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.

The quantum circuits used for this algorithm are custom designed for each choice of N and the random a used in f ( x ) = a < sup > x </ sup > mod N. Given N, find Q = 2 < sup > q </ sup > such that < math > N ^ 2

Given the choice, who wouldn't rather believe their children are special and chosen for some high mission rather than that they have a brain disorder?

Given the choice between chaos at the hands of Chinese or submission to the Japanese, the Taipei elite sent Koo Hsien-jung to Keelung to invite the advancing Japanese forces to proceed to Taipei and restore order.

Given the type of warfare that had been carried out in the conflict — wherein highly mobile groups of soldiers and rebels continued to move to and from on the desert terrain, retreating at a time and then suddenly attacking to regain control of small towns and villages in the Eastern rebel held parts of Libya — had led to the technical becoming a vehicle of choice for both sides.

Given a set of points in the Euclidean plane, selecting any one of them to be called 0 and another to be called 1, together with an arbitrary choice of orientation allows us to consider the points as a set of complex numbers.

Given the number of unpleasant, harmful or even fatal consequences of coming out in world societies, it is questionable to call being closeted a choice.

Given the choice, she chose Heracles over Zeus who went off in search of other pursuits.

The isomorphism is not canonical ; it depends on a choice of basis in V. Given a basis ( e < sub > 1 </ sub >, ..., e < sub > n </ sub >) of V and an automorphism T in GL ( V ), we have

Given the choice, whether one believes that " the lives of entire peoples and societies have been decisively influenced by exceptional individuals " or, conversely, that whatever happens occurs as a result of impersonal forces oblivious to human intentions – Berlin rejected both options and the choice itself as nonsensical.

Given the choice of resigning or calling new elections, Ōhira chose the latter and began campaigning for LDP candidates.

Given the choice between an AdLib card or a fully compatible Sound Blaster card that came with a game port, saved a slot, and included the " DSP " for not much more in price, many consumers opted for the Sound Blaster.

Given a vector bundle V over M, the corresponding field concept is called a section of the bundle: for m varying over M, a choice of vector

Given the massing of the Muslim armies at Yarmouk, however, Vahan had little choice but to respond in kind.

Given a choice, mountain hares in Scotland and Ireland seem to prefer feeding on grasses.

Given the prevalence of disapproval as a tool of government, including the criminal law and diplomatic relations, some fail to see voting as a positive and voluntary choice of a desirable outcome.

Given that Unferth shows his dislike for Beowulf early in the story, Unferth ’ s choice to award Beowulf with Hrunting, which means “ thrusting ,” can be interpreted as a sign of peace and acceptance.

Given a torus T ( not necessarily maximal ), the Weyl group of G with respect to T can be defined as the normalizer of T modulo the centralizer of T. That is, Fix a maximal torus in G ; then the corresponding Weyl group is called the Weyl group of G ( it depends up to isomorphism on the choice of T ).

Given the choice of leaving the United States or being sent back to the Confederacy, Foote fled to Canada and later to London.

Given the predominantly medium-haul route network of the airline, the choice of the Boeing 747SP continues to this day to raise interrogations.

Given the availability of experienced short fiction writers at the time, Elwood's choice of inexperienced authors aroused suspicions.

Given a choice of new classes she could take, she chose communications, in part because her father was a journalist and her mother an actress.

Given two subspaces with, this leads to a definition of angles called canonical or principal angles between subspaces.

Given points P < sub > 0 </ sub > and P < sub > 1 </ sub >, a linear Bézier curve is simply a straight line between those two points.

Given that Bozizé accuses Sudan of supporting the UFDR rebels who are actively fighting the Central African Government, the relation between the two countries has remained good.

Given this basic definition, further criteria are needed to establish a dividing line between postlexical clitics and morphological affixes, since both are characterized by a lack of prosodic autonomy.

Given the similarities between the rep proteins of the alphasatellites and the nanoviruses, it is likely that the alphasatellites evolved from the nanoviruses.

Given the great historical link between Persian and Jewish history, modern day Persian Jews are called " Esther's Children ".

Given the universality of free fall, there is no observable distinction between inertial motion and motion under the influence of the gravitational force.

Given the distances between the stars, the great majority of stellar systems in colliding galaxies will be unaffected.

Given the differences of opinion within the Lord Aberdeen cabinet over the direction of foreign policy with regard to relations between Britain and the French under Napoleon III, it is not surprising that debate raged within the government as Louis Bonaparte, now assuming the title of Emperor Napoleon III of France.

Given a ( random ) sample the relation between the observations Y < sub > i </ sub > and the independent variables X < sub > ij </ sub > is formulated as

Given two secondary stations, the time difference ( TD ) between the primary and first secondary identifies one curve, and the time difference between the primary and second secondary identifies another curve, the intersections of which will determine a geographic point in relation to the position of the three stations.

Given the overall size of trade between Mexico and the United States, there are remarkably few trade disputes, involving relatively small dollar amounts.

Given an arbitrary group G, there is a related profinite group G < sup >^</ sup >, the profinite completion of G. It is defined as the inverse limit of the groups G / N, where N runs through the normal subgroups in G of finite index ( these normal subgroups are partially ordered by inclusion, which translates into an inverse system of natural homomorphisms between the quotients ).

Bernhard Riemann in his memoir " On the Number of Primes Less Than a Given Magnitude " published in 1859 extended the Euler definition to a complex variable, proved its meromorphic continuation and functional equation and established a relation between its zeros and the distribution of prime numbers.

Given the role that many social groups have in the development of public policy and the extensive connections between state bureaucracies and other institutions, it has become increasingly difficult to identify the boundaries of the state.

Given an ongoing rift in the sport during the 1860s between the northern professionals and Surrey, MCC feared the loss of its authority should Grace " throw in his lot with the professionals " so it was considered vital for them and their interests to get him onside.

Given the difference between their roles and emphases, some scholars have speculated that the interactions between the Æsir and the Vanir reflect the types of interaction that were occurring between social classes ( or clans ) within Norse society at the time.

Given the symmetry of circularly polarized light, we could have in fact selected any other two orthogonal components and found the same phase relationship between them.

Given that different languages have different grammatical features, the actual test for which nouns are mass nouns may vary between languages.

Given two dual numbers p, and q, they determine the set of z such that the Galilean angle between the lines from z to p and q is constant.

Given the structural similarities between bacterial flagella and bacterial secretory systems, it is thought that bacterial flagella may have evolved from the type three secretion system ; however, it is not known for certain whether these pores are derived from the bacterial flagella or the bacterial secretory system.