It was possible, however, to decompose the compliance into a sum of a frequency-independent component and two viscoelastic mechanisms, each compatible with the Boltzmann superposition principle and with a consistent set of time-temperature equivalence factors.

Diffraction arises because of the way in which waves propagate ; this is described by the Huygens – Fresnel principle and the principle of superposition of waves.

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 ).

The solution to this system can be found by using the superposition principle ( linearity ).

Multiplying the impulse response shifted in time according to the arrival of each of these delta functions by the amplitude of each delta function, and summing these responses together ( according to the superposition principle, applicable to all linear systems ) yields the output waveform.

The law of summation is in accord with the principle of superposition --- every diagram contributes a factor to the total amplitude for the process.

Nicolas Steno ( 1638 – 1686 ) is credited with the law of superposition, the principle of original horizontality, and the principle of lateral continuity: three defining principles of stratigraphy.

The principle of superposition states that a sedimentary rock layer in a tectonically undisturbed sequence is younger than the one beneath it and older than the one above it.

Because deeper rock is often older, as noted by the principle of superposition, this can result in older rocks moving on top of younger ones.

By the superposition principle, the wavepacket at any time t is:

Using Huygens ' theory and the principle of superposition of waves, the complex amplitude at a further point P is found by summing the contributions from each point on the sphere of radius r < sub > 0 </ sub >.

The principle of superposition of waves states that when two or more waves are incident on the same point, the total displacement at that point is equal to the vector sum of the displacements of the individual waves.

In nonlinear optics, the superposition principle no longer holds.

This was derived empirically by Fresnel in 1815, based on Huygen's hypothesis that each point on a wavefront generates a secondary spherical wavefront, which Fresnel combined with the principle of superposition of waves.

In the absence of nonlinear effects, the superposition principle can be used to predict the shape of interacting waveforms through the simple addition of the disturbances.

To further illustrate, Schrödinger describes how one could, in principle, transpose the superposition of an atom to large-scale systems.

In particular, many media are linear, or nearly so, so the calculation of arbitrary wave behavior can be found by adding up responses to individual sinusoidal waves using the superposition principle to find the solution for a general waveform.

This equation is linear, as the sum of any two solutions is again a solution: in physics this property is called the superposition principle.

The basic wave equation is a linear differential equation and so it will adhere to the superposition principle.

This property, called the principle of superposition, is very useful, e. g., solutions to complex problems can be constructed by summing simple solutions.

Fermat's principle is the main principle of quantum electrodynamics where it states that any particle ( e. g. a photon or an electron ) propagates over all available ( unobstructed ) paths and the interference ( sum, or superposition ) of its wavefunction over all those paths ( at the point of observer or detector ) gives the correct probability of detection of this particle ( at this point ).

The behavior of nonlinear systems is not subject to the principle of superposition while that of linear systems is subject to superposition.

The self-consistency principle guarantees that the sequence of events generating the paradox in the nested conditional has zero probability.

In mathematics, the Banach fixed-point theorem ( also known as the contraction mapping theorem or contraction mapping principle ) is an important tool in the theory of metric spaces ; it guarantees the existence and uniqueness of fixed points of certain self-maps of metric spaces, and provides a constructive method to find those fixed points.

Article 1 of the Basic Law ( in German legal shorthand GG, for Grundgesetz ), which establishes this principle that " human dignity is inviolable " and that human rights are directly applicable law, as well as the general principles of the state in Article 20 GG, which guarantees democracy, republicanism, social responsibility, federalism, and the right of resistance should anybody undertake to abolish this order, remain under the guarantee of perpetuity stated in Article 79 Paragraph 3, i. e., those two cannot be changed even if the normal amendment process is followed.

The superposition principle guarantees that any state can be written as a combination of states of this form with complex coefficients.

; Principle of self-management ( the rangatiratanga principle ): Article 2 guarantees to Māori hapū ( tribes ) the control and enjoyment of those resources and taonga that it is their wish to retain.

Hills argues that the principle of providentially preserved transmission guarantees that the printed Textus Receptus must be the closest text to the Greek autographs ; and consequently he rejects readings in the majority Byzantine text where these are not maintained in the Textus Receptus.

Article 9. 3 of the Spanish Constitution guarantees the principle of non-retroactivity of punitive provisions that are not favorable to or restrictive of individual rights.

Put another way, at any point in spacetime the equivalence principle guarantees the existence of a local inertial frame, and an accelerometer measures the acceleration relative to that frame.

This is an important argument in the King James Only debates: Edward F. Hills argues that the principle of providentially preserved transmission guarantees that the printed Textus Receptus must be the closest text to the Greek autographs.

In 1965 the Supreme Court had ruled in the O ' Callaghan case that the provisions of Article 40. 4, which guarantees personal liberty and the principle of habeas corpus, meant that an individual charged with a crime could only be refused bail if they were likely to flee or to interfere with witnesses or evidence.

This provision guarantees the cardinal principle of child participation in issues concerning them.

In the landmark case of District of Columbia v. Heller, Cruz assembled a coalition of thirty-one states in defense of the principle that the Second Amendment to the United States Constitution guarantees an individual right to keep and bear arms.

