Exchange energy calculation of He-He with supermolecular one-matrix

Exch~nge energy of the He-He system is calculated using the one-density matrix which has been modified according to the supermolecular density formula quoted by Kolos. The exchange energy integrals are computed analytically and by the Monte Carlo method. The results obtained from both ways compared favourably,with the results obtained from the SCF program HONDO

The practical examination and how it correlates with the triple jump, tutorial, and written examination

This study explored the relationship between the practical examination and other course evaluation methods~ specifically, the triple jump, tutorial, and written examination. Studies correlating academic and clinical grades tended to indicate that they may not be highly correlated because each evaluation process contributes different kinds of information regarding student knowledge, skills, and attitudes. Six hypotheses were generated stating a positive relationship between the four evaluation methods. A correlation matrix was produced of the Pearson Product Moment correlation co-efficients on the four evaluation methods in the second and third year Occupational Therapy Technique and Clinical Problem Solving courses of the 1988 and 1989 graduates (n~45). The results showed that the highest correlations existed between the triple jump and the tutorial grades and the lowest correlations existed between the practical examination and written examination grades. Not all of the correlations~ however~ reached levels of significance. The correlations overall. though, were only low to moderate at best which indicates that the evaluation methods may be measuring different aspects of student learning. This conclusion supports the studies researched. The implications and significance of this study is that it will assist the faculty in defining what the various evaluation methods measure which will in turn promote more critical input into curriculum development for the remaining years of the program.

Kinetic and product studies for the oxidtion of organic sulfides and sulfoxides in the presence of transition metal complexes

Rates and products of the oxidation of diphenyl sulfide, phenyl methyl sulfide, p-chlorophenyl methyl sulfide and diphenyl sulfoxide have been determined. Oxidants included t-Bu02H alone, t-Bu02H plus molybdenum or vanadium catalysts and the molybdenum peroxo complex Mo0(02)2*HMPT. Reactions were chiefly carried out in ethanol at temperatures ranging from 20° to 65°C. Oxidation of diphenyl sulfide by t-Bu02H in absolute ethanol at 65°C followed second-order kinetics with k2 = 5.61 x 10 G M~1s"1, and yielded only diphenyl sulfoxide. The Mo(C0)g-catalyzed reaction gave both the sulfoxide and the sulfone with consecutive third-order kinetics. Rate = k3[Mo][t-Bu02H][Ph2S] + k^[Mo][t-Bu02H][Ph2S0], where log k3 = 12.62 - 18500/RT, and log k^ = 10.73 - 17400/RT. In the absence of diphenyl sulfide, diphenyl sulfoxide did not react with t-Bu02H plus molybdenum catalysts, but was oxidized by t-Bu02H-V0(acac)2. The uncatalyzed oxidation of phenyl methyl sulfide by t-Bu02H in absolute ethanol at 65°C gave a second-order rate constant, k = 3.48 x 10~"5 M^s""1. With added Mo(C0)g, the product was mainly phenyl methyl sulfoxide; Rate = k3[Mo][t-Bu02H][PhSCH3] where log k3 = 22.0 - 44500/RT. Both diphenyl sulfide and diphenyl sulfoxide react readily with the molybdenum peroxy complex, Mo0(02)2'HMPT in absolute ethanol at 35°C, yielding diphenyl sulfone. The observed features are mainly in agreement with the literature on metal ion-catalyzed oxidations of organic compounds by hydroperoxides. These indicate the formation of an active catalyst and the complexation of t-Bu02H with the catalyst. However, the relatively large difference between the activation energies for diphenyl sulfide and phenyl methyl sulfide, and the non-reactivity of diphenyl sulfoxide suggest the involvement of sulfide in the production of an active species.

ReAlM - a system to manipulate relations

Given a heterogeneous relation algebra R, it is well known that the algebra of matrices with coefficient from R is relation algebra with relational sums that is not necessarily finite. When a relational product exists or the point axiom is given, we can represent the relation algebra by concrete binary relations between sets, which means the algebra may be seen as an algebra of Boolean matrices. However, it is not possible to represent every relation algebra. It is well known that the smallest relation algebra that is not representable has only 16 elements. Such an algebra can not be put in a Boolean matrix form.[15] In [15, 16] it was shown that every relation algebra R with relational sums and sub-objects is equivalent to an algebra of matrices over a suitable basis. This basis is given by the integral objects of R, and is, compared to R, much smaller. Aim of my thesis is to develop a system called ReAlM - Relation Algebra Manipulator - that is capable of visualizing computations in arbitrary relation algebras using the matrix approach.

Generator Matrix Based Search for Extremal Self-Dual Binary Error-Correcting Codes

Self-dual doubly even linear binary error-correcting codes, often referred to as Type II codes, are codes closely related to many combinatorial structures such as 5-designs. Extremal codes are codes that have the largest possible minimum distance for a given length and dimension. The existence of an extremal (72,36,16) Type II code is still open. Previous results show that the automorphism group of a putative code C with the aforementioned properties has order 5 or dividing 24. In this work, we present a method and the results of an exhaustive search showing that such a code C cannot admit an automorphism group Z6. In addition, we present so far unpublished construction of the extended Golay code by P. Becker. We generalize the notion and provide example of another Type II code that can be obtained in this fashion. Consequently, we relate Becker's construction to the construction of binary Type II codes from codes over GF(2^r) via the Gray map.

The Effects of Perceived Product-Association Incongruity on Consumption Experiences

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Planar Topological Defects in Unconventional Superconductors

In this work, we consider the properties of planar topological defects in unconventional superconductors. Specifically, we calculate microscopically the interaction energy of domain walls separating degenerate ground states in a chiral p-wave fermionic superfluid. The interaction is mediated by the quasiparticles experiencing Andreev scattering at the domain walls. As a by-product, we derive a useful general expression for the free energy of an arbitrary nonuniform texture of the order parameter in terms of the quasiparticle scattering matrix. The thesis is structured as follows. We begin with a historical review of the theories of superconductivity (Sec. 1.1), which led the way to the celebrated Bardeen-Cooper- Schrieffer (BCS) theory (Sec. 1.3). Then we proceed to the treatment of superconductors with so-called "unconventional pairing" in Sec. 1.4, and in Sec. 1.5 we introduce the specific case of chiral p-wave superconductivity. After introducing in Sec. 2 the domain wall (DW) model that will be considered throughout the work, we derive the Bogoliubov-de Gennes (BdG) equations in Sec. 3.1, which determine the quasiparticle excitation spectrum for a nonuniform superconductor. In this work, we use the semiclassical (Andreev) approximation, and solve the Andreev equations (which are a particular case of the BdG equations) in Sec. 4 to determine the quasiparticle spectrum for both the single- and two-DW textures. The Andreev equations are derived in Sec. 3.2, and the formal properties of the Andreev scattering coefficients are discussed in the following subsection. In Sec. 5, we use the transfer matrix method to relate the interaction energy of the DWs to the scattering matrix of the Bogoliubov quasiparticles. This facilitates the derivation of an analytical expression for the interaction energy between the two DWs in Sec. 5.3. Finally, to illustrate the general applicability our method, we apply it in Sec. 6 to the interaction between phase solitons in a two-band s-wave superconductor.