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Given a function of the form y=a+blnx, (1) the coefficients can be found from least squares fitting as b = ...

F(x) = -Li_2(-x) (1) = int_0^x(ln(1+t))/tdt, (2) where Li_2(x) is the dilogarithm.

A Pythagorean triple is a triple of positive integers a, b, and c such that a right triangle exists with legs a,b and hypotenuse c. By the Pythagorean theorem, this is ...

A closed two-form omega on a complex manifold M which is also the negative imaginary part of a Hermitian metric h=g-iomega is called a Kähler form. In this case, M is called ...

Given a function f(x) of a variable x tabulated at m values y_1=f(x_1), ..., y_m=f(x_m), assume the function is of known analytic form depending on n parameters ...

A two-dimensional piecewise linear map defined by x_(n+1) = 1-y_n+|x_n| (1) y_(n+1) = x_n. (2) The map is chaotic in the filled region above and stable in the six hexagonal ...

A Mycielski graph M_k of order k is a triangle-free graph with chromatic number k having the smallest possible number of vertices. For example, triangle-free graphs with ...

Conjugation is the process of taking a complex conjugate of a complex number, complex matrix, etc., or of performing a conjugation move on a knot. Conjugation also has a ...

Given a triangle center X=l:m:n, the line mnalpha+nlbeta+lmgamma=0, where alpha:beta:gamma are trilinear coordinates, is called the trilinear polar (Kimberling 1998, p. 38). ...

n Sloane's 2^n 3^n 4^n 5^n 6^n 7^n 8^n 9^n 1 A000027 2 3 4 5 6 7 8 9 2 A002993 4 9 1 2 3 4 6 8 3 A002994 8 2 6 1 2 3 5 7 4 A097408 1 8 2 6 1 2 4 6 5 A097409 3 2 1 3 7 1 3 5 6 ...