Though the concept of observing a subject from different points in space and time simultaneously ( multiple or mobile perspective ) developed by Metzinger and Gleizes was not derived directly from Albert Einstein's theory of relativity, it was certainly influenced in a similar way, through the work of Jules Henri Poincaré ( particularly Science and Hypothesis ), the French mathematician, theoretical physicist and philosopher of science, who made many fundamental contributions to algebraic topology, celestial mechanics, quantum theory and made an important step in the formulation of the theory of special relativity.

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.

Recall that any vector space V over a field has a basis ; this is a set S such that any element of V is a unique ( finite ) linear combination of elements of S. In the formulation of Poincaré – Birkhoff – Witt theorem we consider bases of which the elements are totally ordered by some relation which we denote ≤.

Moreover, just like in the quadratic form formulation of Poincaré duality, there is a canonical isomorphism of-modules, where denotes the field of fractions of.

In his paper Electromagnetic phenomena in a system moving with any velocity smaller than that of light, Lorentz ( 1904 ) was following the suggestion of Poincaré and attempted to create a formulation of Electrodynamics, which explains the failure of all known aether drift experiments, i. e. the validity of the relativity principle.

In 1907 Minkowski named four predecessors who contributed to the formulation of the relativity principle: Lorentz, Einstein, Poincaré and Planck.

Einstein's presentation differed from the explanations given by FitzGerald, Larmor, and Lorentz, but was similar in many respects to the formulation by Poincaré ( 1905 ).

This relative state formulation, where all states ( sets of measures ) can only be measured relative to other such states, avoids a number of problems in quantum theory, including the original duality – no collapse takes place, the indeterminacy simply grows ( or moves ) to a larger system.

An equivalent formulation that highlights the duality to the inverse limit is that an element is equivalent to all its images under the maps of the directed system, i. e..

It combines with Pontryagin duality to give a clearer if more abstract formulation of the central result, the Artin reciprocity law.

While the role of K above in general Serre duality is played by the determinant line bundle of the cotangent bundle, when V is a manifold, in full generality K cannot merely be a single sheaf in the absence of some hypothesis of non-singularity on V. The formulation in full generality uses a derived category and Ext functors, to allow for the fact that K is now represented by a chain complex of sheaves, namely, the dualizing complex.

The original impulse to develop the " derived " formalism came from the need to find a suitable formulation of Grothendieck's coherent duality theory.

The latter formulation follows from the former through an application of Hölder's inequality and a duality argument.

The formulation of more precise versions of the meaning of compactification in this context has been promoted by discoveries such as the mysterious duality.

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.

Hence, noting the simplicity achieved in Copernicus' formulation does not provide another reason for the acceptance of De Revolutionibus, another reason beyond its systematic superiority.

Third, we can offer technical help in the formulation of programs for development which are adapted to the country's objectives and resources.

the Carleton Student Association includes all students in college and is intended `` to work for the betterment of Carleton College by providing student government and student participation with the college administration in the formulation and execution of policies which pertain to student life and activities ''.

The soiled fabrics used for rapid testing of detergent formulations are made in such a way that only part of the soil is removed by even the best detergent formulation in a single wash.

The K factor, a term used to denote the rate of heat transmission through a material ( B.t.u./sq. ft. of material/hr./*0F./in. of thickness ) ranges from 0.24 to 0.28 for flexible urethane foams and from 0.12 to 0.16 for rigid urethane foams, depending upon the formulation, density, cell size, and nature of blowing agents used.

For example, if one defines categories in terms of sets, that is, as sets of objects and morphisms ( usually called a small category ), or even locally small categories, whose hom-objects are sets, then there is no category of all sets, and so it is difficult for a category-theoretic formulation to apply to all sets.

The formulation for the literary prize being given for a work " in an ideal direction " ( in Swedish ), is cryptic and has caused much confusion.

He is also noted for his mastery of abstract approaches to mathematics and his perfectionism in matters of formulation and presentation.

USAID has programming in the following areas: economic policy reform and restructuring ; private sector development ( the Business Development Program ); infrastructure rebuilding ; democratic reforms in the media, political process and elections, and rule of law / legal code formulation ; and training programs for women and diplomats.

There are two parts to Einstein's theory: the first part consists in the formulation of a diffusion equation for Brownian particles, in which the diffusion coefficient is related to the mean squared displacement of a Brownian particle, while the second part consists in relating the diffusion coefficient to measurable physical quantities.

* PAS 911: Fire strategies-guidance and framework for their formulation

However, a different notion of compactness altogether had also slowly emerged at the end of the 19th century from the study of the continuum, which was seen as fundamental for the rigorous formulation of analysis.

According to this formulation, the state exists for the benefit of citizens and has an obligation to respect and protect the rights of citizens, including civil rights and political rights.

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.

The three elected members of the Board of Health are responsible for the formulation and enforcement of rules and regulations affecting the environment and the public health.

The path integral formulation replaces the classical notion of a single, unique trajectory for a system, with a sum over all possible trajectories.

The British philosopher Simon Blackburn has criticized this formulation by suggesting that we do not want to accept as knowledge beliefs, which, while they " track the truth " ( as Nozick's account requires ), are not held for appropriate reasons.

The dissertation foreshadowed several important trends in Sapir's work: Particularly the careful attention to native speakers ' intuition regarding sound patterns, that would later become the basis for Sapir's formulation of the phoneme.

He also participate in the formulation of a report to the American Anthropological Association regarding the standardization of orthographic principles for writing Indigenous languages.

Tarski proved that his axiomatic formulation of elementary Euclidean geometry is consistent and complete in a certain sense: there is an algorithm that, for every proposition, can be shown either true or false.

This formulation, in turn, laid the groundwork for an independent view of the church as a " sacred society " distinct from civil society, which was so crucial for the development of local churches as non-established entities outside England, and gave direct rise to the Catholic Revival and disestablishmentarianism within England.

The extension ψ is in general not uniquely specified by φ, and the proof gives no explicit method as to how to find ψ: in the case of an infinite dimensional space V, it depends on Zorn's lemma, one formulation of the axiom of choice.

# That by retroactively extending copyright terms, Congress had violated the requirements of the Constitution's Copyright Clause, which gives Congress the following power: " To promote the Progress of Science and useful Arts, by securing for limited Times to Authors and Inventors the exclusive Right to their respective Writings and Discoveries " ( emphasis added ) Plaintiffs argued that by reading this formulation so as to allow for any number of retroactive extensions, Congress could in practice guarantee an unlimited period of copyright protection, thus thwarting the intent of the clause.

This quotient formulation gives to a homogeneous space structure.

The latter statement gives original theorem for or ( in Eisenstein's formulation ) for.

This formulation is of particular use in developing Artificial Intelligence programs, because it gives an indication of the input needed for a system that attempts to emulate human activities.

Under its traditional formulation, truth-conditional semantics gives every necessary truth precisely the same meaning, for all of them are true under precisely the same conditions ( namely, all of them ).

This gives rise to what is termed a volumetric, or volume-wise formulation of the mathematical model.

To get started, we should adopt a suitable initial value formulation of the field equation, which gives two new systems of equations, one giving a constraint on the initial data, and the other giving a procedure for evolving this initial data into a solution.

The Advocate General and his office defends and protects the interest of the provincial government and gives invaluable legal guidance to the provincial government in formulation of its policy and execution of its decision. Advocate-General of the Punjab is also Ex-Officio Chairman of Punjab Bar Council.

Likewise, in the theory of the firm, the lemma gives a similar formulation for the conditional factor demand for each input factor: the derivative of the cost function c ( w, y ) with respect to the factor price: