If A is the major axis of an ellipsoid and B and C are the other two axes, the radius of curvature in the ab plane at the end of the axis Af, and the difference in pressure along the A and B axes is Af.

If T is a linear operator on an arbitrary vector space and if there is a monic polynomial P such that Af, then parts ( A ) and ( B ) of Theorem 12 are valid for T with the proof which we gave.

** If S is a set of sentences of first-order logic and B is a consistent subset of S, then B is included in a set that is maximal among consistent subsets of S. The special case where S is the set of all first-order sentences in a given signature is weaker, equivalent to the Boolean prime ideal theorem ; see the section " Weaker forms " below.

If the valid element indices begin at 0, the constant B is simply the address of the first element of the array.

If the numbering does not start at 0, the constant B may not be the address of any element.

If the minimum legal value for every index is 0, then B is the address of the element whose indices are all zero.

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 and we have for all v, w in V, then we say that B is symmetric.

In addition to acting and occasionally directing, Campbell has become a writer, starting with an autobiography, If Chins Could Kill: Confessions of a B Movie Actor published on August 24, 2002.

If the sets A and B are equal, this is denoted symbolically as A = B ( as usual ).

If the convention B < sub > 1 </ sub >=− is used, this sequence is also known as the first Bernoulli numbers ( / in OEIS ); with the convention B < sub > 1 </ sub >=+ is known as the second Bernoulli numbers ( / in OEIS ).

* Indicative conditional, a conditional in the form of " If A then B " in natural languages

If an atom A is double-bonded to an atom B, A is treated as being singly bonded to two atoms: B and a ghost atom that has the same atomic number as B but is not attached to anything except A.

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 A admits a totally ordered cofinal subset, then we can find a subset B which is well-ordered and cofinal in A.

If two cofinal subsets of B have minimal cardinality ( i. e. their cardinality is the cofinality of B ), then they are order isomorphic to each other.

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 you have neither a legal residence nor a principal place of business in any Internal Revenue district, your return should be filed with the District Director of Internal Revenue, Baltimore 2, Md..

Thus the view from Whitehall early in 1916: If defeat was not imminent, neither was victory ; and the outcome of the war of attrition on the Western Front could not be predicted.

If a simply stable system response neither decays nor grows over time, and has no oscillations, it is marginally stable: in this case the system transfer function has non-repeated poles at complex plane origin ( i. e. their real and complex component is zero in the continuous time case ).

If a criminal were truly aware of the mental and spiritual consequences of his actions, he would neither commit nor even consider committing those actions.

If neither A nor B includes the idea of existence, then " some A are B " simply adjoins A to B. Conversely, if A or B do include the idea of existence in the way that " triangle " contains the idea " three angles equal to two right angles ", then " A exists " is automatically true, and we have an ontological proof of A's existence.

If there come any unto you, and bring not this doctrine, receive him not into your house residence or abode, or " inmates of the house " ( family ), neither bid him God speed: for he that biddeth him God speed is partaker of his evil deeds.

If the firm is a perfect competitor in all input markets, and thus the per-unit prices of all its inputs are unaffected by how much of the inputs the firm purchases, then it can be shown that at a particular level of output, the firm has economies of scale if and only if it has increasing returns to scale, has diseconomies of scale if and only if it has decreasing returns to scale, and has neither economies nor diseconomies of scale if it has constant returns to scale.

If one concept is defined by another, and the other is defined by the first, this is known as circular definition, somewhat similar to a circular reasoning: neither offers us any enlightenment about what we wanted to know.

If a laser is swept across a distant object, the spot of laser light can easily be made to move across the object at a speed greater than c. Similarly, a shadow projected onto a distant object can be made to move across the object faster than c. In neither case does the light travel from the source to the object faster than c, nor does any information travel faster than light.

If the galaxies are of similar size, the resultant galaxy will appear similar to neither of the two galaxies merging, but would instead be an elliptical galaxy.

If the group is neither abelian nor compact, no general satisfactory theory is currently known.

( If neither is the case, then a weighted harmonic mean or weighted arithmetic mean is needed.

If a definite statement is believed plausible by some mathematicians but has been neither proved nor disproved, it is called a conjecture, as opposed to an ultimate goal: a theorem that has been proved.

#* Proof: Then so Thus However, is prime, so or In the former case, hence ( which is a contradiction, as neither 1 nor 0 is prime ) or In the latter case, or If however, which is not prime.

If the request for plea bargain is accepted by the court, the accused stands convicted but neither is sentenced if in trial nor undergoes any sentence previously pronounced by a lower court if in appeal.

If the pole breaks during the execution of a vault, it is considered an equipment failure and is ruled a non-jump, neither a make nor a miss.

If only one of his hands beats the banker then he pushes ( ties ) in which case neither he nor the banker wins the bet.

If a person elected prime minister is neither a member of the Lok Sabha nor Rajya Sabha, then he must become a member of the Lok Sabha or Rajya Sabha within six months.

If P is justified, then another belief Q may be justified by P. If P is not justified, then P cannot be a justifier for any other belief: neither for Q, nor for Qs negation.

If neither player had won by the tenth turn, subsequent turns consisted of moving one of one's own tokens to the remaining empty hole, with the constraint that this move could only be from an adjacent hole.

If the person has been made to stand then that person has no lap and neither of the statements " the person's lap is empty " and " there is something on the person's lap " is true.

If neither player can achieve this, the game is a draw.

: If one were to print only two or three copies, this method would be neither simple nor easy.