While individual equations present a kind of puzzle and have been considered throughout history, the formulation of general theories of Diophantine equations ( beyond the theory of quadratic forms ) was an achievement of the twentieth century.

Though this formulation provided a key link to the low-energy limits of string theories, it was recognized that a full high-energy formulation ( or " UV-completion ") of M-theory was needed.

Though theories of quantum mechanics continue to evolve to this day, there is a basic framework for the mathematical formulation of quantum mechanics which underlies most approaches and can be traced back to the mathematical work of John von Neumann.

: This formulation allows for stochastic theories such as the creation and annihilation of particles.

Also like Newton's Second law, the Schrödinger equation describes time in a way that is inconvenient for relativistic theories, a problem that is not as severe in matrix mechanics and completely absent in the path integral formulation.

Nevertheless, despite the formulation of these theories and others, there is little critical consensus as to the inherent ' meaning ' behind Katherina's speech.

Some of the significant achievements of early Muslim philosophers included the development of a strict science of citation, the isnad or " backing "; the development of a method of open inquiry to disprove claims, the ijtihad, which could be generally applied to many types of questions ( although which to apply it to is an ethical question ); the willingness to both accept and challenge authority within the same process ; recognition that science and philosophy are both subordinate to morality, and that moral choices are prior to any investigation or concern with either ; the separation of theology ( kalam ) and law ( shariah ) during the early Abbasid period, a precursor to secularism ; the distinction between religion and philosophy, marking the beginning of secular thought ; the beginning of a peer review process ; early ideas on evolution ; the beginnings of the scientific method, an important contribution to the philosophy of science ; the introduction of temporal modal logic and inductive logic ; the beginning of social philosophy, including the formulation of theories on social cohesion and social conflict ; the beginning of the philosophy of history ; the development of the philosophical novel and the concepts of empiricism and tabula rasa ; and distinguishing between essence and existence.

* Hamiltonian formulation of Wilson's lattice gauge theories, John Kogut and Leonard Susskind, Phys.

The Journal of Mathematical Physics defines the field as: " the application of mathematics to problems in physics and the development of mathematical methods suitable for such applications and for the formulation of physical theories ".

Many important advances in astronomy and cosmology, and the formulation of new cosmological theories, have occurred through the resolution of apparent violations of the cosmological principle.

Introduced in a 2007 Academy of Management Review article, it synthesizes into a single formulation the primary aspects ( including time as a fundamental term ) of several other major motivational theories, including Incentive Theory, Drive Theory, Need Theory, Self-Efficacy and Goal Setting.

Mathematical physics is concerned with " the application of mathematics to problems in physics and the development of mathematical methods suitable for such applications and for the formulation of physical theories ".

This formulation of Poincaré Duality has become quite popular as it provides a means to define Poincaré Duality for any generalized homology theories provided one has a Thom Isomorphism for that homology theory.

The classical formulation of mirror symmetry relates two Calabi-Yau threefolds M and W whose Hodge numbers h < sup > 1, 1 </ sup > and h < sup > 1, 2 </ sup > are swapped ; string theory compactified on these two manifolds lead to identical effective field theories.

In physics, Faddeev – Popov ghosts ( also called ghost fields ) are additional fields which are introduced into gauge quantum field theories to maintain the consistency of the path integral formulation.

The necessity for Faddeev – Popov ghosts follows from the requirement that in the path integral formulation, quantum field theories should yield unambiguous, non-singular solutions.

Yang – Mills theories met with general acceptance in the physics community after Gerard't Hooft, in 1972, worked out their renormalization, relying on a formulation of the problem worked out by his advisor Martinus Veltman.

In theoretical physics, the Batalin – Vilkovisky ( BV ) formalism ( named for Igor Batalin and Grigori Vilkovisky ) was developed as a method for determining the ghost structure for Lagrangian gauge theories, such as gravity and supergravity, whose corresponding Hamiltonian formulation has constraints not related to a Lie algebra ( i. e., the role of Lie algebra structure constants are played by more general structure functions ).

An idea that underlies this formulation is that translation implies symmetry and transitivity so that if theory T is translatable with theory T ', then T ' can be translated to T, and furthermore if there is a third theory T and this can be translated to T ', then theories T and T ' cannot be incommensurable, as long as the transitive relationship and the symmetrical relationship assures that their statements can be compared one to another.

In the third stage of Kuhn's work the formulation of the thesis of incommensurability became refined in taxonomic terms and is explained as a function of the change in the relations of similarity and difference between two theories.

