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A necessary and sufficient condition for all the eigenvalues of a real n×n matrix A to have negative real parts is that the equation A^(T)V+VA=-I has as a solution where V is ...

A quantified system of real algebraic equations and inequalities in variables {x_1,...,x_n} is an expression QS=Q_1(y_1)Q_2(y_2)...Q_m(y_m)S(x_1,...,x_n;y_1,...,y_m), where Q ...

Surrogate data are artificially generated data which mimic statistical properties of real data. Isospectral surrogates have identical power spectra as real data but with ...

Salem constants, sometimes also called Salem numbers, are a set of numbers of which each point of a Pisot number is a limit point from both sides (Salem 1945). The Salem ...

A power floor prime sequence is a sequence of prime numbers {|_theta^n_|}_n, where |_x_| is the floor function and theta>1 is real number. It is unknown if, though extremely ...

Sylvester's line problem, known as the Sylvester-Gallai theorem in proved form, states that it is not possible to arrange a finite number of points so that a line through ...

If theta is a given irrational number, then the sequence of numbers {ntheta}, where {x}=x-|_x_|, is dense in the unit interval. Explicitly, given any alpha, 0<=alpha<=1, and ...

Infinity, most often denoted as infty, is an unbounded quantity that is greater than every real number. The symbol infty had been used as an alternative to M (1000) in Roman ...

A set A in a first-countable space is dense in B if B=A union L, where L is the set of limit points of A. For example, the rational numbers are dense in the reals. In ...

A real quantity having a value less than zero (<0) is said to be negative. Negative numbers are denoted with a minus sign preceding the corresponding positive number, i.e., ...