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If a univariate real function f(x) has a single critical point and that point is a local maximum, then f(x) has its global maximum there (Wagon 1991, p. 87). The test breaks ...

An outer-totalistic cellular automaton is a generalization of the totalistic cellular automaton. Totalistic rules are a proper superset of outer-totalistic rules. In ...

An oval is a curve resembling a squashed circle but, unlike the ellipse, without a precise mathematical definition. The word oval derived from the Latin word "ovus" for egg. ...

The path covering number (or path-covering number; Slater 1972) of a graph G, variously denoted as summarized below, is the minimum number of vertex-disjoint paths that cover ...

product_(k=1)^(infty)(1-x^k) = sum_(k=-infty)^(infty)(-1)^kx^(k(3k+1)/2) (1) = 1+sum_(k=1)^(infty)(-1)^k[x^(k(3k-1)/2)+x^(k(3k+1)/2)] (2) = (x)_infty (3) = ...

A perfect cuboid is a cuboid having integer side lengths, integer face diagonals d_(ab) = sqrt(a^2+b^2) (1) d_(ac) = sqrt(a^2+c^2) (2) d_(bc) = sqrt(b^2+c^2), (3) and an ...

Petersen's theorem states that every cubic graph with no bridges has a perfect matching (Petersen 1891; Frink 1926; König 1936; Skiena 1990, p. 244). In fact, this theorem ...

For some authors (e.g., Bourbaki, 1964), the same as principal ideal domain. Most authors, however, do not require the ring to be an integral domain, and define a principal ...

A quasi-cubic graph is a quasi-regular graph, i.e., a graph such that degree of every vertex is the same delta except for a single vertex whose degree is Delta=delta+1 ...

A d-repdigit is a number composed of repetition of a single digit (in a given base, generally taken as base 10 unless otherwise specified). For example, the beast number 666 ...