Given these harsh constitutional requirements, neither the pan-greens nor pan-blues can unilaterally change Taiwan ’ s political and legal status with respect to the ROC ’ s constitution.

Given the large numbers involved and the nature of the requirements, they argued, it was unlikely to find any members of Al Qaeda.

Given that NASA and USAF ( as well as government programs in other countries ) are the primary customers and sources of development capital, government regulatory requirements for oversight, parwork, quality, safety, and other documentation tend to inflate the operational costs of any such system.

Given the military-industrial requirements of the Cold War, the authors of the then secret National Security Council Report 68 ( NSC-68 ) proposed the US government undertake a massive permanent national economic expansion that would let it “ siphon off ” a part of the economic activity produced to support an ongoing military buildup to contain the Soviet Union.

Given the strategic requirements of winning the war, British Prime Minister Winston Churchill and U. S. President Franklin D. Roosevelt had no option but to accept the demands of their erstwhile ally, Soviet Premier Joseph Stalin, at Tehran, Yalta and Potsdam, argues retired diplomat Charles G. Stefan.

Given that the installed Mac base at the time still contained large numbers of 68000 based machines like the Mac Plus, these requirements restricted the number of machines it could run on.

Given started his playing career as a youth goalkeeper at Celtic in the early 1990s, leaving in 1994 having been deemed surplus to requirements, Given was part of the Sunderland team who won the Football League First Division title in 1995 – 96, while on loan from Blackburn Rovers.

Given that California's automotive market is one of the largest in the world, CARB wields enormous influence over the emissions requirements that major automakers must meet if they wish to sell into that market.

Given rapid changes in voice and more generally VOIP, centrally hosted solutions also make it easier to continuously adapt to changing requirements by providing one place for managing system change.

Given that such a performance increase necessitates a correspondingly large increase in size, cost, and power requirements, a significant amount of international collaboration over a period of decades would be required to construct such a collider.

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 the practical weight of suitable power sources, the accelerations given by ion thrusters are frequently less than one thousandth of standard gravity.

Given their large size, Great Danes continue to grow ( mostly gaining weight ) longer than most dogs.

: Given two sets, A and T, of equal size, together with a weight function C: A × T → R. Find a bijection f: A → T such that the cost function:

Given the explosion of medical knowledge in the 20th century, it is easily appreciated that this led to a vast expansion of the book, which threatened to collapse under its own weight in a metaphorical and physical sense.

Given the amount of evidence suggesting a link between antipsychotic medications and metabolic syndrome, several agencies have recommended regular clinical monitoring of weight, symptoms of hyperglycemia, glucose, hypertension and signs and symptoms of cardiovascular disease in chronically medicated patients with schizophrenia.

Given that the tank was reaching its viable limit, to avoid a corresponding weight increase, the appliqué steel plates were removed from its side armor, which instead had its base thickness increased to.

* Given the weight of the train and the gradients on the line, both brake-vans should have been at the rear of the train

Given a set S of matrices, each of which is diagonalizable, and any two of which commute, it is always possible to simultaneously diagonalize all of the elements of S. Equivalently, for any set S of mutually commuting semisimple linear transformations of a finite-dimensional vector space V there exists a basis of V consisting of simultaneous eigenvectors of all elements of S. Each of these common eigenvectors v ∈ V, defines a linear functional on the subalgebra U of End ( V ) generated by the set of endomorphisms S ; this functional is defined as the map which associates to each element of U its eigenvalue on the eigenvector v. This " generalized eigenvalue " is a prototype for the notion of a weight.

Given a modular form f ( z ) of weight k, the mth Hecke operator acts by the formula

: Given a weighted directed graph and an integer K, is there a Hamiltonian path ( or Hamiltonian cycle if the salesman must return home ) with total weight less than or equal to K?

Given an integral weight, one of two cases occur: ( 1 ) There is no such that is dominant, equivalently, there exists a nonidentity such that ; or ( 2 ) There is a unique such that is dominant.

Given in weight %

* Given a graph where all its edges have distinct weights, is a given edge in the minimum weight spanning forest?

