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If at least one solution can be determined for a given problem, a solution to that problem is said to exist. Frequently, mathematicians seek to prove the existence of ...

If F is a group, then the extensions G of F of order o with G/phi(G)=F, where phi(G) is the Frattini subgroup, are called Frattini extensions.

The dual of the great truncated cuboctahedron U_(20) and Wenninger dual W_(93).

The determinant of a knot is defined as |Delta(-1)|, where Delta(z) is the Alexander polynomial (Rolfsen 1976, p. 213).

D^*Dpsi=del ^*del psi+1/4Rpsi-1/2F_L^+(psi), where D is the Dirac operator D:Gamma(W^+)->Gamma(W^-), del is the covariant derivative on spinors, R is the scalar curvature, ...

An algorithm for finding roots for quartic equations with complex roots.

The mathematical study of the scattering operator and Schrödinger equation.

The functional equation phi(f(x))=sphi(x), with s!=0,1.

Johnson solid J_(85).

The 6-polyiamond illustrated above, named for its resemblance to the Great Sphinx of Egypt.