If ( remember this is an assumption ) the minimal polynomial for T decomposes Af where Af are distinct elements of F, then we shall show that the space V is the direct sum of the null spaces of Af.

If F ≥ F < sub > Critical </ sub > ( Numerator DF, Denominator DF, α )

If F is algebraically closed and p ( x ) is an irreducible polynomial of F, then it has some root a and therefore p ( x ) is a multiple of x − a.

If F is an antiderivative of f, and the function f is defined on some interval, then every other antiderivative G of f differs from F by a constant: there exists a number C such that G ( x ) = F ( x ) + C for all x.

If the domain of F is a disjoint union of two or more intervals, then a different constant of integration may be chosen for each of the intervals.

If F is also surjective, then the Banach space X is called reflexive.

If F. tularensis were used as a weapon, the bacteria would likely be made airborne for exposure by inhalation.

If evolutionary processes are blind to the difference between function F being performed by conscious organism O and non-conscious organism O *, it is unclear what adaptive advantage consciousness could provide.

If F and G are ( covariant ) functors between the categories C and D, then a natural transformation η from F to G associates to every object X in C a morphism in D such that for every morphism in C, we have ; this means that the following diagram is commutative:

If is any unit vector, the projection of the curl of F onto is defined to be the limiting value of a closed line integral in a plane orthogonal to as the path used in the integral becomes infinitesimally close to the point, divided by the area enclosed.

If certain coordinate systems are used, for instance, polar-toroidal coordinates ( common in plasma physics ) using the notation ∇ × F will yield an incorrect result.

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

If F is clear from context then Ω < sub > F </ sub > may be denoted simply Ω, although different prefix-free universal computable functions lead to different values of Ω.

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 F ( r ) represents gravity, it is a negative term proportional to 1 / r < sup > 2 </ sup >, so the net acceleration in r in the rotating frame depends on a difference of reciprocal square and reciprocal cube terms, which are in balance in a circular orbit but otherwise typically not.

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 only layer C changes, we should find a way to avoid re-blending all of the layers when computing F. Without any special considerations, four full-image blends would need to occur.

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 anything, the conservative Democrats were more opposed to Hearst than the Republicans.

If the work done moving along a path which starts and ends in the same location is zero, then the force is said to be conservative and it is possible to define a numerical value of potential associated with every point in space.

Wender and Klein point out that pessimism can be useful in some circumstances: " If one is subject to a series of defeats, it pays to adopt a conservative game plan of sitting back and waiting and letting others take the risks.

If a force is conservative, it is possible to assign a numerical value for the potential at any point.

If the force is not conservative, then defining a scalar potential is not possible, because taking different paths would lead to conflicting potential differences between the start and end points.

If a rider wishes to stay within normal requirements for higher-level competition, breeches should be white, but beige or another conservative light color is permissible.

If you say something that someone already agrees with, then what's the point, and so we make some more conservative animal protection organizations uncomfortable ; they don't want to be associated with us because it will be embarrassing for them, and I understand that.

If liberals are to understand how conservatives use their words, they will have to understand the conservative conceptual system.

Zinn regularly included it in his lists of recommended readings, and after Barack Obama was elected President of the United States, Zinn wrote, " If Richard Hofstadter were adding to his book The American Political Tradition, in which he found both ' conservative ' and ' liberal ' presidents, both Democrats and Republicans, maintaining for dear life the two critical characteristics of the American system, nationalism and capitalism, Obama would fit the pattern.

If the system is conservative ( i. e. there is no dissipation ), a volume element of the phase space will stay the same along a trajectory.

If conservative medical treatments fail to achieve a full term pregnancy, the physician may suggest the patient undergo in vitro fertilization ( IVF ).

If you go down the list of what makes up a conservative, I'm there almost all the way.

After her proposed bill failed, Short accused the House's predominantly conservative male MPs of not taking the issue seriously, remarking, " If you mention breasts, fifty Tory MPs all giggle and fall over.

If usage preferences are conservative, prescription might ( appear to ) be resistant to language change ; if the usage preferences are radical, prescription may produce neologisms.

In addition to Fame Becomes Me, some of the titles Short has used for his one-man show include Stroke Me Lady Fame, If I'd Saved, I Wouldn't Be Here, and, in more conservative markets, Sunday in the Park with George Michael.

If he still kept some of the old vocabulary, some of the old imagery, he was yet accustoming people to hear moving subjects treated in a manner more free and simple than before ; so that his was a sort of conservative reform, preceding the violent revolution of Victor Hugo and his army of uncompromising romantics.

If two candidates appeal to liberals, but only one appeals to conservatives, the votes of liberals will likely split between the two liberal candidates, for example 25 % may vote for one and 30 % for the other, giving the conservative the office although 55 % preferred to see a liberal in the office.

Over a dozen members of the conservative wing of the RNC submitted a new resolution, to be eventually voted on by the entire RNC, that would call on the Democratic party to rename itself the “ Democrat Socialist Party .” If the RNC adopted this resolution, the RNC ’ s official view would become that Democrats are socialists.

If you want to call me a single-issue candidate, that's fine, just so long as you know that my single issue is the survival and the success of the conservative movement in America.

If is a conservative vector field then the gradient theorem states that

If the vector field associated to a force is conservative then the force is said to be a conservative force.

In Bremer's diary were comments such as " My country tis of thee land of sweet bigotry ," " Never say colored, say Negro, so here is a negro card ," " My blood is black ," " Cheer up Oswald ," " White collar, conservative, middle class, Republican, suburbanite robot ," " A Thundering of hooves and out of the western sky came the colored man ," and " If I live tomorrow then it will be a long time.

" If the counterculture was a shift from conservatism to liberalism, then square was what liberal people called conservative people and things.