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 us also assume the existence of only one class or type of service, all of which is supplied at the same voltage, phase, etc. to residential, commercial, and industrial customers.

Let us suppose that the animal did not in fact fall into the trap and did not suffer at all, but that we mistakenly believe it did, and say as before that its suffering was an evil thing.

Let Af where the maximization is over all admissible policies Af.

Let them be candidly reviewed under a sense of the difficulty of combining in one system the various sentiments and interests of a continent divided into so many sovereign and independent communities, under a conviction of the absolute necessity of uniting all our councils and all our strength, to maintain and defend our common liberties ...

* 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 us suppose ( as is the practical case ) that the star is sufficiently distant that all light from the star travels in parallel paths to the Earth observer, regardless of where the Earth is in its orbit.

:: Let no-one deceive you by any means, for that day will not come unless the falling away comes first, and the man of sin is revealed, the son of perdition, who opposes and exalts himself above all that is called God or that is worshiped, so that he sits as God in the temple of God, showing himself that he is God. Thess 2: 3-4

Let M be a smooth manifold and let x be a point in M. Let I < sub > x </ sub > be the ideal of all functions in C < sup >∞</ sup >( M ) vanishing at x, and let I < sub > x </ sub >< sup > 2 </ sup > be the set of functions of the form, where f < sub > i </ sub >, g < sub > i </ sub > ∈ I < sub > x </ sub >.

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 be an arbitrary set, and let be the set of all bijective functions from to.

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.

Let us call the class of all such formulas R. We are faced with proving that every formula in R is either refutable or satisfiable.

: Let all behold and glorify Jesus Christ,

Let us face reality that " all businesses recover ", whether they planned for recovery or not, simply because business is about earning money for survival.

Let ( I, ≤) be a directed poset ( not all authors require I to be directed ).

Let ( A < sub > i </ sub >)< sub > i ∈ I </ sub > be a family of groups and suppose we have a family of homomorphisms f < sub > ij </ sub >: A < sub > j </ sub > → A < sub > i </ sub > for all i ≤ j ( note the order ) with the following properties:

Indeed, the great mercy of God who desires that all men should be saved, and Jesus ' tenderness toward children which caused him to say: ' Let the children come to me, do not hinder them ,' allow us to hope that there is a way of salvation for children who have died without Baptism.

Psalms 33: 8-9: Let all the earth fear the LORD: let all the inhabitants of the world stand in awe of him.

Let therefore hatred depart from among you, let your quarrels end, let wars cease, and let all dissensions and controversies slumber.

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

Ritts also worked on other projects, including directing and acting, on Mariah Carey's video collection # 1's ( 1999 ), Jennifer Lopez's sepia video " Ain't It Funny ", Janet Jackson's Design of a Decade 1986 / 1996 ( 1996 ), Intimate Portrait: Cindy Crawford ( 1998 ), Murder in the First ( 1995 ), and Britney Spears ' " Don't Let Me Be The Last To Know ( 2001 ).

In 1984, Vaughan participated in one of the more unusual projects of her career, The Planet is Alive, Let It Live a symphonic piece composed by Tito Fontana and Sante Palumbo on Italian translations of Polish poems by Karol Wojtyla, the future Pope John Paul II.

Darrell's projects " Let the River Flow " and " Freedom " both garnered Dove award nominations and influenced a new wave of congregational worship.

These included Ferry Aid's cover of " Let It Be " ( 1987 ); a cover of Cole Porter's " Too Darn Hot ", that was included in 1990s Red Hot + Blue album to raise funds for AIDS and HIV research ; re-making Lene Lovich's " Rage " alongside her to be included in PETAs album ( 1991 ) in favour of a wildlife campaign ; and performing twice on Big Spender's Red Hot and Dance events to support various AIDS projects ( in both December 1994 and November 2004 ).

