Despite these facts, most mathematicians accept the axiom of choice as a valid principle for proving new results in mathematics.

However, stare decisis, the principle that similar cases should be decided according to consistent principled rules so that they will reach similar results, lies at the heart of all common law systems.

The results of early negotiations between the Greek and Turkish politicians resulted in a broad agreement in principle to reunification as a bicameral, bi-zonal federation with territory allocated to the Greek and Turkish communities within a united island.

One of the most common objections to rule-consequentialism is that it is incoherent, because it is based on the consequentialist principle that what we should be concerned with is maximizing the good, but then it tells us not to act to maximize the good, but to follow rules ( even in cases where we know that breaking the rule could produce better results ).

An experiment can show the particle-like properties of matter, or the wave-like properties ; in some experiments both of these complementary viewpoints must be invoked to explain the results, according to the complementarity principle of Niels Bohr.

Dropping the principle that the wave function is a complete description results in a hidden variable theory.

This first, foundational principle by which congregationalism is guided results in confining it to operate with the consent of each gathering of believers.

The blade only moves forward and backward, and any violation of that principle results in skidding.

The underlying principle is that karma is the law that brings back the results of actions to the person performing them.

The strong likelihood principle applies this same criterion to cases such as sequential experiments where the sample of data that is available results from applying a stopping rule to the observations earlier in the experiment.

The tendency to form a ( homoeopolar ) chemical bond ( this means: the formation of a symmetric molecular orbital, i. e. with the + sign ) results through the Pauli principle automatically in an antisymmetric spin state ( i. e. with the-sign ).

This extra energy results from the Pauli exclusion principle allowing an extra neutron to occupy the same nuclear orbital as the last neutron in the nucleus, so that the two form a pair.

During the last meeting with the Prime minister, Musharraf faced a grave criticism on results produced by Kargil infiltration by the principle military intelligence ( MI ) director lieutenant-general Jamshed Gulzar Kiani who maintained in the meeting: "(...) whatever has been written there is against logic.

Thus, although the current standard model of particle physics " in principle " predicts all known non-gravitational phenomena, in practice only a few quantitative results have been derived from the full theory ( e. g., the masses of some of the simplest hadrons ), and these results ( especially the particle masses which are most relevant for low-energy physics ) are less accurate than existing experimental measurements.

After their victory he gave a speech at Hawarden on 23 September in which he said: " In the common interests of humanity, this remarkable strike and the results of this strike, which have tended somewhat to strengthen the condition of labour in the face of capital, is the record of what we ought to regard as satisfactory, as a real social advance tends to a fair principle of division of the fruits of industry ".

The indistinguishability of all particles of each fundamental type ( say, electrons, or photons ) results in the Dirac and Bose quantum statistics which in turn result in the Pauli exclusion principle for fermions and in Bose-Einstein condensation for bosons.

His chief work is his Hydrodynamique ( Hydrodynamica ), published in 1738 ; it resembles Joseph Louis Lagrange's Mécanique Analytique in being arranged so that all the results are consequences of a single principle, namely, conservation of energy.

One of the primary foundations of the precautionary principle, and globally accepted definitions, results from the work of the Rio Conference, or " Earth Summit " in 1992.

This is known as quantum indeterminacy, and underlies results such as the Heisenberg uncertainty principle, information-disturbance theorem and no cloning theorem.

:: This principle, that consciousness causes the collapse, is the point of intersection between quantum mechanics and the mind / body problem ; and researchers are working to detect conscious events correlated with physical events that, according to quantum theory, should involve a wave function collapse ; but, thus far, results are inconclusive.

For a hidden variable theory, if Bell's conditions are correct, then the results which are in agreement with quantum mechanical theory appear to evidence superluminal effects, in contradiction to the principle of locality.

Wiener's Tauberian theorem, a 1932 result of Wiener, developed Tauberian theorems in summability theory, on the face of it a chapter of real analysis, by showing that most of the known results could be encapsulated in a principle taken from harmonic analysis.

Cargo cult programming can also refer to the results of ( over -) applying a design pattern or coding style blindly without understanding the reasons behind that design principle in the first place.

Reason is employed in another way, not as furnishing a sufficient proof of a principle, but as confirming an already established principle, by showing the congruity of its results, as in astronomy the theory of eccentrics and epicycles is considered as established, because thereby the sensible appearances of the heavenly movements can be explained ; not, however, as if this proof were sufficient, forasmuch as some other theory might explain them.

