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 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 the concentration of ( aq ) be denoted by x.

Let ( M, d ) be a metric space, namely a set M with a metric ( distance function ) d. The open ( metric ) ball of radius r > 0 centered at a point p in M, usually denoted by B < sub > r </ sub >( p ) or B ( p ; r ), is defined by

Let K be a field, and let A be a vector space over K equipped with an additional binary operation from A × A to A, denoted here by · ( i. e. if x and y are any two elements of A, x · y is the product of x and y ).

Let denote the space of holomorphic sections of L. This space will be finite-dimensional ; its dimension is denoted.

Let V be a finite-dimensional Euclidean vector space, with the standard Euclidean inner product denoted by.

A divisor corresponding to ω < sub > X </ sub > is called the canonical divisor and is denoted by K. Let l ( D ) be the dimension of.

Let k be a field and L and K be two extensions of k. The compositum, denoted KL is defined to be where the right-hand side denotes the extension generated by K and L. Note that this assumes some field containing both K and L. Either one starts in a situation where such a common over-field is easy to identify ( for example if K and L are both subfields of the complex numbers ); or one proves a result that allows one to place both K and L ( as isomorphic copies ) in some large enough field.

Let V be a finite-dimensional vector space over a field k. The Grassmannian Gr ( r, V ) is the set of all r-dimensional linear subspaces of V. If V has dimension n, then the Grassmannian is also denoted Gr ( r, n ).

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 >

Let this property be represented by just one scalar variable, q, and let the volume density of this property ( the amount of q per unit volume V ) be ρ, and the all surfaces be denoted by S. Mathematically, ρ is a ratio of two infinitesimal quantities:

Let S a multiplicatively closed subset of R, i. e. for any s and t ∈ S, the product st is also in S. Then the localization of M with respect to S, denoted S < sup >− 1 </ sup > M, is defined to be the following module: as a set, it consists of equivalence classes of pairs ( m, s ), where m ∈ M and s ∈ S. Two such pairs ( m, s ) and ( n, t ) are considered equivalent if there is a third element u of S such that

Let the variance-covariance matrix for the observations be denoted by M and that of the parameters by M < sup > β </ sup >.

Let K be a valued field ( with valuation denoted v ) and let L / K be a finite Galois extension with Galois group G. For an extension w of v to L, let I < sub > w </ sub > denote its inertia group.

Let M be a differentiable manifold and p a point of M. Suppose that f is a function defined in a neighborhood of p, and differentiable at p. If v is a tangent vector to M at p, then the directional derivative of f along v, denoted variously as ( see covariant derivative ), ( see Lie derivative ), or ( see Tangent space # Definition via derivations ), can be defined as follows.

Let Φ: V → W be a linear map between vector spaces V and W ( i. e., Φ is an element of L ( V, W ), also denoted Hom ( V, W )), and let

Let a rotation about the origin O by an angle θ be denoted as Rot ( θ ).

Let a reflection about a line L through the origin which makes an angle θ with the x-axis be denoted as Ref ( θ ).

Let the four-dimensional Cartesian coordinates be denoted ( w, x, y, z ) where ( x, y, z ) represent the Cartesian coordinates of the normal position vector r. The three-dimensional momentum vector p is associated with a four-dimensional vector on a three-dimensional unit sphere

Let the net cash flow at time t be denoted by R < sub > t </ sub >, i. e.:

Let the filtered signal be denoted.

Consider two rays emanating from an external homothetic center E. Let the antihomologous pairs of intersection points of these rays with the two given circles be denoted as P and Q, and S and T, respectively.

Let M be a compact smooth manifold, f: M → M a diffeomorphism, and Df: TM → TM the differential of f. An f-invariant subset Λ of M is said to be hyperbolic, or to have a hyperbolic structure, if the restriction to Λ of the tangent bundle of M admits a splitting into a Whitney sum of two Df-invariant subbundles, called the stable bundle and the unstable bundle and denoted E < sup > s </ sup > and E < sup > u </ sup >.