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Some Related Sentences

Let and Af
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 Af.
Let us put Af.
Let us look at the operator Af.
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 Af denote the form of Af.
Let us assume that Af is identical to the form of an occurrence Af which preceded Af in the text.
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 this be denoted by Af.
Let Af where the maximization is over all admissible policies Af.

Let and be
Let the open enemy to it be regarded as a Pandora with her box opened ; ;
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 him be now ''!!
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 T be a linear operator on the finite-dimensional vector space V over the field F.
Let N be a linear operator on the vector space V.
Let T be a linear operator on the finite-dimensional vector space V over the field F.
Let V be a finite-dimensional vector space over an algebraically closed field F, e.g., the field of complex numbers.
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 it be granted then that the theological differences in this area between Protestants and Roman Catholics appear to be irreconcilable.
Let not your heart be troubled, neither let it be afraid ''.
The same God who called this world into being when He said: `` Let there be light ''!!
For those who put their trust in Him He still says every day again: `` Let there be light ''!!
Let us therefore put first things first, and make sure of preserving the human race at whatever the temporary price may be ''.
Let her out, let her out -- that would be the solution, wouldn't it??

Let and null
Let F be the continuous cumulative distribution function which is to be the null hypothesis.
Let them all be relinquished and abandoned, null and void, neither firm nor established.
Let them all be relinquished and abandoned, null and void, neither firm nor established.
This is the affine cone over the projective quadric S. Let N < sup >+</ sup > be the future part of the null cone ( with the origin deleted ).

Let and space
* Theorem Let X be a normed space.
* Corollary Let X be a reflexive normed space and Y a Banach space.
* Corollary Let X be a reflexive normed space.
Let be a Hilbert space and is a vector in.
Let be the dual space of.
Let S be a vector space over the real numbers, or, more generally, some ordered field.
Let M be a smooth manifold and let x be a point in M. Let T < sub > x </ sub > M be the tangent space at x.
Let x, y, z be a system of Cartesian coordinates in 3-dimensional Euclidean space, and let i, j, k be the corresponding basis of unit vectors.
Let X be a topological space, and let x < sub > 0 </ sub > be a point of X.
Theorem: Let V be a topological vector space
Let be a metric space.
Let denote the space of scoring functions.
Let X be a measurable space, let μ be a measure on X, and let N be a measurable set in X.
These assumptions can be summarised as: Let ( Ω, F, P ) be a measure space with P ( Ω )= 1.
Let H be a Hilbert space, and let H * denote its dual space, consisting of all continuous linear functionals from H into the field R or C. If x is an element of H, then the function φ < sub > x </ sub >, defined by
Let X be a locally compact Hausdorff space.

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