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If there exists a critical region C of size alpha and a nonnegative constant k such that (product_(i=1)^(n)f(x_i|theta_1))/(product_(i=1)^(n)f(x_i|theta_0))>=k for points in ...

The geometry of the Lie group consisting of real matrices of the form [1 x y; 0 1 z; 0 0 1], i.e., the Heisenberg group.

Any cubic curve that passes through eight of the nine intersections of two given cubic curves automatically passes through the ninth.

An extremely powerful theorem in physics which states that each symmetry of a system leads to a physically conserved quantity. Symmetry under translation corresponds to ...

Any irreducible curve may be carried by a factorable Cremona transformation into one with none but ordinary singular points.

A geometry in which Archimedes' axiom does not hold.

An algebra which does not satisfy a(bc)=(ab)c is called a nonassociative algebra.

A generalization of Student's t-distribution known as the noncentral Student's t-distribution is given by (1) where Gamma(z) is the gamma function and _1F_1(a;b;z) is a ...

A positive value of n for which x-phi(x)=n has no solution, where phi(x) is the totient function. The first few are 10, 26, 34, 50, 52, ... (OEIS A005278).

A ruled surface parameterization x(u,v)=b(u)+vg(u) is called noncylindrical if gxg^' is nowhere 0. A noncylindrical ruled surface always has a parameterization of the form ...