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Given a nonhomogeneous ordinary differential equation, select a differential operator which will annihilate the right side, and apply it to both sides. Find the solution to ...

Lagrange multipliers, also called Lagrangian multipliers (e.g., Arfken 1985, p. 945), can be used to find the extrema of a multivariate function f(x_1,x_2,...,x_n) subject to ...

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, ...

A complicated polynomial root-finding algorithm which is used in the IMSL® (IMSL, Houston, TX) library and which Press et al. (1992) describe as "practically a standard in ...

The expansion of the two sides of a sum equality in terms of polynomials in x^m and y^k, followed by closed form summation in terms of x and y. For an example of the ...

A deconvolution algorithm (sometimes abbreviated MEM) which functions by minimizing a smoothness function ("entropy") in an image. Maximum entropy is also called the ...

If del xF=0 (i.e., F(x) is an irrotational field) in a simply connected neighborhood U(x) of a point x, then in this neighborhood, F is the gradient of a scalar field phi(x), ...

A prime factorization algorithm.

A prime factorization algorithm which can be implemented in a single-step or double-step form. In the single-step version, a prime factor p of a number n can be found if p-1 ...

For a smooth harmonic map u:M->N, where del is the gradient, Ric is the Ricci curvature tensor, and Riem is the Riemann tensor.