The Ducci map applied to vectors in R is considered. It is shown that for any starting vector, the corresponding sequence of iterates either eventually becomes periodic or, if not eventually periodic, asymptotically approaches the zero vector. A precise characterization of which vectors exhibit each of these separate behaviors is given.

Let be a sequence of weakly negative dependent (denoted by, WND) random variables with common distribution function F and let be other sequence of positive random variables independent of and for some and for all . In this paper, we study the asymptotic behavior of the tail probabilities of the maximum, weighted sums, randomly weighted sums and randomly indexed weighted sums of heavy...

In this work, a non-integer order Airy equation involving Liouville differential operator is considered. Proposing an undetermined integral solution to the left fractional Airy differential equation, we utilize some basic fractional calculus tools to clarify the closed form. A similar suggestion to the right FADE, converts it into an equation in the Laplace domain. An illustration t...

Eccentric connectivity index has been found to have a low degeneracy and hence a significant potential of predicting biological activity of certain classes of chemical compounds. We present here explicit formulas for eccentric connectivity index of various families of graphs. We also show that the eccentric connectivity index grows at most polynomially with the number of vertices and determine ...

In the present paper a generalized Lotka-Volterra food chain system has been studied and also its dynamic behavior such as locally asymptotic stability has been analyzed in case of existing interspecies competition. Furthermore, it has been shown that the said system is permanent (in the sense of boundedness and uniformly persistent). Finally, it is proved that the nontrivial equilibrium point...

In the present paper a solution of the generalizedquadratic functional equation$$f(kx+ y)+f(kx+sigma(y))=2k^{2}f(x)+2f(y),phantom{+} x,yin{E}$$ isgiven where $sigma$ is an involution of the normed space $E$ and$k$ is a fixed positive integer. Furthermore we investigate theHyers-Ulam-Rassias stability of the functional equation. TheHyers-Ulam stability on unbounded domains is also studied.Applic...