** Duality ( projective geometry ), general principle of projective geometry

* Duality principle ( disambiguation )

* Duality principle ( disambiguation )

Duality principle or principle of duality may refer to:

* Duality principle ( Boolean algebra )

* Duality principle for sets

* Duality principle ( optimization theory )

There are two approaches to the subject of duality, one through language ( the Principle of Duality ) and the other a more functional approach.

* Duality, a large format audio mixing console by Solid State Logic

* Duality ( of Patterning ): a large number of meaningful elements are made up of a conveniently small number of independently meaningless yet message-differentiating elements.

The two problems are mathematical duals, and hence the Duality Theorem provides a method of proving the relationships described above.

* Duality: Every statement, theorem, or definition in category theory has a dual which is essentially obtained by " reversing all the arrows ".

* Duality in field theory and statistical systems, Robert Savit, Rev.

** Duality ( order theory ), a concept regarding binary relations

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.

* Duality ( order theory )

A treatment of this theory, Residues and Duality ( 1966 ) by Robin Hartshorne, became an accessible reference.

This is the principle which we will invoke in every case to set up a functional equation.

He defines functional programs as being built up in a hierarchical way by means of " combining forms " that allow an " algebra of programs "; in modern language, this means that functional programs follow the principle of compositionality.

They have demonstrated that it is possible to replicate not just molecules like cellular DNA or RNA, but discrete structures that could in principle assume many different shapes, have many different functional features, and be associated with many different types of chemical species.

BCT1 is used in functional analysis to prove the open mapping theorem, the closed graph theorem and the uniform boundedness principle.

The Herborn school held the principle that every theory has to be functional in practical use, therefore it has to be didactic ( i. e. morally instructive ).

In other words, a silicon-based machine could, in principle, have the same sort of mental life that a human being has, provided that its cognitive system realized the proper functional roles.

This principle was used to distinguish between atoms of silicon, tin and lead on an alloy surface, by comparing these ' atomic fingerprints ' to values obtained from large-scale density functional theory ( DFT ) simulations.

In mathematics, the uniform boundedness principle or Banach – Steinhaus theorem is one of the fundamental results in functional analysis.

This is a generalization of the Euler – Lagrange equation: indeed, the functional derivative was introduced in physics within the derivation of the Lagrange equation of the second kind from the principle of least action in Lagrangian mechanics ( 18th century ).

Depending on the operator and the dimensionality ( and shape, and boundary conditions ) of its domain, many different types of functional decompositions are, in principle, possible.

Rohe's design principle of " less is more " and emphasis on functional amenities created a fine example of early functionalism architecture, a groundbreaking new vision in building design at the time.

A central principle was the inductive, data-driven examination of functional relations, as opposed to the kinds of hypothetico-deductive learning theory that had grown up in the comparative psychology of the 1920 – 1950 period.

Claris Works, a principle product in Apple's wholly owned subsidiary Claris Corporation, was demonstrated as an example of a pre-OpenDoc component architecture application modified to enable it to contain functional OpenDoc components.

The translators of the New English Bible chose to render their translation using a principle of translation called dynamic equivalence ( also referred to as functional equivalence or thought-for-thought translation ).

This is based on the principle that the forces of natural selection cause genes and other functional elements to undergo mutation at a slower rate than the rest of the genome, since mutations in functional elements are more likely to negatively impact the organism than mutations elsewhere.

Loewy formulated his < span id =" MAYA ">" MAYA " ( Most Advanced Yet Acceptable )</ span > principle to express that product designs are bounded by functional constraints of math and materials and logic, but their acceptance is constrained by social expectations.

That is, if the structures in the brain that encode memory and personality have been so disrupted that it is no longer possible in principle to restore them to an appropriate functional state, then the person is dead.

If the structures that encode memory and personality are sufficiently intact that inference of the memory and personality are feasible in principle, and therefore restoration to an appropriate functional state is likewise feasible in principle, then the person is not dead.

In linear algebra and functional analysis, the min-max theorem, or variational theorem, or Courant – Fischer – Weyl min-max principle, is a result that gives a variational characterization of eigenvalues of compact Hermitian operators on Hilbert spaces.

