The S-box used is derived from the multiplicative inverse over GF ( 2 < sup > 8 </ sup >), known to have good non-linearity properties.

Absolute temperature measurement is uniquely determined by a multiplicative constant which specifies the size of the " degree ", so the ratios of two absolute temperatures, T < sub > 2 </ sub >/ T < sub > 1 </ sub >, are the same in all scales.

Every Boolean algebra ( A, ∧, ∨) gives rise to a ring ( A, +, ·) by defining a + b := ( a ∧ ¬ b ) ∨ ( b ∧ ¬ a ) = ( a ∨ b ) ∧ ¬( a ∧ b ) ( this operation is called symmetric difference in the case of sets and XOR in the case of logic ) and a · b := a ∧ b. The zero element of this ring coincides with the 0 of the Boolean algebra ; the multiplicative identity element of the ring is the 1 of the Boolean algebra.

A character χ is a linear functional on A which is at the same time multiplicative, χ ( ab )

Conversion of units is the conversion between different units of measurement for the same quantity, typically through multiplicative conversion factors.

For example, if function div stands for the division operation x / y, then div with the parameter x fixed at 1 ( i. e., div 1 ) is another function: the same as the function inv that returns the multiplicative inverse of its argument, defined by inv ( y )

We will use the notation to denote the multiplicative inverse of, it is defined exactly when and are coprime ; the following construction explains why the coprimality condition is needed.

The simplest, and original, implementation of the protocol uses the multiplicative group of integers modulo p, where p is prime and g is primitive root mod p. Here is an example of the protocol, with non-secret values in < span style =" color: blue "> blue </ span >, and secret values in < span style =" color: red "> boldface red </ span >:

Specifically, it is a non-trivial ring in which every non-zero element a has a multiplicative inverse, i. e., an element x with.

It is used to solve Diophantine equations, such as finding numbers that satisfy multiple congruences ( Chinese remainder theorem ) or multiplicative inverses of a finite field.

In abstract algebra, a field is a commutative ring which contains a multiplicative inverse for every nonzero element, equivalently a ring whose nonzero elements form an abelian group under multiplication.

The most important difference is that fields allow for division ( though not division by zero ), while a ring need not possess multiplicative inverses ; for example the integers form a ring, but 2x = 1 has no solution in integers.

Intuitively, a field is a set F that is a commutative group with respect to two compatible operations, addition and multiplication, with " compatible " being formalized by distributivity, and the caveat that the additive identity ( 0 ) has no multiplicative inverse ( one cannot divide by 0 ).

Likewise, there is an element, called the multiplicative identity element and denoted by 1, such that for all a in F, a · 1 = a.

A related concept, the " Finagle factor ", is an ad hoc multiplicative or additive term in an equation which can only be justified by the fact that it gives more correct results.

In 1973, Morgenstern proved an lower bound on the addition count for algorithms where the multiplicative constants have bounded magnitudes ( which is true for most but not all FFT algorithms ).

Similarly, the multiplicative group of the field is a cyclic group.

This ring is a field because it contains a multiplicative inverse for each element N other than zero ( an integer that, multiplied by the element modulo p yields 1 ), and it has a finite number of elements ( p ), making it a finite field.

* The gcd is a multiplicative function in the following sense: if a < sub > 1 </ sub > and a < sub > 2 </ sub > are relatively prime, then gcd ( a < sub > 1 </ sub >· a < sub > 2 </ sub >, b ) = gcd ( a < sub > 1 </ sub >, b )· gcd ( a < sub > 2 </ sub >, b ).

`` That is, if we can be sure this is Colcord's money '' --

Let me pass over the trip to Sante Fe with something of the same speed which made Mrs. Roebuck `` wonduh if the wahtahm speed limit '' ( 35 m.p.h. ) `` is still in ee-faket ''.

It is the last of the three tests of manhood which the women impose, to discover if a male is worthy of survival there.

There was a measure of protection in its concrete walls and ceiling, but the engineers who hastily installed it were well aware that concrete is not much better than prayer, if as efficacious, when a direct hit comes along.

`` And if the dive goes OK he has the exclusive import rights to your line for this country, is that right ''??

`` All right, if you can't do your arithmetic during school hours you can do it after school is out '', Miss Langford said firmly, not smiling.

