Let-(-M-g-)-be-a-Riemannian-manifold-and-ƒ-M

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Let and M

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 M be a smooth manifold and let x be a point in M. Let T x M be the tangent space at x.

Let M be a smooth manifold and let x be a point in M. Let I x be the ideal of all functions in C < sup >∞</ sup >( M ) vanishing at x, and let I x < sup > 2 </ sup > be the set of functions of the form, where f i , g i ∈ I x .

Let M be a smooth manifold and let f ∈ C < sup >∞</ sup >( M ) be a smooth function.

Let r be a non zero real number and let the r < sup > th </ sup > power mean ( M < sup > r </ sup > ) of a series of real variables ( a 1 , a 2 , a 3 , ... ) be defined as

Let M be a ( pseudo -) Riemannian manifold, which may be taken as the spacetime of general relativity.

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

Let M be an n × n Hermitian matrix.

Let P < sup >− 1 </ sup > DP be an eigendecomposition of M, where P is a unitary complex matrix whose rows comprise an orthonormal basis of eigenvectors of M, and D is a real diagonal matrix whose main diagonal contains the corresponding eigenvalues.

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

Let and g

Let the function g ( t ) be the altitude of the car at time t, and let the function f ( h ) be the temperature h kilometers above sea level.

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

Let G denote the set of bijective functions over A that preserve the partition structure of A: ∀ x ∈ A ∀ g ∈ G ( g ( x ) ∈ ).

Let f and g be any two elements of G. By virtue of the definition of G, = and =, so that =.

Let g

If V is a real vector space, then we replace V by its complexification V ⊗ R C and let g denote the induced bilinear form on V ⊗ R C. Let W be a maximal isotropic subspace, i. e. a maximal subspace of V such that g | W = 0.

Let F be a diagram that picks out three objects X, Y, and Z in C, where the only non-identity morphisms are f: X → Z and g: Y → Z.

Let f ( x ) and g ( x ) be two functions defined on some subset of the real numbers.

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

Let f, g belong to L < sup > 1 </ sup >( R < sup > n </ sup >).

Let A be an abelian group and f and g be two group homomorphisms from A into itself.

Let us consider two patterns made of parallel and equidistant lines, e. g., vertical lines.

Let Y = u ( X 1 , X 2 , ..., X n ) be a statistic whose pdf is g ( y ; θ ).

Let f and g be functions, with and fixed.

Let ƒ and g be functions.

E. g., " Let us lie in wait for the just, because he is not for our turn … He boasteth that he hath the knowledge of God, and calleth himself the son of God … and glorieth that he hath God for his father.

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 ).

Both Kember and Pierce continue to perform some Spacemen 3 songs live ( e. g. " Transparent Radiation ", " Revolution ", " Suicide ", " Set Me Free ", " Che " and " Let Me Down Gently " ; and " Walkin ' with Jesus ", " Amen " and " Lord Can You Hear Me?

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 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 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 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??

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