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riemannian-manifold
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Classification of Different Mental Activities Based on Riemannian Geometry
,
M.Sc. Thesis
Sharif University of Technology
;
Babaiezadeh, Massoud
(Supervisor)
Abstract
Brain-Computer Interface (BCI) presents a way for brain’s direct connection with external world. BCI system is composed of three parts: 1) Signal acquisition, 2) Signal processing and 3) External device control. The main part of this system is signal processing which includes three subparts: 1) Feature extraction, 2) Dimension reduction and 3) Signal separation and classification. In this thesis, we focus on the signal processing section in BCI systems. One of the most successful works done in signal processing is the use of covariance matrices in feature extraction from brain signals. Since covariance matrices are positive semi-definite and symmetric, they belong to certain manifolds called...
Comparison of volumes of Riemannian manifolds
, Article Comptes Rendus Mathematique ; Volume 339, Issue 3 , 2004 , Pages 199-201 ; 1631073X (ISSN) ; Sharif University of Technology
2004
Abstract
Using the rigidity result of Besson, Courtois and Gallot, and also the notion of intersection of metrics, we compare volumes of Riemannian manifolds by means of lengths of their periodic geodesics. © 2004 Académie des sciences. Publié par Elsevier SAS. Tous droits réservés
Nonconvex weak sharp minima on riemannian manifolds
, Article Journal of Optimization Theory and Applications ; Volume 183, Issue 1 , 2019 , Pages 85-104 ; 00223239 (ISSN) ; Mahdavi Amiri, N ; Sharif University of Technology
Springer New York LLC
2019
Abstract
We establish some necessary conditions (of the primal and dual types) for the set of weak sharp minima of a nonconvex optimization problem on a Riemannian manifold. Here, we provide a generalization of some characterizations of weak sharp minima for convex problems on Riemannian manifold introduced by Li et al. (SIAM J Optim 21(4):1523–1560, 2011) for nonconvex problems. We use the theory of the Fréchet and limiting subdifferentials on Riemannian manifold to give some necessary conditions of the dual type. We also consider a theory of contingent directional derivative and a notion of contingent cone on Riemannian manifold to give some necessary conditions of the primal type. Several...
About Space Time
, M.Sc. Thesis Sharif University of Technology ; Rastegar, Arash (Supervisor)
Abstract
Einstein's general theory of relativity is an admirable successful and unifier geometrical modeling among concepts of space, time and gravity. This theory along with special theory of relativity made a massive change in our physical view and this, especially in its historical context, has deep and interesting consequences in man's philosophical viewpoint which can be studied. Some parts of this thesis relates to these consequences. Some of these interesting consequences may be hidden by computional or mathematical viewpoint and often these equations do not contain enough intuition. in one part, we provide a formulizatin of Einstein's equaion that is intuitional which can be translated in...
On the Topological Entropy of Geodesic Flows
, M.Sc. Thesis Sharif University of Technology ; Razvan, Mohammad Reza (Supervisor) ; Nassiri, Meysam (Supervisor)
Abstract
Let M be a connected, compact, Riemannian manifold. Geodesic flow is a flow on the unit tangent bundle of M . This flow can be studied in dynamics prespective. for example entropy or complexity of the geodesic flow. in this thesis we will follow methods of entropy estimation or computing for geodesic flow. we will follow the method of anthony manning and Ricardo Mañe for proving such result. Maning present two results linking the topological entropy of the geodesic flow on M. we expalin how he find exponential growth rate volume of balls in universal cover as a lower bound for topologycal entropy. another theorem , Mañe represent the equlity between exponential growth rate of avrage of...
A Special Stokes’s Theorem For Some Incomplete Riemannian Manifolds
, M.Sc. Thesis Sharif University of Technology ; Bahraini, Alireza (Supervisor)
Abstract
Let (M; g) be a Riemannian manifold. Using classical Stokes’ theorem one can show that the equality (dω; η)L2 = (ω; δη)L2 holds for smooth forms ! and η with compact supports, where δ is the formal adjoint of d . There are some examples of Riemannian manifolds for which the above equality does not hold for general forms ! and η i:e: smooth square-integrable forms such taht d! and δη are also squareintegrable. In the case that the above equality holds for such general forms on a Riemannian manifold (M; g) , we say that the L2 - Stokes theorem holds for (M; g) . In 1952, Gaffney showed that the L2 - Stokes theorem holds for complete Riemannian manifolds. But at that time, there was no powerful...
Ricci-based chaos analysis for roto-translatory motion of a Kelvin-type gyrostat satellite
, Article Proceedings of the Institution of Mechanical Engineers, Part K: Journal of Multi-body Dynamics ; Vol. 228, issue. 1 , 2014 , pp. 34-46 ; ISSN: 14644193 ; Sadati, S. H ; Salarieh, H ; Sharif University of Technology
Abstract
The chaotic dynamics of roto-translatory motion of a triaxial Kelvin-type gyrostat satellite under gravity gradient perturbations is considered. The Hamiltonian approach is used for modelling of the coupled spin-orbit equations of motion. The complex Hamiltonian of the system is reduced via the extended Deprit canonical transformation using the Serret- Andoyer variables. Therefore, this reduction leads to the derivation of the perturbation form of the Hamiltonian that can be used in the Ricci curvature criterion based on the Riemannian manifold geometry for the analysis of chaos phenomenon. The results obtained from Ricci method as well as the values from the Lyapunov exponent demonstrate...