Let Af denote the form of Af.

Let denote the Bézier curve determined by the points P < sub > 0 </ sub >, P < sub > 1 </ sub >, ..., P < sub > n </ sub >.

Let X denote a Cauchy distributed random variable.

Let w denote the weight per unit length of the chain, then the weight of the chain has magnitude

Let denote the equivalence class to which a belongs.

Let '~' denote an equivalence relation over some nonempty set A, called the universe or underlying set.

Let G denote the set of bijective functions over A that preserve the partition structure of A: ∀ x ∈ A ∀ g ∈ G ( g ( x ) ∈ ).

Let G be a set and let "~" denote an equivalence relation over G. Then we can form a groupoid representing this equivalence relation as follows.

Let R denote the field of real numbers.

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.

Let ε ( n ) denote the energy of a particle in state n. As the particles do not interact, the total energy of the system is the sum of the single-particle energies.

Let denote the space of scoring functions.

Let the line of symmetry intersect the parabola at point Q, and denote the focus as point F and its distance from point Q as f. Let the perpendicular to the line of symmetry, through the focus, intersect the parabola at a point T. Then ( 1 ) the distance from F to T is 2f, and ( 2 ) a tangent to the parabola at point T intersects the line of symmetry at a 45 ° angle.

Let us denote the time at which it is decided that the compromise occurred as T.

Let denote the sequence of convergents to the continued fraction for.

Let us denote the mutually orthogonal single-particle states by and so on.

That is, Alice has one half, a, and Bob has the other half, b. Let c denote the qubit Alice wishes to transmit to Bob.

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

If V is a real vector space, then we replace V by its complexification V ⊗< sub > R </ sub > C and let g denote the induced bilinear form on V ⊗< sub > R </ sub > C. Let W be a maximal isotropic subspace, i. e. a maximal subspace of V such that g |< sub > W </ sub > = 0.

Let Q ( x ) denote the number of square-free ( quadratfrei ) integers between 1 and x.

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 π < sub > 2 </ sub >( x ) denote the number of primes p ≤ x such that p + 2 is also prime.

Let be a sequence of independent and identically distributed variables with distribution function F and let denote the maximum.

Let him try another boy ...

Col 3: 16 " Let the word of Christ dwell in you believers richly, teaching and admonishing one another in all wisdom, singing psalms and hymns and spiritual songs, with thankfulness in your hearts to God.

( K. 318 ) Let not a man consent to do those things to another which, he knows, will cause sorrow.

In another experiment, subjects with autism and subjects without autism interpreted ideological and religious sayings ( for example, " Let a thousand flowers bloom " or " To everything there is a season ").

Despite this, the number ends with another example of Sullivan's counterpoint, with the chorus singing the second melody of the piece (" Let us gaily tread the measure ") while the orchestra plays the first (" Climbing over rocky mountain ").

* Let N < sub > h </ sub > be the number of non selfcrossing paths for moving a tower of h disks from one peg to another one.

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

This is particularly true for films that are remade from films produced in another language, such as: Point of No Return ( from the French Nikita ), Vanilla Sky ( from the Spanish Abre los ojos ), The Magnificent Seven ( from the Japanese Seven Samurai ), A Fistful of Dollars ( from the Japanese Yojimbo ), The Departed ( from Hong Kong's Infernal Affairs ), and Let Me In ( from the Swedish film Let the Right One In or Låt den rätte komma in ).

Robinson would follow a similar approach with his next album, Warm Thoughts, which produced another top 40 hit, " Let Me Be the Clock ", though it didn't repeat the success of " Cruisin '".

His motto was " Alterius non sit qui suus esse potest " which means " Let no man belong to another who can belong to himself.

More hits followed into 1971 including " Promises, Promises " (# 19, 1968 ); " Who Is Gonna Love Me " (# 32, 1968 ) with " B " side, "( There's ) Always Something There to Remind Me " becoming another double-sided hit ; " I'll Never Fall in Love Again " (# 6, 1969 ); " You've Lost That Lovin ' Feelin '" (# 15, 1969 ); " This Girl's in Love with You " (# 7, 1969 ); " Make It Easy on Yourself " (# 37, 1970 ); " Who Is Gonna Love Me " (# 33, 1968 ); " The April Fools " (# 37, 1969 ); " Let Me Go to Him " (# 32, 1970 ); and " Paper Mache " (# 43, 1970 ).

Let the number of particles with the same energy be, the number of particles possessing another energy be, and so forth for all the possible energies

Death to Israel ", and at another: " Let us damn America, let us damn Israel, let us damn them and their allies until death ".

In the late 70s, Capitol's parent company EMI later purchased United Artists Records and Capitol gained the American rights to the Let It Be soundtrack album ( along with the America rights to another, earlier, UA Beatles movie soundtrack LP, 1964's A Hard Day's Night ).

During the September 2008 discussion between the Slovenian philosopher Slavoj Žižek and Bernard-Henri Lévy on the issues surrounding the historical and social significance of May 1968 in France, Žižek brought up Underground and Kusturica to Lévy by saying: " Let me find another point of contact with you.

According to another source, Noel told Liam and the rest of the group after having heard them play for the first time: " Let me write your songs and I'll take you to superstardom, or else you'll rot here in Manchester ".

Barry also composed the music for another Faith film, Never Let Go, orchestrated the score for Mix Me a Person, and composed, arranged and conducted the score for The Amorous Prawn.

After another five-year layoff, Zevon signed with industry veteran Danny Goldberg's Artemis Records and again rebounded with the mortality-themed 2000 release Life'll Kill Ya, containing the hymn-like " Don't Let Us Get Sick " and an austere version of Steve Winwood's 1980s hit " Back in the High Life Again ".

Let there be a system or piece of substance a of amount m < sub > a </ sub > and another piece of substance b of amount m < sub > b </ sub > which can be combined without interaction.

Let us, the inhabitants of the Cape Colony, be swift to recognize that we are one people, cast together under a glorious flag of liberty, with heads clear enough to appreciate the freedom we enjoy, and hearts resolute to maintain our true privileges ; let us desist from reproaching and insulting one another, and, rejoicing that we have this goodly land as a common heritage, remember that by united action only can we realize its grand possibilities.

Later in the same rally another Reform Party supporter stood up and said “ Let them go.

Goo Goo Dolls plan to release another single from Let Love In, " Without You Here ", as well as a song from the July 2007 Transformers movie called " Before It's Too Late ", originally titled " Fiction ".

In interviews on the Galaxie 500 DVD Don't Let Our Youth Go to Waste, Wareham cites Spacemen 3 as another key inspiration.

Glenn Cowan later bought a T-shirt with a red, white and blue, peace emblem flag and the words " Let It Be ," which he presented to Zhuang Zedong at another chance meeting.