Given a complete Boolean algebra B there is a Boolean-valued model denoted by V < sup > B </ sup >, which is the Boolean-valued analogue of the von Neumann universe V. ( Strictly speaking, V < sup > B </ sup > is a proper class, so we need to reinterpret what it means to be a model appropriately.

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 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 postwar urban erosion of support, Lenin designed propaganda campaigns as a supplement to the New Economic Policy to further increase backing of the Bolsheviks.

An example of an off the beach catamaran is the Ron Given of New Zealand designed Paper Tiger Catamaran

Given that an expanding Field is obviously far more effective at protecting a ship than a static one, all Motie Field generators were designed to expand as necessary.

Given the considerable overall width of this design, new suburban freeways are often designed with interchanges spaced far enough apart to avoid the need for parallel roadways.

Given the high stakes nature of many of these assessment purposes, it is crucial that assessment practices be guided by sound principles to insure that they are valid, fair, and appropriate to the context and purposes for which they designed.

Given the losses at each reflection, this " backscatter " signal is extremely small, which is one reason why OTH radars were not practical until the 1960s, when extremely low-noise amplifiers were first being designed.

Given that Communist Romania was a police state, and unprecedented measures of strict control and surveillance were supposed to have been enforced in all areas of society ( phone calls were routinely monitored, correspondence was intercepted, and secret police informants were common ) a plan such as the one allegedly designed by the group would have been exceedingly difficult to carry out.

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 a general algorithm for integer factorization, one can factor any integer down to its constituent prime factors by repeated application of this algorithm.

Given a set of training examples of the form, a learning algorithm seeks a function, where is the input space and

Given unlimited resources, a classical computer can simulate an arbitrary quantum algorithm so quantum computation does not violate the Church – Turing thesis.

Given these facts, algorithm defined by the following pseudocode:

Given the rules of any two-person game with a finite number of positions, one can always trivially construct a minimax algorithm that would exhaustively traverse the game tree.

Given a set of training examples, each marked as belonging to one of two categories, an SVM training algorithm builds a model that assigns new examples into one category or the other.

Given an algorithm for integer factorization, one can factor any integer down to its constituent primes by repeated application of this algorithm.

Given a set of training examples, each marked as belonging to one of two categories, an SVM training algorithm builds a model that predicts whether a new example falls into one category or the other.

Given Bluestein's algorithm, such a transform can be used, for example, to obtain a more finely spaced interpolation of some portion of the spectrum ( although the frequency resolution is still limited by the total sampling time ), enhance arbitrary poles in transfer-function analyses, etcetera.

Given decision problems A and B and an algorithm N which solves instances of B, we can use a many-one reduction from A to B to solve instances of A in:

Given the Cantor – Dedekind axiom, this algorithm can be regarded as an algorithm to decide the truth of any statement in Euclidean geometry.

The 1st generalized division algorithm: Given integers,, with, there exist unique integers and with < math > d

Given a polynomial g, polynomials ( f < sub > 1 </ sub >, ..., f < sub > m </ sub >) and an order on the monomials in k ..., x < sub > n </ sub >, we construct the reduction of g modulo f < sub > 1 </ sub >, ..., f < sub > m </ sub > by the following algorithm.

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 a presentation of a group G by generators and relations and a subgroup H of G, the algorithm enumerates the cosets of H on G and describes the permutation representation of G on the space of the cosets.

Given first 12 digits 979-0-9016791-7, the ISMN algorithm evaluates

Given M intervals of the form c ± r ( which means ), the algorithm seeks to find an interval with M − f sources.

Given an incompressible objective function, there is no basis for choosing one algorithm over another.

Given that the movement of Careys from Ireland has been almost exclusively one way ( outbound ), this significantly reduces the dilemma over the origin of their surname.

Given the absolute magnitude, for objects within our galaxy you can also calculate the apparent magnitude from any distance ( in parsecs ):

Given the absolute magnitude, you can also compute apparent magnitude from its parallax:

Idealists are skeptics about the physical world, maintaining either: 1 ) that nothing exists outside the mind, or 2 ) that we would have no access to a mind-independent reality even if it may exist ; the latter case often takes the form of a denial of the idea that we can have unconceptualised experiences ( see Myth of the Given ).

Given the complexity of the calculations involved and the convoluted structure that a convertible bond can have, an arbitrageur often relies on sophisticated quantitative models in order to identify bonds that are trading cheap versus their theoretical value.

* Given any combination of complex numbers, bras, kets, inner products, outer products, and / or linear operators, written in bra-ket notation, its Hermitian conjugate can be computed by reversing the order of the components, and taking the Hermitian conjugate of each.

Given enough resources, this can result in a vast collection.

Given this popular understanding of the term, it can also be used illegitimately and inappropriately, as a means to dismiss what are in fact substantial and well-evidenced accusations.

Given a fixed budget, this can allow an increased sample size.

Given the federal nature of the holiday, celebrating Canada Day can be a cause of friction in the province of Quebec, where the holiday is overshadowed by Quebec's National Holiday, on June 24.

Given an asymmetric subunit on a triangular face of a regular isosahedron, with three subunits per face 60 such subunits can be placed in an equivalent manner.

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 r, the rate of rotation is easy to infer from the constant angular momentum L, so a 2D solution can be easily reconstructed from a 1D solution of this equation.

Given a simple, binary component feed, analytical methods such as the McCabe-Thiele method or the Fenske equation can be used.

Given these connotations, dandyism can be seen as a political protestation against the rise of levelling egalitarian principles, often including nostalgic adherence to feudal or pre-industrial values, such as the ideals of " the perfect gentleman " or " the autonomous aristocrat ", though paradoxically, the dandy required an audience, as Susann Schmid observed in examining the " successfully marketed lives " of Oscar Wilde and Lord Byron, who exemplify the dandy's roles in the public sphere, both as writers and as personae providing sources of gossip and scandal.

) Given a smooth Φ < sup > t </ sup >, an autonomous vector field can be derived from it.

Given that genes are universal to living organisms, genetics can be applied to the study of all living systems, from viruses and bacteria, through plants and domestic animals, to humans ( as in medical genetics ).

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

We have seen a few cavities of the appropriate size and shape for ivory-bills, but these can be old, or exceptionally large Pileated Woodpecker cavities, or mammal-enlarged Pileated Woodpecker cavities .… Given the results, it is unlikely a population of any meaningful size of Ivory-billed Woodpeckers exists in south Florida.

Given significant distance from the magnetic poles, one can figure which hand is which using a magnetic compass and the sun.

Given a basis of a vector space, every element of the vector space can be expressed uniquely as a finite linear combination of basis vectors.

Given high enough cooling rates and appropriate alloy composition, metallic bonding can occur even in glasses with an amorphous structure.

Given that the cost of replacing an executive can run over 100 % of his or her annual salary, any investment of time and energy in re-recruitment will likely pay for itself many times over if it helps a business retain just a handful of key players that would have otherwise left.

Given an arithmetic function, one can generate a bi-infinite sequence of other arithmetic functions by repeatedly applying the first summation.

Given the proposition that ' a persons life prospects should not be decided by factors outside of their control or for which a person cannot claim personal credit ' ( i. e. social status, inherited wealth, race and other accidents of birth ) a meritocracy proposes a system where people are rewarded based on their efforts, and if everyone can start on equal footing with the same opportunity to advance, then the results are just.