If it's true that contented cows give more milk, why shouldn't happy ball players produce more base hits??

If one takes the middle number, 5, and multiplies it by 3 ( the base number of the magic square of three ), the result is 15, which is also the constant sum of all the rows, columns, and two main diagonals.

If nectaries are present, they are in the septa of the ovaries rather than at the base of the tepals or stamens.

* Let Q be a set enclosed between two step regions S and T. A step region is formed from a finite union of adjacent rectangles resting on a common base, i. e. S ⊆ Q ⊆ T. If there is a unique number c such that a ( S ) ≤ c ≤ a ( T ) for all such step regions S and T, then a ( Q )

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

If the batter gets a base hit, which would have scored the runner anyway, the run now becomes earned.

If a batter reaches first base because of offensive interference by a preceding runner ( including if a preceding runner is hit by a batted ball ), he is also credited with a hit.

If the pitcher allows no runners to reach base, the no-hitter is a perfect game.

If the defense makes no attempt to put the baserunner out ( for example, if the catcher doesn't even look his way ), the play is scored as defensive indifference ( also called fielder's indifference ), and no stolen base is credited to the runner.

If the ball is dead on the pitch run on, such as from a foul ball ( except caught fly-out ), the steal is not allowed and the runner returns to his time-of-pitch base.

If he begins to run too soon, the pitcher may throw to a base rather than to home — in this case, the runner is picked off, and will most likely be tagged out.

If the game has been scored correctly, the total number of plate appearances for a team should equal the total of that team's runs, men left on base, and men put out.

If instead the roll is 4, 5, 6, 8, 9, 10 then the come bet will be moved by the base dealer onto a box representing the number the shooter threw.

If instead the roll is 4, 5, 6, 8, 9, 10 then the don't come bet will be moved by the base dealer onto a box representing the number the shooter threw.

* If is the norm ( usually noted as ) defined in the sequence space ℓ < sup >∞</ sup > of all bounded sequences ( which also matches the non-linear distance measured as the maximum of distances measured on projections into the base subspaces, without requiring the space to be isotropic or even just linear, but only continuous, such norm being definable on all Banach spaces ), and is lower triangular non-singular ( i. e., ) then

If frequency-hopping is avoided, each base station can provide up to 120 channels in the DECT spectrum before frequency reuse.

If implemented using remainders of Euclidean division rather than subtractions, Euclid's algorithm computes the GCD of large numbers efficiently: it never requires more division steps than five times the number of digits ( base 10 ) of the smaller integer.

If the base field is over the rationals, care must be taken when extending the field to add the needed transcendental constants.

If the baseband data signal ( the message ) to be transmitted is and the sinusoidal carrier is, where f < sub > c </ sub > is the carrier's base frequency and A < sub > c </ sub > is the carrier's amplitude, the modulator combines the carrier with the baseband data signal to get the transmitted signal:

If f: X → Y morphism of pointed spaces, then every loop in X with base point x < sub > 0 </ sub > can be composed with f to yield a loop in Y with base point y < sub > 0 </ sub >.

If f: X → Y is a continuous map, x < sub > 0 </ sub > ∈ X and y < sub > 0 </ sub > ∈ Y with f ( x < sub > 0 </ sub >) = y < sub > 0 </ sub >, then every loop in X with base point x < sub > 0 </ sub > can be composed with f to yield a loop in Y with base point y < sub > 0 </ sub >.

If the base manifold is four-dimensional, the Kaluza – Klein manifold P is five-dimensional.

If a text ( such as this one ) discusses multiple bases, and if ambiguity exists, the base ( itself represented in base 10 ) is added in subscript to the right of the number, like this: number < sub > base </ sub >.

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 T is a linear operator on an arbitrary vector space and if there is a monic polynomial P such that Af, then parts ( A ) and ( B ) of Theorem 12 are valid for T with the proof which we gave.

If Af denotes the space of N times continuously differentiable functions, then the space V of solutions of this differential equation is a subspace of Af.

If D denotes the differentiation operator and P is the polynomial Af then V is the null space of the operator p (, ), because Af simply says Af.

If Af is the null space of Af, then Theorem 12 says that Af.

If the argument is accepted as essentially sound up to this point, it remains for us to consider whether the patient's difficulties in orienting himself spatially and in locating objects in space with the sense of touch can be explained by his defective visual condition.

If, on the other hand, they opted for representation, it had to be representation per se -- representation as image pure and simple, without connotations ( at least, without more than schematic ones ) of the three-dimensional space in which the objects represented originally existed.

If a child loses a molar at the age of two, the adjoining teeth may shift toward the empty space, thus narrowing the place intended for the permanent ones and producing a jumble.

If elements in the sample space increase arithmetically, when placed in some order, then the median and arithmetic average are equal.

If antimatter-dominated regions of space existed, the gamma rays produced in annihilation reactions along the boundary between matter and antimatter regions would be detectable.

If X is a Banach space and K is the underlying field ( either the real or the complex numbers ), then K is itself a Banach space ( using the absolute value as norm ) and we can define the continuous dual space as X ′ = B ( X, K ), the space of continuous linear maps into K.

* Theorem If X is a normed space, then X ′ is a Banach space.

If F is also surjective, then the Banach space X is called reflexive.

* Corollary If X is a Banach space, then X is reflexive if and only if X ′ is reflexive, which is the case if and only if its unit ball is compact in the weak topology.

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 the norm of a Banach space satisfies this identity, the associated inner product which makes it into a Hilbert space is given by the polarization identity.

If X is a real Banach space, then the polarization identity is

If this suggestion is correct, the beginning of the world happened a little before the beginning of space and time.