Converting three-space matrices to equivalent six-space matrices for Delone scalars in S6.

The transformations from the primitive cells of the centered Bravais lattices to the corresponding centered cells have conventionally been listed as three-by-three matrices that transform three-space lattice vectors. Using those three-by-three matrices when working in the six-dimensional space of lattices represented as Selling scalars as used in Delone (Delaunay) reduction, one could transform to the three-space representation, apply the three-by-three matrices and then back-transform to the six-space representation, but it is much simpler to have the equivalent six-by-six matrices and apply them directly. The general form of the transformation from the three-space matrix to the corresponding matrix operating on Selling scalars (expressed in space S6) is derived, and the particular S6matrices for the centered Delone types are listed. (Note: in his later publications, Boris Delaunay used the Russian version of his surname, Delone.)

Risks and returns in the globalised South African equity market

Includes abstract.Includes bibliographical references (leaves 114-119).The South African financial economics literature has produced many findings regarding the drivers of South African equity returns. In contrast, this thesis investigates the behaviour of South African risks and returns directly, as well as their fundamental relationship to each other (the central risk-return principle). As the Johannesburg Securities Exchange (JSE) is integrated with the international equity market, there is also a significant globalised aspect to these South African risks and returns which must be examined

A comparison of soil stabilization additives to determine parameters affecting soil strength values

Thesis (M.S.)--University of Oklahoma, 2010.Includes bibliographical references (leaves 150-152)

Soil Accretion and Organic Carbon Accumulation in the Tidal Salt Marshes of the Liaohe Delta, China

Wetlands provide a multitude of functions to people and ecosystems and because of this, maintaining or increasing wetland area is important. Wetlands can be significant carbon sinks because of the relatively high primary productivity and slow decomposition of organic matter in these systems and can thus impact the global carbon cycle and potentially climate change. The marshes of the Liaohe Delta are the largest in Liaoning Province; however, very little research has been done in this area to determine the rate of accretion and organic carbon sequestration in the salt marshes there. By using Cs-137 and Pb-210 dating techniques and organic matter combustion, I analyzed nine cores to determine accretion and organic carbon accumulation rates in three vegetation density treatments of Suaeda salsa (mudflat, half cover, full cover) and at different marsh elevations. Results from Cs-137 analysis showed no cores with a distinctive peak at depth that might have corresponded to the peak fallout year of Cs-137 (1963) or a depth at which Cs-137 activity was undetectable (pre-1954). Accretion rates were estimated to be greater than 1.09 cm yr^–1 at all sites based on Cs-137 techniques, from 0.85 to 9.73 cm yr^–1 at all sites based on Pb-210 techniques combined with the c.r.s. and c.f.:c.s. models, and were highest at the two sites below sea level. Organic carbon accumulation rates ranged from 137 to 1,522 g m^-2 yr^–1 at all sites and were highest at the two sites below sea level. No differences in accretion or organic carbon accumulation were found among different vegetation density treatments; however, accretion and organic carbon accumulation were significantly greater at sites below sea level (p \u3c 0.02). It is likely that lower elevation sites were inundated for longer periods of time, which would provide greater opportunity for suspended sediment deposition. Higher organic carbon accumulation rates at sites resulted from increased accretion with similar percent organic carbon. Additional research is needed to provide insight on the accuracy of calculated accretion and OC accumulation rates from this study and proper application of Pb-210 dating models on salt marshes in this region

Interpersonal change as an outcome of time-limited interpersonal therapy.

