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Let and S
* 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 )
Let S ( fig. 5 ) be any optical system, rays proceeding from an axis point O under an angle u1 will unite in the axis point O ' 1 ; and those under an angle u2 in the axis point O ' 2.
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 ").
Using terms from formal language theory, the precise mathematical definition of this concept is as follows: Let S and T be two finite sets, called the source and target alphabets, respectively.
Let S be a vector space over the real numbers, or, more generally, some ordered field.
* Let A be a commutative ring with unity and let S be a multiplicative subset of A.
Let ( S ,*) be a set S with a binary operation * on it ( known as a magma ).
* Bowman, Durrell S. " Let Them All Make Their Own Music: Individualism, Rush and the Progressive / Hard Rock Alloy ," in Progressive Rock Reconsidered, Kevin Holm-Hudson ( ed ), Routledge, 2002.
Let S be a set of languages that is nontrivial, meaning
Let be a non-negative real-valued function of the interval, and let < math > S =
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.
A possible definition of spoiling based on vote splitting is as follows: Let W denote the candidate who wins the election, and let X and S denote two other candidates.
Let S be a subgroup of G, and let N be a normal subgroup of G. Then:
Let ( S, f ) be a game with n players, where S < sub > i </ sub > is the strategy set for player i, S = S < sub > 1 </ sub > × S < sub > 2 </ sub > ... × S < sub > n </ sub > is the set of strategy profiles and f =( f < sub > 1 </ sub >( x ), ..., f < sub > n </ sub >( x )) is the payoff function for x S. Let x < sub > i </ sub > be a strategy profile of player i and x < sub >- i </ sub > be a strategy profile of all players except for player i. When each player i < nowiki >

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 group
* Let H be a group, and let G be the direct product H × H. Then the subgroups
The Supremes, The group that made Ross famous and without which there probably wouldn't be any Diana Ross, scored a handful of hits in the disco clubs without Ross, most notably 1976's " I'm Gonna Let My Heart Do the Walking " and, their last charted single before disbanding, 1977's " You're My Driving Wheel ".
Moving to groups in general, let H be a subgroup of some group G. Let ~ be an equivalence relation on G, such that a ~ b ↔ ( ab < sup >− 1 </ sup > ∈ H ).
Let function composition interpret group multiplication, and function inverse interpret group inverse.
Let function composition, notated by infix, interpret the group operation.
" Let there arise from you a group of people inviting to what is good, enjoining what is right, and forbidding what is wrong ; these are the ones who will be successful.
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.
A discussion group called Let Lawrence Live was formed by the English department at the university and dozens from the Humanities department gathered on the Kansas campus in front of the Memorial Campanile and lit candles in a peace vigil.
Let G be a group.
Let G be a group.
Sylows ' test: Let n be a positive integer that is not prime, and let p be a prime divisor of n. If 1 is the only divisor of n that is equal to 1 modulo p, then there does not exist a simple group of order n.
Let G be a group with identity element e, N a normal subgroup of G ( i. e., N ◁ G ) and H a subgroup of G. The following statements are equivalent:
In 1988, the group released the album Let It Be, featuring cover versions of all the songs from the Beatles album of the same name, with the exception of the title track, which they did not record owing to lack of studio time, and " Maggie Mae ", which was replaced by the German anthems " Auf der Lüneburger Heide " and " Was Gleicht Wohl Auf Erden ".
On the Let it Be album where Preston's performances are used the song credits list " with Billy Preston ", clearly identifying him as separate from the main group, yet also giving him a level of individuality that separated him from studio session players.
Let A be an abelian group and f and g be two group homomorphisms from A into itself.
Suppose G is an ordered abelian group, meaning an abelian group with a total ordering "<" respecting the group's addition, so that a < b if and only if a + c < b + c for all c. Let I be a well-ordered subset of G, meaning I contains no infinite descending chain.
According to the jacket notes of the Let Freedom Sing CD set, Crothers was part of the music group The Ramparts who sang A. C. Bilbrew's " The Death of Emmett Till ".
Originally known as The Hi-Fi's, the group changed its name to The 5th Dimension in late 1966 and was best-known during the late 1960s and early 1970s for popularizing the hits " Up, Up and Away ", " Stoned Soul Picnic ", " Aquarius / Let the Sunshine In ", " Wedding Bell Blues ", " One Less Bell to Answer ", "( Last Night ) I Didn't Get to Sleep at All ", and The Magic Garden LP.
The group performed and sang a medley consisting of " What the World Needs Now Is Love " and The Beatles ' " All You Need Is Love " on 23 February 1969 and performed and sang " Aquarius / Let the Sunshine In " on 18 May 1969, the day after the medley fell from the Hot 100 summit.
The group came back for the last fifteen minutes of the show and sang their hits " Up, Up and Away ", " One Less Bell to Answer ", " Stoned Soul Picnic ", " Wedding Bell Blues ", and finished up with " Aquarius / Let the Sunshine In ".
Even though group member Geri Halliwell had returned to the group at this point, she does not take part in this song as with " Let Love Lead the Way ", which signals her departure from the group in the concert's storyline ( performing " Viva Forever " when Geri is leveled under the stage ).

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