Given a sinewave generator of very low inherent distortion, it can be used as input to amplification equipment, whose distortion at different frequencies and signal levels can be measured by examining the output waveform.

Given this inherent distortion, it is not unusual for a television or video projector to truthfully claim a linear contrast ratio ( difference between darkest and brightest output levels ) of 1000: 1 or greater, equivalent to 10 bits of audio precision even though it may only accept signals with 8-bit precision and use an LCD panel that only represents 6 or 7 bits per channel.

Given the inherent goodness of Ṛta and its absolute power over the operation of the universe, the presence of gross inequality and injustice in the world represented a serious religious, philosophical and ethical dilemma.

Given the inherent technical limitations of the visible and palpable signs from these sacroiliac joint mobility maneuvers another broad category of clinical signs have been described called provocative maneuvers.

Given the inherent variability of the technology, a new gene could insert into the targeted genome in a way that could lead to deleterious interactions with other genes.

Given that authors of documents try to formulate sentences which contain a single idea, or cluster of related ideas within neighboring sentences or organized into paragraphs, there is an inherent, relatively high, probability within the document structure that words used together are related.

Given the inherent complex nature of CRTs, a variety of factors combine to produce a monitor ’ s image.

* Given any Banach space X, the continuous linear operators A: X → X form a unitary associative algebra ( using composition of operators as multiplication ); this is a Banach algebra.

* Given any topological space X, the continuous real-or complex-valued functions on X form a real or complex unitary associative algebra ; here the functions are added and multiplied pointwise.

Given any vector space V over a field F, the dual space V * is defined as the set of all linear maps ( linear functionals ).

Given a topological space X, let G < sub > 0 </ sub > be the set X.

Given a finite dimensional real quadratic space with quadratic form, the geometric algebra for this quadratic space is the Clifford algebra Cℓ ( V, Q ).

Given a vector space V over the field R of real numbers, a function is called sublinear if

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 two Lie algebras and, their direct sum is the Lie algebra consisting of the vector space

Given a basis of a vector space, every element of the vector space can be expressed uniquely as a finite linear combination of basis vectors.

Given infinite space, there would, in fact, be an infinite number of Hubble volumes identical to ours in the universe.

Given a set of training examples of the form, a learning algorithm seeks a function, where is the input space and

Given an operator on Hilbert space, consider the orbit of a point under the iterates of.

Given a point x in a topological space, let N < sub > x </ sub > denote the set of all neighbourhoods containing x.

Given a vector space V and a quadratic form g an explicit matrix representation of the Clifford algebra can be defined as follows.

Given the date of his publication and the widespread, permanent distribution of his work, it appears that he should be regarded as the originator of the concept of space sailing by light pressure, although he did not develop the concept further.

Given an arbitrary topological space ( X, τ ) there is a universal way of associating a completely regular space with ( X, τ ).

Given any embedding of a Tychonoff space X in a compact Hausdorff space K the closure of the image of X in K is a compactification of X.

Given a completely regular space X there is usually more than one uniformity on X that is compatible with the topology of X.

Given any vector space V over K we can construct the tensor algebra T ( V ) of V. The tensor algebra is characterized by the fact:

Given the space X = Spec ( R ) with the Zariski topology, the structure sheaf O < sub > X </ sub > is defined on the D < sub > f </ sub > by setting Γ ( D < sub > f </ sub >, O < sub > X </ sub >) = R < sub > f </ sub >, the localization of R at the multiplicative system

Given the low efficiency of the laser amplification process ( about 1 to 1. 5 %), and the losses in generation ( steam-driven turbine systems are typically about 35 % efficient ), fusion gains would have to be on the order of 350 just to break even.

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 von Spee ’ s superiority in speed, firepower, efficiency and numbers, why Cradock chose to engage puzzles historians.

According to Peter C. Newman ’ s analysis financing could not have come from investors, “ who would have had to be kept in ignorance of the project ’ s significance .” The government had the mine immediately “ drained and cemented … and employed prospectors to search for additional uranium deposits .” The miners hired to reopen Eldorado were screened by the RCMP and sworn to secrecy Given this notion it seems secrecy was conducted the same way uranium contracts had been allocated ; efficiency and development of an atomic weapon took precedent over political concerns like communist attitude amongst the workforce or homage to Britain.

