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 the latter knows nothing about the absent sitter except his name ( given by the experimenter ), he cannot possibly give any clues, conscious or unconscious, far less ask leading questions.

If you can possibly avoid it, you don't hand out any extra chances.

If foreign objects are not the cause, a doctor will incise and drain the abscess and prescribe painkillers and possibly antibiotics.

If, however, the numbers are referring to allies it could possibly include forces from Tyre, Judah, Edom, and Moab.

If proteins in a living cell are denatured, this results in disruption of cell activity and possibly cell death.

If the letter is not considered to be an authentic part of the Pauline corpus it might be dated during the late 1st century, possibly as late as 80 AD.

If they had gone it alone, the IRB and the Volunteers would possibly have come to their aid ; however, the IRB leaders met with Connolly in January 1916 and convinced him to join forces with them.

If the Flynn effect has ended in developed nations, then this may possibly allow national differences in IQ scores to diminish if the Flynn effect continues in nations with lower average national IQs.

Theorem 1: If a property is positive, then it is consistent, i. e., possibly exemplified.

If we should say that no one could possibly know whether water exists a priori, it seems either we cannot know content externalism to be true on the basis of thought experiments or we cannot know what we are thinking without first looking into the world to see what it is like.

In The Origin of Species, he wrote, " If it could be demonstrated that any complex organ existed, which could not possibly have been formed by numerous, successive, slight modifications, my theory would absolutely break down.

If the court finds that the respondent is " seriously mentally impaired ," he or she will be placed in a psychiatric hospital for further evaluation and possibly treatment.

If there were a large ( possibly infinite ) number of universes, each with possibly different physical laws ( or different fundamental physical constants ), some of these universes, even if very few, would have the combination of laws and fundamental parameters that are suitable for the development of matter, astronomical structures, elemental diversity, stars, and planets that can exist long enough for life to emerge and evolve.

If too large a dose of opioid antagonist is given to a dependent patient, it will result in withdrawal symptoms ( possibly severe ).

( If the machine is deterministic, the possible computations are the prefixes of a single, possibly infinite, path.

If the owner of a deactivated, or frozen, account finds the reason for deactivation invalid, they may contact the Neopets support team and possibly have their account reactivated.

If the surface has any transparent or translucent properties, it refracts a portion of the light beam into itself in a different direction while absorbing some ( or all ) of the spectrum ( and possibly altering the color ).

If the core of the star is not too massive ( less than approximately 1. 4 solar mass, taking into account mass loss that has occurred by this time ), it may then form a white dwarf ( possibly surrounded by a planetary nebula ) as described above for less massive stars, with the difference that the white dwarf is composed chiefly of oxygen, neon, and magnesium.

If this letter is authentic, then it might have been written soon after Paul's first letter to this community — or possibly years later.

Darwin concludes: " If it could be demonstrated that any complex organ existed, which could not possibly have been formed by numerous, successive, slight modifications, my theory would absolutely break down.

Any collection of objects and morphisms defines a ( possibly large ) directed graph G. If we let J be the free category generated by G, there is a universal diagram F: J → C whose image contains G. The limit ( or colimit ) of this diagram is the same as the limit ( or colimit ) of the original collection of objects and morphisms.

If the individual has taken a sufficiently large dose of cannabis, the level of intoxication progresses to the stage of being “ stoned ,” and the user may feel calm, relaxed, and possibly in a dreamlike state.

He concluded by saying his family are highest priority and, " If I see somewhere that seems safer, happier and will give them a better life than the UK, I ’ ll take them there if I possibly can.

The next citations are not found until 1955, when the May – June issue of Aviation Mechanics Bulletin included the line " Murphy's Law: If an aircraft part can be installed incorrectly, someone will install it that way ," and Lloyd Mallan's book, Men, Rockets and Space Rats, referred to: " Colonel Stapp's favorite takeoff on sober scientific laws — Murphy's Law, Stapp calls it —' Everything that can possibly go wrong will go wrong '.