A number of approaches for discretizing partial differential equations with random data are based on generalized polynomial chaos expansions of random variables. These constitute generalizations of the polynomial chaos expansions introduced by Norbert Wiener to expansions in polynomials orthogonal with respect to non-Gaussian probability measures. We present conditions on such measures which im...

In this note we examine the solution and the impulsive behavior of autonomous linear multivariable systems whose pseudo-state β (t) obeys a linear matrix differential equation A (ρ)β (t) = 0 where A (ρ) is a polynomial matrix in the differential operator ρ := d dt . We thus generalize to the general polynomial matrix case some results obtained in [2][3] which regard the impulsive behavior of th...

Abstract: Generalized predictive control (GPC) is nowadays, widely ,spread in control theory as well as in the industrial world. Generalized predictive control (GPC) belong to this family has been demonstrated as a powerful controlling process plants, In this work a polynomial approach of generalized predictive control is proposed whose aim to find optimal values for the tuning control and appl...

In this paper we address a general Goal Programming problem with linear objectives, convex constraints, and an arbitrary componentwise nondecreasing norm to aggregate deviations with respect to targets. In particular, classical Linear Goal Programming problems, as well as several models in Location and Regression Analysis are modeled within this framework. In spite of its generality, this probl...

In this paper we present an adaptive multi-element generalized polynomial chaos (ME-gPC) method, which can achieve hp-convergence in random space. ME-gPC is based on the decomposition of random space and generalized polynomial chaos (gPC). Using proper numerical schemes to maintain the local orthogonality on-the-fly, we perform gPC locally and adaptively. The key idea is to combine the polynomi...

We develop parallel versions of Buchbergers Gröbner Basis algorithm for a virtual shared memory KSR1 computer. A coarse grain version does S-polynomial reduction concurrently and respects the same critical pair selection strategy as the sequential algorithm. A fine grain version parallelizes polynomial reduction in a pipeline and can be combined with the parallel S-polynomial reduction. The alg...

This paper presents a generalized associative memory model, which stores a collection of tuples whose components are sets rather than scalars. It is shown that all library patterns are stored stably. On the other hand spurious memories may develop. Applications of this model to storage and retrieval of naturallyarising generalized sequences in bioinformatics are presented. The model is shown to...

From the generating matrix of a linear code one can construct a sequence of generalized star configurations which are strongly connected to the generalized Hamming weights and the underlying matroid of the code. When the code is MDS, the matrix is generic and we obtain the usual star configurations. In our main result, we show that the degree of a generalized star configuration as a projective ...

We present a new approach to obtain solutions for general random oscillators using a broad class of polynomial chaos expansions, which are more efficient than the classical Wiener–Hermite expansions. The approach is general but here we present results for linear oscillators only with random forcing or random coefficients. In this context, we are able to obtain relatively sharp error estimates i...