Given the difficulty of this position, it is not uncommon for the best player on the team to play Number Two so long as another strong player is available to play Three.

Given the difficulty in treating scleroderma, treatments with a smaller evidence base are often tried to control the disease.

Given the difficulty in specifying exact distributions of sample statistics, many methods have been developed for approximating these.

Given this view, the difficulty or impossibility of finding a plausible explanation for evil in a world created by God is to be expected, and so the argument from evil is assumed to fail unless it can be proven that God's reasons would be comprehensible to us.

Given a desired backbone conformation, side chain packing can be designed using variations of the dead-end elimination algorithm ; however, attempts to design proteins of novel folds have difficulty using this method due to an absence of plausible backbone models.

Given the difficulty of distinguishing these differences, an accurate and reliable schizoaffective disorder diagnosis usually requires an extended period of observation and treatment.

Given this fundamental logical difficulty, there has been very little experimental investigation by parapsychologists of retrocognition.

Given the difficulty of scoring directly from the point due to the distance to the goal, goals scored from the point are typically either on screens, or are tipped goals.

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

Given the difficulty of identifying the Messianic figure, Jews also pray for the coming of the prophet Elijah to serve as the Messiah's herald and to properly identify him.

Given the Narodniks ' generally middle-and upper-middle-class social background, they found difficulty relating to the impoverished peasants and their culture.

Given the difficulty of this task as proven in Book I, Socrates in Book II leads his interlocutors into a discussion of justice in the city, which Socrates suggests may help them see justice not only in the person, but on a larger scale, " first in cities searching for what it is ; then thusly we could examine also in some individual, examining the likeness of the bigger in the idea of the littler "

Given the difficulty of constructing explicit small families of solutions, much less presenting something like a " general " solution to the Einstein field equation, or even a " general " solution to the vacuum field equation, a very reasonable approach is to try to find qualitative properties which hold for all solutions, or at least for all vacuum solutions.

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 Ω microstates at a particular energy, the probability of finding the system in a particular microstate is p = 1 / Ω.

Given a set of integers, FIND-SUBSET-SUM is the problem of finding some nonempty subset of the integers that adds up to zero ( or returning the empty set if there is no such subset ).

Given a set of integers, SUBSET-SUM is the problem of finding whether there exists a subset summing to zero.

Given on 16 October 1732, they amounted only to recreating his first expedition, but with the added task of heading east and finding North America ( a feat which had in fact just been completed by Mikhail Gvozdev, though this was not known at the time ).

Given a positive integer n, Fermat's factorization method relies on finding numbers x, y satisfying the equality

Given a, gcd ( a, n ) = 1, finding x satisfying ax ≡ 1 ( mod n ) is the same as solving ax + ny = 1, which can be done by Bézout's lemma.

Given the rarity and importance of these books, rumors of finding new ones often develop interest.

Given a collection ( ensemble ) of particles, the probability of finding a particle at a certain position in phase space is specified by a probability distribution, the Liouville density.

Given a position, one obtains its Zobrist hash by finding out which pieces are on which squares, and combining the relevant bitstrings together.

Given a directed graph G, the minimum path cover problem consists of finding a path cover for G having the least number of paths.

Given the disparate nature of the voices in the Singaporean blogosphere, these sessions received a mixed response at best, with many ( including the local newspapers ) finding them boring.

The wavelets forming a continuous wavelet transform ( CWT ) are subject to the uncertainty principle of Fourier analysis respective sampling theory: Given a signal with some event in it, one cannot assign simultaneously an exact time and frequency response scale to that event.

Given that Rothko had known in advance about the luxury decor of the restaurant and the social class of its future patrons, the exact motives for his abrupt repudiation remain mysterious.

Given a short exact sequence with maps q and r:

Given a commutative diagram, a proof by diagram chasing involves the formal use of the properties of the diagram, such as injective or surjective maps, or exact sequences.

Given that there are many historical definitions of the keystone species concept, and without a consensus on its exact definition, a list of examples best illustrates the concept of keystone species.

The Mastermind satisfiability problem is a decision problem that asks, " Given a set of guesses and the number of colored and white pegs scored for each guess, is there at least one secret pattern that generates those exact scores?

Given the lengths of the sides of any cyclic quadrilateral, Brahmagupta gave an approximate and an exact formula for the figure's area,

Given a module, M, a projective resolution of M is an infinite exact sequence of modules

Given approximations of A from three distinct step sizes h, h / t, and h / s, the exact relationship

Given R-modules A and B, an extension of A by B is a short exact sequence of R-modules

Given the tendency of the legends of different seafarers – Greek, Norse, Irish, Arab and Iberian – to cross-fertilize and influence each other, the exact source of some legendary Atlantic islands – such as the mythical islands of Brasil and the Isle of Mam – are impossible to disentangle.

Given a subspace, one may form the short exact sequence

Given the possibility that symptoms of a known disease may have mutated over time, or that the plague was caused by a disease which no longer exists, the exact nature of the Athenian plague may never be known.

The exponential map is surjective on the stalks: Given a germ g of an holomorphic function at a point P such that g ( P ) ≠ 0, one can take the logarithm of g in a neighborhood of P. The long exact sequence of sheaf cohomology shows that we have an exact sequence

Given an exact differential equation defined on some simply connected and open subset D of R < sup > 2 </ sup > with potential function F then a differentiable function f with ( x, f ( x )) in D is a solution if and only if there exists real number c so that