Gegenstand dieser Dissertation ist Galois-Korrespondenz für von Neumann Algebren und deren Zusamm... more Gegenstand dieser Dissertation ist Galois-Korrespondenz für von Neumann Algebren und deren Zusammenspiel mit nichtkommutativer Wahrscheinlichkeitstheorie. Nach einer kurzen Einführung in die Darstellungstheorie für kompakte Gruppen, insbesondere in das Theorem von Peter-Weyl, und in Operatoralgebren, einschließlich von Neumann Algebren, Gruppen von Automorphismen, semidirekte Produkte und Dekompositionstheorie, formulieren wir die ersten Schritte einer nichtkommutativen Version der Wahrscheinlichkeitstheorie und präsentieren nachtabelsche Analoge für stochastische Prozesse und Martingale. Die zentralen Objekte dieser Arbeit sind eine von Neumann Algebra M und eine kompakte Gruppe G, die auf M wirkt, für die wir in drei aufeinander aufbauenden Fällen, d.h. für innere, äußere und allgemeine Gruppen von Automorphismen, bijektive Korrespondenzen zwischen Untergruppen von G und von Neumann Unteralgebren von M angeben. Darüberhinaus identifizieren wir in unserem Formalismus nichtabelsche ...
The subject of this thesis is the modular group of automorphisms ( σt) m t∈R, m> 0, acting on ... more The subject of this thesis is the modular group of automorphisms ( σt) m t∈R, m> 0, acting on the massive algebra of local observables Mm(O) having their support in O ⊂ R4. After a compact introduction to micro-local analysis and the theory of one-parameter groups of automorphisms, which are used exensively throughout the investigation, we are concerned with modular theory and its consequences in mathematics, e.g., Connes ’ cocycle theorem and classification of type III factors and Jones ’ index theory, as well as in physics, e.g., the determination of local von Neumann algebras to be hyperfinite factors of type III1, the formulation of thermodynamic equilibrium states for infinitedimensional quantum systems (KMS states) and the discovery of modular action as geometric transformations. However, our main focus are its applications in physics, in particular the modular action as Lorentz boosts on the Rindler wedge, as dilations on the forward light cone and as conformal mappings on...
International Journal of Infectious Diseases, 2020
Background: Environmental factors plays a very crucial role in the spread of infectious diseases ... more Background: Environmental factors plays a very crucial role in the spread of infectious diseases especially those that are transmitted via pathogenic droplets such as MERS-CoV and Ebola. Recent data suggest a higher prevalence of MERS-CoV infection in dromedary camels in winter months compared to summer months within middle eastern countries. It is speculated that increase animal-to-human transmission in winter could exacerbate the putative human-to-human transmission via respiratory secretions. Therefore, this study focuses on investigating the effects of temperature variability and exposure to dromedary on the risk of MERS. Methods and materials: Often, exposure to certain environmental factors produces effects lasting well beyond the exposure period and with an increase in risk occurring from few hours to later in the future. In this study, we used time-varying distributed lag nonlinear models with doubly penalized spline to provide greater flexibility to the temperature-lag-MERS association. We also estimate the burden of the disease that can be attributed to temperature among patients exposed to dromedary camels. Results: Preliminary results revealed that the optimal temperature for MERS in the study area was 27.2 °C. The increased risk of MERS associated with high temperature indicates that environmental and dromedary interactions at plays a significant role in the transportation of the pathogens. Conclusion: Temperature variability in the winter months is associated with high risk of MERS as well as dromedary contact. MERS should not be regarded as seasonal infection because it occurs throughout the year, however the increased risk and timing of MERS peaks in lower temperatures clearly present a challenge
Gegenstand dieser Dissertation ist Galois-Korrespondenz für von Neumann Algebren und deren Zusamm... more Gegenstand dieser Dissertation ist Galois-Korrespondenz für von Neumann Algebren und deren Zusammenspiel mit nichtkommutativer Wahrscheinlichkeitstheorie. Nach einer kurzen Einführung in die Darstellungstheorie für kompakte Gruppen, insbesondere in das Theorem von Peter-Weyl, und in Operatoralgebren, einschließlich von Neumann Algebren, Gruppen von Automorphismen, semidirekte Produkte und Dekompositionstheorie, formulieren wir die ersten Schritte einer nichtkommutativen Version der Wahrscheinlichkeitstheorie und präsentieren nachtabelsche Analoge für stochastische Prozesse und Martingale. Die zentralen Objekte dieser Arbeit sind eine von Neumann Algebra M und eine kompakte Gruppe G, die auf M wirkt, für die wir in drei aufeinander aufbauenden Fällen, d.h. für innere, äußere und allgemeine Gruppen von Automorphismen, bijektive Korrespondenzen zwischen Untergruppen von G und von Neumann Unteralgebren von M angeben. Darüberhinaus identifizieren wir in unserem Formalismus nichtabelsche ...
The subject of this thesis is the modular group of automorphisms ( σt) m t∈R, m> 0, acting on ... more The subject of this thesis is the modular group of automorphisms ( σt) m t∈R, m> 0, acting on the massive algebra of local observables Mm(O) having their support in O ⊂ R4. After a compact introduction to micro-local analysis and the theory of one-parameter groups of automorphisms, which are used exensively throughout the investigation, we are concerned with modular theory and its consequences in mathematics, e.g., Connes ’ cocycle theorem and classification of type III factors and Jones ’ index theory, as well as in physics, e.g., the determination of local von Neumann algebras to be hyperfinite factors of type III1, the formulation of thermodynamic equilibrium states for infinitedimensional quantum systems (KMS states) and the discovery of modular action as geometric transformations. However, our main focus are its applications in physics, in particular the modular action as Lorentz boosts on the Rindler wedge, as dilations on the forward light cone and as conformal mappings on...
International Journal of Infectious Diseases, 2020
Background: Environmental factors plays a very crucial role in the spread of infectious diseases ... more Background: Environmental factors plays a very crucial role in the spread of infectious diseases especially those that are transmitted via pathogenic droplets such as MERS-CoV and Ebola. Recent data suggest a higher prevalence of MERS-CoV infection in dromedary camels in winter months compared to summer months within middle eastern countries. It is speculated that increase animal-to-human transmission in winter could exacerbate the putative human-to-human transmission via respiratory secretions. Therefore, this study focuses on investigating the effects of temperature variability and exposure to dromedary on the risk of MERS. Methods and materials: Often, exposure to certain environmental factors produces effects lasting well beyond the exposure period and with an increase in risk occurring from few hours to later in the future. In this study, we used time-varying distributed lag nonlinear models with doubly penalized spline to provide greater flexibility to the temperature-lag-MERS association. We also estimate the burden of the disease that can be attributed to temperature among patients exposed to dromedary camels. Results: Preliminary results revealed that the optimal temperature for MERS in the study area was 27.2 °C. The increased risk of MERS associated with high temperature indicates that environmental and dromedary interactions at plays a significant role in the transportation of the pathogens. Conclusion: Temperature variability in the winter months is associated with high risk of MERS as well as dromedary contact. MERS should not be regarded as seasonal infection because it occurs throughout the year, however the increased risk and timing of MERS peaks in lower temperatures clearly present a challenge
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