Kinetic energy operator approach to the quantum three-body problem with Coulomb interactions

We present a non-variational, kinetic energy operator approach to the solution of quantum three-body problem with Coulomb interactions, based on the utilization of symmetries intrinsic to the kinetic energy operator, i.e., the three-body Laplacian operator with the respective masses. Through a four-step reduction process, the nine dimensional problem is reduced to a one dimensional coupled system of ordinary differential equations, amenable to accurate numerical solution as an infinite-dimensional algebraic eigenvalue problem. A key observation in this reduction process is that in the functional subspace of the kinetic energy operator where all the rotational degrees of freedom have been projected out, there is an intrinsic symmetry which can be made explicit through the introduction of Jacobi-spherical coordinates. A numerical scheme is presented whereby the Coulomb matrix elements are calculated to a high degree of accuracy with minimal effort, and the truncation of the linear equations is carried out through a systematic procedureComment: 56 pages, 11 figure

An investigation of continuous prestressed concrete structures

This thesis presents an analysis of the behavior of continuous prestressed concrete structures. From this analysis the governing equations for various types of geometry for prestressing cables are derived. The calculation of fixed-end moments due to the prestressing force using the equations derived is quite cumbersome, however, in order to simplify the calculations, design charts are developed. A cable with reverse curvature is analyzed using the design charts. It is shown that the fixed-end moments calculated by neglecting the effect of reverse curvature differ significantly from the fixed-end moments calculated by considering this effect. Hence the effect of reverse curvature should be considered for greater accuracy is design --Abstract, page 2

VIRAL RNA ELEMENTS AND HOST GENES AFFECTING RNA RECOMBINATION IN TOMBUSVIRUSES

RNA recombination is a major factor driving viral evolution and contributing to new disease outbreaks. Therefore, understanding the mechanism of RNA recombination can help scientists to develop longer lasting antiviral strategies. Tombusviruses are one of the best model RNA viruses to study RNA virus recombination. My goals were to dissect the mechanism of tombusviral RNA recombination. To do so, in my thesis, I describe my results on the roles of (i) the viral replicase and the viral RNA templates; and (ii) the effect of host factors on tombusvirus recombination events. To study the mechanism of RNA recombination without the influence of selection pressure on the emerging recombinants, we developed an in vitro RNA recombination assay based on viral RNA templates and purified viral replicase preparations. Using this in vitro assay, we demonstrated that replicase driven template switching is the mechanism of recombination, whereas RNA ligation seems less likely to be a major mechanism. In addition, we also studied the role of RNA substrates, in more detail. Our results showed that viral replicase preferred to use functional RNA domains in the acceptor RNAs over random switching events. Host factors may also play important roles in RNA recombination. Using yeast as a model system for studying replication and recombination of a tombusvirus replicon, we identified 9 host genes affecting tombusvirus RNA recombination. Separate deletion of five of these genes enhanced generation of novel viral RNA recombinants. Further studies on one of these genes, XRN1, a 5-3 exoribonuclease, indicated that it might be involved in degradation of tombusvirus RNAs. Lack of Xrn1p resulted in accumulation of truncated (partially degraded) replicon RNAs, which became good templates for RNA recombination. To further study Xrn1p, we overexpressed Xrn4p of Arabidopsis thaliana, a functional analogue of the yeast Xrn1p, in Nicotiana benthamiana plants. After superinfecting the Xrn4p-overexpressing N. benthamiana with tombusvirus, truncated tombusvirus genomic and subgenomic RNA1 were observed. Some of the identified tombusvirus variants were infectious in protoplasts and could systemically infected N. benthamiana plants. Overall, this is the first report that a single host gene can affect rapid viral evolution and RNA recombination

Program for Missing Data in the Multivariate Normal Distribution

Missing data can often cause many problems in research work. Therefore for carrying out analysis, some procedure for obtaining estimates in the presence of missing data should be applied. Various theories and techniques have been developed for different types of problems. Analysis of the Multivariate Normal Distribution with missing data is one of the areas studied. It has been discussed earlier by Wilkes (1932), Lord (1955), Edgett (1956) and Hartley (1958). They have established some basic concepts and an outline in the way of estimation. In the last ten years, A. A. Afifi and R. M. Elasfoff also have contributed some important techniques in estimating the parameters respective to mean, variance and covariance. R.R. Hocking, H. H. Oxpring and W. B. Smith are continuously improving it toward a more practical method of calculation. In their paper (1971), they gave the derivation of equations and a numerical example without explanation of the details. The main purpose of this report is to evaluate the reliability and feasibility of this method by programming it. The procedure will be a general one avaliable for large samples so that research workers can apply it conveniently in estimating the parameters when some observations are missing

Detrended fluctuation analysis on the correlations of complex networks under attack and repair strategy

We analyze the correlation properties of the Erdos-Renyi random graph (RG) and the Barabasi-Albert scale-free network (SF) under the attack and repair strategy with detrended fluctuation analysis (DFA). The maximum degree k_max, representing the local property of the system, shows similar scaling behaviors for random graphs and scale-free networks. The fluctuations are quite random at short time scales but display strong anticorrelation at longer time scales under the same system size N and different repair probability p_re. The average degree , revealing the statistical property of the system, exhibits completely different scaling behaviors for random graphs and scale-free networks. Random graphs display long-range power-law correlations. Scale-free networks are uncorrelated at short time scales; while anticorrelated at longer time scales and the anticorrelation becoming stronger with the increase of p_re.Comment: 5 pages, 4 figure

Fair trade in insurance industry: Premium determination of Taiwan automobile insurance

This paper examines premium determination of voluntary automobile insurance policy and risk classification under a heavily regulated rating system in Taiwan. We investigate the distribution of actual premium and pure premium, based on unique data to test if premium reflect appropriate gender-age factor. The reasonableness of loading and the difference in driving exposure between policyholder and driver are investigated for three different types of policy. An adjustment of gender-age premium coefficients is called for