Testergebnisse der PostScript Extraktionstools

Die folgende Seite gibt einen Überblick über die Ergebnisse der Extraktionstools im Bereich mathematischer Preprints (im PostScrip-Format). Dazu wurden zunächst 240 (zufällig ausgewählte) Dokumente mit dem Programm prescript in HTML Dokumente konvertiert. Danach wurden mit den entwickelten Extraktionstools die Metadaten Abstracts, Keywords, MSC Klassifikation und Referenzen extrahiert.

Aus Copyright gründen sind hier jeweils die konvertierten HTML Dokumente referenziert (nicht die orginal PostScript Dokumente).

30 der 240 Dokumente wurden vollständig analysiert. Die folgende Tabelle zeigt die Anzahl des Vorkommens der einzelnen Metadaten, die Anzahl der davon korrekt erkannten Metadaten, die Anzahl der falsch bzw. unvollständig erkannten Metadaten und die Anzahl der nicht erkannten Metadaten.

VorhandenRichtig erkannt Unvollst. erkannt Nicht erkannt
Abstracts 3027 2 1
Keywords 2120 1 0
MSC 2222 0 0
Referenzen 3026 2 2

Damit wurden 90% der vohandenen Abstracts, 95% der vorhandenen Keywords, 100% der vorhandenen MSC Klassifikationen und 86% der vorhandenen Referenzen korrekt erkannt!

Die Testresultate im Einzelnen:

File: file0.html

Abstract:Generalizing Lyons and Zheng ([13]) we study Dirichlet processes admitting a decomposition into the sum of a forward and a backward local martingale plus a bounded variation process. We develop a framework of stochastic calculus for these processes and deal with existence and uniqueness for stochastic differential equations driven by such processes. In particular, Bessel processes turn out to be an interesting example of LyonsZheng processes. Key words: Dirichlet processes, time reversal, Bessel processes

Keywords: Dirichlet processes, time reversal, Bessel processes

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File: file1.html

Abstract:Let T be a measure-preserving and ergodic automorphism of a probability space (X; S; µ). By modifying an argument in [3] we obtain a suÖcient condition for recurrence of the d-dimensional stationary random walk deøned by a Borel map f : X 7?! Rd, d >= 1, in terms of the asumptotic distributions of the maps (f +fT +? ? ?+fTn?1)=n1=d; n >= 1. If d = 2, and if f : X 7?! R2 satisøes the central limit theorem with respect to T (i.e. if the sequence (f + fT + ? ? ? + fT n?1)=pn converges in distribution to a Gaussian law on R2), then our condition implies that the two-dimensional random walk deøned by f is recurrent.

Keywords: Stationary random walk, recurrence, central limit theorem.

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File: file10.html

Abstract:I consider the problem of composing Berezin-Toeplitz operators on the Hilbert space of Gaussian square-integrable entire functions on complex nspace, Cn. For several interesting algebras of functions on Cn, we have T'T = T'? for all '; in the algebra, where T' is the Berezin-Toeplitz operator associated with ' and ' ? is a \twisted" associative product on the algebra of functions. On the other hand, there is a C1 function ' for which T' is bounded but T'T' 6= T for any .

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Abstract:In this paper we outline a rigorous proof of the existence of solutions to one{dimensional initial{boundary value problems for the general and complete version of the Frémond thermo{ mechanical model applying to shape memory alloys.

Keywords: Shape memory alloys, Frémond model, nonlinear hyperbolic { parabolic systems, variational inequalities.

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File: file101.html

Abstract:Polynomial bounds for fi-mixing and for the rate of convergence
to the invariant measure are established for discrete time Markov pro-
cesses and solutions of SDEs under weak stability assumptions.

Keywords: Mixing, recurrence, Markov process, SDE, polynomial convergence.

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File: file103.html

Abstract:For a von Neumann algebra with a cyclic and separating vector it will be shown that the von Neumann subalgebras with the same cyclic vector can uniquely be characterized by one{ parametric operator{valued functions obeying a set of conditions. Since the properties contain no reference to the subalgebra these operator{valued functions will be called characteristic functions. On the set of characteristic functions there exists a natural topology under which this set is complete.

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File: file104.html

Abstract:A jump system is a nonempty set of integral vectors that satisfy a certain exchange axiom. This notion was introduced by Bouchet and Cunningham, and popularized by recent results of Lovász. A degree system of a graph G is the set of degree sequences of all subgraphs of G. Degree systems are the primary example of jump systems. Other examples come from matroids and from two generalizations of matroids (polymatroids and delta{matroids). Discussion of these special cases will be kept to a minimum, and will only be used to motivate certain results.
The main result is a min{max formula of Lovász for the distance of an integral point from a jump system. This formula generalizes two of the more important min{max theorems in combinatorial optimization; namely, Tutte's f{factor{theorem, and Edmonds' matroid intersection theorem. Other points of interest are the existence of a greedy algorithm for optimizing linear functions, and a characterization of the convex hulls of jump systems. Even apart from the possibility of obtaining very general theorems, jump systems are appealing due to their simple definition and elegant structure.

