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If R is the direct sum of the rings R < sub > 1 </ sub >,..., R < sub > n </ sub >, then the identity elements of the rings R < sub > i </ sub > are central idempotents in R, pairwise orthogonal, and their sum is 1.
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If and R
If the rake angle **yc of the knife is high enough and the friction angle **yt between the front of the knife and the back of the chip is low enough to give a positive value for Af, the resultant vector R will lie above the plane of the substrate.
If all the operating variables were varied simultaneously, Af operations would be required to do the same job, and as R increases this increases very much more rapidly than the number of operations required by the dynamic program.
If Af denotes the net profit from stage R and Af, then the principle of optimality gives Af.
* Every rectangle R is in M. If the rectangle has length h and breadth k then a ( R ) =
* If the balance factor of P is-2 then the right subtree outweighs the left subtree of the given node, and the balance factor of the right child ( R ) must be checked.
* If the balance factor of R is-1, a single left rotation ( with P as the root ) is needed ( Right-Right case ).
* If the balance factor of R is + 1, two different rotations are needed.
If the function R is well-defined, its value must lie in the range, with 1 indicating perfect correlation and − 1 indicating perfect anti-correlation.
If the thumb points in the direction of the 4th substitutent, the enantiomer is R. Otherwise, it's S.
If the relative priorities of these substituents need to be established, R takes priority over S. When this happens, the descriptor of the stereocenter is a lowercase letter ( r or s ) instead of the uppercase letter normally used.
If a is a point in R < sup > n </ sup >, then the higher dimensional chain rule says that:
If is an outward pointing in-plane normal, whereas is the unit vector perpendicular to the plane ( see caption at right ), then the orientation of C is chosen so that a tangent vector to C is positively oriented if and only if forms a positively oriented basis for R < sup > 3 </ sup > ( right-hand rule ).
If the ideals A and B of R are coprime, then AB = A ∩ B ; furthermore, if C is a third ideal such that A contains BC, then A contains C. The Chinese remainder theorem is an important statement about coprime ideals.
If, i. e., it has a large norm with each value of s, and if, then Y ( s ) is approximately equal to R ( s ) and the output closely tracks the reference input.
If a vector field F with zero divergence is defined on a ball in R < sup > 3 </ sup >, then there exists some vector field G on the ball with F = curl ( G ).
* If x < sub > 0 </ sub > is a real number, we can turn the set R −
( If X is also empty then R is reflexive.
*( EF1 ) If a and b are in R and b is nonzero, then there are q and r in R such that and either r = 0 or.
If R is a commutative ring, and a and b are in R, then an element d of R is called a common divisor of a and b if it divides both a and b ( that is, if there are elements x and y in R such that d · x = a and d · y = b ).
If R is an integral domain then any two gcd's of a and b must be associate elements, since by definition either one must divide the other ; indeed if a gcd exists, any one of its associates is a gcd as well.
If and is
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 and direct
If ( remember this is an assumption ) the minimal polynomial for T decomposes Af where Af are distinct elements of F, then we shall show that the space V is the direct sum of the null spaces of Af.
If the problem is enlarged to require a complete coverage of feed states, Af operations are needed by the dynamic program and Af by the direct search.
If a party has gained more direct mandates in a Land than it is entitled to according to the results of the second vote, it does not forfeit these mandates because all directly elected candidates are guaranteed a seat in the Bundestag.
If a " clinch " – a defensive move in which a boxer wraps his or her opponents arms and holds on to create a pause – is broken by the referee, each fighter must take a full step back before punching again ( alternatively, the referee may direct the fighters to " punch out " of the clinch ).
If is a ket in V and is a ket in W, the direct product of the two kets is a ket in.
If the descent were truly unbroken, father-to-son, since Confucius's lifetime, the males in the family would all have the same Y chromosome as their direct male ancestor, with slight mutations due to the passage of time.
If the court does so, the lawyer may thereafter ply the witness with leading questions during direct examination.
If Wisda's Landscaping breaks the contract, and Neal Townsend is forced to hire another service for $ 60 an hour, expectation ( direct ) damages paid to Neal Townsend would equal $ 100 ($ 10 an hour, the difference in price between the original contract and the new contract ).
If there is a direct object, the indirect object can be expressed by an object pronoun placed between the verb and the direct object.
* If we think of as the set of real numbers, then the direct product is precisely just the cartesian product,.
* If we think of as the group of real numbers under addition, then the direct product still consists of.
* If we think of as the ring of real numbers, then the direct product again consists of.
If not to make a direct change, this movement is in place to raise awareness about the effects that take place because of the physical things around us.
If a player contacts the ground inside the goal perimeter he must take the most direct path out of it.
If an inductor is connected to a direct current source with value I via a resistance R, and then the current source is short-circuited, the differential relationship above shows that the current through the inductor will discharge with an exponential decay:
If a decomposition exists with each c < sub > i </ sub > a centrally primitive idempotent, then R is a direct sum of the corner rings c < sub > i </ sub > Rc < sub > i </ sub >, each of which is ring irreducible.
If the judge concurs, he will direct the police to escort the individual to the hospital.
If there is no direct effect or legislation, there are two theories to justify the courts incorporating international into municipal law:
If the territory was already on a war footing, the whole society alert and inflamed, then why not direct all this ramped up energy toward something useful?
If the position angle of the body's Prime Meridian increases with time, the body has a direct ( or prograde ) rotation ; otherwise the rotation is said to be retrograde.
If the disease is associated with cancer, direct treatment of the cancer often relieves the symptoms of LEMS.
If a past storyline wherein a direct depictions of a then-current president or similar is referenced in a later era, it tends to become updated accordingly, sometimes with an " in-joke " acknowledgement.
If the nation state begins to disappear, it may well be the direct or indirect result of globalization and internationalism.
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