University of Twente Publications
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Smooth approximation of data on the sphere with splines - Traas, C.R.
A computable function, defined over the sphere, is constructed, which is of classC1 at least and which approximates a given set of data. The construction is based upon tensor product spline basisfunctions, while at the poles of the spherical system of coordinates modified basisfunctions, suggested by the spherical harmonics expansion, are introduced to recover the continuity order at these points. Convergence experiments, refining the grid, are performed and results are compared with similar results available in literature.
The approximation accuracy is compared with that of the expansion in terms of spherical harmonics. The use of piecewise approximation, with locally supported basisfunctions,...
The development of the representation of conceptual knowledge in memory and the design of instruction - Dijkstra, S.
Knowledge comprises facts, concepts and principles. Skills are categorized as either cognitive or motor skills, which are essential for solving problems. The acquisition of knowledge and skills is guided by instructions and by presenting problems to students. Firstly, the instructions for acquiring concepts, based on principles, are discussed and a model for teaching is presented. Further, the integration of class and relational concepts, together with principles, is shown to be necessary for solving problems.
On Cournot-Nash equilibria with exogenous uncertainty - Aaftink, J.; Ireland, N.; Sertel, M.
A large body of literature has accumulated which examines how the optimal solution of an agent maximizing the expectation of a real-valued function, depending on a random parameterp and the agent's behaviorx, reacts to perturbations in the first and second moments ofp. Here, by an approximation valid for small uncertainty, we allow many agents and consider their behavior in a Cournot-Nash equilibrium. We also allowp to depend on the behaviors of the participating agents. We apply the analysis to two models, one of a Cournot oligopoly, the other of a cooperative of individuals where there is uncertainty in the return...
Geometrical interpretation of the bilinear equations for the KP hierarchy - Helminck, G.F.; Post, G.F.
The Grassmann manifold approach to the KP hierarchy, in the spirit of Segal and Wilson, is used to define the wavefunction ψW and its adjoint ψW⊥. From the fact that ψW and ψW⊥ are the orthogonal, we derive the bilinear equations. The modified equations are treated at the same time
Note on prime representations of convex polyhedral sets - Boneh, A.; Caron, R.J.; Lemire, F.W.; McDonald, J.F.; Telgen, J.; Vorst, T.
Consider a convex polyhedral set represented by a system of linear inequalities. A prime representation of the polyhedron is one that contains no redundant constraints. We present a sharp upper bound on the difference between the cardinalities of any two primes.
A note on a core catcher of a cooperative game - Driessen, T.S.H.
In Driessen (1986) it is shown that for games satisfying a certain condition the core of the game is included in the convex hull of the set of certain marginal worth vectors of the game, while it is conjectured that the inclusion holds without any condition on the game. In this note it is proved that the inclusion holds for all games.
Deviations of Fischer-Tropsch products from an Anderson-Schulz-Flory distribution - Snel, Ruud
Negative deviations from an Anderson-Schulz-Flory distribution have been observed for the product of the Fischer-Tropsch synthesis. The catalyst was a complex-derived iron-calcium catalyst promoted with cesium sulphate, therefore, neither carrier acidity nor shape selectivity can explain the deviations. This is the first time that chemical modifications of the catalyst are observed to result in negative ASF deviations.
Homogeneity analysis with k sets of variables: An alternating least squares method with optimal scaling features - Burg van der, Eeke; Leeuw de, Jan; Verdegaal, Renée
Homogeneity analysis, or multiple correspondence analysis, is usually applied tok separate variables. In this paper we apply it to sets of variables by using sums within sets. The resulting technique is called OVERALS. It uses the notion of optimal scaling, with transformations that can be multiple or single. The single transformations consist of three types: nominal, ordinal, and numerical. The corresponding OVERALS computer program minimizes a least squares loss function by using an alternating least squares algorithm. Many existing linear and nonlinear multivariate analysis techniques are shown to be special cases of OVERALS. An application to data from an epidemiological...
Quantitative Auger depth profiling of LPCVD and PECVD silicon nitride films - Keim, Enrico G.; Aïte, Kamal
Thin silicon nitride films (100–210 nm) with refractive indices varying from 1.90 to 2.10 were deposited on silicon substrates by low pressure chemical vapour deposition (LPCVD) and plasma enhanced chemical vapour deposition (PECVD). Rutherford backscattering spectrometry (RBS), ellipsometry, surface profiling measurements and Auger electron spectroscopy (AES) in combination with Ar+ sputtering were used to characterize these films. We have found that the use of (p-p)heights of the Si LVV and N KLL Auger transitions in the first derivative of the energy distribution (dN(E)/dE) leads to an accurate determination of the silicon nitride composition in Auger depth profiles over a wide...
On the derivation of some fundamental expressions for the average stress tensor in systems of interacting particles - Jongschaap, R.J.J.
The so-called generalized Kramers-Kirkwood expression for the average stress tensor of a system of interacting point particles, derived by Bird and Curtiss on using a phase-space-kinetic formalism has been reconsidered from different points of view. First a derivation based upon volume averaging is discussed, and after that a derivation based upon a virtual work principle. The latter approach offers the possibility of distinguishing reversible (including thermodynamic and Brownian) and dissipative forces and stresses by using a projection operator, associated with the constraints of the system.
A new finite difference scheme adapted to the one-dimensional Schrödinger equation - Geurts, Bernard J.
We present a new discretisation scheme for the Schrödinger equation based on analytic solutions to local linearisations. The scheme generates the normalised eigenfunctions and eigenvalues simultaneously and is exact for piecewise constant potentials and effective masses. Highly accurate results can be obtained with a small number of mesh points and a robust and flexible algorithm using continuation techniques is derived. An application to the Hartree approximation for SiGe heterojunctions is discussed in which we solve the coupled Schrödinger-Poisson model problem selfconsistently.