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- Case Based Reasoning (4)
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Programs are linguistic structures which contain identifications of individuals: memory locations, data types, classes, objects, relations, functions etc. must be identified selectively or definingly. The first part of the essay which deals with identification by showing and designating is rather short, whereas the remaining part dealing with paraphrasing is rather long. The reason is that for an identification by showing or designating no linguistic compositions are needed, in contrast to the case of identification by paraphrasing. The different types of functional paraphrasing are covered here in great detail because the concept of functional paraphrasing is the foundation of functional programming. The author had to decide whether to cover this subject here or in his essay Purpose versus Form of Programs where the concept of functional programming is presented. Finally, the author came to the conclusion that this essay on identification is the more appropriate place.

In system theory, state is a key concept. Here, the word state refers to condition, as in the example Since he went into the hospital, his state of health worsened daily. This colloquial meaning was the starting point for defining the concept of state in system theory. System theory describes the relationship between input X and output Y, that is, between influence and reaction. In system theory, a system is something that shows an observable behavior that may be influenced. Therefore, apart from the system, there must be something else influencing and observing the reaction of the system. This is called the environment of the system.

In this paper we study a particular class of \(n\)-node recurrent neural networks (RNNs).In the \(3\)-node case we use monotone dynamical systems theory to show,for a well-defined set of parameters, that,generically, every orbit of the RNN is asymptotic to a periodic orbit.Then, within the usual 'learning' context of NeuralNetworks, we investigate whether RNNs of this class can adapt their internal parameters soas to 'learn' and then replicate autonomously certain external periodic signals.Our learning algorithm is similar to identification algorithms in adaptivecontrol theory. The main feature of the adaptation algorithm is that global exponential convergenceof parameters is guaranteed. We also obtain partial convergence results in the \(n\)-node case.

In this paper we present a domain decomposition approach for the coupling of Boltzmann and Euler equations. Particle methods are used for both equations. This leads to a simple implementation of the coupling procedure and to natural interface conditions between the two domains. Adaptive time and space discretizations and a direct coupling procedure leads to considerable gains in CPU time compared to a solution of the full Boltzmann equation. Several test cases involving a large range of Knudsen numbers are numerically investigated.

Application of Moment Realizability Criteria for Coupling of the Boltzmann and Euler Equations
(1998)

The moment realizability criteria have been used to test the domains of validity of the Boltzmann and Euler Equations. With the help of this criteria teh coupling of the Boltzmann and Euler equations have been performed in two dimensional spatial space. The time evolution of domain decompositions for such equations have been presented in different time steps. The numerical resulta obtained from the coupling code have been compared with those from the pure Boltzmann one.

We present a particle method for the numerical simulation of boundary value problems for the steady-state Boltzmann equation. Referring to some recent results concerning steady-state schemes, the current approach may be used for multi-dimensional problems, where the collision scattering kernel is not restricted to Maxwellian molecules. The efficiency of the new approach is demonstrated by some numerical results obtained from simulations for the (two-dimensional) BEnard's instability in a rarefied gas flow.

The paper studies differential and related properties of functions of a real variable with values in the space of signed measures. In particular the connections between different definitions of differentiability are described corresponding to different topologies on the measures. Some conditions are given for the equivalence of the measures in the range of such a function. These conditions are in terms of socalled logarithmic derivatives and yield a generalization of the Cameron-Martin-Maruyama-Girsanov formula. Questions of this kind appear both in the theory of differentiable measures on infinite-dimensional spaces and in the theory of statistical experiments.

We report on the exchange bias effect as a function of the in-plane direction of the applied field in twofold symmetric, epitaxial Ni 80 Fe 20 /Fe 50 Mn 50 bilayers grown on Cu~110! single-crystal substrates. An enhancement of the exchange bias field, H eb , up to a factor of 2 is observed if the external field is nearly, but not fully aligned perpendicular to the symmetry direction of the exchange bias field. From the measurement of the exchange bias field as a function of the in-plane angle of the applied field, the unidirectional, uniaxial and fourfold anisotropy contributions are determined with high precision. The symmetry direction of the unidirectional anisotropy switches with increasing NiFe thickness from [110] to [001].

