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The root separation (or zero separation) of a polynomial P(x) with roots r_1, r_2, ... is defined by Delta(P)=min_(i!=j)|r_i-r_j|. There are lower bounds on how close two ...

Rubik's Clock is a puzzle consisting of 18 small clocks, 14 of which are independent, each of which may be set to any 12-hour position. There are therefore 12^(14) possible ...

Let the minimal length of an addition chain for a number n be denoted l(n). Then the Scholz conjecture, also called the Scholz-Brauer conjecture or Brauer-Scholz conjecture, ...

Searching refers to locating a given element or an element satisfying certain conditions from some (usually ordered or partially ordered) table, list, tree, etc.

The second Fermat point X^' or F_2 (also known as the second isogonic center) can be constructed by drawing equilateral triangles on the inside of a given triangle and ...

A point process N is called self-correcting if cov(N(s,t),N(t,u))<0 for s<t<u where here, cov denotes the covariance of the two quantities. Intuitively, a process is ...

A triangle that is equal to its polar triangle with respect to a given conic is said to be self-polar with respect to that conic. Any triangle is self-polar with respect to ...

A "split" extension G of groups N and F which contains a subgroup F^_ isomorphic to F with G=F^_N^_ and F^_ intersection N^_={e} (Ito 1987, p. 710). Then the semidirect ...

A connected graph having e graph edges is said to be sequential if it is possible to label the nodes i with distinct integers f_i in {0,1,2,...,e-1} such that when graph edge ...

The general sextic equation x^6+a_5x^5+a_4x^4+a_3x^3+a_2x^2+a_1x+a_0=0 can be solved in terms of Kampé de Fériet functions, and a restricted class of sextics can be solved in ...