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, 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 F is a vector space of linear functionals on X which separates points of X, then the continuous dual of X with respect to the topology σ ( X, F ) is precisely equal to F.

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, it is defined as the largest cardinality of an algebraically independent subset of L over K.

Specifically, the isoperimetric inequality states, for the length L of a closed curve and the area A of the planar region that it encloses, that

Specifically, LapTrap is described as being a Turbo T. U. R. T. L. E.

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, it implies that as a Galois extension of K, L is uniquely determined by the set of primes of K that split completely in it.

In the report by Major General Antonio M. Taguba regarding the alleged acts of brutality, abuse, and torture at the Enemy Prisoner of War facility at Abu Ghraib and other Enemy Prisoner of War Camps in Iraq and Afghanistan, Taguba said, "' Specifically I suspect that Col. Thomas M. Pappas, Lt. Col. Steve L. Jordan, Mr. Steven Stephanowicz and Mr. John Israel were either directly or indirectly responsible for the abuses at Abu Ghraib and strongly recommend immediate disciplinary actions ..."

Specifically, let L be a tame oriented knot or link in Euclidean 3-space ( or in the 3-sphere ).

Specifically, a small-world network is defined to be a network where the typical distance L between two randomly chosen nodes ( the number of steps required ) grows proportionally to the logarithm of the number of nodes N in the network, that is:

Specifically, the House managers said Ritter engaged in champerty (" a proceeding whereby a person having no legitimate interest in a lawsuit abets it with money or services in the hope of profit ") by " corruptly and unlawfully " receiving $ 4, 500 from a former law partner, Albert L. Rankin.

Specifically, L is the gas-liquid partition constant on hexadecane at 298 K ; E the excess molar refraction ; S the ability of a solute to stabilize a neighboring dipole by virtue of its capacity for orientation and induction interactions ; A the solute ’ s effective hydrogen bond acidity ; and B the solute ’ s effective hydrogen-bond basicity.

Specifically, the pumping lemma says that for any regular language L there exists a constant p such that any word w in L with length at least p can be split into three substrings, w = xyz, where the middle portion y must not be empty, such that the words xz, xyz, xyyz, xyyyz, … constructed by repeating y an arbitrary number of times ( including zero times ) are still in L. This process of repetition is known as " pumping ".

Specifically, the model must assign to each constant symbol of L an element of M, and to each n-ary function symbol f of L and each n-tuple < a < sub > 0 </ sub >,..., a < sub > n-1 </ sub >> of elements of M, the model must assign an element of M to the term f ( a < sub > 0 </ sub >,..., a < sub > n-1 </ sub >).

Specifically, the H factor is described as sincere, honest, faithful / loyal, modest / unassuming, fair-minded, VERSUS sly, deceitful, greedy, pretentious, hypocritical, boastful and pompous.

Specifically, Brunvand argued that the Petruchio / Katherina story represents a subtype of Type 901 (' Shrew-taming Complex ') in the Aarne – Thompson classification system.

Specifically, A and E will no longer be the meter / pixel measurement on their respective axes.

Specifically, given two quantities, p and q, and a rational number m / n we can say that the ratio of p to q is less than, equal to, or greater than m / n when np is less than, equal to, or greater than mq respectively.

Specifically, a signed semiring consists of a pair ( Γ, ε ) where Γ is a semiring and ε: Γ → Z / 2Z is a homomorphism of additive monoids.

Specifically, the interest rate ( I / m ) is a percent of principal ( I ) paid at some rate ( m ).

Specifically there were practitioners of the technique that said of a mesmerized person " the person is back animal " meaning " the person is back in a natural mental state where she / he recovers his / her most primitive part of the mind ".

Specifically, diagenesis “ is the cumulative physical, chemical and biological environment ; these processes will modify an organic object ’ s original chemical and / or structural properties and will govern its ultimate fate, in terms of preservation or destruction ”.

Specifically, it explored the feasibility of symmetric and asymmetric data rates exceeding 10 Mbit / s on short phone lines.

Specifically in low income neighborhoods, the presence of a local grocery store is correlated with lower BMI / overweight risk.

Specifically, Visual PinMAME is for emulating CPUs and the connected ROMs used in modern pinball tables, as opposed to tables with solid-state electronics / electro-mechanical mechanisms that contain no ROMs or advanced ICs in their hardware design.

Specifically, it denoted the perspective that human behavior is largely determined by a person's immediate social environment, that modes of social organization were not supernatural or metaphysical constructs but products of the social system and social environment, which were in turn products of the level of technology / mode of production ( the material world ), and were therefore constantly changing.

Specifically, the manuals and other content at MediaWiki. org are Creative Commons-licensed, while the set of help pages intended to be freely copied into fresh wiki installations and / or distributed with MediaWiki software is public domain.

" Specifically on the subject of creation / evolution, some Anglicans view " Big Bang cosmology " as being " in tune with both the concepts of creation out of nothing and continuous creation.

Specifically, people with mildly elevated levels of bilirubin ( 1. 1 mg / dl to 2. 7 mg / dl ) were at lower risk for CAD and at lower risk for future heart disease.

Specifically, if K / Q is a finite Galois extension then to each ( positive ) prime p which does not ramify in K and to each prime ideal P lying over p in K there is a unique element g of Gal ( K / Q ) satisfying the condition g ( x ) = x < sup > p </ sup > ( mod P ) for all integers x of K. Varying P over p changes g into a conjugate ( and every conjugate of g occurs in this way ), so the conjugacy class of g in the Galois group is canonically associated to p. This is called the Frobenius conjugacy class of p and any element of