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Tue, 25 Nov 2014 12:40:41 +0100Tue, 25 Nov 2014 12:40:41 +0100Numerical solution of a nonstandard Darcy flow model
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/3933
We consider a Darcy flow model with saturation-pressure relation extended
with a dynamic term, namely, the time derivative of the saturation.
This model was proposed in works of J.Hulshof and J.R.King (1998), S.M.Hassanizadeh and W.G.Gray (1993),
F.Stauffer (1978).
We restrict ourself to one spatial dimension and strictly positive
initial saturation. For this case we transform the initial-boundary value
problem into combination of elliptic boundary-value problem and initial
value problem for abstract Ordinary Differential Equation. This splitting
is rather helpful both for theoretical aspects and numerical methods.Vsevolod Laptevstudythesishttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/3933Tue, 25 Nov 2014 12:40:41 +0100Construction of Moduli Spaces for Space Curve Singularities of Multiplicity 3
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1257
Anne Frühbis-Krügerpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1257Thu, 31 May 2001 00:00:00 +0200Spektralsequenzen
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/755
Das Lehrskript "Spektralsequenzen" fuehrt die Begriffe der exakten und abgeleiteten Paare sowie der Spektralsequenzen in der Kategorie der m-graduierten Moduln ein. Naeher betrachtet werden die Begriffe dann fuer Doppelkomplexe mit Filtrationen.Mathias Schulzepreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/755Tue, 13 Mar 2001 00:00:00 +0100Monodromie von Differentialgleichungen
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/857
Einführung und Grundlagen. SS 1996 und WS 1996/7.Mathias Schulzelecturehttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/857Tue, 13 Mar 2001 00:00:00 +0100Computation of the Monodromy of an Isolated Hypersurface Singularity
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1146
This thesis deals with the implementation of an algorithm to compute the monodromy of an isolated hypersurface singularity in the computer algebra system Singular.Mathias Schulzediplomhttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1146Tue, 13 Mar 2001 00:00:00 +0100Some Applications of Impulse Control in Mathematical Finance
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1143
We consider three applications of impulse control in financial mathematics, a cash management problem, optimal control of an exchange rate, and portfolio optimisation under transaction costs. We sketch the different ways of solving these problems with the help of quasi-variational inequalities. Further, some viscosity solution results are presented.Ralf Kornpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1143Wed, 04 Oct 2000 00:00:00 +0200Hyperplane transversals of homothetical, centrally symmetric polytopes
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1136
Let P c R^n, n >= 2, be a centrally symmetric, convex n-polytope with 2r vertices, and P be a family of m >= n + 1 homothetical copies of P. We show that a hyperplane transversal of all members of P (it it exists) can be found in O(rm) time.Horst Martini; Anita Schöbelpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1136Wed, 30 Aug 2000 00:00:00 +0200A Fuzzy Programming Approach to Multicriteria Facility Location Problems
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1124
Facility Location Problems are concerned with the optimal location of one or several new facilities, with respect to a set of existing ones. The objectives involve the distance between new and existing facilities, usually a weighted sum or weighted maximum. Since the various stakeholders (decision makers) will have different opinions of the importance of the existing facilities, a multicriteria problem with several sets of weights, and thus several objectives, arises. In our approach, we assume the decision makers to make only fuzzy comparisons of the different existing facilities. A geometric mean method is used to obtain the fuzzy weights for each facility and each decision maker. The resulting multicriteria facility location problem is solved using fuzzy techniques again. We prove that the final compromise solution is weakly Pareto optimal and Pareto optimal, if it is unique, or under certain assumptions on the estimates of the Nadir point. A numerical example is considered to illustrate the methodology.Matthias Ehrgott; Rakesh Vermapreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1124Tue, 29 Aug 2000 00:00:00 +0200Multicriteria Ordered Weber Problems
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1126
In this paper we deal with the determination of the whole set of Pareto-solutions of location problems with respect to Q general criteria.These criteria include median, center or cent-dian objective functions as particular instances.The paper characterizes the set of Pareto-solutions of a these multicriteria problems. An efficient algorithm for the planar case is developed and its complexity is established. Extensions to higher dimensions as well as to the non-convexcase are also considered.The proposed approach is more general than the previously published approaches to multi-criteria location problems and includes almost all of them as particular instances.Stefan Nickel; Justo Puerto; Antonio M. Rodriguez-Chiapreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1126Tue, 29 Aug 2000 00:00:00 +0200On value preserving and growth optimal portfolios
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1133