In order to understand the theological significance of Acacianism as a critical episode in both the logical and historical progress of Arianism, it is needful to recall that the great definition of the Homoousion, promulgated at Nicaea in 325, rather than putting an end to further discussion, became the occasion for keener debate and for still more confusion of statement in the formulation of theories on the relationship of Our Lord to His Father.

Between 1890 and 1919 the world became a geostrategist's paradise, leading to the formulation of the classical geopolitical theories.

All modern theories of syntax have some part of the theory which deals with the correct formulation of the rules for wh-movement.

* Afri-Cola, a German brand, had a higher caffeine content ( about 250 mg / L ) until the product was relaunched with a new formulation in 1999.

Many-worlds is often referred to as a theory, rather than just an interpretation, by those who propose that many-worlds can make testable predictions ( such as David Deutsch ) or is falsifiable ( such as Everett ) or by those who propose that all the other, non-MW interpretations, are inconsistent, illogical or unscientific in their handling of measurements ; Hugh Everett argued that his formulation was a metatheory, since it made statements about other interpretations of quantum theory ; that it was the " only completely coherent approach to explaining both the contents of quantum mechanics and the appearance of the world.

Among the goals of ethnology have been the reconstruction of human history, and the formulation of cultural invariants, such as the incest taboo and culture change, and the formulation of generalizations about " human nature ", a concept which has been criticized since the 19th century by various philosophers ( Hegel, Marx, structuralism, etc .).

After a dose of conventional oral oxycodone, peak plasma levels of the drug are attained in approximately one hour ; in contrast, after a dose of OxyContin ( an oral continuous release formulation ), peak plasma levels of oxycodone occur in about three hours.

This formulation implicitly acknowledges that Sapir and Whorf were not the first or only scholars to have theorized about relations between language and thought and that other strands of thinking about the issue also exist.

While Hobbes justifies absolute monarchy, this work is the first to posit that the temporal power of a monarch comes about, not because God has ordained that he be monarch, but because his subjects have freely yielded their own power and freedom to him-in other words, Hobbes replaces the divine right of kings with an early formulation of the social contract.

A similar criticism, responding to large software company complaints about the slow pace of W3C's formulation of XML / web services standards, appeared in Cnet's news. com in 2002:

Insightful book about the application of General Semantics to psychotherapy ; was an acknowledged influence on Richard Bandler and John Grinder in their formulation of Neuro-Linguistic Programming.

One formulation is that if journals in a field are sorted by number of articles into three groups, each with about one-third of all articles, then the number of journals in each group will be proportional to 1: n: n².

The ancient Roman Republic's " citizen lawmaking " – citizen formulation and passage of law, as well as citizen veto of legislature-made law – began about 449 BC and lasted the approximately 400 years to the death of Julius Caesar in 44 BC.

Polypropylene ( PP ) is easy to repeatedly autoclave ; however, autoclaving in excess of about ( depending on the chemical formulation: typical commercial grade polypropylene melts in excess of ), can warp or damage polypropylene graduated cylinders, affecting accuracy.

Since the precise notion of " manifold " was not available to Hilbert, there is room for some debate about the formulation of the problem in contemporary mathematical language.

The spiritual bearing in strategy, which Musashi writes about concerns your temperament and spirituality whilst in the midst of, or in formulation of a battle.

Michele Pujol points to five specific historical assumptions about woman that arose, became embedded in the formulation of economics, and continue to be used to maintain that women are different from the masculinized norms and exclude them.

Goffman's greatest contribution to social theory is his formulation of symbolic interaction as dramaturgical perspective in his 1959 book The Presentation of Self in Everyday Life, which begins with an epigraph by George Santayana about masks.

Together with the mathematical formulation of quantum mechanics, in large measure due to John von Neumann, this gave the treatment familiar since about 1930.

Loop quantum gravity ( LQG ), in its current formulation, predicts no additional spatial dimensions, nor anything else about particle physics.

Given that finite fields are discrete in nature, and topology speaks only about the continuous, the detailed formulation of Weil ( based on working out some examples ) was striking and novel.

But the credit for the formulation of the principle as it applies to the action is often given to Pierre-Louis Moreau de Maupertuis, who wrote about it in 1744 and 1746.

His Methods in Structural Linguistics ( 1951 ) is the definitive formulation of descriptive structural work as he had developed it up to about 1945.

As an epistemological theory about the possibility of knowledge of objects in the external world, however, it is probable that the most easily understandable formulation of phenomenalism is to be found in the transcendental aesthetics of Immanuel Kant.

In this context, the recognition of different types of cities on the basis of, for example, their functional specialization may enable the identification of spatial regularities in the distribution and structure of urban functions and the formulation of hypotheses about the resulting patterns.