Maximum principle preserving high order schemes for convection-dominated diffusion equations

The maximum principle is an important property of solutions to PDE. Correspondingly, it's of great interest for people to design a high order numerical scheme solving PDE with this property maintained. In this thesis, our particular interest is solving convection-dominated diffusion equation. We first review a nonconventional maximum principle preserving(MPP) high order finite volume(FV) WENO scheme, and then propose a new parametrized MPP high order finite difference(FD) WENO framework, which is generalized from the one solving hyperbolic conservation laws. A formal analysis is presented to show that a third order finite difference scheme with this parametrized MPP flux limiters maintains the third order accuracy without extra CFL constraint when the low order monotone flux is chosen appropriately. Numerical tests in both one and two dimensional cases are performed on the simulation of the incompressible Navier-Stokes equations in vorticity stream-function formulation and several other problems to show the effectiveness of the proposed method.

Production of Iron-Tin Compacts by Powder Metallurgy and a Synopsis of their Principle Properties

This thesis is concerned primarily with the production of metal powder compacts of iron and tin. In producing these compacts, the effects of process­ing variables on some of the essential properties of the pellets made were investigated.

One-year outcomes of repeated adjunctive photodynamic therapy during periodontal maintenance: a proof-of-principle randomized-controlled clinical trial

BACKGROUND: Single photodynamic therapy (PDT) has been effective in initial periodontal therapy, but only improved bleeding on probing (BoP) in maintenance patients after a single use. Repeated PDT has not been addressed. OBJECTIVES: To study the possible added benefits of repeated adjunctive PDT to conventional treatment of residual pockets in patients enrolled in periodontal maintenance. MATERIAL AND METHODS: Ten maintenance patients with 70 residual pockets [probing pocket depth (PPD)>or=5 mm] were randomly assigned for treatment five times in 2 weeks (Days 0, 1, 2, 7, 14) with PDT (test) or non-activated laser (control) following debridement. The primary outcome variable was PPD, and the secondary variables were clinical attachment level (CAL) and BoP. These were assessed at 3, 6 and 12 months following the interventions. RESULTS: Greater PPD reductions were observed in the test (-0.67 +/- 0.34; p=0.01) compared with the control patients (-0.04 +/- 0.33; NS) after 6 months. Significant CAL gain (+0.52 +/- 0.31; p=0.01) was noted for the test, but not in the control (-0.27 +/- 0.52; NS) patients after 6 months. BoP percentages decreased significantly in test (97-64%, 67%, 77%), but not control patients after 3, 6 and 12 months. CONCLUSIONS: Repeated (five times) PDT adjunctive to debridement yielded improved clinical outcomes in residual pockets in maintenance patients. The effects were best documented after 6 months.

A stochastic principle behind polar properties of condensed molecular matter

A statistical mechanics view leads to the conclusion that polar molecules allowed to populate a degree of freedom for orientational disorder in a condensed phase thermalize into a bi-polar state featuring zero net polarity. In cases of orientational disorder polar order of condensed molecular matter can only exist in corresponding sectors of opposite average polarities. Channel type inclusion compounds, single component molecular crystals, solid solutions, optically anomalous crystals, inorganic ionic crystals, biomimetic crystals and biological tissues investigated by scanning pyroelectric and phase sensitive second harmonic generation microscopy all showed domains of opposite polarities in their final grown state. For reported polar molecular crystal structures it is assumed that kinetic hindrance along one direction of the polar axis is preventing the formation of a bi-polar state, thus allowing for a kinetically controlled mono-domain state. In this review we summarize theoretical and experimental findings leading to far reaching conclusions on the polar state of solid molecular matter. “… no stationary state … of a system has an electrical dipole moment.” P. W. Anderson, Science, 1972, 177, 393.

