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Let w < sub > j </ sub > be the ' price ' ( the rental ) of a certain factor j, let MP < sub > j1 </ sub > and MP < sub > j2 </ sub > be its marginal product in the production of goods 1 and 2, and let p < sub > 1 </ sub > and p < sub > 2 </ sub > be these goods ' prices.
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Let and w
Let w denote the weight per unit length of the chain, then the weight of the chain has magnitude
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
She had a related UK single release as " Jennifer " on London HLU 10278 in June 1969 with " Let The Sunshine In " c / w " Easy To Be Hard ", licensed from US Parrot label.
* " Don't Let It Bother You " w. Mack Gordon m. Harry Revel from the film The Gay Divorcee
* " Don't Let Your Love Go Wrong " w. George Whiting & Nat Schwartz m. J. C. Johnson
* " Let Me Sing And I'm Happy " w. m.
* " Let A Smile Be Your Umbrella " w. Irving Kahal & Francis Wheeler m. Sammy Fain
* " Don't Wake Me Up, Let Me Dream " w. L .. Wolfe Gilbert m. Mabel Wayne
* " Let Yourself Go " w. m.
* " Let Me Linger Longer In Your Arms " w. Cliff Friend m. Abel Baer
* " Let The Rest Of The World Go By " w. J. Keirn Brennan m. Ernest R. Ball
* " Open Up The Golden Gates To Dixieland And Let Me Into Paradise " w. Jack Yellen m. Gus Van & Joe Schenck
* " Never Let The Same Bee Sting You Twice " w. m.
* " Let Me Call You Sweetheart " w. Beth Slater Whitson m. Leo Friedman
* " Let Me Live And Stay In Dixieland " w. m.
* " Plant A Watermelon On My Grave And Let The Juice Soak Through " w. m.
* " Let Bygones Be Bygones And Let Us Be Sweethearts Again " w. Alex Rogers m. Bert Williams
* " Let It Alone " w. Alex Rogers m. Bert Williams
* " Please Go ' Way And Let Me Sleep " w. Cecil Mack m. J. Tim Brymn
* " Yes, Let Me Like A Soldier Fall " ( w. Edward Fitzball m. Vincent Wallace )-Ferruccio Giannini on Berliner Records
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 and <
Let ( m, n ) be a pair of amicable numbers with m < n, and write m = gM and n = gN where g is the greatest common divisor of m and n. If M and N are both coprime to g and square free then the pair ( m, n ) is said to be regular, otherwise it is called irregular or exotic.
Let denote the Bézier curve determined by the points P < sub > 0 </ sub >, P < sub > 1 </ sub >, ..., P < sub > n </ sub >.
Let P < sub > F </ sub > be the domain of a prefix-free universal computable function F. The constant Ω < sub > F </ sub > is then defined as
Let M be a smooth manifold and let x be a point in M. Let T < sub > x </ sub > M be the tangent space at x.
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 M be a smooth manifold and let f ∈ C < sup >∞</ sup >( M ) be a smooth function.
Let e be the error in b. Assuming that A is a square matrix, the error in the solution A < sup >− 1 </ sup > b is A < sup >− 1 </ sup > e.
Let us for simplicity take, then < math > 0 < c =- 2a </ math > and.
Let and j
Let x, y, z be a system of Cartesian coordinates in 3-dimensional Euclidean space, and let i, j, k be the corresponding basis of unit vectors.
Let ( A < sub > i </ sub >)< sub > i ∈ I </ sub > be a family of groups and suppose we have a family of homomorphisms f < sub > ij </ sub >: A < sub > j </ sub > → A < sub > i </ sub > for all i ≤ j ( note the order ) with the following properties:
* Let I consist of three elements i, j, and k with i ≤ j and i ≤ k ( not directed ).
Let the mutation rate correspond to the probability that a j type parent will produce an i type organism.
Let J be a directed poset ( considered as a small category by adding arrows i → j if and only if i ≤ j ) and let F: J < sup > op </ sup > → C be a diagram.
Let A be an observable of the system, and suppose the ensemble is in a mixed state such that each of the pure states occurs with probability p < sub > j </ sub >.
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 P < sub > i </ sub > and P < sub > j </ sub > be two program segments.
A more formal way of expressing this is: Let j and k be elements of some finite set K. F is a minimal perfect hash function iff F ( j )
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 E < sub > i </ sub > be a basis of sections of TG consisting of left-invariant vector fields, and θ < sup > j </ sup > be the dual basis of sections of T < sup >*</ sup > G such that θ < sup > j </ sup >( E < sub > i </ sub >) = δ < sub > i </ sub >< sup > j </ sup >, the Kronecker delta.
* Let and be sets representing the non-zero patterns of columns i and j ( below the diagonal only, and including diagonal elements ) of matrices and respectively.
Let Q < sub > n </ sub > denote the m-by-n matrix formed by the first n Arnoldi vectors q < sub > 1 </ sub >, q < sub > 2 </ sub >, …, q < sub > n </ sub >, and let H < sub > n </ sub > be the ( upper Hessenberg ) matrix formed by the numbers h < sub > j, k </ sub > computed by the algorithm:
Let denote the j < sup > th </ sup > bit of x and the j < sup > th </ sup > bit of r. Then
Let where if i and j are neighbors and otherwise.
Let be all information that is common knowledge at time t ( this is often subscripted below the expectation operator ); then the expected value of the realisation of X, j time-steps in the future, can be written equivalently as:
0.434 seconds.