Let $\Omega$ be an exterior domain in $\R^n\,(n=2,3,4)$ , with boundary being not necessarily smooth. For any initial velocity ${\bf u}_0\in L^2(\Omega)^n$ such that $\nabla\cdot {\bf u}_0=0$ (in sense of distribution) and ...

An optimal feedback control has been obtained for linear-quadratic optimal control problems with constraints described by differential-algebraic equations. For that purpose, a new implicit Riccati equation (Riccati ...

In this paper, the previously formulated conjecture concerning the existence of fine and complete decouplings of regular DAEs with tractability index $\mu$ is verified.

This paper establishes a unified framework for the a posteriori error analysis of a large class of nonconforming finite element methods. The theory assures reliability and efficiency of explicit residual error estimates ...

For linear differential-algebraic equations (DAEs) with properly stated leading terms the property of being numerically qualified guarantees that qualitative properties of DAE solutions are reflected by the numerical ...

A geometric Brownian motion with delay is the solution of a stochastic differential equation where the drift and diffusion coefficient depend linearly on the past of the solution, i.e. a linear stochastic functional ...

We show existence and uniqueness for global weak solutions of a moving boundary problem for a coupled system of three quasi-linear diffusion-reaction equations. The model is briefly described. The proofs are based on ...

In this paper we give sharp explicit estimates for the difference of the Weil height and the Néron - Tate height on the elliptic curve $v^2 = u^3 - cu$. We then apply this in the proof of the fact that if c > 2 is a fourth ...

We present a modification of the fictitious play algorithm for matrix games by aggregating trivial original steps. The resulting new algorithm consists of comparable simple steps but has a much better rate of convergence. ...