Search Results for ""

The Yff circles are the two triplets of congruent circle in which each circle is tangent to two sides of a reference triangle. In each case, the triplets intersect pairwise ...

Given a real number q>1, the series x=sum_(n=0)^inftya_nq^(-n) is called the q-expansion, or beta-expansion (Parry 1957), of the positive real number x if, for all n>=0, ...

A number of interesting graphs are associated with the work of van Cleemput and Zamfirescu (2018). Two 13- and 15-node graphs, denoted alpha and beta respectively, were used ...

A real number that is b-normal for every base 2, 3, 4, ... is said to be absolutely normal. As proved by Borel (1922, p. 198), almost all real numbers in [0,1) are absolutely ...

For a single variate X having a distribution P(x) with known population mean mu, the population variance var(X), commonly also written sigma^2, is defined as ...

A double sum is a series having terms depending on two indices, sum_(i,j)b_(ij). (1) A finite double series can be written as a product of series ...

Let S(x) denote the number of positive integers not exceeding x which can be expressed as a sum of two squares (i.e., those n<=x such that the sum of squares function ...

alpha_n(z) = int_1^inftyt^ne^(-zt)dt (1) = n!z^(-(n+1))e^(-z)sum_(k=0)^(n)(z^k)/(k!). (2) It is equivalent to alpha_n(z)=E_(-n)(z), (3) where E_n(z) is the En-function.

Probability and Statistics

A variable x is memoryless with respect to t if, for all s with t!=0, P(x>s+t|x>t)=P(x>s). (1) Equivalently, (P(x>s+t,x>t))/(P(x>t)) = P(x>s) (2) P(x>s+t) = P(x>s)P(x>t). (3) ...