Thesis (doctoral)--Friedrich-Wilhelms-Universität zu Breslau, 1918. / Cover title. Vita.

Thesis (Ph. D.)--Lehigh University, 2000. / Includes vita. Includes bibliographical references (leaves 49-50).

Qin, Guiming. / "August 2010." / Thesis (M.Phil.)--Chinese University of Hong Kong, 2010. / Includes bibliographical references (p. 72-74). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.5 / Chapter 1.1 --- B splines and B-splines surfaces --- p.5 / Chapter 1. 2 --- Box spline --- p.6 / Chapter 1. 3 --- Biorthogonal subdivision wavelets based on the lifting scheme --- p.7 / Chapter 1.4 --- Geometrically-constrained subdivision wavelets --- p.9 / Chapter 1.5 --- Contributions --- p.9 / Chapter 2 --- Explicit symbol formulae for B-splines --- p.11 / Chapter 2. 1 --- Explicit formula for a general recursion scheme --- p.11 / Chapter 2. 2 --- Explicit formulae for de Boor algorithms of B-spline curves and their derivatives --- p.14 / Chapter 2.2.1 --- Explicit computation of de Boor Algorithm for Computing B-Spline Curves --- p.14 / Chapter 2.2.2 --- Explicit computation of Derivatives of B-Spline Curves --- p.15 / Chapter 2. 3 --- Explicit power-basis matrix fomula for non-uniform B-spline curves --- p.17 / Chapter 3 --- Biorthogonal subdivision wavelets with geometric constraints --- p.23 / Chapter 3. 1 --- Primal subdivision and dual subdivision --- p.23 / Chapter 3. 2 --- Biorthogonal Loop-subdivision-based wavelets with geometric constraints for triangular meshes --- p.24 / Chapter 3.2.1 --- Loop subdivision surfaces and exact evaluation --- p.24 / Chapter 3.2.2 --- Lifting-based Loop subdivision wavelets --- p.24 / Chapter 3.2.3 --- Biorthogonal Loop-subdivision wavelets with geometric constraints --- p.26 / Chapter 3. 3 --- Biorthogonal subdivision wavelets with geometric constraints for quadrilateral meshes --- p.35 / Chapter 3.3.1 --- Catmull-Clark subdivision and Doo-Sabin subdivision surfaces --- p.35 / Chapter 3.3.1.1 --- Catmull-Clark subdivision --- p.36 / Chapter 3.3.1.2 --- Doo-Sabin subdivision --- p.37 / Chapter 3.3.2 --- Biorthogonal subdivision wavelets with geometric constraints for quadrilateral meshes --- p.38 / Chapter 3.3.2.1 --- Biorthogonal Doo-Sabin subdivision wavelets with geometric constraints --- p.38 / Chapter 3.3.2.2 --- Biorthogonal Catmull-Clark subdivision wavelets with geometric constraints --- p.44 / Chapter 4 --- Experiments and results --- p.49 / Chapter 5 --- Conclusions and future work --- p.60 / Appendix A --- p.62 / Appendix B --- p.67 / Appendix C --- p.69 / Appendix D --- p.71 / References --- p.72

No description available.

No / Wavelets are constructed from the basis sets of their parent scaling functions of the two-scale dilation equation (1). Whereas orthogonal wavelets come from one orthogonal basis set, the biorthogonal wavelets project from different basis sets. Each basis set is correspondingly weighted to form filters, either highpass or lowpass, which form the constituents of quadrature mirror filter (QMF) banks. Consequently, these filters can be used to design wavelets, the differently weighted parameters contributing respective wavelet properties which influence the performance of the transforms in applications, for example multicarrier modulation. This study investigated applications for onward multicarrier modulation applications. The results show that the optimum choice of particular wavelet adopted in digital multicarrier communication signal processing may be quite different from choices in other areas of wavelet applications, for example image and video compression.

Title from title page of PDF (University of Missouri--St. Louis, viewed April 5, 2010). Includes bibliographical references (p. 84-89).

Stochastic delay differential equations naturally arise in models of complex natural phenomena, yet continue to resist efforts to find analytical solutions to them: general solutions are limited to linear systems with additive noise and a single delayed term. In this work we solve the case of distributed delays in linear systems with additive noise. Key to our solution is the development of a consistent interpretation for integrals over stochastic variables, obtained by means of a virtual discretization procedure. This procedure makes no assumption on the form of noise, and would likely be useful for a wider variety of cases than those we have considered. We show how it can be used to map the distributed delay equation to a known multivariate system, and obtain expressions for the system's time-dependent mean and autocovariance. These are in the form of series over the system's natural modes and completely define the solution. — An interpretation of the system as an amplitude process is explored. We show that for a wide range of realistic parameters, dynamics are dominated by only a few modes, implying that most of the observed behaviour of stochastic delayed equations is constrained to a low-dimensional subspace. — The expression for the autocovariance is given particular attention. A recurring problem for stochastic delay equations is the description of their temporal structure. We show that the series expression for the autocovariance does converge over a meaningful range of time lags, and therefore provides a means of describing this temporal structure.

