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In this article a diffusion equation is obtained as a limit of a reversible kinetic equation with an ad hoc scaling. The diffusion is produced by the collisions of the particles with the boundary. These particles are assumed to be reflected according to a reversible law having convenient mixing properties. Optimal convergence results are obtained in a very simple manner. This is made possible because the model, based on Arnold" s cat map can be handled with Fourier series instead of the symbolic dynamics associated to a Markow partition.
Lernen von Abstraktionshierarchien zur Optimierung der Auswahl von maschinell abstrahierten Plänen
(1994)
Mit Hilfe von "Multistrategy" Ansätzen, die erklärungsbasiertes und induktives Lernen integrieren, ist es möglich, die Performanz von Planungssystemen signifikant zu verbessern. Dabei können gelöste Planungsprobleme zunächst mit einem wissensintensiven Verfahren abstrahiert und generalisiert werden. Durch den in diesem Beitrag im Vordergrund stehenden induktiven inkrementellen Lernalgorithmus ist es dann weiterhin möglich, die Gesamtheit des deduktiv generierten Wissens in einer Abstraktionshierarchie anzuordnen. Dabei wird die, im allgemeinen unentscheidbare, "spezieller-als-Relation" zwischen generalisierten Plänen, induktiv aus den gegebenen Planungsfällen gelernt. Diese Abstraktionshierarchie dient dann zur Klassifikation neuer Problemstellungen und damit zur Bestimmung einer speziellsten anwendbaren abstrakten Problemlösung.
The Boltzmann equation solutions are considered for the small Knudsen number. The main attention is devoted to certain deviations from the classical Navier-Stokes description. The equations for the quasistationary slow flows are derived. These equations do not contain the Knudsen number and provide in this sense a limiting description of hydrodynamical variables. Two well-known special cases are also indicated. In the isothermal case the equations are equivalent to the incompressible Navier-Stokes equations, in stationary case they coincide with the equations of slow non-isothermal flows. It is shown that the derived equations possess all principal properties of the Boltzmann equation on contrast to the Burnett equations. In one dimension the equations reduce to the nonlinear diffusion equations, being exactly solvable for Maxwell molecules. Multidimensional stationary heat-transfer problems are also discussed. It is shown that one can expect an essential difference between the Boltzmann equaiton solution in the limit of the continuous media and the corresponding solution of the Navier-Stokes equations.
The paper presents some approximation methods for the Boltzmann equation. In the first part fully implicit discretization techniques for the spatially homogeneous Boltzmann equation are investigated. The implicit equation is solved using an iteration process. It is shown that the iteration converges to the correct solution for the moments of the distribution function as long as the mass conservation is strictly fulfilled. For a simple model Boltzmann equation some unexpected features of the implicit scheme and the corresponding iteration process are clarified. In the second part a new iteration algorithm is proposed which should be used for the stationary Boltzmann equation. The realization of the method is very similar to the standard splitting algorithms except some new stochastic elements.
A Case Study on Specifikation,Detection and Resolution of IN Feature Interactions with Estelle
(1994)
We present an approach for the treatment of Feature Interactions in Intelligent Networks. The approach is based on the formal description technique Estelle and consists of three steps. For the first step, a specification style supporting the integration of additional features into a basic service is introduced . As a result, feature integration is achieved by adding specification text, i.e . on a purely syntactical level. The second step is the detection of feature interactions resulting from the integration of additional features. A formal criterion is given that can be used for the automatic detection of a particular class of feature interactions. In the third step, previously detected feature interactions are resolved. An algorithm has been devised that allows the automatical incorporation of high-level design decisions into the formal specification. The presented approach is applied to the Basic Call Service and several supplementary interacting features.
We introduce the concept of streamballs for fluid flow visualization. Streamballs are based upon implicit surface generation techniques adopted from the well-known metaballs. Their property to split or merge automatically in areas of significant divergence or convergence makes them an ideal tool for the visualization of arbitrary complex flow fields. Using convolution surfaces generated by continuous skeletons for streamball construction offers the possibility to visualize even tensor fields.
