E – E < sub > C </ sub >, and in particular we can define Sommerfeld's parameter ζ

The strongest appeal of the Copernican formulation consisted in just this: ideally, the justification for dealing with special problems in particular ways is completely set out in the basic ' rules ' of the theory.

What with traders trading for so many different objectives, and what with there being so many unique and individualized market theories and trading techniques in use, and more coming into use all the time, it is hard to imagine how any particular theory or technique could acquire enough `` fans '' to invalidate itself.

However, that particular case is a theorem of Zermelo – Fraenkel set theory without the axiom of choice ( ZF ); it is easily proved by mathematical induction.

It is possible to prove many theorems using neither the axiom of choice nor its negation ; such statements will be true in any model of Zermelo – Fraenkel set theory ( ZF ), regardless of the truth or falsity of the axiom of choice in that particular model.

Instead of starting from theory and applying theory to a particular case, casuists start with the particular case itself and then ask what morally significant features ( including both theory and practical considerations ) ought to be considered for that particular case.

Field automorphisms are important to the theory of field extensions, in particular Galois extensions.

Atle Selberg ( 14 June 1917 – 6 August 2007 ) was a Norwegian mathematician known for his work in analytic number theory, and in the theory of automorphic forms, in particular bringing them into relation with spectral theory.

La Longue Marche à travers la théorie de Galois Long March Through Galois Theory is an approximately 1600-page handwritten manuscript produced by Grothendieck during the years 1980 – 1981, containing many of the ideas leading to the Esquisse d ' un programme ( see below, and also a more detailed entry ), and in particular studying the Teichmüller theory.

In the 1990s, Jürgen Schmidhuber described an algorithmic theory of beauty which takes the subjectivity of the observer into account and postulates: among several observations classified as comparable by a given subjective observer, the aesthetically most pleasing one is the one with the shortest description, given the observer ’ s previous knowledge and his particular method for encoding the data.

However, Davy failed to develop a new theory, concluding that " acidity does not depend upon any particular elementary substance, but upon peculiar arrangement of various substances ".

The inability to comprehend any aspect of the thing other than its properties implies, this argument maintains, that one cannot conceive of a bare particular ( a substance without properties ), an implication that directly opposes substance theory.

Chaos theory and the sensitive dependence on initial conditions was described in the literature in a particular case of the three-body problem by Henri Poincaré in 1890.

Much of anthropological theory has originated in an appreciation of and interest in the tension between the local ( particular cultures ) and the global ( a universal human nature, or the web of connections between people in distinct places / circumstances ).

Aside from controversies over the merits of particular conspiratorial claims, the general discussion of conspiracy theory is itself a matter of some public contention.

In particular, the photon model accounted for the frequency dependence of light's energy, and explained the ability of matter and radiation to be in thermal equilibrium.

It also accounted for anomalous observations, including the properties of black body radiation, that other physicists, most notably Max Planck, had sought to explain using semiclassical models, in which light is still described by Maxwell's equations, but the material objects that emit and absorb light, do so in amounts of energy that are quantized ( i. e., they change energy only by certain particular discrete amounts and cannot change energy in any arbitrary way ).

This is the actual intersection of the two planes at any particular moment, with all motions accounted for.

Taken to its extreme, the " epigenetic code " could represent the total state of the cell, with the position of each molecule accounted for in an epigenomic map, a diagrammatic representation of the gene expression, DNA methylation and histone modification status of a particular genomic region.

The participative / inclusive process leading to a particular design, and the supporting resources available with it should be accounted when we talk about Open Standards:

In the case of Bell test experiments, if there are sources of error ( that are not accounted for by the experimentalists ) that might be of enough importance to explain why a particular experiment gives results in favor of quantum entanglement as opposed to local realism, they are called loopholes.

In particular, she suggests that inter-Service friction accounted for much of the poor liaison in Hawaii.

In particular, beginning in 1892, he wrote about the function of countershading in nature, by which forms appear less round and less solid through inverted shading, by which he accounted for the white undersides of animals.

In the particular case of stretching DNA in physiological buffer ( near neutral pH, ionic strength approximately 100 mM ) at room temperature, the compliance of the DNA along the contour must be accounted for.

If a work is divided into several large segments, a last-minute drawing of random numbers may determine the order of the segments for any particular performance.

Each will decide on his own course somewhere between these two extreme cases according to the sense of responsibility which is determined for him by the particular circumstances of his own life.

In particular, Governor Nelson Rockefeller has expressed as cogently and clearly as anyone the case for a resumption of atmospheric tests.

Second, we can make assistance for particular projects conditional on the consistency of such projects with the program.

It would seem, then, that movable property and equipment is not taxed as a whole but that certain types are taxed in towns where this is bound to be expedient for that particular kind of personal property.

The Armed Forces Epidemiological Board agreed to submit each month a report for one of its 12 commissions, so that each commission will report once a year on some phase of its work calculated to be of particular interest and value to medical officers of the Armed Forces.

Determine for each State ( except the Virgin Islands, Guam and Puerto Rico, and, prior to 1962, Alaska and Hawaii ) that percentage which bears the same ratio to 50% as the particular State's average per capita income bears to the average per capita income of the U. S..

If the resulting difference for the particular State is less or more than these extremes, the State's allotment percentage must be raised or lowered to the appropriate extreme.

Determine the particular State's unadjusted allotment for the particular fiscal year.

Determine for each State ( except the Virgin Islands, Guam, Puerto Rico, and, prior to 1962, Alaska and Hawaii ), that percentage which bears the same ration to 40% as the particular State's average per capita income bears to the average per capita income of the United States.

If the resulting difference for the particular State is less or more than these extremes, the State's Federal share must be raised or lowered to the appropriate extreme.

Petitioner was not entitled to have the hearing officer's notes and report, especially since he failed to show any particular need for them and he did have a copy of the Department of Justice's recommendation to the appeal board.

Petitioner was not entitled, either in the administrative hearing at the Department of Justice or at his trial, to inspect the original report of the Federal Bureau of Investigation, since he was furnished a resume of it, did not challenge its accuracy, and showed no particular need for the original report.

In addition, petitioner has failed to show any particular need for the report and notes.

The 20-to-1 ratio for cochannel interference embodies one of the fundamental limiting principles which we must always take into account in AM assignments and allocations -- that signals from a particular station are potential sources of objectionable interference over an area much greater than that within which they provide useful service.

For this reason, the more uncertain skywave service was denominated `` secondary '' in our rules, as compared to the steadier, more reliable groundwave `` primary service '', and, for both skywave service and skywave interference, signal strength is expressed in terms of percentage of time a particular signal-intensity level is exceeded -- 50 percent of the time for skywave service, 10 percent of the time for skywave interference.

Perhaps the outstanding standard bearer of Mr. Brown's tradition for accuracy was Mr. Oscar J. Beale, whose mechanical genius closely paralleled that of Mr. Brown, and whose particular forte was the development of the exceedingly accurate measuring machinery that enabled Brown & Sharpe to manufacture gages, and therefore its products, with an accuracy exceeding anything then available elsewhere in the world.

Our instructions assume you are building this particular frame, which is for a junction.

It is, I am reliably given to understand, the technical argot for those who engage in your particular branch of the boost ; ;

With due consideration for the limits of precision in assessing, expected rate of change in ossification of girls age 2 years, and the known variations in rate of ossification of these children as described in our preceding paper in the Supplement, each arrow with a `` shaft length '' of four months or less was selected as indicating `` same schedule '' at Onset and Completion, for this particular epiphysis.