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There are at least three theorems known as Jensen's theorem. The first states that, for a fixed vector v=(v_1,...,v_m), the function |v|_p=(sum_(i=1)^m|v_i|^p)^(1/p) is a ...

A goodness-of-fit test for any statistical distribution. The test relies on the fact that the value of the sample cumulative density function is asymptotically normally ...

A merge sort (or collation sort) is the combination of two or more ordered lists into a single ordered list (Knuth 1998, p. 158). Merge sorting was one of the first methods ...

The middle layer graph of order n is the graph whose vertex set consists of all bitstrings of length 2n+1 that have exactly n or n+1 entries equal to 1, with an edge between ...

What is the sofa of greatest area S which can be moved around a right-angled hallway of unit width? Hammersley (Croft et al. 1994) showed that S>=pi/2+2/pi=2.2074... (1) ...

A problem is assigned to the NP (nondeterministic polynomial time) class if it is solvable in polynomial time by a nondeterministic Turing machine. A P-problem (whose ...

A pair of elements (p_i,p_j) is called an inversion in a permutation p if i>j and p_i<p_j (Skiena 1990, p. 27; Pemmaraju and Skiena 2003, p. 69). For example, in the ...

A set of ascending sequences in a permutation is called a run (Graham et al. 1994) or sometimes a rise (Comtet 1974, p. 241). A sorted permutation consists of a single run, ...

For every positive integer n, there is a unique finite sequence of distinct nonconsecutive (not necessarily positive) integers k_1, ..., k_m such that ...

Every nonconstant entire function attains every complex value with at most one exception (Henrici 1988, p. 216; Apostol 1997). Furthermore, every analytic function assumes ...