This study examined two questions related to interpersonal change as an outcome of Time-Limited Interpersonal Therapy (TLIPT). The first asked if clients experience both symptom change and interpersonal change when treated with TLIPT. The second explored factors that contribute to interpersonal changes in clients treated with TLIPT. The study examined a sample of 61 clients who identified interpersonal problems as a primary therapeutic issue and were treated with between 9 and 76 sessions of TLIPT. Repeated measures analysis of variance (ANOVA) of the first question revealed that clients experienced significant reductions in measures of symptoms and interpersonal distress. Clients also experienced significant increases in therapist-rated interpersonal affiliation dimension (i.e., clients increased in friendliness and decreased in hostility) and self-rated interpersonal control (i.e., clients increased in dominance and decreased in submissiveness). Additionally, statistical trends suggested that clients experienced modest reductions in the self-rated and therapist-rated measures of interpersonal rigidity and extremity; modest increases in self-rated and significant other-rated affiliation; and modest increases in therapist-rated control. Analyses of the second question explored the role of early alliance, early symptom reduction, early stage and middle stage therapist and client complementarity in contributing to interpersonal change. ANOVA comparisons of those with high interpersonal changes and those with low interpersonal changes indicated that there were no statistically significant differences in these variables between the two groups. However, statistical trends indicate that higher early complementarity on the control dimension may be associated with reductions in interpersonal rigidity and increases on the control dimension; and that higher affiliation complementarity in the middle of therapy may be associated with increases on the affiliation dimension. Further analyses revealed that therapists and clients had significantly lower complementarity on the affiliation dimension in the middle phase of therapy than in the early phase of therapy. Implications for future research are discussed

Access and Interconnection Pricing: How Efficient is the Efficient Component Pricing Rule?

This paper critiques some of the properties of the so-called 'efficient component pricing rule' (ECPR) for access to a bottleneck (monopoly) facility. When an entrant/rival and the bottleneck monopolist both produce a complementary component to the bottleneck service, the ECPR specifies that the access fee paid by the rival to the monopolist should be equal to the monopolist's opportunity costs of providing access, including any forgone revenues from a concomitant reduction in the monopolist's sales of the complementary component. We focus especially on the case in which the monopolist's price for the complementary component is above all relevant marginal costs. In this case the ECPR's exclusion of rivals may be socially harmful, since it may be preventing a substantial decrease in the price of the complementary component

The Inefficiency of the ECPR Yet Again: A Reply to Larson

We extend the results of our article, "Access and Interconnection Pricing? How Efficient Is the "Efficient Component Pricing Rule?," Antitrust Bulletin (1995). In the presence of a monopolized essential input, we show that application of the Efficient Component Pricing Rule ("ECPR") in pricing this input to downstream competitors perpetuates monopoly distortions and high prices of final goods services. We show these results for various demand conditions, including conditions that are accepted to hold in the telecommunications sector. We also respond to various criticisms raised by A. Larson in "The Efficiency of the Efficient-Component-Pricing Rule: A Comment," Antitrust Bulletin, (this issue) (1998)

Spectral methods for the wave equation in second-order form

Current spectral simulations of Einstein's equations require writing the equations in first-order form, potentially introducing instabilities and inefficiencies. We present a new penalty method for pseudo-spectral evolutions of second order in space wave equations. The penalties are constructed as functions of Legendre polynomials and are added to the equations of motion everywhere, not only on the boundaries. Using energy methods, we prove semi-discrete stability of the new method for the scalar wave equation in flat space and show how it can be applied to the scalar wave on a curved background. Numerical results demonstrating stability and convergence for multi-domain second-order scalar wave evolutions are also presented. This work provides a foundation for treating Einstein's equations directly in second-order form by spectral methods.Comment: 16 pages, 5 figure

Comparing Gravitational Waveform Extrapolation to Cauchy-Characteristic Extraction in Binary Black Hole Simulations

We extract gravitational waveforms from numerical simulations of black hole binaries computed using the Spectral Einstein Code. We compare two extraction methods: direct construction of the Newman-Penrose (NP) scalar $\Psi_4$ at a finite distance from the source and Cauchy-characteristic extraction (CCE). The direct NP approach is simpler than CCE, but NP waveforms can be contaminated by near-zone effects---unless the waves are extracted at several distances from the source and extrapolated to infinity. Even then, the resulting waveforms can in principle be contaminated by gauge effects. In contrast, CCE directly provides, by construction, gauge-invariant waveforms at future null infinity. We verify the gauge invariance of CCE by running the same physical simulation using two different gauge conditions. We find that these two gauge conditions produce the same CCE waveforms but show differences in extrapolated-$\Psi_4$ waveforms. We examine data from several different binary configurations and measure the dominant sources of error in the extrapolated-$\Psi_4$ and CCE waveforms. In some cases, we find that NP waveforms extrapolated to infinity agree with the corresponding CCE waveforms to within the estimated error bars. However, we find that in other cases extrapolated and CCE waveforms disagree, most notably for $m=0$ "memory" modes.Comment: 26 pages, 20 figure