Quantum dynamics calculations using symmetrized, orthogonal Weyl-Heisenberg wavelets with a phase space truncation scheme. III. Representations and calculations

In a previous paper [J. Theo. Comput. Chem. 2, 65 (2003)], one of the authors (B.P.) presented a method for solving the multidimensional Schrodinger equation, using modified Wilson-Daubechies wavelets, and a simple phase space truncation scheme. Unprecedented numerical efficiency was achieved, enabling a ten-dimensional calculation of nearly 600 eigenvalues to be performed using direct matrix diagonalization techniques. In a second paper [J. Chem. Phys. 121, 1690 (2004)], and in this paper, we extend and elaborate upon the previous work in several important ways. The second paper focuses on construction and optimization of the wavelength functions, from theoretical and numerical viewpoints, and also examines their localization. This paper deals with their use in representations and eigenproblem calculations, which are extended to 15-dimensional systems. Even higher dimensionalities are possible using more sophisticated linear algebra techniques. This approach is ideally suited to rovibrational spectroscopy applications, but can be used in any context where differential equations are involved.     

Algebraic methods for the Natanzon potentials

It is shown that the Schrödinger equation can be solved by means of spectrum-generating algebra techniques for the most general class of Natanzon potentials based on the SO(2, 1) algebra. This paper describes in detail thelinear spectrum generating algebra method which is then applied to solve the Natanzon confluent potentials, and it is extended to one example with spin-orbit coupling. Further, the method is used to explain in detail how to find the energy spectrum for the Dirac equation with a Coulomb potential. Afterwards thequadratic spectrum generation algebra method is presented, and it is used to solve the most general hypergeometric Natanzon potential: The bound state problem and the corresponding wave functions are given. A simple example further illustrates the use of the quadratic method.Partially supported by grant FONDECYT 90-1240.     

Revisiting non-perturbative effects in the jet broadenings

We show that taking into account the interplay between perturbative and non-perturbative effects, the power-suppressed shift to the broadening distributions becomes B dependent, and the non-perturbative contribution to the mean values becomes proportional to . The new theoretical treatment greatly improves the consistency of the phenomenology with the notion of the universality of confinement effects in jet shapes.This work was supported in part by the EU Fourth Framework Programme ‘Training and Mobility of Researchers’, Network ‘Quantum Chromodynamics and the Deep Structure of Elementary Particles’, contract FMRX-CT98-0194 (DG 12-MIHT).     

Estimation of parameter matrices based on measured data

Finite element structural updating based on measured data may inherent significant errors due to uncertainties in the updated physical parameter matrices. This study presents analytical equations to estimate the change in the physical parameter matrices based on the measured modal data of dynamic systems and the measured displacement data of static systems. The equations for the parameter estimation are derived by minimizing cost functions in the satisfaction of the eigenvalue equation, the mode shape orthogonality requirements for the dynamic system, and the satisfaction of the measured displacement data for the static systems. The proposed method utilizes the Moore–Penrose inverse for the inverse of the rectangular matrices without using Lagrange multipliers. Comparing the analytical results with Berman & Nagy’s method and Yang & Chen’s method, this study demonstrates that the derived equations take simpler forms and produce more accurate results. The proposed method can be widely utilized in predicting static or dynamic parameter matrices for the design and analysis of any structure.     

Effect of conductive fillers on the cyclic stress-strain and nano-scale free volume properties of silicone rubber

The effect of carbon black(CB) and graphite(G) powders on the macroscopic and nano-scale free volume properties of silicone rubber based on poly(di-methylsiloxane)(PDMS) was studied through thermal and cyclic mechanical measurements, as well as with positron annihilation lifetime spectroscopy(PALS). The melting temperature of the composites(Tm) and the endothermic enthalpy of melting(?Hm) were estimated by differential scanning calorimetry(DSC). Tm and the degree of crystallinity(χc) of PDMS composites were found to decrease with increasing the CB content. This can be explained due to the increase in physical cross-linking which results in a decrease in the crystallite thickness. Besides, χc was found to be dependent on the filler type. Cyclic stress-strain behavior of PDMS loaded with different contents of filler has been studied. Mullins ratio(RM) was found to be dependent on the filler type and content. It was found that, RM increases with increasing the filler content due to the increase in physical cross-linking which results in a decrease in the size of free volume, as observed through a decrease of the o-Ps lifetime τ3 measured by PALS. Moreover, the hysteresis in PDMS-CB composites was more pronounced than in PDMS-G composites. Furthermore, a correlation was established between the free volume Vf and the mechanical properties of PDMS composites containing different fillers. A negative correlation was observed between Vf and RM.     

Validated and optimized high-performance liquid chromatographic determination of tizoxanide, the main active metabolite of nitazoxanide in human urine, plasma and breast milk

A high-performance liquid chromatographic method was optimized and validated for the determination of desacetyl nitazoxanide (tizoxanide), the main active metabolite of nitazoxanide in human plasma, urine and breast milk. The proposed method used a CN column with mobile phase consisting of acetonitrile-12mM ammonium acetate-diethylamine in the ratio of 30:70:0.1 (v/v/v) and buffered at pH 4.0 with acetic acid, with a flow rate of 1.5 mL/min. Quantitation was achieved with UV detection at 260 nm using nifuroxazide as internal standard. A simplified direct injection of urine samples without extraction in addition to the urinary excretion pattern were calculated using the proposed method. Also, the effectiveness of protein precipitation and a clean-up procedure were investigated for biological plasma and human breast milk samples. The validation study of the proposed method was successfully carried out in an assay range between 0.2 and 20 μg/mL.