Given the first n digits of Ω and a k ≤ n, the algorithm enumerates the domain of F until enough elements of the domain have been found so that the probability they represent is within 2 < sup >-( k + 1 )</ sup > of Ω.

Given two groups A and H there exist two variations of the wreath product: the unrestricted wreath product A Wr H ( also written A ≀ H ) and the restricted wreath product A wr H. Given a set Ω with an H-action there exists a generalisation of the wreath product which is denoted by A Wr < sub > Ω </ sub > H or A wr < sub > Ω </ sub > H respectively.

Given a hermitian structure on a vector space, J and Ω are related via

Given a function f belonging to L ^< sup > 1 </ sup >( Ω ), the total variation of f in Ω is defined as

Given a complex manifold M, a differential of the first kind ω is therefore the same thing as a 1-form that is everywhere holomorphic ; on an algebraic variety V that is non-singular it would be a global section of the coherent sheaf Ω < sup > 1 </ sup > of Kähler differentials.

: Given an isolated system in equilibrium, it is found with equal probability in each of its accessible microstates.

: Given any set X of pairwise disjoint non-empty sets, there exists at least one set C that contains exactly one element in common with each of the sets in X.

Given this, the bidding is said to start at the one-level when contracting for a total of seven tricks, at the two-level for eight tricks and so on to the seven-level to contract to take all thirteen tricks.

Given a surface through which a metal wire passes, electrons move in both directions across the surface at an equal rate.

Given a function f ∈ I < sub > x </ sub > ( a smooth function vanishing at x ) we can form the linear functional df < sub > x </ sub > as above.

Given the age of the Rig Veda being at least 1500 BC or before, this must rank as the earliest practice of beating of the war drum in the history of mankind.

Given that a natural language such as English contains, at any given time, a finite number of words, any comprehensive list of definitions must either be circular or rely upon primitive notions.

Given the limited budget for schools, it is claimed that a voucher system would weaken public schools while at the same time not necessarily providing enough money for people to attend private schools.

* Frederick Douglass lecture on Haiti – Given at the World's Fair in Chicago, January 1893.

Given away at theatrical showings was a comic herald that told a simplified version of the film.

Given a complex-valued function ƒ of a single complex variable, the derivative of ƒ at a point z < sub > 0 </ sub > in its domain is defined by the limit

Given the state at some initial time ( t = 0 ), we can solve it to obtain the state at any subsequent time.

Along with a hand-picked escort led by Given Campbell, Davis and his wife were captured on May 10, 1865, at Irwinville in Irwin County, Georgia.

Given civilian status, he recovered his teaching position at Lycée Pasteur near Paris, settled at the Hotel Misgiven a new position at Lycée Condorcet, replacing a Jewish teacher who had been forbidden to teach by Vichy law.

Given that bodhisattvas are known to incarnate at will as living people according to the sutras, the princess Miaoshan is generally viewed as an incarnation of Avalokitesvara.

Given the choice between nylon and gut, many luthiers prefer to use gut, as it conforms more readily to the sharp angle at the edge of the fingerboard.

Given the need for such fine regulation of Ca < sup > 2 +</ sup > signaling, it is perhaps unsurprising that dysregulated mitochondrial Ca < sup > 2 +</ sup > has been implicated in several neurodegenerative diseases, while the catalogue of tumor suppressors includes a few that are enriched at the MAM.

Given printing practices at the time ( which included type-setting from dictation ), no two editions turned out to be identical, and it is relatively rare to find even two copies that are exactly the same.

Given a year to complete the work, Gibson undertook the actual writing out of " blind animal terror " at the obligation to write an entire novel – a feat which he felt he was " four or five years away from ".

Given the task of overhauling the Cardinals by owner Gussie Busch, Herzog was looking to trade Templeton when he was approached by Padres General Manager Jack McKeon at the 1981 baseball winter meetings.

Given prevailing views on homosexuality at the time, circulation of the diaries helped undermine support for clemency for Casement.