Groups can be studied using methods from different fields such as combinatorial group theory or string rewriting. Recently techniques from Gröbner basis theory for free monoid rings (non-commutative polynomial rings) respectively free group rings have been added to the set of methods due to the fact that monoid and group presentations (in terms of string rewriting systems) can be linked to special polynomials called binomials. In the same mood, the aim of this paper is to discuss the relation between Nielsen reduced sets of generators and the Todd-Coxeter coset enumeration procedure on the one side and the Gröbner basis theory for free group rings on the other. While it is well-known that there is a strong relationship between Buchberger's algorithm and the Knuth-Bendix completion procedure, and there are interpretations of the Todd-Coxeter coset enumeration procedure using the Knuth-Bendix procedure for special cases, our aim is to show how a verbatim interpretation of the Todd-Coxeter procedure can be obtained by linking recent Gröbner techniques like prefix Gröbner bases and the FGLM algorithm as a tool to study the duality of ideals. As a side product our procedure computes Nielsen reduced generating sets for subgroups in finitely generated free groups.

Todd and Coxeter's method for enumerating cosets of finitely generated subgroups in finitely presented groups (abbreviated by Tc here) is one famous method from combinatorial group theory for studying the subgroup problem. Since prefix string rewriting is also an appropriate method to study this problem, prefix string rewriting methods have been compared to Tc. We recall and compare two of them briefly, one by Kuhn and Madlener [4] and one by Sims [15]. A new approach using prefix string rewriting in free groups is derived from the algebraic method presented by Reinert, Mora and Madlener in [14] which directly emulates Tc. It is extended to free monoids and an algebraic characterization for the "cosets" enumerated in this setting is provided.

On the one hand, in the world of Product Data Technology (PDT), the ISO standard STEP (STandard for the Exchange of Product model data) gains more and more importance. STEP includes the information model specification language EXPRESS and its graphical notation EXPRESS-G. On the other hand, in the Software Engineering world in general, mainly other modelling languages are in use - particularly the Unified Modeling Language (UML), recently adopted to become a standard by the Object Management Group, will probably achieve broad acceptance. Despite a strong interconnection of PDT with the Software Engineering area, there is a lack of bridging elements concerning the modelling language level. This paper introduces a mapping between EXPRESS-G and UML in order to define a linking bridge and bring the best of both worlds together. Hereby the feasibility of a mapping is shown with representative examples; several problematic cases are discussed as well as possible solutions presented.

Thermal Properties of Interacting Bose Fields and Imaginary-Time Stochastic Differential Equations
(1998)

Abstract: Matsubara Green's functions for interacting bosons are expressed as classical statistical averages corresponding to a linear imaginary-time stochastic differential equation. This makes direct numerical simulations applicable to the study of equilibrium quantum properties of bosons in the non-perturbative regime. To verify our results we discuss an oscillator with quartic anharmonicity as a prototype model for an interacting Bose gas. An analytic expression for the characteristic function in a thermal state is derived and a Higgs-type phase transition discussed, which occurs when the oscillator frequency becomes negative.

The term enterprise modeling, synonymous with enterprise engineering, often refers to methodologies, developed for modeling activities, states, time, and cost within an enterprise architecture. They serve as a vehicle for evaluating and modeling activities resources and so on. CIM - OSA (Computer Integrated Manufacturing Open Systems Architecture) is a methodology for modeling computer integrated environments, and its major objective is the appropriate integration of enterprise operations by means of efficient information exchange within the enterprise. Although there are other methodo- logies in the industry that serve the same purpose, most of them concentrate on the internal aspect of an enterprise. The paper is concerned with the modeling of the links between enterprises. The aim is to examine these relationships or links in detail and suggest a method for modeling enterprise networks drawing on the methodologies currently used in the industry and extending with the method proposed here.

The term enterprise modelling, synonymous with enterprise engineering, refers to methodologies developed for modelling activities, states, time, and cost within an enterprise architecture. They serve as a vehicle for evaluating and modelling activities resources etc. CIM - OSA (Computer Integrated Manufacturing Open Systems Architecture) is a methodology for modelling computer integrated environments, and its major objective is the appropriate integration of enterprise operations by means of efficient information exchange within the enterprise. PERA is another methodology for developing models of computer integrated manufacturing environments. The department of industrial engineering in Toronto proposed the development of ontologies as a vehicle for enterprise integration. The paper reviews the work carried out by various researchers and computing departments on the area of enterprise modelling and points out other modelling problems related to enterprise integration.

