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The biconjugate gradient method often displays rather irregular convergence behavior. Moreover, the implicit LU decomposition of the reduced tridiagonal system may not exist, ...

The Galton board, also known as a quincunx or bean machine, is a device for statistical experiments named after English scientist Sir Francis Galton. It consists of an ...

Ruffini's rule a shortcut method for dividing a polynomial by a linear factor of the form x-a which can be used in place of the standard long division algorithm. This method ...

A technique used by André (1887) to provide an elegant solution to the ballot problem (Hilton and Pederson 1991) and in study of Wiener processes (Doob 1953; Papoulis 1984, ...

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 ...

A number which can be represented by a finite number of additions, subtractions, multiplications, divisions, and finite square root extractions of integers. Such numbers ...

Let a Gram point g_n be called "good" if (-1)^nZ(g_n)>0, and "bad" otherwise (Rosser et al. 1969; Edwards 2001, p. 180). Then the interval between two consecutive good Gram ...

A handle is a topological structure which can be thought of as the object produced by puncturing a surface twice, attaching a zip around each puncture travelling in opposite ...

A homogeneous ideal I in a graded ring R= direct sum A_i is an ideal generated by a set of homogeneous elements, i.e., each one is contained in only one of the A_i. For ...

The spherical harmonics form a complete orthogonal system, so an arbitrary real function f(theta,phi) can be expanded in terms of complex spherical harmonics by ...