Most Recent Articles: Research in the Mathematical Scienceshttp://resmathsci.springeropen.comMost Recent Articles: Research in the Mathematical SciencesOptimal convergence rate of the universal estimation errorhttp://resmathsci.springeropen.com/articles/10.1186/s40687-016-0093-6Fri, 10 Feb 2017 00:00:00 GMThttp://resmathsci.springeropen.com/articles/10.1186/s40687-016-0093-6E. Weinan and Yao Wang2017-02-10T00:00:00ZFast Ewald summation for free-space Stokes potentialshttp://resmathsci.springeropen.com/articles/10.1186/s40687-016-0092-7We present a spectrally accurate method for the rapid evaluation of free-space Stokes potentials, i.e., sums involving a large number of free space Green’s functions. We consider sums involving stokeslets, str...Wed, 01 Feb 2017 00:00:00 GMThttp://resmathsci.springeropen.com/articles/10.1186/s40687-016-0092-7Ludvig af Klinteberg, Davoud Saffar Shamshirgar and Anna-Karin Tornberg2017-02-01T00:00:00ZStochastic homogenization of viscous superquadratic Hamilton–Jacobi equations in dynamic random environmenthttp://resmathsci.springeropen.com/articles/10.1186/s40687-016-0090-9We study the qualitative homogenization of second-order Hamilton–Jacobi equations in space-time stationary ergodic random environments. Assuming that the Hamiltonian is convex and superquadratic in the momentu...Fri, 27 Jan 2017 00:00:00 GMThttp://resmathsci.springeropen.com/articles/10.1186/s40687-016-0090-9Wenjia Jing, Panagiotis E. Souganidis and Hung V. Tran2017-01-27T00:00:00ZStochastic regularity of a quadratic observable of high-frequency waveshttp://resmathsci.springeropen.com/articles/10.1186/s40687-016-0091-8We consider high-frequency waves satisfying the scalar wave equation with highly oscillatory initial data. The wave speed, and the phase and amplitude of the initial data are assumed to be uncertain, described...Tue, 24 Jan 2017 00:00:00 GMThttp://resmathsci.springeropen.com/articles/10.1186/s40687-016-0091-8G. Malenová, M. Motamed and O. Runborg2017-01-24T00:00:00ZConvergence analysis of the fast sweeping method for static convex Hamilton–Jacobi equationshttp://resmathsci.springeropen.com/articles/10.1186/s40687-016-0083-8In this work, we study the convergence of an efficient iterative method, the fast sweeping method (FSM), for numerically solving static convex Hamilton–Jacobi equations. First, we show the convergence of the F...Wed, 14 Dec 2016 00:00:00 GMThttp://resmathsci.springeropen.com/articles/10.1186/s40687-016-0083-8Songting Luo and Hongkai Zhao2016-12-14T00:00:00Z