A popular approach to solving a decision process with non-Markovian rewards (NMRDP) is to exploit a compact representation of the reward function to automatically translate the NMRDP into an equivalent Markov decision process (MDP) amenable to our favorite MDP solution method. The contribution of this paper is a representation of non-Markovian reward functions and a translation into MDP aimed a...

In this paper, we show that the entropy solution u(t) of a scalar conservation law enjoys the properties: • u is continuous outside a 1-rectifiable set Ξ⊂ R+ × R, • up to a countable set, for each point (t̄, x̄) ∈ Ξ there exists two cone shaped regions arbitrarily close to half planes where u is left/right continuous at (t̄, x̄). We provide examples showing that these estimates are nearly optimal. ...

In this paper we study a two-phase free boundary problem for a semilinear elliptic equation on a bounded domain $Dsubset mathbb{R}^{n}$ with smooth boundary‎. ‎We give some results on the growth of solutions and characterize the free boundary points in terms of homogeneous harmonic polynomials using a fundamental result of Caffarelli and Friedman regarding the representation of functions whose ...

A mathematical model is considered to investigate the behavior of horizontally polarized shear waves (SH-waves) in fluid saturated porous medium sandwiched between heterogeneous half-spaces. Heterogeneity in the upper half-space is due to linear variation of elastic parameters, whereas quadratic variation has been considered for lower half-space. The method of separation of variables and Whitta...