We prove that a smooth generic embedded CR submanifold of C^n obeys the maximum principle for continuous CR functions if and only if it is weakly 1-concave. The proof of the maximum principle in the original manuscript has later been generalized to embedded weakly q-concave CR submanifolds of certain complex manifolds. We give a generalization of a known result regarding automatic smoothness of solutions to the homogeneous problem for the tangential CR vector fields given local holomorphic extension. This generalization ensures that a given locally integrable structure is hypocomplex at the origin if and only if it does not allow solutions near the origin which cannot be represented by a smooth function near the origin. We give a sufficient condition under which it holds true that if a smooth CR function f on a smooth generic embedded CR submanifold, M, of C^n, vanishes to infinite order along a C^infty-smooth curve  \gamma in M, then f vanishes on an M-neighborhood of \gamma. We prove a local maximum principle for certain locally integrable structures. / <p>Funding  by FMB, based at Uppsala University.</p>

Includes bibliographical references / 123, [10] leaves ; 30 cm. / Title page, contents and abstract only. The complete thesis in print form is available from the University Library. / Thesis (Ph.D.)--University of Adelaide, Dept. of Pure Mathematics, 1984

[Formulae and special characters in this field can only be approximated. See PDF version for accurate reproduction] In this thesis we investigate the properties of k-closures of certain finite permutation groups. Given a permutation group G on a finite set Ω, for k ≥ 1, the k-closure G(k) of G is the largest subgroup of Sym(Ω) with the same orbits as G on the set Ωk of k-tuples from Ω. The first problem in this thesis is to study the 3-closures of affine permutation groups. In 1992, Praeger and Saxl showed if G is a finite primitive group and k ≥ 2 then either G(k) and G have the same socle or (G(k),G) is known. In the case where the socle of G is an elementary abelian group, so that G is a primitive group of affine transformations of a finite vector space, the fact that G(k) has the same socle as G gives little information about the relative sizes of the two groups G and G(k). In this thesis we use Aschbacher’s Theorem for subgroups of finite general linear groups to show that, if G ≤ AGL(d, p) is an affine permutation group which is not 3-transitive, then for any point α ∈ Ω, Gα and (G(3) ∩ AGL(d, p))α lie in the same Aschbacher class. Our results rely on a detailed analysis of the 2-closures of subgroups of general linear groups acting on non-zero vectors and are independent of the finite simple group classification. In addition, modifying the work of Praeger and Saxl in [47], we are able to give an explicit list of affine primitive permutation groups G for which G(3) is not affine. The second research problem is to give a partial positive answer to the so-called Polycirculant Conjecture, which states that every transitive 2-closed permutation group contains a semiregular element, that is, a permutation whose cycles all have the same length. This would imply that every vertex-transitive graph has a semiregular automorphism. In this thesis we make substantial progress on the Polycirculant Conjecture by proving that every vertex-transitive, locally-quasiprimitive graph has a semiregular automorphism. The main ingredient of the proof is the determination of all biquasiprimitive permutation groups with no semiregular elements. Publications arising from this thesis are [17, 54].

Thesis (Ph.D.)--York University, [2004]. Graduate Programme in [Mathematics]. / Typescript. Includes bibliographical references (leaves 163-166). Also available on the Internet. MODE OF ACCESS via web browser by entering the following URL: http://wwwlib.umi.com/cr/yorku/fullcit?pNQ99158

In recent years, more and more efforts have been expended on the study of $n$-dimensional asymptotically anti-de Sitter spacetimes $(\mathcal{M},g)$ as solutions to the Einstein vacuum equations \begin{align*} \mathrm{Ric}(g)=\frac{2}{n-2}\Lambda\, g \end{align*} with negative cosmological constant $\Lambda$. This has been motivated mainly by the conjectured instability of these solutions. The author of this thesis joins these efforts with two contributions, which are themselves independent of each other. In the first part, we are concerned with a superradiant instability for $n=4$. For any cosmological constant $\Lambda=-3/\ell^2$ and any $\alpha < 9/4$, we find a Kerr-AdS spacetime $(\mathcal{M},g_{\mathrm{KAdS}})$, in which the Klein-Gordon equation \begin{align*} \Box_g\psi+\frac{\alpha}{\ell^2}\psi=0 \end{align*} has an exponentially growing mode solution satisfying a Dirichlet boundary condition at infinity. The spacetime violates the Hawking-Reall bound $r_+^2 > |a|\ell$. We obtain an analogous result for Neumann boundary conditions if $5/4 < \alpha < 9/4$. Moreover, in the Dirichlet case, one can prove that, for any Kerr-AdS spacetime violating the Hawking-Reall bound, there exists an open family of masses $\alpha$ such that the corresponding Klein-Gordon equation permits exponentially growing mode solutions. Our result provides the first rigorous construction of a superradiant instability for a negative cosmological constant. In the second part, we study perturbations of five-dimensional Eguchi-Hanson-AdS spacetimes exhibiting biaxial Bianchi IX symmetry. Within this symmetry class, the Einstein vacuum equations are equivalent to a system of non-linear partial differential equations for the radius $r$ of the spheres, the Hawking mass $m$ and $B$, a quantity measuring the squashing of the spheres, which satisfies a non-linear wave equation. First we prove that the system is well-posed as an initial-boundary value problem around infinity $\mathcal{I}$ with $B$ satisfying a Dirichlet boundary condition. Second, we show that initial data in the biaxial Bianchi IX symmetry class around Eguchi-Hanson-AdS spacetimes cannot form horizons in the dynamical evolution.