After the proof of principle research, a functional system must be created to couple the solid state pore and sensing devices.

In principle, there is no difference between resting membrane potential and dynamic voltage changes like action potential from biophysical point of view: all these phenomena are caused by specific changes in membrane permeabilities for potassium, sodium, calcium, and chloride, which in turn result from concerted changes in functional activity of various ion channels, ion transporters, and exchangers.

It is the principle on which functional magnetic resonance imaging is based.

* Argument principle, a theorem in complex analysis about meromorphic functions inside and on a closed contour

As a basic starting point it is normally assumed that, for the purposes of analysis, the general algorithm is known ; this is Shannon's Maxim " the enemy knows the system " -- in its turn, equivalent to Kerckhoffs ' principle.

The basic principle of dimensional analysis was known to Isaac Newton ( 1686 ) who referred to it as the " Great Principle of Similitude ".

The analysis of linear systems is possible because they satisfy a superposition principle: if u ( t ) and w ( t ) satisfy the differential equation for the vector field ( but not necessarily the initial condition ), then so will u ( t ) + w ( t ).

Further analysis of this process, known as electromagnetic induction, enabled him to state the principle, now known as Faraday's law of induction, that the potential difference induced in a closed circuit is proportional to the rate of change of magnetic flux through the loop.

This is a very elementary form of an uncertainty principle in a harmonic analysis setting.

The Huygens – Fresnel principle ( named after Dutch physicist Christiaan Huygens and French physicist Augustin-Jean Fresnel ) is a method of analysis applied to problems of wave propagation both in the far-field limit and in near-field diffraction.

The use of velocity in the static analysis of a lever is an application of the principle of virtual work.

For example, in his 1997 book Numerology: Or What Pythagoras Wrought, mathematician Underwood Dudley uses the term to discuss practitioners of the Elliott wave principle of stock market analysis.

More generally, non-standard analysis is any form of mathematics that relies on non-standard models and the transfer principle.

A field which satisfies the transfer principle for real numbers is a hyperreal field, and non-standard real analysis uses these fields as non-standard models of the real numbers.

Syntactic non-standard analysis requires a great deal of care in applying the principle of set formation ( formally known as the axiom of comprehension ) which mathematicians usually take for granted.

Nutcrackers usually work on the principle of moments as described in Archimedes ' analysis of the lever.

Thus followed the line of Lomonosov and the contributions of the Russian school became more frequent through his disciples, and in the nineteenth century we have great geographers as Vasily Dokuchaev who performed works of great importance as a " principle of comprehensive analysis of the territory " and " Russian Chernozem " latter being the most important where introduces the geographical concept of soil, as distinct from a simple geological strata, and thus founding a new geographic area of study: the Pedology.

However, a more detailed analysis based on the Archimedean principle and the densities of magnesium and its combustion product shows that just being lighter than air cannot account for the increase in mass.

Deeper theorems from real analysis were not included, but by the end of the third volume it was clear to experts that a large amount of known mathematics could in principle be developed in the adopted formalism.

The Court noted that this analysis was " unsound in principle and unworkable in practice ", and rejected it without providing a replacement.

This systemic and geological analysis of living systems complements Charles Darwin's theory of natural selection, which looks at each individual species, rather than at its relationship to a subsuming principle.

It is well known from the theory of Fourier analysis, or from the Heisenberg uncertainty principle ( in the case of quantum mechanics ) that a narrow range of wavelengths is necessary to produce a localized wave packet, and the more localized the envelope, the larger the spread in required wavelengths.

The wavelets forming a continuous wavelet transform ( CWT ) are subject to the uncertainty principle of Fourier analysis respective sampling theory: Given a signal with some event in it, one cannot assign simultaneously an exact time and frequency response scale to that event.

The application of hyperreal numbers and in particular the transfer principle to problems of analysis is called non-standard analysis.

An analysis of the Báb's writings throughout the three stages shows that all of his teachings were animated by a common principle that had multiple dimensions and forms.

General semantics considers all human behavior ( including all human decisions ) as, in principle, fully determined once all relevant doctrinal and linguistic factors are included in the analysis, regarding theories of ' free will ' as failing to include the doctrinal and linguistic environments as environments in the analysis of human behavior.