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Given a core geometry, the B field needed for a given force can be calculated from ( 2 ); if it comes out to much more than 1. 6 T, a larger core must be used.
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Given and core
Given the limited market for a very expensive product of variable quality, Morganite also decided that carbon-fiber production was peripheral to its core business, leaving Courtaulds as the only big UK manufacturer.
Given IBM's resources, the 750 core will be produced with new features as long as there is a willing buyer.
Given a 3-manifold ( not necessarily compact ) with finitely generated fundamental group, there is a compact three-dimensional submanifold, called the compact core or Scott core, such that its inclusion map induces an isomorphism on fundamental groups.
Given and geometry
Given their vertical-cavity geometry, VCSOAs are resonant cavity optical amplifiers that operate with the input / output signal entering / exiting normal to the wafer surface.
Given the geometric approach, the consideration of homogeneous equations and homogeneous co-ordinates is fundamental, for the same reasons that projective geometry is the dominant approach in algebraic geometry.
Given the Cantor – Dedekind axiom, this algorithm can be regarded as an algorithm to decide the truth of any statement in Euclidean geometry.
Given the geometry of the array, the delays or phase differences can be used to estimate the incident angle.
Given and B
Given a morphism f: B → A the associated natural transformation is denoted Hom ( f ,–).
: Given any set A and any set B, if for every set C, C is a member of A if and only if C is a member of B, then A is equal to B.
: 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.
: Given any set A and any set B, there is a set C such that, given any set D, D is a member of C if and only if D is equal to A or D is equal to B.
: Given any set A, there is a set B such that, given any set x, x is a member of B if and only if x is a member of A and φ holds for x.
: Given any set A, there is a set such that, given any set B, B is a member of if and only if B is a subset of A.
: Given any set A, there is a set B such that, for any element c, c is a member of B if and only if there is a set D such that c is a member of D and D is a member of A.
Given a circle A, find a circle B such that the area of the intersection of A and B is equal to the area of the symmetric difference of A and B ( the sum of the area of A − B and the area of B − A ).
Given two candidates, A and B, A is better than B on a constraint if A incurs fewer violations than B.
With regard to African Americans, Gilman wrote in the American Journal of Sociology: “ The problem, is this: Given: in the same country, Race A, progressed in social evolution, say, to Status 10 ; and Race B, progressed in social evolution, say, to Status 4..
Given and field
Given a field F, the assertion “ F is algebraically closed ” is equivalent to other assertions:
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 smooth Φ < sup > t </ sup >, an autonomous vector field can be derived from it.
Given the difficulty of finding exact solutions, Einstein's field equations are also solved frequently by numerical integration on a computer, or by considering small perturbations of exact solutions.
Given a field K, the corresponding general linear groupoid GL < sub >*</ sub >( K ) consists of all invertible matrices whose entries range over K. Matrix multiplication interprets composition.
Given a vector space V over the field R of real numbers, a function is called sublinear if
Given a field ordering ≤ as in Def 1, the elements such that x ≥ 0 forms a positive cone of F. Conversely, given a positive cone P of F as in Def 2, one can associate a total ordering ≤< sub > P </ sub > by setting x ≤ y to mean y − x ∈ P. This total ordering ≤< sub > P </ sub > satisfies the properties of Def 1.
" Given that science continually seeks to adjust its theories structurally to fit the facts, i. e., adjusts its maps to fit the territory, and thus advances more rapidly than any other field, he believed that the key to understanding sanity would be found in the study of the methods of science ( and the study of structure as revealed by science ).
Given the currently keen interest in biotechnology and the high levels of funding in that field, attempts to exploit the replicative ability of existing cells are timely, and may easily lead to significant insights and advances.
Given the union's commitment to international solidarity, its efforts and success in the field come as no surprise.
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 that this is a plane wave, each vector represents the magnitude and direction of the electric field for an entire plane that is perpendicular to the axis.
Given a bounded sequence, there exists a closed ball that contains the image of ( is a subset of the scalar field ).
Given a vector space V over a field K, the span of a set S ( not necessarily finite ) is defined to be the intersection W of all subspaces of V which contain S. W is referred to as the subspace spanned by S, or by the vectors in S. Conversely, S is called a spanning set of W.
