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

If x is held fixed, then the Bessel functions are entire functions of α.

If α is an integer, the limit has to be calculated.

* Scanning: If a is the next symbol in the input stream, for every state in S ( k ) of the form ( X → α • a β, j ), add ( X → α a • β, j ) to S ( k + 1 ).

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 A is a directed set, we often write a net from A to X in the form ( x < sub > α </ sub >), which expresses the fact that the element α in A is mapped to the element x < sub > α </ sub > in X.

If ( x < sub > α </ sub >) is a net from a directed set A into X, and if Y is a subset of X, then we say that ( x < sub > α </ sub >) is eventually in Y ( or residually in Y ) if there exists an α in A so that for every β in A with β ≥ α, the point x < sub > β </ sub > lies in Y.

If ( x < sub > α </ sub >) is a net in the topological space X, and x is an element of X, we say that the net converges towards x or has limit x and write

If c, h, and e were all changed so that the values they have in metric ( or any other ) units were different when we looked them up in our tables of physical constants, but the value of α remained the same, this new world would be observationally indistinguishable from our World.

If I is an index set and X < sub > I </ sub > is the set of indeterminates X < sub > i </ sub > for i ∈ I, then a monomial X < sup > α </ sup > is any finite product of elements of X < sub > I </ sub > ( repetitions allowed ); a formal power series in X < sub > I </ sub > with coefficients in a ring R is determined by any mapping from the set of monomials X < sup > α </ sup > to a corresponding coefficient c < sub > α </ sub >, and is denoted.

If we consider a cell of the " net ", we can see that the cell is a rhombus: it is a parallelogram with the four sides equal to d = p / sin α ; ( we have a right triangle which hypothenuse is d and the side opposed to the α angle is p ).

If f is assumed to be continuous as well then this can be extended to show that homogeneity for α any real number, using the fact that rationals form a dense subset of the reals.

* If α is an algebraic integer then is another algebraic integer.

If a test of significance gives a p-value lower than the significance level α, the null hypothesis is rejected.

If you were a man '' --

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

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

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

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

If it were not for an old professor who made me read the classics I would have been stymied on what to do, and now I understand why they are classics ; ;

If it were not that I knew who it was I could have mistaken it for my Aunt so well did her clothes fit him.

If an automobile were approaching him, he would know what was required of him, even though he might not be able to act quickly enough.

If there were only darkness, all would be clear.

If there were only the mess, all would be clear ; ;

If these people were denied a voice ( do they have a moral right to a voice??

If we were creating a wholly new society, we could insist that our social, political, economic and philosophic institutions foster rather than hamper man ; ;

If living Jews were unavailable for study, the Bible was at hand.

If his scholarship and formal musicianship were not all they might have been, Mercer demonstrated at an early age that he was gifted with a remarkable ear for rhythm and dialect.

If she were not at home, Mama would see to it that a fresh white rose was there.

If the Stearns were not there, grace would be omitted.

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

If the hardships of the winter at Valley Forge were trying for healthy men, they were, of course, much more so for those not in good health.

If his circumspection in regard to Philip's sensibilities went so far that he even refused to grant a dispensation for the marriage of Amadee's daughter, Agnes, to the son of the dauphin of Vienne -- a truly peacemaking move according to thirteenth-century ideas, for Savoy and Dauphine were as usual fighting on opposite sides -- for fear that he might seem to be favoring the anti-French coalition, he would certainly never take the far more drastic step of ordering the return of Gascony to Edward, even though, as he admitted to the English ambassadors, he had been advised that the original cession was invalid.

If there were no West Berlin problem, imperialist quarters would have invented an excuse for stepping up the armaments race to try to solve the internal and external problems besetting the United States and its NATO partners.

If the new Soviet series has followed the general pattern of previous Russian tests, the shots were roughly half fission and half fusion, meaning a fission yield of 30 to 40 megatons thus far.

If the Hessian troops sent here willy-nilly by the Hessian Government to fight for England in the 1770's were mercenaries, what shall we call the UN troops sent to the Congo willy-nilly by their governments to fight for the United Nations??

If the UN troops are not mercenaries then the Hessians were not mercenaries either.

If he were to go with White, he would be out there two days, not just listening in the dark at some point between here and Papa-san, but moving ever deeper into enemy land -- behind Papa-san -- itself.

* If it is required to use a single number X as an estimate for the value of numbers, then the arithmetic mean does this best, in the sense of minimizing the sum of squares ( x < sub > i </ sub > − X )< sup > 2 </ sup > of the residuals.

If the method is applied to an infinite sequence ( X < sub > i </ sub >: i ∈ ω ) of nonempty sets, a function is obtained at each finite stage, but there is no stage at which a choice function for the entire family is constructed, and no " limiting " choice function can be constructed, in general, in ZF without the axiom of choice.

If K is a number field, its ring of integers is the subring of algebraic integers in K, and is frequently denoted as O < sub > K </ sub >.

If M is a Turing Machine which, on input w, outputs string x, then the concatenated string < M > w is a description of x.

Theorem: If K < sub > 1 </ sub > and K < sub > 2 </ sub > are the complexity functions relative to description languages L < sub > 1 </ sub > and L < sub > 2 </ sub >, then there is a constant c – which depends only on the languages L < sub > 1 </ sub > and L < sub > 2 </ sub > chosen – such that

If the first allele is dominant to the second, then the fraction of the population that will show the dominant phenotype is p < sup > 2 </ sup > + 2pq, and the fraction with the recessive phenotype is q < sup > 2 </ sup >.

If activated cytotoxic CD8 < sup >+</ sup > T cells recognize them, the T cells begin to secrete various toxins that cause the lysis or apoptosis of the infected cell.