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Let a convex polygon be inscribed in a circle and divided into triangles from diagonals from one polygon vertex. The sum of the radii of the circles inscribed in these ...

A system of curvilinear coordinates in which two sets of coordinate surfaces are obtained by revolving the curves of the elliptic cylindrical coordinates about the x-axis, ...

A quadratic form involving n real variables x_1, x_2, ..., x_n associated with the n×n matrix A=a_(ij) is given by Q(x_1,x_2,...,x_n)=a_(ij)x_ix_j, (1) where Einstein ...

A sequence which arises in the hypothetical reproduction of a population of rabbits. Let the substitution system map 0->1 correspond to young rabbits growing old, and 1->10 ...

A moment mu_n of a probability function P(x) taken about 0, mu_n^' = <x^n> (1) = intx^nP(x)dx. (2) The raw moments mu_n^' (sometimes also called "crude moments") can be ...

Ede (1958) enumerates 13 basic series of stellations of the rhombic triacontahedron, the total number of which is extremely large. Pawley (1973) gave a set of restrictions ...

In his famous paper of 1859, Riemann stated that the number N(T) of Riemann zeta function zeros sigma+it with 0<t<=T is asymptotically given by ...

Let psi_1(x) and psi_2(x) be any two real integrable functions in [a,b], then Schwarz's inequality is given by |<psi_1|psi_2>|^2<=<psi_1|psi_1><psi_2|psi_2>. (1) Written out ...

The Siegel theta function is a Gamma_n-invariant meromorphic function on the space of all p×p symmetric complex matrices Z=X+iY with positive definite imaginary part. It is ...

In general, a singularity is a point at which an equation, surface, etc., blows up or becomes degenerate. Singularities are often also called singular points. Singularities ...