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Let H be a complex Hilbert space, and define a nest as a set N of closed subspaces of H satisfying the conditions: 1. 0,H in N, 2. If N_1,N_2 in N, then either N_1 subset= ...

The functions theta_s(u) = (H(u))/(H^'(0)) (1) theta_d(u) = (Theta(u+K))/(Theta(k)) (2) theta_c(u) = (H(u))/(H(K)) (3) theta_n(u) = (Theta(u))/(Theta(0)), (4) where H(u) and ...

Several flavors of the open mapping theorem state: 1. A continuous surjective linear mapping between Banach spaces is an open map. 2. A nonconstant analytic function on a ...

If (1-z)^(alpha+beta-gamma-1/2)_2F_1(2alpha,2beta;2gamma;z)=sum_(n=0)^inftya_nz^n, (1) where _2F_1(a,b;c;z) is a hypergeometric function, then (2) where (a)_n is a Pochhammer ...

Given two paired sets X_i and Y_i of n measured values, the paired t-test determines whether they differ from each other in a significant way under the assumptions that the ...

An expanded paper bag, cushion, or pillow has a distinctive shape. Given the dimensions of a flat rectangular bag with dimensions a, b, bounds for the maximum volume of ...

The pentagrammic prism is the self-intersecting uniform polyhedron with Maeder index 78 (Maeder 1997), Coxeter index 33 (Coxeter et al. 1954), and Har'El index 3 (Har'El ...

A point group is a group of symmetry operations which all leave at least one point unmoved. Although an isolated object may have an arbitrary Schönflies symbol, the ...

The Poisson-Charlier polynomials c_k(x;a) form a Sheffer sequence with g(t) = e^(a(e^t-1)) (1) f(t) = a(e^t-1), (2) giving the generating function ...

Define a power difference prime as a number of the form n^n-(n-1)^(n-1) that is prime. The first few power difference primes then have n=2, 3, 4, 7, 11, 17, 106, 120, 1907, ...