arXiv subjects
Publications and source records attributed to Dongho Joseph.
In this paper, we study the geometric nonlinearity properties, such as curvature and torsion, in a dual coordinate system of the Riemannian manifold defined by the Gaussian distribution. We also give the Amari formulas explicitly in this new coordinate system, which allows us to characterize existing geometric invariants, such as the dual potential function and the Fisher metric.
In this paper, we study the stochastic-periodic homogenization of Non-stationary Navier-Stokes Type Equations on anisotropic heterogeneous media. More precisely, we are interested in the stochastic-periodic homogenization of its variational formulation. This problematic relies on the notion of dynamical system. It is shown by the stochastic two-scale convergence method that the resulting homogenized limit equation is of the same form of this variational formulation with suitable coefficients.
We develop the stochastic two-scale convergence method in the framework of Orlicz-Sobolev spaces, in order to deal with the homogenization of coupled stochastic-periodic problems in such spaces. One fundamental in this topic is the extension of compactness results for this method to the Orlicz setting. For the application, we show that the sequence of minimizers of a class of highly oscillatory minimizations problems involving integral functionals with convex and nonstandard growth integrands, converges to the minimizer of a homogenized problem.
In this paper, we study quatization condition of logsymplectic struc- ture using integrality of such structue on the complement of associated divisor D.