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A set of 15 open problems on Schrödinger operators proposed by mathematical physicist Barry Simon (2000). This set of problems follows up a 1984 list of open problems in ...

If k is the elliptic modulus of an elliptic integral or elliptic function, then k^'=sqrt(1-k^2) (1) is called the complementary modulus. Complete elliptic integrals with ...

Let 0<k^2<1. The incomplete elliptic integral of the third kind is then defined as Pi(n;phi,k) = int_0^phi(dtheta)/((1-nsin^2theta)sqrt(1-k^2sin^2theta)) (1) = ...

If the sampling of an interferogram is modulated at a definite frequency instead of being uniformly sampled, spurious spectral features called "ghosts" are produced (Brault ...

Lambda_0(phi|m)=(F(phi|1-m))/(K(1-m))+2/piK(m)Z(phi|1-m), where phi is the Jacobi amplitude, m is the parameter, Z is the Jacobi zeta function, and F(phi|m^') and K(m) are ...

A hexahedral graph is a polyhedral graph on six vertices. There are seven distinct hexahedral graphs (illustrated above) which, through duality, correspond to seven convex ...

If and only if (i.e., necessary and sufficient). The terms "just if" or "exactly when" are sometimes used instead. A iff B is written symbolically as A<->B, A<=>B, A<->B, or ...

Denoted zn(u,k) or Z(u). Z(phi|m)=E(phi|m)-(E(m)F(phi|m))/(K(m)), where phi is the Jacobi amplitude, m is the parameter, and F(phi|m) and K(m) are elliptic integrals of the ...

Long division is an algorithm for dividing two numbers, obtaining the quotient one digit at a time. The example above shows how the division of 123456/17 is performed to ...

A polyhedral graph on five nodes. There are two topologically distinct pentahedral graphs which, through duality, correspond to the skeletons of the square pyramid (left ...