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A vector bundle is special class of fiber bundle in which the fiber is a vector space V. Technically, a little more is required; namely, if f:E->B is a bundle with fiber R^n, ...

A schematic diagram used in logic theory to depict collections of sets and represent their relationships. The Venn diagrams on two and three sets are illustrated above. The ...

Let c_k be the number of vertex covers of a graph G of size k. Then the vertex cover polynomial Psi_G(x) is defined by Psi_G(x)=sum_(k=0)^(|G|)c_kx^k, (1) where |G| is the ...

An e-prime is a prime number appearing in the decimal expansion of e. The first few are 2, 271, 2718281, ...

Salem constants, sometimes also called Salem numbers, are a set of numbers of which each point of a Pisot number is a limit point from both sides (Salem 1945). The Salem ...

An (ordinary) torus is a surface having genus one, and therefore possessing a single "hole" (left figure). The single-holed "ring" torus is known in older literature as an ...

A Boolean algebra is a mathematical structure that is similar to a Boolean ring, but that is defined using the meet and join operators instead of the usual addition and ...

The curve a hanging flexible wire or chain assumes when supported at its ends and acted upon by a uniform gravitational force. The word catenary is derived from the Latin ...

Let there be n>=2 integers 0<a_1<...<a_n with GCD(a_1,a_2,...,a_n)=1. The values a_i represent the denominations of n different coins, where these denominations have greatest ...

The complex numbers are the field C of numbers of the form x+iy, where x and y are real numbers and i is the imaginary unit equal to the square root of -1, sqrt(-1). When a ...