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If and depends
Theorem: If K < sub > 1 </ sub > and K < sub > 2 </ sub > are the complexity functions relative to description languages L < sub > 1 </ sub > and L < sub > 2 </ sub >, then there is a constant c – which depends only on the languages L < sub > 1 </ sub > and L < sub > 2 </ sub > chosen – such that
* If the operation is associative, ( ab ) c = a ( bc ), then the value depends only on the tuple ( a, b, c ).
* If the operation is commutative, ab = ba, then the value depends only on
If F ( r ) represents gravity, it is a negative term proportional to 1 / r < sup > 2 </ sup >, so the net acceleration in r in the rotating frame depends on a difference of reciprocal square and reciprocal cube terms, which are in balance in a circular orbit but otherwise typically not.
If the XML document depends on parsable external entities ( including the specified external subset, or parsable external entities declared in the internal subset ), it should assert in its XML declaration.
If the partition is removed, some molecules of A move towards the region occupied by B, their number depends on the number of molecules at the point considered.
If the diffusion coefficient is not a constant, but depends upon the coordinate and / or concentration, Fick's Second Law yields
If there is more than one allograph of a unit of writing, and the choice between them depends on context or on the preference of the author, they now have to be treated as separate glyphs, because mechanical arrangements have to be available to differentiate between them and to print whichever of them is required.
If the force depends on time, the change in momentum ( or impulse ) between times and is
If the input feature vectors have very high dimension, the learning problem can be difficult even if the true function only depends on a small number of those features.
If successful, these effort could usher in a new era of neural computing that is a step beyond digital computing, because it depends on learning rather than programming and because it is fundamentally analog rather than digital even though the first instantiations may in fact be with CMOS digital devices.
If the Euler-Lagrange equations are solved for this system, it is found that the motion depends on two constants and ( each related to a constant of motion ).
If, however, there is no quantifier, the variable is called free, and the truth-value of the proposition depends on the value of the variable.
If this susceptibility itself depends upon the electric field, one can obtain a nonlinear optical effect of magneto-optical parametric generation ( somewhat analogous to a Pockels effect whose strength is controlled by the applied magnetic field ).
If a probability distribution depends on a parameter, one may on the one hand consider — for a given value of the parameter — the probability ( density ) of the different outcomes, and on the other hand consider — for a given outcome — the probability ( density ) this outcome has occurred for different values of the parameter.
If a rule depends not only on a single symbol but also on its neighbours, it is termed a context-sensitive L-system.
* If the inferior power is in an aggressive position, however, and / or turns to tactics prohibited by the laws of war ( jus in bello ), its success depends on the superior power's refraining from like tactics.
If x and y are vectors, then the best linear approximation to the graph of f depends on how f changes in several directions at once.
If security depends on keeping that secret, then disclosure leads to major logistic difficulties in developing, testing, and distributing implementations of a new algorithm: it is " brittle.
If this project is in a family for which this applies, Help: Interlanguage link demo may demonstrate what is explained below ( this depends on whether the same language codes are used ).
* If he rolls an 11 or 12, the result depends on the main:
If the resistance of the absorbing element depends on the electron temperature, then the resistance can be used as a thermometer of the electron system.
If a shared library that an executable depends on is deleted, moved, or renamed, or if an incompatible version of the library is copied to a place that is earlier in the search, the executable would fail to load.
If the chain complex depends on the object X in a covariant manner ( meaning that any morphism X → Y induces a morphism from the chain complex of X to the chain complex of Y ), then the H < sub > n </ sub > are covariant functors from the category that X belongs to into the category of abelian groups ( or modules ).

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

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