@misc{DeuflhardLangNowak1995, author = {Deuflhard, Peter and Lang, Jens and Nowak, Ulrich}, title = {Adaptive Algorithms in Dynamical Process Simulation}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-1823}, number = {SC-95-16}, year = {1995}, abstract = {Dynamical simulation of industrially relevant processes strongly advises the use of algorithms, which are {\em adaptive} both in time and in space discretization. The paper presents two alternatives: (a) a fully adaptive method of lines approach, which is based on finite difference methods and essentially applicable to 1D problems; (b) a fully adaptive Rothe method, which is based on a fast multilevel finite element method and applicable to 1D up to 3D.}, language = {en} } @phdthesis{Schultz1995, author = {Schultz, R{\"u}diger}, title = {Structure and Stability in Two-Stage Stochastic Programming}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-1819}, number = {SC-95-15}, year = {1995}, abstract = {{\begin{footnotesize} This thesis is concerned with structural properties and the stability behaviour of two-stage stochastic programs. Chapter~1 gives an introduction into stochastic programming and a summary of the main results of the thesis. In Chapter~2 we present easily verifiable sufficient conditions for the strong convexity of the expected-recourse function in a stochastic program with linear complete recourse. Different levels of randomness in the data are considered. We start with models where only the right-hand side of the constraints is random and extend these results to the situation where also the technology matrix contains random entries. The statements on strong convexity imply new stability estimates for sets of optimal solutions when perturbing the underlying probability measure. We work out H{\"o}lder estimates (in terms of the \$\mbox{L}_1\$-Wasserstein distance) for optimal solution sets to linear recourse models with random technology matrix. In Chapter~3 ({\it joint work with Werner R{\"o}misch, Berlin}) we are aiming at the Lipschitz stability of optimal solution sets to linear recourse models with random right-hand side. To this end , we first adapt the distance notion for the underlying probability measures to the structure of the model and derive a Lipschitz estimate for optimal solutions based on that distance. Here, the strong convexity established in Chapter~2 turns out as an essential assumption. For applications, however, a Lipschitz estimate with respect to a more accesssible probability distance is desirable. Structural properties of the expected-recourse function finally permit such an estimate in terms of the Kolmogorov-Smirnov distance of linear transforms of the underlying measures. The general analysis is specified to estimation via empirical measures. We obtain a law of iterated logarithm, a large deviation estimate and an estimate for the asymptotic distribution of optimal solution sets. Chapters~4 and~5 deal with two-stage linear stochastic programs where integrality constraints occur in the second stage. In Chapter~4 we study basic continuity properties of the expected-recourse function for models with random right-hand side and random technology matrix. The joint continuity with respect to the decision variable and the underlying probability measure leads to qualitative statements on the stability of local optimal values and local optimal solutions. In Chapter~5 we demonstrate that a variational distance of probability measures based on a suitable Vapnik-\v{C}ervonenkis class of Borel sets leads to convergence rates of the H{\"o}lder type for the expected recourse as a function of the underlying probability measure. The rates carry over to the convergence of local optimal values. As an application we again consider estimation via empirical measures. Beside qualitative asymptotic results for optimal values and optimal solutions we obtain a law of iterated logarithm for optimal values. \end{footnotesize}}}, language = {en} } @misc{Schuette1995, author = {Sch{\"u}tte, Christof}, title = {Smoothed Molecular Dynamics for Thermally Embedded Systems}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-1809}, number = {SC-95-14}, year = {1995}, abstract = {This paper makes use of statistical mechanics in order to construct effective potentials for Molecular Dynamics for systems with nonstationary thermal embedding. The usual approach requires the computation of a statistical ensemble of trajectories. In the context of the new model the evaluation of only one single trajectory is sufficient for the determination of all interesting quantities, which leads to an enormous reduction of computational effort. This single trajectory is the solution to a corrected Hamiltonian system with a new potential \$\tilde{V}\$. It turns out that \$\tilde{V}\$ can be defined as spatial average of the original potential \$V\$. Therefore, the Hamiltonian dynamics defined by \$\tilde{V}\$ is smoother than that effected by \$V\$, i.e. a numerical integration of its evolution in time allows larger stepsizes. Thus, the presented approach introduces a Molecular Dynamics with smoothed trajectories originating from spatial averaging. This is deeply connected to time--averaging in Molecular Dynamics. These two types of {\em smoothed Molecular Dynamics} share advantages (gain in efficiency, reduction of error amplification, increased stability) and problems (necessity of closing relations and adaptive control schemes) which will be explained in detail.