Given their wide historical distribution, red wolves probably utilized a large suite of habitat types at one time.

Given a particular query, the DBMS ' query optimizer is responsible for devising the most efficient strategy for finding matching data.

Given a particular query, the DBMS ' query optimizer is responsible for devising the most efficient strategy for finding matching data.

Given this reliance on literary sources, it is doubtful whether Nostradamus used any particular methods for entering a trance state, other than contemplation, meditation and incubation.

Given a particular wing and its velocity through the air, debates over which mathematical approach is the most convenient to use can be misperceived by novices as differences of opinion about the basic principles of flight.

Given a topological space X, denote F the set of filters on X, x ∈ X a point, V ( x ) ∈ F the neighborhood filter of x, A ∈ F a particular filter and the set of filters finer than A and that converge to x.

Given the particular differential operators involved, this is a linear partial differential equation.

Given the evidence of A. C. Elias about the acrimony of Swift's departure from the Temple household, evidence from Swift's Journal to Stella about how uninvolved in the Temple household Swift had been, and the number of repeated observations about himself by the Tale's author, it seems reasonable to propose that the digressions reflect a single type of man, if not a particular character.

Given four points in general linear position ( no three collinear ; in particular, no two coincident ), there are exactly three pairs of lines ( degenerate conics ) passing through them, which will in general be intersecting, unless the points form a trapezoid ( one pair is parallel ) or a parallelogram ( two pairs are parallel ).

According to pioneering Angkor scholar Maurice Glaize, " Given the very particular charm of Banteay Srei — its remarkable state of preservation and the excellence of a near perfect ornamental technique — one should not hesitate, of all the monuments of the Angkor group, to give it the highest priority.

Given two jointly distributed random variables X and Y, the conditional probability distribution of Y given X is the probability distribution of Y when X is known to be a particular value.

Given a particular ℓ, m is entitled to be any integer from-ℓ up to ℓ.

Given the preceding jurisprudence regarding due process, Chief Justice Taney was not entirely breaking ground in his Dred Scott opinion when, without elaboration, he pronounced the Missouri Compromise unconstitutional because an " act of Congress that deprived a citizen of his liberty or property merely because he came himself or brought his property into a particular territory of the United States, and who had committed no offence against the laws, could hardly be dignified with the name of due process of law.

Given a particular input, it will always produce the same output, and the underlying machine will always pass through the same sequence of states.

Given his adept use of angle, depth, and pace, his opponents often have difficulty breaking down one particular side.

Given the variability of wave height, the largest individual waves are likely to be somewhat less than twice the reported significant wave height for a particular day or storm.

Given a 3D audio " picture " of the scene, a specialised algorithm generates secondary sound waves necessary to recreate it in the particular room and then instructs a large number of speakers ( 300-400 ) to generate the " audio hologram ".

Given these facts, waiting more than 48 hours between bouts of training for a particular muscle is a waste of time.

Given the ordinary irreducible and irreducible Brauer characters of a particular finite group, the irreducible ordinary characters may be decomposed as non-negative integer combinations of the irreducible Brauer characters.

Given the population growth over the past 50 years, a particular concern is the potential eutrophication of currently oligotrophic Lake Ohrid from increased pollution.

Given the fact that these meeting dates are well-established, it is a normal practice for senior DoD personnel interested in the particular study topics for that year to come to the last day of the meeting and be briefed in person on the study findings to-date.

Given the quasi-legal status of the sport in New York at the time, it was not unusual that no record was kept of any particular encounter.

Given a single, stereoisomerically pure starting material, a stereospecific mechanism will give 100 % of a particular stereoisomer ( or no reaction ), although loss of stereochemical integrity can easily occur through competing mechanisms with different stereochemical outcomes.

Given that disadvantaged students generally have fewer opportunities to learn academic content outside of school, wasted class time due to an unfocused lesson presents a particular problem.