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The G-transform of a function f(x) is defined by the integral (Gf)(x)=(G_(pq)^(mn)|(a_p); (b_q)|f(t))(x) (1) =1/(2pii)int_sigmaGamma[(b_m)+s, 1-(a_n)-s; (a_p^(n+1))+s, ...

A partial differential equation of second-order, i.e., one of the form Au_(xx)+2Bu_(xy)+Cu_(yy)+Du_x+Eu_y+F=0, (1) is called hyperbolic if the matrix Z=[A B; B C] (2) ...

A partial differential equation whose solution does not depend continuously on its parameters (including but not limited to boundary conditions) is said to be ill-posed.

A polynomial factorization algorithm that proceeds by considering the vector of coefficients of a polynomial P, calculating b_i=P(i)/a_i, constructing the Lagrange ...

The Kuhn-Tucker theorem is a theorem in nonlinear programming which states that if a regularity condition holds and f and the functions h_j are convex, then a solution ...

Simple majority vote is the only procedure which is anonymous, dual, and monotonic.

A module homomorphism is a map f:M->N between modules over a ring R which preserves both the addition and the multiplication by scalars. In symbols this means that ...

A pair of functions phi_i(x) and phi_j(x) are orthonormal if they are orthogonal and each normalized so that int_a^b[phi_i(x)]^2w(x)dx = 1 (1) int_a^b[phi_j(x)]^2w(x)dx = 1. ...

A partial differential equation (PDE) is an equation involving functions and their partial derivatives; for example, the wave equation ...

A function or curve is piecewise continuous if it is continuous on all but a finite number of points at which certain matching conditions are sometimes required.