}, language = {en} } @misc{OPUS4-969, title = {Jahresbericht 1994}, issn = {0934-5892}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-9699}, number = {1994}, year = {1995}, language = {de} } @misc{Gatermann1995, author = {Gatermann, Karin}, title = {Testing for Sn-Symmetry with a Recursive Detective}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-1786}, number = {SC-95-12}, year = {1995}, abstract = {In the recent years symmetric chaos has been studied intensively. One knows which symmetries are admissible as the symmetry of an attractor and which transitions are possible. The numeric has been developed using equivariant functions for detection of symmetry and augmented systems for determination of transition points. In this paper we look at this from a sophisticated group theoretic point of view and from the view of scientific computing, i.e. efficient evaluation of detectives is an important point. The constructed detectives are based on Young's seminormal form for \$S_n\$. An application completes the paper.}, language = {en} } @misc{Koepf1995, author = {Koepf, Wolfram}, title = {The Identification Problem for Transcendental Functions}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-1791}, number = {SC-95-13}, year = {1995}, abstract = {In this article algorithmic methods are presented that have essentially been introduced into computer algebra within the last decade. The main ideas are due to Stanley[1980] and Zeilberger[1990]. Some of them had already been discovered in the last century (see e.\ g.\ Beke[1894]), but because of the complexity of the underlying algorithms have fallen into oblivion. The combination of these ideas leads to a solution of the identification problem for a large class of transcendental functions. We present implementations of these algorithms in computer algebra systems.}, language = {en} } @misc{DellnitzHohmann1995, author = {Dellnitz, Michael and Hohmann, Andreas}, title = {A Subdivision Algorithm for the Computation of Unstable Manifolds and Global Attractors}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-1770}, number = {SC-95-11}, year = {1995}, abstract = {Each invariant set of a given dynamical system is part of the global attractor. Therefore the global attractor contains all the potentially interesting dynamics, and, in particular, it contains every (global) unstable manifold. For this reason it is of interest to have an algorithm which allows to approximate the global attractor numerically. In this article we develop such an algorithm using a subdivision technique. We prove convergence of this method in a very general setting, and, moreover, we describe the qualitative convergence behavior in the presence of a hyperbolic structure. The algorithm can successfully be applied to dynamical systems of moderate dimension, and we illustrate this fact by several numerical examples.}, language = {en} } @misc{HegePolthier1995, author = {Hege, Hans-Christian and Polthier, Konrad}, title = {Visualization and Mathematics. International Workshop}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-5179}, number = {TR-95-02}, year = {1995}, abstract = {International Workshop with support of the Deutsche Forschungsgemeinschaft (DFG) and Max-Planck-Gesellschaft (MPG) Berlin (Dahlem), Germany, May 30 - June 2, 1995}, language = {en} } @misc{GroetschelLuegger1995, author = {Gr{\"o}tschel, Martin and L{\"u}gger, Joachim}, title = {Wissenschaftliche Kommunikation am Wendepunkt - Bibliotheken im Zeitalter globaler elektronischer Netze -}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-5164}, number = {TR-95-01}, year = {1995}, abstract = {Durch extrem steigende Preise f{\"u}r traditionelle wissenschaftliche Zeitschriften bei gleichzeitiger Stagnation der Bibliotheksetats an den Hochschulen und bei weltweit weiterhin anwachsenden Forschungsleistungen ist die ad{\"a}quate Versorgung der Wissenschaften mit relevanter Literatur gef{\"a}hrdet. Dokumentenliefersysteme werden vielerorts als L{\"o}sung dieser ``Bibliothekskrise'' propagiert. Dieser Weg ist f{\"u}r den derzeitigen Literaturversorgungsmarkt sinnvoll, aber er bietet keine langfristig stabile