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- Alzheimer disease (1)
- Asymptotic Expansion (1)
- Atrophy (1)
- Boundary value problems (1)
- Conformal Perturbation (1)
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- Edge-degenerate differential operators (1)
- Gait (1)
- Holomorphic approximation (1)
- Logarithmic Sobolev Inequality (1)
- Magnetic resonance imaging (1)
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- Mild cognitive impairment (1)
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- Noncommutative Tori (1)
- Pseudodifferential Operators (1)
- Resting state function magnetic resonance imaging (1)
- Riemann Surfaces (1)
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- Zero-free approximation (1)
Articles 1 - 4 of 4
Full-Text Articles in Physical Sciences and Mathematics
Development Of Anatomical And Functional Magnetic Resonance Imaging Measures Of Alzheimer Disease, Samaneh Kazemifar
Development Of Anatomical And Functional Magnetic Resonance Imaging Measures Of Alzheimer Disease, Samaneh Kazemifar
Electronic Thesis and Dissertation Repository
Alzheimer disease is considered to be a progressive neurodegenerative condition, clinically characterized by cognitive dysfunction and memory impairments. Incorporating imaging biomarkers in the early diagnosis and monitoring of disease progression is increasingly important in the evaluation of novel treatments. The purpose of the work in this thesis was to develop and evaluate novel structural and functional biomarkers of disease to improve Alzheimer disease diagnosis and treatment monitoring. Our overarching hypothesis is that magnetic resonance imaging methods that sensitively measure brain structure and functional impairment have the potential to identify people with Alzheimer’s disease prior to the onset of cognitive decline. …
On Logarithmic Sobolev Inequality And A Scalar Curvature Formula For Noncommutative Tori, Sajad Sadeghi
On Logarithmic Sobolev Inequality And A Scalar Curvature Formula For Noncommutative Tori, Sajad Sadeghi
Electronic Thesis and Dissertation Repository
In the first part of this thesis, a noncommutative analogue of Gross' logarithmic Sobolev inequality for the noncommutative 2-torus is investigated. More precisely, Weissler's result on the logarithmic Sobolev inequality for the unit circle is used to propose that the logarithmic Sobolev inequality for a positive element $a= \sum a_{m,n} U^{m} V^{n} $ of the noncommutative 2-torus should be of the form $$\tau(a^{2} \log a)\leqslant \underset{(m,n)\in \mathbb{Z}^{2}}{\sum} (\vert m\vert + \vert n\vert) \vert a_{m,n} \vert ^{2} + \tau (a^{2})\log ( \tau (a^2))^{1/2},$$ where $\tau$ is the normalized positive faithful trace of the noncommutative 2-torus. A possible approach to prove this …
Moduli Space And Deformations Of Special Lagrangian Submanifolds With Edge Singularities, Josue Rosario-Ortega
Moduli Space And Deformations Of Special Lagrangian Submanifolds With Edge Singularities, Josue Rosario-Ortega
Electronic Thesis and Dissertation Repository
Special Lagrangian submanifolds are submanifolds of a Calabi-Yau manifold calibrated by the real part of the holomorphic volume form. In this thesis we use elliptic theory for edge- degenerate differential operators on singular manifolds to study general deformations of special Lagrangian submanifolds with edge singularities. We obtain a general theorem describing the local structure of the moduli space. When the obstruction space vanishes the moduli space is a smooth, finite dimensional manifold.
Uniform Approximation On Riemann Surfaces, Fatemeh Sharifi
Uniform Approximation On Riemann Surfaces, Fatemeh Sharifi
Electronic Thesis and Dissertation Repository
This thesis consists of three contributions to the theory of complex approximation on
Riemann surfaces. It is known that if E is a closed subset of an open Riemann surface R and f is a holomorphic function on a neighbourhood of E, then it is usually not possible to approximate f uniformly by functions holomorphic on all of R. Firstly, we show, however, that for every open Riemann surface R and every closed subset E of R; there is closed subset F of E, which approximates E extremely well, such that every function holomorphic on F can be approximated much …