In 1821, Cauchy began to put calculus on a firm logical foundation by rejecting the principle of the generality of algebra widely used in earlier work, particularly by Euler.

However, scholarship indicates that this claim of priority is not so clear ; Leonhard Euler discussed the principle in 1744, and there is evidence that Gottfried Leibniz preceded both by 39 years.

Leonhard Euler gave a formulation of the action principle in 1744, in very recognizable terms, in the Additamentum 2 to his Methodus Inveniendi Lineas Curvas Maximi Minive Proprietate Gaudentes.

Thus, Euler made an equivalent and ( apparently ) independent statement of the variational principle in the same year as Maupertuis, albeit slightly later.

In Lagrangian mechanics, because of Hamilton's principle of stationary action, the evolution of a physical system is described by the solutions to the Euler – Lagrange equation for the action of the system.

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 ).

From the perspective of the splitting principle, this corresponds to the stability of symmetric polynomials, and the instability of alternating polynomials, specifically the Vandermonde polynomial, which represents the Euler class.

where denotes the Euler class of E, and denotes the cup product of cohomology classes ; under the splitting principle, this corresponds to the square of the Vandermonde polynomial being the discriminant.

His short stay as a postdoctoral student in Dale's laboratory was very fruitful: in 1931 he discovered with John H. Gaddum an important autopharmacological principle, substance P. After returning to Stockholm, von Euler pursued further this line of research, and successively discovered four other important endogenous active substances, prostaglandin, vesiglandin ( 1935 ), piperidine ( 1942 ) and noradrenaline ( 1946 ).

By the middle of the 18th century, the principle of angular momentum was discovered gradually by Daniel Bernoulli and Leonhard Euler and Patrick d ' Arcy ; d ' Arcy's version of the principle was phrased in terms of swept area.

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.

This principle has frequently been called the " Sapir – Whorf hypothesis ", after him and his mentor Edward Sapir, but Whorf called it the principle of linguistic relativity, because he saw the idea as having implications similar to Einstein's principle of physical relativity.

Existence is not being ; it gives being – here a customary phrase is used, existence is a principle ( a source ) of being, not a previous source, but one which is continually in effect.

It is a legitimate goal therefore for philosophers of being to try to find a principle or element – a " something " – accounting for the presence of the object over the other possibility, its non-presence.

This incident, coupled with Stalin's demands for the restitution of the Turkish provinces of Kars, Artvin and Ardahan to the Soviet Union ( which were lost by Turkey with the Russo – Turkish War of 1877 – 1878, but were regained with the Treaty of Kars in 1921 ) was one of the main reasons why Turkey decided to give up its general principle of neutrality in foreign affairs.

The cosmological principle implies that the metric should be homogeneous and isotropic on large scales, which uniquely singles out the Friedmann – Lemaître – Robertson – Walker metric ( FLRW metric ).

An attempt to increase majority elements by tweaking the system parameters ( more smaller districts, d ' Hondt method used ) by ČSSD and ODS during their " opposition agreement " 1998 – 2002 was vehemently opposed by smaller parties and blocked by the Constitutional Court as going too much against the constitution-stated proportional principle ; only a moderated form was adopted.

This teaching is the foundation of the Christian Science principle that disease – and any other adversity – can be cured through prayerful efforts, made possible only by God's grace, to fully understand this spiritual relationship.

Later on, during the nineteenth and early twentieth centuries, this French revolutionary principle – though not of course its specific way to identify the “ general will ” – percolated into first Socialist and then Fascist political thinking.

They come in various forms, such as the one pictured, and are often used in science museums to illustrate " radiation pressure " – a scientific principle that they do not in fact demonstrate.

* Lev Pontryagin ( 1908 – 1988 ) introduced the maximum principle and the bang-bang principle.

The uncertainty principle is ultimately a theorem about such commutators, by virtue of the Robertson – Schrödinger relation.

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.

This result establishes the principle known as wave – particle duality.

The Huygens – Fresnel principle is one such model ; it states that each point on a wavefront generates a secondary spherical wavelet, and that the disturbance at any subsequent point can be found by summing the contributions of the individual wavelets at that point.