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Let and N

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 ( m, n ) be a pair of amicable numbers with m < n, and write m = gM and n = gN where g is the greatest common divisor of m and n. If M and N are both coprime to g and square free then the pair ( m, n ) is said to be regular, otherwise it is called irregular or exotic.

Let the program for which the halting problem is to be solved be N bits long.

Let g be a smooth function on N vanishing at f ( x ).

Let X be a measurable space, let μ be a measure on X, and let N be a measurable set in X.

Let M and N be ( left or right ) modules over the same ring, and let f: M → N be a module homomorphism.

Let N be a function assigning to each x in X a non-empty set N ( x ) of subsets of X.

Let S be the group of all permutations of N, the natural numbers, that fixes all but finitely many numbers then:

Let F: J → C be a diagram of type J in a category C. A cone to F is an object N of C together with a family ψ X : N → F ( X ) of morphisms indexed by the objects of J, such that for every morphism f: X → Y in J, we have F ( f ) o ψ X

Let S be a subgroup of G, and let N be a normal subgroup of G. Then:

Let N and K be normal subgroups of G, with

Let G be a group with identity element e, N a normal subgroup of G ( i. e., N ◁ G ) and H a subgroup of G. The following statements are equivalent:

Let M and N be smooth manifolds and be a smooth map.

Let ( M, g ) and ( N, h ) be Riemannian manifolds.

* Let N h be the number of non selfcrossing paths for moving a tower of h disks from one peg to another one.

) Let N be the ( possibly fractional ) number of submovements required to fall within the target.

Let N =

Let p be the nth decimal of the nth number of the set E ; we form a number N having zero for the integral part and p + 1 for the nth decimal, if p is not equal either to 8 or 9, and unity in the contrary case.

Let N represent the common nine-point center and P be an arbitrary point in the plane of the orthocentric system.

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 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 be the null space of Af.

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 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 this be denoted by Af.

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 linear

Let us now regard D as a linear operator on the subspace V.

Let us define a linear operator P, called the exchange operator.

Let V and W be vector spaces over the same field K. A function f: V → W is said to be a linear map if for any two vectors x and y in V and any scalar α in K, the following two conditions are satisfied:

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 x , defined by

Let be the input to a general linear time-invariant system, and be the output, and the bilateral Laplace transform of and be

Let X be a normed topological vector space over F, compatible with the absolute value in F. Then in X *, the topological dual space X of continuous F-valued linear functionals on X, all norm-closed balls are compact in the weak -* topology.

Let the linear, angular and internal momenta of a molecule be given by the set of r variables

Let T be a linear operator represented by the matrix

Let V and W be vector spaces ( or more generally modules ) and let T be a linear map from V to W. If 0 W is the zero vector of W, then the kernel of T is the preimage of the zero subspace

Let U, V, and W be vector spaces over the same field with given bases, S: V → W and T: U → V be linear transformations and ST: U → W be their composition.

Using the natural isomorphism between and the space of linear transformations from V to V ,< ref name =" natural iso "> Let L ( V, V ) be the space of linear transformations from V to V. Then the natural map

Let V be a finite-dimensional vector space over some field K and suppose T: V → V is a linear map.

Let U be a unitary operator on a Hilbert space H ; more generally, an isometric linear operator ( that is, a not necessarily surjective linear operator satisfying ‖ Ux ‖

Let E and F be two vector bundles over a differentiable manifold M. An R-linear mapping of sections is said to be a kth-order linear differential operator if it factors through the jet bundle J k ( E ).

Let denote the tangent space of M at a point p. For any pair of tangent vectors at p, the Ricci tensor evaluated at is defined to be the trace of the linear map given by

Let L n be the space of all complex n × n matrices, and let adX be the linear operator defined by adX Y = for some fixed X ∈ L n .

Let F: U → Y be continuously differentiable and assume that the derivative ( dF ) 0 : X → Y of F at 0 is a bounded linear isomorphism of X onto Y.

Let W be a linear subspace of V. Define the symplectic complement of W to be the subspace

Let be the linear field of view in feet per 1000 yd.

Let be the linear field of view in millimeters per meter.

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