Keywords: matching, matroid, combinatorial optimization

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Abstract:We consider a perturbation H = H0 + V of a periodic Schrödinger (or more general) operator H0 by a short-range potential V . A strong form of the limiting absorption principle for the operator H is established. The stationary scattering theory for the pair H0; H is developed. The results obtained allow us to give a representation for the scattering matrix in terms of the spectral representation of H0 and of the resolvent of H. The asymptotics of the spectrum of the scattering matrix is calculated for asymptotically homogeneous V .

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File: file11.html

Abstract:For linear differential algebraic equations of tractability index 1 the notion of the adjoint equation is analysed in full detail. Its solvability is shown at the lowest possible smoothness. The fundamental matrices of both equations are defined and their relationships are characterized. Keywords: linear differential algebraic equations of index 1, adjoint equation, solvability, fundamental matrices. Mathematics Subject Classification: 34A09, 34A30

Keywords: linear differential algebraic equations of index 1, adjointequation, solvability, fundamental matrices

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File: file110.html

Abstract:The paper is devoted to the study of the relationship between integral manifolds of ordinary diöerential equations and duck>=trajectories. We derive suÖcient conditions for the existence of continuous slow integral surfaces that are devided into stable and unstable parts and propose a method of construction of surfaces consisting of duck>=trajectories.

Keywords: Integral manifolds, duck-trajectories, singularly perturbed systems.

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File: file112.html

Abstract:Proofs of classical Chernoff-Hoeffding bounds has been used to obtain polynomial-time implementations of Spencer's derandomization method of conditional probabilities on usual finite machine models: given m events whose complements are large deviations corresponding to weighted sums of n mutually independent Bernoulli trials, Raghavan's lattice approximation algorithm constructs for 0 ? 1 weights and integer deviation terms in O(mn)-time a point for which all events hold. For rational weighted sums of Bernoulli trials the lattice approximation algorithm or Spencer's hyperbolic cosine algorithm are deterministic precedures, but a polynomial-time implementation was not known. We resolve this problem with an O(mn2 log mnffl )-time algorithm, whenever the probability that all events hold is at least ffl > 0. Since such algorithms simulate the proof of the underlying large deviation inequality in a constructive way, we call it the algorithmic version of the inequality. Applications to general packing integer programs and resource constrained scheduling result in tight and polynomial-time approximations algorithms.

Keywords: randomized algorithms, derandomization, approximation algorithms, integer programming, resource constrained scheduling

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File: file113.html

Abstract:This paper studies stochastic particle systems related to the coagulation-fragmentation equation. For a certain class of unbounded coagulation kernels and fragmentation rates, relative compactness of the stochastic systems is established and weak accumulation points are characterized as solutions. These results imply a new existence theorem. Finally a simulation algorithm based on the particle systems is proposed.

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File: file114.html

Abstract:We prove that for a class of massless rÖ interface models on Z2 an introduction of an arbitrary small pinning self-potential leads to exponential decay of correlation, or, in other words,
to creation of mass.

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File: file116.html

Abstract:Coagulation of particles in turbulent flows is studied. The size distribution of particles is governed by Smoluchowski equation with random collision coefficient. The random coagulation coefficient is derived by a generalization of the approach suggested by Saffman and Turner [12]. The coagulation process is analysed in three main cases: (1) Tc, the characteristic coagulation time is much less than Tw, the characteristic Lagrangian time of the turbulent flow, (2) conversely, Tw << Tc, and (3), these times are of the same order: Tw ? Tc. A special stochastic time is introduced which drastically simplifies the analysis of the influence of the intermittency. A detailed numerical study is given for two cases with known explicit solutions of Smoluchowski equation. The numerical analysis in the turbulent collision regime is based on the stochastic algorithm presented in the book [9] and developed in [11], [10], and [4].

File: file118.html

Abstract:A shape optimization problem is considered related to the design of induction hardening facilities. The mathematical model consists of a vector potential formulation for Maxwell's equations coupled with the energy balance and an ODE to describe the solid>=solid phase transition in steel during heating. Depending on the shape of the coil we control the volume fraction of the high temperature phase. The coil is modeled as a tube and is deøned by a unit>=speed curve. The shape optimization problem is formulated over the set of admissible curves. The existence of an optimal control is proved. To obtain the form of the shape gradient of the cost functional, the material derivative method is applied. Finally, the ørst order necessary optimality conditions are estabished for an optimal tube.

