: Given any set X of pairwise disjoint non-empty sets, there exists at least one set C that contains exactly one element in common with each of the sets in X.

* 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 is each element's name, atomic number, year of first report, name of the discoverer, and some notes related to the discovery.

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.

* Named entity recognition ( NER ): Given a stream of text, determine which items in the text map to proper names, such as people or places, and what the type of each such name is ( e. g. person, location, organization ).

* Part-of-speech tagging: Given a sentence, determine the part of speech for each word.

* Topic segmentation and recognition: Given a chunk of text, separate it into segments each of which is devoted to a topic, and identify the topic of the segment.

# Given an array of values to be sorted, set up an auxiliary array of initially empty " pigeonholes ," one pigeonhole for each key through the range of the original array.

Given the above expression, evidently the result of her ( local ) measurement is that the three-particle state would collapse to one of the following four states ( with equal probability of obtaining each ):

: Given an isolated system in equilibrium, it is found with equal probability in each of its accessible microstates.

Given a list of cities and their pairwise distances, the task is to find the shortest possible route that visits each city exactly once and returns to the origin city.

Given two school classes, one with 20 students, and one with 30 students, the grades in each class on a test were:

Given that this is a plane wave, each vector represents the magnitude and direction of the electric field for an entire plane that is perpendicular to the axis.

Given the maximum observed frequency ( MOF ) for a mode on each day of the month at a given hour, the MUF is the highest frequency for which an ionospheric communications path is predicted on 50 % of the days of the month.

* Given an infinite string where each character is chosen uniformly at random, any given finite string almost surely occurs as a substring at some position.

* Given an infinite sequence of infinite strings, where each character of each string is chosen uniformly at random, any given finite string almost surely occurs as a prefix of one of these strings.

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 fixed physical relationship in space between the different individual microphone transducer array elements, simultaneous DSP ( digital signal processor ) processing of the signals from each of the individual microphone array elements can create one or more " virtual " microphones.

Given " mappings " of input variables into membership functions and truth values, the microcontroller then makes decisions for what action to take, based on a set of " rules ", each of the form:

BONUS: " Given a pair of resistors, give their equivalent resistance if they were connected in parallel with each other.

* Given two hypothetical point particles each of Planck mass and elementary charge, separated by any length, α is the ratio of their electrostatic repulsive force to their gravitational attractive force.

Given a testing procedure E applied to each prepared system, we obtain a sequence of values

Given a differentiable manifold M, a vector field on M is an assignment of a tangent vector to each point in M. More precisely, a vector field F is a mapping from M into the tangent bundle TM so that is the identity mapping

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

Given the leadership of Rockwell and Koehl the American Nazi Party and its successor the National Socialist White People's Party were the main constituent groups of the WUNS.

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.

Given by the Georgia Historical Society, in conjunction with the Governor of Georgia, to individuals whose accomplishments and community service reflect the ideals of the founding body of Trustees, which governed the Georgia colony from 1732 to 1752.

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.

Given the task of arresting dishonest businessmen who hoarded supplies for profit during the inflationary spiral, he attempted to assuage the business community by explaining that his team would only go after big war profiteers.

When the measure was sent in May to the parliament they said " Given the damage it produces on those rules which allow the life in community, ensure the dignity of the person and equality between sexes, this practice, even if it is voluntary, cannot be tolerated in any public place ".

Given by the Georgia Historical Society, in conjunction with the Governor of Georgia, to individuals whose accomplishments and community service reflect the ideals of the founding body of Trustees, which governed the Georgia colony from 1732 to 1752.

Given that it is still legal to discriminate against individuals on the basis of gender identity within New Zealand, the transgender community often finds that many of its younger members require survival sex for food, shelter and rest.

Given by the Georgia Historical Society, in conjunction with the Governor of Georgia, to individuals whose accomplishments and community service reflect the ideals of the founding body of Trustees, which governed the Georgia colony from 1732 to 1752.

Given that gated communities are spatially a type of enclave, Setha M. Low, among other anthropologists, has argued that they have a negative effect on the overall social capital of the broader community outside the gated community.

Given the intensity of community involvement in all these process related activities, many staff members have developed their own forms of practice, and some of them have become well known teachers.

Given the relative invisibility of references to AIDS in mainstream Hollywood filmmaking, the work of New Queer Cinema was hailed by the gay community as a welcome correction to a history of under-representation and stereotyping of gay and lesbian people.

Given the editorial style of the books, it is not surprising that they were ( and to some extent remain ) controversial within the numerical analysis community.

Given the fact that they are the least violent non-parody finishing moves in Mortal Kombat history, Heroic Brutalities were not well received among either the MK series ' fans or the comic book fan community, as even the DC comics themselves are often far more brutal.

Given the size of the Catholic community at the time, the massive bluestone Gothic cathedral was an immense and very expensive undertaking, and there were long delays while funds were raised.

Given that the dinosaurs and other fauna of Cretaceous were well adapted for living in long periods of dark and cold weather, it has been postulated that this community might have survived the Cretaceous – Paleogene extinction event ( 65. 5 Ma ) which exterminated the non-avian dinosaurs and many other of the world's species at the time.

Given the tonal design of the train whistle, the sound level, how often trains pass through a given community, the number of grade crossings in proximity, and the time of day ( night ) of occurrence, community residents residing near crossing sometimes feel that train whistles have a serious detrimental effect on the quality of life despite the gain in safety that sounding the horn provides to motorists.

Given the widely recognized importance of proteins as cellular catalysts and recognition elements, the ability to precisely control the composition and connectivity of polypeptides is a valued tool in the chemical biology community and is an area of active research.

Given the variances of demography within the City of Atlanta, the idea that a one-size fits all system of community governance would successfully reflect each community's view is unrealistic.

Given the size of the international community, the practice does not have to encompass all states or be completely uniform.

Given by the Georgia Historical Society, in conjunction with the Governor of Georgia, to individuals whose accomplishments and community service reflect the ideals of the founding body of Trustees, which governed the Georgia colony from 1732 to 1752.

Given by the Georgia Historical Society, in conjunction with the Governor of Georgia, to individuals whose accomplishments and community service reflect the ideals of the founding body of Trustees, which governed the Georgia colony from 1732 to 1752.

Given this, one day met the strongest men of the population determined from the mountains to fill the huge birds ' nests, but the initiative was not bad, neighbors were able to seal the tunnels, the birds could not leave nests there were dead and never again do more harm to the community.