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A sequence {a_n}_(n=1)^N forms a (binary) heap if it satisfies a_(|_j/2_|)<=a_j for 2<=j<=N, where |_x_| is the floor function, which is equivalent to a_i<a_(2i) and ...

By way of analogy with the usual tangent tanz=(sinz)/(cosz), (1) the hyperbolic tangent is defined as tanhz = (sinhz)/(coshz) (2) = (e^z-e^(-z))/(e^z+e^(-z)) (3) = ...

Jacobi's imaginary transformations relate elliptic functions to other elliptic functions of the same type but having different arguments. In the case of the Jacobi elliptic ...

The Kakeya needle problems asks for the plane figure of least area in which a line segment of width 1 can be freely rotated (where translation of the segment is also ...

There are two sets of constants that are commonly known as Lebesgue constants. The first is related to approximation of function via Fourier series, which the other arises in ...

Find the plane lamina of least area A which is capable of covering any plane figure of unit generalized diameter. A unit circle is too small, but a hexagon circumscribed on ...

A 24-dimensional Euclidean lattice. An automorphism of the Leech lattice modulo a center of two leads to the Conway group Co_1. Stabilization of the one- and two-dimensional ...

The Lyapunov characteristic exponent [LCE] gives the rate of exponential divergence from perturbed initial conditions. To examine the behavior of an orbit around a point ...

A multiplication table is an array showing the result of applying a binary operator to elements of a given set S. For example, the following table is the multiplication table ...

The nearest integer function, also called nint or the round function, is defined such that nint(x) is the integer closest to x. While the notation |_x] is sometimes used to ...