Keywords: shape optimization, Maxwell's equations, induction heating, necessary optimality conditions

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File: file119.html

Abstract:We study a Hopøeld model whose number of patterns M grows to inønity with the system size N , in such a way that M(N)2 log M(N)=N tends to zero. In this model the unbiased Gibbs state in volume N can essentially be decomposed into M(N) pairs of disjoint measures. We investigate the distributions of the corresponding weights, and show, in particular, that these weights concentrate for any given N very closely to one of the pairs, with probability tending to one. Our analysis is based upon a new result on the asymptotic distribution of order statistics of certain correlated exchangeable random variables.

Keywords: Hopøeld model, extreme values, order statistics, metastates, chaotic size-dependence.

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Abstract:For many typical instances where Monte Carlo methods are applied attempts were made to find unbiased estimators, since for them the Monte Carlo error reduces to the statistical error. These problems usually take values in the scalar field. If we study vector valued Monte Carlo methods, then we are confronted with the question whether there can exist unbiased estimators. This problem is apparently new. Below it is settled precisely. Partial answers are given, indicating relations to several classes of linear operators in Banach spaces.

Keywords: unbiased Monte Carlo methods, operator ideals .

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File: file123.html

Abstract:We analyze existence results in constrained optimal design problems governed by variational inequalities of obstacle type. The main applications that we discuss concern the optimal packaging problem and the electrochemical machining process. Our assumptions, in order to obtain the existence of at least one optimal domain, are just boundedness and uniform continuity (the uniform segment property) for the boundaries of the unknown regions where the free boundary problems are defined. No restrictions on the dimension are imposed.

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File: file124.html

Abstract:We consider adaptive estimating the value of a linear functional from indirect white noise observations. For a Äexible approach, the problem is embedded in an abstract Hilbert scale. We develop an adaptive estimator that is rate optimal within a logarithmic factor simultaneously over a wide collection of balls in the Hilbert scale. It is shown that the proposed estimator has the best possible adaptive properties for a wide range of linear functionals. The case of discretized indirect white noise observations is studied, and the adaptive estimator in this setting is developed.

Keywords: Adaptive estimation, discretization, Hilbert scales, inverse problems, linear functionals, regularization, minimax risk.

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File: file125.html

Abstract:With the df F of the rv X is associated the natural exponential family of dfs F>= where dF>=(x) = e>=xdF (x)=Ee>=X

Keywords: asymptotic normality, asymptotically parabolic, convolution, domain of attraction, exponential family, Esscher transform, gamma approximation, gamma distribution, Laplace transform, normal distribution, regular variation, saddlepoint approximation, selfneglecting, weak limit law.

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File: file126.html

Abstract:We calculate the asymptotic form of the quantum current/magnetisation of a non-interacting electron gas at zero temperature. The calculation
uses coherent states and a novel commutator identity for the current
operator.

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File: file127.html

Abstract:In this article, dissipative perturbations of the nonlinear Schrödinger equation (NLS) are considered. For dissipative equations, when determining the stability of a solitary wave, one must locate both the point spectrum and the continuous spectrum. If the wave is to be stable, all the spectrum must reside in the left-half plane, except for the translational eigenvalue(s) at the origin. However, for the NLS the continuous spectrum is located on the imaginary axis, as the NLS can be thought of as an infinite-dimensional Hamiltonian system. Since dissipative perturbations will destroy this feature, it is then possible for eigenvalues to bifurcate out of the continuous spectrum and into the right-half plane, leading to an unstable wave. Here we show that the Evans function can be extended across the continuous spectrum, and hence it can be used to track these bifurcating eigenvalues. The extension is done for a general class of equations, and the result should therefore be useful for a larger class of problems than that presented here. Using the extended Evans function, we are then able to locate the spectrum for bright solitary-wave solutions to various perturbed nonlinear Schrödinger equations, and discuss their stability. In addition, we discuss the existence and stability of multi-bump solitary waves for a particular perturbation, the parametrically forced NLS equation.

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File: file128.html

Abstract:We study singularly perturbed elliptic and parabolic diöerential equations under the assumption that the associated equation has intersecting families of equilibria (exchange of stabilities). We prove by means of the method of asymptotic lower and upper solutions that the asymptotic behavior with respect to the small parameter changes near the curve of exchange of stabilities. The application of that result to systems modelling fast bimolecular reactions in a heterogeneous environment implies a transition layer (jumping behavior) of the reaction rate. This behavior has to be taken into account for identiø- cation problems in reaction systems.

Keywords: Singular perturbation, asymptotic methods, upper and lower solutions, jumping behavior of reaction rates.

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File: file130.html

Abstract:We are interested in algorithms for constructing surfaces ? of possibly small measure that separate a given domain ? into two regions of equal measure. Using the integral formula for the total gradient variation, we show that such separators can be constructed approximatively by means of sign changing eigenfunctions of the p-Laplacians, p ! 1, under homogeneous Neumann boundary conditions. These eigenfunctions are proven to be limits of a steepest descent methods applied to suitable norm quotients. Finally we use these ideas for the construction of separators on simplex grids.

