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A compact Kahler manifold X is shown to be simply connected if its 'symmetric cotangent algebra' is trivial. Conjecturally, such a manifold should even be rationally connected. The relative version is also shown: a proper surjective connected holomorphic m ...
We construct a one parameter family of nite time blow ups to the co-rotational wave maps problem from S2×R to S2 parameterized by νϵ(21,1]. The longitudinal function u(t,α) which is the main object of study will be ...
A novel method for approximating structured singular values (also known as μ- values) is proposed and investigated. These quantities constitute an important tool in the stability analysis of uncertain linear control systems as well as in structured eig ...
We construct a one parameter family of finite time blow-ups to the co-rotational wave maps problem from S-2 x R to S-2, parameterized by nu is an element of (1/2, 1]. The longitudinal function u(t, alpha) which is the main object of study will be obtained ...
In this thesis, we present a Riemannian framework for the solution of high-dimensional optimization problems with an underlying low-rank tensor structure. Here, the high-dimensionality refers to the size of the search space, while the cost function is scal ...
A multimodal haptic device operating as a closed-loop system, the device including a pipeline configured to allow a closed-loop flow of a fluid medium, a manifold operatively connected to the pipeline, the manifold having a pump and a valve to control and ...
In this paper we show that the incompressible Euler equation on the Sobolev space H-s(R-n), s> n/2+1, can be expressed in Lagrangian coordinates as a geodesic equation on an infinite dimensional manifold. Moreover the Christoffel map describing the geodesi ...
A reduced basis Darcy-Stokes finite element heterogeneous multiscale method (RB-DS-FE-HMM) is proposed for the Stokes problem in porous media. The multiscale method is based on the Darcy-Stokes finite element heterogeneous multiscale method (DS-FE-HMM) int ...
2-level polytopes naturally appear in several areas of mathematics, including combinatorial optimization, polyhedral combinatorics, communication complexity, and statistics. We investigate upper bounds on the product of the number of facets and the number ...
Dynamic functional connectivity (dFC) measured by functional magnetic resonance imaging (fMRI) shows evidence of large-scale networks with highly dynamic (re) configurations. We propose a novel approach to extract traces of human brain function by the cons ...