Recent findings show that the classical Riemann's non-differentiable function has a physical and geometric nature as irregular trajectory of polygonal vortex filament driven by binormal flow. In this article, we give an upper estimate its Hausdorff dimension. We also adapt result to multifractal setting. To prove these results, recalculate asymptotic behavior around rationals from novel perspec...

Abstract In the case of quantum systems interacting with multiple environments, time-evolution reduced density matrix is described by Liouvillian. For a variety physical observables, long-time limit or steady state (SS) solution needed for computation desired observables. inverse design optimal control such systems, common approaches are based on brute-force search strategies. Here, we present ...

We present a primal–dual memory efficient algorithm for solving a relaxed version of the general transportation problem. Our approach approximates the original cost function with a differentiable one that is solved as a sequence of weighted quadratic transportation problems. The new formulation allows us to solve differentiable, non– convex transportation problems.

We discuss a general technique that forms a differentiable bound on non-differentiable objective functions by bounding the function optimum by its expectation with respect to a parametric variational distribution. We describe sufficient conditions for the bound to be convex with respect to the variational parameters. As example applications we consider variants of sparse linear regression and S...

In this work, we extend the existing local fractional Sumudu decomposition method to solve the nonlinear local fractional partial differential equations. Then, we apply this new algorithm to resolve the nonlinear local fractional gas dynamics equation and nonlinear local fractional Klein-Gordon equation, so we get the desired non-differentiable exact solutions. The steps to solve the examples a...