Let ( q < sub > 1 </ sub >, w, x < sub > 1 </ sub > x < sub > 2 </ sub >... x < sub > m </ sub >) ( q < sub > 2 </ sub >, y < sub > 1 </ sub > y < sub > 2 </ sub >... y < sub > n </ sub >) be a transition of the GPDA

Let p, q > 2 be two distinct prime numbers.

Let q < sup >*</ sup >

Let T: X → X be a contraction mapping on X, i. e.: there is a nonnegative real number q < 1 such that

# Let p = ( p < sub > 1 </ sub >, p < sub > 2 </ sub >) and q = ( q < sub > 1 </ sub >, q < sub > 2 </ sub >) be elements of W, that is, points in the plane such that p < sub > 1 </ sub > = p < sub > 2 </ sub > and q < sub > 1 </ sub > = q < sub > 2 </ sub >.

Let q and r denote the inclusion map and the sign map respectively, so that

Let q denote the probability that a given neutron induces fission in a nucleus.

Let ( S, Σ, μ ) be a measure space and let 1 ≤ p, q ≤ ∞ with 1 / p + 1 / q = 1.

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

Let p < sub > 1 </ sub > and p < sub > 2 </ sub > be any two points on l < sub > 1 </ sub >, and let q < sub > 1 </ sub > and q < sub > 2 </ sub > be any two points on l < sub > 2 </ sub >.

Let A be the matrix of the quadratic form q in a given basis.

Let q be the probability of losing ( e. g. for American double-zero roulette, it is 10 / 19 for a bet on black or red ).

Let q denote the Lorentzian quadratic form on R < sup > n + 2 </ sup > defined by

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 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 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 R be the quadratic mean ( or root mean square ).

Let V be a vector space over a field K, and let be a quadratic form on V. In most cases of interest the field K is either R, C or a finite field.

Indeed, let K be an imaginary quadratic field with class field H. Let E be an elliptic curve with complex multiplication by the integers of K, defined over H. Then the maximal abelian extension of K is generated by the x-coordinates of the points of finite order on some Weierstrass model for E over H.

Let Af denote the form of Af.

Let us assume that Af is identical to the form of an occurrence Af which preceded Af in the text.

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 G be a set and let "~" denote an equivalence relation over G. Then we can form a groupoid representing this equivalence relation as follows.

In his Commentary on Daniel, he noted, “ Let us not follow the opinion of some commentators and suppose him to be either the Devil or some demon, but rather, one of the human race, in whom Satan will wholly take up his residence in bodily form .” In interpreting 2 Thessalonians's claim that the Antichrist will sit in God's temple, Jerome preferred the view that the " temple " should be interpreted as the Church, not as the Temple in Jerusalem.

Let be any basis for the column space of and place them as column vectors to form the × matrix.

Let be an oriented smooth manifold of dimension n and let be an n-differential form that is compactly supported on.

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

Let φ ( ξ, η, ζ ) be an arbitrary function of three independent variables, and let the spherical wave form F be a delta-function: that is, let F be a weak limit of continuous functions whose integral is unity, but whose support ( the region where the function is non-zero ) shrinks to the origin.

Let us now imagine a Lorentz transformation to have been performed on the space and time coordinates, and on the derivative operators, which form a covariant vector.

Let the curve be a unit speed curve and let t = u × T so that T, u, t form an orthonormal basis: the Darboux frame.

When Romulus complains that a low fertility rate has rendered the abduction of the Sabine women pointless, Juno, in her guise as the birth goddess Lucina, offers an instruction: " Let the sacred goat go into the Italian matrons " ( Italidas matres … sacer hirtus inito, with the verb inito a form of inire ).

Let p be the nth decimal of the nth number of the set E ; we form a number N having zero for the integral part and p + 1 for the nth decimal, if p is not equal either to 8 or 9, and unity in the contrary case.

Much of this documentation is in the form of illegal ( but widely available ) bootleg recordings, and is recounted in the book Get Back: The Unauthorized Chronicle of the Beatles ' Let It Be Disaster by Doug Sulpy and Ray Schweighardt.

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

Let L ( x ) be the interpolation polynomial in the Lagrange form for the given data points, then

The maxim fiat justitia, ruat caelum (" Let justice be done, though the heavens fall "), used by Lord Mansfield in Somersett's Case and in reversing the outlawry of John Wilkes, and in the alternate form fiat iustitia, et pereat mundus by Ferdinand of Habsburg, is sometimes attributed to Piso, but this is disputed.

Let X be a g-dimensional torus given as X = V / L where V is a complex vector space of dimension g and L is a lattice in V. Then X is an abelian variety if and only if there exists a positive definite hermitian form on V whose imaginary part takes integral values on L × L.

Let ω be a form on a n-dimensional real vector space V, ω ∈ Λ < sup > 2 </ sup >( V ).

Let V = TCP < sup > 1 </ sup > be the bundle of complex tangent vectors having the form a ∂/∂ z at each point, where a is a complex number.