrained.

Such Christians prefer to use the term fundamental, as opposed to fundamentalist ( e. g., Independent Fundamental Baptist and Independent Fundamental Churches of America ).

Such a fundamental understanding can result in what looks like slowness and can hide a mathematical intelligence potentially higher than that of a child who quickly memorizes the multiplication table despite possessing a less detailed understanding of the process of multiplication.

Such integrity is a fundamental principle of information assurance.

Such groups may perceive " freedom of knowledge " as a right, and / or as fundamental in realising the right to education, which is an internationally recognised human right, as well as the right to a free culture and the right to free communication.

Such credulity among scientists occurs only in relation to the deepest and most fundamental hypotheses for which they lack the facility to think differently in a comparably detailed and consistent way.

Such interactions would violate the fundamental laws of physics.

Such counter evidence and critiques did not dissuade the program however, and fundamental and heated disagreements between the two sides continued.

Such great early-20th century international operatic stars as Enrico Caruso, Rosa Ponselle and Titta Ruffo developed vocal techniques which harmoniously managed to combine fundamental bel canto precepts with a more ' modern ', straightforward mode of ripe-toned singing when delivering Verismo music, and their example has influenced operatic performers down to this day ( see Scott ).

Such mappings are fundamental to the algebraic geometry of finite fields.

Such a nondual unity is a fundamental aspect of this level of experience.

Such ' helper ranks " that sound at the fifth just above or fourth below the fundamental ( e. g., Bourdon 16 '), can create the impression of a stop an octave lower than the fundamental ( i. e., Bourdon 32 '), saving the space and money otherwise needed for larger bass pipes.

Such laws do not have to be consistent with the fundamental liberties under Articles 5 ( Right to Life and Personal Liberty ), 9 ( No Banishment from Malaysia and Freedom of movement within Malaysia ), 10 ( Freedom of Speech, Assembly and Association ) or 13 ( Rights to Property ).< Ref > The laws passed under Article 149 must contain in its recital one or more of the statements in Article 149 ( 1 )( a ) to ( f ).

Such branches of pharmacognosy are still of fundamental importance, particularly for pharmacopoeial identification and quality control purposes, but rapid development in other areas has enormously expanded the subject.

Such an appreciation, i. e. the understanding of how the model behaves in response to changes in its inputs, is of fundamental importance to ensure a correct use of the models.

Such jokes expose the fundamental criterion for joke definition, " funniness ", via its deletion.

Such spacetime transformations represent shifts between the reference frames of different observers, and so by Noether's theorem invariance under a transformation represents a fundamental conservation law.

Such a fundamental immorality justifies any difficulty or expense to bring to an end.

Such plenum cases often involve fundamental questions or cases that might alter the Supreme Courts own precedence.

Such information will advance understanding of the fundamental high-energy processes at the core of the solar flare problem.

Such a lens space has fundamental group for all, so spaces with different are not homotopy equivalent.