This paper formally presents a class of planning problems which allows non-binary state variables and parallel execution of actions. The class is proven to be tractable, and we provide a sound and complete polynomial time algorithm for planning within this class. This result means that we are getting closer to tackling realistic planning problems in sequential control, where a restricted proble...

In [Ans08a, Ans08b], we investigated monic multivariate non-commutative orthogonal polynomials, their recursions, states of orthogonality, and corresponding continued fraction expansions. In this note, we collect a number of examples, demonstrating what these general results look like for the most important states on non-commutative polynomials, namely for various product states. In particular,...

This paper formally presents a class of planning problems which allows non-binary state variables and parallel execution of actions. The class is proven to be tractable, and we provide a sound and complete polynomial time algorithm for planning within this class. This result means that we are getting closer to tackling realistic planning problems in sequential control, where a restricted proble...

In this thesis algorithmic improvements and variants for two-flavor lattice QCD simulations with dynamical fermions are studied using the O(a) improved Dirac-Wilson operator in the Schrödinger functional setup and employing a hybrid Monte Carlo-type (HMC) update. Both, the Hermitian and the Non-Hermitian operator are considered. For the Hermitian Dirac-Wilson operator we investigate the advanta...

To use this lemma, we first design a polynomial, p, such that whether p is the 0-polynomial or non-zero is meaningful to us. To differentiate those cases, we choose a set S, set the xi randomly and evaluate p. If p evaluates to something non-zero, then it must be a non-zero polynomial. Conversely if p evaluates to 0, by the lemma, we conclude that it it most likely because p is in fact the 0 po...

A Class of new methods based on a septic non-polynomial spline function for the numerical solution one-dimensional Bratu's problem are presented. The local truncation errors and the methods of order 2th, 4th, 6th, 8th, 10th, and 12th, are obtained. The inverse of some band matrixes are obtained which are required in proving the convergence analysis of the presented method. Associated boundary f...

In this paper, we consider the problem of computing estimates of the domain-ofattraction for non-polynomial systems. A polynomial approximation technique, based on multivariate polynomial interpolation and error analysis for remaining functions, is applied to compute an uncertain polynomial system, whose set of trajectories contains that of the original non-polynomial system. Experiments on the...

design of crystal-like lattices can be achieved by using some net operations. hypothetical networks, thus obtained, can be characterized in their topology by various counting polynomials and topological indices derived from them. the networks herein presented are related to the dyck graph and described in terms of omega polynomial and piv polynomials.