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 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 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, the distribution of this trait suggests that this need may have ( initially ) grown so intense at certain ( early ) points that those among said ( initially more deeply pigmented skinned ) Northern-migrants with mutations for straighter hair survived and had children at ( somewhat ) higher rates.

Specifically, the relevant findings indicate that the EDAR mutation coding for the predominant East Asian ' coarse ' or thick, straight hair texture arose within the past ~ 65, 000 years, which is a time frame that covers from the earliest of the ' Out of Africa ' migrations up to now.

Specifically, the active amplification function of the outer hair cells is very sensitive to damage from exposure to trauma from overly-loud sounds or to certain ototoxic drugs.

Specifically, 3D terrain using RAW height maps suffered from a lack of working examples, shadows were substandard ( consisting only of a spherical shadow texture projected on the terrain ), the ability to use skinned meshes for animated models was not working ( non-skinned meshes worked ), and the 3D rigid-body physics suffered from several issues.

Specifically, the Yemeni Arabs were unhappy that the prince was mounted on a fine Spanish steed.

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, neocolonialism refers to the theory that former or existing economic relationships, such as the General Agreement on Tariffs and Trade and the Central American Free Trade Agreement, created by former colonial powers were or are used to maintain control of their former colonies and dependencies after the colonial independence movements of the post – World War II period.

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

Specifically, " every man heard them speak in his own language " and wondered " how hear we every man in our own tongue, wherein we were born?

Specifically, Epstein argues that guilds were cost-sharing rather than rent-seeking institutions.

Specifically, they were instructed in geography, astronomy, ethnology, climatology, mineralogy, meteorology, botany, ornithology, and zoology.

Specifically, the nomenklatura consisted of two separate lists: one was for key positions, appointments to which were made by authorities within the party ; the other was for persons who were potential candidates for appointment to those positions.

Specifically, a Mario game ( titled Hotel Mario ), and three Legend of Zelda games were released: Link: The Faces of Evil, Zelda: The Wand of Gamelon and Zelda's Adventure.

Specifically, Young points to Coubertin's assertion that ancient Olympic athletes were amateurs as incorrect.

Specifically, results showed that those who believed that racial profiling was widespread and that racial tension would never be fixed were more likely to be opposed to racial profiling than those who did not believe racial profiling was as widespread or that racial tensions would be fixed eventually.

Specifically, those tables used for most of the 20th century were Newcomb's Tables of the Sun ( used from 1900 through 1983 ) and Brown's Tables of the Moon ( used from 1923 through 1983 ).

Specifically, Bell ruled that McDonald's endangered the health of their workers and customers by " misleading advertising ", that they " exploit children ", that they were " culpably responsible " in the infliction of unnecessary cruelty to animals, and that they were " antipathetic " to unionisation and paid their workers low wages.

Specifically, it was developed by the Muslim jurist and historian Al-Maqrizi ( 1364 – 1442 ) who wrote about a particular period in the Mamluk dynasty when the rulers were simultaneously increasing the supply of a lower valued ( copper ) currency and hoarding the more valued ( gold and silver ) currencies.

Specifically, as to civil law, the many different bodies of law used in different parts of France were to be replaced by a single legal code.

Specifically, the heuristics they used were deference to scientific authority, trust in scientific institutions, and whether they had seen media coverage of biotechnology.

Specifically, the People's Republics in Romania, Bulgaria, Hungary, and Poland were dominated by the Soviet Union.

:: Example: " Specifically, under Roberts, there may have been cases in which courts erroneously determined that testimonial statements were reliable.

Specifically, research has demonstrated continuity in the disorders such that conduct disorder is often diagnosed in children who have been previously diagnosed with oppositional defiant disorder, and most adults with antisocial personality disorder were previously diagnosed with conduct disorder.

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 Lowell was planned as reaction to the mill communities in Great Britain, which were perceived as cramped and inhumane.