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A generalized mobile automaton is a generalization of the mobile automaton in which the automaton may have more than one active cell. Generalized mobile automata allow for ...

The system of partial differential equations u_t = (u^2-u_x+2v)_x (1) v_y = (2uv+v_x)_x. (2)

The system of partial differential equations S_t=SxS_(xx).

The system of partial differential equations del ^2s-(|a|^2+1)s = 0 (1) del ^2a-del (del ·a)-s^2a = a. (2)

The system of partial differential equations U_t = [V,W] (1) V_t = [W,U] (2) W_t = [U,V], (3) where [A,B] denotes the commutator.

A diagram used in the solution of ordinary differential equations of the form (dw)/(dz)=(g(z,w))/(h(z,q)) which vanish when z=0, where g(0,0)=h(0,0)=0 (Ince 1956, pp. 298 and ...

The cubic formula is the closed-form solution for a cubic equation, i.e., the roots of a cubic polynomial. A general cubic equation is of the form z^3+a_2z^2+a_1z+a_0=0 (1) ...

A linear recurrence equation is a recurrence equation on a sequence of numbers {x_n} expressing x_n as a first-degree polynomial in x_k with k<n. For example ...

Let B_t={B_t(omega)/omega in Omega}, t>=0, be one-dimensional Brownian motion. Integration with respect to B_t was defined by Itô (1951). A basic result of the theory is that ...

Stationary iterative methods are methods for solving a linear system of equations Ax=b, where A is a given matrix and b is a given vector. Stationary iterative methods can be ...