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 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 a person ’ s occupational performance that influences their health and personal satisfaction of their individual needs.

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, Articles 37 and 38 recognize the " freedom of the person " and the " personal dignity of citizens " as " inviolable.

One recent study using this paradigm found that 16-month-olds tend to attribute beliefs to a person whose visual perception was previously witnessed as being “ reliable ” compared to someone whose visual perception was “ unreliable .” Specifically, 16-month-olds were trained to expect a person's excited vocalization and gaze into a container to be associated with finding a toy in the reliable looker condition or an absence of a toy in the unreliable looker condition.

Specifically, in the program implemented in Nea Erithréa bicycles are rented for one week to six months, on condition that the person concerned must submit to the Municipality the sum of 75 euros as a guarantee.

Specifically, emotions such as joy and grief tell us about the " good or bad fortune " of the person we are observing them in, whereas anger tells us about the bad fortune with respect to another person.

Specifically, although we sympathize with the offended person, we fear that the offended person may do harm to the offender, and thus also fear for and sympathize with the danger that faces the offender.

Specifically, if the offended person seems just and temperate in coping with the offense, then this magnifies the misdeed done to the offended in the mind of the spectator, increasing sympathy.

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, many of the benign fainting events are caused by excessive parasympathetic and vagal activity leading to dilation of blood vessels, slowing of the heart and decreased perfusion of the brain thus leading to decreased muscle tone in general and postural muscles in particular, allowing the person to collapse.

Specifically, he parodies the highbrow claim that the products a person uses distinguishes his or her level of cultural worth, by satirically identifying the products that would identify a middlebrow person.

Specifically, the belief that the Holy Spirit is the spirit / power of God and of Christ Jesus rather than a separate person in the Godhead.

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 pertaining to CROs providing clinical-trials services, the ICH-GCP ( E6 1. 20 ) defines a Contract Research Organization ( CRO ) as: " A person or an organization ( commercial, academic, or other ) contracted by the sponsor to perform one or more of a sponsor's trial-related duties and functions.

Specifically, any unsolicited actions of others that physically affect an individual ’ s property or person ( which may also be considered that person's property ), no matter if the result of those actions is damaging, beneficial, or neutral to the owner, are considered violent or aggressive when they are against the owner ’ s free will and interfere with his right to self-determination or the principle of self-ownership.

Specifically, in the simple Rasch model, the probability of a correct response is modeled as a logistic function of the difference between the person and item parameter.

Specifically, does this person have the ability to reward ( or punish ) you in the future?

Specifically, a minister who is placed in charge of a person training for the ministry is referred to as the student's bishop.