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A two-dimensional piecewise linear map defined by x_(n+1) = 1-y_n+|x_n| (1) y_(n+1) = x_n. (2) The map is chaotic in the filled region above and stable in the six hexagonal ...

For the hyperbolic partial differential equation u_(xy) = F(x,y,u,p,q) (1) p = u_x (2) q = u_y (3) on a domain Omega, Goursat's problem asks to find a solution u(x,y) of (3) ...

Let A be an involutive algebra over the field C of complex numbers with involution xi|->xi^♯. Then A is a left Hilbert algebra if A has an inner product <·,·> satisfying: 1. ...

A Lie group is a group with the structure of a manifold. Therefore, discrete groups do not count. However, the most useful Lie groups are defined as subgroups of some matrix ...

The word "normal form" is used in a variety of different ways in mathematics. In general, it refers to a way of representing objects so that, although each may have many ...

The so-called rule of three is an educational tool utilized historically to verbalize the process of solving basic linear equations with four terms where three of the terms ...

A tesseral harmonic is a spherical harmonic of the form cos; sin(mphi)P_l^m(costheta). These harmonics are so named because the curves on which they vanish are l-m parallels ...

A zonal harmonic is a spherical harmonic of the form P_l(costheta), i.e., one which reduces to a Legendre polynomial (Whittaker and Watson 1990, p. 302). These harmonics are ...

Let P(1/x) be a linear functional acting according to the formula <P(1/x),phi> = Pint(phi(x))/xdx (1) = ...

The numbers of eigenvalues that are positive, negative, or 0 do not change under a congruence transformation. Gradshteyn and Ryzhik (2000) state it as follows: when a ...