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In his pioneering work in 1860, Riemann proposed the Riemann problem and solved it for isentropic gas in terms of shocks and rarefaction waves. It eventually became the foundation of the theory of one...
This talk will survey some results for the two- or three-space dimensional compressible Euler equations. We shall present non-uniqueness results of weak entropy solutions using convex integration and ...
I started looking at log-concave distributions when I was searching for an appropriate model for subpopulations of multivariate flow cytometry data about ten years ago. The use of log-concave ...
This paper considers multi-dimensional infinite impulse response (IIR) filters that are iteratively implemented. The focus is on zero-phase filters with symmetric polynomials in the numerator and deno...
A Fortran90 input/output library, "gtool5", is developed for use with numerical simulation models in the fields of Earth and planetary sciences. The use of this library will simplify implementation of...
We consider the summability of one- and multi-dimensional trigonometric Fourier series. The Fej{\'e}r and Riesz summability methods are investigated in detail. Different types of summation and converg...
Abstract: We establish conditions for uniform $r$-th moment bound of certain $\R^d$-valued functions of a discrete-time stochastic process taking values in a general metric space. The conditions inclu...
Abstract: The Cauchy problem of a multi-dimensional ($d\geqslant 2$) compressible viscous gas-liquid two-phase flow model is concerned in this paper. We investigate the global existence and uniqueness...
Least squares trees, multi-dimensional scaling and Neighbor Nets are all different and popular ways of visualizing multi-dimensional data. The method of flexi-Weighted Least Squares (fWLS) is a powerf...
Define a chi-square random field on a multi-dimensional lattice points index set with a direct-product covariance structure, and consider the distribution of the maximum of this random field. We provi...
We study the invariant measure of a discretized stochastic Allen-Cahn equation in d+1 dimensions in the low noise limit. We consider a cuboidal domain and impose the two stable phases as boundary con...
We consider quasilinear, multi-variable, constant coefficient, lattice equations defined on the edges of the elementary square of the lattice, modeled after the lattice modified Boussinesq (lmBSQ) eq...
We consider a zero-sum stochastic differential controller-and-stopper game in which the state process is a controlled jump-diffusion evolving in a multi-dimensional Euclidean space.
We present a new general relativistic (GR) code for hydrodynamic supernova simulations with neutrino transport in spherical and azimuthal symmetry (1D/2D). The code is a combination of the CoCoNuT hyd...
The distribution of ice layers in the polar summer mesosphere (called polar mesospheric clouds or PMCs) is sensitive to background atmospheric conditions and therefore affected by global-scale dynamic...

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