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

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

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

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.

Given its heavy dependence on imported energy, Japan has aimed to diversify its sources.

Given that the cost of replacing an executive can run over 100 % of his or her annual salary, any investment of time and energy in re-recruitment will likely pay for itself many times over if it helps a business retain just a handful of key players that would have otherwise left.

Given Ω microstates at a particular energy, the probability of finding the system in a particular microstate is p = 1 / Ω.

Given a gain of about 100 and a laser efficiency of about 1 %, HiPER produces about the same amount of fusion energy as electrical energy was needed to create it.

Given the small temperature range kinetic studies occur in, it is reasonable to approximate the activation energy as being independent of the temperature.

Given any energy eigenstate, we can act on it with the lowering operator, a, to produce another eigenstate with-less energy.

Given its great distance, the daytime " guest star " observed by the Chinese could only have been a supernova — a massive, exploding star, having exhausted its supply of energy from nuclear fusion and collapsed in on itself.

Given an inelastic reaction with total incoming energy larger than the total detected energy ( i. e. not all outgoing particles are detected in the experiment ), the invariant mass ( also known as the " missing mass ") of the reaction is defined as follows:

Given that the audio signal is unlikely to be at peak all the time, the ratio of energy is, in practice, even greater.

Given the unequal distribution of talent, energy, and luck, Classical legal thought posited that a self-executing, decentralized, competitive market economy would inevitably result in organized inequality.

Given a heat value of a fuel, it would be trivial to convert from fuel units ( such as litres of gasoline ) to energy units ( such as MJ ) and conversely.

Given sufficient magic energy in her surroundings she has even effortlessly turned into a female copy of the Silver Surfer.

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 a specified distribution of matter and energy in the form of a stress – energy tensor, the EFE are understood to be equations for the metric tensor, as both the Ricci tensor and scalar curvature depend on the metric in a complicated nonlinear manner.

Given mastery over the cosmic flame, Firelord wields a flaming staff and is capable of energy projection via his eyes and staff.

Given the total energy E and the length ( magnitude ) p of the total momentum vector, the invariant mass is given by:

Given the same energy source and operating conditions, a higher COP heat pump will consume less purchased energy than one with a lower COP.

Given the current energy mixes in other countries, it has been predicted that such emissions would decrease by 40 % in the U. K., and 19 % in China.

Given the apparent magnitude (> 20 ) of all but the biggest trans-Neptunian objects, the physical studies are limited to the following:

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

Given that the trademarked " Windows " name was in some jeopardy, Microsoft paid to settle the lawsuit they initiated with a $ 20 million payment to Lindows and certain licenses with Lindows agreeing to change their name worldwide to Linspire.

Given: side a = 20, side c = 24, and angle C = 40 °

" Given the chance to relive his life by switching bodies with " a talentless 20 year-old wannabe rock star with all the looks and charm Rocky used to have ," the series deals with the subsequent soul-searching and reflection over such a decision.

Given the price of 1 / 32 Mark for six small fruit pies ( as seen in Dragonsinger ), it places the value at around $ 20 to the Mark.

Given that no majority supported either a leader or a split, a registration campaign, enabling membership for only 20 euros, and a closed primary was organized, which Ségolène Royal won.

Given that both companies have a work force of approximately 100, 000 employees, and a U. S. employment base of roughly 20, 000 H-1B holders, this indicates that roughly 1 / 5 of the Indian workforce of Infosys & Wipro applied for a visa in 2006.

Given 20 minutes a game, Szczerbiak averaged 7 points, 3. 2 rebounds, and 1. 1 assists while shooting. 450 % from the field and. 411 % from 3.

Séamus John James " Shay " Given ( born 20 April 1976 ) is an Irish footballer who plays as a goalkeeper for Aston Villa and, formerly, for the Republic of Ireland national football team, receiving a national record of 125 international caps between 1996 and 2012.

An attempt by Adrian Davies to launch parallel proceedings in Belgium without notifying the Belgian Court of English proceedings was blocked by a landmark anti-suit injunction granted by Miss Sarah Asplin QC on 20 May 2011, where she stated " Given that the present defendants had submitted to the hearing of that issue and allowed costs to be incurred, in my judgement such conduct is vexatious and oppressive ".

Given the murder rate in this town, it has about the same murder rate of a town 20 times its size.

Given that switchgrass contains approximately 18. 8 GJ / ODT of biomass, the energy output-to-input ratio for the crop can be up to 20: 1.

Given Australia has a population of only around 20 million people ( ranked 53rd in the world ) this fact is frequently cited as noteworthy by the mainstream Australia media due to a strong sporting culture.

* 20 April-Shay Given, international soccer player.

Given that High Sensitivity GPS receivers may be up to 30 dB more sensitive, this is sufficient to track through 3 layers of dry bricks, or up to 20 cm of steel reinforced concrete for example.

Given that this came days after a series of attacks on U. S. embassies in the Middle East, in response to the anti-Islamic film Innocence of Muslims, the French government decided to increase security at certain French embassies, as well as to close the French embassies, consulates, cultural centers, and international schools in about 20 Muslim countries.

Given a single start worm, a 20 tooth worm gear will reduce the speed by the ratio of 20: 1.