If anyone thought of the John Harvey, it was to observe that she was straddled by a pair of ships heavily laden with high explosive and if they were hit the John Harvey would likely be blown up with her own ammo and whatever else it was that she carried.

If this article / noun pair is used as the object of a verb, it ( usually ) changes to the accusative case, which entails an article shift in German – Ich sehe den Wagen.

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.

If a pair cannot hit downwards, they will use flat strokes in an attempt to gain the attack.

If a pair is forced to lift or clear the shuttlecock, then they must defend: they will adopt a side-by-side position in the rear midcourt, to cover the full width of their court against the opponents ' smashes.

If all four players pass in the first round, the deal is not played ; in rubber bridge the deal is not scored and the hand is redealt by the original dealer, while in duplicate the score is recorded as zero for each pair and returned to the board.

* 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.

If ( 1a ) and ( 1b ) hold for a differentiable pair of functions u and v, then so do

If breeding hamsters, separation of the pair after mating is recommended, or they will attack each other.

If this binding energy is higher than the energy provided by kicks from oscillating atoms in the conductor ( which is true at low temperatures ), then the electron pair will stick together and resist all kicks, thus not experiencing resistance.

If correct, the teacher would read the next word pair.

If one wishes to employ the notation for a different purpose ( such as denoting open intervals on the real number line ) the ordered pair may be denoted by the variant notation

If Mary says she has no pair, but in fact she has a flush, her cards speak and her hand is viewed for its genuine value, that of a flush.

If all masses were doubled in value you cannot tell, because all the pure numbers defined by the ratios of any pair of masses are unchanged.

If a Day or Teen tile is used with an eight, the pair is worth ten instead of the usual zero.

If a hand contained one of the tiles on the left and one of the tiles on the right, these would not form a pair at all, since the tiles that make pairs are defined by tradition.

) If a hand is made up of a pair, it always scores higher than a non-pair, no matter what the value of the pips are.

* If a player has nothing but a single pair, he can set it in his five-card hand and put the two highest remaining cards in his two-card hand.

If a player's side cards are small or his larger pair is large, he should split the pairs.

If a player has no side cards higher than a jack, he should always split pairs, even 2s and 3s ( most house ways split if there's a pair of 6s or higher, and split small pairs if there's no ace for the low hand ).

Straight or Flush with one pair: If you can play a face pair with an ace-face top when the straight or flush gives only a Q-x or lower top, play the strong pair with an ace-face top.

If your full house ’ s pair is 5 ’ s or less, and your hand has an AK ( AQ with 4 ’ s or 3 ’ s, AJ with 2 ’ s ), then keep the full house, and play the Ace-face up.

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 we define the function f ( n ) = A ( n, n ), which increases both m and n at the same time, we have a function of one variable that dwarfs every primitive recursive function, including very fast-growing functions such as the exponential function, the factorial function, multi-and superfactorial functions, and even functions defined using Knuth's up-arrow notation ( except when the indexed up-arrow is used ).

If f is not a function, but is instead a partial function, it is called a partial operation.

The tensor product X ⊗ Y from X and Y is a K-vector space Z with a bilinear function T: X × Y → Z which has the following universal property: If T ′: X × Y → Z ′ is any bilinear function into a K-vector space Z ′, then only one linear function f: Z → Z ′ with exists.

If f is also surjective and therefore bijective ( since f is already defined to be injective ), then S is called countably infinite.

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 k, m, and n are 1, so that and, then the Jacobian matrices of f and g are.

If f is a function of as above, then the second derivative of is:

If we let f be a function

If a probability distribution has a density function f ( x ), then the mean is

If the function f is not linear ( i. e. its graph is not a straight line ), however, then the change in y divided by the change in x varies: differentiation is a method to find an exact value for this rate of change at any given value of x.

If the limit exists, then f is differentiable at a.

If f is a continuous function, meaning that its graph is an unbroken curve with no gaps, then Q is a continuous function away from.

If the limit exists, meaning that there is a way of choosing a value for Q ( 0 ) that makes the graph of Q a continuous function, then the function f is differentiable at a, and its derivative at a equals Q ( 0 ).

If y = f ( x ) is differentiable at a, then f must also be continuous at a.

If in the third identity we take H = G, we get that the set of commutators is stable under any endomorphism of G. This is in fact a generalization of the second identity, since we can take f to be the conjugation automorphism.

If f is a surjection and a ~ b ↔ f ( a ) = f ( b ), then g is a bijection.

If m and n are natural numbers and f ( x ) is a smooth ( meaning: sufficiently often differentiable ) function defined for all real numbers x in the interval, then the integral

* 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 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 P is a program which outputs a string x, then P is a description of x.

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

If the filter shows amplitude ripple within the passband, the x dB point refers to the point where the gain is x dB below the nominal passband gain rather than x dB below the maximum gain.

* 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 a Banach algebra has unit 1, then 1 cannot be a commutator ; i. e., for any x, y ∈ A.

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

If the exponent r is even, then the inequality is valid for all real numbers x.

If x is a member of A, then it is also said that x belongs to A, or that x is in A.

If ( x < sub > 1 </ sub >, x < sub > 2 </ sub >, x < sub > 3 </ sub >) are the Cartesian coordinates and ( u < sub > 1 </ sub >, u < sub > 2 </ sub >, u < sub > 3 </ sub >) are the orthogonal coordinates, then