Binary trees are essential structures in Computer Science. The leaf (leaves) of a binary tree is one of the most significant aspects of it. In this study, we prove that the order of a leaf (leaves) of a binary tree is the same in the main tree traversals; preorder, inorder, and postorder. Then, we prove that given the preorder and postorder traversals of a binary tree, the leaf (leaves) of a bi...

In this work we introduce the triangular arrays of depth greater than 1 given by linear recurrences, that generalize some well-known recurrences that appear in enumerative combinatorics. In particular, we focussed on triangular arrays of depth 2, since they are closely related to the solution of linear three–term recurrences. We show through some simple examples how these triangular arrays appe...

By proposing a predictive method with no adjustable parameter and by using infinite dilution activity coefficients of components in binary mixtures obtained from UNIFAC model, the binary interaction parameters (k12) in van der Waals mixing rule (vdWMR) and Orbey-Sandler mixing rule (OSMR) have been evaluated. The predicted binary interaction parameters are used in Peng-Robinson-S...

the srk two-parameter cubic equation of state has been used for the calculation of the equilibrium constant using the liquid and vapor fugacity coefficients for three binary mixtures. dew and bubble points have been determined using the equilibrium constants and the phase envelope has been plotted showing dearly that retrograde condenstaion occurs. the following percent deviations have been obt...

We analyze the statistical properties of Poincaré recurrences of Homo sapiens, mammalian and other DNA sequences taken from Ensembl Genome data base with up to fifteen billions base pairs. We show that the probability of Poincaré recurrences decays in an algebraic way with the Poincaré exponent β ≈ 4 even if oscillatory dependence is well pronounced. The correlations between recurrences decay w...

longitudinal  study  plays  an  important  role  in  the  epidemiological,  clinical,  and  social  science studies. in these kinds of studies, every individual is observed frequently during a period of time. the statistical analysis of longitudinal presents special opportunities  and challenges. the repeated outcomes for one individual tend to be correlated among themselves also one of the pro...

the concept of  -semihypergroups is a generalization of semigroups, a generalization of semihypergroups and a generalization of  -semigroups. in this paper, we study the concept of semiprime ideals in a  -semihypergroup and prove some results. also, we introduce the notion of  -hypergroups and closed  -subhypergroups. finally, we study the concept of  -semihypergroups associated to binary...