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 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 g is the metric on this manifold, one defines the action S ( g ) as

If the underlying manifold is supersymmetric, the resulting theory is a supersymmetric Yang – Mills theory.

If the underlying manifold is allowed to be infinite dimensional ( for example, a Hilbert manifold ), then one arrives at the notion of an infinite-dimensional Lie group.

# If G is any group acting smoothly on the manifold M, then it acts on the vector fields, and the vector space of vector fields fixed by the group is closed under the Lie bracket and therefore also forms a Lie algebra.

If the manifold is a circle these are called loop groups, and have central extensions whose Lie algebras are ( more or less ) Kac – Moody algebras.

* If M is a smooth manifold, R is the ring of smooth real functions on M, and x is a point in M, then the set of all smooth functions f with f ( x )

If M is an open subset of R < sup > n </ sup >, then M is a C < sup >∞</ sup > manifold in a natural manner ( take the charts to be the identity maps ), and the tangent spaces are all naturally identified with R < sup > n </ sup >.

If the manifold is the surface of the Earth,

If the range of each chart is the n-dimensional Euclidean space, then M is said to be an n-dimensional manifold.

If the manifold M is smooth ( respectively analytic )--- that is, the change of coordinates are smooth ( respectively analytic )--- then one can make sense of the notion of smooth ( respectively analytic ) vector fields.

If such a collection of inner products on the tangent bundle of a manifold varies smoothly as one traverses the manifold, then concepts that were defined only pointwise at each tangent space can be extended to yield analogous notions over finite regions of the manifold.

If γ: b → M is a continuously differentiable curve in the Riemannian manifold M, then we define its length L ( γ ) in analogy with the example above by

If the field is a real vector field, then the target manifold is isomorphic to R < sup > 3 </ sup >.

If is continuously differentiable then the hypersurface is a differentiable manifold in the neighbourhood of the points where the gradient is not null.

If M is a simply connected compact n-dimensional Riemannian manifold with sectional curvature strictly pinched between 1 / 4 and 1 then M is diffeomorphic to a sphere.

If M is a non-compact complete non-negatively curved n-dimensional Riemannian manifold, then M contains a compact, totally geodesic submanifold S such that M is diffeomorphic to the normal bundle of S ( S is called the soul of M .) In particular, if M has strictly positive curvature everywhere, then it is diffeomorphic to R < sup > n </ sup >.

# If M is a complete Riemannian manifold with sectional curvature bounded above by a strictly negative constant k then it is a CAT ( k ) space.

If a compact Riemannian manifold has positive Ricci curvature then its fundamental group is finite.

If a complete n-dimensional Riemannian manifold has nonnegative Ricci curvature and a straight line ( i. e. a geodesic which minimizes distance on each interval ) then it is isometric to a direct product of the real line and a complete ( n-1 )- dimensional Riemannian manifold which has nonnegative Ricci curvature.