Given these changes, the classical terms " system ", " expansion " and " peripheral " no longer have the same connotations.

If V is finite-dimensional, then V * has the same dimension as V. Given a basis

Given the limited budget for schools, it is claimed that a voucher system would weaken public schools while at the same time not necessarily providing enough money for people to attend private schools.

Given a groupoid G, the vertex groups or isotropy groups or object groups in G are the subsets of the form G ( x, x ), where x is any object of G. It follows easily from the axioms above that these are indeed groups, as every pair of elements is composable and inverses are in the same vertex group.

Given the same bullet and cartridge, a faster burning powder will generally use a smaller charge of powder than required with a slower powder.

Given these two assumptions, the coordinates of the same event ( a point in space and time ) described in two inertial reference frames are related by a Galilean transformation.

Given the same set of verifiable facts, some societies or individuals will have a fundamental disagreement about what one ought to do based on societal or individual norms, and one cannot adjudicate these using some independent standard of evaluation.

Given the proposition that ' a persons life prospects should not be decided by factors outside of their control or for which a person cannot claim personal credit ' ( i. e. social status, inherited wealth, race and other accidents of birth ) a meritocracy proposes a system where people are rewarded based on their efforts, and if everyone can start on equal footing with the same opportunity to advance, then the results are just.

Given printing practices at the time ( which included type-setting from dictation ), no two editions turned out to be identical, and it is relatively rare to find even two copies that are exactly the same.

* Coreference resolution: Given a sentence or larger chunk of text, determine which words (" mentions ") refer to the same objects (" entities ").

Given a general statement such as all ravens are black, a form of the same statement that refers to a specific observable instance of the general class would typically be considered to constitute evidence for that general statement.

Given two affine spaces and, over the same field, a function is an affine map if and only if for every family of weighted points in such that

Given the same set of resources, IS-IS can support more routers in an area than OSPF.

Given a diagram F: J → C ( thought of as an object in C < sup > J </ sup >), a natural transformation ψ: Δ ( N ) → F ( which is just a morphism in the category C < sup > J </ sup >) is the same thing as a cone from N to F. The components of ψ are the morphisms ψ < sub > X </ sub >: N → F ( X ).

Given any two similar polygons, corresponding sides taken in the same sequence are proportional and corresponding angles taken in the same sequence are equal in measure.

Given that multiple people often consume food from the same source, it is common for more than a single person to be affected simultaneously.

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 symmetry of circularly polarized light, we could have in fact selected any other two orthogonal components and found the same phase relationship between them.

Given that radio communication channels are allocated by agencies such as the Federal Communication Commission giving a prescribed ( maximum ) bandwidth, the advantage of QPSK over BPSK becomes evident: QPSK transmits twice the data rate in a given bandwidth compared to BPSK-at the same BER.

Given the choice between playing a game at an arcade three or four times ( perhaps 15 minutes of play for a typical arcade game ), and renting, at about the same price, exactly the same game — for a video game console — the console became the preferred choice.

: Given any set A and any set B, if A is a nonempty set ( that is, if there exists a member C of A ), then if A and B have precisely the same members, then they are equal.

Pope Saint Adeodatus I or Deodatus I ( which is Given by God in Latin, also called Deusdedit, which is God Has Given ; both are now considered variants of the same name ) ( died 8 November 618 ) was Pope from 13 November 615 to his death.

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

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

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 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 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 time t, the source produces ωt oscillations.

Given its exposed spot on the top of Stow Hill, the town is often referred to with the couplet " Stow on the Wold, where the winds blow cold and the cooks can't roast their dinners ", but there is no source for this.

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 a normalized light vector l ( pointing from the light source toward the surface ) and a normalized plane normal vector n, one can work out the normalized reflected and refracted rays:

Given source XML containing at least

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 that Moria was an ancient source of mithril, this might be a nod to Scandinavian associations of the will-o '- the-wisp with treasure.

Given a source of white light, they produce a white shine.

Given a network of seven nodes, source A, sink G, and capacities as shown below:

Given a statement regarding the category C, by interchanging the source and target of each morphism as well as interchanging the order of composing two morphisms, a corresponding dual statement is obtained regarding the opposite category C < sup > op </ sup >.

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 a transmission line source with a fixed source impedance, this " reflectionless impedance matching " at the end of the transmission line is the only way to avoid reflecting echoes back to the transmission line.

* Given a sufficient power source, laser weapons could essentially have limitless ammunition.

Given enough time, natural change in isolated language can obliterate any meaningful linguistic evidence of a known common genetic source for the languages.

Given the goals of the first Five Year Plan, the state sought increased political control of agriculture, hoping to feed the rapidly growing urban areas and to export grain, a source of foreign currency needed to import technologies necessary for heavy industrialization.

Given certain legal traditions of copyright, blogs may not be " open source " in the sense that one is prohibited from taking the blogger's words or visitor comments and re-using them in another form without breaching the author's copyright or making payment.

Given its proximity to Vietnam the province has traditionally been a source for raw materials and forest products for adjacent regions in Vietnam.

Given an isogeny f of degree n, one can prove using linear algebra on weights and faithfully flat descent that there exists a dual isogeny g such that gf is the nth power map on the source torus.

The SPR went on to say the stories relating to battlefield " visions " which circulated during the spring and summer of 1915, " prove on investigation to be founded on mere rumour, and cannot be traced to any authoritative source ".” Given that the Society for Psychical Research believed in the existence of supernatural forces, the conclusions of this report are highly significant.