Keywords: p-Laplacian, eigenfunctions, separators.

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File: file132.html

Abstract:We define Picard-Einstein metrics on complex algebraic surfaces as Kähler-Einstein metrics with negative constant sectional curvature pushed down from the unit ball via Picard modular groups allowing degenerations along cycles. We demonstrate how the tool of orbital heights, especially the Proportionality Theorem presented in [H98], works for detecting such orbital cycles on the projective plane. The simplest cycle we found on this way is supported by a quadric and three tangent lines (Apollonius configuration). We give a complete proof for the fact that it belongs to the congruence subgroup of level 1 + i of the full Picard modular group of Gauß numbers together with precise octahedral- symmetric interpretation as moduli space of an explicit Shimura family of curves of genus 3. Proofs are based only on the Proportionality Theorem and classification results for hermitian lattices and algebraic surfaces.

Keywords: algebraic curves, moduli space, Shimura surface, Picard modular group, arithmetic group, Gauß lattice, Kähler-Einstein metric, negative constant curvature, unit ball

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File: file133.html

Abstract:We calculate some deønite integrals which (up to now) computer algebra systems like Maple or Mathematica are unable to evaluate. The ørst one is a simply looking integral involving cos and log , the others are some integrals containing polylogarithmic functions. It is shown that they can be evaluated by rational combinations of ?>=functions and products of ?>=functions at positive integers.

Keywords: Riemann zeta function, polylogarithms.

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File: file136.html

Abstract:In this paper we study 2-dimensional Ising spin glasses on a grid with nearest neighbor and periodic boundary interactions, based on a Gaussian bond distribution, and an exterior magnetic field. We show how using a technique called branch and cut, the exact ground states of grids of sizes up to 100 ? 100 can be determined in a moderate amount of computation time, and we report on extensive computational tests. With our method we produce results based on more than 20 000 experiments on the properties of spin glasses whose errors depend only on the assumptions on the model and not on the computational process. This feature is a clear advantage of the method over other more popular ways to compute the ground state, like Monte Carlo simulation including simulated annealing, evolutionary, and genetic algorithms, that provide only approximate ground states with a degree of accuracy that cannot be determined a priori. Our ground state energy estimation at zero field is ?1:317.

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File: file137.html

Abstract:We observe an infinitely dimensional Gaussian random vector x = ? + v where ? is a sequence of standard Gaussian variables and v 2 l2 is an unknown mean. Let V"(ø; æ") æ l2 be sets which correspond to lq-ellipsoids of power semi-axes ai = i?sR=" with lp-ellipsoid of semi-axes bi = i?ræ"=" removed or to similar Besov bodies Bq;t;s(R=") with Besov bodies Bp;h;r(æ"=") removed. Here ø = (<=; R) or ø = (<=; h; t; R); <= = (p; q; r; s) are the parameters which define the sets V" for given radiuses æ" ! 0, 0 < p; q; h; t <= 1; ?1 < r; s < 1; R > 0; " ! 0 is asymptotical parameter. For the case ø is known hypothesis testing problem H0 : v = 0 versus alternatives H";ø : v 2 V"(ø; æ") have been considered by Ingster and Suslina [11] in minimax setting. It was shown that there is a partition of the set of <= on to regions with different types of asymptotics: classical, trivial, degenerate and Gaussian (of two main and some "boundary" types). Also there is

Keywords: nonparametric hypotheses testing, minimax hypotheses testing,

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File: file14.html

Abstract:Semiuniform convergence spaces form a common generalization of filter spaces (in- cluding symmetric convergence spaces [and thus symmetric topological spaces] as well as Cauchy spaces) and uniform limit spaces (including uniform spaces) with many convenient properties such as cartesian closedness, hereditariness and the fact that products of quotients are quotients. Here, for each semiuniform convergence space a completion is constructed, called the simple completion. This one generalizes Császár's >={completion of filter spaces. Thus, filter spaces are characterized as subspaces of convergence spaces. Furthermore, Wyler's completion of separated uniform limit spaces can be easily derived from the simple completion. Mathematics Subject Classifications (1991). 54A05, 54A20, 54E15, 54E52, 18A40.

Keywords: Semiuniform convergence spaces, filter spaces, uniform convergence spaces (= uniform limit spaces), completions, universal constructions.

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Abstract:Conventional approaches to lattice gauge theories do not properly consider the topology of spacetime or of its fields. In this paper, we develop a formulation which tries to remedy this defect. It starts from a cubical decomposition of the supporting manifold (compactified spacetime or spatial slice) interpreting it as a finite topological approximation in the sense of Sorkin. This finite space is entirely described by the algebra of cochains with the cup product. The methods of Connes and Lott are then used to develop gauge theories on this algebra and to derive Wilson's actions for the gauge and Dirac fields therefrom which can now be given geometrical meaning. We also describe very natural candidates for the QCD ?-term and Chern-Simons action suggested by this algebraic formulation. Some of these formulations are simpler than currently available alternatives. The paper treats both the functional integral and Hamiltonian approaches.

