If the circumstances are faced frankly it is not reasonable to expect this to be true.

If his dancers are sometimes made to look as if they might be creatures from Mars, this is consistent with his intention of placing them in the orbit of another world, a world in which they are freed of their pedestrian identities.

If a work is divided into several large segments, a last-minute drawing of random numbers may determine the order of the segments for any particular performance.

If they avoid the use of the pungent, outlawed four-letter word it is because it is taboo ; ;

If Wilhelm Reich is the Moses who has led them out of the Egypt of sexual slavery, Dylan Thomas is the poet who offers them the Dionysian dialectic of justification for their indulgence in liquor, marijuana, sex, and jazz.

If he is the child of nothingness, if he is the predestined victim of an age of atomic wars, then he will consult only his own organic needs and go beyond good and evil.

If it is an honest feeling, then why should she not yield to it??

If he thus achieves a lyrical, dreamlike, drugged intensity, he pays the price for his indulgence by producing work -- Allen Ginsberg's `` Howl '' is a striking example of this tendency -- that is disoriented, Dionysian but without depth and without Apollonian control.

If love reflects the nature of man, as Ortega Y Gasset believes, if the person in love betrays decisively what he is by his behavior in love, then the writers of the beat generation are creating a new literary genre.

If he is good, he may not be legal ; ;

If the man on the sidewalk is surprised at this question, it has served as an exclamation.

If the existent form is to be retained new factors that reinforce it must be introduced into the situation.

If we remove ourselves for a moment from our time and our infatuation with mental disease, isn't there something absurd about a hero in a novel who is defeated by his infantile neurosis??

If many of the characters in contemporary novels appear to be the bloodless relations of characters in a case history it is because the novelist is often forgetful today that those things that we call character manifest themselves in surface behavior, that the ego is still the executive agency of personality, and that all we know of personality must be discerned through the ego.

If he is a traditionalist, he is an eclectic traditionalist.

If our sincerity is granted, and it is granted, the discrepancy can only be explained by the fact that we have come to believe hearsay and legend about ourselves in preference to an understanding gained by earnest self-examination.

If to be innocent is to be helpless, then I had been -- as are we all -- helpless at the start.

If an unknown force is applied at right angles to the ends of the bar, the bar will rotate, twisting the fiber, until it reaches an equilibrium where the twisting force or torque of the fiber balances the applied force.

If the hair is to be worn up, brushing, backcombing, blow-drying, and twisting are required, as well as the application of sprays and in some cases other holding agents like white or clear glue, egg whites, cornstarch, or gelatin.

If the knee is not tracking over the toes during the movement this results in twisting / shearing of the joint and unwanted torque affecting the ligaments which can soon result in injury.

If he falls in any other position, face up, feet toward the slope, etc., he must first orient his body in the optimal position by twisting his body and using the pick of the ice axe as a pivot point.

If sheaf values are in the category of sets, applying the local identity axiom to the empty family shows that over the empty set, there is at most one section, and applying the gluing axiom to the empty family shows that there is at least one section.

If X is a manifold with some extra structure, we can also take the sheaf of differentiable, or complex-analytic functions.

A local section of a fiber bundle is a continuous map s: U → E where U is an open set in B and π ( s ( x )) = x for all x in U. If ( U, φ ) is a local trivialization of E, where φ is a homeomorphism from π < sup >− 1 </ sup >( U ) to U × F ( where F is the fiber ), then local sections always exist over U in bijective correspondence with continuous maps from U to F. The ( local ) sections form a sheaf over B called the sheaf of sections of E.

If X is an affine algebraic variety, and if U is an open subset of X, then K < sub > X </ sub >( U ) will be the field of fractions of the ring of regular functions on U. Because X is affine, the ring of regular functions on U will be a localization of the global sections of X, and consequently K < sub > X </ sub > will be the constant sheaf whose value is the fraction field of the global sections of X.

If μ < sub > n </ sub > is the sheaf of nth roots of 1 and n is prime to the characteristic of the field k, then H < sup > i </ sup >( X, μ < sub > n </ sub >) is μ < sub > n </ sub >( k ) if i = 0, the group of n-division points of Pic ( X ) if i = 1, and Z / nZ if i = 2, and 0 if i ≥ 3.

* If X is the spectrum of a field K with absolute Galois group G, then étale sheaves over X correspond to continuous sets ( or abelian groups ) acted on by the ( profinite ) group G, and étale cohomology of the sheaf is the same as the group cohomology of G, i. e. the Galois cohomology of K.

* If F is a coherent sheaf ( or G < sub > m </ sub >) then the étale cohomology of F is the same as Serre's coherent sheaf cohomology calculated with the Zariski topology ( and if X is a complex variety this is the same as the sheaf cohomology calculated with the usual complex topology ).

If X has dimension at most n and F is a torsion sheaf then these cohomology groups with compact support vanish if q > 2n, and if in addition X is affine of finite type over a separably closed field the cohomology groups vanish for q > n ( for the last statement, see SGA 4, XIV, Cor. 3. 2 ).

