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...

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...

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...

a capillary electrophoresis method was used for assay of some degradation products of carvedilol. the optimized parameters were as; running buffer 80 mm acetate dissolved in methanol/ethanol mixture (65:35 v/v), applied voltage of 19 kv, temperature is 20 ºc and the wavelength range of 200-350 nm. the results indicate that the proposed ce method could effectively separate carvedilol from its de...

infinite dilution activity coefficients have been measured for seven binary systems at three different pressures using a newly - designed ebulliometer. the results obtained through these experimental measurements have been compared to literature values for four of the seven binary systems and the calculated deviation has been less than five percent in most cases. having verified the soundness a...

Density, viscosity and refractive index of pure, binary and ternary mixtures of diethanolamine (DEA) and methyl diethanolamine (MDEA) with water have been measured at different temperatures from 288.15 K to 323.15 K at atmospheric pressure. Also, this study presents the effects of mixture composition and temperature upon these thermo- physical properties. To measure the density and refractive i...

a simple and reliable method for quick estimation of the dielectric constant of a binary solvent mixture is proposed. the validity of the proposed method has been tested for a broad range of binary solvent mixtures

In this article, multiple-product PVRP with pickup and delivery that is used widely in goods distribution or other service companies, especially by railways, was introduced. A mathematical formulation was provided for this problem. Each product had a set of vehicles which could carry the product and pickup and delivery could simultaneously occur. To solve the problem, two meta-heuristic methods...