Adaptive dynamic programming (ADP) is a novel approximate optimal control scheme, which has recently become a hot topic in the field of optimal control. As a standard approach in the field of ADP, a function approximation structure is used to approximate the solution of Hamilton-Jacobi-Bellman (HJB) equation. The approximate optimal control policy is obtained by using the offline iteration algo...

We study the stochastic model for bioremediation in a bioreactor with ideal mixing. The dynamics of the examined system is described by stochastic differential equations. We consider an optimal control problem with quadratic costs functional for the linearized model of a well-stirred bioreactor. The optimal control is based on the optimal robust state estimates. The approximate optimal solution...

Simultaneous reactions between solids and gases are very important in the chemical and metallurgical processes. In the modeling, the chemical reaction and diffusion of gases must be considered. Therefore, a set of coupled partial differential equations is found. When the kinetic is a function of solid concentration, there is not any analytical solution for these equations. Therefore, numerical ...

For appropriately adapted mesh-refinements, optimal order error estimates are proved for the finite element approximate solution of the Neumann problem for the second-order elliptic equation Lu = 8, where S is the Dirac distribution.

We show that a modification of the Kenyon-Remila algorithm for the strip-packing problem yields an improved bound on the value of the approximate solution. As a corollary we derive that there exists a polynomial-time algorithm that always finds a solution of value OPT +O( √ OPT logOPT ) where OPT is the optimal value.

Music sequences can be treated as texts in order to perform music retrieval tasks on them. However, the text search problems that result from this modeling are unique to music retrieval. Up to date, several approaches derived from classical string matching have been proposed to cope with the new search problems, yet each problem had its own algorithms. In this paper we show that a technique rec...

We consider an axisymmetric inverse heat conduction problem of determining the surface temperature from a fixed location inside a cylinder. This problem is ill-posed; the solution if it exists does not depend continuously on the data. A special project method—dual least squares method generated by the family of Shannon wavelet is applied to formulate regularized solution. Meanwhile, an order op...

In math.CO/0111309, we used admissible permutations and a variant of the Floyd-Warshall Algorithm to obtain an optimal solution to the Assignment Problem and an approximate solution to the Traveling Salesman Problem. Here we give a large, detailed illustration of how the algorithms are applied.

In the polytope membership problem, a convex polytope K in R is given, and the objective is to preprocess K into a data structure so that, given a query point q ∈ R, it is possible to determine efficiently whether q ∈ K. We consider this problem in an approximate setting and assume that d is a constant. Given an approximation parameter ε > 0, the query can be answered either way if the distance...