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Let u, v be arbitrary vectors in a vector space V over F with an inner product, where F is the field of real or complex numbers.
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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 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 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 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 >.
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 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 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 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 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 it be granted then that the theological differences in this area between Protestants and Roman Catholics appear to be irreconcilable.
Let us therefore put first things first, and make sure of preserving the human race at whatever the temporary price may be ''.
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