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For all integers n and nonnegative integers t, the harmonic logarithms lambda_n^((t))(x) of order t and degree n are defined as the unique functions satisfying 1. ...

The construction of polyhedra using identical building blocks. The illustrations above show such constructions for the cuboctahedron, octahedron rhombic dodecahedron, and ...

The mean triangle area of a triangle picked inside a regular hexagon with unit area is A^_=289/3888 (Woolhouse 1867, Pfiefer 1989). This is a special case of a general ...

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 ...

Extend Hilbert's inequality by letting p,q>1 and 1/p+1/q>=1, (1) so that 0<lambda=2-1/p-1/q<=1. (2) Levin (1937) and Stečkin (1949) showed that (3) and ...

Define F(1)=1 and S(1)=2 and write F(n)=F(n-1)+S(n-1), where the sequence {S(n)} consists of those integers not already contained in {F(n)}. For example, F(2)=F(1)+S(1)=3, so ...

The pair of sequences defined by F(0)=1, M(0)=0, and F(n) = n-M(F(n-1)) (1) M(n) = n-F(M(n-1)). (2) The first few terms of the "male" sequence M(n) for n=0, 1, ... are 0, 0, ...

There are two possible definitions: 1. Possessing similarity of form, 2. Continuous, one-to-one, in surjection, and having a continuous inverse. The most common meaning is ...

As of 2014, the IEEE 754-2008 is the most commonly implemented standard for floating-point arithmetic. This framework is a massive overhaul of its predecessor IEEE 754-1985 ...

The jinc function is defined as jinc(x)=(J_1(x))/x, (1) where J_1(x) is a Bessel function of the first kind, and satisfies lim_(x->0)jinc(x)=1/2. The derivative of the jinc ...