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??

Suppose we have an n-dimensional oriented Riemannian manifold, M and a target manifold T. Let be the configuration space of smooth functions from M to T. ( More generally, we can have smooth sections of a fiber bundle over M .)

Let C be a positively oriented, piecewise smooth, simple closed curve in the plane < sup > 2 </ sup >, and let D be the region bounded by C. If L and M are functions of ( x, y ) defined on an open region containing D and have continuous partial derivatives there, then

Let be a spin structure on a Riemannian manifold that is, an equivariant lift of the oriented orthonormal frame bundle with respect to the double covering

Let be a compact oriented manifold of dimension.

Let C be a positively oriented ( i. e., counterclockwise ) circle centered at a, lying within that open disk but farther from a than z is.

Let and be two smooth, oriented manifolds of equal dimension and a smooth, closed, oriented manifold, embedded as a submanifold into both and.

Let V and W be handlebodies of genus g, and let ƒ be an orientation reversing homeomorphism from the boundary of V to the boundary of W. By gluing V to W along ƒ we obtain the compact oriented 3-manifold

The phrase in reverse is echoed in Abraham Lincoln's words in his February 26, 1860, Cooper Union Address (" Let us have faith that right makes might, and in that faith, let us, to the end, dare to do our duty as we understand it ") in his attempt to defend a policy of neutral engagement with those who practised slavery, perhaps to appear more nationally oriented and religiously convicted in hopes of winning the presidential election later that year ( which he did ).

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

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

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

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

Let x = x ( u, v, w ), y = y ( u, v, w ), z = z ( u, v, w ) be defined and smooth in a domain containing, and let these equations define the mapping of into.

Let M be a smooth manifold of dimension n ; for instance a surface ( in the case n = 2 ) or hypersurface in the Cartesian space R < sup > n + 1 </ sup >.

Let be the sheaf of germs of smooth functions on M × M which vanish on the diagonal.

Let X be a compact complex manifold of complex dimension n. Then X is an orientable smooth manifold of real dimension 2n, so its cohomology groups lie in degrees zero through 2n.

Let M be a smooth manifold.

Let E → M be a vector bundle with covariant derivative ∇ and γ: I → M a smooth curve parameterized by an open interval I.

Let M be a smooth manifold.

Let M be a smooth manifold and an open cover of M. Define the disjoint union with the obvious submersion.

Let X be a smooth projective variety where all of its irreducible components have dimension n. Then one has the following version of the Serre duality: for any locally free sheaf on X,

Let E → M be a smooth vector bundle over a differentiable manifold M. Denote the space of smooth sections of E by Γ ( E ).

Let ( f < sub > 1 </ sub >, …, f < sub > k </ sub >) be another smooth local frame over U and let the change of coordinate matrix be denoted t ( i. e. f < sub > α </ sub >