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 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 D denotes the differentiation operator and P is the polynomial Af then V is the null space of the operator p (, ), because Af simply says Af.

# If P, then Q.

If P is a program which outputs a string x, then P is a description of x.

* 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 P is 2, then the left subtree outweighs the right subtree of the given node, and the balance factor of the left child ( L ) must be checked.

* If the balance factor of L is + 1, a single right rotation ( with P as the root ) is needed ( Left-Left case ).

If we assume the controller C, the plant P, and the sensor F are linear and time-invariant ( i. e., elements of their transfer function C ( s ), P ( s ), and F ( s ) do not depend on time ), the systems above can be analysed using the Laplace transform on the variables.

If either P or Q is true and P is false, then Q is true.

If the partial pressure of A at x < sub > 1 </ sub > is P < sub > A < sub > 1 </ sub ></ sub > and x < sub > 2 </ sub > is P < sub > A < sub > 2 </ sub ></ sub >, integration of above equation,

If ~ is an equivalence relation on X, and P ( x ) is a property of elements of X, such that whenever x ~ y, P ( x ) is true if P ( y ) is true, then the property P is said to be well-defined or a class invariant under the relation ~.

The well-known historian of physics, C. P. Snow, says about him, " If Fermi had been born a few years earlier, one could well imagine him discovering Rutherford's atomic nucleus, and then developing Bohr's theory of the hydrogen atom.

If the cause of the crash is uncertain, this number is rendered as 48454C50, which stands for " HELP " in hexadecimal ASCII characters ( 48 = H, 45 = E, 4C = L, 50 = P ).

If the quantity of powder stored for personal use exceeds 75 kg, then a Propellant Magazine Licence ( Type P ) is required.

If one chooses a critical value of the test statistic D < sub > α </ sub > such that P ( D < sub > n </ sub > > D < sub > α </ sub >)

If the base manifold is four-dimensional, the Kaluza – Klein manifold P is five-dimensional.

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.

The Council of Trent decreed: " If anyone shall say that a man once justified can sin no more, nor lose grace, and that therefore he who falls and sins was never truly justified ; or, on the contrary, that throughout his whole life he can avoid all sins even venial sins, except by a special privilege of God, as the Church holds in regard to the Blessed Virgin: let him be anathema.

If this pronouncement seems hardly justified, now that Wycliffe's writings are in print, it must be borne in mind that not all his philosophical works are extant.

If one presupposes a cognitivist interpretation of moral sentences, morality is justified by the moralist's knowledge of moral facts, and the theories to justify moral judgements are epistemological theories.

If a belief is justified, there is something that justifies it.

If a belief is justified, then it has at least one justifier.

If there is a new theory which is better at explaining and predicting phenomena than an older theory ( i. e. it has more explanatory power ), we are justified in believing that the newer theory describes reality more correctly.

: If we are justified in assuming that the scope of the generalization ' All ravens are black ' can be restricted to ravens, then this means that we have some outside information which we can rely on concerning the factual situation.

If it fails to do so its presence could not be justified.

This is justified by observing that in order for the omnipotent agent to create such a stone, the omnipotent agent must already be more powerful than itself: such a stone is too heavy for the omnipotent agent to lift, but the omnipotent agent already can create such a stone ; If an omnipotent agent already is more powerful than itself, then it already is just that powerful.

If the ruler became immoral, then rebellion is justified and heaven would take away that mandate and give it to another.

If the quality of rule became questionable because of repeated natural disasters such as flood or famine, or for other reasons, then rebellion was justified.

: If a man has put a spell upon another man and it is not justified, he upon whom the spell is laid shall go to the holy river ; into the holy river shall he plunge.

Mill ’ s application of the general principles of liberty is expressed in his book On Liberty: " If all mankind minus one, were of one opinion, and one, and only one person were of the contrary opinion, mankind would be no more justified in silencing that one person, than he, if he had the power, would be justified in silencing mankind ".

Even a teacher, though, is usually justified in saying, " If you didn't want to fail the quiz, then you should have done your homework instead of skateboarding / watching TV / etc.

If it was “ debatable ” whether Glass-Steagall was justified in the 1930s, it was easier to argue that Glass-Steagall served no legitimate purpose when the distinction between commercial and investment banking activities had been blurred by “ market developments ” since the 1960s.

Martin and Lyon justified the name, writing later, " If anyone asked us, we could always say we belong to a poetry club.

He says of Abraham, " If the task had been different, if the Lord had commanded Abraham to bring Isaac up to Mount Moriah so that he could have his lightning strike Isaac and take him as a sacrifice in that way, then Abraham plainly would have been justified in speaking as enigmatically as he did, for then he himself could not have known what was going to happen.