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File: file142.html

Abstract:A bidouble cover is a finite flat Galois morphism with Galois group (Z=2)2?. The structure theorem for smooth Galois (Z=2)2? covers was given in [Cat2] [pag. 491-493] where bidouble covers of P1 ? P1 were introduced in order to find interesting properties of the moduli spaces of surfaces of general type. In this paper we develop general formulae for the case of resolutions of singular bidouble covers. P. Burniat used singular bidouble covers in order to fill out sectors of surface geography. In this paper instead, the main application is for the construction of surfaces with birational canonical map (so called simple canonical surfaces) and high K2, for instance we construct such surfaces with pg = 4; 11 <= K2 <= 28, against a prediction of F. Enriques that 24 should be the maximum allowed. Moreover, we find, among several new examples of surfaces, some surfaces with pg = q = 1, K2 = 4; 5, and also some infinite series of surfaces whose canonical map is composed of a pencil of curves of genus 2 or 3, with non costant moduli.

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File: file143.html

Abstract:We prove the existence of localized states at the edges of the bands for the two-dimensional Landau Hamiltonian with a random potential, of arbitrary disorder, provided that the magnetic field is sufficiently large. The corresponding eigenfunctions decay exponentially with the magnetic field and distance. We also prove that the integrated density of states is Lipschitz continuous away from the Landau energies. The proof relies on a Wegner estimate for the finite-area magnetic Hamiltonians with random potentials and exponential decay estimates for the finite-area Green's functions. The proof of the decay estimates for the Green's functions uses fundamental results from two-dimensional bond percolation theory.

Keywords:Key-Words : Landau Hamiltonians, random operators, localization.

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File: file144.html

Abstract:In this paper we show that the canonical solution operator to @ restricted to holomorphic (0; 1)- forms can be expressed by an integral operator using the Bergman kernel. For the unit disk D in C we prove that this operator is a Hilbert Schmidt operator.

Keywords: @-equation, Bergman kernel.

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File: file145.html

Abstract:The points homoclinic to 0 under a hyperbolic toral automorphism form the intersection of the stable and unstable manifolds of 0. This is a subgroup isomorphic to the fundamental group of the torus. Suppose that two hyperbolic toral automorphisms commute so that they determine a Z2-action, which we assume is irreducible. We show, by an algebraic investigation of their eigenspaces, that they either have exactly the same homoclinic points or have no homoclinic point in common except 0 itself. We prove the corresponding result for a compact connected abelian group, and compare the two proofs.

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File: file146.html

Abstract:This paper deals with the k-factor extension of the long memory Gegenbauer process proposed by Gray and al. (1989). We give the analytic expression of the prediction function derived from this long memory process and we give the h-step-ahead prediction error when parameters are either known or estimated. We investigate the predictive ability of the k-factor Gegenbauer model on real data of urban transport traffic in Paris area, in comparison with other short and long memory models.

Keywords: Long memory, k-factor Gegenbauer process, prediction function, prediction error, urban transport traffic.

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Abstract:We prove that a compact Hermitian surface with J-invariant Ricci tensor is Kähler provided that the difference of its scalar and conformal scalar curvature is constant. In particular, there are no locally homogeneous examples of such surfaces with odd first Betti number.

Keywords: Hermitian surfaces, J-invariant Ricci tensor.

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File: file148.html

Abstract:We consider the entropy of systems of random transformations, where the transformations are chosen from the set of generators of a Zd action. We show that the classical definition gives unsatisfactory entropy results in the higher-dimensional case, i.e. when d >= 2. We propose a new definition of the entropy for random group actions which agrees with the classical definition in the one-dimensional case, and which gives satisfactory results in higher dimensions. We identify the entropy by a concrete formula which makes it possible to compute the entropy in certain cases. Along the way, we show that the random version of Krieger's theorem on the existence of finite generators is not valid.

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Abstract:A general framework for integration over certain infinite dimensional spaces is first developed using projective limits of a projective family of compact Hausdorff spaces. The procedure is then applied to gauge theories to carry out integration over the non-linear, infinite dimensional spaces of connections modulo gauge transformations. This method of evaluating functional integrals can be used either in the Euclidean path integral approach or the Lorentzian canonical approach. A number of measures discussed are diffeomorphism invariant and therefore of interest to (the connection dynamics version of) quantum general relativity. The account is pedagogical; in particular prior knowledge of projective techniques is not assumed. 1

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Abstract:The known correspondence between the Kronig{Penney model and certain Jacobi matrices is extended to a wide class of Schrödinger operators on graphs. Examples include rectangular lattices with and without a magnetic field, or comb{ shaped graphs leading to a Maryland{type model.

