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, when doing global inline substitutions, a static compilation process may need run-time checks and ensure that a virtual call would occur if the actual class of the object overrides the inlined method, and boundary condition checks on array accesses may need to be processed within loops.

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

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, a topological space X is compactly generated if it satisfies the following condition:

Specifically, P is pure in M if and only if the following condition holds: for any m-by-n matrix ( a < sub > ij </ sub >) with entries in R, and any set y < sub > 1 </ sub >,..., y < sub > m </ sub > of elements of P, if there exist elements x < sub > 1 </ sub >,..., x < sub > n </ sub > in M such that

Specifically, the court held that patent owners could condition the sale of patented goods with a restrictive notice and thereby restrict the disposition of the goods by the purchasers, with the exception of antitrust law violations, such as price-fixing and tie-in restrictions, or violations of " some other law or policy.

Specifically, he told interrogators that Iraq provided training to al-Qaeda in the area of weapons of mass destruction.

Specifically, an excited atom will act like a small electric dipole which will oscillate with the external field provided.

Specifically, is the probability that the call will be exercised provided one assumes that the asset drift is the risk-free rate.

Specifically, if u is the density at equilibrium of some quantity such as a chemical concentration, then the net flux of u through the boundary of any smooth region V is zero, provided there is no source or sink within V:

Specifically, it legalizes the process of cloning a human embryo, and implanting the clone into a womb, provided that the clone is then aborted and used for medical research.

Specifically, differences in the learning rates of list 2 provided clear evidence of the negative transfer phenomenon.

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, Lites was a multi-threaded server and emulation library that provided unix functionality to a Mach based system.

Specifically, the Act expanded the Medicare program to provide protection against catastrophic medical expenses and for the first time, provided coverage under the Medicare program for prescription drugs.

Specifically the USA has provided helicopters, night-vision goggles and nuclear detection equipment.

Specifically, GLC and the MCCs only provided 16 % and 26 % of services in their areas respectively-however the shire county councils provided 87 % of services in their areas.

Specifically, the force provided by the propeller is pushing towards the engine, rather than away.

Specifically, it emerged that Delamere had approved permanent residency for a group of Chinese businessmen provided they invested generously in various Māori development schemes.

Specifically, he drew attention to special vanity license plates that Ryan's office provided for clout-heavy motorists.

Specifically, MIGA has provided a US $ 86 million guarantee to Fortis Bank of Belgium against the risks of expropriation, breach of contract, war and civil disturbance, as well as transfer inconvertibility in both Laos and Thailand.

Specifically, the services that will eventually be provided include but are not limited to: youth sports / life training, residential care for expectant teenage mothers, short term care for mothers in crisis, family and leadership training, counselling centre, and tearoom and bed and breakfast.

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, commodities such as sugar are heavily distorted by subsidies on behalf of powerful economies ( the United States, Europe, and Japan ), who have a disproportionate influence in the WTO.

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

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, a male secondary school enrollment 10 % above the average reduced the chance of a conflict by about 3 %, while a growth rate 1 % higher than the study average resulted in a decline in the chance of a civil war of about 1 %.

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, this demand for political democracy implies complete freedom to agitate for secession and for a referendum on secession by the seceding nation.

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.

Specifically, the law makes it illegal to publicly " deny, play down, justify or approve of the genocide committed by the German National Socialist regime during the Second World War ".

Specifically, the process was first used by the English " Good Parliament " against Baron Latimer in the second half of the 14th century.

Specifically, they require that a patient must have pain associated with the bladder, accompanied by one other urinary symptom.

Specifically, the left invariant extension of an element v of the tangent space at the identity is the vector field defined by v ^< sub > g </ sub > =

Specifically, the Massiah rule applies to the use of testimonial evidence in criminal proceedings deliberately elicited by the police from a defendant after formal charges have been filed.

Specifically, he participated in the attempt to take Fushimi castle by assault in July 1600, in the defense of the besieged Gifu Castle in August of the same year, and finally in the Battle of Sekigahara.

Specifically, it is the worldwide, publicly accessible network of interconnected computer networks that transmit data by packet switching using the standard Internet Protocol ( IP ).

According to Stephen Suleyman Schwartz, in his book " The Two Faces of Islam ", “ some say that during this vagabondage Ibn Abdul Wahhab came into contact with certain Englishmen who encouraged him to personal ambition as well as to a critical attitude about Islam .” Specifically, Mir ’ at al Harramin, a Turkish work by Ayyub Sabri Pasha, written in 1888, states that in Basra, Abdul Wahhab had come into contact with a British spy by the name of Hempher, who “ inspired in him the tricks and lies that he had learned from the British Ministry of the Commonwealth .”

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, in 1895 Pierre-Hector Coullié, archbishop of Lyon, voiced his official decision on the reinstatement of sports to Pierre de Coubertin, the founder of the Modern Olympic Games, by stating " Nous acceptons tout, sauf pankration " meaning " We accept all to be reinstated, except pankration ".

Specifically, in an environment where it is considered important to know the probability of a fraudulent login in order to accept the risk, one can ensure that the total number of possible passwords multiplied by the time taken to try each one ( assuming the greatest conceivable computing resources ) is much greater than the password lifetime.

Specifically, the campaign raised $ 253. 7 million for undergraduate financial aid, as well as $ 2. 33 billion for its initiative in " Seeking Solutions " to global problems, $ 1. 61 billion for " Educating Leaders " by improving K-12 education, and $ 2. 11 billion for " Foundation of Excellence " aimed at providing academic support for Stanford students and faculty.

Specifically, for sailing boats, red and green sidelights and a white sternlight are required, although for vessels under 7 metres ( 23. 0 ft ) in length, these may be substituted by a torch or white all-round lantern.