abstract: Mobile ad hoc networks (MANETs) have attracted attention for mission critical applications. This dissertation investigates techniques of statistical monitoring and control for overhead reduction in a proactive MANET routing protocol. Proactive protocols transmit overhead periodically. Instead, we propose that the local conditions of a node should determine this transmission decision. While the goal is to minimize overhead, a balance in the amount of overhead transmitted and the performance achieved is required. Statistical monitoring consists of techniques to determine if a characteristic has shifted away from an in-control state. A basic tool for monitoring is a control chart, a time-oriented representation of the characteristic. When a sample deviates outside control limits, a significant change has occurred and corrective actions are required to return to the in-control state. We investigate the use of statistical monitoring of local conditions in the Optimized Link State Routing (OLSR) protocol. Three versions are developed. In A-OLSR, each node uses a Shewhart chart to monitor betweenness of its two-hop neighbourhood. Betweenness is a social network metric that measures a node's influence; betweenness is larger when a node has more influence. Changes in topology are associated with changes in betweenness. We incorporate additional local node conditions including speed, density, packet arrival rate, and number of flows it forwards in A+-OLSR. Response Surface Methodology (RSM) is used to optimize timer values. As well, the Shewhart chart is replaced by an Exponentially Weighted Moving Average (EWMA) chart, which is more sensitive to small changes in the characteristic. It is known that control charts do not work as well in the presence of correlation. Hence, in A*-OLSR the autocorrelation in the time series is removed and an Auto-Regressive Integrated Moving Average (ARIMA) model found; this removes the dependence on node speed. A*-OLSR also extends monitoring to two characteristics concurrently using multivariate cumulative sum (MCUSUM) charts. The protocols are evaluated in simulation, and compared to OLSR and its variants. The techniques for statistical monitoring and control are general and have great potential to be applied to the adaptive control of many network protocols. / Dissertation/Thesis / Ph.D. Computer Science 2012

abstract: In this era of fast computational machines and new optimization algorithms, there have been great advances in Experimental Designs. We focus our research on design issues in generalized linear models (GLMs) and functional magnetic resonance imaging(fMRI). The first part of our research is on tackling the challenging problem of constructing exact designs for GLMs, that are robust against parameter, link and model uncertainties by improving an existing algorithm and providing a new one, based on using a continuous particle swarm optimization (PSO) and spectral clustering. The proposed algorithm is sufficiently versatile to accomodate most popular design selection criteria, and we concentrate on providing robust designs for GLMs, using the D and A optimality criterion. The second part of our research is on providing an algorithm that is a faster alternative to a recently proposed genetic algorithm (GA) to construct optimal designs for fMRI studies. Our algorithm is built upon a discrete version of the PSO. / Dissertation/Thesis / Doctoral Dissertation Statistics 2014