In a discrete-time financial market setting, the paper relates various concepts introduced for dynamic portfolios (both in discrete and in continuous time). These concepts are: value preserving portfolios, numeraire portfolios, interest oriented portfolios, and growth optimal portfolios. It will turn out that these concepts are all associated with a unique martingale measure which agrees with the minimal martingale measure only for complete markets.Ralf Korn; Manfred Schälpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1133Tue, 29 Aug 2000 00:00:00 +0200Value Preserving Strategies and a General Framework for Local Approaches to Optimal Portfolios
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1120
We present some new general results on the existence and form of value preserving portfolio strategies in a general semimartingale setting. The concept of value preservation will be derived via a mean-variance argument. It will also be embedded into a framework for local approaches to the problem of portfolio optimisation.Ralf Kornpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1120Mon, 28 Aug 2000 00:00:00 +0200Portfolio management and market risk quantification using neural networks
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1121
We discuss how neural networks may be used to estimate conditional means, variances and quantiles of nancial time series nonparametrically. These estimates may be used to forecast, to derive trading rules and to measure market risk.Jürgen Frankepreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1121Mon, 28 Aug 2000 00:00:00 +0200Discretizations for the Incompressible Navier-Stokes Equations based on the Lattice Boltzmann Method
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/652
A discrete velocity model with spatial and velocity discretization based on a lattice Boltzmann method is considered in the low Mach number limit. A uniform numerical scheme for this model is investigated. In the limit, the scheme reduces to a finite difference scheme for the incompressible Navier-Stokes equation which is a projection method with a second order spatial discretization on a regular grid. The discretization is analyzed and the method is compared to Chorin's original spatial discretization. Numerical results supporting the analytical statements are presented.Michael Junk; Axel Klarpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/652Sun, 25 Jun 2000 08:20:00 +0200Numerical Modeling of Gas Flows in the Transition between Rarefied and Continuum Regimes
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/631
In this paper we derive fluid dynamic equations byperforming asymptotic analysis for the generalized Boltzmann equationfor polyatomic gases. In particular, we consider the steady state,one-dimensional Boltzmann equation with one additional internal energyand different relaxation times. Moreover, we present a new approachto define coupling procedures for the Boltzmann equation and Navier-Stokesequations based on the 14-moments expansion of Levermore. These coupledmodels are validated by numerical simulations.M. Guenther; P. Le Tallec; J.P. Perlat; J. Struckmeierpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/631Sun, 25 Jun 2000 00:00:00 +0200A Pyramid Scheme for Spherical Wavelets
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/605
We consider a scale discrete wavelet approach on the sphere based on spherical radial basis functions. If the generators of the wavelets have a compact support, the scale and detail spaces are finite-dimensional, so that the detail information of a function is determined by only finitely many wavelet coefficients for each scale. We describe a pyramid scheme for the recursive determination of the wavelet coefficients from level to level, starting from an initial approximation of a given function. Basic tools are integration formulas which are exact for functions up to a given polynomial degree and spherical convolutions.Michael Schreinerpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/605Sat, 24 Jun 2000 00:00:00 +0200Moment inequalities for the Boltzmann equation and applications to spatially homogeneous problems
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/607
Some inequalities for the Boltzmann collision integral are proved. These inequalities can be considered as a generalization of the well-known Povzner inequality. The inequalities are used to obtain estimates of moments of solution to the spatially homogeneous Boltzmann equation for a wide class of intermolecular forces. We obtained simple necessary and sufficient conditions (on the potential) for the uniform boundedness of all moments. For potentials with compact support the following statement is proved. .....A.V. Bobylevpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/607Sat, 24 Jun 2000 00:00:00 +0200On analytic semigroups and cosine functions in Banach spaces
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/786
If \(A\) generates a bounded cosine function on a Banach space \(X\) then the negative square root \(B\) of \(A\) generates a holomorphic semigroup, and this semigroup is the conjugate potential transform of the cosine function. This connection is studied in detail, and it is used for a characterization of cosine function generators in terms of growth conditions on the semigroup generated by \(B\). This characterization relies on new results on the inversion of the vector-valued conjugate potential transform. Peter Vieten; Valentin Keyantuopreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/786Mon, 03 Apr 2000 00:00:00 +0200Min-Max Formulation of the Balance Number in Multiobjetive Global Optimization
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/515
The notion of the balance number introduced in [3,page 139] through a certain set contraction procedure for nonscalarized multiobjective global optimization is represented via a min-max operation on the data of the problem. This representation yields a different computational procedure for the calculation of the balance number and allows us to generalize the approach for problems with countably many performance criteria.Matthias Ehrgott; Efim A. Galperinpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/515Mon, 03 Apr 2000 00:00:00 +0200Wavelet Smoothing of Evolutionary Spectra by Non-Linear Thresholding
