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 this natural tendency to glide forward, terza rima is especially well-suited to narration and description ".

Given a method of description, however, there may be more than one description that represents the same knot.

: Given a description of a Turing machine and its initial input, determine whether the program, when executed on this input, ever halts ( completes ).

Critique by Fritz Lehman: Given that this book is intended as a textbook for Pakistani undergraduates, Shaikh Ahmed Sarhindi predictably appears as the chief preserver of separate Islamic identity in India, yet only a very general and most inadequate description of his ideas and his influence is given.

The invariance theorem follows: Given any description language, our optimal description language is at least as efficient as, with some constant overhead.

Given the lack of details and the imprecision contemporary diagnosis and description, Viceroy Revillagigedo's statement official statement that Bodega died " of natural causes " is indisputable.

Given a description of a system in the s-domain, the zero-state response can be described as Y ( s )= Init ( s )/ a ( s ) where a ( s ) and Init ( s ) are system-specific.

Given some encrypted data (" ciphertext "), the goal of the cryptanalyst is to gain as much information as possible about the original, unencrypted data (" plaintext ").

* Given any set X, there is an equivalence relation over the set of all possible functions X → X.

Given the broad scope of environmental law, no fully definitive list of environmental laws is possible.

Given the existence of a Godlike object in one world, proven above, we may conclude that there is a Godlike object in every possible world, as required.

Given sufficient travel time and engineering work, both unmanned and generational interstellar travel seem possible, though present considerable technological and economic challenges are unlikely to be met in the near future, particularly for manned probes.

Given the widespread expansion in the tenth revision, it is not possible to convert ICD-9 data sets directly into ICD-10 data sets, although some tools are available to help guide users.

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.

:( a ) Given player 2's strategy, the best payoff possible for player 1 is V, and

:( b ) Given player 1's strategy, the best payoff possible for player 2 is − V.

Given the notion of a lexeme, it is possible to distinguish two kinds of morphological rules.

Given this ( relative ) philosophic flexibility, variant viewpoints are possible, particularly in areas not explicitly demarcated by the Halakha.

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 current trends in the UMC — with overseas churches growing, especially in Africa, and U. S. churches collectively losing about 1, 000 members a week — it has been estimated that Africans will make up at least 30 % of the delegates at the 2012 General Conference, and it is also possible that 40 % of the delegates will be from outside the U. S. One Congolese bishop has estimated that typical Sunday attendance of the UMC is higher in his country than in the entire United States.

Given the being's chaotic nature, almost anything is possible.

Given the structure of the experiment, it may or may not be possible to actually perform it, and, in the case that it is possible for it to be performed, there need be no intention of any kind to actually perform the experiment in question.

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 that coconuts are ideally suited for ocean dispersal, it seems possible that individuals from one population could have floated to the other.

Given X and Y, several different embeddings of X in Y may be possible.

Given Russia's often inadequately trained conscript armies and the use of inaccurate smooth-bore muskets, Russian officers preferred to use the bayonet charge in lieu of musket volley fire where possible.

* Aggregate signature-a signature scheme that supports aggregation: Given n signatures on n messages from n users, it is possible to aggregate all these signatures into a single signature whose size is constant in the number of users.

Given a set A of N people, it has 2 < sup > N </ sup > possible subsets.

Given Zelazny's academic interest in the Medieval European period, it is not a stretch to see a possible influence in Henry Adams ' 1905 work Mont Saint-Michel and Chartres, wherein he discusses the building of Chartres Cathedral, and the tidal-islet of Mont Saint-Michel, on the Normandy coast of France.

Given any input, GEN generates an infinite number of candidates, or possible realizations of that input.

Given that the Liber historiae Francorum admits four years for Chlothar's reign, it remains possible that Chlothar began to exert some real authority when his mentors deemed him an adult, 669.

Given the state at some initial time ( t = 0 ), we can solve it to obtain the state at any subsequent time.

Given the initial energy of 20 TJ, the Space Shuttle is about 16 % energy efficient at launching the orbiter.

Given a functor F: J → C ( thought of as an object in C < sup > J </ sup >), the limit of F, if it exists, is nothing but a terminal morphism from Δ to F. Dually, the colimit of F is an initial morphism from F to Δ.

Given a functor U and an object X as above, there may or may not exist an initial morphism from X to U. If, however, an initial morphism ( A, φ ) does exist then it is essentially unique.

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 an initial allocation of goods among a set of individuals, a change to a different allocation that makes at least one individual better off without making any other individual worse off is called a Pareto improvement.

Given initial speed u, one can calculate how high the ball will travel before it begins to fall.

Given a closed system in an initial state, if work is done on the system in an adiabatic ( i. e. no heat transfer ) way, and given the final state after a process, the amount of work required to be transferred to the system is the same, irrespective of how this work is performed.

Given the absurdity of the conclusion, Chalmers ’ rejects the initial premise that agents with identical causal organization can have different experiences.

Given the initial positions ( e. g. from theoretical knowledge ) and velocities ( e. g. randomized Gaussian ), we can calculate all future ( or past ) positions and velocities.

Given that much of the first half of the novel focuses on the initial encounter, blossoming friendship and eventual estrangement of these central characters, this issue continues to pique the curiosity of readers.

* 7 " Promo ( Given away free with initial copies of Sweaty Handshake album, 27 January 1995 )

Given the observation space, the state space, a sequence of observations, transition matrix of size such that stores the transition probability of transiting from state to state, emission matrix of size such that stores the probability of observing from state, an array of initial probabilities of size such that stores the probability that. We say a path is a sequence of states that generate the observations.

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 ).

Given its heritage, MCC continues to participate in the administration of English cricket, and in 2010 offered Lord's as a neutral venue for Pakistan to stage a " home " Test match, as scheduled by the ICC, versus Australia ; although the outcome of that game proved controversial the club's initial offering was made with the intention that Pakistan, whose terrorist-stricken country had rendered it a no-go area for international cricket, could remain within the international cricketing fold.

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 initial velocity of a particle launched from the ground, the downward ( i. e. gravitational ) acceleration, and the projectile's angle of projection θ ( measured relative to the horizontal ), then a simple rearrangement of the SUVAT equation

Given the initial condition

Although the fee for Given was expected to be around £ 8 million, in February 2009 Newcastle United Managing Director Derek Llambias revealed at a supporters panel meeting that Given had been sold for an initial £ 5. 9 million.

Given the relatively non-specific symptoms of initial hypothyroidism, Hashimoto's thyroiditis is often misdiagnosed as depression, cyclothymia, PMS, chronic fatigue syndrome, fibromyalgia and, less frequently, as ED or an anxiety disorder.

Given distinct points A and B, they determine a unique ray with initial point A.