" In the 2000s, she started singing background vocals on hip-hop songs for rappers such as Kanye West (" Slow Jamz " and " Never Let Me Down " from The College Dropout ), 50 Cent (" Back Down " from Get Rich Or Die Tryin '), and Eve as well as songwriting for other artist's projects.

Bonnet's post-Alcatrazz projects have all been short-lived and included Blackthorne ( working with ex-Balance guitarist Bob Kulick, brother of Kiss guitarist Bruce Kulick ), backing vocals for the Danish heavy metal band Pretty Maids ' Future World and numerous session work for Forcefield, appearing on To Oz and Back and Let The Wild Run Free.

Wonderworks has been involved in 6 projects for children: Kidsarts in the Apple, a two-day festival celebrating the creativity of city kids and the myriad arts-in-education programs in New York City ; the 20th Anniversary Retrospective of the Touchstone Center for Children which involved conferences, special events, and publications ; Let the River Connect Us, an award -

: Take the large white gooseberries before they are very ripe, but at full growth, stone and wash them, and to a pound of gooseberries put a pound and half of sugar, beat very fine, and half a pint of water ; set them on the fire ; when the sugar is melted, let them boil, but not too fast ; take them off once or twice, that they may not break ; when they begin to look clear, they are enough: Let them stand all night in the pan they are boiled in, with a paper laid close to them ; the next day scald them very well, and let them stand a day or two ; then lay them on plates, sift them with sugar very well, and put them in the stove, turning them every day till they are dry ; the third time of turning, you may lay them on a sieve, if you please ; when they are pretty dry, place them in a box, with paper betwixt every row.

... Let them show where I am a heretic, or dry up their spittle.

Let it dry in the sun for a day or two.

Let the body down slowly, taking at least five seconds for the letting down.

Joe Kennedy, vice president of marketing for GM marque Saturn, accepted concerns regarding the EV1's cost, the outdated lead-acid battery technology, and the car's limited range, saying " Let us not forget that technology starts small and grows slowly before technology improves and costs go down.

She invites him to take a walk with her, and the two wander from one end of Florence to the other as the sun slowly sets and the night comes on (" Let ’ s Walk ").

Let Senora Brannon live in her father's house for a time.

Let me quote him even more fully, for his analysis is important to my theme.

Let us not confuse the issue by labeling the objective or the method `` psychoanalytic '', for this is a well established term of art for the specific ideas and procedures initiated by Sigmund Freud and his followers for the study and treatment of disordered personalities.

Let us survey for a moment the development of modern thought -- turning our attention from the Reformation toward the revolutionary and romantic movements that follow and dwelling finally on more recent decades.

Let us prepare for peace, instead of for a war which would mean the end of civilization.

He heard the words: `` Rock of Ages, cleft for me, Let me hide myself in Thee!!

-- Let me help him, for the love of God!!

Let this boil gently for twenty minutes, then strain.

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 us now put some flesh on the theoretical bones we have assembled by giving illustrations of roleplaying used for evaluation and analysis.

Let us therefore consider each of the three types of cost in turn, recognizing that this simplified classification is used only for illustrative purposes ; ;

He said, `` Let me take her blows, for there are demons in me too ''.

Parsons had already acted as assistant engineer on The Beatles ' Abbey Road and Let It Be, had recently engineered Pink Floyd's The Dark Side of the Moon, and had produced several acts for EMI Records.

Let him call for the elders of the church, and let them pray over him, anointing him with oil in the name of the Lord ; and the prayer of faith will save the sick man, and the Lord will raise him up ; and if he has committed sins, he will be forgiven.

In 2009, Toyota commissioned Haden to perform three songs for television commercials for the third-generation Toyota Prius, including an a cappella version of the Bellamy Brothers 1970s song " Let Your Love Flow ".

For a compilation album of the Glenmark duo Gemini, Andersson had Björn Ulvaeus write new Swedish lyrics for the re-recording of two old songs ; Ulvaeus also wrote new English lyrics to older Swedish language songs for opera singer Anne Sofie von Otter tribute album " I Let The Music Speak ".