abstract: This thesis aims to investigate the impacts of foreign banks’ management model on their degree of localization and operating efficiency. I decompose their management model into five major factors, including two formative factors and three reflective factors. The two formative factors are (1) strategic orientation and (2) target customers, and the three reflective factors are (1) top management team composition, (2) organizational structure, and (3) managerial authority and incentives. I propose that the formative factors influence foreign banks’ degree of localization, as demonstrated by the reflective factors, which subsequently influence foreign banks’ operating efficiency in China. To test the above proposition, I conduct the empirical analysis in three steps. In the first step, I investigate foreign banks’ management model by surveying 13 major foreign banks locally incorporated in Mainland China. The results suggest that these 13 foreign banks can be categorized into three distinct groups based on their management model: intergrators, customer-followers, and parent-followers. The results also indicate that intergrators have the highest level of localization while parent-followers have the lowest level of localization. In the second step, I conduct DEA (Data Envelope Analysis) and CAMEL (Capital Adequacy, Asset Quality, Management, Earnings, Liquidity Analysis) to assess the operating efficiency of these 13 foreign banks. The assessment is conducted in two ways: 1) the inter-group comparison between foreign banks and local Chinese banks; 2) the intra-group comparison between the three distinct groups of foreign banks identified in the first step. The results indicates that the principal factor driving the operating efficiency of both local Chinese banks and foreign banks is the comprehensive technical efficiency, which includes both the quality of management and the quality of technical elements. I also find the uptrend of technical efficiency of the integrators is more stable than that of the other two groups of foreign banks. Finally, I integrate the results from step one and step two to assess the relevance between foreign banks’ localization level and operating efficiency. I find that foreign banks that score higher in localization tend to have a higher level of operating efficiency. Although this finding is not conclusive about the causal relationship between localization and operating efficiency, it nevertheless suggests that the management model of the higher performing integrators can serve as references for the other foreign banks attempting to enhance their localization and operating efficiency. I also discuss the future trends of development in the banking industry in China and what foreign banks can learn from local Chinese banks to improve their market positions. / Dissertation/Thesis / Doctoral Dissertation Business Administration 2016

abstract: This study concerns optimal designs for experiments where responses consist of both binary and continuous variables. Many experiments in engineering, medical studies, and other fields have such mixed responses. Although in recent decades several statistical methods have been developed for jointly modeling both types of response variables, an effective way to design such experiments remains unclear. To address this void, some useful results are developed to guide the selection of optimal experimental designs in such studies. The results are mainly built upon a powerful tool called the complete class approach and a nonlinear optimization algorithm. The complete class approach was originally developed for a univariate response, but it is extended to the case of bivariate responses of mixed variable types. Consequently, the number of candidate designs are significantly reduced. An optimization algorithm is then applied to efficiently search the small class of candidate designs for the D- and A-optimal designs. Furthermore, the optimality of the obtained designs is verified by the general equivalence theorem. In the first part of the study, the focus is on a simple, first-order model. The study is expanded to a model with a quadratic polynomial predictor. The obtained designs can help to render a precise statistical inference in practice or serve as a benchmark for evaluating the quality of other designs. / Dissertation/Thesis / Doctoral Dissertation Statistics 2017

Orientador: Mario Carvalho de Matos / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica / Made available in DSpace on 2018-08-10T04:31:29Z (GMT). No. of bitstreams: 1 Favaro_ViniciusVieira_D.pdf: 758368 bytes, checksum: 1618ae17ed57109a9f307089c59fdbb6 (MD5) Previous issue date: 2007 / Resumo: Neste trabalho introduzimos os espaços de funções (s , m (r , q))-somantes de um dado tipo e uma dada ordem, definidas em E, e os espaços de funções (s; (r; q))-quase-nucleares de um dado tipo e uma dada ordem, definidas em E, e provamos que a transformada de Fourier-Borel identica o dual do espaço de funções (s ; (r' , q'))-quase-nucleares de um dado tipo e uma dada ordem, definidas em E, com o espaço de funções (s';m (r' , q'))-somantes de um correspondente tipo e uma correspondente ordem, definidas em E'. Provamos também teoremas de divisão para funções (s ; m (r , q))-somantes de um dado tipo e uma dada ordem e teoremas de divisão envolvendo a transformada de Fourier-Borel. Como consequencia, provamos resultados de existência e aproximação de soluções de equações de convulção nos espaços de funções (s; (r , q))-quase-nucleares de um dado tipo e uma dada ordem / Abstract: In this work we introduce the spaces of (s; m (r , q))-summing functions of a given type and order defined in E, and the spaces of (s; (r, q))-quasi-nuclear functions of a given type and order defined in E, and we prove that the Fourier-Borel transform identify the dual of the space of (s; (r; q))-quasi-nuclear functions of a given type and order defined in E, with the space of (s' ; m (r'; q'))-summing functions of a corresponding type and order defined in E'. We also prove division theorems for (s; m (r; q))-summing functions of a given type and order and division theorems involving the Fourier-Borel transform. As a consequence we prove the existence and approximation results for convolution equations on the spaces of (s; (r; q))-quasi-nuclear functions of a given type and order / Doutorado / Analise Funcional / Doutor em Matemática