Given the abundance of such optimization problems in everyday life, a positive answer to the " P vs. NP " question would likely have profound practical and philosophical consequences.

Given the fact that overseas learners of Mandarin are not taught Tongyong Pinyin either, there are few people in the world who use it in any practical sense.

Given their small size and large number, it is not practical to intercept bullets and shells in a gun battle.

Given her confinement, the use of these mediums in her work is practical and gives insight to the viewer of how Sadie has been mostly interacting with the world.

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 the company's workers had become more mobile and that the majority of them now lived in these suburban areas, Brown & Sharpe saw an easy opportunity to relocate into a more practical facility.

Given this stance, it emphasises the practical teachings of subjects with a sound theoretical background, while at the same time actively adapting the lesson material and courses to the job market demands and the realities of today ’ s society.

Given the high dimensionality of this function, practical methods place constraints on the parameters in order to reduce this number ( typically to 2 to 4 ).

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 requirements of weight, and fragment density required this dictated using approximately 700 fragments, and being able to aim the mine with an accuracy of around two feet ( 0. 6 m ) at the center of the target zone.

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 both Einstein's equations and suitable equations for the properties of matter, such a solution consists of a specific semi-Riemannian manifold ( usually defined by giving the metric in specific coordinates ), and specific matter fields defined on that manifold.

Given that hearing impairments can vary by frequency and that audiograms are plotted with a logarithmic scale, the idea of a percentage of hearing loss is somewhat arbitrary, but where decibels of loss are converted via a recognized legal formula, it is possible to calculate a standardized " percentage of hearing loss " which is suitable for legal purposes only.

Given suitable infrastructure, permissions and vehicles, BEVs can be recharged while the user drives.

Given the minister's " current crusade on financial literacy ," Fullard believed a suitable charitable cause would be a scholarship for business education.

Given suitable conditions most Epimedium will form beautiful ground cover plants, often with magnificent new leaves tinted in bronze, copper and reds combining with a huge variety of flower colours and forms in spring.

Given government compensation for the loss of his ship the Sydney while under government charter, Robert Campbell, sent James Ainslie to collect 700 sheep from the government flocks at Bathurst and to go southward looking for suitable pasture.

Given the Minister's " current crusade on financial literacy ," Fullard believed a suitable charitable cause would be a scholarship for business education.

Given local concerns about infrastructure and lack of suitable land, this is likely to be one of the last new structures to be built in the village for the foreseeable future.

Given the lack of atmospheric pollution in this area, it is particularly suitable for astronomical observations.

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.

Given also a measure on set, then, sometimes also denoted or, has as its vectors equivalence classes of measurable functions whose absolute value's-th power has finite integral, that is, functions for which one has

Given the high thermal design power of high-speed computer CPUs and components, modern motherboards nearly always include heat sinks and mounting points for fans to dissipate excess heat.

Given the abundance of mountain streams and lakes, the potential for hydroelectric power is substantial.

Given free rein to change the story however he wanted, Aki's version is a violent saga focused primarily on fighting and has Hitomi transforming into a " curvaceous nymph " that is the power source of the mecha Escaflowne.

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 his socialist agenda in Egypt, the Ba ' ath should have been his natural ally, but Nasser was hesitant to share power.

Given a system of n-dimensional variables ( physical variables ), in k ( physical ) dimensions, write the dimensional matrix M, whose rows are the dimensions and whose columns are the variables: the ( i, j ) th entry is the power of the ith unit in the jth variable.

Given formal power series

Given a formal power series

Given the display of imperial power Henry III had inflicted on the Romans in intervening against Pope Gregory VI and installing Clement II, it is not surprising that on Christmas Day of 1047, an emissary was sent by the Roman people bringing news of Clement II's death to Henry III and asking him, in his position as Patricius of the Romans, to appoint a successor.

Given the inherent goodness of Ṛta and its absolute power over the operation of the universe, the presence of gross inequality and injustice in the world represented a serious religious, philosophical and ethical dilemma.

Given that Kent was under Frankish influence, while Bede sees the mission as being " Roman " in origin, the Franks were equally interested in converting their fellow Germans, and in extending their power and influence.

Given that power is not innate and can be granted to others, to acquire power you must possess or control a form of power currency.

Given the sheer power of leverage the Rothschild family had at its disposal, this profit was an enormous sum.

Given the disparity in power between Hungary and the Allies, Hungarian chances for victory were slim at best.

Given a strictly increasing integer sequence / function ( n ≥ 1 ) we can produce a faster growing sequence ( where the superscript n denotes the n < sup > th </ sup > functional power ).

Given the large amount of power that was generated by this collision, it has been deduced that a large portion of the Moon would have been liquified, and this

* Monitoring by large shareholders and / or monitoring by banks and other large creditors: Given their large investment in the firm, these stakeholders have the incentives, combined with the right degree of control and power, to monitor the management.

Given a source with a fixed voltage and fixed source impedance, the maximum power theorem says this is the only way to extract the maximum power from the source.

Given the initial presentation of Guellen, Claire's power, the history between Claire and Ill, and the nature of Claire's decree, Ill's death appears almost inevitable.

Given the time scale of a few billionths of a second, the peak UV power delivered to the target is correspondingly very high, 500 TW.