Given any such interpretation of a set of points as complex numbers, the points constructible using valid compass and straightedge constructions alone are precisely the elements of the smallest field containing the original set of points and closed under the complex conjugate and square root operations ( to avoid ambiguity, we can specify the square root with complex argument less than π ).
Given a subset S in R < sup > n </ sup >, a vector field is represented by a vector-valued function V: S → R < sup > n </ sup > in standard Cartesian coordinates ( x < sub > 1 </ sub >, ..., x < sub > n </ sub >).
Given a differentiable manifold M, a vector field on M is an assignment of a tangent vector to each point in M. More precisely, a vector field F is a mapping from M into the tangent bundle TM so that is the identity mapping
Given such a field, an absolute value can be defined on it.
Given a locally compact topological field K, an absolute value can be defined as follows.
Given a grid point field of geopotential height, storm tracks can be visualized by contouring its average standard deviation, after the data has been band-pass filtered.
Given an algebraically closed field A containing K, there is a unique splitting field L of p between K and A, generated by the roots of p. If K is a subfield of the complex numbers, the existence is automatic.
Given a separable extension K ′ of K, a Galois closure L of K ′ is a type of splitting field, and also a Galois extension of K containing K ′ that is minimal, in an obvious sense.
Given and needed
Given this basic definition, further criteria are needed to establish a dividing line between postlexical clitics and morphological affixes, since both are characterized by a lack of prosodic autonomy.
Given its roughly constant size, the encyclopaedia has needed to reduce or eliminate some topics to accommodate others, resulting in controversial decisions.
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 exclusivity of the criteria needed to become a magician, much magic is performed by specialists.
Given Deja had worked with three villains before, he was first offered Hades, but asked to animate the protagonist instead-" I knew if would be more difficult and more challenging, but I just needed that experience to have that in your repertoire.
Given the social state that was emerging, Tocqueville believed that a " new political science " would be needed.
Given the finite supply of natural resources at any specific cost and location, agriculture that is inefficient or damaging to needed resources may eventually exhaust the available resources or the ability to afford and acquire them.
Given that both analyses are guided by the same goal, why is it that logistic regression is needed for analyses with a dichotomous criterion?
Given that each letter has uppercase and lowercase forms, and the number of various punctuation marks and ligatures ( e. g. the sequence ' fi ' combined in one character, commonly used in writing ) the Gutenberg Bible needed a set of 290 master characters.
Given the time he needed Sanada's forces were able to successfully retreat from the Eastern army.
Given the New York Central's axle load limits, the Pacific type could not be made any larger ; a new locomotive type would be required to carry the larger boiler that Kiefer's research indicated was needed.
Given the time that is needed to build a new stadium, in the absence of significant work improving Windsor Park, Northern Ireland may be forced to play their home games at a venue outside Northern Ireland for a period.
Given that sleep apnea is a chronic health issue which commonly doesn't go away, ongoing care is usually needed to maintain CPAP therapy.
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 an m × n matrix, the number of connectors needed to address the display is m + n ( just like in passive matrix technology ).
Given its small staff of only 24 men, the Einsatzgrupppe Ägypten would have needed as much help as possible from the local Arabs and from the Afrika Korps to kill the roughly 50, 000 Jews of Egypt, to say nothing of the half million or so Jews of the Yishuv.
Given reasonable estimates of the time needed to compute the hash, this would take about 1 second to find.
Given that Suzanne's uncle Antonio works for the Count, it seems likely she was hired on his recommendation when the Countess moved into the palace and a maid was needed for her, in which case she and Figaro would have met after the events of The Barber of Seville.
Given how heavily entrenched apartheid was in the South African legal system at the time, Mr. de Klerk needed to nullify many previous bills and pass many new ones, making a series of individual referenda impractical.
Given the importance of agriculture for poverty reduction, additional policies and institutional capacity are needed to ensure an effective supply response to market incentives provide by better market access.
Given names or initials are not needed unless the work cites two authors with the same surname, as the whole purpose of using op.
Given Ariel Ultra's success, and with Persil Micro System lagging, Unilever needed a new super-compact Persil line.
Given the low number of AVLBs available a solution was needed to bridge these gaps quickly and cheaply and, if required, under fire.
Given the interconnection of s and k in steady state, noted above, the question can be phrased: " How much capital per worker ( k ) is needed to achieve the maximum level of consumption per worker in the steady state?
1.436 seconds.