We propose a new discretization scheme for solving ill-posed integral equations of the third kind. Combining this scheme with Morozov's discrepancy principle for Landweber iteration we show that for some classes of equations in such method a number of arithmetic operations of smaller order than in collocation method is required to appoximately solve an equation with the same accuracy.

A multi-phase composite with periodic distributed inclusions with a smooth boundary is considered in this contribution. The composite component materials are supposed to be linear viscoelastic and aging (of the non-convolution integral type, for which the Laplace transform with respect to time is not effectively applicable) and are subjected to isotropic shrinkage. The free shrinkage deformation can be considered as a fictitious temperature deformation in the behavior law. The procedure presented in this paper proposes a way to determine average (effective homogenized) viscoelastic and shrinkage (temperature) composite properties and the homogenized stress-field from known properties of the components. This is done by the extension of the asymptotic homogenization technique known for pure elastic non-homogeneous bodies to the non-homogeneous thermo-viscoelasticity of the integral non-convolution type. Up to now, the homogenization theory has not covered viscoelasticity of the integral type. Sanchez-Palencia (1980), Francfort & Suquet (1987) (see [2], [9]) have consid- ered homogenization for viscoelasticity of the differential form and only up to the first derivative order. The integral-modeled viscoelasticity is more general then the differential one and includes almost all known differential models. The homogenization procedure is based on the construction of an asymptotic solution with respect to a period of the composite structure. This reduces the original problem to some auxiliary boundary value problems of elasticity and viscoelasticity on the unit periodic cell, of the same type as the original non-homogeneous problem. The existence and uniqueness results for such problems were obtained for kernels satisfying some constrain conditions. This is done by the extension of the Volterra integral operator theory to the Volterra operators with respect to the time, whose 1 kernels are space linear operators for any fixed time variables. Some ideas of such approach were proposed in [11] and [12], where the Volterra operators with kernels depending additionally on parameter were considered. This manuscript delivers results of the same nature for the case of the space-operator kernels.

The greybody factors in BTZ black holes are evaluated from 2D CFT in the spirit of AdS3/CFT correspondence. The initial state of black holes in the usual calculation of greybody factors by effective CFT is described as Poincar'e vacuum state in 2D CFT. The normalization factor which cannot be fixed in the effective CFT without appealing to string theory is shown to be determined by the normalized bulk-to-boundary Green function. The relation among the greybody factors in different dimensional black holes is exhibited. Two kinds of (h; _h) = (1; 1) operators which couple with the boundary value of massless scalar field are discussed.

A new method of determining some characteristics of binary images is proposed based on a special linear filtering. This technique enables the estimation of the area fraction, the specific line length, and the specific integral of curvature. Furthermore, the specific length of the total projection is obtained, which gives detailed information about the texture of the image. The influence of lateral and directional resolution depending on the size of the applied filter mask is discussed in detail. The technique includes a method of increasing directional resolution for texture analysis while keeping lateral resolution as high as possible.

Robust facility location
(1998)

Let A be a nonempty finite subset of R^2 representing the geographical coordinates of a set of demand points (towns, ...), to be served by a facility, whose location within a given region S is sought. Assuming that the unit cost for a in A if the facility is located at x in S is proportional to dist(x,a) - the distance from x to a - and that demand of point a is given by w_a, minimizing the total trnsportation cost TC(w,x) amounts to solving the Weber problem. In practice, it may be the case, however, that the demand vector w is not known, and only an estimator {hat w} can be provided. Moreover the errors in sich estimation process may be non-negligible. We propose a new model for this situation: select a threshold valus B 0 representing the highest admissible transportation cost. Define the robustness p of a location x as the minimum increase in demand needed to become inadmissible, i.e. p(x) = min{||w^*-{hat w}|| : TC(w^*,x) B, w^* = 0} and solve then the optimization problem max_{x in S} p(x) to get the most robust location.

The pure-Skyrme limit of a scale-breaking Skyrmed O(3) sigma model in 1+1 dimensions is employed to study the effect of the Skyrme term on the semiclassical analysis of a field theory with instantons. The instantons of this model are self-dual and can be evaluated explicitly. They are also localised to an absolute scale, and their fluctuation action can be reduced to a scalar subsystem. This permits the explicit calculation of the fluctuation determinant and the shift in vacuum energy due to instantons. The model also illustrates the semiclassical quantisation of a Skyrmed field theory.

