The standard definition focuses on the thematic and harmonic organization of tonal materials that are presented in an exposition, elaborated and contrasted in a development and then resolved harmonically and thematically in a recapitulation.

The first three movements are relatively traditional in structure and character, with a standard sonata form first movement ( even including an exact repeat of the exposition, unusual in Mahler ) leading to the middle movements-one slow, the other a scherzo-with-trios.

The movement can be explained structurally in terms of sonata form, but it departs from the standard model in a number of ways ( just before the recapitulation, for example, new material is introduced, which might have been used as the second subject in the exposition in a more conventional work ).

Those who accept it as their doctrinal standard recognize it to be a faithful exposition of the Holy Scriptures.

Coverup operation was extensive, consisting in partly admitting the undeniable, shifting the blame ( standard method of diffusion ), and minimizing the damage arisen from this unfortunate exposition of daily torture practices of USA soldiery.

Like many other concerti, the opening movement is written in the standard sonata-allegro form, but with considerably more emphasis placed on the exposition.

It is the standard textbook from which to learn forcing, though it has the disadvantage that the exposition of forcing relies somewhat on the earlier presentation of Martin's axiom, and the style is perhaps overly concise.

But standard perturbation theory techniques don't work at distances, where the running coupling constant reaches 1.

sum rules, and perturbation theory anomalies helped lay the foundations for the current standard model of elementary particle physics.

Because of this, the Coulomb gauge is not used in covariant perturbation theory, which has become standard for the treatment of relativistic quantum field theories such as quantum electrodynamics.

This is particularly important in cases such as bond-breaking reactions, diradicals, and first-row transition metals, where electronic near-degeneracies can invalidate the approximations inherent in many standard methods such as Hartree – Fock theory, multireference configuration interaction, finite-order Møller – Plesset perturbation theory, and coupled cluster theory.

Although originally controversial, the axiom of choice is now used without reservation by most mathematicians, and it is included in ZFC, the standard form of axiomatic set theory.

On the other hand, other foundational descriptions of category theory are considerably stronger, and an identical category-theoretic statement of choice may be stronger than the standard formulation, à la class theory, mentioned above.

A standard solution to this problem is found in Zermelo's set theory, which does not allow the unrestricted formation of sets from arbitrary properties.

Today the harmonized ISO / IEC 80000-13: 2008 – Quantities and units — Part 13: Information science and technology standard cancels and replaces subclauses 3. 8 and 3. 9 of IEC 60027-2: 2005, namely those related to Information theory and Prefixes for binary multiples.

The earliest and most direct kinds of observational evidence are the Hubble-type expansion seen in the redshifts of galaxies, the detailed measurements of the cosmic microwave background, the relative abundances of light elements produced by Big Bang nucleosynthesis, and today also the large scale distribution and apparent evolution of galaxies predicted to occur due to gravitational growth of structure in the standard theory.

The contributions of Kurt Gödel in 1940 and Paul Cohen in 1963 showed that the hypothesis can neither be disproved nor be proved using the axioms of Zermelo – Fraenkel set theory, the standard foundation of modern mathematics, provided ZF set theory is consistent.

A real number a is first-order definable in the language of set theory, without parameters, if there is a formula φ in the language of set theory, with one free variable, such that a is the unique real number such that φ ( a ) holds in the standard model of set theory ( see Kunen 1980: 153 ).

The related concept of " standard " numbers, which can only be defined within a finite time and space, is used to motivate axiomatic internal set theory, and provide a workable formulation for illimited and infinitesimal number.

Another theory is that the standard longhair dachshund was developed by breeding smooth dachshunds with various land and water spaniels.

* Down ( game theory ), a standard position in mathematical game theory

All the experiments conducted to date have found behavior in line with the predictions of standard quantum mechanics theory.

These models afford advantages over classical test theory, including the capacity to produce standard errors of measurement for each score or pattern of scores on assessments and the capacity to handle missing responses.

Von Neumann's original proof used Brouwer's fixed-point theorem on continuous mappings into compact convex sets, which became a standard method in game theory and mathematical economics.

Set theory has come to play the role of a foundational theory in modern mathematics, in the sense that it interprets propositions about mathematical objects ( for example, numbers and functions ) from all the traditional areas of mathematics ( such as algebra, analysis and topology ) in a single theory, and provides a standard set of axioms to prove or disprove them.

The fusion of the ideas coming from mathematics with those coming from chemistry is at the origin of a part of the standard terminology of graph theory.

In theory, only stereo equipment that met the standard could bear the words ' Hi-Fi '.

Theories of bounded rationality relax one or more assumptions of standard expected utility theory ”.

It was Thomas Young who in 1813 first used the term Indo-European, which became the standard scientific term through the work of Franz Bopp, whose systematic comparison of these and other old languages supported the theory.

As it is, they consider that the North is now reaping the fruits of excess egalitarianism, that in spite of its high standard of living the `` American way '' has been proved inferior to the English and Scandinavian ways, although they disapprove of the socialistic features of the latter.

This, however, cannot be done by a community whose very experience of truth is confused and incoherent: it has no absolute standard, and consequently cannot distinguish the absolute from the contingent.

This condition will undoubtedly continue until such time as a state uniform system of evaluation is established, or through mutual agreement of the local assessing officials for a method of standard assessment practice to be adopted.

The present proceeding is concerned with the standard broadcast ( AM ) band, from 540 kc. to 1600 kc..

By this standard, it is determined that where two stations operating on the same frequency are involved, objectionable interference from station A exists at any point within the service area of station B where station A's signal is of an intensity one-twentieth or more of the strength of station B's signal at that point.

A second fundamental principle is that involved particularly in the present proceeding -- the difference between nighttime and daytime propagation conditions with respect to the standard broadcast frequencies.

Several efforts were made in this direction, and though not all of them survive to this day, the Brown & Sharpe wire gage system was eventually adopted as the American standard and is still in common use today.

Another growth factor is increased consumer demand for better quality and larger quantities of fabrics that go with a rising standard of living.

Any alteration of one of these factors is distortion, although we generally use that word only for effects so pronounced that they can be stated quantitatively on the basis of standard tests.

The symbol for subtraction is the standard minus sign.

Actually, the engine displacement formula is the standard formula for computing the volume of a cylinder of any type with an added factor that represents the number of cylinders in the engine.

The most intriguing aspect of the S & W Magnum chambered for the new Jet is that it can also fire standard

The action is a drop-block, handling all the standard

For example, a Browning trap version of the Superposed over/under, the Broadway ( from $350 up, depending on grade ), differs from standard models in that it is equipped with a full beavertail fore end, a cushion recoil pad and a barrel-wide ventilated rib for fast sighting.

Most of it is panelized and utilizes standard materials, and requires the use of only simple tools.

The proper correlation of the art with the academic can be achieved only if this standard is observed.

Although the standard deviation values on which spread of the lines is based are relatively larger for those centers which begin to ossify early ( Table 1 ), there are considerable differences in this value between centers having the closely timed Onsets.

The second situation is illustrated by the operator T on Af ( F any field ) represented in the standard basis by Af.

In the stock market, the normal trading package is a hundred shares, just as 5,000 bushels is the standard grain contract package.

To the extent that a tale is twice told, its final author must be suspect, although plagiarism in an oral tradition is less a misdemeanor than the standard modus dicendi.

Specimens are allowed to reach moisture equilibrium with a standard atmosphere of Af and Af and then laid out without tension on a flat, polished surface, care being taken that the fabric is free from wrinkles or creases.