") appears to be much easier than the problem of actually finding the factors of N. Specifically, the former can be solved in polynomial time ( in the number n of digits of N ) with the AKS primality test.

Specifically it takes time, demonstrating that the integer factorization problem can be efficiently solved on a quantum computer and is thus in the complexity class BQP.

Specifically, solving a heat conduction ( Fourier ) problem with temperature ( the driving " force ") and flux of heat ( the rate of flow of the driven " quantity ", i. e. heat energy ) variables also solves an analogous electrical conduction ( Ohm ) problem having electric potential ( the driving " force ") and electric current ( the rate of flow of the driven " quantity ", i. e. charge ) variables.

Specifically, decoherence does not attempt to explain the measurement problem.

Specifically, they solved a 20-variable SAT problem having more than 1 million potential solutions.

Specifically, it will contribute to solving the problem by fund raising to finance rangers in the field.

Specifically, Fock showed that the Schrödinger wavefunction in the momentum space for the Kepler problem was the stereographic projection of the spherical harmonics on the sphere.

Specifically, a Turing machine is a universal Turing machine if its halting problem ( i. e., the set of inputs for which it eventually halts ) is many-one complete.

Specifically, the following decision problem, known as the domatic number problem, is NP-complete: given a graph and an integer, determine whether the domatic number of is at least.

Specifically, suppose that M and N are a pair of manifolds each carrying a G-structure for a structure group G. This amounts to giving a special class of coframes on M and N. Cartan's method addresses the question of whether there exists a local diffeomorphism φ: M → N under which the G-structure on N pulls back to the given G-structure on M. An equivalence problem has been " solved " if one can give a complete set of structural invariants for the G-structure: meaning that such a diffeomorphism exists if and only if all of the structural invariants agree in a suitably defined sense.

Specifically, in quantum mechanics, the state of an atom, i. e. an eigenstate of the atomic Hamiltonian, is approximated by an expansion ( see configuration interaction expansion and basis set ) into linear combinations of anti-symmetrized products ( Slater determinants ) of one-electron functions.

Specifically, he demonstrated an upper limit, known as Bell's inequality, regarding the strength of correlations that can be produced in any theory obeying local realism, and he showed that quantum theory predicts violations of this limit for certain entangled systems.

Specifically, it assumes either that there is only one timeline, or that any alternative timelines ( such as those postulated by the many-worlds interpretation of quantum mechanics ) are not accessible.

Specifically, for a sample of area A, in magnetic field B, the degeneracy of each Landau level is ( where g < sub > s </ sub > represents a factor of 2 for spin degeneracy, and φ < sub > 0 </ sub > is the magnetic flux quantum ).

Specifically, the CPT theorem states that any Lorentz invariant local quantum field theory with a Hermitian Hamiltonian must have CPT symmetry.

Specifically, the effect describes the phenomenon resulting from electrons and electron holes being squeezed into a dimension that approaches a critical quantum measurement, called the exciton Bohr radius.

Specifically, the term describes results in quantum mechanics like Bell's theorem and the Kochen – Specker theorem that constrain the permissible types of hidden variable theories which try to explain the apparent randomness of quantum mechanics as a deterministic model featuring hidden states.

( Specifically, since this convolution is invertible, in fact, no information has been sacrificed, and the full quantum entropy has not increased, yet.

Specifically it is a quantum field theory in which, unlike most other quantum field theories, the pair of observables is not required to always commute.

Specifically, the term Galilean invariance today usually refers to this principle as applied to Newtonian mechanics, that is, Newton's laws hold in all inertial frames.

Specifically, experiments will study the adaptation of the vestibular system and space adaptation syndrome, the adaptation of the central nervous system and the pathways which control the ability to sense location in the absence of gravity, and the effect of microgravity on a developing nervous system.

" Specifically, Magnotta and Strohl focus on The Marine Biologist, in which George becomes embroiled in yet another lie, and on The Red Dot in which George tries to save a few dollars at Elaine's expense by giving her a marked-down cashmere sweater.

Specifically, for film and television actors, an actor not in the union who becomes a " principal performer " ( says a line ) is immediately eligible to join the Screen Actors Guild and is covered under the SAG contract with the production company for 30 days, at which point he or she must either join SAG or cease working on any union productions ; this same provision applies to so-called " background actors " ( extras ) who work on a SAG covered production for 3 or more days.

Specifically important are the individual's " view of persons " and their " social perspective level ", each of which becomes more complex and mature with each advancing stage.

Specifically, Lehman and Carey's article describes a T-tree balanced like an AVL tree: it becomes out of balance when a node's child trees differ in height by at least two levels.

Specifically, the product promises to build muscle, and Cartman believe it has fulfilled this function even after he only becomes extremely overweight.

