As a consequence, the kernel of the Gelfand representation A → C < sub > 0 </ sub >( Φ < sub > A </ sub >) may be identified with the Jacobson radical of A.

The most accepted theory of how these structures came to be is that all the large-scale structure of the cosmos we observe today was formed as a consequence of the growth of the primordial fluctuations, which are small changes in the density of the universe in a confined region.

As the two atoms become closer together, their atomic orbitals overlap to produce areas of high electron density, and, as a consequence, molecular orbitals are formed between the two atoms.

Large-scale wildebeest migration is quite likely a consequence of decisions being made by individuals at multiple spatial scales, involving a balance of food abundance, food quality, local density of other wildebeest, social interactions, surface water, perceived predation risk, and culturally ( or possibly genetically ) learned routes and ranges.

This is a direct consequence of the linearity of Maxwell's equations in the fields and the current density.

They observe that this version of the problem may be solved as a 2-SAT instance, in which the constraints relate the orientations of pairs of modules that are directly across the channel from each other ; as a consequence, the optimal density may also be calculated efficiently, by performing a binary search in which each step involves the solution of a 2-SAT instance.

* The detection of Baryon acoustic oscillations, and as a consequence the relationship between the density of baryonic matter and dark matter

One consequence of the fires in 2003 has been the increased density of invasive and non-native plant species that have quickly colonized burned areas, especially those that had already been burned in the previous 15 years.

As a consequence of the Hahn – Banach theorem, this map is injective, and isometric.

* The Hilbert cube is compact, again a consequence of Tychonoff's theorem.

In this situation, the chain rule represents the fact that the derivative of is the composite of the derivative of f and the derivative of g. This theorem is an immediate consequence of the higher dimensional chain rule given above, and it has exactly the same formula.

As a consequence of the Nyquist – Shannon sampling theorem, any spatial waveform that can be displayed must consist of at least two pixels, which is proportional to image resolution.

According to Noether's theorem, the conservation of energy is a consequence of the fact that the laws of physics do not change over time.

As a consequence of Liouville's theorem, any function that is entire on the whole Riemann sphere ( complex plane and the point at infinity ) is constant.

Although the logical consequence relation is only semidecidable, much progress has been made in automated theorem proving in first-order logic.

It is deduced from the model existence theorem as follows: if there is no formal proof of a formula then adding its negation to the axioms gives a consisten theory, which has thus a model, so that the formula is not a semantic consequence of the initial theory.

An important consequence of the completeness theorem is that it is possible to recursively enumerate the semantic consequences of any effective first-order theory, by enumerating all the possible formal deductions from the axioms of the theory, and use this to produce an enumeration of their conclusions.

The compactness theorem says that if a formula φ is a logical consequence of a ( possibly infinite ) set of formulas Γ then it is a logical consequence of a finite subset of Γ.

This is an immediate consequence of the completeness theorem, because only a finite number of axioms from Γ can be mentioned in a formal deduction of φ, and the soundness of the deduction system then implies φ is a logical consequence of this finite set.

Conversely, for many deductive systems, it is possible to prove the completeness theorem as an effective consequence of the compactness theorem.

As a consequence of the polynomial remainder theorem, the entries in the third row are the coefficients of the second-degree polynomial, the quotient of on division by.

An important consequence of the KAM theorem is that for a large set of initial conditions the motion remains perpetually quasiperiodic.

A multiplicative function is completely determined by its values at the powers of prime numbers, a consequence of the fundamental theorem of arithmetic.

That is, conservation of momentum is a consequence of the fact that the laws of physics do not depend on position ; this is a special case of Noether's theorem.

is a consequence of Stone's theorem on one-parameter unitary groups.

The embedding property is a consequence of a result known as Desargues ' theorem.

Quines are possible in any programming language that has the ability to output any computable string, as a direct consequence of Kleene's recursion theorem.

As a consequence of the noisy-channel coding theorem, noise limits the information content of an analog information carrier to be finite.

One consequence of Toda's theorem is that a polynomial-time machine with a # P oracle ( P < sup ># P </ sup >) can solve all problems in PH, the entire polynomial hierarchy.

As a consequence of the Weierstrass approximation theorem, one can show that the space C is separable: the polynomial functions are dense, and each polynomial function can be uniformly approximated by one with rational coefficients ; there are only countably many polynomials with rational coefficients.

It is the consequence of the system of ideas that constitutes the frame of our international -- and in some degree our domestic -- policy.

One consequence is the occurrence of occasional conflicts because private owners of some inholdings object to public programs of use on neighboring National Forest or other Federal land, or because such ownerships are developed for uses that are not compatible with use for the public of neighboring National Forest land.

In the event the total of rupees accruing to the Government of the United States of America as a consequence of sales made pursuant to this Agreement is different from the rupee equivalent of $1,276 million, the amounts available for the purposes specified in paragraph 1, Article 2, will be adjusted proportionately.

According to the theory proposed, this is a consequence of the severe condition of perceived threat that persists unabated for the anxious child in an ambiguous sort of school environment.

) Functionalism as a sociological credo is, therefore, not a direct consequence of observations, but rather an indirect consequence of philosophical inference and judgment.

The consequence of this is that the girls at Brooklyn College outnumber the boys and do somewhat better academically.

This last point is important because if high school pupils are aware that few, if any, graduates who have chosen a certain vocational program have obtained a job as a consequence of the training, the whole idea of relevance disappears.

Existence is created and willed by God and is not the consequence of a pre-existent rebellion or of a cosmic descent from eternity into history.

Nevertheless, the consequence of the policy proposed is everywhere subtly qualified: it is `` a possible result, however improbable '' ; ;

:: One consequence is that people are more cooperative if it is more likely that individuals will interact again in the future.

A simple illustration of such cause and effect is the case of experiencing the effects of what I cause: if I cause suffering, then as a natural consequence I will experience suffering ; if I cause happiness, then as a natural consequence I will experience happiness.

As a consequence, it is difficult to define concisely or precisely.

Each element has a specific set of chemical properties as a consequence of the number of electrons present in the neutral atom, which is Z ( the atomic number ).

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.

that is, for any statement that is a logical consequence of there actually exists a deduction of the statement from.

One consequence of the Hindu and Spiritist beliefs is that our current lives are both afterlife and a beforelife.

The outer surface of an agate, freed from its matrix, is often pitted and rough, apparently in consequence of the removal of the original coating.

As a consequence, the balance of anti-apoptotic and proapoptotic effectors is upset in favour of the former, and the damaged cells continue to replicate despite being directed to die.