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A square matrix A is said to be unipotent if A-I, where I is an identity matrix is a nilpotent matrix (defined by the property that A^n is the zero matrix for some positive ...

An illusion invented by the German psychologist Wilhelm Wundt in the 19th century. In the figure above, the two red horizontal lines are both straight, but they look as if ...

Zero is the integer denoted 0 that, when used as a counting number, means that no objects are present. It is the only integer (and, in fact, the only real number) that is ...

Let a divisor d of n be called a 1-ary (or unitary) divisor if d_|_n/d (i.e., d is relatively prime to n/d). Then d is called a k-ary divisor of n, written d|_kn, if the ...

A busy beaver is an n-state, 2-color Turing machine which writes a maximum number Sigma(n) of 1s before halting (Rado 1962; Lin and Rado 1965; Shallit 1998). Alternatively, ...

Regge calculus is a finite element method utilized in numerical relativity in attempts of describing spacetimes with few or no symmetries by way of producing numerical ...

Let b(k) be the number of 1s in the binary expression of k, i.e., the binary digit count of 1, giving 1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3, ... (OEIS A000120) for k=1, 2, .... ...

Let L(n,d) be the smallest tour length for n points in a d-D hypercube. Then there exists a smallest constant alpha(d) such that for all optimal tours in the hypercube, lim ...

Probability and Statistics

The above topological structure, composed of a countable union of compact sets, is called Alexander's horned sphere. It is homeomorphic with the ball B^3, and its boundary is ...