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The Randić index of a graph is defined as half the sum of the matrix elements of its Randić matrix. While the index was introduced to model the branching of the carbon-atom ...

The sample mean of a set {x_1,...,x_n} of n observations from a given distribution is defined by m=1/nsum_(k=1)^nx_k. It is an unbiased estimator for the population mean mu. ...

z^p-y^p=(z-y)(z-zetay)...(z-zeta^(p-1)y), where zeta=e^(2pii/p) (a de Moivre number) and p is a prime.

The number 1. There are n nth roots of unity, known as the de Moivre numbers.

If an integrable quasiperiodic system is slightly perturbed so that it becomes nonintegrable, only a finite number of n-map cycles remain as a result of mode locking. One ...

The ABC (atom-bond connectivity) matrix A_(ABC) of a simple graph is a weighted adjacency matrix with weight f(d_i,d_j)=sqrt((d_i+d_j-2)/(d_id_j)), (1) where d_i are the ...

The ABC (atom-bond connectivity) spectral radius rho_(ABC) of a graph is defined as the largest eigenvalue of its ABC matrix. Chen (2019) showed that for a tree on 3 or more ...

A distribution with probability function P(x)=(x^(alpha-1)(1+x)^(-alpha-beta))/(B(alpha,beta)), where B is a beta function. The mode of a variate distributed as ...

The winding number W(theta) of a map f(theta) with initial value theta is defined by W(theta)=lim_(n->infty)(f^n(theta)-theta)/n, which represents the average increase in the ...

De Grey (2018) found the first examples of unit-distance graphs with chromatic number 5, thus demonstrating that the solution to the Hadwiger-Nelson problem (i.e., the ...