Computed Ultrasound Tomography in Echo Mode for Imaging Speed of Sound Using Pulse-Echo Sonography: Proof of Principle

The limitations of diagnostic echo ultrasound have motivated research into novel modalities that complement ultrasound in a multimodal device. One promising candidate is speed of sound imaging, which has been found to reveal structural changes in diseased tissue. Transmission ultrasound tomography shows speed of sound spatially resolved, but is limited to the acoustically transparent breast. We present a novel method by which speed-of-sound imaging is possible using classic pulse-echo equipment, facilitating new clinical applications and the combination with state-of-the art diagnostic ultrasound. Pulse-echo images are reconstructed while scanning the tissue under various angles using transmit beam steering. Differences in average sound speed along different transmit directions are reflected in the local echo phase, which allows a 2-D reconstruction of the sound speed. In the present proof-of-principle study, we describe a contrast resolution of 0.6% of average sound speed and a spatial resolution of 1 mm (laterally) × 3 mm (axially), suitable for diagnostic applications.

The application of principal component analysis on human development indicators: Temporal approach from 1999 to 2010

Background and Objective. Ever since the human development index was published in 1990 by the United Nations Development Programme (UNDP), many researchers started searching and corporative studying for more effective methods to measure the human development. Published in 1999, Lai’s “Temporal analysis of human development indicators: principal component approach” provided a valuable statistical way on human developmental analysis. This study presented in the thesis is the extension of Lai’s 1999 research. ^ Methods. I used the weighted principal component method on the human development indicators to measure and analyze the progress of human development in about 180 countries around the world from the year 1999 to 2010. The association of the main principal component obtained from the study and the human development index reported by the UNDP was estimated by the Spearman’s rank correlation coefficient. The main principal component was then further applied to quantify the temporal changes of the human development of selected countries by the proposed Z-test. ^ Results. The weighted means of all three human development indicators, health, knowledge, and standard of living, were increased from 1999 to 2010. The weighted standard deviation for GDP per capita was also increased across years indicated the rising inequality of standard of living among countries. The ranking of low development countries by the main principal component (MPC) is very similar to that by the human development index (HDI). Considerable discrepancy between MPC and HDI ranking was found among high development countries with high GDP per capita shifted to higher ranks. The Spearman’s rank correlation coefficient between the main principal component and the human development index were all around 0.99. All the above results were very close to outcomes in Lai’s 1999 report. The Z test result on temporal analysis of main principal components from 1999 to 2010 on Qatar was statistically significant, but not on other selected countries, such as Brazil, Russia, India, China, and U.S.A.^ Conclusion. To synthesize the multi-dimensional measurement of human development into a single index, the weighted principal component method provides a good model by using the statistical tool on a comprehensive ranking and measurement. Since the weighted main principle component index is more objective because of using population of nations as weight, more effective when the analysis is across time and space, and more flexible when the countries reported to the system has been changed year after year. Thus, in conclusion, the index generated by using weighted main principle component has some advantage over the human development index created in UNDP reports.^

An Oka principle for equivariant isomorphisms

Let G be a reductive complex Lie group acting holomorphically on normal Stein spaces X and Y, which are locally G-biholomorphic over a common categorical quotient Q. When is there a global G-biholomorphism X → Y? If the actions of G on X and Y are what we, with justification, call generic, we prove that the obstruction to solving this local-to-global problem is topological and provide sufficient conditions for it to vanish. Our main tool is the equivariant version of Grauert's Oka principle due to Heinzner and Kutzschebauch. We prove that X and Y are G-biholomorphic if X is K-contractible, where K is a maximal compact subgroup of G, or if X and Y are smooth and there is a G-diffeomorphism ψ : X → Y over Q, which is holomorphic when restricted to each fibre of the quotient map X → Q. We prove a similar theorem when ψ is only a G-homeomorphism, but with an assumption about its action on G-finite functions. When G is abelian, we obtain stronger theorems. Our results can be interpreted as instances of the Oka principle for sections of the sheaf of G-biholomorphisms from X to Y over Q. This sheaf can be badly singular, even for a low-dimensional representation of SL2(ℂ). Our work is in part motivated by the linearisation problem for actions on ℂn. It follows from one of our main results that a holomorphic G-action on ℂn, which is locally G-biholomorphic over a common quotient to a generic linear action, is linearisable.