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 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 private brand competition hasn't been felt in your product field as yet, have you thought how you will cope with it if and when it does appear??

If Af is the change per unit volume in Gibbs function caused by the shear field at constant P and T, and **yr is the density of the fluid, then the total potential energy of the system above the reference height is Af.

If laying ties on a railroad track, which he once did for $1 an hour, paid more than playing right field for the Yankees, Maris would lay ties on a railroad track.

If working in a zinc mine, which he once did for 87-1/2 cents an hour, paid more than playing center field for the Yankees, Mantle would work in a zinc mine.

If K is a number field, its ring of integers is the subring of algebraic integers in K, and is frequently denoted as O < sub > K </ sub >.

If one quantizes a real scalar field, then one finds that there is only one kind of annihilation operator ; therefore, real scalar fields describe neutral bosons.

If under the existing system he could not assemble forces quickly enough to intercept mobile Viking raiders, the obvious answer was to have a standing field force.

If a is algebraic over K, then K, the set of all polynomials in a with coefficients in K, is not only a ring but a field: an algebraic extension of K which has finite degree over K. In the special case where K = Q is the field of rational numbers, Q is an example of an algebraic number field.

If a Game 5 is needed, the teams return to the higher seed's field.

If a Game 5 is needed, the teams return to the higher seed's field.

If X and Y are Banach spaces over the same ground field K, the set of all continuous K-linear maps T: X → Y is denoted by B ( X, Y ).

If X is a Banach space and K is the underlying field ( either the real or the complex numbers ), then K is itself a Banach space ( using the absolute value as norm ) and we can define the continuous dual space as X ′ = B ( X, K ), the space of continuous linear maps into K.

If a bubble touches identically-colored bubbles, forming a group of three or more, those bubbles — as well as any bubbles hanging from them — are removed from the field of play, and points are awarded.

If the ball has left the field along the sidelines, the referee must decide which team touched the ball last, and award a restart stroke to the opposing team, just like football's throw-in.

If the vector field represents the flow velocity of a moving fluid, then the curl is the circulation density of the fluid.

If φ is a scalar valued function and F is a vector field, then

If one set is used, pieces race across the field into empty, opposite corners.

If a team fails to gain ten yards in two downs they usually punt the ball on third down or try to kick a field goal ( see below ), depending on their position on the field.

* If the offence scores a field goal, the scoring team must kickoff from their own 35-yard line.

If a kicked ball goes out of bounds, or the kicking team scores a single or field goal as a result of the kick, the other team likewise gets possession.

If they make what would normally be a field goal, they score one point ; what would normally be a touchdown scores two points ( a " two-point conversion ").

If not " true " crannogs, small occupied islets ( often at least partially artificial in nature ) may be referred to as island duns, although rather confusingly, 22 islet-based sites are classified as ' proper ' crannogs due to the different interpretations of the inspectors or excavators who drew up field reports Canmore search for crannog in the Western Isles Hebridean island dwellings or crannogs were commonly built on both natural and artificial islets, usually reached by means of a stone causeway.