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A Bäcklund transformation allows additional solutions to a nonlinear partial differential equations to be found if one particular solution is already known.

The differential equation obtained by applying the biharmonic operator and setting to zero: del ^4phi=0. (1) In Cartesian coordinates, the biharmonic equation is del ^4phi = ...

The Bôcher Memorial Prize is awarded by the American Mathematical Society every five years for notable research in analysis that has appeared in a recognized North American ...

The Byzantine generals problem considers a computer with many programs running, some of them possibly unfriendly, and asks how the computer can function properly. More ...

A dimension also called the fractal dimension, Hausdorff dimension, and Hausdorff-Besicovitch dimension in which nonintegral values are permitted. Objects whose capacity ...

For any system that seeks to minimize a function, only seven different local forms of catastrophe "typically" occur for four or fewer variables: 1. Fold catastrophe, 2. Cusp ...

The characteristic equation is the equation which is solved to find a matrix's eigenvalues, also called the characteristic polynomial. For a general k×k matrix A, the ...

A Gaussian quadrature-like formula for numerical estimation of integrals. It uses weighting function W(x)=1 in the interval [-1,1] and forces all the weights to be equal. The ...

Chió pivotal condensation is a method for evaluating an n×n determinant in terms of (n-1)×(n-1) determinants. It also leads to some remarkable determinant identities (Eves ...

A subset S of a topological space X is compact if for every open cover of S there exists a finite subcover of S.