Specifically, if A is a linear operator and is a bra, then is another bra defined by the rule

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, if p is the natural length of a section of spring, then the length of the spring with tension T applied has length

Specifically, if one or more of the produced neutrons themselves interact with other fissionable nuclei, and these also undergo fission, then there is a possibility that the macroscopic overall fission reaction will not stop, but continue throughout the reaction material.

Specifically, if a judge consistently gives low scores for all divers, or consistently gives high scores for the same divers, the judging will yield fair relative results and will cause divers to place in the correct order.

Specifically, if he / she chooses to determine the path, then he / she has no influence whatsoever over which of the two paths, the left one or the right one, nature will tell him / her is the one in which the particle is found.

Specifically, if hair texture were simply the result of adaptively arbitrary human aesthetic preferences, one would expect that the global distribution of the various hair textures would be fairly random.

Specifically, if ƒ is an invertible function with domain X and range Y, then its inverse ƒ < sup >− 1 </ sup > has domain Y and range X, and the inverse of ƒ < sup >− 1 </ sup > is the original function ƒ.

Specifically, if the cylinders are oriented parallel to one another, there is very little volume that is excluded from the center-of-mass of the approaching cylinder ( it can come quite close to the other cylinder ).

Specifically, umpires were now given the power — and the responsibility — to intervene if they considered a bowler was deliberately aiming at a batsman with intent to injure.

Specifically, if the angular momentum is high enough the event horizons will disappear.

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

Specifically, if L / K is a Galois extension, we consider the group G = Gal ( L / K ) consisting of all field automorphisms of L which keep all elements of K fixed.

Specifically, extra management is needed if multiple threads are allowed to perform find operations concurrently.

Specifically, a construct in a language is called syntactic sugar if it can be removed from the language without any effect on what the language can do: functionality and expressive power will remain the same.

Specifically, if v is a tangent vector of M at a point x ( thought of as a derivation ) then define the directional derivative in the direction v by

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, it is unique up to a unique isomorphism: if ( A ′, φ ′) is another such pair, then there exists a unique isomorphism k: A → A ′ such that φ ′

Specifically, if the vacuum energy is negative and its absolute value is substantially larger than it appears to be in the observed universe ( say, a factor of 10 larger ), holding all other variables ( e. g. matter density ) constant, that would mean that the universe is closed ; furthermore, its lifetime would be shorter than the age of our universe, possibly too short for the intelligent life to form.

Specifically, the above argument would become a fallacious ad baculum if the conclusion stated:

Specifically, when the scale of the universe doubles, the density of matter is reduced by a factor of 8, but the density of dark energy is nearly unchanged ( it is exactly constant if the dark energy is a cosmological constant ).

A category C is said to have limits of type J if every diagram of type J has a limit in C. Specifically, a category C is said to

Specifically, if one freezes a right-handed wave in time, when one curls the fingers of one ’ s right hand around the helix, the thumb will point in the direction which the helix progresses given that sense of rotation.

Specifically, if 〈 F, G, ε, η 〉 is an adjunction between C and D and 〈 F ′, G ′, ε ′, η ′〉 is an adjunction between D and E then the functor

Specifically, the authors proved that the positivity required of an analytic function F ( z ) which de Branges would use to construct his proof would also force it to assume certain inequalities that, according to them, the functions actually relevant to a proof do not satisfy.

Specifically, f (' F ', ' F ', ..., ' F ') = ' F ', and these functions correspond to linear maps over the Boolean vector space.

Specifically, the symbol F in a formal language is a functional symbol if, given any symbol X representing an object in the language, F ( X ) is again a symbol representing an object in that language.

Specifically, if you can prove that for every X ( or every X of a certain type ), there exists a unique Y satisfying some condition P, then you can introduce a function symbol F to indicate this.

Specifically, if F has domain type T and codomain type U, then it can be replaced with a predicate P of type ( T, U ).

Specifically, the similarity between the fiber bundle E and a product space B × F is defined using a continuous surjective map

Specifically, if F is a diagram in Top and ( L, φ ) is a limit of UF in Set, the corresponding limit of F in Top is obtained by placing the initial topology on ( L, φ ).

Specifically, the burglars were interested in information they thought was held by Lawrence F. O ' Brien, head of the DNC.

Specifically, a straight line on a log-log plot containing points ( F < sub > 0 </ sub >, x < sub > 0 </ sub >) and ( F < sub > 1 </ sub >, x < sub > 1 </ sub >) will have the function:

Specifically, if H is a subgroup of Gal ( E / F ), then | H | = and | Gal ( E / F )/ H | =.

Specifically, the air temperature at the altitude where the air pressure is 850 millibars ( or altitude ) should be 13 ° C ( 24 ° F ) lower than the temperature of the air at the surface.

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, is the neuter plural of, an adjective related to the verb ἀποκρύπτω ἀποκρύπτειν ( apocriptein ), " to hide something away.

Specifically, at speeds of OC-3 and above, the cost of segmentation and reassembly ( SAR ) hardware makes ATM less competitive for IP than Packet Over SONET ( POS ); because of its fixed 48-byte cell payload, ATM is not suitable as a data link layer directly underlying IP ( without the need for SAR at the data link level ) since the OSI layer on which IP operates must provide a maximum transmission unit ( MTU ) of at least 576 bytes.

* Specifically, a text added to the end of a book or an article, containing information that is important to, but is not the main idea of, the main text

Specifically, in one of his last works, De scientia divina, he concludes that the idea of plurality itself is strictly temporal, a human notion.

Specifically it is the amount of a substance that contains as many elementary entities ( atoms, molecules or ions ) as there are atoms in 0. 012 kilogram ( or 12 grams ) of carbon-12, where the carbon-12 atoms are unbound, at rest and in their ground state.

Specifically for fluids, the Knudsen number is used to assess to what extent the approximation of continuity can be made.

Specifically, after acknowledging the various popular theories in vogue at the time, of how atoms were reasoned to attach to each other, i. e. " hooked atoms ", " glued together by rest ", or " stuck together by conspiring motions ", Newton states that he would rather infer from their cohesion, that " particles attract one another by some force, which in immediate contact is exceedingly strong, at small distances performs the chemical operations, and reaches not far from the particles with any sensible effect.

Specifically, to minimize the cutting down of trees for fuel, kerosene is being subsidized, and efforts are being made to replace the loss of the forest cover caused by ylang-ylang distillation for perfume.

Specifically, the timescale for beta-decay of radioactive nuclei produced is faster than the timescale for fusion.

Specifically, the table provides conflicting answers to the question of what this particular employee's address is.

Specifically, it is a non-trivial ring in which every non-zero element a has a multiplicative inverse, i. e., an element x with.

Specifically, it is a vector field.

Specifically, it is claimed that Ezekiel himself may have suffered from temporal lobe epilepsy, which has several characteristic symptoms that are apparent from his writing.

Specifically, by the Casorati – Weierstrass theorem, for any transcendental entire function f and any complex w there is a sequence with, is necessarily a polynomial, of degree at least n.