If you've got any ideas ''.

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

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

If the old fool argues about the price, tell him I shall order my husband not to treat him as a patient any longer.

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 any had escaped expulsion by hiding, they certainly would not frequent the market-place.

If in any one calculation Ptolemy had had to invoke 83 epicycles all at once, while Copernicus never required more than one third this number, then ( in the sense obvious to Margenau ) Ptolemaic astronomy would be simpler than Copernican.

If `` Jack the Courtier '' is really to be taken as Swift, the following remark is obviously Steele's comment on Swift's change of parties and its effect on their friendship: `` I assure you, dear Jack, when I first found out such an Allay in you, as makes you of so malleable a Constitution, that you may be worked into any Form an Artificer pleases, I foresaw I should not enjoy your Favour much longer ''.

If she wanted to borrow any sum of money in expecting the arrangements of Congress, it would not become a stranger, unknown to her, to offer himself for that purpose.

If any one of them has any power to veto the Secretary General's decisions the nature of the organization will have changed.

Mr. Richard Preston, executive director of the New Hampshire State Planning and Development Commission, in his remarks to the Governors Conference on Industrial Development at Providence on October 8, 1960, warned against the fallacy of attempting to attract industry solely to reduce the tax rate or to underwrite municipal services such as schools when he said: `` If this is the fundamental reason for a community's interest or if this is the basic approach, success if any will be difficult to obtain ''.

If an atom bomb in 1945 could destroy an entire city surely the atomic arsenal we now have is more than adequate to fulfill any military objective required of it.

If any are left, presently, we may expect to see signs specifically prohibiting the feeding of them too.

The Vice President said, `` If you hear of any names that would fix me cheap in return for advertising they decorated the Vice President's home, let me know.

If he had any worries, it was only the small ones, about Mother in New York, and his daughter Edwina and what she might be doing at this hour, with her Aunt Asia, in Philadelphia.

If he bothers you, don't pay him any mind.

If, in the trustee's judgment, `` reasonable market conditions '' did not prevail during any given year, he was to be allowed to petition the court for an extension of time within the ten-year period.

If any official operation abroad begins to go wrong, we shall look to the ambassador to find out why and to get suggestions for remedial action.

If you use a fiscal year, a year ending on the last day of any month other than December, your return is due on or before the 15th day of the 4th month after the close of your tax year.

If the last day ( due date ) for performing any act for tax purposes, such as filing a return or making a tax payment, etc., falls on Saturday, Sunday, or a legal holiday, you may perform that act on the next succeeding day which is not a Saturday, Sunday, or legal holiday.

If you file Form 1040A and the District Director computes your tax, any refund to which you are entitled will be mailed to you.

If you have neither a legal residence nor a principal place of business in any Internal Revenue district, your return should be filed with the District Director of Internal Revenue, Baltimore 2, Md..

If your principal place of abode for the tax year is outside the United States ( including Alaska and Hawaii ), Puerto Rico, or the Virgin Islands and you have no legal residence or principal place of business in any Internal Revenue district in the United States, you should file your return with the Office of International Operations, Internal Revenue Service, Washington 25, D.C..

If your state has no provisions for the numbering of pleasure boats, you must apply for a number from the U.S. Coast Guard for any kind of boat with mechanical propulsion rated at more than 10 horsepower before it can be used on Federal waterways.

If the list is a simply linked list, then the item's location is its reference, and Λ is usually the null pointer.

# If x is a variable, then x ∈ Λ

# If x is a variable and M ∈ Λ, then ( λx. M ) ∈ Λ

# If M, N ∈ Λ, then ( M N ) ∈ Λ

If is an eigendecomposition where the columns of U are unit eigenvectors and Λ is a diagonal matrix of the eigenvalues, then we have

If you compute S < sub > Λ ′</ sub > from S < sub > Λ </ sub > and then compute S < sub > Λ ″</ sub > from S < sub > Λ ′</ sub >, this gives you the same Wilsonian action as computing S < sub > Λ ″</ sub > directly from S < sub > Λ </ sub >.

If these interactions are CP-violating, as they well may be, the constraint from the ε-parameter is that the effective Λ < sub > ETC </ sub > > 10 < sup > 4 </ sup > TeV.

If p, q ∈ S and α ∈ Λ, then ( p, α, q ) ∈ → is written as

If we assign a uniform density to the joint distribution of Φ and Λ, what is its conditional density on a great circle?

If α is a differential k-form, i. e., a section of the exterior bundle Λ < sup > k </ sup > T * N of ( fiberwise ) alternating k-forms on TN, then the pullback of α is the differential k-form on M defined by the same formula as in the previous section:

If Λ is a lattice with period ratio τ then we write j ( Λ ) for j ( τ ).

If further Λ is an ideal a in a ring of integers O of a quadratic imaginary field K then we write j ( a ) for the corresponding singular modulus.

If the axion is fundamental, or emerges at a scale far higher than the QCD scale, the dimension 5 axion coupling term is suppressed by 1 / Λ where Λ is the scale where the axion appears.

If Q is diagonalizable, the matrix exponential can be computed directly: let Q = U < sup >− 1 </ sup > Λ U be a diagonalization of Q, with

If Λ is hyperbolic then there exists a Riemannian metric for which c = 1 — such a metric is called adapted.

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

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 ΔS and / or T are small, the condition ΔG < 0 may imply that ΔH < 0, which would indicate an exothermic reaction.

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.

If ADH production is excessive in heart failure, Na < sup >+</ sup > level in the plasma may fall ( hyponatremia ), and this is a sign of increased risk of death in heart failure patients.

If we define r < sub > i </ sub > as the displacement of particle i from the center of mass, and v < sub > i </ sub > as the velocity of particle i with respect to the center of mass, then we have

Let ( m, n ) be a pair of amicable numbers with m < n, and write m = gM and n = gN where g is the greatest common divisor of m and n. If M and N are both coprime to g and square free then the pair ( m, n ) is said to be regular, otherwise it is called irregular or exotic.

* The Lusternik – Schnirelmann theorem: If the sphere S < sup > n </ sup > is covered by n + 1 open sets, then one of these sets contains a pair ( x, − x ) of antipodal points.

Some authors require in addition that μ ( C ) < ∞ for every compact set C. If a Borel measure μ is both inner regular and outer regular, it is called a regular Borel measure.

If A is expressed as an N × N matrix, then A < sup >†</ sup > is its conjugate transpose.

* If G is a locally compact Hausdorff topological group and μ its Haar measure, then the Banach space L < sup > 1 </ sup >( G ) of all μ-integrable functions on G becomes a Banach algebra under the convolution xy ( g ) = ∫ x ( h ) y ( h < sup >− 1 </ sup > g ) dμ ( h ) for x, y in L < sup > 1 </ sup >( G ).