We deal with the Hamiltonian hierarchy problem of the Hulthén potential within the frame of the supersymmetric quantum mechanics and find that the associated superymmetric partner potentials simulate the effect of the centrifugal barrier. Incorporating the supersymmetric solutions and using the first-order perturbation theory we obtain an expression for the energy levels of theHulthén potential which gives satisfactory values for the non-zero angular momentum states.

Within the frame of a novel treatment we make a complete mathematical analysis of exactly solvable one-dimensional quantum systems with non-constant mass, involving their ordering ambiguities. This work extends the results recently reported in the literature and clarifies the relation between physically acceptable effective mass Hamiltonians.

The eigenvalues of the potentials V 1 (r) = r 6 , and of the special cases of these potentials such as the Kratzer and Goldman-Krivchenkov potentials, are obtained in Ndimensional space. The explicit dependence of these potentials in higherdimensional space is discussed, which have not been previously covered.

In this simulation study, five correlation coefficients, namely, Pearson, Spearman, Kendal Tau, Permutation-based, and Winsorized were compared in terms of Type I error rate and power under different scenarios where the underlying distributions of the variables of interest, sample sizes and correlation patterns were varied. Simulation results showed that the Type I error rate and power of Pearson correlation coefficient were negatively affected by the distribution shapes especially for small sample sizes, which was much more pronounced for Spearman Rank and Kendal Tau correlation coefficients especially when sample sizes were small. In general, Permutationbased and Winsorized correlation coefficients are more robust to distribution shapes and correlation patterns, regardless of sample size. In conclusion, when assumptions of Pearson correlation coefficient are not satisfied, Permutation-based and Winsorized correlation coefficients seem to be better alternatives.

Polyethylene (PE) is the principal component of postconsumer plastic wastes. It is important to develop chemical techniques to decompose PE with a view to recycling and production of compounds that are valuable as fuel or industrial raw materials. The most common reactors in polymer pyrolysis are fluidized-bed types. Free-fall reactors do not suffer the disadvantages of fluidized beds related to inert gas employment. This flash pyrolysis study has shown that low density polyethylene (LDPE) can be continuously degraded in a free-fall reactor under vacuum to give a product quality superior to other methods. The total conversion (i.e., the sum of liquid and gas yield) is 43% at 8758C when the feed is 150-75 mm LDPE particles. Over 99% of the gaseous product is C 1 to C 4 , the ethylene monomer exceeding 64%. The bulk of the liquid product is paraffinic;