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Let B be an arbitrary Banach space, and let B < sup >*</ sup > be its dual, that is, the space of bounded linear functionals on B.
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Let and B
Let exactly 1'' '' of `` A '' extend beyond `` B '' and use a square to check your angle to exactly 90 degrees.
Gloria Gaynor ( born September 7, 1949 ) is an American singer, best known for the disco era hits ; " I Will Survive " ( Hot 100 number 1, 1979 ), " Never Can Say Goodbye " ( Hot 100 number 9, 1974 ), " Let Me Know ( I Have a Right )" ( Hot 100 number 42, 1980 ) and " I Am What I Am " ( R & B number 82, 1983 ).
Let the input power to a device be a force F < sub > A </ sub > acting on a point that moves with velocity v < sub > A </ sub > and the output power be a force F < sub > B </ sub > acts on a point that moves with velocity v < sub > B </ sub >.
Let us take a hypothetical single scan line, with B representing a black pixel and W representing white:
Other chart hits by White included " Never, Never Gonna Give Ya Up " (# 2 R & B, # 7 Pop in 1973 ), " Can't Get Enough of Your Love, Babe " (# 1 Pop and R & B in 1974 ), " You're the First, the Last, My Everything " (# 1 R & B, # 2 Pop in 1974 ), " What Am I Gonna Do with You " (# 1 R & B, # 8 Pop in 1975 ), " Let the Music Play " (# 4 R & B in 1976 ), " It's Ecstasy When You Lay Down Next to Me " (# 1 R & B, # 4 Pop in 1977 ) and " Your Sweetness is My Weakness " (# 2 R & B in 1978 ).
Let M be the intersection of all subgroups of the free Burnside group B ( m, n ) which have finite index, then M is a normal subgroup of B ( m, n ) ( otherwise, there exists a subgroup g < sup >-1 </ sup > Mg with finite index containing elements not in M ).
Let and be
Let every policeman and park guard keep his eye on John and Jane Doe, lest one piece of bread be placed undetected and one bird survive.
Let us assume that it would be possible for an enemy to create an aerosol of the causative agent of epidemic typhus ( Rickettsia prowazwki ) over City A and that a large number of cases of typhus fever resulted therefrom.
Let p be the minimal polynomial for T, Af, where the Af, are distinct irreducible monic polynomials over F and the Af are positive integers.
Let V be a finite-dimensional vector space over an algebraically closed field F, e.g., the field of complex numbers.
Let N be a positive integer and let V be the space of all N times continuously differentiable functions F on the real line which satisfy the differential equation Af where Af are some fixed constants.
Let Q be a nonsingular quadric surface bearing reguli Af and Af, and let **zg be a Af curve of order K on Q.
Let us take a set of circumstances in which I happen to be interested on the legislative side and in which I think every one of us might naturally make such a statement.
Let the state of the stream leaving stage R be denoted by a vector Af and the operating variables of stage R by Af.
Let it be granted then that the theological differences in this area between Protestants and Roman Catholics appear to be irreconcilable.
Let us therefore put first things first, and make sure of preserving the human race at whatever the temporary price may be ''.
Let and arbitrary
Let φ ( ξ, η, ζ ) be an arbitrary function of three independent variables, and let the spherical wave form F be a delta-function: that is, let F be a weak limit of continuous functions whose integral is unity, but whose support ( the region where the function is non-zero ) shrinks to the origin.
Let u, v be arbitrary vectors in a vector space V over F with an inner product, where F is the field of real or complex numbers.
Let N represent the common nine-point center and P be an arbitrary point in the plane of the orthocentric system.
Let us examine some other cases ; we shall find that Peacock's principle is not a solution of the difficulty ; the great logical process of generalization cannot be reduced to any such easy and arbitrary procedure.
Let us very roughly consider the line between the " leftmost " and " rightmost " two points of the k selected points ( for some arbitrary left / right axis: we can choose top and bottom for the exceptional vertical case ).
Let s be an arbitrary dimension and b < sub > 1 </ sub >, ..., b < sub > s </ sub > be arbitrary coprime integers greater than 1.
Let be an arbitrary system subject to changes in time and let be an arbitrary event that is a stimulus for the system: we say that is an adaptive system if and only if when t tends to infinity the probability that the system change its behavior in a time step given the event is equal to the probability that the system change its behavior independently of the occurrence of the event.
Let be the coordinate vector of an arbitrary point in the body with respect to the body-fixed frame.
1.877 seconds.