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File: file150.html

Abstract:This paper studies the perturbation of a Lie-Poisson (or, equivalently an Euler-Poincaré) system by a special dissipation term that has Brockett's double bracket form. We show that a formally unstable equilibrium of the unperturbed system becomes a spectrally and hence nonlinearly unstable equilibrium after the perturbation is added. We also investigate the geometry of

File: file151.html

Abstract:We study the graded derivation-based noncommutative differential geometry of the Z2-graded algebra M (njm) of complex (n + m) ? (n + m)-matrices with the \usual block matrix grading" (for n 6= m). Beside the (infinite-dimensional) algebra of graded forms the graded Cartan calculus, graded symplectic structure, graded vector bundles, graded connections and curvature are introduced and investigated. In particular we prove the universality of the graded derivation-based first-order differential calculus and show, that M (njm) is a \noncommutative graded manifold" in a stricter sense: There is a natural body map and the cohomologies of M (njm) and its body coincide (as in the case of ordinary graded manifolds).

Keywords: Supermanifolds, Lie superalgebras, noncommutative differential geometry, matrix geometry

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Abstract:The study of the QAP-Polytope was started by Rijal (1995), Padberg and Rijal (1996), and Jünger and Kaibel (1996), investigating the structure of the feasible points of a (Mixed) Integer Linear Programming formulation of the QAP that provides good lower bounds by its continious relaxation. Rijal (1995) and Padberg and Rijal (1996) propose an alternative (Mixed) Integer Linear Programming formulation for the case that the QAP-instance is symmetric in a certain sense and define analogously the SQAP-Polytope. They give a conjecture about the dimension of that polytope, whose proof is one part of this paper. Moreover, we investigate the trivial faces of the SQAP- Polytope and present a first class of non-trivial facets of it. The polyhedral results are used to compute lower bounds for symmetric QAPs. Keywords: Symmetric Quadratic Assignment Problem, Polyhedral Combinatorics, SQAP-Polytope
MSC Classification: 90C09, 90C10, 90C27

Keywords: Symmetric Quadratic Assignment Problem, Polyhedral Combinatorics, SQAP-Polytope MSC Classification: 90C09, 90C10, 90C27

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Abstract:In this paper, we consider nonconvex optimization problems whose objective functions are composed of parts easily to optimize on polyhedral sets. This allows to develop algorithms which take advantage of the special structure of the problems. We present a one{parametric algorithm { based on the approved simplex method { that yields a global solution to the problem of optimizing a sum or a product of two linear fractional functions under linear constraints. Results of computational experiments reported at the end of the paper show that our algorithm is promising in comparison with algorithms recently published.

Keywords: Fractional programming, composite objective functions, linear fractional functions, Charnes{Cooper transformation, parametrized modified simplex method.

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Abstract:Two new characterizations of Hill>=tetrahedra are given, using a
canonical dissection of simplices and an equidissection of prisms.

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File: file155.html

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Abstract:In the wake of decoupling and linearization semiconductor device simulation based on van Roosbroecks's equations requires the solution of convection{diffusion equations. It is well known that due to the occurrence of local regions of strong convection standard discretizations do not behave properly. As an alternative among others, mixed methods have been suggested having their roots in the dual variational formulation of the convection{diffusion problem. Their efficient implementation has to make use of Lagrangian multipliers. In a novel approach we already introduce the multiplier prior to discretizing, through a process called hybridization. In the sequel we use the resulting variational problem to develop a new discretization scheme. Next, we outline how to implement a standard mixed scheme and investigate some of its aspects. Finally, the behaviour of the mixed method is illustrated by a series of numerical experiments.

Keywords: convection{diffusion problem, flux oriented schemes, hybridization, Lagrangian multipliers, mixed finite elements, Raviart{Thomas elements

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File: file157.html

Abstract:Forward and backward stochastic Lagrangian trajectory simulation methods for calculation of the mean concentration of scalars and their Äuxes for sources arbitrarily distributed in space and time are constructed and justiøed. Generally, absorption of scalars by medium is taken into account. A special case of the source structure, when the scalar is generated by a plane source, say, located close to the ground, is treated. This practically interesting particular case is known in the literature as the footprint problem.

Keywords: Turbulent Äows, Lagrangian trajectories, forward and backward random

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File: file158.html

Abstract:According to a formula that was put forward many decades ago the ground state energy per particle of an interacting, dilute Bose gas at density æ is 2ß~2æa=m to leading order in æa3 ø 1, where a is the scattering length of the interaction potential and m the particle mass. This result, which is important for the theoretical description of current experiments on Bose-Einstein condensation, has recently been established rigorously for the first time. We give here an account of the proof that applies to nonnegative, spherically symmetric potentials decreasing faster than 1=r3 at infinity.

