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Let be the position vector of some known point in the plane, and let n be a nonzero vector normal to the plane.
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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 ''.
Let and position
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 our position be absolutely clear: An attempt by any outside force to gain control of the Persian Gulf region will be regarded as an assault on the vital interests of the United States of America, and such an assault will be repelled by any means necessary, including military force.
Let T < sub > ij </ sub > := e < sub > ij </ sub >( 1 ) be the elementary matrix with 1's on the diagonal and in the ij position, and 0's elsewhere ( and i ≠ j ).
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 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 p < sub > i </ sub > be the best known position of particle i and let g be the best known position of the entire swarm.
Let us introduce the factor f < sub > j </ sub > that describes how the actual charge density differs from the average and itself on a position on the surface of the j-th conductor:
: Let our position be absolutely clear: An attempt by any outside force to gain control of the Persian Gulf region will be regarded as an assault on the vital interests of the United States of America, and such an assault will be repelled by any means necessary, including military force.
Let these rotations and reflections operate on all points on the plane, and let these points be represented by position vectors.
Let r ( t ) be a curve in Euclidean space, representing the position vector of the particle as a function of time.
Let the four-dimensional Cartesian coordinates be denoted ( w, x, y, z ) where ( x, y, z ) represent the Cartesian coordinates of the normal position vector r. The three-dimensional momentum vector p is associated with a four-dimensional vector on a three-dimensional unit sphere
" However, Frank Knight, founder of the Chicago School of Economics, wrote in a scholarly review of the Wootton book: " Let me repeat that the Wootton book is in no logical sense an answer to The Road to Serfdom, whatever may be thought of the cogency of Hayek's argument, or the soundness of his position.
" Let It Be " made number one in the UK Singles Chart in its first week on 4 April 1987, and remained at that position for three weeks.
On 27 January 2005, a Farnair Hungary Let L-410 aircraft was carrying out a non-directional beacon let-down with radar assistance at Iaşi Airport, Romania, but when the crew notified air traffic control of their position over the airport beacon and their intention to turn right outbound, they were seen to turn left.
0.601 seconds.