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If a is a point in R < sup > n </ sup >, then the higher dimensional chain rule says that:
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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 point
If he had been `` liquidated '' in some way, he would have become a martyr, a rallying point for people who shared his ideas.
If we examine the three types of change from the point of view of their internal structure we find an additional profound difference between the third and the first two, one that accounts for the notable difference between the responses they evoke.
If he were to go with White, he would be out there two days, not just listening in the dark at some point between here and Papa-san, but moving ever deeper into enemy land -- behind Papa-san -- itself.
If their schedules were to synchronize, there was no point in wasting time.
If design head has a deep cavity, clay lid will be quite thick at this point ; ;
If the argument is accepted as essentially sound up to this point, it remains for us to consider whether the patient's difficulties in orienting himself spatially and in locating objects in space with the sense of touch can be explained by his defective visual condition.
If this attitude is seriously questioned in the Soviet Union, it does not necessarily follow that the majority of the society in which I live is too aware of the necessity for clarity on this ethical as well as aesthetic point of view.
If the Southerners were sufficiently aroused, they could very well cut the Kennedy legislative program to ribbons from their vantage point of committee chairmanships, leaving Sam Rayburn leading a truncated, unworkable party.
If it was, then it must have been God's intention to translate him at a certain point from time to eternity.
If one also removes the second postulate (" a line can be extended indefinitely ") then elliptic geometry arises, where there is no parallel through a point outside a line, and in which the interior angles of a triangle add up to more than 180 degrees.
If the object point be infinitely distant, all rays received by the first member of the system are parallel, and their intersections, after traversing the system, vary according to their perpendicular height of incidence, i. e. their distance from the axis.
If the object point O is infinitely distant, u1 and u2 are to be replaced by h1 and h2, the perpendicular heights of incidence ; the sine condition then becomes sin u ' 1 / h1 = sin u ' 2 / h2.
If, in an unsharp image, a patch of light corresponds to an object point, the center of gravity of the patch may be regarded as the image point, this being the point where the plane receiving the image, e. g., a focusing screen, intersects the ray passing through the middle of the stop.
If a system consists of several particles, the total angular momentum about a point can be obtained by adding ( or integrating ) all the angular momenta of the constituent particles.
If the net force on some body is directed always toward some fixed point, the center, then there is no torque on the body with respect to the center, and so the angular momentum of the body about the center is constant.
If the score reaches 20-all, then the game continues until one side gains a two point lead ( such as 24 – 22 ), up to a maximum of 30 points ( 30 – 29 is a winning score ).
If the filter shows amplitude ripple within the passband, the x dB point refers to the point where the gain is x dB below the nominal passband gain rather than x dB below the maximum gain.
If the player and dealer have the same point total, this is called a " push " and the player typically doesn't win or lose money on that hand.
If the heat of vaporization and the vapor pressure of a liquid at a certain temperature is known, the normal boiling point can be calculated by using the Clausius-Clapeyron equation thus:
If the large-scale Universe appears isotropic as viewed from Earth, the cosmological principle can be derived from the simpler Copernican principle, which states that there is no preferred ( or special ) observer or vantage point.
If a player is one point away from winning a match, that player's opponent will always want to double as early as possible in order to catch up.
If the holes are closed, the gas will only mix with ambient air at the point of combustion, that is, only after it has exited the tube at the top.
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 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.
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