L{\"o}sung. Wenn die Grundversorgung der Bibliotheken weiter schrumpft, wird Dokumentenlieferung in der zur Zeit {\"u}blichen bzw. geplanten Form die Kosten nur noch zus{\"a}tzlich in die H{\"o}he treiben. Wir pl{\"a}dieren in diesem Aufsatz f{\"u}r einen grunds{\"a}tzlich neuen Ansatz. Wir sind der Meinung, da\ss{} einzig der {\"U}bergang auf elektronische Medien eine bezahlbare, umfassende und benutzerfreundliche Versorgung der Wissenschaftler mit Literatur sichern kann. Wir zeigen -- unter anderem anhand elektronischer Zeitschriften -- wie zum Beispiel durch Kooperation von Bibliotheken mit Fachbereichen und wissenschaftlichen Gesellschaften neue Wege der Informationsversorgung beschritten werden k{\"o}nnen. Dieser Vorschlag einer neuen Organisation des wissenschaftlichen Publikationswesen erfordert Umdenken in vielen Bereichen. Neue Organisationsformen sind erforderlich, Rechte m{\"u}ssen anders verteilt, Aufgaben auf andere Schultern geladen werden. Die Bibliotheken werden besonders betroffen sein. Aber f{\"u}r sie ist die konsequente Nutzung der sich rasch ausbreitenden Informationstechnik (darunter verstehen wir u. a. globale elektronische Netze, leistungsf{\"a}hige Rechner, kosteng{\"u}nstige Speichermedien, benutzerfreundliche Such- und Retrieval-Systeme, Entwicklung weltweit akzeptierter Datenformate) eine wirkliche und m{\"o}glicherweise die einzige Chance, ihrem Auftrag zur umfassenden Versorgung der Wissenschaften mit Literatur zu gesamtwirtschaftlich niedrigen Kosten weiterhin nachzukommen. Au\ss{}erdem bietet die Bereitstellung und Archivierung wissenschaftlicher Literatur auf elektronischem Wege bedeutende Vorteile gegen{\"u}ber der traditionellen Dokumentation auf Papier, die im {\"u}brigen, falls erw{\"u}nscht, weiterhin betrieben werden kann.}, language = {de} } @misc{KoepfSchmersau1995, author = {Koepf, Wolfram and Schmersau, Dieter}, title = {On the De Branges Theorem}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-1765}, number = {SC-95-10}, year = {1995}, abstract = {Recently, Todorov and Wilf independently realized that de Branges' original proof of the Bieberbach and Milin conjectures and the proof that was later given by Weinstein deal with the same special function system that de Branges had introduced in his work. In this article, we present an elementary proof of this statement based on the defining differential equations system rather than the closed representation of de Branges' function system. Our proof does neither use special functions (like Wilf's) nor the residue theorem (like Todorov's) nor the closed representation (like both), but is purely algebraic. On the other hand, by a similar algebraic treatment, the closed representation of de Branges' function system is derived. Our whole contribution can be looked at as the study of properties of the Koebe function. Therefore, in a very elementary manner it is shown that the known proofs of the Bieberbach and Milin conjectures can be understood as a consequence of the L{\"o}wner differential equation, plus properties of the Koebe function.}, language = {en} } @misc{ThomasWeismantel1995, author = {Thomas, Rekha R. and Weismantel, Robert}, title = {Truncated Gr{\"o}bner Bases for Integer Programming}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-1750}, number = {SC-95-09}, year = {1995}, abstract = {{\def\N{{\mbox{{\rm I\kern-0.22emN}}}}In this paper we introduce a multivariate grading of the toric ideal associated with the integer program \$min \{ cx : Ax = b, x \in \N^n \}\$, and a truncated Buchberger algorithm to solve the program. In the case of \$max \{ cx : Ax \leq b, x \leq u, x \in \N^n \}\$ in which all data are non-negative, this algebraic method gives rise to a combinatorial algorithm presented in UWZ94}.}, language = {en} } @misc{SchulzWeismantelZiegler1995, author = {Schulz, Andreas S. and Weismantel, Robert and Ziegler, G{\"u}nter M.}, title = {0/1-Integer Programming: Optimization and Augmentation are Equivalent}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-1744}, number = {SC-95-08}, year = {1995}, abstract = {{\def\xnew{x^{\mbox{\tiny new}}}\def\Z{{{\rm Z}\!\! Z}}For every fixed set \${\cal F}\subseteq\{0,1\}^n\$ the following problems are strongly polynomial time equivalent: given a feasible point \$x\in\cal F\$ and a linear objective function \$c\in\Z^n\$, \begin{itemize} \item find a feasible point \$x^*\in\cal F\$ that maximizes \$cx\$ (Optimization), \item find a feasible point \$\xnew\in\cal F\$ with \$c\xnew>cx\$ (Augmentation), and \item find a feasible point \$\xnew\in\cal F\$ with \$c\xnew>cx\$ such that \$\xnew-x\$ is ``irreducible''\\(Irreducible Augmentation). \end{itemize} This generalizes results and techniques that are well known for \$0/1\$--integer programming problems that arise from various classes of combinatorial optimization problems.