Cylindrical algebraic decomposition is a powerful algorithmic technique in semi-algebraic geometry. Nevertheless, there is a disparity between what algorithms output and what the abstract definition of a cylindrical algebraic decomposition allows. Some work has been done in trying to understand what the ideal class of cylindrical algebraic decom- positions should be — especially from a topological point of view. We prove a special case of a conjecture proposed by Lazard in [22]; the conjecture relates a special class of cylindrical algebraic decompositions to regular cell complexes. Moreover, we study the properties that define this special class of cell decompositions, as well as their implications for the actual topology of the cells that make up the cell decompositions.

Until this present work, the acoustics of waveguides has been divided into two broadly distinct fields---linear acoustics in ducts of complex geometry such as those with curvature or varying width, and nonlinear acoustics restricted to simple geometry ducts without curvature or flare. This PhD unites these distinct branches to give a complete mathematical description of weakly nonlinear wave propagation in a general shaped duct in both two and three dimensions. Such ducts have important applications---the clearest example is that of brass instruments, where it has been demonstrated that nonlinear wave steepening gives rise to the characteristic 'brassy' sounds of, for example, the trombone. As the ducts of these instruments have a very complicated geometry involving curvature, torsion and varying width, the goal of the PhD is to address what effect, if any, such changes in duct geometry have on the acoustic properties of such instruments. Other potential applications include the study of acoustics in curved aircraft engine intakes and even the nonlinear sound propagation through the trunk of an elephant. The first results chapter is focused on the exposition of the method used for the remainder of the paper, with the introduction of a new ``nonlinear admittance term'' as well as the associated algebra for it. An elegant notation for the nonlinear algebra is also developed, greatly simplifying the equations. The method is applied to one and two dimensional ducts and some analytical results are derived relating the work to previously published results. Numerical results are also presented and compared to other sources. The concept of nonlinear reflectance is also introduced---illustrating the effect of wave amplitude on the amount of energy reflected in a duct. The next results chapter builds on this work extending it to three dimensions. Numerical results are presented for three characteristic ducts---a curved duct, a horn and a helical duct, being one of the first works to study acoustics in helical pipes for both linear and nonlinear sound propagation. The final results chapter, utilising all of the previous work, addresses the problem of an open ended duct of finite length with nonlinear effects included. Results are compared with the linear results from the Wiener-Hopf method and new results are presented illustrating the effect of geometry and nonlinearity on the resonances of finite length waveguides culminating in the study of the resonances of a trombone.

by Hu Guangda. / "June 2000." / The numerals in the title are subscript. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2000. / Includes bibliographical references (p. 131-141). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Mode of access: World Wide Web. / Abstracts in English and Chinese.

This thesis examines the catalytic characteristics of two materials with respect to the decomposition of Formic Acid. The decomposition of formic acid proceeds via two principal reaction pathways: dehydration and dehydrogenation. Dehydrogenation is a valuable reaction producing Hydrogen suitable for use in fuel cells whereas the dehydration pathway produces carbon monoxide, a poison for many fuel cell materials. One of the surface species, the formate ion, is also implicated in other important chemical reactions, most notably the water gas shift and the decomposition of methanol. The author seeks to document various intermediate surface species associated with the two reaction pathways with hope to use this information to future tailoring of catalysts for greater selectivity.

The thermochemical copper-chlorine (Cu-Cl) cycle for hydrogen production includes three chemical reactions of hydrolysis, decomposition and electrolysis. The decomposition of copper oxychloride establishes the high-temperature limit of the cycle. Between 430 and 530 oC, copper oxychloride (Cu2OCl2) decomposes to produce a molten salt of copper (I) chloride (CuCl) and oxygen gas. The conditions that yield equilibrium at high conversion rates are not well understood. Also, the impact of feed streams containing by-products of incomplete reactions in an integrated thermochemical cycle of hydrogen production are also not well understood. In an integrated cycle, the hydrolysis reaction where CuCl2 reacts with steam to produce solid copper oxychloride precedes the decomposition reaction. Undesirable chlorine may be released as a result of CuCl2 decomposition and mass imbalance of the overall cycle and additional energy requirements to separate chlorine gas from the oxygen gas stream. In this thesis, a new phase change predictive model is developed and compared to the reaction rate kinetics in order to better understand the nature of resistances. A Stefan boundary condition is used in a new particle model to track the position of the moving solid-liquid interface as the solid particle decomposes under the influence of heat transfer at the surface. Results of conversion of CuO*CuCl2 from both a thermogravimetric (TGA) microbalance and a laboratory scale batch reactor experiments are analyzed and the rate of endothermic reaction determined. A second particle model identifies parameters that impact the transient chemical decomposition of solid particles embedded in the bulk fluid consisting of molten and gaseous phases at high temperature and low Reynolds number. The mass, energy, momentum and chemical reaction equations are solved for a particle suddenly immersed in a viscous continuum. Numerical solutions are developed and the results are validated with experimental data of small samples of chemical decomposition of copper oxychloride (CuO*CuCl2). This thesis provides new experimental and theoretical reference for the scale-up of a CuO*CuCl2 decomposition reactor with consideration of the impact on the yield of the thermochemical copper-chlorine cycle for the generation of hydrogen. / UOIT

