Matrix interpretation of multiple orthogonality

In this work we give an interpretation of a (s(d + 1) + 1)-term recurrence relation in terms of type II multiple orthogonal polynomials.We rewrite this recurrence relation in matrix form and we obtain a three-term recurrence relation for vector polynomials with matrix coefficients. We present a matrix interpretation of the type II multi-orthogonality conditions.We state a Favard type theorem and the expression for the resolvent function associated to the vector of linear functionals. Finally a reinterpretation of the type II Hermite- Padé approximation in matrix form is given

Selbstbewusstsein in kognitiven Systemen

Beckermann A. Selbstbewusstsein in kognitiven Systemen. In: Peschl M, ed. Die Rolle der Seele in der Kognitionswissenschaft und der Neurowissenschaft. Der Begriff der Seele. Vol 3. Würzburg: Königshausen und Neumann; 2005: 171-187

Effects of Simplified Enthalpy Relations on the Prediction of Heat Transfer during Solidification of a Lead-Tin Alloy

An investigation into the effects of enthalpy junctions that vary with both concentration and temper

The Trigonometric Rosen-Morse Potential in the Supersymmetric Quantum Mechanics and its Exact Solutions

The analytic solutions of the one-dimensional Schroedinger equation for the trigonometric Rosen-Morse potential reported in the literature rely upon the Jacobi polynomials with complex indices and complex arguments. We first draw attention to the fact that the complex Jacobi polynomials have non-trivial orthogonality properties which make them uncomfortable for physics applications. Instead we here solve above equation in terms of real orthogonal polynomials. The new solutions are used in the construction of the quantum-mechanic superpotential.Comment: 16 pages 7 figures 1 tabl

Subresultants in multiple roots: an extremal case

We provide explicit formulae for the coefficients of the order-d polynomial subresultant of (x-\alpha)^m and (x-\beta)^n with respect to the set of Bernstein polynomials \{(x-\alpha)^j(x-\beta)^{d-j}, \, 0\le j\le d\}. They are given by hypergeometric expressions arising from determinants of binomial Hankel matrices.Comment: 18 pages, uses elsart. Revised version accepted for publication at Linear Algebra and its Application

A method for effective use of enterprise modelling techniques in complex dynamic decision making

Effective organisational decision-making requires information pertaining to various organisational aspects, precise analysis capabilities, and a systematic method to capture and interpret the required information. The existing Enterprise Modelling (EM) and actor technologies together seem suitable for the specification and analysis needs of decision making. However, in absence of a method to capture required information and perform analyses, the decision-making remains a complex endeavour. This paper presents a method that captures required information in the form of models and performs what-if calculations in a systematic manner

Modeling of reoxidation inclusion formation in steel sand casting

Abstract A model is developed that predicts the motion and growth of oxide inclusions during pouring, as well as their final locations on the surface of steel sand castings. Inclusions originate on the melt free surface, and their subsequent growth is controlled by oxygen transfer from the atmosphere. Inclusion motion is modeled in a Lagrangian sense, taking into account drag and buoyancy forces. The inclusion model is implemented in a general-purpose casting simulation code. Parametric studies are performed to investigate the sensitivity of the predictions to various model parameters. The model is validated by comparing the simulation results to measurements made on production steel sand castings. Good overall agreement is obtained

Phase Field Model for Three-Dimensional Dendritic Growth with Fluid Flow

We study the effect of fluid flow on three-dimensional (3D) dendrite growth using a phase-field model on an adaptive finite element grid. In order to simulate 3D fluid flow, we use an averaging method for the flow problem coupled to the phase-field method and the Semi-Implicit Approximated Projection Method (SIAPM). We describe a parallel implementation for the algorithm, using Charm++ FEM framework, and demonstrate its efficiency. We introduce an improved method for extracting dendrite tip position and tip radius, facilitating accurate comparison to theory. We benchmark our results for two-dimensional (2D) dendrite growth with solvability theory and previous results, finding them to be in good agreement. The physics of dendritic growth with fluid flow in three dimensions is very different from that in two dimensions, and we discuss the origin of this behavior