Many mechanical, electrical, magnetic, optical and chemical properties of solids are the direct consequence of Pauli exclusion.

Pauli had introduced the 2 × 2 sigma matrices as pure phenomenology — Dirac now had a theoretical argument that implied that spin was somehow the consequence of the marriage of quantum mechanics to relativity.

Many mechanical, electrical, magnetic, optical and chemical properties of solids are the direct consequence of the Pauli exclusion principle.

The existence of a Fermi surface is a direct consequence of the Pauli exclusion principle, which allows a maximum of one electron per quantum state.

Pauli had introduced the 2 × 2 sigma matrices as pure phenomenology — Dirac now had a theoretical argument that implied that spin was somehow the consequence of incorporating relativity into quantum mechanics.

A consequence of using waveforms to describe particles is that it is mathematically impossible to obtain precise values for both the position and momentum of a particle at the same time ; this became known as the uncertainty principle, formulated by Werner Heisenberg in 1926.

Huygens ' principle can be seen as a consequence of the isotropy of space-all directions in space are equal.

Combining the likelihood principle with the law of likelihood yields the consequence that the parameter value which maximizes the likelihood function is the value which is most strongly supported by the evidence.

In the context of security the minimality principle of microkernels is a direct consequence of the principle of least privilege, according to which all code should have only the privileges needed to provide required functionality.

The property of spin relates to another basic property concerning systems of N identical particles: Pauli's exclusion principle, which is a consequence of the following permutation behaviour of an N-particle wave function ; again in the position representation one must postulate that for the transposition of any two of the N particles one always should have

Another consequence of this principle is that only those penalties that had already been established for the offence in the time when it was committed can be imposed.

This is understood to be a direct consequence of the metaphysical principle that " existence is identity.

One particularly important consequence of the principle is the elaborate electron shell structure of atoms and the way atoms share electrons, explaining the variety of chemical elements and their chemical combinations.

A speculative solution is that many or all of these possibilities are realised in one or another of a huge number of universes, but that only a small number of them are habitable, and hence the fundamental constants of the universe are ultimately the result of the anthropic principle rather than a consequence of the theory of everything.

Classically, Fermat's principle can be considered as a mathematical consequence of Huygens ' principle.

One important constitutional principle which is stated in Article 8 of the Legislation Law of the People's Republic of China is that an action can become a crime only as a consequence of a law passed by the full NPC and that other organs of the Chinese government do not have the power to criminalize activity.

As a consequence of its great impact, this theory brings back the uncertainty principle to distances around extrema of action, distances corresponding to reductions in entropy.

The transfer principle states that true first order statements about R are also valid in * R. For example, the commutative law of addition, x + y = y + x, holds for the hyperreals just as it does for the reals ; since R is a real closed field, so is * R. Since for all integers n, one also has for all hyperintegers H. The transfer principle for ultrapowers is a consequence of Łoś ' theorem of 1955.

In 1715, in consequence of the rebellion, this power was created in respect of the forces in the kingdom, but apart from and in no respect affected the principle acknowledged all this time that the crown of its mere prerogative could make laws for the government of the army in foreign countries in time of war.

From then on, all dissolutions that were not a consequence of convictions for treason, were legally " voluntary "-a principle that was taken a stage further with the voluntary surrender of Lewes priory in November 1537, when for the first time the monks were offered life pensions if they co-operated, and were not accorded the option of transfer to another house.

The principle upon which depends the power of sensation regulates all our external actions, as the principle of life does our internal, and the two act mutually on each other in consequence of changes produced in the brain.

The basic principle is one of preventing excessive beer and yeast loss through foaming, but the consequence is that the beer is both in contact with more wood and in contact with more beer ( fermenting in a bigger volume ).

The success or failure of a particular issue is of little consequence compared with the all-important principle of a fearless and honest newspaper.

One consequence of Babinet's principle is a paradox that in the diffraction limit, the radiation removed from the beam due to a particle is equal to twice the particle's cross section times the flux.

The great power in viewing a mind as a society of agents, as opposed to the consequence of some basic principle or some simple formal system, is that different agents can be based on different types of processes with different purposes, ways of representing knowledge, and methods for producing results.

" The superiority of reward is not here the consequence of competition, but of its absence: not a compensation for disadvantages inherent in the employment, but an extra advantage ; a kind of monopoly price, the effect not of a legal, but of what has been termed a natural monopoly ... independently of ... artificial monopolies grants by government, there is a natural monopoly in favour of skilled labourers against the unskilled, which makes the difference of reward exceed, sometimes in a manifold proportion, what is sufficient merely to equalize their advantages.

During World War II, Taranto became famous as a consequence of the November 1940 British air attack on the Regia Marina naval base stationed here, which today called the Battle of Taranto.