Effective image compression requires a non-expansive discrete wavelet transform (DWT) be employed; consequently, image border extension is a critical issue. Ideally, the image border extension method should not introduce distortion under compression. It has been shown in literature that symmetric extension performs better than periodic extension. However, the non-expansive, symmetric extension using fast Fourier transform and circular convolution DWT methods require symmetric filters. This precludes orthogonal wavelets for image compression since they cannot simultaneously possess the desirable properties of orthogonality and symmetry. Thus, biorthogonal wavelets have been the de facto standard for image compression applications. The viability of symmetric extension with biorthogonal wavelets is the primary reason cited for their superior performance. Recent matrix-based techniques for computing a non-expansive DWT have suggested the possibility of implementing symmetric extension with orthogonal wavelets. For the first time, this thesis analyzes and compares orthogonal and biorthogonal wavelets with symmetric extension. Our results indicate a significant performance improvement for orthogonal wavelets when they employ symmetric extension. Furthermore, our analysis also identifies that linear (or near-linear) phase filters are critical to compression performance---an issue that has not been recognized to date. We also demonstrate that biorthogonal and orthogonal wavelets generate similar compression performance when they have similar filter properties and both employ symmetric extension. The biorthogonal wavelets indicate a slight performance advantage for low frequency images; however, this advantage is significantly smaller than recently published results and is explained in terms of wavelet properties not previously considered. / Master of Science

In the everlasting battle against cancer the development of drugs targeting new therapeutic pathways is of crucial importance. In the attempt to develop new anticancer agents we have synthesized a library of anthraquinone compounds that show selectivity against leukemia. Mechanistic evaluation of the lead compound reveal that this class of compounds achieve their effects through inhibition of MDM2-MDM4 heterodimer and upregulation of the tumor suppressor p53. Computer aided rational design resulted in the development of a number of compounds with activities in the nanomolar range against various cancer cells. Analysis of the physicochemical properties of selected compounds allowed for their evaluation as potential drug candidates. The successful development of non-toxic formulations permits for the further in vivo investigation of the compounds. Click reactions have found wide spread applications in sensing, materials chemistry, bioconjugation, and biolabeling. A number of very useful click reactions have been discovered, which allow for various applications. In bioconjugation applications, the ability to conduct a secondary conjugation will be very useful in, e.g., protein pull down and binding site identification. Along this line, we describe a neighboring group-assisted facile condensation between an aldehyde and a vicinal aminothiol moiety, leading to the formation of benzothiazoles. The conversion is completed within 5 minutes at low micromolar concentrations at ambient temperature. The facile reaction was attributed to the presence of a neighboring boronic acid, which functions as an intramolecular Lewis Acid in catalyzing the reaction. The boronic acid group is compatible with most functional groups in biomolecules and yet can also be used for further functionalization via a large number of well-known coupling reactions.

Este trabalho tem como objetivo principal aplicar elementos de teoria dos conjuntos no estudo de sistemas biortogonais em espaços de Banach. Inicialmente, estudamos o Teorema de Markushevic, que garante que todo espaço de Banach separável admite um sistema biortogonal enumerável. Assim, partimos para o estudo de espaços de Banach não separáveis, mais especificamente, estudamos a existência de sistemas biortogonais não enumeráveis em espaços de Banach da forma C(K), com K compacto Hausdorff não metrizável. Nesta direção, estudamos dois teoremas devido a S. Todorcevic. O primeiro teorema nos dá condições que um compacto Hausdorff K deve satisfazer de tal modo que o respectivo espaço de Banach C(K) possua sistemas biortogonais não enumeráveis. O segundo teorema nos diz que, assumindo o Axioma de Martin, todo espaço de Banach não separável da forma C(K) possui um sistema biortogonal não enumerável. Em seguida, consideramos algumas funções cardinais definidas por P. Koszmider para espaços de Banach, associadas aos sistemas biortogonais e estudamos suas relações com funções cardinais conhecidas. Em particular, obtemos um resultado original que relaciona o peso de um espaço compacto Hausdorff K com o tamanho de tipos especiais de sistemas biortogonais em C(K), generalizando um resultado de S. Todorcevic sobre álgebras de Boole. Finalmente, construímos um espaço de Ostaszewski K usando o Princípio Diamante. O espaço K é um compacto disperso não metrizável tal que todas suas potências finitas são hereditariamente separáveis. Este espaço é um exemplo consistente de um espaço compacto Hausdorff não metrizável tal que o respectivo espaço de Banach C(K) não admite sistemas biortogonais não enumeráveis. / The main purpose of this work is to apply elements of set theory to the study of biorthogonal systems in Banach spaces. Initially, we study Markushevic\'s Theorem, which ensures that every separable Banach space has a countable biorthogonal system. With this result, we focus our attention to the study of nonseparable Banach spaces, more especifically, we study the existence of uncountable biorthogonal systems in Banach spaces of the form C(K), with K a nonmetrizable compact Hausdorff space. In this direction, we study two theorems of S. Todorcevic. The first one gives us sufficient conditions that a compact Hausdorff space K must satisfy in order to get that the respective Banach space C(K) has an uncountable biorthogonal system. The second one tells us that under Martin\'s Axiom, every nonseparable Banach space of the form C(K) has an uncountable biorthogonal system. Next, we consider some cardinal functions defined by P. Koszmider for Banach spaces, related with biorthogonal systems, and we study its relations with well - known cardinal functions. In particular, we obtain an original result relating the weight of a compact Hausdorff space K to the size of certain biorthogonal systems in C(K), generalizing a result of S. Todorcevic for Boolean algebras. Finally, we construct an Ostaszewski space K using the Diamond Principle. The compact space K is a scattered nonmetrizable Hausdorff space such that all its finite powers are hereditarily separable. This space is a consistent example of a nonmetrizable compact Hausdorff space such that the respective Banach space C(K) does not have an uncountable biorthogonal system.