The Kallianpur-Robbins law describes the long term asymptotic behaviour of the distribution of the occupation measure of a Brownian motion in the plane. In this paper we show that this behaviour can be seen at every typical Brownian path by choosing either a random time or a random scale according to the logarithmic laws of order three. We also prove a ratio ergodic theorem for small scales outside an exceptional set of vanishing logarithmic density of order three.

The lowest resonant frequency of a cavity resonator is usually approximated by the classical Helmholtz formula. However, if the opening is rather large and the front wall is narrow this formula is no longer valid. Here we present a correction which is of third order in the ratio of the diameters of aperture and cavity. In addition to the high accuracy it allows to estimate the damping due to radiation. The result is found by applying the method of matched asymptotic expansions. The correction contains form factors describing the shapes of opening and cavity. They are com- puted for a number of standard geometries. Results are compared with numerical computations.

The paper addresses two problems of comprehensible proof presentation, the hierarchically structured presentation at the level of proof methods and different presentation styles of construction proofs. It provides solutions for these problems that can make use of proof plans generated by an automated proof planner.

The paper presents a process-oriented view on knowledge management in software development. We describe requirements on knowledge management systems from a process-oriented perspective, introduce a process modeling language MILOS and its use for knowledge management. Then we explain how a process-oriented knowledge management system can be implemented using advanced but available information technologies.

The light-cone Hamiltonian approach is applied to the super D2- brane, and the equivalent area-preserving and U(1) gauge-invariant effective Lagrangian, which is quadratic in the U(1) gauge field, is derived. The latter is recognised to be that of the three- dimensional U(1) gauge theory, interacting with matter supermultiplets, in a special external induced supergravity metric and the gravitino field, depending on matter fields. The duality between this theory and 11d supermembrane theory is demonstrated in the light-cone gauge.

Rewriting techniques have been applied successfully to various areas of symbolic computation. Here we consider the notion of prefix-rewriting and give a survey on its applications to the subgroup problem in combinatorial group theory. We will see that for certain classes of finitely presented groups finitely generated subgroups can be described through convergent prefix-rewriting systems, which can be obtained from a presentation of the group considered and a set of generators for the subgroup through a specialized Knuth-Bendix style completion procedure. In many instances a finite presentation for the subgroup considered can be constructed from such a convergent prefix-rewriting system, thus solving the subgroup presentation problem. Finally we will see that the classical procedures for computing Nielsen reduced sets of generators for a finitely generated subgroup of a free group and the Todd-Coxeter coset enumeration can be interpreted as particular instances of prefix-completion. Further, both procedures are closely related to the computation of prefix Gr"obner bases for right ideals in free group rings.

Abstract: The effect of intracavity Electromagnetically Induced Transparency on the properties of optical resonators and active laser devices is discussed theoretically. A pronounced frequency pulling and cavity linewidth narrowing are predicted. The effect can be used to substantially reduce classical and quantum phase noise of the beat-note of optical oscillators. Fundamental limits of this stabilization mechanism are discussed as well as its potential application to high-resolution spectroscopy.

Abstract: We predict the possibility of sharp, high-contrast resonances in the optical response of a broad class of systems, wherein interference effects are generated by coherent perturbation or interaction of dark states. The properties of these resonances can be manipulated to design a desired atomic response.

Abstract: We investigate the quantum properties of fields generated by resonantly enhanced wave mixing based on atomic coherence in Raman systems. We show that such a process can be used for generation of pairs of Stokes and anti-Stokes fields with nearly perfect quantum correlations, yielding almost complete (i.e. 100%) squeezing without the use of a cavity. We discuss the extension of the wave mixing interactions into the domain of a few interacting light quanta.

The tunneling splitting of the energy levels of a ferromagnetic particle in the presence of an applied magnetic field - previously derived only for the ground state with the path integral method - is obtained in a simple way from Schr"odinger theory. The origin of the factors entering the result is clearly understood, in particular the effect of the asymmetry of the barriers of the potential. The method should appeal particularly to experimentalists searching for evidence of macroscopic spin tunneling.

For the numerical simulation of 3D radiative heat transfer in glasses and glass melts, practically applicable mathematical methods are needed to handle such problems optimal using workstation class computers. Since the exact solution would require super-computer capabilities we concentrate on approximate solutions with a high degree of accuracy. The following approaches are studied: 3D diffusion approximations and 3D ray-tracing methods.

Transitions from classical to quantum behaviour in a spin system with two degenerate ground states separated by twin energy barriers which are asymmetric due to an applied magnetic field are investigated. It is shown that these transitions can be interpreted as first- or second-order phase transitions depending on the anisotropy and magnetic parameters defining the system in an effective Lagrangian description.

Superselection rules induced by the interaction with the environment are investigated with the help of exactly soluble Hamiltonian models. Starting from the examples of Araki and of Zurek more general models with scattering are presented for which the projection operators onto the induced superselection sectors do no longer commute with the Hamiltonian. The example of an environment given by a free quantum field indicates that infrared divergence plays an essential role for the emergence of induced superselection sectors. For all models the induced superselection sectors are uniquely determined by the Hamiltonian, whereas the time scale of the decoherence depends crucially on the initial state of the total system.

The notion of formal description techniques for timed systems (T-FDTs) has been introduced in [EDK98a] to provide a unifying framework for description techniques that are formal and that allow to describe the ongoing behavior of systems. In this paper we show that three well known temporal logics, MTL, MTL-R , and CTL*, can be embedded in this framework. Moreover, we provide evidence that a large number of dioeerent kinds of temporal logics can be considered as T-FDTs.

This paper describes a tableau-based higher-order theorem prover HOT and an application to natural language semantics. In this application, HOT is used to prove equivalences using world knowledge during higher-order unification (HOU). This extended form of HOU is used to compute the licensing conditions for corrections.

In the present paper multilane models for vehicular traffic are considered. A microscopic multilane model based on reaction thresholds is developed. Based on this model an Enskog like kinetic model is developed. In particular, care is taken to incorporate the correlations between the vehicles. From the kinetic model a fluid dynamic model is derived. The macroscopic coefficients are deduced from the underlying kinetic model. Numerical simulations are presented for all three levels of description in [10]. Moreover, a comparison of the results is given there.

In this paper the work presented in [6] is continued. The present paper contains detailed numerical investigations of the models developed there. A numerical method to treat the kinetic equations obtained in [6] are presented and results of the simulations are shown. Moreover, the stochastic correlation model used in [6] is described and investigated in more detail.

In this paper domain decomposition methods for radiative transfer problems including conductive heat transfer are treated. The paper focuses on semi-transparent materials, like glass, and the associated conditions at the interface between the materials. Using asymptotic analysis we derive conditions for the coupling of the radiative transfer equations and a diffusion approximation. Several test cases are treated and a problem appearing in glass manufacturing processes is computed. The results clearly show the advantages of a domain decomposition approach. Accuracy equivalent to the solution of the global radiative transfer solution is achieved, whereas computation time is strongly reduced.

In the following an introduction to the level set method will be givenso that one becomes aware of the arising problems, which lead to the needof reinitialization. The problems concerning reinitialization itself will be analysed more detailed and a solution for area loss will be proposed. This solution consists in a combination of the commonly used PDE for reinitialization and extrapolation around the zero level set. Numericalexperiments show rather satisfactory results as far as area loss and computation of curvature are concerned.

In this paper the kinetic model for vehicular traffic developed in [3,4] is considered and theoretical results for the space homogeneous kinetic equation are presented. Existence and uniqueness results for the time dependent equation are stated. An investigation of the stationary equation leads to a boundary value problem for an ordinary differential equation. Existence of the solution and some properties are proved. A numerical investigation of the stationary equation is included.

We derive a new class of particle methods for conservation laws, which are based on numerical flux functions to model the interactions between moving particles. The derivation is similar to that of classical Finite-Volume methods; except that the fixed grid structure in the Finite-Volume method is substituted by so-called mass packets of particles. We give some numerical results on a shock wave solution for Burgers equation as well as the well-known one-dimensional shock tube problem.

We develop a constructive method to derive exactly solvable quantum mechanical models of rational (Calogero) and trigonometric (Sutherland) type. This method starts from a linear algebra problem: finding eigenvectors of triangular finite matrices. These eigenvectors are transcribed into eigenfunctions of a selfadjoint Schrödinger operator. We prove the feasibility of our method by constructing a new "\(AG_3\) model" of trigonometric type (the rational case was known before from Wolfes 1975). Applying a Coxeter group analysis we prove its equivalence with the \(B_3\) model. In order to better understand features of our construction we exhibit the \(F_4\) rational model with our method.