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More generally, let V be a vector space over a field K, and let
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More and generally
More generally, suppose that an experiment consists of a number of independent trials, that each trial results in either a `` success '' or a `` non-success '' ( `` failure '' ), and that the probability of success remains constant from trial to trial.
More generally, in a k-dimensional array, the address of an element with indices i < sub > 1 </ sub >, i < sub > 2 </ sub >, …, i < sub > k </ sub > is
More generally, one curve is a curvilinear asymptote of another ( as opposed to a linear asymptote ) if the distance between the two curves tends to zero as they tend to infinity, although usually the term asymptote by itself is reserved for linear asymptotes.
More generally, a new component is said to be backward compatible if it provides all of the functionality of the old component.
More generally, an n-piece cubic Bézier curve can approximate a circle, when each inner control point is the distance from an outer control point on a unit circle, where t is 360 / n degrees, and n > 2.
More generally, calculus ( plural calculi ) refers to any method or system of calculation guided by the symbolic manipulation of expressions.
More generally, many philosophers and scientists have been unhappy about the difficulty of producing a definition that does not involve circularity or fuzziness.
More broadly, philosophers who do not accept the possibility of zombies generally believe that consciousness is reflected in behavior ( including verbal behavior ), and that we attribute consciousness on the basis of behavior.
Among the teachings of Jesus Christ in the Gospel of Luke and the Gospel of Matthew, the message to his followers that one should " Turn the other cheek " and his example in the story Pericope Adulterae, in which Jesus intervenes in the stoning of an adulteress, are generally accepted as his condemnation of physical retaliation ( though most scholars agree that the latter passage was " certainly not part of the original text of St John's Gospel ") More militant Christians consider Romans 13: 3 – 4 to support the death penalty.
* More generally, compact groups such as an orthogonal group are compact, while groups such as a general linear group are not.
More generally, compact sets can be separated by open sets: if K < sub > 1 </ sub > and K < sub > 2 </ sub > are compact and disjoint, there exist disjoint open sets U < sub > 1 </ sub > and U < sub > 2 </ sub > such that and.
More generally, electric current can be represented as the rate at which charge flows through a given surface as:
More generally, unspecific coercion may be the form taken by disciplinary coercion, and this appears to be in fact the case within the most effective command systems of the modern world.
More generally, judges look at the difficulty and execution of jumps, stunts and tumbling, synchronization, creativity, the sharpness of the motions, showmanship, and overall routine execution.
More generally among Baptists, a variety of parachurch agencies and evangelical educational institutions may be supported generously or not at all, depending entirely upon the local congregation's customs and predilections.
More and let
Love initially began several music projects in the 1980s, first forming Sugar Babydoll, and then having a brief stint as a singer in Faith No More after " demanding " them to let her be in their band.
More specifically, let be the set of all polynomials with integer coefficients ( such a polynomial is also referred to as a polynomial over ), with addition and multiplication defined to be natural polynomial addition and multiplication.
More recently it has been proposed that it serves to guard against infidelity — that the male sings to attract a mate, and the female joins in to let her rivals know that this particular male is already taken.
More generally, let be a continuous map to X from a path connected and locally path connected space Z.
Even Roger Bacon recommended Rythmomachia to his students, while Sir Thomas More let the inhabitants of the fictitious Utopia play it for recreation.
More precisely, let M be a complete Riemannian manifold, and let xyz be a geodesic triangle in M ( a triangle each of whose sides is a length-minimizing geodesic ).
More generally, let T be a real topological vector space, and X a T-valued integrable random variable.
More precisely, let F be a field, and let F be the ring of polynomials in one variable, X, with coefficients in F. Then each f < sub > i </ sub > lies in F. ∂< sub > X </ sub > is the derivative with respect to X.
More formally, let W < sub > n </ sub >< sup > H </ sup > be the set of words of length H over an alphabet with n letters ; that is, the set of sequences of
As Sir Thomas More climbed a rickety scaffold where he would be executed, he said to his executioner: " I pray you, Mr. Lieutenant, see me safe up ; and for my coming down, let me shift for myself.
More explicitly, let be a dominant integral weight ; then it is still true that for all, but it is no longer true that this G-module is simple in general, although it does contain the unique highest weight module of highest weight as a G-submodule.
More precisely, at any point R on C, let T be the tangent line at R. There is then a unique point X on T which is either P ( in case P lies on T ) or forms with P a line perpendicular to T. The pedal curve is the set of such points X, called the foot of the perpendicular to T from P, as R ranges over points C.
More precisely, let be the Minkowski fiber bundle over the spacetime manifold M. For each point, the fiber is an affine space.
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