:( 1 ) the postulate of the principle, or the Cogitatio natural universalis ( good will of the thinker and good nature of thought ); ( 2 ) the postulate of the ideal, or common sense ( common sense as the concordia facultatum and good sense as the distribution which guarantees this concord ); ( 3 ) the postulate of the model, or of recognition ( recognition inviting all the faculties to exercise themselves upon an object supposedly the same, and the consequent possibility of error in the distribution when one faculty confuses one of its objects with a different object of another faculty ); ( 4 ) the postulate of the element or of representation ( when difference is subordinated to the complimentary dimensions of the Same and the Similar, the Analogous and the Opposed ; ( 5 ) the postulate of the negative, or of error ( in which error expresses everything which can go wrong in thought, but only as the product of external mechanisms ); ( 6 ) the postulate of logical function, or the proposition ( designation is taken to be the locus of truth, sense being no more than the neutralized double or the infinite doubling of the proposition ); ( 7 ) the postulate of modality, or solutions ( problems being materially traced from propositions or indeed, formally defined by the possibility of their being solved ); ( 8 ) the postulate of the end, or result, the postulate of knowledge ( the subordination of learning to knowledge, and of culture to method.

Nonetheless, although few in number they are a stubborn crew, as tenacious of life as the Hardshell Baptists, which suggests that there is some kind of vital principle embodied in their faith.

Such a decision should have placed a powerful weapon in the hands of the entire housing industry, but there is little evidence that realtors, or at least their associations, have repudiated the principle in such clauses.

Pythagoras believed that behind the appearance of things, there was the permanent principle of mathematics, and that the forms were based on a transcendental mathematical relation.

It is clear that widespread respect was paid to animals as the abode of dead ancestors, and much of the cults to dangerous animals is traceable to this principle ; though there is no need to attribute an animistic origin to it.

Some early scientists such as Georg Ernst Stahl ( 1659-1734 ) and Francisque Bouillier ( 1813 – 1899 ) had supported a form of animism which life and mind, the directive principle in evolution and growth, holding that all cannot be traced back to chemical and mechanical processes, but that there is a directive force which guides energy without altering its amount.

He argues that there must be some universal principle that must account for the various sorts of connections that exist between ideas.

Critics of the SAP argue in favor of a weak anthropic principle ( WAP ) similar to the one defined by Brandon Carter, which states that the universe's ostensible fine tuning is the result of selection bias: i. e., only in a universe capable of eventually supporting life will there be living beings capable of observing any such fine tuning, while a universe less compatible with life will go unbeheld.

In principle and in academic use, an arbitrage is risk-free ; in common use, as in statistical arbitrage, it may refer to expected profit, though losses may occur, and in practice, there are always risks in arbitrage, some minor ( such as fluctuation of prices decreasing profit margins ), some major ( such as devaluation of a currency or derivative ).

If the large-scale Universe appears isotropic as viewed from Earth, the cosmological principle can be derived from the simpler Copernican principle, which states that there is no preferred ( or special ) observer or vantage point.

By the well ordering principle, if there are positive integers that satisfy a given property, then there is a smallest positive integer that satisfies that property ; therefore, there is a smallest positive integer satisfying the property " not definable in under eleven words ".

In almost all areas of the law ( even those where there is a statutory framework, such as contracts for the sale of goods, or the criminal law ), legislature-enacted statutes generally give only terse statements of general principle, and the fine boundaries and definitions exist only in the common law ( connotation 1 ).

One is that there is no compelling reason, using current particle physics, to expect the universe to be flat, homogeneous and isotropic ( see the cosmological principle ).

But under orders of Spanish judge Baltasar Garzón, he was arrested there, attracting worldwide attention, not only because of the history of Chile and South America, but also because this was one of the first arrests of a former president based on the universal jurisdiction principle.

The convention also offers decision-makers guidance based on the precautionary principle that where there is a threat of significant reduction or loss of biological diversity, lack of full scientific certainty should not be used as a reason for postponing measures to avoid or minimize such a threat.

In civil contempt cases there is no principle of proportionality.

( The system is not limited to alphabets in the strict technical sense ; languages that use a syllabary or abugida, for example Cherokee, can use the same ordering principle provided there is a set ordering for the symbols used.

Although the Church of the Holy Sepulchre has its tomb just a few yards away from its Golgotha, there is no particular reason to regard this close juxtaposition as a necessity ; however, Gordon followed this principle, concluding that his site for Golgotha must also be the approximate location for Jesus ' burial, identifying a nearby tomb, now called the Garden Tomb, as the location for the event.

Second, there are many cases in which the use of a single computer would be possible in principle, but the use of a distributed system is beneficial for practical reasons.

This principle is exploited in the lightning conductor, the sharp spike of which acts to encourage the lightning stroke to develop there, rather than to the building it serves to protect.

This argument is embodied in the Copernican principle, which states that the Earth does not occupy a unique position in the Universe, and the mediocrity principle, which holds that there is nothing special about life on Earth.

According to Carnot's principle, work can only be done when there is a temperature difference, and the work should be some function of the difference in temperature and the heat absorbed.