However, he was in a seriously weakened condition ; Wilson's diary entry for 14 January reads: " Shackleton has been anything but up to the mark, and today he is decidedly worse, very short winded and coughing constantly, with more serious symptoms that need not be detailed here but which are of no small consequence one hundred and sixty miles from the ship ".

As a consequence, for convergence of a sequence of elements of it then suffices that the coefficient of each power of Y converges to a formal power series in X, a weaker condition that stabilizing entirely ; for instance in the second example given here the coefficient of Y converges to, so the whole summation converges to.

Equivalently, a different quantity may be defined, termed the energy of the curve ; minimizing the energy leads to the same equations for a geodesic ( here " constant velocity " is a consequence of minimisation ).

Disruption of established relationships certainly causes pain, which is at least an unintended consequence of the practices described here, though it may also in many cases be an intended, coercive consequence.

As a consequence Newman's name is fully visible first here.

During the Fascist period, many deputies of the opposition retired on this hill after the murder of Giacomo Matteotti, here ending-by the so-called " Aventine Secession "-their presence at the Parliament and, as a consequence, their political activity.

As a consequence of its flood relief function, the channel here is classified as a " main river ".

The great mass of these ignorant immigrants come here at an age when education is unlikely if not impossible and when the work of Americanizing them is in consequence correspondingly difficult.

It must suffice here to note that in consequence of St. Francis's severe requirements concerning the practice of poverty, his followers divided into two branches, the Zelanti, or Spirituals, and the Relaxati, known later as the Conventuals.

An important consequence here, however, is that inequalities can actually be just on Rawls ' view, as long as they are to the benefit of the least well off.

As a consequence there is no base ( written as ∞) for the first ( most significant ) digit, since here the " next larger unit " does not exist ( and note that one could not add a larger unit of " month " or " year " to the sequence of units, as they are not integer multiples of " week ").

As a consequence of the war, the site of a post-World War II work camp for the remaining ethnic Germans ( Donauschwaben ) was formed here under new communist administration.

Situated in the centre of the pleasure-going Westend population, the Haymarket is a great place for hotels, supper-houses, and foreign cafés ; and it need hardly be added here, that so many of its taverns became the resort of the loosest characters, after the closing of the theatres, who turned night into day, and who were so constantly appearing before the sitting magistrates in consequence of drunken riots and street rows, that the Legislature interfered, and an Act of Parliament was passed, compelling the closing of such houses of refreshment at twelve o ' clock.

The slow convergence here can be seen as a consequence of the curse of dimensionality.

of the previous equation would be replaced by 0, which would have the consequence of one-and-the-same set of eigenfunctions ( and / or eigendistributions ) for both and, whereas here common eigenfunctions or eigendistributions of the operators p and q don't exist.

Senator Paul Sarbanes ( D-MD ) said of Nelson's complaint: " I'm not sure a head of state ought to be able to wander over here for the prayer breakfast and, in effect, compel the president of the United States to meet with him as a consequence .... Getting these meetings with the president is a process that's usually very carefully vetted and worked up.

" Fish speak Klingon " is the consequent here, but intuitively is not a consequence of ( nor does it have anything to do with ) the claim made in the antecedent that " monkeys are purple ".

In a highly inflammatory section of the Apology, Socrates claims that no greater good has happened to Athens than his concern for his fellow citizens, that wealth is a consequence of goodness ( and not the other way around ), that God does not permit a better man to be harmed by a worse, and that, in the strongest statement he gives of his task, he is a stinging gadfly and the state a lazy horse, " and all day long I will never cease to settle here, there and everywhere, rousing, persuading and reproving every one of you.

These lines of thought include equating the Holocaust with resettlement is referring to the Expulsion of Germans after World War II | expulsion of Germans from Eastern Europe here ; calling into question the purposefulness of the assassination attempt of July 20, 1944, in face of the threat from the Red Army, shifting German responsibility for the Second World War and Auschwitz to the British politics of appeasement and its pacifistic practitioners ; the notion that Weimar had failed primarily because of the bonds of the peace treaty, the “ edict ” of Versailles, the notion that the nonexistent national consciousness of the Germans was also a consequence of postwar reeducation, and the notion that in the last analysis it was the Communists who ( along with the National Socialists ) had buried the republican system ”.

Sadly enough, the spell also befalls the diver-which admits, however, a glimpse of hope: the figures are now in slightly different positions as a consequence of their progress during their brief period of freedom, and the intrepid diver has left his imperishable mark, as a mural in his likeness-the background music featuring, for a last time, the chorus: That's why we are here.

:: " It is not necessary to enter into the mathematics of the theory to state its simple consequence ... Each mass has an " inertia-contributing " power, a voting power, equal to its mass, there, divided by the distance from there to here.