If M is a compact orientable manifold equipped with a smooth metric g, and Ω < sup > k </ sup >( M ) is the sheaf of smooth differential forms of degree k on M, then the de Rham complex is the sequence of differential operators

* If F is a quasi-coherent sheaf of finite presentation on Y ( in particular, if F is coherent ), and if J is the annihilator of F on Y, then, the pullback of the inclusion map, is an injection, and the image of f < sup >*</ sup > J in is the annihilator of f < sup >*</ sup > F </ sup > on X .< ref > EGA IV < sub > 2 </ sub >, Proposition 2. 1. 11 .</ ref >

If f is quasi-compact and L is an invertible sheaf on X, then L is f-ample or f-very ample if and only if its pullback L ′ is f ′- ample or f ′- very ample, respectively .< ref > EGA IV < sub > 2 </ sub >, Corollaire 2. 7. 2 .</ ref > However, it is not true that f is projective if and only if f ′ is projective.

If is coherent, then the converse is true and each sheaf of finite presentation over is coherent.

* Ideal sheaves: If Z is a closed complex subspace of a complex analytic space X, the sheaf I < SUB > Z </ SUB > of all holomorphic functions vanishing on Z is coherent.

If is a coherent analytic sheaf of modules over X < sup > an </ sup > then there exists a coherent algebraic sheaf of-modules and an isomorphism.

If M is a supermanifold of dimension ( p, q ), then the underlying space M inherits the structure of a differentiable manifold whose sheaf of smooth functions is O < sub > M </ sub >/ I, where I is the ideal generated by all odd functions.

If is a closed immersion and is the quasi-coherent sheaf of ideals cutting out Z, then the direct image from the category of quasi-coherent sheaves over Z to the category of quasi-coherent sheaves over X is exact, fully faithful with the essential image consisting of such that.

# Sheaves on topoi: If E is a topos and S is an object in E, the category E < sub > S </ sub > of S-objects is also a topos, interpreted as the category of sheaves on S. If f: T → S is a morphism in E, the inverse image functor f < sup >*</ sup > can be described as follows: for a sheaf F on E < sub > S </ sub > and an object p: U → T in E < sub > T </ sub > one has f < sup >*</ sup > F ( U )

In the case Spec A for a ring A, the global sections of the structure sheaf form A itself, whereas the global sections of here form only the degree-zero elements of S. If we define

If S has the additional property that is a coherent sheaf and locally generates S over ( that is, when we pass to the stalk of the sheaf S at a point x of X, which is a graded algebra whose degree-zero elements form the ring then the degree-one elements form a finitely-generated module over and also generate the stalk as an algebra over it ) then we may make a further construction.

He said: `` If it's all right with you, Mr. Morgan, I'll sleep out here on the couch.

If she sensed any unusual preoccupation on the part of her mother, she did not comment upon it.

If he spun out now, he would join his opponent on the ground.

If it were not for an old professor who made me read the classics I would have been stymied on what to do, and now I understand why they are classics ; ;

`` If you want to see something, he's back on the other side by the trunk of the car ''.

If `` Jack the Courtier '' is really to be taken as Swift, the following remark is obviously Steele's comment on Swift's change of parties and its effect on their friendship: `` I assure you, dear Jack, when I first found out such an Allay in you, as makes you of so malleable a Constitution, that you may be worked into any Form an Artificer pleases, I foresaw I should not enjoy your Favour much longer ''.

If his circumspection in regard to Philip's sensibilities went so far that he even refused to grant a dispensation for the marriage of Amadee's daughter, Agnes, to the son of the dauphin of Vienne -- a truly peacemaking move according to thirteenth-century ideas, for Savoy and Dauphine were as usual fighting on opposite sides -- for fear that he might seem to be favoring the anti-French coalition, he would certainly never take the far more drastic step of ordering the return of Gascony to Edward, even though, as he admitted to the English ambassadors, he had been advised that the original cession was invalid.

If it proclaims that the best is yet to be, it always arouses, at least in the young, either a suspicious question or perhaps the exclamation of the Negro youth who saw on a tombstone the inscription, `` I am not dead but sleeping ''.

If the would-be joiner asks these questions he is not likely to be duped by extremists who are seeking to capitalize on the confusions and the patriotic apprehensions of Americans in a troubled time.

If the decision goes wrong, it may be -- as Mr. Stevenson fears -- `` the first step on the slippery path downhill '' to a U.N. without operational responsibilities and without effective meaning.

If you're lyin' out in the hammock at night, and it gets kinda cool -- you know -- you just take these sides with the fringe on -- see -- and wrap 'em right over you.

If the record buyer's tastes are somewhat eclectic or even the slightest bit esoteric, he will find them satisfied on educational records.

If it will simply delay the debates until the qualifications are closed next spring, and then carry all the candidates on a tour of debates, it can provide a service to the state.

Mr. Richard Preston, executive director of the New Hampshire State Planning and Development Commission, in his remarks to the Governors Conference on Industrial Development at Providence on October 8, 1960, warned against the fallacy of attempting to attract industry solely to reduce the tax rate or to underwrite municipal services such as schools when he said: `` If this is the fundamental reason for a community's interest or if this is the basic approach, success if any will be difficult to obtain ''.

`` If the day should ever come that foreign invaders swarm ashore along the Gulf Coast '', the account reads, `` they can count on heavy opposition from a group of commando-trained telephone employees -- all girls.

If we make it established custom that whenever butchery on the highways grows excessive, say beyond 25,000 per annum, then somebody is going to hang, it follows that the more eminent the victim, the more impressive the lesson.

If it comes down too hard on the potential dangers of fallout, it will box the President on resuming atmospheric tests.

`` If William agrees, we should insist on a public debate '', he said at length.

If you want to fight, go down on the sidewalk ''.

If there is anything which we can do in the executive branch of the Government to speed up the processes by which we come to decisions on matters on which we must act promptly, that in itself would be a major contribution to the conduct of our affairs.