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Let and U
The Beatles ' 1968 track " Back in the U. S. S. R " references the instrument in its final verse (" Let me hear your balalaikas ringing out / Come and keep your comrade warm ").
: Let U be a simple right R-module and write D
Let U and V be two open sets in R < sup > n </ sup >.
Let U be an open subset of R < sup > n </ sup > and f: U → R a function.
Consider an open subset U of the complex plane C. Let a be an element of U, and f: U
Weeks later the group's success broke wide open, with " Aquarius / Let the Sunshine In " from the musical Hair topping the Hot 100 in April and May and " Wedding Bell Blues " doing so in November, with a U. S. # 20 cover of Neil Sedaka's " Workin ' On A Groovy Thing " in-between.
Al Gore used " Let the Day Begin " as his campaign song in the 2000 U. S. Presidential Election and Tom Vilsack used it as his song during his brief 2008 U. S. Presidential Election campaign.
They distinguish the struck ( yàle ), including both beaten and plucked, and the blown ( fêe ), as revealed by Ruth Stone in Let the Inside Be Sweet: the interpretation of music among the Kpelle of Liberia, 1982, Indiana U. Press ( Kartomi, 1990 ).
Let U, V, and W be vector spaces over the same field with given bases, S: V → W and T: U → V be linear transformations and ST: U → W be their composition.
Kilroy went Platinum in 1983, boasting two Top Ten hits, the synthesizer-based " Mr. Roboto " (# 3 U. S .) and power ballad " Don't Let It End.
All of his studio albums and EPs charted on the Billboard 200, and many of his singles —" Eazy-Duz-It ", " We Want Eazy ", " Real Muthaphuckkin G's ", and " Just tah Let U Know "— also charted in the U. S. On March 30, 1995, four days after Eazy-E's death, Tom Elerwine, a Daily Arts editor for The Michigan Daily covered Eazy's career in a feature story.
The followup single, " Never Let You Go ", failed to chart in the U. S., but did reach No. 42 in the UK Singles Chart and No. 18 in the Canadian charts.
The album was propelled by four hits, " Hold My Hand " ( U. S. No. 10 ), " Let Her Cry " ( U. S. No. 9 ), " Only Wanna Be with You " ( U. S. No. 6 ), and " Time " ( U. S. No. 14 ).
* Let U be a random variable constructed as U =

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??

Let and functor
Let J and C be categories with J a small index category and let C < sup > J </ sup > be the corresponding functor category.
Let F be an arbitrary functor from C to Set.
: Let X be a projective scheme over C. Then the functor associating the coherent sheaves on X to the coherent sheaves on the corresponding complex analytic space X < sup > an </ sup > is an equivalence of categories.
Let ( C, F ) be a concrete category ( i. e. F: C → Set is a faithful functor ), let X be a set ( called basis ), A ∈ C an object, and i: X → F ( A ) a map between sets ( called canonical injection ).
Let L / k be a finite extension of fields, and X a variety defined over L. The functor from k-schemes < sup > op </ sup > to sets is defined by
Let be the functor taking each graph to the set of its edges, and let be ( a functor selecting ) some particular set: then is the category of graphs whose edges are labelled by elements of.
* Let F: Set → Set be the functor which maps every set to the empty set and every function to the empty function.
Let P be the power set construction on the category of sets, considered as a covariant functor.
Let C be a category, and let F be a functor from C to the category of sets Set.
Let c be an object of the category C, and consider the functor Hom (−, c ).
Let F be a functor from the category of ringed spaces to the category of sets, and let G ⊆ F. Suppose that this inclusion morphism G → F is representable by open immersions, i. e., for any representable functor Hom (−, X ) and any morphism Hom (−, X )→ F, the fibered product G ×< sub > F </ sub > Hom (−, X ) is a representable functor Hom (−, Y ) and the morphism Y → X defined by the Yoneda lemma is an open immersion.
Let C be a category with binary products and let Y and Z be objects of C. The exponential object Z < sup > Y </ sup > can be defined as a universal morphism from the functor –× Y to Z.
Let be a compact group and let be the forgetful functor from finite-dimensional complex representations of G to complex finite-dimensional vector spaces.

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