Given a simple mathematical or functional description of an input or output to a system, the Laplace transform provides an alternative functional description that often simplifies the process of analyzing the behavior of the system, or in synthesizing a new system based on a set of specifications.

Given inconsistencies and the lack of reliable data and completely contradicting and unpredictable behavior, the true nature of ball lightning is still unknown and was often regarded as a fantasy or a hoax.

Given the chance to repeat some futile behavior endlessly, people can notice the futility of it, and by an act of free will do something else.

Given the complex macro-rheological behavior of blood, it is not surprising that a single equation fails to completely describe the effects of various rheological variables ( e. g., hematocrit, shear rate ).

" Given that involuntarily celibate individuals by definition are compelled by circumstance, rather than choice, towards the state of not having a sex life, Galloway's proclamations may be viewed psychoanalytically as exhibiting some or another form of self-justifying behavior, but may be significant nevertheless.

Given two actors, oneself and someone else, there are four types of possible behavior directly impacting the welfare of the actors: selfishness, altruism, spite, and cooperation.

Given input M and w ( a Turing machine and some input string ), define S ( M, w ) with the following behavior: S creates a Turing machine N that accepts only if the input string to N is w and M halts on input w, and does not halt otherwise.

Given behavior adaptation and migration, the current rigorous Interstate effectiveness of 14 % and CLRS on single-lane highways effectiveness of 14 % could be over-estimations of the actual " big-picture " reduction.

Given two groups of people, the interaction between them is such that a behavior X from one side elicits a behavior Y from the other side, The two behaviors complement one another, exemplified in the dominant-submissive behaviors of a class struggle.

Given a generating function, analytic combinatorics attempts to describe the asymptotic behavior of a counting sequence using algebraic techniques.

Given the predictable timeline of childhood behavior, he proposed " libido development " as a model of normal childhood sexual development, wherein the child progresses through five psychosexual stages — ( i ) the oral, ( ii ) the anal, ( iii ) the phallic, ( iv ) the latent, and ( v ) the genital — in which the source pleasure is in a different erogenous zone.

Given that field experiments necessarily take place in a specific geographic and political setting, the extent to which findings can be extrapolated to formulate a general theory regarding economic behavior is a concern.

Given that an individual's behavior ( e. g., health-related decision-making such as diet, condom use, quitting smoking and drinking, etc.

Given a set of rows in columns ( i. e., an matrix ), the biclustering algorithm generates biclusters-a subset of rows which exhibit similar behavior across a subset of columns, or vice versa.

Given its origin and behavior it is classified as a sarcoma.

Given that branded entertainment involves very different viewer behavior and perception of content than thirty-second magazine format advertising, the genre may well require a wholly different understanding of the psychological processes involved, as well as new terms for assessing market effectiveness.

Given no other choice, Mercury stabs her through the chest, killing her and ending the fight.

Given this, the bidding is said to start at the one-level when contracting for a total of seven tricks, at the two-level for eight tricks and so on to the seven-level to contract to take all thirteen tricks.

Given a subset X of a manifold M and a subset Y of a manifold N, a function f: X → Y is said to be smooth if for all p in X there is a neighborhood of p and a smooth function g: U → N such that the restrictions agree ( note that g is an extension of f ).

On poverty, Hoover said that " Given the chance to go forward with the policies of the last eight years, we shall soon with the help of God, be in sight of the day when poverty will be banished from this nation ", and promised, " We in America today are nearer to the final triumph over poverty than ever before in the history of any land ," but within months, the Stock Market Crash of 1929 occurred, and the world's economy spiraled downward into the Great Depression.

Given a binary operation ★ on a set S, an element x is said to be idempotent ( with respect to ★) if

Given to Graham with the working title " Ballet for Martha ," it was named by her for the scenario she had in mind, though Copland often said he was thinking of neither Appalachia nor Spring while he wrote it.

Given the harsh conditions of the retreat, the infant was left with a local family ( Two Europeans retracing the Long March route in 2003 met a woman in rural Yunnan province, said by local officials to be Mao and He Zizhen's long-lost daughter ).

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 the situation in Spain for several years regarding terrorist attacks, these ties can be considered objectively as a threat to democracy ," the court said, also adding that these parties " contradicted the concept of a ' democratic society ' and presented a major danger to Spain's democracy ".

About the new markets, Ergen said, " Given the assets we've been accumulating, I don't think it's hard to see we're moving in a different direction from simply pay-TV, which is a market that's becoming increasingly saturated.

Given the early and constant association of Nekhbet with being a good mother, in later myths she was said to have adopted children.

Denis MacShane, a former Foreign Office minister, said: “ Given the appalling suffering and repression of the Bahraini people, it would be a fitting gesture for the Countess of Wessex to auction these trinkets and distribute the proceeds to the victims of the regime .”

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 ".

On September 18, the EPA released a report in which Whitman said, " Given the scope of the tragedy from last week, I am glad to reassure the people of New York and Washington, D. C. that their air is safe to breathe and their water is safe to drink.

Given a relation R, a set of attributes X in R is said to functionally determine another attribute Y, also in R, ( written X → Y ) if, and only if, each X value is associated with precisely one Y value.

Given two sequences X and Y, a sequence G is said to be a common subsequence of X and Y, if G is a subsequence of both X and Y.

Given a function w on U × Y, with finite integral of its modulus for any input function u and initial state x ( 0 ) over any finite time t, called the " supply rate ", a system is said to be dissipative if there exist a continuous nonnegative function V ( x ), with x ( 0 ) = 0, called the storage function, such that for any input u and initial state x ( 0 ) the difference V ( x ( t )) − V ( x ( 0 )) does not exceed the integral of the supply over ( 0, t ) for any t ( dissipation inequality ).

Weekly Standard Editor William Kristol said at the time, " Given that Reagan obviously couldn't be here, I think it was important to have Mrs. Thatcher because she and Reagan are really the great heroes of conservatism in the last few decades and still today.

Brown said that " Given that it was near Charles ' home Highgrove, my assumption was that this might involve the Royal Family.

Given this and the personal animosity towards Dowding the Air Ministry view of the Battle of Britain cannot be said to be " even-handed ".

Given a line l and a point P not on l, right-and left-limiting parallels to l through P are said to meet l at omega points.

The day after the resignation of Cllr Colin Barrow's resignation as Leader of Westminster City Council in January 2012 on the BBC's inaugural Sunday Politics, Field said about the West End parking charges plan: " Given the furore, given the strength of the campaign by the Evening Standard, I would be very surprised if his successor runs along with this.

Given the outlandish idea that a blind man could be a detective, in the introduction to the second Carrados book The Eyes of Max Carrados Bramah compared his hero ’ s achievements to those of real life blind people such as Nicholas Saunderson, Lucasian Professor of Mathematics at Cambridge, Blind Jack of Knaresborough the road builder, John Fielding the Bow Street Magistrate of whom it was said he could identify 3, 000 thieves by their voices, and Helen Keller.

Another partition of the given interval, Q, is defined as a refinement of the partition, P, when it contains all the points of P and possibly some other points as well ; the partition Q is said to be “ finer ” than P. Given two partitions, P and Q, one can always form their common refinement, denoted P ∨ Q, which consists of all the points of P and Q, re-numbered in order.

" Susan Savage-Rumbaugh said in an interview that, " Given matches and marshmallows, Kanzi snapped twigs for a fire, lit them with the matches and toasted the marshmallows on a stick.