Abstract. This paper proposes a thorough investigation of the convergence of the volume averaging method described in [36] as applied to convection-diffusion problems inside a cylinder. A spectral description of volume averaging brings to the fore new perspectives about the mathematical analysis of those approximations. This spectral point of view is complementary with the Liapounov-Schmidt red...

This dissertation focuses on the approximation problem of models in the form of linear operators and in the form of polynomial dynamical systems. For approximation of linear operators, Schmidt and Mirsky have shown the existence of an optimal approximant which minimizes the induced Euclidean norm distance between the original operator and all possible lower rank approximant. This result is rega...

This paper proposes a thorough investigation of the convergence of the volume averaging method described by Whitaker [The Method of Volume Averaging, Kluwer Academic, Norwell, MA, 1999] as applied to convection-diffusion problems inside a cylinder. A spectral description of volume averaging brings to the fore new perspectives about the mathematical analysis of those approximations. This spectra...

The behavior of the Hasse–Schmidt algebra under étale extension is used to show that the Hasse–Schmidt algebra of a smooth algebra of finite type over a field equals the ring of differential operators. These techniques show that the formation of Hasse–Schmidt derivations does not commute with localization, providing a counterexample to a question of Brown and Kuan; their conjecture is reformula...

Schmidt numbers of bipartite mixed states ([1]) characterize the minimum Schmidt ranks of pure states that are needed to construct such mixed states. It is the minimum number of degrees of freedom of a bipartite mixed state entangled between two parties. We give a lower bound of Schmidt numbers of low rank bipartite mixed states and conclude that generic (i.e., all outside a measure zero set) l...

Quantum information processing is the study of methods and efficiency in storage, manipulation and conversion of information represented by quantum states. Many quantum information theoretic concepts are closely related to geometry. For instance, trace distance and fidelity, which come out of the study of distinguishability between quantum states, are closely linked with Bures and Fubini-Study ...

We describe a 47 year old woman with a 30-year history of generalized myasthenia gravis whose condition had been stable and well controlled on a combination of pyridostigmine and ephedrine until she presented. At this time she gave a 2 month history of weakness, nausea, vomiting and more recently intermittent confusion. Investigations confirmed both primary hypothyroidism and primary adrenal fa...

this paper is concerned with a technique for solving volterra integral equations in the reproducing kernel hilbert space. in contrast with the conventional reproducing kernel method, the gram-schmidt process is omitted here and satisfactory results are obtained.the analytical solution is represented in the form of series.an iterative method is given to obtain the approximate solution.the conver...