If D denotes the differentiation operator and P is the polynomial Af then V is the null space of the operator p (, ), because Af simply says Af.

If F and G are ( covariant ) functors between the categories C and D, then a natural transformation η from F to G associates to every object X in C a morphism in D such that for every morphism in C, we have ; this means that the following diagram is commutative:

If φ is C < sup > k </ sup >, then the inhomogeneous equation is explicitly solvable in any bounded domain D, provided φ is continuous on the closure of D. Indeed, by the Cauchy integral formula,

If this output is then used as the clock signal for a similarly arranged D flip-flop ( remembering to invert the output to the input ), you will get another 1 bit counter that counts half as fast.

If v < sub > n </ sub > is the number of vertices of degree n and D is the maximum degree of any vertex,

If you work as a No. 2 in a New York City D. A.

If one chooses a critical value of the test statistic D < sub > α </ sub > such that P ( D < sub > n </ sub > > D < sub > α </ sub >)

In 2001, David Wiley criticized learning object theory in his paper, The Reusability Paradox which is summarized by D ' Arcy Norman as, If a learning object is useful in a particular context, by definition it is not reusable in a different context.

The " diamond problem " ( sometimes referred to as the " deadly diamond of death ") is an ambiguity that arises when two classes B and C inherit from A, and class D inherits from both B and C. If D calls a method defined in A ( and does not override the method ), and B and C have overridden that method differently, then from which class does it inherit: B, or C?

If ( D ) is the wheel diameter, the torque on the runner is: T = F ( D / 2 ) = ρQD ( V < sub > i </ sub > − u ).

* Matter, William D. If It Takes All Summer: The Battle of Spotsylvania ( 1988 )

If this type of contact utilizes a " make before break " functionality, then it is called a Form D contact.

If chiral pairs ( D and S ) are considered as identical, the remaining seven pieces can fill a 7 × 2 × 2 box.

If D is a derivation at x, then D ( ƒ )

If every object X < sub > i </ sub > of C admits a initial morphism to U, then the assignment and defines a functor V from C to D. The maps φ < sub > i </ sub > then define a natural transformation from 1 < sub > C </ sub > ( the identity functor on C ) to UV.

Similar statements apply to the dual situation of terminal morphisms from U. If such morphisms exist for every X in C one obtains a functor V: C → D which is right-adjoint to U ( so U is left-adjoint to V ).

If the ratio of the two resistances in the known leg is equal to the ratio of the two in the unknown leg, then the voltage between the two midpoints ( B and D ) will be zero and no current will flow through the galvanometer.

If the opponent places a stone at B or D, the remaining hex can be filled to join the original two stones into a single group.

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 a customer wishes a special cut, it will not be available.

If you provide inter-plant transportation, can this be replaced by available public transportation??

If you would like to start your tour in Italy, where the rental fees are actually the lowest in Europe, Fiats in all sizes are available, as are Alfa Romeo Giulietta models.

If Af leads to an address Af that is equal to the address computed from Af, even though Af does not match Af, the chain of information cells is extended from Af by storing the address of the next available cell in the Y-region, Af, in Af.

If the symbolic name or actual address of an index word or electronic switch appears or is included in the operand of an XRELEASE or SRELEASE statement ( see page 101 ), the specified index word or electronic switch will again be made available, regardless of the method by which it was reserved.

If, at any time during the assignment pass, the compiler finds that there are no more index words available for assignment, the warning message `` No More Index Words Available '' will be placed in the object program listing, the table will be altered to show that index words 1 through 96 are available, and the assignment will continue as before.

If the compiler finds that there are no more electronic switches available for assignment, the warning message `` No More Electronic Switches Available '' will be placed in the object program listing, the table will be altered to show that electronic switches 1 through 30 are available, and assignment will continue as before.

If you have a planting of half an acre or more you may want to buy a small garden tractor ( available for $300 to $500 with attachments, 1960 prices ).

If separate Chinese-language menus are available, they typically feature delicacies like liver, chicken feet or other meat dishes that might deter American customers.

If oil blessed by the bishop is not available, the priest administering the sacrament may bless the oil, but only within the framework of the celebration.

If the sick person wishes to receive the sacrament of penance, it is preferable that the priest make himself available for this during a previous visit ; but if the sick person must confess during the celebration of the sacrament of anointing, this confession replaces the penitential rite A passage of Scripture is read, and the priest may give a brief explanation of the reading, a short litany is said, and the priest lays his hands on the head of the sick person and then says a prayer of thanksgiving over the already blessed oil or, if necessary, blesses the oil himself.

If the next data item is not available when it is needed, the codec has no choice but to produce silence or guess — and if the data is late, it is useless, because the time period when it should have been converted to a signal has already passed.

If administrative appeal is available, no appeal to the judicial system may be made.

If a small heater is available for the coldest nights, a slab or basement cistern can inexpensively provide the required thermal mass.

If enough electric power is available, cooling can be provided by conventional air conditioning using a heat pump.

* Split ( only available as first decision of a hand ): If the first two cards have the same value, the player can split them into two hands, by moving a second bet equal to the first into an area outside the betting box of the original bet.

If the other player also knows to offer sacrifices, the expert also has to manipulate the number of available sacrifices through earlier play.

" If both opponents roll the same opening number, the doubling cube is incremented on each occasion yet remains in the middle of the board, available to either player.

If so they are dispatched to available execution units, resulting in the ability for several instructions to be executed simultaneously.

If a suitably sized quantum computer capable of running Grover's algorithm reliably becomes available, it would reduce a 128-bit key down to 64-bit security, roughly a DES equivalent.

If that class is not available, or unknown at compile time, the application simply won't compile.

If something goes wrong, ed is sometimes the only editor available.

If total cash available is less than cash needs, a deficiency exists.