Let, denote a random sample from a distribution having the pdf f ( x, θ ) for γ < θ < δ.

Let v ∈ T < sub > p </ sub > M be a tangent vector to the manifold at p. Then there is a unique geodesic γ < sub > v </ sub > satisfying γ < sub > v </ sub >( 0 )

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

Let γ be a differentiable curve in M with initial point γ ( 0 ) and initial tangent vector X

A connection ∇ on a vector bundle E → M defines a notion of parallel transport on E along a curve in M. Let γ: → M be a smooth path in M. A section σ of E along γ is said to be parallel if

Let γ be the boundary of B ( z < sub > 0 </ sub >, r ), taken with its positive orientation.

Let γ: → M be a differentiable curve with γ ( 0 )

Let E be a rank k vector bundle over a smooth manifold M and let ∇ be a connection on E. Given a piecewise smooth loop γ: → M based at x in M, the connection defines a parallel transport map P < sub > γ </ sub >: E < sub > x </ sub > → E < sub > x </ sub >.

Let γ be the small circle of radius ε, Γ the larger, with radius R, then

Let γ ( s ) be a plane curve, parameterized by its arclength s. The unit tangent vector to the curve is, by virtue of the arclength parameterization,

Let γ be a periodic orbit through a point p and S be a local differentiable and transversal section of φ through p, called Poincaré section through p.

Let ( R, M, φ ) be a differentiable dynamical system with periodic orbit γ through p. Let

Let M be a connected Riemannian manifold and p a point of M. A map f defined on a neighborhood of p is said to be a geodesic symmetry, if it fixes the point p and reverses geodesics through that point, i. e. if γ is a geodesic and then It follows that the derivative of the map at p is minus the identity map on the tangent space of p. On a general Riemannian manifold, f need not be isometric, nor can it be extended, in general, from a neighbourhood of p to all of M.

Let γ ( s ) be a regular parametric plane curve, where s is the arc length, or natural parameter.

Let T < sup > a </ sup > be the tangent vector to a given geodesic γ, and X < sup > a </ sup > a vector field along γ connecting it to an infinitesimally near geodesic ( the deviation vector ).

Let M be a pseudo-Riemannian manifold ( or any manifold with an affine connection ) and let p be a point in M. Then for every V in T < sub > p </ sub > M there exists a unique geodesic γ: I → M for which γ ( 0 )

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??

: Let U be a simple right R-module and write D

Sylows ' test: Let n be a positive integer that is not prime, and let p be a prime divisor of n. If 1 is the only divisor of n that is equal to 1 modulo p, then there does not exist a simple group of order n.

Let us take a very simple example of a Magical Act: that of a man blowing his nose.

Let us now consider the following very simple program:

One simple way ( at least for mathematicians ) to determine whether an optimization is worthwhile is as follows: Let the original time and space requirements ( generally in Big O notation ) of the algorithm be and.

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 there be N individuals, and to keep this calculation simple, let the individuals be haploid ( i. e. have one copy of each gene ).

Let us be simple.

Let G be a finite simple undirected graph with edge set E. The power set of E becomes a Z < sub > 2 </ sub >- vector space if we take the symmetric difference as addition, identity function as negation, and empty set as zero.

simple: Let Go

Let M < sub > p </ sub > = 2 < sup > p </ sup > − 1 be the Mersenne number to test with p an odd prime ( because p is exponentially smaller than M < sub > p </ sub >, we can use a simple algorithm like trial division for establishing its primality ).

Let C be a simple closed curve on a sphere of radius 1.

Let be the Cartan matrix of the Kac-Moody algebra, and let q be a nonzero complex number distinct from 1, then the quantum group, U < sub > q </ sub >( G ), where G is the Lie algebra whose Cartan matrix is A, is defined as the unital associative algebra with generators ( where λ is an element of the weight lattice, i. e. for all i ), and and ( for simple roots, ), subject to the following relations:

Let be an n-vertex simple graph with no ( r + 1 )- clique and with the maximum number of edges.

Let R be a ring and let U be a simple right R-module.

: Let U be a simple right R-module and write D

: Let U be a simple right R-module and let D

Let R be a simple ring which is not right Artinian.

Suppose that c is a simple closed curve in a closed, orientable surface S. Let A be a tubular neighborhood of c. Then A is an annulus and so is homeomorphic to the Cartesian product of

Let now v and w be two vertices in G. Any spanning tree contains precisely one simple path between v and w. Taking this path in the uniform spanning tree gives a random simple path.

Let G = ( V, E ) be a simple graph and let K consist of all 2-element subsets of V. Then H = ( V, K

As in the film, No fitted himself with metal manual prostheses, but the book describes them as simple pincers ( apparently similar to those of Tee-Hee in Live and Let Die ), and judging by the lack of descriptive detail, they presumably lack the articulation of human hands.

V. Let us pray: O God, who to us in this wonderful Sacrament, bequeathed a memorial of your Passion: grant, we beseech, that we, in worshiping in addition to simple worship, may also mean worshiping in order to receive favor the Holy Mysteries of your body and blood, may within ourselves continually, sensibly perceive the fruit of your redemption.