}}, language = {en} } @misc{DellnitzGolubitskyHohmannetal.1995, author = {Dellnitz, Michael and Golubitsky, Martin and Hohmann, Andreas and Stewart, Ian}, title = {Spirals in Scalar Reaction-Diffusion Equations}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-1720}, number = {SC-95-06}, year = {1995}, abstract = {Spiral-like patterns are an often observed phenomenon in chemical experiments such as the Belousov-Zhabotinskii reaction. The talk is concerned with a new PDE model whose solutions have the form of rotating spirals. In contrast to previous approaches it is based on a {\em scalar\/} reaction diffusion equation defined on a disk. A particular choice of boundary conditions leads to a non-selfadjoint operator which permits non-trivial dynamics. We study this equation using a combination of equivariant bifurcation theory and numerical simulations. The latter involves the direct simulation of the time dependent system as well as the computation of rotating waves and their stability.}, language = {en} } @misc{RenautFroehlich1995, author = {Renaut, Rosemary and Fr{\"o}hlich, Jochen}, title = {A Pseudospectral Chebychev method for the 2D Wave Equation with Domain Stretching and Absorbing Boundary Conditions}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-1730}, number = {SC-95-07}, year = {1995}, abstract = {In this paper we develop a method for the simulation of wave propagation on artificially bounded domains. The acoustic wave equation is solved at all points away from the boundaries by a pseudospectral Chebychev method. Absorption at the boundaries is obtained by applying one-way wave equations at the boundaries, without the use of damping layers. The theoretical reflection coefficient for the method is compared to theoretical estimates of reflection coefficients for a Fourier model of the problem. These estimates are confirmed by numerical results. Modification of the method by a transformation of the grid to allow for better resolution at the center of the grid reduces the maximum eigenvalues of the differential operator. Consequently, for stability the maximum timestep is \$O(1/N)\$ as compared to \$O(1/N^2)\$ for the standard Chebychev method. Therefore, the Chebychev method can be implemented with efficiency comparable to that of the Fourier method. Moreover, numerical results presented demonstrate the superior performance of the new method.}, language = {en} } @misc{Wolf1995, author = {Wolf, Thomas}, title = {Programs for Applying Symmetries of PDEs}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-1710}, number = {SC-95-05}, year = {1995}, abstract = {In this paper the programs {\tt APPLYSYM}, {\tt QUASILINPDE} and {\tt DETRAFO} are described which aim at the utilization of infinitesimal symmetries of differential equations. The purpose of {\tt QUASILINPDE} is the general solution of quasilinear PDEs. This procedure is used by {\tt APPLYSYM} for the application of point symmetries for either \begin{itemize} \item calculating similarity variables to perform a point transformation which lowers the order of an ODE or effectively reduces the number of explicitly occuring independent variables in a PDE(-system) or for \item generalizing given special solutions of ODEs/PDEs with new constant parameters. \end{itemize} The program {\tt DETRAFO} performs arbitrary point- and contact transformations of ODEs/PDEs and is applied if similarity and symmetry variables have been found. The program {\tt APPLYSYM} is used in connection with the program {\tt LIEPDE} for formulating and solving the conditions for point- and contact symmetries which is described in LIEPDE(1992). The actual problem solving is done in all these programs through a call to the package {\tt CRACK} for solving overdetermined PDE-systems.}, language = {en} } @misc{GatermannLauterbach1995, author = {Gatermann, Karin and Lauterbach, Reiner}, title = {Automatic classification of normal forms}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-1692}, number = {SC-95-03}, year = {1995}, abstract = {The aim of this paper is to demonstrate a specific application of Computer Algebra to bifurcation theory with symmetry. The classification of different bifurcation phenomena in case of several parameters is automated, based on a classification of Gr{\"o}bner bases of possible tangent spaces. The computations are performed in new coordinates of fundamental invariants and fundamental equivariants, with the induced weighted ordering. In order to justify the approach the theory of intrinsic modules is applied. Results for the groups \$D_3, Z_2,\$ and \$ Z_2\times Z_2\$ demonstrate that the algorithm works independent of the group and that new results are obtained.