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Let be a number field with ring of integers, and a nonzero ideal of.
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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 number
Let us look at the heavy-electrical-goods industry in which General Electric, Westinghouse and a number of other manufacturers were recently convicted of engaging in a conspiracy to rig prices and allocate the market.
* Let Q be a set enclosed between two step regions S and T. A step region is formed from a finite union of adjacent rectangles resting on a common base, i. e. S ⊆ Q ⊆ T. If there is a unique number c such that a ( S ) ≤ c ≤ a ( T ) for all such step regions S and T, then a ( Q )
They have appeared together in a number of films, including Edie & Pen ( 1996 ), American Perfekt ( 1997 ) and Let the Devil Wear Black ( 1999 ).
Suppose that in a mathematical language L, it is possible to enumerate all of the defined numbers in L. Let this enumeration be defined by the function G: W → R, where G ( n ) is the real number described by the nth description in the sequence.
Peaking at number six in the UK, the album yielded the hits " Day-In, Day-Out " ( his 60th single ), " Time Will Crawl ", and " Never Let Me Down ".
It is unclear which version of the paradox is stronger .< ref group =" Note "> Let be the number of civilizations ( per unit volume ) that can be seen at a radius.
Gloria Gaynor ( born September 7, 1949 ) is an American singer, best known for the disco era hits ; " I Will Survive " ( Hot 100 number 1, 1979 ), " Never Can Say Goodbye " ( Hot 100 number 9, 1974 ), " Let Me Know ( I Have a Right )" ( Hot 100 number 42, 1980 ) and " I Am What I Am " ( R & B number 82, 1983 ).
Let r be a non zero real number and let the r < sup > th </ sup > power mean ( M < sup > r </ sup > ) of a series of real variables ( a < sub > 1 </ sub >, a < sub > 2 </ sub >, a < sub > 3 </ sub >, ... ) be defined as
* Let be the least number such that there is a file with length bits that compresses to something shorter.
Let π ( x ) be the prime-counting function that gives the number of primes less than or equal to x, for any real number x.
Also, when The Beatles ' Let It Be was released in 1970, the magazine originally gave the album a poor review, yet in 2003, Rolling Stone ranked it number 86 in the magazine's list of the 500 Greatest Albums of All Time.
Their first album, Let Them Eat Bingo, included the number one single " Dub Be Good to Me ", which caused a legal dispute revolving around allegations of infringement of copyright through the liberal use of unauthorised samples: the bassline was a note-for-note lift from " The Guns of Brixton " by The Clash and the lyrics borrowed heavily from " Just Be Good to Me " by The S. O. S.
Let and field
Let V and W be vector spaces over the same field K. A function f: V → W is said to be a linear map if for any two vectors x and y in V and any scalar α in K, the following two conditions are satisfied:
Let H be a Hilbert space, and let H * denote its dual space, consisting of all continuous linear functionals from H into the field R or C. If x is an element of H, then the function φ < sub > x </ sub >, defined by
Let C be the category of vector spaces K-Vect over a field K and let D be the category of algebras K-Alg over K ( assumed to be unital and associative ).
Let K be a topological field, namely a field with a topology such that addition, multiplication, and division are continuous.
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 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.
Let V be a vector space over a field K, and let be a quadratic form on V. In most cases of interest the field K is either R, C or a finite field.
Let the field K be the set R of real numbers, and let the vector space V be the Euclidean space R < sup > 3 </ sup >.
Let K be R, C, or any field, and let V be the set P of all polynomials with coefficients taken from the field K.
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