Given a simple, binary component feed, analytical methods such as the McCabe-Thiele method or the Fenske equation can be used.

A conceptually very simple method for generating exponential variates is based on inverse transform sampling: Given a random variate U drawn from the uniform distribution on the unit interval ( 0, 1 ), the variate

Given a desired backbone conformation, side chain packing can be designed using variations of the dead-end elimination algorithm ; however, attempts to design proteins of novel folds have difficulty using this method due to an absence of plausible backbone models.

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

Given a simple, binary component feed, analytical methods such as the McCabe-Thiele method or the Fenske equation can be used.

Given a simple, binary component feed, analytical methods such as the McCabe-Thiele method or the Fenske equation can be used.

Given the size of many NLPs arising from a direct method, it may appear somewhat counter-intuitive that solving the nonlinear optimization problem is easier than solving the boundary-value problem.

Given a DMS ( Degrees, Minutes, Seconds ) coordinate such as W87 ° 43 ′ 41 ″, convert it to a number of decimal degrees using the following method:

Given a MinDec ( Degrees, Minutes, Decimal Minutes ) coordinate such as 40 ° 26. 7717N, 79 ° 56. 93172W, convert it to a number of decimal degrees using the following method ( for example for 79 ° 56. 93172W ):

Given that it has been argued and demonstrated that measuring exposure to violent content is a more appropriate method for cultivation analyses than measuring overall television exposure levels.

Given a positive integer n, Fermat's factorization method relies on finding numbers x, y satisfying the equality

Given a method for establishing the satisfaction ( or not ) of every atomic sentence of the form A (... x < sub > k </ sub >...), the usual rules for truth-functional connectives and quantifiers yield a definition for the satisfaction condition of all sentences of the object language.

Given that the nation was at peace, archery as well as other military martial arts became more of a method of personal development rather than military training.

Given the reduction in the rate of spread once screening for Hepatitis C in blood products was implemented in the 1990s it would seem that at least in recent times blood transfusion has been an important method of spreading for this virus.

Given the meaninglessness of theistic claims, Ayer opined that there was " no logical ground for antagonism between religion and natural science ", as theism alone does not entail any propositions which the scientific method can falsify.

Most methods of lipid extraction and isolation from biological samples exploit the high solubility of hydrocarbon chains in organic solvents. Given the diversity in lipid classes, it is not possible to accommodate all classes with a common extraction method.

Given the numerous descriptions of courses, distances, and directions in the log, this method seems more likely to pinpoint the location, and has been by far the most frequently used method of historians.

Given below is the five point method for the first derivative ( five-point stencil in one dimension ).

Given that recorded vocalizations are an effective means to attract owls, and given the similarity of a distant accordion's tune to the call of the Laughing Owl as reported, it is apparent that the method might have worked.

Given that there is an asset underlying the value of the certificate, there may be, depending on the value of the asset, more security for the investors involved, accounting for the additional appeal of Sukuk as a method of financing for investors.

Given the flexible method of counting syllables in Spanish verse, where an " octosyllabic " line could easily have seven or nine syllables ( as normally counted ), in writing a décima in English it would seem not unreasonable to write in iambic pentameter ( theoretically ten syllables ), which comes more naturally to English verse.

Given the uncertainty of this method, this method likely could not be used in criminal prosecutions where the guilt must be found beyond a reasonable doubt.

Given the difficulty of scoring directly from the point due to the distance to the goal, goals scored from the point are typically either on screens, or are tipped goals.

Given recent comebacks such as The Miracle at the New Meadowlands ( where the Philadelphia Eagles won by scoring 28 points in the last 7 minutes ) and how quickly points can be accumulated ( through interception returns, onside kicks and kick returns ) it is understandable that coaches are cautious about becoming overconfident in their offenses and they normally prefer to run out the clock rather than risk an unlikely but certainly possible comeback late in the game, particularly for teams who have a strong offence but a weaker defense.

Given the similarities of scoring and the use of chases, it is highly likely palla and tennis share a common sporting ancestor, the various games of palla being more primal in form.

: 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.