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Hilbert's problems are a set of (originally) unsolved problems in mathematics proposed by Hilbert. Of the 23 total appearing in the printed address, ten were actually ...

Every modular system has a modular system basis consisting of a finite number of polynomials. Stated another way, for every order n there exists a nonsingular curve with the ...

A determinant which arises in the solution of the second-order ordinary differential equation x^2(d^2psi)/(dx^2)+x(dpsi)/(dx)+(1/4h^2x^2+1/2h^2-b+(h^2)/(4x^2))psi=0. (1) ...

If f:[a,b]->[a,b] (where [a,b] denotes the closed interval from a to b on the real line) satisfies a Lipschitz condition with constant K, i.e., if |f(x)-f(y)|<=K|x-y| for all ...

The second-order ordinary differential equation (d^2y)/(dx^2)+[theta_0+2sum_(n=1)^inftytheta_ncos(2nx)]y=0, (1) where theta_n are fixed constants. A general solution can be ...

The upper and lower hinges are descriptive statistics of a set of N data values, where N is of the form N=4n+5 with n=0, 1, 2, .... The hinges are obtained by ordering the ...

The hinge theorem says that if two triangles DeltaABC and DeltaA^'B^'C^' have congruent sides AB=A^'B^' and AC=A^'C^' and ∠A>∠A^', then BC>B^'C^'.

A tessellation which can be thought of consisting of a number of pieces which are hinged at their vertices and therefore can be opened or closed to yield a series of ...

The hippopede, also known as the horse fetter, is a curve given by the polar equation r^2=4b(a-bsin^2theta). Hippopedes are plotted above for values of a/b=0.2 to 2.0.

The system of partial differential equations u_t = 1/2u_(xxx)+3uu_x-6ww_x (1) w_t = -w_(xxx)-3uw_x. (2)