Given the very light weight of the " pin top ," the. 22 is quite capable of removing the target from the table with a single well-placed shot.

: Given two sets, P (" facilities ") and L (" locations "), of equal size, together with a weight function w: P × P → R and a distance function d: L × L → R. Find the bijection f: P → L (" assignment ") such that the cost function:

Given the size and weight of the memorial, even in its early design stages, a solid foundation for the structure was critical.

Given their lighter weight, Pony models were known for their ability to deliver excellent fuel economy — mileage upwards of in highway driving was not uncommon.

Given its continental origin as a fragment of Zealandia, unlike many of the islands of the Pacific such as the Hawaiian chain, New Caledonia is not of geographically recent volcanic provenance.

Given that it is more likely that the main mass loss occurred near aphelion before the 1845 apparition, it seems possible that fragment A at least may still exist as a ' dormant ' comet.

Given the low tensile strength of such bodies, if a fragment of an icy comet were to strike the Earth, the most likely outcome would be for it to disintegrate in the upper atmosphere, leading to an air burst explosion analogous to that of the Tunguska event.

Given a statistical ensemble of quantum mechanical systems with the density matrix, it is given by

Given that noise-equivalent power can be expressed as a function of the responsivity ( in units of or ) and the noise spectral density ( in units of or ) as, it's common to see the specific detectivity expressed as.

Given a parameterized family of probability density functions ( or probability mass functions in the case of discrete distributions )

Given a constant density and volume the self-potential of such body depends only on the eccentricity ε of the ellipsoid:

Dr. Tennison states: " Given the account of Elliot Paul, and given that Lead Belly witnessed boogie-woogie in 1899 in the Arklatex ; and given the North to South migration of the Thomas family ; and given the Texas & Pacific headquarters in Marshall in the early 1870s ; and given that Harrison County had the largest slave population in the state of Texas ; and given the fact that the best-documented and largest-scale turpentine camps in Texas did not occur until after 1900 in Southeast Texas, it is most probable that boogie-woogie spread from Northeast to Southeast Texas, rather than from Southeast to Northeast Texas, or by having developed diffusely with an even density over all of the Piney Woods of East Texas.

Given a total interaction cross section σ ( typically measured in barns ), the mean free path of a prompt neutron is where n is the nuclear number density.

Given its much higher density, a CPU designer may be inclined to use MRAM to offer a much larger but somewhat slower cache, rather than a smaller but faster one.

Given the right overall conditions of the compressed fuel — high enough density and temperature — this heating process will result in a chain reaction, burning outward from the center where the shock wave started the reaction.

Given this property, the lifetime distribution function and event density ( F and f below ) are well-defined.

Given their low metabolic rate and the low density of prey at such depths, vampire squid must use innovative predator avoidance tactics to conserve energy.

Given the specific gravity of a substance, its actual density can be calculated by rearranging the above formula:

Given our current estimate of the parameters θ < sup >( t )</ sup >, the conditional distribution of the Z < sub > i </ sub > is determined by Bayes theorem to be the proportional height of the normal density weighted by τ:

) Given a fixed density, one may construct a nilpotent BV Δ operator as

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 a probability density function w ( meaning that w is nonnegative and integrates to 1 ), the function

Given that this mass is confined inside a 44 million km diameter sphere, this yields a density ten times higher than previous estimates.

Given a field tensor, a scalar called the Lagrangian density can be constructed from and its derivatives.

Given a volume form ω on an oriented manifold, the density | ω | is a volume pseudo-form on the nonoriented manifold obtained by forgetting the orientation.

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 the relatively small geographical area and high population density of the UK, online DVD rentals have some differences from in the US, as a single shipping facility can serve the entire country.

Given the RG theorem, the next step in developing a computationally useful method is to determine the fictitious non-interacting system which has the same density as the physical ( interacting ) system of interest.

Given the unique mapping between densities and wave function, Runge and Gross then treated the Dirac action as a density functional,

Given that pastoralism and highland living could not support a very concentrated settlement density, pastoralist tribes often searched for more arable lowlands suitable for agriculture.