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Bisection is the division of a given curve, figure, or interval into two equal parts (halves). A simple bisection procedure for iteratively converging on a solution which is ...

Let V(r) be the volume of a ball of radius r in a complete n-dimensional Riemannian manifold with Ricci curvature tensor >=(n-1)kappa. Then V(r)<=V_kappa(r), where V_kappa is ...

Bit rate (i.e., bits per second, abbreviated bps) is a measure of the number of data bits (digital 0s and 1s) transmitted each second in a digital communications channel. If ...

Let s(x,y,z) and t(x,y,z) be differentiable scalar functions defined at all points on a surface S. In computer graphics, the functions s and t often represent texture ...

Let alpha(z),gamma(z):(a,b)->R^3 be curves such that |gamma|=1 and alpha·gamma=0, and suppose that alpha and gamma have holomorphic extensions alpha,gamma:(a,b)×(c,d)->C^3 ...

If {a_j} subset= D(0,1) (with possible repetitions) satisfies sum_(j=1)^infty(1-|a_j|)<=infty, where D(0,1) is the unit open disk, and no a_j=0, then there is a bounded ...

Any bounded planar region with positive area >A placed in any position of the unit square lattice can be translated so that the number of lattice points inside the region ...

The qubit |psi>=a|0>+b|1> can be represented as a point (theta,phi) on a unit sphere called the Bloch sphere. Define the angles theta and phi by letting a=cos(theta/2) and ...

A block diagonal matrix, also called a diagonal block matrix, is a square diagonal matrix in which the diagonal elements are square matrices of any size (possibly even 1×1), ...

Let (x_0x_1x_2...) be a sequence over a finite alphabet A (all the entries are elements of A). Define the block growth function B(n) of a sequence to be the number of ...