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Given and inherent
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 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 space efficiency of front-wheel-drive ( FWD ) relative to rear-wheel-drive ( RWD ) platforms, this allowed MMAL to offer a passenger cabin that was as spacious, if not more spacious, than that of the market-dominant Ford Falcon and Holden Commodore.
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 and distortion
# Given a maximum distortion constraint, minimize the bit rate
# Given a maximum bit rate constraint, minimize the distortion

Given and is
: Given any family of nonempty sets, their Cartesian product is a nonempty set.
Given the similarities in the two characters ' names, professions, written works and generally dark subject matter, it is likely that Lovecraft's Alhazred provided the main inspiration for al-Hazir.
Given a field F, the assertion “ F is algebraically closed ” is equivalent to other assertions:
* Given an algebraic number, there is a unique monic polynomial ( with rational coefficients ) of least degree that has the number as a root.
" Given that Thomas Aquinas died six years before Albertus Magnus ' death, this legend as stated is unlikely.
Given Ealdred's known support of Godwin's family, John of Worcester is probably correct.
* 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 an R-module M, the endomorphism ring of M, denoted End < sub > R </ sub >( M ) is an R-algebra by defining ( r · φ )( x ) = r · φ ( x ).
Given the other ZF axioms, the axiom of regularity is equivalent to the axiom of induction.
After Christians in Ephesus first wrote to their counterparts recommending Apollos to them, he went to Achaia where Paul names him as an apostle ( 1 Cor 4: 6, 9-13 ) Given that Paul only saw himself as an apostle ' untimely born ' ( 1 Cor 15: 8 ) it is certain that Apollos became an apostle in the regular way ( as a witness to the risen Lord and commissioned by Jesus-1 Cor 15: 5-9 ; 1 Cor 9: 1 ).< ref > So the Alexandrian recension ; the text in < sup > 38 </ sup > and Codex Bezae indicate that Apollos went to Corinth.
Given its " blue-water " bias, the navy is even less inclined to become involved in counterdrug operations than the army or air force.
Given any element x of X, there is a function f < sup > x </ sup >, or f ( x ,·), from Y to Z, given by f < sup > x </ sup >( y ) := f ( x, y ).
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.
While tests have been done to support this with fixed pieces of flat metal, the result is inconclusive with respect to the curved armour of the period. Given the following actions of the archers, it seems likely Froissart was correct.
Given a ket of norm 1, the orthogonal projection onto the subspace spanned by is
Given this influence, it is unfortunate that many of the details of his life remain shrouded in mystery, perhaps forever ; even the only known picture of him, shown above, is heavily retouched, with a fake tie painted in by hand.
Given points P < sub > 0 </ sub > and P < sub > 1 </ sub >, a linear Bézier curve is simply a straight line between those two points.
Given the then GDP ($ 7. 095 bln ) of the country, military spending is roughly estimated to be about $ 300 million.
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 the federal nature of the holiday, celebrating Canada Day can be a cause of friction in the province of Quebec, where the holiday is overshadowed by Quebec's National Holiday, on June 24.
Given that many journeys are for relatively short distances, there is considerable scope to replace car use with walking or cycling, though in many settings this may require some infrastructure modification, particularly to attract the less experienced and confident.
Given such a sweeping definition, it is apparent that cognition is involved in everything a human being might possibly do ; that every psychological phenomenon is a cognitive phenomenon.

Given and unusual
Given the unusual casting and production demands, Pacific Overtures remains one of the least-performed musicals by Stephen Sondheim.
Given the unusual form and fabric of Beaker pottery, and its abrupt appearance in the archaeological record, along with a characteristic group of other artefacts, known as the Bell Beaker " package ", the explanation for the Beaker culture until the last decades of the 20th century was to interpret it as a diffusion of one group of people across Europe.
Given that the retail environment in Taiwan is already highly competitive, it is not unusual to see such stores fail.
Given the then lack of antibiotics, this " could not be considered an unusual pattern for pneumonia in a man in his seventh decade.
Given that the high latitudes in this period were warm and tropical, it is hypothesized that the deciduous habit evolved in response to the unusual light availability patterns, not to major seasonal variations in temperature.
Given his background in industry, and given President Eisenhower's predominance in defense matters, McElroy's appointment was not unusual.
Given that the details of characters ' physical appearances are not often given in His Dark Materials ( for example, it is a long time before it is mentioned that the protagonist, Lyra, is blonde ), this is an unusual attention to physical detail.
Given the existence of other raw image formats, Adobe's creation of DNG as a competing format implies that DNG is unusual and satisfies objectives that other raw image formats do not.
Given the sometimes forcible merger of small craft unions into large industrial unions in Australia, it is unusual that the AIMPE has not merged with the industrial union in the maritime industry, the MUA.
Given its unusual ability to " fly " tools around a work site, it has many possible applications, including stone carving, ship building, bridge construction, inspection, pipe or beam fitting and welding.
Given the quasi-legal status of the sport in New York at the time, it was not unusual that no record was kept of any particular encounter.
Given the ( then highly unusual ) driver-only operation, the branch line was equipped with a two wire emergency telephone system at window level, a feature normally found only in tunnels on the London Underground.
Given its size and unusual mouth structure, it may take larger insects than other swallows.
Given his unusual voice, he is able to perform a wide melodramatic and chamber repertoire going far beyond the Baroque repertoire and including compositions specially written for his vocality.
Given its unusual composition for an igneous rock, the magmatic nature of the carbonatite was not proposed for a long time and remained doubtful subsequently.
Given the growing problem of identity theft and the importance of the Social Security number as a personal identifier in the United States, it might seem unusual that these identifiers are released publicly.

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