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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, ...

There are two camps of thought on the meaning of general recursive function. One camp considers general recursive functions to be equivalent to the usual recursive functions. ...

If mu is a real measure (i.e., a measure that takes on real values), then one can decompose it according to where it is positive and negative. The positive variation is ...

Given n points, find the line segments with the shortest possible total length which connect the points. The segments need not necessarily be straight from one point to ...

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 ...

A sum of the digits in a given transmission modulo some number. The simplest form of checksum is a parity bit appended on to 7-bit numbers (e.g., ASCII characters) such that ...

Let Jones and Smith be the only two contestants in an election that will end in a deadlock when all votes for Jones (J) and Smith (S) are counted. What is the expectation ...

A formula satisfied by all Hamiltonian cycles with n nodes. Let f_j be the number of regions inside the circuit with j sides, and let g_j be the number of regions outside the ...

If 0<=a,b,c,d<=1, then (1-a)(1-b)(1-c)(1-d)+a+b+c+d>=1. This is a special case of the general inequality product_(i=1)^n(1-a_i)+sum_(i=1)^na_i>=1 for 0<=a_1,a_2,...,a_n<=1. ...

Gaussian curvature, sometimes also called total curvature (Kreyszig 1991, p. 131), is an intrinsic property of a space independent of the coordinate system used to describe ...