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 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 he had married her, he'd have been asking for trouble.

He said: `` If it's all right with you, Mr. Morgan, I'll sleep out here on the couch.

If we let them go, they won't stay away, they'll find men to ride with them and they'll be back.

He added, `` If this doesn't work out, the three of you barricade yourself in the house and talk terms with them ''.

If you've got any ideas ''.

If she did, he could stand it better in the light.

If you ever try anything without my orders I'll kill you ''.

`` If you hadn't I'd have killed you ''.

If she sensed any unusual preoccupation on the part of her mother, she did not comment upon it.

If she, Pamela, were being held responsible for his crimes, then hers must be the final act of expiation.

If, as she walked, her steps fumbled from time to time, she chose to ignore that omen.

If the slope grew steeper and the groves more dim, she tried not to heed.

If, when this was all over, she found the words to tell him about it, she wondered if he would ever understand.

If you take the one, you'd better take both ''.

If the bluff failed and they ran into trouble, Brannon had told the others, they would withdraw -- and he would come after his son another time.

If you don't leave this country within 3 days, your life will be taken the same as Powell's was.

If someone were to drop a match in here, this place would go up like a haystack ''.

If we was both armed, you wouldn't talk so tough ''.

`` If you spot Carmer give a yell before you move in ''.

If he wondered whether the attackers would allow him to pull away unmolested, he had his answer a moment later.

If the other pilots were worried, they did not show it.

If it were the enemy, tactically his position was correct.

If they're Japs.

If any of us miss, they can pick up the pieces.

If the turn was too tight, a barrel roll would bring them out.