Specifically, it must meet less than two of the five Hugo criteria for consideration as a semiprozine: that the magazine had an average press run of at least one thousand copies per issue, paid its contributors and / or staff in other than copies of the publication, provided at least half the income of any one person, had at least fifteen percent of its total space occupied by advertising, and announced itself to be a semiprozine.

Specifically, the issue is whether private landowners should be permitted to utilize the machinery of government to exclude others from engaging in free speech on their property ( which means balancing the speakers ' First Amendment rights against the Takings Clause ).

Specifically, the conceptual diagram graph 1 identifies only three boxes, two ellipses, and four arrows ( and their five labels ), whereas the picture 1 shows much more pictorial detail, with the scores of implied relationships as implicit in the picture rather than with the nine explicit details in the graph.

Specifically, a topological space is compact if, whenever a collection of open sets covers the space, some subcollection consisting only of finitely many open sets also covers the space.

( Specifically, as of October 2007, Fiji's military had 3527 full-time members, of whom only 15 were Indo-Fijians.

Specifically, in these enclaves, the federal government may have proprietary jurisdiction ( only the rights of any other landowner ), concurrent jurisdiction ( the right to legislate concurrently with the state government ), or exclusive jurisdiction over the land where an act was committed in order to establish jurisdiction over the actor.

Specifically, some cardrooms only grant the right to view a mucked losing hand if the requesting player articulates a concern about possible collusion.

Specifically, since logical language can only reflect the world, any discussion of the mystical, that which lies outside of the metaphysical subject's world, is meaningless.

This can be shown using the concept of left cosets of H in G. The left cosets are the equivalence classes of a certain equivalence relation on G and therefore form a partition of G. Specifically, x and y in G are related if and only if there exists h in H such that x

Specifically, they share the idea that the reality of God is completely inaccessible to human beings and that man can only come to see God through a spiritual journey in which knowledge < nowiki >< nowiki ></ nowiki > is rejected in favour of meditation.

Specifically, a ( locally small ) complete category C has an initial object if and only if there exist a set I ( not a proper class ) and an I-indexed family ( K < sub > i </ sub >) of objects of C such that for any object X of C there at least one morphism K < sub > i </ sub > → X for some i ∈ I.

Specifically, monothelitism teaches that Jesus Christ had two natures but only one will.

Specifically, decrypted data will only ever be passed to authenticated, trusted applications, and will only ever be stored in curtained memory, making it inaccessible to other applications and the Operating System.

Specifically, critics argue that the costs and energy used in collection and transportation detract from ( and outweigh ) the costs and energy saved in the production process ; also that the jobs produced by the recycling industry can be a poor trade for the jobs lost in logging, mining, and other industries associated with virgin production ; and that materials such as paper pulp can only be recycled a few times before material degradation prevents further recycling.

Specifically, a polynomial equation is solvable by radicals if and only if the corresponding Galois group is solvable.

Specifically, it states that for every ε > 0 there exist only finitely many triples ( a, b, c ) of positive coprime integers with a + b = c such that

Specifically, as of 2007, it is recommended that such prophylaxis be limited only to 1. those with prosthetic heart valves, 2. those with previous episode ( s ) of endocarditis, and 3. those with certain types of congenital heart disease .< sup > Link </ sup >

Specifically: a table is in 2NF if and only if it is in 1NF and no non prime attribute is dependent on any proper subset of any candidate key of the table.

Specifically, the failure of the map to be a local homeomorphism at certain points is referred to as gimbal lock, and is demonstrated in the animation at the right – at some points ( when the axes are coplanar ) the rank of the map is 2, rather than 3, meaning that only 2 dimensions of rotations can be realized from that point by changing the angles.

Specifically, the inquiry is focused upon a thing that has no immediately apparent characteristics and therefore has only factors for consideration held within itself hidden from immediate observation.

Specifically addressing the use of the death penalty, article 6, paragraph 2 provides in relevant part that a death sentence may only be imposed "... for the most serious crimes in accordance with the law in force at the time of the commission of the crime ...."

Specifically, DoD policy stated that " the medal will be issued only to those taken prisoner by an enemy during armed conflict ," and further states that " hostages of terrorists and persons detained by governments with which the US is not actively engaged in armed conflict are not eligible for the medal .” However, the 1989 amendment to the POW Medal Statute that created an exception to the armed conflict requirement was overlooked in the July 1990 version of the DoD Manual of Military Decorations and Awards, presumably because the 1989 amendment occurred in November, during the staffing window for the 1990 revision to the manual.

Specifically, if indeed local protein synthesis underlies L-LTP, only dendritic spines receiving LTP-inducing stimuli will undergo LTP ; the potentiation will not be propagated to adjacent synapses.

Specifically, he corrected Ptolmey ’ s estimate of the length of the Mediterranean sea from 62 degrees to the correct value of 42 degrees In his treatise on the solar year, which survives only in a Hebrew translation, he was the first to demonstrate the motion of the solar apogee relative to the fixed background of the stars.