Why, in the first place, call himself a liberal if he is against laissez-faire and favors an authoritarian central government with womb-to-tomb controls over everybody??

And if he is so scornful of the rights of states, why not advocate a different sort of constitution that he could more sincerely support??

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.

I think it is essential, however, to pinpoint here the difference between the two concepts of sovereignty that went to war in 1861 -- if only to see better how imperative is our need today to clarify completely our far worse confusion on this subject.

Unruly hair goes straight up from his forehead, standing so high that the top falls gently over, as if to show that it really is hair and not bristle.

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.

He will not curb his instinctual desires but release the energy within him that makes him feel truly and fully alive, even if it is only for this brief moment before the apocalypse of annihilation explodes on earth.

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.

And if I have gone into so much detail about so small a work, that is because it is also so typical a work, representing the germinal form of a conflict which remains essential in Mann's writing: the crude sketch of Piepsam contains, in its critical, destructive and self-destructive tendencies, much that is enlarged and illuminated in the figures of, for instance, Naphta and Leverkuhn.

All such imitations of negative quality have given rise to a compensatory response in the form of a heroic and highly individualistic humanism: if man can neither know nor love reality as it is, he can at least invent an artistic `` reality '' which is its own world and which can speak to man of purely personal and subjective qualities capable of being known and worthy of being loved.

But Aristotle kept the principle of levels and even augmented it by describing in the Poetics what kinds of character and action must be imitated if the play is to be a vehicle of serious and important human truths.

Operating as a one man police force in fact if not in name, he is at once more independent and more dedicated than the police themselves.

`` All I have to do to set the record is to go on down.

And the best way to conceal and disguise the elements of an incest story is not to set out to write an incest story.

The strongest appeal of the Copernican formulation consisted in just this: ideally, the justification for dealing with special problems in particular ways is completely set out in the basic ' rules ' of the theory.

Once the scene is set, Trevelyan skilfully builds up the tense story until it reaches its climax in the dramatic victory of Marlborough and Eugene of Savoy at Blenheim.

Criticism is as old as literary art and we can set the stage for our study of three moderns if we see how certain critics in the past have dealt with the ethical aspects of literature.

To say this is to set aside the realness of time.

I refer to the notion that the structure of society is a microcosm of the cosmic design and that history conforms to patterns of justice and chastisement as if it were a morality play set in motion by the gods for our instruction.

Even to be `` from hope and fear set free '' is at least better than to have lost the first without having got rid of the second.

I believe it is an area in which professional planners have failed to set adequate guide posts ; ;

It is high time the United States began to realize that the God-given rights of men set forth in that document are applicable today to Katanga.

One of the inescapable realities of the Cold War is that it has thrust upon the West a wholly new and historically unique set of moral dilemmas.

The day is now appropriately set aside to honor the American men and women who have contributed to the success of our merchant marine fleet in peace and war.

The Act further provides for a `` floor '' or minimum allotment, set at the 1954 level, which is called the `` base '' allotment, and a `` ceiling '' or maximum allotment, for each State.

The method used in computing the allotments is specifically set forth in the Act.

The method used for computing the respective Federal and State shares in total program costs is specifically set forth in the Act.

It is equipped with electronic controls that can be set to hold precise tension and speed.

the purpose of producing plays at the College is three-fold: to provide the Carleton students with the best possible opportunity for theater-going within the limits set by the maturity and experience of the performers and the theatrical facilities available ; ;

The first substantially complete stereo Giselle ( and the only one of its scope since Feyer's four-sided LP edition of 1958 for Angel ), this set is, I'm afraid, likely to provide more horrid fascination than enjoyment.

The Rio Grande KC is also considering having their Junior Classes set up so that Juniors can qualify with points for Westminster.

There is no limit to what you can spend, yet it is easily possible to keep within a set budget.

The main set of bars are the `` tappets '' and one tappet is connected to each lever.

He is a fine-looking colt with a good body, good set of legs and nice way of going.

This one was set up here in 390 A.D. on a pedestal, the faces of which are carved with statues of the emperor and his family watching games in the Hippodrome, done so realistically that the obelisk itself is included in them.

There is even one set that has `` barbecue '' written on it.