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

Given the limitations of older hardware, and even today's relative limitations, a fetch of a program, be it a single 4K record or many, is expensive.

Given its stability, similarity and relative proximity to the Sun, Tau Ceti is consistently listed as a target for the Search for Extra-Terrestrial Intelligence ( SETI ), and it appears in some science fiction literature.

Given the prominence of the concept of Pax Romana, historians have coined variants of the term to describe systems of relative peace that have been established, attempted or argued to have existed.

Given their relative isolation, the cult participants generally have little knowledge of modern manufacturing and are liable to be skeptical about modern explanations.

Given the extremely distorted shape of the primary, the relative orbital motion may be notably altered with respect to the two-body purely Keplerian scenario because of non-negligible long-term orbital perturbations affecting, for example, its orbital period.

Given the small likelihood of his older brothers producing heirs, and William's relative youth and good health, it had long been considered extremely likely that he would become King in due course.

Given its relative proximity with the cold to frigid air masses in Siberia, extreme lows are recorded in wintertime, sometimes well below.

Given that nearly all Jews of their day were poor or middle-class ( even the rich of that time were only rich relative to the poor ), they ruled that one should not give away more than a fifth of his income to charity, while yet being obligated to give away no less than 10 % of his income to charity.

Given Soane's youth and relative inexperience, his appointment was down to the influence of William Pitt then the Prime Minister and his friend from the Grand Tour Richard Bosanquet whose brother was Samuel Bosanquet, Director and later Governor of the Bank of England.

Given a condition number, the relative error of compensated summation is effectively independent of n. In principle, there is the O ( nε < sup > 2 </ sup >) that grows linearly with n, but in practice this term is effectively zero: since the final result is rounded to a precision ε, the nε < sup > 2 </ sup > term rounds to zero unless n is roughly 1 / ε or larger.

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 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 no other choice, Kolish contacted his only remaining adult relative, a brother who lived in Hollywood, and left instructions for the care of Sarria and his family.

Given that the angle of incidence is larger than the critical angle ( with respect to the normal of the surface ) and the refractive index is lower on the other side of the boundary relative to the incident ray, TIR will occur and no light will be able to pass through.

Given the relative closeness in age and same father's name indicated by the patronym ( Jonas was born about 1600, Pieter, born in 1616 ) it has been claimed that Pieter was a brother or cousin to Jonas Bronck, and not a son as had been surmised.

Given its superior strength, durability and long life relative to the more expensive composite fillings, it will likely be around for many more years to come.

Given that the measurement uncertainty in the mass measured on a standard analytical balance is ± 0. 1 mg, the relative uncertainty in the mass of oxalic acid dihydrate would be about one part in a thousand, similar to the measurement uncertainty in the volume measurement in the titration.

Given their relative isolation, several mistaken rumours regarding the Torres Islands and their people have become widespread by way of travel guides, inter-island gossip and the mass media.

Given a sequence ( f < sub > n </ sub >) of M-valued measurable functions on some measure space ( X, Σ, μ ), and a measurable subset A of finite μ-measure such that ( f < sub > n </ sub >) converges μ-almost everywhere on A to a limit function f, the following result holds: for every ε > 0, there exists a measurable subset B of A such that μ ( B ) < ε, and ( f < sub > n </ sub >) converges to f uniformly on the relative complement A

Given relative proportions shown on the show, the giants are about 72 feet tall

Given the small market and relative high number of breweries, many breweries have spare capacity.

Given its lengthy history and various changes in relative international status, properly qualifying hostility toward France and its people with one term is difficult.

Given b < a + c, the shape of the curve is determined by the relative magnitude of b and d. If d is imaginary, that is if a < sup > 2 </ sup >+ b < sup > 2 </ sup >=< c < sup > 2 </ sup > then the curve has fthe form of a figure eight.