426 research outputs found
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
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