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Given and length
: Given two points, determine the azimuth and length of the line ( straight line, arc or geodesic ) that connects them.
Given the dimensions of the ellipsoid, the conversion from lat / lon / height-above-ellipsoid coordinates to X-Y-Z is straightforward — calculate the X-Y-Z for the given lat-lon on the surface of the ellipsoid and add the X-Y-Z vector that is perpendicular to the ellipsoid there and has length equal to the point's height above the ellipsoid.
* Given two hypothetical point particles each of Planck mass and elementary charge, separated by any length, α is the ratio of their electrostatic repulsive force to their gravitational attractive force.
Given a grammar in GNF and a derivable string in the grammar with length n, any top-down parser will halt at depth n.
Given two points P and Q on C, let s ( P, Q ) be the arc length of the portion of the curve between P and Q and let d ( P, Q ) denote the length of the line segment from P to Q.
Hypothesis: Given AD is a straight line, and AB, BC, and CD are all equal length,
Given the length of the hypotenuse and of a cathetus, the ratio is:
Given two large integers, a and b, Toom – Cook splits up a and b into k smaller parts each of length l, and performs operations on the parts.
Given an arbitrary ( n ; m ; p ) machine S, such that every two of its states are distinguishable from one another, then there exists an experiment of length
Given that the Atlas was the higher priority of the two ICBM projects and its production was fully accounted for, ABMA focussed on " backup " design, Titan, although they proposed extending it in length in order to carry additional fuel.
Given its length and a basin that covers an area of 102, 000 km², it is one of the largest rivers of the Caucasus.
Given a sequence ( X < sub > n </ sub >, p < sub > n </ sub >) of locally compact complete length metric spaces with distinguished points, it converges to ( Y, p ) if for any R > 0 the closed R-balls around p < sub > n </ sub > in X < sub > n </ sub > converge to the closed R-ball around p in Y in the usual Gromov – Hausdorff sense.
Given the total energy E and the length ( magnitude ) p of the total momentum vector, the invariant mass is given by:
The original problem was stated in the form that has become known as the Euclidean Steiner tree problem or geometric Steiner tree problem: Given N points in the plane, the goal is to connect them by lines of minimum total length in such a way that any two points may be interconnected by line segments either directly or via other points and line segments.
The problem in more mathematical terms is: Given a needle of length dropped on a plane ruled with parallel lines t units apart, what is the probability that the needle will cross a line?
Given that opcodes on these processors were only one byte ( 8-bit ) in length, memory addresses could make up a significant part of code size.
For instance, consider the following problem: Given a directed acyclic graph, determine if the graph has a path of length 10.
Given two strings, of length and of length, find the longest strings which are substrings of both and.
Given the length of occupancy of Crow Village by the native population, the site has had several archaeological digs.

Given and canal
Given the enlargement of the canal to accommodate larger shipping, it is unlikely in the foreseeable future that Panama would likely succumb to international pressure toward transparency.
Given its historic importance, the " Lachine Canal Manufacturing Complex " was designated a National Historic Site of Canada in 1996, in addition to the designation already enjoyed by the canal itself.

Given and however
Given the limited success of the Charity School, however, Wheelock intended his new College as one primarily for whites.
Given its limitations, however, NAALC has not produced ( and in fact was not intended to achieve ) convergence in employment, productivity and salary trend in North America.
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 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 the structural similarities between bacterial flagella and bacterial secretory systems, it is thought that bacterial flagella may have evolved from the type three secretion system ; however, it is not known for certain whether these pores are derived from the bacterial flagella or the bacterial secretory system.
( Please note that Japan has a guideline of a limit of 1 % of GDP on defense spending, however, Japan defines a number of activities as non-defense spending ) Given these circumstances, some have viewed Article 9 as increasingly irrelevant.
Given the well-publicized hoopla, some sources still consider this as a nomination for Davis ; however, the Academy does not officially record this as a nomination.
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 their sting, however, they must always be treated with caution, and the discovery of men o ' war washed up on a beach may lead to the closure of the whole beach.
Given a method of description, however, there may be more than one description that represents the same knot.
Given the advent of high-throughput protein analysis and lower limits of detection, however, there has been interest in developing one-step probing systems that would allow the process to occur faster and with less consumables.
Given the informal setting, this might be unimportant ; however, teachers see this as a problem, fearing and claiming that contemporary young people are inappropriately and incorrectly extending the practice to academic homework and essays.
Given its native distribution the species is also a potential natural vagrant to Western Europe and there have been records in areas such as Cornwall and the Isles of Scilly which some observers consider may relate to wild birds ; however, given the Wood Duck's popularity in captivity it would be extremely difficult to prove their provenance one way or another.
Given the massing of the Muslim armies at Yarmouk, however, Vahan had little choice but to respond in kind.
Given that the darker-skinned Calormenes differed in appearance from northern peoples ( like Telmarines and Archenlanders ), it is possible that they are descended from another group from the world of men ; however, this is not stated in the books.
Given the wide expectation that the war was going to be a short one, the majority however supported the war effort and the call to restore the " freedom of small nations " on the European continent.
Given the complicated legal process and the sheer number of exiting cul-de-sac streets, however, such efforts would be slow to produce results and may only have a marginal impact in changing the landscape of existing districts.
Given that realities of the North Atlantic in winter, however, the reinforcements would have to land in Nova Scotia, since the St. Lawrence begins to ice up in December.
Given that the archaeological record demonstrates Irish settlement on the Llŷn Peninsula however and possible raids as far west as Wroxeter by the late 4th century, it is difficult to conceive of either Roman or allied British forces having presented an effective defence in Wales.
Given the dramatic nature of the game, however, Core Earth had slightly better technology than the real world as well as some basic access to magic and miracles.
Given what later came to light, however, Wooden granted that he may have had " tunnel vision " and that he perhaps " trusted too much ".
Given the transnational nature of Böhme's influence, however, the term at least implies manifold international connections between Behmenists.
Given did make his 400th appearance for the club during the season, however, in a New Year's Day match.
Given was part of the team for most of the 2006 FIFA World Cup qualifying campaign ; however a draw with Switzerland meant Ireland failed to qualify for the finals of the competition in Germany.
Given the municipality ’ s weak legal position, however, the legal dispute, which went on for 7 years, can no longer be further pursued.

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