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An algebraic equation is algebraically solvable iff its group is solvable. In order that an irreducible equation of prime degree be solvable by radicals, it is necessary and ...

The Diophantine equation x^2+y^2=p can be solved for p a prime iff p=1 (mod 4) or p=2. The representation is unique except for changes of sign or rearrangements of x and y. ...

A formula for numerical solution of differential equations, (1) where k_1 = hf(x_n,y_n) (2) k_2 = hf(x_n+1/2h,y_n+1/2k_1) (3) k_3 = ...

A generalization of an ordinary two-dimensional surface embedded in three-dimensional space to an (n-1)-dimensional surface embedded in n-dimensional space. A hypersurface is ...

The pedal curve for an n-cusped hypocycloid x = a((n-1)cost+cos[(n-1)t])/n (1) y = a((n-1)sint-sin[(n-1)t])/n (2) with pedal point at the origin is the curve x_p = ...

A function which is not defined explicitly, but rather is defined in terms of an algebraic relationship (which can not, in general, be "solved" for the function in question). ...

A generalization of the Runge-Kutta method for solution of ordinary differential equations, also called Rosenbrock methods.

A sequence X_1, X_2, ... of random variates is called Markov (or Markoff) if, for any n, F(X_n|X_(n-1),X_(n-2),...,X_1)=F(X_n|X_(n-1)), i.e., if the conditional distribution ...

A quadratic surface given by the equation x^2+2rz=0.

If f is a continuous function that satisfies the Lipschitz condition |f(x,t)-f(y,t)|<=L|x-y| (1) in a surrounding of (x_0,t_0) in Omega subset ...