The aim of this study was to investigate the influence of soft tissue decomposition on the stability of drugs incorporated in hair antemortem. Two burial trials were conducted: in the first trial, rats were administered oxycodone over five days; in the second trial, rats were administered heroin over nine days then drug abstinent for another nine days. After each respective treatment the rats were sacrificed and buried in controlled burial microcosms. Concentrations of oxycodone and selected metabolites or the metabolites of heroin; 6-monoacetylmorphine and morphine, incorporated within rat hair and liver were measured before and during the decomposition process. Oxycodone was analysed in hair and liver samples, while morphine and 6-monoacetylmorphine were analysed in hair samples by ultra-performance liquid chromatography-tandem mass spectrometry (UPLC-MS/MS). Oxycodone concentrations in both hair and liver decreased as the interment period and decomposition of the carcasses progressed. 6-Monoacetylmorphine was not detected in any hair samples collected from the exhumed carcasses. / UOIT

Spherical Harmonics (SPHARM) and Singular Value Decomposition (SVD) utilize the orthogonal relations of its parameters to represent and process images. The process involve mapping of the image from its original parameter domain to a new domain where the processing is performed. This process induces distortion and smoothing is required. The image now mapped to the new parameter domain is descripted using SPHARM and SVD using one at a time. The least significant values for the SPHARM coefficients and singular values of SVD are truncated which induces compression in the reconstructed image keeping the memory allocation in view. In this thesis, we have applied SPHARM and SVD tools to represent and reconstruct an image. The image is first mapped to the unit sphere (a sphere with unit radius). The image gets distorted that is maximum at the north and south poles, for which smoothing is approached by leaving 0.15*π space blank at each pole where no mapping is done. Sampling is performed for the θ and φ parameters and the image is represented using spherical harmonics and its coefficients are calculated. The same is then repeated for the SVD and singular values are computed. Reconstruction is performed using the calculated parameters, but defined over some finite domain, which is done by truncating the SPHARM coefficients and the singular values inducing image compression. Results are formulated for the various truncation choices and analyzed and finally it is concluded that SPHARM is better as compared with SVD as compression tool as there is not much difference in the quality of the reconstructed image with both tools, though SVD seem better quality wise, but with much higher memory allocation than SPHARM.

This paper is concerned about an implementation of an accelerated domain decomposition iterative procedure. In [4], Douglas and Huang had shown the convergence for one dimensional partitioning case. This time we make an implementation to show the numerical results, and further more extend our procedure to two dimensional partitioning case. Our results show that the parameter sequence do accelerate our iterative procedure. In one dimensional partitioning case, we have the rule to choose the parameter sequence[4], but in two dimensional partitioning case, we still have no idea about the rule, but we still try to find some parameters to make our procedure more e cient. After some tests, we find that the sequence {0.4, 0.43, 0.45, 0.47, 0.5} works. Though the iteration steps in two dimensional partitioning are not decreasing, our results show the computation time is almost the same as which in the two dimensional partitioning case. It means that the parallelized program could cut down the computation cost.

Hydroxylamine nitrate (HAN), an important agent for the nuclear industry and the U.S. Army, has been involved in several costly incidents. To prevent similar incidents, the study of HAN safe storage and handling boundary has become extremely important for industries. However, HAN decomposition involves complicated reaction pathways due to its autocatalytic behavior and therefore presents a challenge for definition of safe boundaries of HAN storage and handling. This research focused on HAN decomposition behavior under various conditions and proposed isothermal aging testing and kinetic-based simulation to determine safety boundaries for HAN storage and handling. Specifically, HAN decomposition in the presence of glass, titanium, stainless steel with titanium, or stainless steel was examined in an Automatic Pressure Tracking Adiabatic Calorimeter (APTAC). n-th order kinetics was used for initial reaction rate estimation. Because stainless steel is a commonly used material for HAN containers, isothermal aging tests were conducted in a stainless steel cell to determine the maximum safe storage time of HAN. Moreover, by changing thermal inertia, data for HAN decomposition in the stainless steel cell were examined and the experimental results were simulated by the Thermal Safety Software package. This work offers useful guidance for industries that manufacture, handle, and store HAN. The experimental data acquired not only can help with aspects of process safety design, including emergency relief systems, process control, and process equipment selection, but also is a useful reference for the associated theoretical study of autocatalytic decomposition behavior.

Fast Fourier transformation (FFT) is a powerful analytical tool with wide-ranging applications in many fields. The standard FFT algorithms inherently assume that the length of the input and output sequence are equal. In practice, it is not always an accurate assumption. In certain case only some of the inputs to the transformation function are non-zero but lot of other are zero. In this thesis, a novel architecture of a 1024-point FFT, which adopts the transform decomposition (TD) algorithm, is presented to further reduce the complexity when the non-zero input data are consecutive. To implement this FFT processor, fixed point simulation is a conducted by using MATLB. The hardware implementation is realized by using the Verilog Hardware Description Language (HDL) which is taped out in TSMC0.18 Cell-Based Library for system verification.