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 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 q be a quadratic form defined on an n-dimensional real vector space.

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 p be an odd prime number.

Let p be an odd prime.

Let π < sub > 2 </ sub >( x ) denote the number of primes p ≤ x such that p + 2 is also prime.

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 p be an odd prime and a an integer coprime to p. Then

Let π ( x, a, d ) denote the number of prime numbers in this progression which are less than or equal to x.

Let p be an odd prime.

* Let p be a prime number.

|| x ||< sub > p </ sub > on Q for some prime p. Let R be the subring of K defined by

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 ).

U Nu, after his release from prison in October 1966, had left Burma in April 1969, and formed the Parliamentary Democracy Party ( PDP ) the following August in Bangkok, Thailand with the former Thirty Comrades, Bo Let Ya, co-founder of the CPB and former Minister of Defence and deputy prime minister, Bo Yan Naing, and U Thwin, ex-BIA and former Minister of Trade.

For example, let P be an irreducible polynomial with integer coefficients and p be a prime number which does not divides the leading coefficient of P. Let Q be the polynomial over the finite field with p elements, which is obtained by reducing modulo p the coefficients of P. Then, if Q is separable ( which is the case for every p but a finite number ) then the degrees of the irreducible factors of Q are the lengths of the cycles of some permutation of the Galois group of P.

Let P be a finitely generated projective module over a commutative ring R and X be the spectrum of R. The rank of P at a prime ideal in X is the rank of the free-module.

Let R be the ring of integers of an algebraic number field K and P a prime ideal of R. For each extension field L of K we can consider the integral closure S of R in L and the ideal PS of S. This may or may not be prime, but assuming is finite it is a product of prime ideals

Let p be a prime number and let K = Q ( μ < sub > p </ sub >) be the field generated over Q by the pth roots of unity.

* Let p be any prime, and let μ < sub > p < sup >∞</ sup ></ sub > denote the set of all pth-power roots of unity in C, i. e.

Let p be an odd prime and let.

Let R be a ( Noetherian, commutative ) regular local ring and P and Q be prime ideals of R. In 1958, Serre realized that classical algebraic-geometric ideas of multiplicity could be generalized using the concepts of homological algebra.

Let R ⊆ S be a map of complete local domains, and let Q be a height one prime ideal of S lying over xR, where R and R / xR are both regular.

Let n be a composite integer with prime factor p. By Fermat's little theorem, we know that for all integers a coprime to p and for all positive integers K: