Walter Krämer, Hans-jürgen Buhl, Fachbereich Mathematik, ...
6 Die Standard-Template-Library (STL) 47
Concept Graphs as Semantic Structures for Contextual Judgment Logic (2008)
Rudolf Wille, Fachbereich Mathematik
Abstract. This paper presents a mathematization of the philosophical doctrine of judgments as an extension of the mathematization of the philosophical doctrine of concepts developed in Formal Concept...
EXISTENTIALLY CLOSED GROUPS IN SPECIFIC CLASSES (2008)
Felix Leinen, Fachbereich Mathematik
Abstract. This survey article is supposed to make the reader familiar with the algebraic structure of existentially closed groups in specific group classes, and with the ideas and methods involved in...
Dieter Spreen, Fachbereich Mathematik
We present a purely domain-theoretic model of Coquand and Huet’s Calculus of Construction [3], which is one of the most powerful type systems proposed in the literature. The well-formed expressions...
V. Levandovskyy, Fachbereich Mathematik
The aim of this poster is to demonstrate different aspects (from theoretical background to practical usefulness) of the algorithms, implemented in the computer algebra system SINGULAR::PLURAL (or...
Nested Concept Graphs with Cuts: (2008)
Mathematical Foundations Frithjof, Frithjof Dau, Joachim Hereth Correia, Fachbereich Mathematik
Conceptual graphs (CGs) have been developed as a graphic representation system for logic with the very goal to be humanly readable and understandable. They are designed to serve in di#erent fields,...
Concept Graphs without Negations: Standardmodels and Standardgraphs Frithjof Dau (2008)
Frithjof Dau, Fachbereich Mathematik
In this article, we provide di#erent possibilities for doing reasoning on simple concept(ual) graphs without negations or nestings. First of all, we have on the graphs the usual semantical entailment...
Michael Hinze, Fachbereich Mathematik
Minimal surfaces bounded by a polygon \Gamma ae IR q (q 2) correspond in a one-to-one mannner to the critical points of Shiffman's function \Theta. For arbitrary, but fixed polygons this...
Knot Removal for B-Spline Curves 1 (2007)
Matthias Eck, Jan Hadenfeld, Fachbereich Mathematik
In the present paper the problem of removing one inner knot from the knot sequence of a B-spline curve is discussed. Doing so, a local (geometric) construction of the new control points from the...
J.W. Goethe-Universitat (2007)
Lars Grune, Fachbereich Mathematik
Abstract: We consider numerical one-step approximations of ordinary differential equations and present two results on the persistence of attractors appearing in the numerical system. First, we show...
The Quantum Zero Space Charge Model for Semiconductors (2007)
Andreas Unterreiter Fachbereich, Andreas Unterreiter, Fachbereich Mathematik
The thermal equilibrium state of a bipolar, isothermal quantum fluid confined to a bounded domain\Omega ae IR d ; d = 1; 2 or d = 3 is the minimizer of the total energy E ffl ; E ffl involves the...
Computation of Maximal Reachability Submodules (2007)
Wiland Schmale, Fachbereich Mathematik
A new and conceptually simple procedure is derived for the computation of the maximal reachability submodule of a given submodule of the state space of a linear discrete time system over a Noethenian...
Function Spaces for Uniformly Locally Bounded Quasi-Uniform Spaces (2007)
Philipp Sunderhauf Fachbereich, Fachbereich Mathematik
In a previous paper [Sun95b], we described a function space constructor for complete totally bounded quasi-uniform spaces. The present paper generalizes this construction to the wider class of...
Growth and Range Conditions for the Laplace Representation of Vector-valued Functions (2007)
Edlyn Teske Fachbereich, Edlyn Teske, Fachbereich Mathematik, Tu Berlin, Lutz Weis
this paper we present vector-valued theorems of this kind, e. g. Theorem 1.1 Let X be a Banach space and let 1 p 1. Let 0 M ! 1. Then for every C
Continuous and Inverse Shadowing (2007)
P. E. Kloeden, Fachbereich Mathematik, J. Ombach, A. V. Pokrovskii
By the Shadowing Lemma we can shadow any sufficient accurate pseudo--trajectory of a hyperbolic system by a true trajectory of a hyperbolic system. If we are interested in finite trajectories, at...
The Quantum Zero Space Charge Model for Semiconductors (2007)
Andreas Unterreiter, Fachbereich Mathematik
The thermal equilibrium state of a bipolar, isothermal quantum fluid confined to a bounded domain\Omega ae IR d ; d = 1; 2 or d = 3 is the minimizer of the total energy E ffl ; E ffl involves the...
The Quantum Zero Space Charge Model for Semiconductors (2007)
Andreas Unterreiter, Fachbereich Mathematik
The thermal equilibrium state of a bipolar, isothermal quantum fluid confined to a bounded domain\Omega ae IR d ; d = 1; 2 or d = 3 is the minimizer of the total energy E ffl ; E ffl involves the...
Stochastic Symmetry-Breaking In A Gaussian Hopfield-Model (2007)
Anton Bovier, Fachbereich Mathematik
: We study a "two-pattern" Hopfield model with Gaussian disorder. We find that there are infinitely many pure states at low temperatures in this model, and we find that the metastate is...
Volkmar Welker, Fachbereich Mathematik, In C
partitions and a generalization of the braid arrangement
Supported by HCM-grant no. ERBCHBGCT930421 while spending the academic year 1994-95 (2007)
R. Hofstad, F. Hollander, W. Konig, Mathematisch Instituut, Mathematisch Instituut, Fachbereich Mathematik
The Edwards model in one dimension is a transformed path measure for standard Brownian motion discouraging self-intersections. We prove a central limit theorem for the endpoint of the path, extending...
Le Numbers of Arrangements and Matroid Identities (2007)
David B. Massey, Rodica Simion, Richard P. Stanley, Dirk Vertigan, Gunter M. Ziegler, ...
We present several new polynomial identities associated with matroids and geometric lattices, and relate them to formulas for the characteristic polynomial and the Tutte polynomial. The identities...
On nodal solutions to generalized Emden-Fowler equations (2007)
Tobias Weth, Fachbereich Mathematik, Staudinger Weg, Ru L
We introduce a new variational method in order to derive results concerning existence and nodal properties of solutions to superlinear equations, and we focus on applications to the equation...
Classical Logic, Continuation Semantics and Abstract Machines Th. STREICHER (2007)
Fachbereich Mathematik, B. Reus
One of the goals of this paper is to demonstrate that denotational semantics is useful for operational issues like implementation of functional languages by abstract machines. This is exemplified in...
Denotational Completeness Revisited (2007)
Thomas Streicher, Fachbereich Mathematik, Tu Darmstadt
We define a notion of Kripke logical predicate for models of classical linear logic. A Kripke logical predicate on a type A will be a set of generalised elements of A satisfying certain closure...
Bernd Groh, Rudolf Wille, Fachbereich Mathematik
Abstract. TOSCANA is a computer program which allows an online interaction with data bases to analyse and explore data conceptually. Such interaction uses conceptual data systems which are based on...
Otto-von-Guericke-Universitat (2007)
W. Willems, Fachbereich Mathematik, Fakultat Fur Mathematik
Let A and B be stochastic matrices of the same type (n; n). It is natural to consider perturbations A(t) of A of the form A(t) = (1 \Gamma t)A + tB (0 t 1): Now, the following two questions come up...
Reiner Lauterbach, Fachbereich Mathematik
Abstract. We would like to discuss some aspects of forced symmetry breaking in equivariant systems. This topic is of signicance for applications since in real life systems symmetries occur only as...
Convergent Semidiscretization of a Nonlinear Fourth Order Parabolic System (2007)
Ansgar J Ungel, Fachbereich Mathematik
A semidiscretization in time of a fourth order nonlinear parabolic system in several space dimensions arising in quantum semiconductor modelling is studied. The system is numerically treated by...
Regression Fixed Point Clusters: Motivation, Consistency and Simulations (2007)
Christian Hennig, Fachbereich Mathematik
In this paper, the theoretical foundation of Least Squares-Fixed Point Clusters for clusterwise linear regression is given in full detail, as well as a discussion of the computation and application...
Categorical Models of Constructive Logic (2007)
Thomas Streicher Fachbereich, Thomas Streicher, Fachbereich Mathematik, Tu Darmstadt
Introduction If asked why one should be interested in constructive (intuitionistic) logic besides saying that it is a nice subject that makes a lot of fun I could give the following two more serious...
Thomas Streicher Fachbereich, Thomas Streicher, Fachbereich Mathematik, Tu Darmstadt
We discuss a notion of universe in toposes which from a logical point of view gives rise to an extension of Higher Order Intuitionistic Arithmetic (HAH) that allows one to construct families of types...
Pavel Valtr, Pavel Valtr, Fachbereich Mathematik, Martin Klazar, Martin Klazar, Martin Klazar
The extremal function Ex(u; n) (introduced in the theory of DavenportSchinzel sequences in other notation) denotes for a fixed finite alternating sequence u = ababa: : : the maximum length of a...
Regularized Fixed-Point Iterations for Nonlinear Inverse Problems (2005)
S. S. Pereverzyev, R. Pinnau, N. Siedow, Fachbereich Mathematik
In this paper we introduce a derivative-free, iterative method for solving nonlinear illposed problems F x = y, where instead of y noisy data yδ with �y − yδ � ≤ δ are given and F: D(F)...
Variables in Concept Graphs (2005)
Frithjof Dau, Fachbereich Mathematik
A main feature of many logics used in computer science is a means to express quantification. Usually, syntactical devices like variables and quantifiers are used for this purpose. In contrast to...
M.: Geometric Reasoning with polymake (2005)
Ewgenij Gawrilow, Michael Joswig, Fachbereich Mathematik, Tu Darmstadt
The mathematical software system polymake provides a wide range of functions for convex polytopes, simplicial complexes, and other objects. A large part of this paper is dedicated to a tutorial which...
Types and Tokens for Logic with Diagrams (2004)
Frithjof Dau, Fachbereich Mathematik
It is well accepted that diagrams play a crucial role in human reasoning. But in mathematics, diagrams are most often only used for visualizations, but it is doubted that diagrams are rigor enough to...
Multiple Precision Interval Packages: Comparing Different Approaches (2003)
École Normale, Supérieure Lyon, M. Grimmer, K. Petras, N. Revol, M. Grimmer, ...
We give a survey on packages for multiple precision interval arithmetic, with the main focus on three specific packages. One is within a Maple environment, intpakX, and two are C/C++ libraries,...
From Formal Concept Analysis (2003)
To Contextual Logic, Frithjof Dau, Julia Klinger, Fachbereich Mathematik
A main goal of Formal Concept Analysis from its very beginning has been the support of rational communication. The source of this goal lies in our understanding of mathematics as a science which...
N. Sidorova, Fachbereich Mathematik, O. G. Smolyanov, O. Wittich
We construct the surface measure on the space C([0, 1], M) of paths in a compact Riemannian manifold M without boundary embedded into R n which is induced by the usual flat Wiener measure on C([0,...
Reverse Pivoting in Conceptual Information Systems (2001)
Jo Hereth, Gerd Stumme, Fachbereich Mathematik
Abstract. In database marketing, the behavior of customers is analyzed by studying the transactions they have performed. In order to get a global picture of the behavior of a customer, his single...
CEM - a Conceptual Email Manager (2000)
Richard Cole, Gerd Stumme, Fachbereich Mathematik
Abstract. CEM is an email management system which stores its email in a concept lattice rather than in the usual tree structure. By using such a conceptual multi-hierarchy, the system provides more...
The Largest Cartesian Closed Category of Domains, Considered Constructively (2000)
Dieter Spreen, Fachbereich Mathematik, Theoretische Informatik
A conjecture of Smyth [10] is discussed which says that if D and [D # D] are e#ectively algebraic directedcomplete partial orders with least element (cpo's), then D is an e#ectively strongly...
An Annotated Bibliography of Multiobjective Combinatorial Optimization (2000)
Xavier G, Multiobjective Combinatorial, Matthias Ehrgott, Matthias Ehrgott, Fachbereich Mathematik, Xavier Gandibleux, ...
This paper provides an annotated bibliography of multiple objective combinatorial optimization, MOCO. We present a general formulation of MOCO problems, describe the main characteristics of MOCO...
Conceptual Knowledge Discovery and Data Analysis (2000)
Joachim Hereth, Gerd Stumme, Rudolf Wille, Uta Wille, Fachbereich Mathematik
Abstract. In this paper, we discuss Conceptual Knowledge Discovery in Databases (CKDD) in its connection with Data Analysis. Our approach is based on Formal Concept Analysis, a mathematical theory...
Inductive Construction of Repletion (1999)
Thomas Streicher, Fachbereich Mathematik, Th Darmstadt
In [2] Martin Hyland has proposed the notion of "S-replete object " relative to a given object S as the appropriate generalisation of predomain for the purposes of
Bifurcations of one-dimensional stochastic differential equations (1999)
Hans Crauel, Fachbereich Mathematik, Sekr Ma, Peter Imkeller, Marcus Steinkamp
We consider families of random dynamical systems induced by parametrized one dimensional stochastic differential equations. We give necessary and sufficient conditions on the invariant measures of...
Numerical Solution of Second Order Stochastic Fluid Models (1999)
Andrea Zisowsky, Fachbereich Mathematik, Katinka Wolter
In this paper a numerical method to solve second order stochastic uid models is presented. Starting with the system of dierential equations underlying the stochastic process a -method is discussed....
A Positivity-preserving Numerical Scheme for a Nonlinear Fourth Order Parabolic System (1999)
Ansgar Jüngel, René Pinnau, Fachbereich Mathematik
A positivity{preserving numerical scheme for a fourth order nonlinear parabolic system arising in quantum semiconductor modelling is studied. The system is numerically treated by introducing an...
A Positivity{preserving Numerical Scheme for a Nonlinear Fourth Order Parabolic System (1999)
Ansgar Ungel Fachbereich, Ansgar J Ungel, Fachbereich Mathematik
A positivity{preserving numerical scheme for a fourth order nonlinear parabolic system arising in quantum semiconductor modelling is studied. The system is numerically treated by introducing an...
Bifurcation of One--Dimensional Stochastic Differential Equation (1999)
Hans Crauel, Fachbereich Mathematik, Sekr Ma, Peter Imkeller, Marcus Steinkamp
We consider families of random dynamical systems induced by parametrized one dimensional stochastic differential equations. We give necessary and sufficient conditions on the invariant measures of...
Zonotopes Associated with Higher Bruhat Orders (1999)
Stefan Felsner, Günter M. Ziegler, Fachbereich Mathematik
The higher Bruhat orders B(n, k) are combinatorially defined partial orders (and hence graphs) that "look like" the graphs of (n k)-dimensional zonotopes -- and they are, for small...
Bifurcation of One-Dimensional Stochastic Differential Equation (1999)
Hans Crauel, Fachbereich Mathematik, Sekr Ma, Peter Imkeller, Marcus Steinkamp
We consider families of random dynamical systems induced by parametrized one dimensional stochastic differential equations. We give necessary and sufficient conditions on the invariant measures of...
Zero-relaxation-time limits in hydrodynamic models for plasmas revisited (1999)
Yue-jun Peng, Fachbereich Mathematik, Strasse Des Juni
Abstract A rigorous proof of the zero-relaxation-time limits in the hydrodynamic equations for plasmas is given. The equations consist of the Euler equations for the electrons and/or ions coupled...
Semidefinite Relaxations for Parallel Machine Scheduling (1998)
Martin Skutella, Fachbereich Mathematik
We consider the problem of scheduling unrelated parallel machines so as to minimize the total weighted completion time of jobs. Whereas the best previously known approximation algorithms for this...
Concept Exploration - A Tool for Creating and Exploring Conceptual Hierarchies (1997)
Gerd Stumme, Fachbereich Mathematik
. Concept exploration is a knowledge acquisition tool for interactively exploring the hierarchical structure of finitely generated lattices. Applications comprise the support of knowledge engineers...
Weber's Problem with attraction and repulsion under Polyhedral Gauges (1997)
Stefan Nickel, Fachbereich Mathematik, Eva-Maria Dudenhöffer
Given a finite set of points in the plane and a forbidden region R, we want to find a point X 62 int(R), such that the weighted sum to all given points is minimized. This location problem is a...
Topological Equivalence of Tilings (1997)
Johannes Kellendonk, Fachbereich Mathematik, At Berlin
. We introduce a notion of equivalence on tilings which is formulated in terms of their local structure. We compare it with the known concept of locally deriving one tiling from another and show that...