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File: file16.html

Abstract:We investigate whether the eigenfunctions of the two-dimensional magnetic Schrö- dinger operator have a Gaussian decay of type exp(?Cx2) at infinity (the magnetic field is rotationally symmetric). We establish this decay if the energy (E) of the eigenfunction is below the bottom of the essential spectrum (B), and if the angular Fourier components of the external potential decay exponentially (real analyticity in the angle variable). We also demonstrate that almost the same decay is necessary. The behavior of C in the strong field limit and in the small (B ? E) limit is also studied.

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Abstract:We consider the statistical experiment given by a sample y(1); : : : ; y(n) of a stationary Gaussian process with an unknown smooth spectral density. Asymptotic equivalence with a nonparametric regression in discrete Gaussian white noise is established. The key is a local limit theorem for an increasing number of empirical covariance coefficients.

Keywords: Stationary Gaussian process, spectral density, Le Cam's distance, asymptotic equivalence, local limit theorem, signal in Gaussian white noise.

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Abstract:The time step truncation error in direct simulation Monte Carlo calculations is found to be O(?t2) for a variety of simple Äows, both transient and steady state. The measured errors in the transport coeÖcients (viscosity, thermal conductivity, and self-diöusion) are in good agreement with predictions from Green-Kubo analysis (N. Hadjiconstantinou, Phys. Fluids, submitted 1999).

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Abstract:In a recent paper J. Matou>=sek gave a simple proof of a weak form of the zone theorem which estimates the number of facets in the zone of a (Pseudo-)Hyperplane arrangement. In the Pseudo-Case he gave the full proof only for the 3-dimensional case. In this short note we want to point out, that his proof in fact uses Linear Programming duality and so can be generalized easily to all dimensions using duality of Oriented Matroids.

References:

File: file164.html

Abstract:Let Gn = (A?n ; A+n ); n >= 1; denote the set of gaps of the Hill operator T = ?d2=dx2 + V (x) in L2(R) where V is an even 1-periodic real potential from L2(0; 1) and hn be heights of the corresponding slits on the quasimomentum domain, M?n be effective masses associated with the edges of the gap Gn. Let gn; n >= 1; denote the gaps of the operator T0 = pT ? N0 >= 0 where N0 is the beginning of the spectrum of T , and µ?n be the reduced masses (analog of the effective masses) connected with the gap gn. We study the inverse problem for the mappings V ! fjgnjg; V ! fhng; V ! fµ?n g and V ! fM?n g by a direct approach.

File: file166.html

Abstract:The group of diffeomorphisms of a compact manifold acts isometrically on the space of Riemannian metrics with its L2 metric. Following [1], [15], we define minimal orbits for this action by a zeta function regularization. We show that odd dimensional isotropy irreducible homogeneous spaces give rise to minimal orbits, and find a flat two torus giving a stable minimal orbit. We also define an infinite dimensional family of elliptic operators on a bundle over a manifold M with an action by automorphisms of the bundle. The orbits are parametrized by the metrics on M . In odd dimensions, all orbits are minimal if the cohomology of the elliptic complex vanishes. In this case, the determinant of an associated elliptic operator is a smooth invariant of M . This invariant is defined for some classes of 3-manifolds. It is similar to analytic torsion, and has a combinatorial analogue.

References:

File: file167.html

Abstract:The derivation dT on the exterior algebra of forms on a manifold M with values in the exterior algebra of forms on the tangent bundle T M is extended to multivector fields. These tangent lifts are studied with applications to the theory of Poisson structures, canonical vector fields and Poisson-Lie groups.

References:

File: file168.html

Abstract:In this paper, we study a global bifurcation of codimension one connected with the disappearance (for positive values of a parameter µ) of a saddle-node periodic orbit L0 under the condition that all orbits from the locally unstable manifold W u of L0 tend to L0 as t ! +1. Conditions are presented which guarantee the blue sky catastrophe: the appearance of a stable periodic orbit Lµ which exists for any small positive values of µ but its length and period unboundedly increase as µ ! +0.

Keywords: boundaries of stability, saddle-node, homoclinic orbits, nonlocal bi- furcations, embedding into the Äow.

MSC:

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File: file169.html

Abstract:We report on a hierarchical nearest-neighbor classifier algorithm which we conceived for the recognition of handwritten characters. Distances to all classes are used both as a decision criterion in the classification hierarchy and for generating class membership coefficients. These likelihood values can be easily integrated in a multi-agent cognitive environment. We introduce a new completely binary version of the k-means cluster algorithm and explain how a highly efficient implementation can be achieved using binary patterns. Performances for large character databases are presented. Keywords: pattern recognition, binary techniques, nearest-neighbor classifiers

Keywords: pattern recognition, binary techniques, nearest-neighbor classifiers

References:

File: file17.html

Abstract:A natural metric on the space of all almost hermitian structures on a given manifold is investigated.

