* 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 ).

If Af is the operator induced on Af by T, then evidently Af, because by definition Af is 0 on the subspace Af.

If the distribution of the 71 items were wholly concordant in the two families, the distance would of course be 0.

If the color were fully green, its RGBA would be ( 0, 1, 0, 0. 5 ).

If the valid element indices begin at 0, the constant B is simply the address of the first element of the array.

If the numbering does not start at 0, the constant B may not be the address of any element.

If the minimum legal value for every index is 0, then B is the address of the element whose indices are all zero.

If Acorn had thought to include this small modification in the original Electron design it is likely the machine would have had a much greater impact as it would have nearly doubled the amount of motion possible in games and saved modes 0 – 3 ( including the only 16 colour mode ) from being nearly useless due to contended memory timings.

If no address is provided, one is picked at random from the " base subnet ", 0.

If the balance factor becomes 0 then the height of the subtree has decreased by one and the retracing needs to continue.

If the rotation leaves the subtree's balance factor at 0 then the retracing towards the root must continue since the height of this subtree has decreased by one.

If the maximum gain is 0 dB, the 3 dB gain is the range where the gain is more than-3dB, or the attenuation is less than + 3dB.

If a DFS ROM is installed, will cause the computer to search for and load a file called on the floppy disk in drive 0.

If not, the curve is subdivided parametrically into two segments, 0 ≤ t ≤ 0. 5 and 0. 5 ≤ t ≤ 1, and the same procedure is applied recursively to each half.

If we attempt to use the above formula to compute the derivative of f at zero, then we must evaluate 1 / g ′( f ( 0 )).

If we set, then η is continuous at 0.

If sender0 has code ( 1, – 1 ) and data ( 1, 0, 1, 1 ), and sender1 has code ( 1, 1 ) and data ( 0, 0, 1, 1 ), and both senders transmit simultaneously, then this table describes the coding steps:

If this limit exists, then it may be computed by taking the limit as h → 0 along the real axis or imaginary axis ; in either case it should give the same result.

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.