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Page "Cauchy–Schwarz inequality" ¶ 15
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Let and u
Let the quantities u and v be the horizontal and vertical components of the velocity field of a steady incompressible, irrotational flow in two dimensions.
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.
Let m < sub > 1 </ sub > and m < sub > 2 </ sub > be the masses, u < sub > 1 </ sub > and u < sub > 2 </ sub > the velocities before collision, and v < sub > 1 </ sub > and v < sub > 2 </ sub > the velocities after collision.
Let Y = u ( X < sub > 1 </ sub >, X < sub > 2 </ sub >, ..., X < sub > n </ sub >) be a statistic whose pdf is g ( y ; θ ).
Let u = x < sup > 3 </ sup >.
Let y be a function given by the sum of two functions u and v, such that:
Let x: y: z be a variable point in trilinear coordinates, and let u
Let vectors < u > a </ u >, < u > b </ u >, < u > c </ u > and < u > h </ u > determine the position of each of the four orthocentric points and let < u > n </ u > = (< u > a </ u > + < u > b </ u > + < u > c </ u > + < u > h </ u >) / 4 be the position vector of N, the common nine-point center.

Let and v
Let the input power to a device be a force F < sub > A </ sub > acting on a point that moves with velocity v < sub > A </ sub > and the output power be a force F < sub > B </ sub > acts on a point that moves with velocity v < sub > B </ sub >.
Let the ship moves with velocity v. In the ship reference frame, capturing the 4 hydrogen we losing a momentum:
Let A be an m × n matrix, with column vectors v < sub > 1 </ sub >, v < sub > 2 </ sub >, ..., v < sub > n </ sub >.
Let x = x ( u, v, w ), y = y ( u, v, w ), z = z ( u, v, w ) be defined and smooth in a domain containing, and let these equations define the mapping of into.
Let v be the last vertex before u on this path.
Here is Leibniz's argument: Let u ( x ) and v ( x ) be two differentiable functions of x.
Let f = uv and suppose u and v are positive functions of x.
Let u and v be continuous functions in x, and let dx, du and dv be infinitesimals within the framework of non-standard analysis, specifically the hyperreal numbers.
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 v be an arbitrary vector in V. There exist unique scalars such that:
Let S be the number of particles in the swarm, each having a position x < sub > i </ sub > ∈ < sup > n </ sup > in the search-space and a velocity v < sub > i </ sub > ∈ < sup > n </ sup >.
Proof: Let ( v, λ ) be an eigenvector-eigenvalue pair for a matrix A.
Let s be the function mapping the sphere to itself, and let v be the tangential vector function to be constructed.

Let and be
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??

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