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 be a simple rectifiable loop in X around P. The ramification index of ƒ at P is

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 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 t and s ( t > s ) be the sides of the two inscribed squares in a right triangle with hypotenuse c. Then s < sup > 2 </ sup > equals half the harmonic mean of c < sup > 2 </ sup > and t < sup > 2 </ sup >.

: Let ’ s lay off the excessive groaning.

: Let ’ s deal with the common benefits first off,

Let s = x < sub > 1 </ sub > ⊕ ... ⊕ x < sub > n </ sub > and t = y < sub > 1 </ sub > ⊕ ... ⊕ y < sub > n </ sub >.

Proof: Let d be the position of the leftmost ( most significant ) nonzero bit in the binary representation of s, and choose k such that the dth bit of x < sub > k </ sub > is also nonzero.

Let It Be < nowiki >'</ nowiki > s release had attracted attention from the major record labels, and by late 1984 several had expressed interest in signing the Replacements.

* " Identity " / " Let ’ s Submerge " ( July 1978: EMI International, INT 563 )-No.

Let ’ s tell them the truth, that there are no gains without pains, that we are now on the eve of great decisions.

Let ’ s leave it to the gods to set his mind on that.

Traditional Bayram ( Turkey ) | Bayram wishes from the Istanbul Metropolitan Municipality, stating " Let us love, Let us be loved ", in the form of mahya lights stretched across the minaret s of the Sultan Ahmed Mosque ( Istanbul ) | Blue Mosque in Istanbul

It was: Let ’ s try to do something together.

Let c, h, s be the sides of three squares associated with the right

While their next release, " Never to be Forgotten " brought a regional hit, the band ’ s next single, " Let Her Dance " brought the band ’ s first national hit, barely missing the Billboard Hot 100 at 133, though bringing in a Top 40 hit.

Let ’ s first imagine a cube with sides of length 2, and its center positioned at the axis origin.

Given an integer n, choose some integer a < n. Let 2 < sup > s </ sup > d = n − 1 where d is odd.

Many episode titles parodied the titles of Bond films, e. g. “ Live and Let ’ s Dance .”

As well as the songs he would go on to perform on the day, his list included “ All Things Must Pass ” (“ with Leon ”, apparently ) and “ Art of Dying ” − both from All Things Must Pass − and “ Bangla Desh ”’ s B-side, “ Deep Blue ”; Clapton ’ s song “ Let It Rain ” appeared also, implying that the guitarist was expected to have his own solo spot ; while the suggestions for Dylan ’ s set were “ If Not for You ”, “ Watching the River Flow ” ( his recent, Leon Russell-produced single ) and “ Blowin ' in the Wind ”.

Let q be a prime number, s a complex variable, and define a Dirichlet L-function as

While each concert was professionally mastered, the recordings capture everything that happened onstage and for preservation's sake the band chose not to edit anything out, singer / guitarist Guy Picciotto explained to the New York Times "“ We liked this idea of, ‘ Let ’ s just let it be everything ,’ “ Mr. Picciotto said.

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??