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Let (x_1,x_2) and (y_1,y_2) be two sets of complex numbers linearly independent over the rationals. Then the four exponential conjecture posits that at least one of ...

The frame bundle on a Riemannian manifold M is a principal bundle. Over every point p in M, the Riemannian metric determines the set of orthonormal frames, i.e., the possible ...

An equation of the form f(x,y,...)=0, where f contains a finite number of independent variables, known functions, and unknown functions which are to be solved for. Many ...

A solid such that the area A_y of any section parallel to and a distance y from a fixed plane can be expressed as A_y=ay^3+by^2+cy+d. The volume of such a solid is the same ...

A d-dimensional framework is a pair (G,p) where G=(V,E) is a graph with vertex set V and edge set E and p:V->R^d is a map that assigns a point in R^d to each vertex of G. The ...

A Goldbach number is a positive integer that is the sum of two odd primes (Li 1999). Let E(x) (the "exceptional set of Goldbach numbers") denote the number of even numbers ...

The great rhombidodecahedron is the uniform polyhedron with Maeder index 73 (Maeder 1997), Wenninger index 109 (Wenninger 1989), Coxeter index 89 (Coxeter et al. 1954), and ...

A set of vectors in Euclidean n-space is said to satisfy the Haar condition if every set of n vectors is linearly independent (Cheney 1999). Expressed otherwise, each ...

The second-order ordinary differential equation (d^2y)/(dx^2)-2x(dy)/(dx)+lambday=0. (1) This differential equation has an irregular singularity at infty. It can be solved ...

Let H be a Hilbert space and (e_i)_(i in I) is an orthonormal basis for H. The set S(H) of all operators T for which sum_(i in I)||Te_i||^2<infty is a self-adjoint ideal of ...