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Conformal upper bounds for the eigenvalues of the Laplacian and Steklov problem
, Article Journal of Functional Analysis ; Volume 261, Issue 12 , 2011 , Pages 3419-3436 ; 00221236 (ISSN) ; Sharif University of Technology
2011
Abstract
In this paper, we find upper bounds for the eigenvalues of the Laplacian in the conformal class of a compact Riemannian manifold (M,g). These upper bounds depend only on the dimension and a conformal invariant that we call "min-conformal volume". Asymptotically, these bounds are consistent with the Weyl law and improve previous results by Korevaar and Yang and Yau. The proof relies on the construction of a suitable family of disjoint domains providing supports for a family of test functions. This method is interesting for itself and powerful. As a further application of the method we obtain an upper bound for the eigenvalues of the Steklov problem in a domain with C1 boundary in a complete...
Co-microencapsulation of Probiotic Bacteria and DHA Fatty Acid; Optimization and Evaluation of the Viability of Probiotic and Oxidative Stability of DHA during Gastrointestinal Tract
, M.Sc. Thesis Sharif University of Technology ; Alemzadeh, Iran (Supervisor) ; Vossoughi, Manouchehr (Supervisor)
Abstract
Due to the increased public awareness about the role of food on health, an increased interest of consuming fortified food has grown rapidly. Probiotic bacteria and DHA poly-unsaturated fatty acid are two major bioactive ingredients becoming increasingly popular in food fortification industry due to their beneficial effects. However, high susceptibility of probiotic bacteria during production, maintenance and digestion in acidic and enzymatic conditions of gastrointestinal tract results in decreasing the survivability and therefore reducing health effects in body. Besides, having multiple double bonds in the structure of DHA fatty acid leads to oxidative degradation that produces volatile...
Comparison of Pulse-Compression’s Techniques in Presence of Doppler
, M.Sc. Thesis Sharif University of Technology ; Bastani, Mohammad Hassan (Supervisor)
Abstract
- Pulse-compression is one of the spread spectrum techniques that allows a radar to simultaneously achieve the energy of a long pulse and the resolution of a short pulse. The long pulse band-width is increased by phase or frequency modulation, then this modulated long pulse is compressed by matched filter of the receiver. A simple class of pulse-compression waveforms is Binary phase-coded pulse that uses rectangular sub pulses. When the transmitted signal encounters a moving target, the performance of radar degrades due to Doppler frequency shift of received signal. Binary codes have high side lobe levels for long Codes, so to solve this problem the Quadriphase-coded pulse that constructed...
Upper Bounds for Eigenvalues of Natural Operators on Compact Riemannian Manifolds
, M.Sc. Thesis Sharif University of Technology ; Colbois, Bruno (Supervisor) ; El Soufi, Ahmad (Supervisor) ; Ranjbar-Motlagh, Alireza (Supervisor)
Abstract
The purpose of this thesis is to find upper bounds for the eigenvalues of natural operators acting on functions on a compact Riemannian man-ifold (M, g) such as the Laplace–Beltrami operator and Laplace-type operators. In the case of the Laplace–Beltrami operator, two aspects are investigated:
The first aspect is to study relationships between the intrinsic geometry and eigenvalues of the Laplace–Beltrami operator. In this regard, we obtain upper bounds depending only on the dimension and a conformal invariant called min-conformal volume. Asymptotically, these bounds are consistent with the Weyl law. They improve previous results by Korevaar and Yang and Yau. The proof relies on the...
The first aspect is to study relationships between the intrinsic geometry and eigenvalues of the Laplace–Beltrami operator. In this regard, we obtain upper bounds depending only on the dimension and a conformal invariant called min-conformal volume. Asymptotically, these bounds are consistent with the Weyl law. They improve previous results by Korevaar and Yang and Yau. The proof relies on the...