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/534
We consider wavelet estimation of the time-dependent (evolutionary) power spectrum of a locally stationary time series. Allowing for departures from stationary proves useful for modelling, e.g., transient phenomena, quasi-oscillating behaviour or spectrum modulation. In our work wavelets are used to provide an adaptive local smoothing of a short-time periodogram in the time-freqeuncy plane. For this, in contrast to classical nonparametric (linear) approaches we use nonlinear thresholding of the empirical wavelet coefficients of the evolutionary spectrum. We show how these techniques allow for both adaptively reconstructing the local structure in the time-frequency plane and for denoising the resulting estimates. To this end a threshold choice is derived which is motivated by minimax properties w.r.t. the integrated mean squared error. Our approach is based on a 2-d orthogonal wavelet transform modified by using a cardinal Lagrange interpolation function on the finest scale. As an example, we apply our procedure to a time-varying spectrum motivated from mobile radio propagation.Rainer von Sachs; Kai Schneiderarticlehttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/534Mon, 03 Apr 2000 00:00:00 +0200A short note on functions of bounded semivariation and countably additive vector measures
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/759
In the scalar case one knows that a complex normalized function of boundedvariation \(\phi\) on \([0,1]\) defines a unique complex regular Borel measure\(\mu\) on \([0,1]\). In this note we show that this is no longer true in generalin the vector valued case, even if \(\phi\) is assumed to be continuous. Moreover, the functions \(\phi\) which determine a countably additive vectormeasure \(\mu\) are characterized.Peter Vietenarticlehttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/759Mon, 03 Apr 2000 00:00:00 +0200Two equivalent norms for vector-valued holomorphic functions
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/769
The following two norms for holomorphic functions \(F\), defined on the right complex half-plane \(\{z \in C:\Re(z)\gt 0\}\) with values in a Banach space \(X\), are equivalent:
\[\begin{eqnarray*} \lVert F \rVert _{H_p(C_+)} &=& \sup_{a\gt0}\left( \int_{-\infty}^\infty \lVert F(a+ib) \rVert ^p \ db \right)^{1/p}
\mbox{, and} \\ \lVert F \rVert_{H_p(\Sigma_{\pi/2})} &=& \sup_{\lvert \theta \lvert \lt \pi/2}\left( \int_0^\infty \left \lVert F(re^{i \theta}) \right \rVert ^p\ dr \right)^{1/p}.\end{eqnarray*}\] As a consequence, we derive a description of boundary values ofsectorial holomorphic functions, and a theorem of Paley-Wiener typefor sectorial holomorphic functions.Peter Vietenarticlehttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/769Mon, 03 Apr 2000 00:00:00 +0200Characterization of operators of positive scalar type
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/787
Let \(X\) be a Banach lattice. Necessary and sufficient conditions for a linear operator \(A:D(A) \to X\), \(D(A)\subseteq X\), to be of positive \(C^0\)-scalar type are given. In addition, the question is discussed which conditions on the Banach lattice imply that every operator of positive \(C^0\)-scalar type is necessarily of positive scalar type.Peter Vietenarticlehttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/787Mon, 03 Apr 2000 00:00:00 +0200On an implementation of standard bases and syzygies in SINGULAR
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/461
Hubert Grassmann; Gert-Martin Greuel; Bernd Martin; W. Neumann; Gerhard Pfister; W. Pohl; Hans Schönemann; Thomas Siebertpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/461Mon, 03 Apr 2000 00:00:00 +0200A Proposal for Syntactic Data Integration for Math Protocols
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/462
The problem of providing connectivity for a collection of applications is largely one of data integration: the communicating parties must agree on thesemantics and syntax of the data being exchanged. In earlier papers [#!mp:jsc1!#,#!sg:BSG1!#], it was proposed that dictionaries of definitions foroperators, functions, and symbolic constants can effectively address the problem of semantic data integration. In this paper we extend that earlier work todiscuss the important issues in data integration at the syntactic level and propose a set of solutions that are both general, supporting a wide range of dataobjects with typing information, and efficient, supporting fast transmission and parsing.Olaf Bachmann; Hans Schönemannpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/462Mon, 03 Apr 2000 00:00:00 +0200Effective Simplification of CR expressions
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/463
Chains of Recurrences (CRs) are a tool for expediting the evaluation of elementary expressions over regular grids. CR based evaluations of elementaryexpressions consist of 3 major stages: CR construction, simplification, and evaluation. This paper addresses CR simplifications. The goal of CRsimplifications is to manipulate a CR such that the resulting expression is more efficiently to evaluate. We develop CR simplification strategies which takethe computational context of CR evaluations into account. Realizing that it is infeasible to always optimally simplify a CR expression, we give heuristicstrategies which, in most cases, result in a optimal, or close-to-optimal expressions. The motivations behind our proposed strategies are discussed and theresults are illustrated by various examples.Olaf Bachmannpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/463Mon, 03 Apr 2000 00:00:00 +0200