Michael Neumann Weierstra, Michael H. Neumann, Rainer Von Sachs, Fachbereich Mathematik
. We derive minimax rates for estimation in anisotropic smoothness classes. This rate is attained by a coordinatewise thresholded wavelet estimator based on a tensor product basis with separate scale...
Conceptual Graphs and Formal Concept Analysis (1997)
Rudolf Wille, Fachbereich Mathematik
. It is shown how Conceptual Graphs and Formal Concept Analysis may be combined to obtain a formalization of Elementary Logic which is useful for knowledge representation and processing. For this, a...
On a generalization of Extended Resolution (1997)
O. Kullmann, Fachbereich Mathematik
Motivated by improved SAT algorithms ([13, 14, 15]; yielding new worst case upper bounds) a natural parameterized generalization GER of Extended Resolution (ER) is introduced. ER can simulate...
On error estimates for the Trotter-Kato product formula (1997)
H. Neidhardt, Fachbereich Mathematik, V. A. Zagrebnov
We study the error bound in the operator norm topology for the Trotter exponential product formula as well as for its generalization `a la Kato. In the frame of the abstract setting we give a simple...
Symbolic Objects in Formal Concept Analysis (1997)
Susanne Prediger, Fachbereich Mathematik
. Symbolic objects are the basic elements for knowledge representation in symbolic data analysis. This paper aims to integrate symbolic objects into formal concept analysis in order to compare and...
Logical Scaling in Formal Concept Analysis (1997)
Susanne Prediger, Fachbereich Mathematik
. Logical scaling is a new method to transform data matrices which are based on object-attribute-value-relationships into data matrices from which conceptual hierarchies can be explored. The...
Note on shortest and nearest lattice vectors (1997)
Martin Henk, Fachbereich Mathematik
We show that with respect to a certain class of norms the so called shortest lattice vector problem is polynomial-time Turing (Cook) reducible to the nearest lattice vector problem. This gives a...
The Concept Classification of a Terminology Extended by Conjunction and Disjunction (1996)
Gerd Stumme, Fachbereich Mathematik
this paper we show how a classification algorithm providing still more information can be obtained by choosing another acquisition tool of formal concept analysis. Much work has been done to develop...
Local Scaling in Conceptual Data Systems (1996)
Gerd Stumme, Fachbereich Mathematik
this paper we present the technique of local scaling, where only concepts of the outer scale, which are differentiated further by the inner scale, are refined. This is also called dynamic scaling,...
Martin Hofmann, Wolfgang Naraschewski, Martin Steffen, Terry Stroup, Fachbereich Mathematik
The Curry--Howard isomorphism, a fundamental property shared by many type theories, establishes a direct correspondence between programs and proofs. This suggests that the same structuring principles...
A note on a generalization of Extended Resolution (1996)
O. Kullmann, Fachbereich Mathematik
Motivated by improved SAT algorithms ([Ku96], [KuLu96]; yielding new worst case upper bounds) a natural parametrized generalization GER of Extended Resolution (ER) is introduced. ER can simulate...
The Strength of the CCITT/ISO Hash Function (1996)
Achim Jung, Fachbereich Mathematik
The attack against CCITT recommendation X.509 (ISO IS 95948) by Don Coppersmith is described and analyzed in detail. General principles for hash functions are presented and discussed. An enhancement...
Locating Least-Distant Lines in the Plane (1996)
Anita Schöbel, Fachbereich Mathematik
: In this paper we deal with locating a line in the plane. If d is a distance measure our objective is to find a straight line l which minimizes f(l) = M X m=1 wmd(Exm
Conceptual Structures of Multicontexts (1996)
Rudolf Wille, Fachbereich Mathematik
. Formal Concept Analysis is based on a formalization of context. Since there are situations where the consideration of one context is not sufficient, it is desirable to introduce a formalization of...
Multicriteria Network Location Problems with Sum Objectives (1996)
Horst W. Hamacher, Martine Labbe, Stefan Nickel, Fachbereich Mathematik, Fachbereich Mathematik
In this paper network location problems with several objectives are discussed, where every single objective is a classical median objective function. We will look at the problem of finding Pareto...
Exploration Tools in Formal Concept Analysis (1995)
Gerd Stumme, Fachbereich Mathematik
The development of conceptual knowledge systems specifically requests knowledge acquistion tools within the framework of Formal Concept Analysis. In this paper, the existing tools are presented, and...
