) 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.

Euclid poses the problem: " Given two numbers not prime to one another, to find their greatest common measure ".

Given any expression involving complex numbers, bras, kets, inner products, outer products, and / or linear operators ( but not addition ), written in bra-ket notation, the parenthetical groupings do not matter ( i. e., the associative property holds ).

* 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 a vector space V over the field R of real numbers, a function is called sublinear if

Without doubt, the single most significant paper concerning the distribution of prime numbers was Riemann's 1859 memoir On the Number of Primes Less Than a Given Magnitude, the only paper he ever wrote on the subject.

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 basic sound blocks, that a machine digitized, one has a bunch of numbers which describe a wave and waves describe words.

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 that France maintained a strong standing army, and that Prussia and the other German states would need weeks to mobilise their conscript armies, the French held the initial advantage of troop numbers and experience.

Given two metric spaces ( X, d < sub > X </ sub >) and ( Y, d < sub > Y </ sub >), where d < sub > X </ sub > denotes the metric on the set X and d < sub > Y </ sub > is the metric on set Y ( for example, Y might be the set of real numbers R with the metric d < sub > Y </ sub >( x, y )

: Given: a function f: A R from some set A to the real numbers

Given two numbers in scientific notation,

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 any such interpretation of a set of points as complex numbers, the points constructible using valid compass and straightedge constructions alone are precisely the elements of the smallest field containing the original set of points and closed under the complex conjugate and square root operations ( to avoid ambiguity, we can specify the square root with complex argument less than π ).

Given a series with values in a normed abelian group G and a permutation σ of the natural numbers, one builds a new series, said to be a rearrangement of the original series.

Given that only six vessels were constructed after the Coast Guard takeover, the " LV -" series numbers are most commonly used.

Given an ordered sequence of real numbers: the first difference is defined as

Given these numbers, the VW 166 is the most mass-produced amphibious car in history.

Given that the Austrians, with their superior numbers and overwhelming artillery firepower, were now intent upon seizing the opportunity to launch a counterattack of their own, retreat was most difficult.

Given an algebraically closed field A containing K, there is a unique splitting field L of p between K and A, generated by the roots of p. If K is a subfield of the complex numbers, the existence is automatic.

Given von Spee ’ s superiority in speed, firepower, efficiency and numbers, why Cradock chose to engage puzzles historians.

Given two normed vector spaces V and W ( over the same base field, either the real numbers R or the complex numbers C ), a linear map A: V → W is continuous if and only if there exists a real number c such that

Given a real dynamical system ( R, M, Φ ), I ( x ) is an open interval in the real numbers, that is.