We examine the notion of a-strong singularity for subfactors N of a II1 factor M, which is a metric quantity that relates the distance of a unitary to a subalgebra with the distance between that subalgebra and its unitary conjugate. Using work of Popa, Sinclair, and Smith, we show that there exists an absolute constant 0 < c < 1 such that all singular subfactors are c-strongly singular. Under the hypothesis that N0 \ hM, eNi is 2-dimensional, we prove that finite index subfactors are 1-strongly singular with a constant that tends to 1 as the Jones Index tends to infinity and infinite index subfactors are 1-strongly singular. We provide examples of subfactors satisfying these conditions using group theoretic constructions. Specifically, if P is a II1 factor and G is a countable discrete group acting on P by outer automorphisms, we characterize the elements x of PoG such that x(PoH)x0 PoH for some subgroup H of G. We establish that proper finite index singular subfactors do not have the weak asymptotic homomorphism property, in contrast to the case for masas. In the infinite index setting, we discuss the role of the semigroup of one-sided normalizers with regards to the question of whether all infinite index singular subfactors have the weak asymptotic homomorphism property. Finally, we provide a characterization of singularity for finite index subfactors in terms of the traces of projections in N0 \ hM, eNi and use this result to show that fixed point subfactors of outer Zp for p prime are regular. The characterization extends to infinite index subfactors by replacing singular with contains its one-sided normalizers.

Thesis (Ph. D.)--University of Wisconsin--Madison, 1980. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references (leaves 20-21).

No description available.

Seja L \'= PONTO\' \'\\partial IND. t\' + [\'a(t) + ib (t)] \'\\partial IND. x\' um operador diferencial parcial agindo em distribuições definidas no toro bidimensional \'T POT. 2\'; onde a; b : \'T POT. 1\' \' SETA\' R são funções analíticas reais. Suponhamos que L não ée globalmente analítico hipoelítico e b não é uma função identicamente nula. O objetivo principal deste trabalho é o estudo das soluções singulares de L; através da natureza e da localização das suas singularidades. Com este intuito, primeiramente abordaremos a teoria das séries parciais de Fourier, que nos permitem relacionar o comportamento assintótico dos coeficientes parciais de Fourier de um dado objeto com a regularidade do mesmo / Let L \'= PONTO\' \'\\partial ind. t\' + [ a (t) + ib (t) ] \'\\partial IND. x\' be a partial differential operator acting on distributions on the two-torus \'T POT. 2\' , where a; b : \'T POT. 1\' \'ARROW\' R are real analytic functions. Assume that L is not a globally analytic hypoelliptic operator and b is not identically zero. The main goal of this work is the study of the singular solutions of L; by means of the nature and localization of their singularities. To this end, we first study the theory of partial Fourier series, which are a useful tool to analyze the regularity of a given distribution

Kong Yin To. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1999. / Includes bibliographical references (leaves 53-55). / Abstracts in English and Chinese. / Chapter 1 --- On the Role of Robin Function in Some Singular Per- turbation Problems with Zero Mass --- p.4 / Chapter 1.1 --- Introduction --- p.4 / Chapter 1.2 --- Preliminary Results and Set-up of a Min-Max Scheme --- p.9 / Chapter 1.3 --- Proof of Theorem 1.1 --- p.25 / Chapter 2 --- On a Singularly Perturbed Dirichlet Problem in Con- vex Domain --- p.29 / Chapter 2.1 --- Introduction --- p.29 / Chapter 2.2 --- Preliminary Analysis --- p.33 / Chapter 2.3 --- Location of Multiple Peaks --- p.37 / Chapter 2.4 --- Proof of No Multiple-Peaked Solutions in Convex Do- mains --- p.48

Thesis (Ph. D.)--Oregon State University, 2001. / Typescript (photocopy). Includes bibliographical references (leaves 30). Also available on the World Wide Web.

Thesis--University of Helsinki, 2009. / Includes bibliographical references (p. 109-111).

Thesis (Ph. D.)--University of Wisconsin--Madison, 1980. / Typescript. Vita. Description based on print version record. Includes bibliographical references (leaf 28).

Seja L \'= PONTO\' \'\\partial IND. t\' + [\'a(t) + ib (t)] \'\\partial IND. x\' um operador diferencial parcial agindo em distribuições definidas no toro bidimensional \'T POT. 2\'; onde a; b : \'T POT. 1\' \' SETA\' R são funções analíticas reais. Suponhamos que L não ée globalmente analítico hipoelítico e b não é uma função identicamente nula. O objetivo principal deste trabalho é o estudo das soluções singulares de L; através da natureza e da localização das suas singularidades. Com este intuito, primeiramente abordaremos a teoria das séries parciais de Fourier, que nos permitem relacionar o comportamento assintótico dos coeficientes parciais de Fourier de um dado objeto com a regularidade do mesmo / Let L \'= PONTO\' \'\\partial ind. t\' + [ a (t) + ib (t) ] \'\\partial IND. x\' be a partial differential operator acting on distributions on the two-torus \'T POT. 2\' , where a; b : \'T POT. 1\' \'ARROW\' R are real analytic functions. Assume that L is not a globally analytic hypoelliptic operator and b is not identically zero. The main goal of this work is the study of the singular solutions of L; by means of the nature and localization of their singularities. To this end, we first study the theory of partial Fourier series, which are a useful tool to analyze the regularity of a given distribution

Electronic textiles are a sound platform for wearable computing. Many applications have been devised that use sensors placed on these textiles for fields such as medical monitoring and military use or for display purposes. Most of these applications require that the sensors have known locations for accurate results. Activity recognition is one application that is highly dependent on knowledge of the sensor position. Therefore, this thesis presents the design and implementation of a method whereby the location of the sensors on the electronic textile garments can be automatically identified when the user is performing an appropriate activity. The software design incorporates principle component analysis using singular value decomposition to identify the location of the sensors. This thesis presents a method to overcome the problem of bilateral symmetry through sensor connector design and sensor orientation detection. The scalability of the solution is maintained through the use of culling techniques. This thesis presents a flexible solution that allows for the fine-tuning of the accuracy of the results versus the number of valid queries, depending on the constraints of the application. The resulting algorithm is successfully tested on both motion capture and sensor data from an electronic textile garment. / Master of Science