Let P be the root of the unbalanced subtree, with R and L denoting the right and left children of P respectively.

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.

Let L be a first-order language.

Let f, g belong to L < sup > 1 </ sup >( R < sup > n </ sup >).

Let L be an ordered set, called a concrete set and let L ′ be another ordered set, called an abstract set.

Let L < sub > 1 </ sub >, L < sub > 2 </ sub >, L ′< sub > 1 </ sub > and L ′< sub > 2 </ sub > be ordered sets.

Let us suppose that L is a complete lattice and let f be a monotonic function from L into L. Then, any x ′ such that f ′( x ′) ≤ x ′ is an abstraction of the least fixed-point of f, which exists, according to the Knaster – Tarski theorem.

Theorem: Let R be a Dedekind domain with fraction field K. Let L be a finite degree field extension of K and denote by S the integral closure of R in L. Then S is itself a Dedekind domain.

Let A be the set of all subfields of L that contain K, ordered by inclusion.

Let B be the set of subgroups of Gal ( L / K ), ordered by inclusion.

* " Don't Wake Me Up, Let Me Dream " w. L .. Wolfe Gilbert m. Mabel Wayne

Let us now consider a three-dimensional cubical box that has a side length L ( see infinite square well ).

: Let L be a complete lattice and let f: L → L be an order-preserving function.

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 n denote a complete set of ( discrete ) quantum numbers for specifying single-particle states ( for example, for the particle in a box problem we can take n to be the quantized wave vector of the wavefunction.

In early November 2005, Staind released the limited edition 2-CD / DVD set of Chapter V. The set included several rarities and fan favorites — music videos ; a complete, 36-page booklet with exclusive artwork ; an audio disc with an acoustic rendition of " This is Beetle "; the original, melodic rendition of " Reply "; the previously released B-side singles " Novocaine " and " Let It Out "; and live versions of " It's Been Awhile " and " Falling ", among many others.

Let ( X, d ) be a non-empty complete metric space.

It was backed by the more traditional " Let The Juke Box Keep On Playing ," complete with fiddle, " Western Boogie " bass line, steel guitar and weepy vocal.

Among the more complete rehearsed songs that have been featured on bootlegs are " Watching Rainbows ", " Commonwealth ", Suzy's Parlor ( published under the name Suzy Parker ), and " The Palace of the King of the Birds " ( later recorded but not released by McCartney as " Castle of the King of the Birds "); " All Things Must Pass ", " Let It Down ", " Isn't It A Pity ", and " Hear Me Lord '", later released by Harrison ; " Gimme Some Truth " and " Oh My Love ", later released by Lennon ; and " Teddy Boy " and " Hot as Sun ", later released by McCartney.

Portions of the rooftop concert were seen in the Let It Be film and the Anthology documentary, and three tracks were used for the Let It Be album, while the complete recording has been bootlegged.

Some gadgets from the James Bond film series are featured in the game and are often used to complete particular mission objectives ; for example, in one level the electromagnetic watch from Live and Let Die is used to acquire a jail cell key.

Let us continue on in the direction in which we now are moving, and we shall see ... not a re-establishment of the Union, but a complete and final disruption of it.

Let R ⊆ S be a map of complete local domains, and let Q be a height one prime ideal of S lying over xR, where R and R / xR are both regular.

Let R → S be a local homomorphism of complete local domains.

Let be a complete lattice, with infimum and minimum symbolized by and, respectively.

Let be a complete lattice, with infimum and minimum symbolized by and, respectively.

Let q be a positive integer, and let G be the complete bipartite graph K < sub > q, q < sup > q </ sup ></ sub >.

Let and complete this to get an orthonormal basis at.

Let be a complete n-dimensional Riemannian manifold whose Ricci curvature satisfies the lower bound

It gives a complete history of The Beatles ' recording sessions, from 4 September 1962, shortly after the Beatles had returned to England from Germany, to 2 April 1970, when their final album, Let It Be, was mixed.

One of Kert's last recordings was the 1987 2-CD studio cast album of the complete scores of two George and Ira Gershwin musicals: Of Thee I Sing and its sequel Let ' Em Eat Cake.

The CD reissue of the year 2000 revised the cover art including a different concert photo of Elvis, omitted the track " Let Me Be There ", due to its presence on Elvis: As Recorded Live on Stage in Memphis, and it added the complete album From Elvis Presley Boulevard, Memphis, Tennessee as tracks 10-19-in effect compiling the Graceland sessions rather than reissuing the album.

More audio tracks from Liévin are available on the " In Your Room " singles (" Policy of Truth ", " World in My Eyes ", " Death's Door ", " Never Let Me Down Again " and " Fly on the Windscreen "), and the complete soundtrack of Liévin is now available on the re-release on 2DVD set of Devotional.

If the exaltation of the cross has been performed, after the veneration of the cross the augmented litany, " Have mercy on us, O God …," is not pronounced, as is usual at a vigil ; instead the supplicatory litany is immediately said: " Let us complete our morning prayer unto the Lord.

Let the Fire Burn, a complete acoustic album, was released on April 24, 2012.