No description available.

This thesis provides sufficient conditions for total differentiability almost everywhere of a real-valued function of a complex variable defined on a bounded region in IRn. This thesis extends H. Rademacher's 1918 results in IR2 which culminated in total differentiability, to IRn

Thesis (Ph. D.)--University of Missouri-Columbia, 2003. / Typescript. Vita. Includes bibliographical references (leaves 83-89). Also available on the Internet.

Thesis (Ph. D.)--University of Missouri-Columbia, 2003. / Typescript. Vita. Includes bibliographical references (leaves 83-89). Also available on the Internet.

No description available.

Hui, Chun Yin. / On t.p. "n" is a superscript. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2008. / Includes bibliographical references (leaves 80-83). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.5 / Chapter 2 --- Basic properties of real hypersurfaces in CN --- p.9 / Chapter 2.1 --- Hypersurfaces in CN and some nondegeneracy conditions --- p.9 / Chapter 2.2 --- CR functions and their holomorphic extensions --- p.15 / Chapter 2.3 --- Normal coordinates for real analytic hypersurfaces --- p.18 / Chapter 3 --- The algebraic results for reflection principle --- p.22 / Chapter 4 --- Reflection principle for real analytic hypersurfaces in higher complex dimensions --- p.30 / Chapter 4.1 --- Reflection principle for Levi nondegenerate hypersurfaces --- p.31 / Chapter 4.2 --- Essentially finite real analytic hypersurfaces and not totally degenerate CR mappings --- p.38 / Chapter 4.3 --- Reflection principle for essentially finite hypersurfaces --- p.44 / Chapter 4.4 --- Reflection principle for CR mappings and bounded domains --- p.54 / Chapter 4.5 --- Futher results on the reflection principle --- p.64 / Chapter 5 --- An extension result of CR functions by a general Schwarz reflection principle --- p.66 / Chapter 5.1 --- A general Schwarz reflection principle --- p.66 / Chapter 5.2 --- "Holomorphic extension of CR functions on a real analytic, generic CR submanifold in CN" --- p.69 / Bibliography --- p.80

Huge amount of data flows around the Internet every second, but for the data to be useful at its destination, it must be presented in a way such that the target has little problem interpreting it. Current data exchange technologies may rearrange the structure of data to suit expectations at the target. However, there may be semantics behind data (e.g. knowing the title of a book can determine its #pages) that may be violated after data translation. These semantics are expressed as integrity constraints (IC) in a database. Currently, there is no guarantee that the exchanged data conforms to the target’s ICs. As a result, existing applications (e.g. user queries) that assume such semantics will no longer function correctly. Current constraint repair techniques deal with data after it has been translated; thus take no consideration of the integrity constraints at the source. Moreover, such constraint repair methods usually involve addition/deletion/modification of data, which may yield incomplete or false data. We consider the constraints of both source and target schemas; together with the mapping, we can efficiently detect which constraint is violated and suggest ways to correct the mappings.

Huge amount of data flows around the Internet every second, but for the data to be useful at its destination, it must be presented in a way such that the target has little problem interpreting it. Current data exchange technologies may rearrange the structure of data to suit expectations at the target. However, there may be semantics behind data (e.g. knowing the title of a book can determine its #pages) that may be violated after data translation. These semantics are expressed as integrity constraints (IC) in a database. Currently, there is no guarantee that the exchanged data conforms to the target’s ICs. As a result, existing applications (e.g. user queries) that assume such semantics will no longer function correctly. Current constraint repair techniques deal with data after it has been translated; thus take no consideration of the integrity constraints at the source. Moreover, such constraint repair methods usually involve addition/deletion/modification of data, which may yield incomplete or false data. We consider the constraints of both source and target schemas; together with the mapping, we can efficiently detect which constraint is violated and suggest ways to correct the mappings.

Tandem source-channel coding is proven to be optimal by Shannon given unlimited delay and complexity in the coders. Under low delay and low complexity constraints, joint source-channel coding may achieve better performance. Although digital joint source-channel coding has shown a noticeable gain in terms of reconstructed signal quality, coding delay, and complexity, it suffers from the leveling-off effect. However, analog systems do not suffer from the leveling-off effect. In this thesis, we investigate the advantage of analog systems based on the Shannon-Kotel’nikov approach and hybrid digital-analog coding systems, which combine digital and analog schemes to achieve a graceful degradation/improvement over a wide range of channel conditions. First, we propose a low delay and low complexity hybrid digital-analog coding that is able to achieve high (integer) expansion ratios ( >3). This is achieved by combining the spiral mapping with multiple stage quantizers. The system is simulated for a 1 : 3 bandwidth expansion and the behavior for a 1 : M (with M an integer >3) system is studied in the low noise level regime. Next, we propose an analog joint source-channel coding system that is able to achieve a low (fractional) expansion ratio between 1 and 2. More precisely, this is an N : M bandwidth expansion system based on combining uncoded transmission and a 1 : 2 bandwidth expansion system (with N < M < 2N).Finally, a 1 : 2 analog bandwidth expansion system using the (Shannon-Kotel’nikov) Archimedes’ spiral mapping is used in the compressed sensing context, which is inherently analog, to increase the system’s immunity against channel noise. The proposed system is compared to a conventional compressed sensing system that assumes noiseless transmission and a compressed sensing based system that account for noise during signal reconstruction. / Thesis (Master, Electrical & Computer Engineering) -- Queen's University, 2011-07-29 02:30:11.978

It is well known that, as a consequence of the Identity Theorem, we cannot "glue" together two analytic functions to create a new globally analytic function. In this paper we will both introduce and investigate special homeomorphisms, called quasiconformal maps, that are generalizations of the well known conformal maps. We will show that quasiconformal maps make this "gluing," up to conjugation, possible. Quasiconformal maps are a valuable tool in the field of complex dynamics. We will see how quasiconformal maps of infinitesimal circles have an image of an infinitesimal ellipse. Although quasiconformal maps are nice homeomorphisms, they might only be differentiable in the real sense almost everywhere and, surprisingly, complex differentiable nowhere. We shall rely on the work of Lehto and Virtanen as well as Shishikura in exploring these interesting complex valued functions. / Department of Mathematical Sciences