}, language = {en} } @misc{AbdelHamidAscheuerGroetscheletal.1995, author = {Abdel-Hamid, Atef Abdel-Aziz and Ascheuer, Norbert and Gr{\"o}tschel, Martin and Schorer, Herbert}, title = {Simulation und Optimierung einer PC-Fertigung unter Echtzeitbedingungen}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-1700}, number = {SC-95-04}, year = {1995}, abstract = {Die Business Unit PC in Augsburg ist die zentrale Produktionsst{\"a}tte der Siemens--Nixdorf Informationssysteme (SNI) AG f{\"u}r Personal Computer sowie f{\"u}r einige Periph{\"a}rger{\"a}te. Das Werk, entworfen nach modernen CIM/CAI--Konzepten (Computer Integrated Manufacturing/ Computer Aided Industry), wurde 1987 errichtet. Bald zeigte sich jedoch, daß es f{\"u}r ein zu geringes Produktionsvolumen ausgelegt war und einige Komponenten des Systems Engp{\"a}sse im Produktionsbetrieb darstellen. Das Management suchte nach M{\"o}glichkeiten, den Produktionsfluß zu verbessern, ohne teure technische {\"A}nderungen am System vornehmen zu m{\"u}ssen. Eine Forschungsgruppe des Konrad--Zuse--Zentrums f{\"u}r Informationstechnik (die ehemals an der Universit{\"a}t Augsburg ans{\"a}ssig war) analysierte, unterst{\"u}tzt von einigen Studenten und Ingenieuren der SNI, den Produktionsfluß und lokalisierte Schwachstellen. Basierend auf diesen Erkenntnissen wurden mathematische Fragestellungen erarbeitet und auf mathematischen Optimierungsverfahren basierende Softwarepakete entwickelt, die jetzt teilweise bei SNI im Einsatz sind. Im folgenden werden einige dieser Fragestellungen, deren Modellierung und mathematische Behandlung beschrieben. Einige der Ans{\"a}tze, die hier dargestellt werden sollen, sind teilweise schon in Gr{\"o}tschel [Gr{\"o}92] angesprochen worden.}, language = {de} } @misc{BrandFreedenFroehlich1995, author = {Brand, R{\"u}diger and Freeden, Willi and Fr{\"o}hlich, Jochen}, title = {An Adaptive Hierarchical Approximation Method on the Sphere Using Axisymmetric Locally Supported Basis Functions}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-1682}, number = {SC-95-02}, year = {1995}, abstract = {The paper discusses the approximation of scattered data on the sphere which is one of the major tasks in geomathematics. Starting from the discretization of singular integrals on the sphere the authors devise a simple approximation method that employs locally supported spherical polynomials and does not require equidistributed grids. It is the basis for a hierarchical approximation algorithm using differently scaled basis functions, adaptivity and error control. The method is applied to two examples one of which is a digital terrain model of Australia.}, language = {en} } @misc{Koepf1995, author = {Koepf, Wolfram}, title = {Identities for Families of Orthogonal Polynomials and Special Functions}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-1675}, number = {SC-95-01}, year = {1995}, abstract = {In this article we present new results for families of orthogonal polynomials and special functions, that are determined by algorithmical approaches. In the first section, we present new results, especially for discrete families of orthogonal polynomials, obtained by an application of the celebrated Zeilberger algorithm. Next, we present algorithms for holonomic families \$f(n,x)\$ of special functions which possess a derivative rule. We call those families {\sl admissible}. A family \$f(n,x)\$ is holonomic if it satisfies a holonomic recurrence equation with respect to \$n\$, and a holonomic differential equation with respect to \$x\$, i.\ e. linear homogeneous equations with polynomial coefficients. The rather rigid property of admissibility has many interesting consequences, that can be used to generate and verify identities for these functions by linear algebra techniques. On the other hand, many families of special functions, in particular families of orthogonal polynomials, are admissible. We moreover present a method that generates the derivative rule from the holonomic representation of a holonomic family. \% whenever one exists. As examples, we find new identities for the Jacobi polynomials and for the Whittaker functions, and for families of discrete orthogonal polynomials by the given approach. Finally, we present representations for the parameter derivatives of the Gegenbauer and the generalized Laguerre polynomials.}, language = {en} } @misc{SchmidtMaerz1995, author = {Schmidt, Frank and M{\"a}rz, Reinhard}, title = {On the Reference Wave Vector pf Paraxial Helmholtz Equations}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-1660}, number = {SC-94-38}, year = {1995}, abstract = {The reference wave vector of the paraxial Helmholtz equation is determined using various strategies which result all in similar expressions. The effort for its evaluation is so small that the reference wave vector can be adapted for each propagation step of an arbitrary BPM-algorithm.}, language = {en} }