The problem to interpolate Hermite-type data (i.e. two points with attached tangent vectors) with elastic curves of prescribed tension is known to have multiple solutions. A method is presented that finds all solutions of length not exceeding one period of its curvature function. The algorithm is based on algebraic relations between discrete curvature information which allow to transform the problem into a univariate one. The method operates with curves that by construction partially interpolate the given data. Hereby the objective function of the problem is drastically simplified. A bound on the maximum curvature value is established that provides an interval containing all solutions.
Automatic proof systems are becoming more and more powerful.However, the proofs generated by these systems are not met withwide acceptance, because they are presented in a way inappropriatefor human understanding.In this paper we pursue two different, but related, aims. First wedescribe methods to structure and transform equational proofs in away that they conform to human reading conventions. We developalgorithms to impose a hierarchical structure on proof protocols fromcompletion based proof systems and to generate equational chainsfrom them.Our second aim is to demonstrate the difficulties of obtaining suchprotocols from distributed proof systems and to present our solutionto these problems for provers using the TEAMWORK method. Wealso show that proof systems using this method can give considerablehelp in structuring the proof listing in a way analogous to humanbehaviour.In addition to theoretical results we also include descriptions onalgorithms, implementation notes, examples and data on a variety ofexamples.
In dieser Arbeit wird eine Kombinationsmöglichkeit von fallbasiertem und induktivem Schliessen, basierend auf k-d- und Entscheidungsbäumen, entwickelt. Dabei wurde versucht, die Vorteile des induktiven Mechanismus, wie z. B. die sehr effiziente Klassifiz ierung und automatische Generierung, in den fallbasierten Mechanismus zu integrieren. Die Aufgabe zerfällt dabei in zwei Teilaufgaben, die im folgenden zusammengefasst werden.
This paper presents the systematic synthesis of a fairly complex digitalcircuit and its CPLD implementation as an assemblage of communicatingasynchronous sequential circuits. The example, a VMEbus controller, waschosen because it has to control concurrent processes and to arbitrateconflicting requests.
Best-Fit Pattern Matching
(1994)
This report shows that dispatching of methods in object oriented languages is in principle the same as best fit pattern matching. A general conceptual description of best fit pattern matching is presented. Many object oriented features are modelled by means of the general concept. This shows that simple methods, multi methods, overloading of functions, pattern matching,
dynamic and union types, and extendable records can be combined in a single comprehensive concept.
In this paper the complexity of the local solution of Fredholm integral equations
is studied. For certain Sobolev classes of multivariate periodic functions with dominating mixed derivative we prove matching lower and upper bounds. The lower bound is shown using relations to s-numbers. The upper bound is proved in a constructive way providing an implementable algorithm of optimal order based on Fourier coefficients and a hyperbolic cross approximation.
We study the complexity of local solution of Fredholm integral equations. This means that we want to compute not the full solution, but rather a functional (weighted mean, value in a point) of it. For certain Sobolev classes of multivariate periodic functions we prove matching upper and lower bounds and construct an algorithm of the optimal order, based on Fourier coefficients and a hyperbolic cross approximation.
A method for efficiently handling associativity and commutativity (AC) in implementations of (equational) theorem provers without incorporating AC as an underlying theory will be presented. The key of substantial efficiency gains resides in a more suitable representation of permutation-equations (such as f(x,f(y,z))=f(y,f(z,x)) for instance). By representing these permutation-equations through permutations in the mathematical sense (i.e. bijective func- tions :{1,..,n} {1,..,n}), and by applying adapted and specialized inference rules, we can cope more appropriately with the fact that permutation-equations are playing a particular role. Moreover, a number of restrictions concerning application and generation of permuta- tion-equations can be found that would not be possible in this extent when treating permu- tation-equations just like any other equation. Thus, further improvements in efficiency can be achieved.