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Page "John Barnard" ¶ 8
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Given and large
) Given the exclusionary and ancestral conception of citizenship held by Greek city-states, a relatively large portion of the population took part in the government of Athens and of other radical democracies like it.
Given the United States ' large size it has numerous regional variations.
Given the large number of U. S. military personnel and their dependents residing in Europe, it was expected that over 7 % of donors would be deferred due to the policy.
Given that drug poisoning causes a large portion of patients in a coma, hospitals first test all comatose patients by observing pupil size and eye movement, through the vestibular-ocular reflex.
Given Guatemala's large expatriate community in the United States, it is the top remittance recipient in Central America, with inflows serving as a primary source of foreign income equivalent to nearly two-thirds of exports.
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.
The knapsack problem or rucksack problem is a problem in combinatorial optimization: Given a set of items, each with a weight and a value, determine the number of each item to include in a collection so that the total weight is less than or equal to a given limit and the total value is as large as possible.
Given barely two months to assemble a large sea-going invasion fleet, the Kriegsmarine opted to convert inland river barges into makeshift landing craft.
Given their wide historical distribution, red wolves probably utilized a large suite of habitat types at one time.
Given the current size of the Web, even large search engines cover only a portion of the publicly available part.
Given typical workloads, Cray felt that the small cost incurred by being required to break large sequential memory accesses into segments was a cost well worth paying.
# Given a large enough beta-tester and co-developer base, almost every problem will be characterized quickly and the fix obvious to someone.
Given that ipê trees typically grow in densities of only one or two trees per acre, large areas of forest must be searched and cut down to create paths to harvest and fill orders for boardwalks and, to a lesser extent, homeowner decks.
Given that many open source projects fail due to lack of developer support, exposure to such a large community of developers can continually breathe new life into a project.
The law states that " given enough eyeballs, all bugs are shallow "; or more formally: " Given a large enough beta-tester and co-developer base, almost every problem will be characterized quickly and the fix will be obvious to someone.
Given their large size, Great Danes continue to grow ( mostly gaining weight ) longer than most dogs.
Given the slow speed and the coarse resolution this was not a feasible technique for printing large images, but could usefully print a small logo onto a letterhead and then the following letter, all in a single unattended print run without changing the print element.
Kendall West is home to a large concentration of Colombians and Colombian Americans in the U. S. Given the local name " Little Bogota ".
Given that the businesses in Miami Springs had always relied upon the large disposable incomes of the employees of the large airline carriers, the bankruptcy of both corporations in the same year created a chain reaction, eventually causing many small businesses to close their doors.
Given the large amount of gold discovered in California from the late 1840s on, that mint handled the national needs of gold mint production.
Given a large enough audience, peers, readers and commentators, almost all problematic content will be quickly noticed highlighted and fixed.
Given the large force facing him and the defects of the fort's site, Montcalm opted for a strategy of defending the likely approaches to the fort.
Given the ( particularly modern ) prevalence of crowd events, and the potential safety issues associated with such large gatherings of people, the topic is receiving increasing attention from agencies responsible for crowd management and also from governments.
Given the large allowed error, it is not expected that this is too onerous a requirement.

Given and sum
Given a set of integers, does some nonempty subset of them sum to 0?
Given that estimation is undertaken on the basis of a least squares analysis, estimates of the unknown parameters β < sub > j </ sub > are determined by minimising a sum of squares function
Given two Lie algebras and, their direct sum is the Lie algebra consisting of the vector space
** Closure axiom for addition: Given two integers a and b, their sum, a + b is also an integer.
Solomonoff's universal prior probability of any prefix p of a computable sequence x is the sum of the probabilities of all programs ( for a universal computer ) that compute something starting with p. Given some p and any computable but unknown probability distribution from which x is sampled, the universal prior and Bayes ' theorem can be used to predict the yet unseen parts of x in optimal fashion.
Given two ultrafilters and on, we define their sum by
Given a circle A, find a circle B such that the area of the intersection of A and B is equal to the area of the symmetric difference of A and B ( the sum of the area of A − B and the area of B − A ).
Given a set of points in Euclidean space, the first principal component corresponds to a line that passes through the multidimensional mean and minimizes the sum of squares of the distances of the points from the line.
Given the sheer power of leverage the Rothschild family had at its disposal, this profit was an enormous sum.
* Given 27 same-size cubes whose nominal values progress from 1 to 27, a 3 × 3 × 3 magic cube can be constructed such that every row, column, and corridor, and every diagonal passing through the center, is composed of 3 cubes whose sum of values is 42.
The universal prior probability of any prefix p of a computable sequence x is the sum of the probabilities of all programs ( for a universal computer ) that compute something starting with p. Given some p and any computable but unknown probability distribution from which x is sampled, the universal prior and Bayes ' theorem can be used to predict the yet unseen parts of x in optimal fashion.
Given the rapid growth in absolute value of Γ ( z + k ) when k → ∞, and the fact that the reciprocal of Γ ( z ) is an entire function, the coefficients in the rightmost sum are well-defined, and locally the sum converges uniformly for all complex s and x.
Given a faithful irreducible representation ρ of G, the lattice Yang-Mills action is the sum over all lattice sites of the ( real component of the ) trace over the n links e < sub > 1 </ sub >, ..., e < sub > n </ sub > in the Wilson loop,
Given a finite set of probability density functions p < sub > 1 </ sub >( x ), …, p < sub > n </ sub >( x ), or corresponding cumulative distribution functions P < sub > 1 </ sub >( x ), …, P < sub > n </ sub >( x ) and weights w < sub > 1 </ sub >, …, w < sub > n </ sub > such that and the mixture distribution can be represented by writing either the density, f, or the distribution function, F, as a sum ( which in both cases is a convex combination ):
* Given two representations ρ < sub > 1 </ sub >, ρ < sub > 2 </ sub > we may construct their direct sum ρ < sub > 1 </ sub > ⊕ ρ < sub > 2 </ sub > by ( ρ < sub > 1 </ sub > ⊕ ρ < sub > 2 </ sub >) ( g )( v, w )
Given two I-graded vector spaces V and W, their direct sum has underlying vector space V ⊕ W with gradation
Given two positive integers N and i, there is a unique way to expand N as a sum of binomial coefficients as follows:
Given a sequence, the nth partial sum is the sum of the first n terms of the sequence, that is,
Given two objects A and B, their direct sum is written as.
Given a indexed family of objects A < sub > i </ sub >, indexed with i ∈ I from an index set I, one may write their direct sum as.
Given two abelian groups ( A, ∗) and ( B, ·), their direct sum A ⊕ B is the same as their direct product, i. e. its underlying set is the Cartesian product A × B with the group operation ○ given componentwise:
Given a finite family of rings R < sub > 1 </ sub >, ..., R < sub > n </ sub >, the direct product of the R < sub > i </ sub > is sometimes called the direct sum.

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