Knowledge Acquisition by Distributive Concept Exploration (1995)
Gerd Stumme, Fachbereich Mathematik
this paper is devoted to the discussion of this tool. The main difference between Concept Exploration and Distributive Concept Exploration lies in the treatment of joins. While the meet corresponds...
A Geometrical Heuristic for Drawing Concept Lattices (1995)
Gerd Stumme, Rudolf Wille, Fachbereich Mathematik
. Concept lattices are used in formal concept analysis to represent data conceptually so that the original data are still recognizable. Their line diagrams should reflect the semantical relationships...
Integer Groups of Coinvariants Associated to Octagonal Tilings (1995)
Johannes Kellendonk, Fachbereich Mathematik, At Berlin
. The integer groups of coinvariants associated to undecorated and decorated octagonal tilings are computed. Introduction A tiling T defines a topological groupoid R whose continuous groupoid...
Function Spaces for Uniformly Locally Bounded Quasi-Uniform Spaces (1995)
Philipp Sünderhauf, Fachbereich Mathematik
In a previous paper [Sun95b], we described a function space constructor for complete totally bounded quasi-uniform spaces. The present paper generalizes this construction to the wider class of...
Semicontinuity for representations of one-dimensional Cohen-Macaulay Rings (1995)
Y.A. Drozd, Fachbereich Mathematik
this paper is to refine them in such a way that they could be applied to non--commutative Cohen--Macaulay algebras, too. For this purpose we introduce the notion of "dense subrings" which...
Consistency for Non-Linear Functions of the Periodogram of Tapered Data (1995)
Daniel Janas, Rainer Von Sachs, Fachbereich Mathematik
In this paper we investigate the merits of using a data taper in non--linear functionals of the periodogram of a stationary time series. To this end, we show consistency for a general class of...
“Algebraic Combinatorics ” network (CHRX-CT93-0400) (1995)
Günter M. Ziegler, Jürgen Richter-gebert, Martin Henk, Eva Maria Feichtner, Ulrich Hund, Jörg Rambau, ...
Supported by the
Control and Estimation of the Boundary Heat Transfer Function in Stefan Problems (1994)
V. Barbu, K. Kunisch, Fachbereich Mathematik, W. Ring
An approximation procedure for the identification of a nonlinear boundary heat transfer function in a one phase Stefan problem is presented. Alternatively the problem can be viewed as constructing a...
Constructing a Quasi-Uniform Function Space (1993)
Philipp Sünderhauf, Fachbereich Mathematik
This paper attacks the problem of constructing function spaces for a convenient class of quasi-uniform spaces. As, for the sake of completeness, multi-valued functions have to be considered, we...
Martin Klazar, Pavel Valtr, Martin Klazar, Pavel Valtr, Fachbereich Mathematik, ...
3 The extremal function Ex(u, n) (introduced in the theory of Davenport-Schinzel sequences in other notation) denotes for a fixed finite alternating sequence u = ababa... the maximum length of a...
Michael Hanke, Fachbereich Mathematik, Inmaculada Higueras-sanz
Abstract In an earlier paper [12] we were able to show the existence of asymptotic expansions for the solutions of some regularization procedures fo r higher index differential-algebraic equations in...
Power Series in Computer Algebra WOLFRAM KOEPF (1991)
Formal power series (FPS) of the form ak(x − x0) k=0 k are important in calculus and complex analysis. In some Computer Algebra Systems (CASs) it is possible to define an FPS by direct or recursive...
Relational Constructions on Semiconcept Graphs
Silke Pollandt, Fachbereich Mathematik
The aim of the paper is to develop a logic of relations on semiconcept graphs corresponding to the Contextual Logic of Relations on power context families. Semiconcept graphs allow the representation...
Zonotopes Associated with Higher Bruhat Orders
Stefan Felsner, Günter M. Ziegler, Fachbereich Mathematik
The higher Bruhat orders B(n; k) are combinatorially defined partial orders (and hence graphs) that "look like" the graphs of (n k)-dimensional zonotopes -- and they are, for small...
Background Knowledge in Concept Graphs
Frithjof Dau, Fachbereich Mathematik
Traditional logic can be understood as the investigation of the three main essential functions of thinking -- concepts, judgements and conclusions.