Keywords: Metrics on manifolds of structures.

MSC:

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File: file170.html

Abstract:It was recently shown that the renormalization of quantum field theory is organized by the Hopf algebra of decorated rooted trees, whose coproduct identifies the divergences requiring subtraction and whose antipode achieves this. We automate this process in a few lines of recursive symbolic code, which deliver a finite renormalized expression for any Feynman diagram. We thus verify a representation of the operator product expansion, which generalizes Chen's lemma for iterated integrals. The subset of diagrams whose forest structure entails a unique primitive subdivergence provides a representation of the Hopf algebra HR of undecorated rooted trees. Our undecorated Hopf algebra program is designed to process the 24,213,878 BPHZ contributions to the renormalization of 7,813 diagrams, with up to 12 loops. We consider 10 models, each in 9 renormalization schemes. The two simplest models reveal a notable feature of the subalgebra of Connes and Moscovici, corresponding to the commutative part of the Hopf algebra HT of the diffeomorphism group: it assigns to Feynman diagrams those weights which remove zeta values from the counterterms of the minimal subtraction scheme. We devise a fast algorithm for these weights, whose squares are summed with a permutation factor, to give rational counterterms.

References:

File: file171.html

Abstract:A construction is given to find a global analytic [resp. algebraic] equation for the connected sum of two compact, analytic [resp. algebraic] hypersurfaces having global equation. As an application we give explicit algebraic equations for a model of the connected sum of k copies of RP3 in R5.

Keywords: anlytic manifold, algebraic model, connected sum, projective space.

MSC:

References:

File: file173.html

Abstract:The Generalized Baues Problem asks whether for a given point con?guration the order complex of all its proper polyhedral subdivisions, partially ordered by re?nement, is homotopy equivalent to a sphere. In this paper, an af?rmative answer is given for the vertex sets of cyclic polytopes in all dimensions. This yields the ?rst non-trivial class of point con?gurations with neither a bound on the dimension, the codimension, nor the number of vertices for which this is known to be true. Moreover, it is shown that all triangulations of cyclic polytopes are lifting triangulations. This contrasts the fact that in general there are many non-regular triangulations of cyclic polytopes. Beyond this, we ?nd triangulations of C(11;5) with ?ip de?ciency. This proves?among other things?that there are triangulations of cyclic polytopes that are non-regular for every choice of points on the moment curve.

References:

File: file174.html

Abstract:We prove that the explicit formula [2] for viscosity solutions of Hamilton-Jacobi equation @u=@t +H(u; rxu) = 0 in (0; +1)? lRn with u(0; x) = ö(x) is still valid while the initial data ö(x) is continuous in lRn (not necessarily Lipschitz continuous and bounded in lRn). The solution is given by u(t; x) = min y2lRn ? h ?x? y t ? _ ö(y) ?
;

Keywords: Hopf formula, Viscosity solutions, Hamilton-Jacobi equa- tions, quasiconvex function

MSC:

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File: file175.html

Abstract:A survey on solution techniques for the resource-constrained project scheduling problem (RCPSP) with generalized precedence constraints is given. These techniques include constraint propagation, lower bound calculations, branch- and-bound algorithms, and heuristics. Relations between the RCPSP and machine scheduling problems and services scheduling problems are described.

Keywords: Project scheduling/resource constraints, machine scheduling, audit scheduling, timetabling, constraint propagation, linear programming.

References:

File: file176.html

References:

File: file177.html

Abstract:With the help of the multigraded Nijenhuis{ Richardson bracket and the multigraded Gerstenhaber bracket from [7] for every n >= 2 we define n-ary associative algebras and their modules and also n-ary Lie algebras and their modules, and we give the relevant formulas for Hochschild and Chevalley cohomogy.

Keywords: n-ary associative algebras, n-ary Lie algebras.

MSC:

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File: file178.html

Abstract:Solutions of equation of viscoelasticity with capillarity are studied. The special features of the problem are that the stored energy function has two minima and the equation is considered on a cylinder. Existence of limit as time goes to infinity is shown for initial states with small energy.

MSC:

File: file179.html

MSC:

File: file18.html

Abstract:The probabilistic approach is used for constructing special layer methods to solve the Cauchy problem for semilinear parabolic equations with small parameter. In spite of the probabilistic nature these methods are nevertheless deterministic. The algorithms are tested by simulating the Burgers equation with small viscosity and the generalized KPP-equation with a small parameter. 1991 Mathematics Subject Classiøcation. 35K55, 60H10, 60H30, 65M99.
Key words and phrases. Semilinear parabolic equations, reaction-diöusion systems, probabilistic representations for equations of mathematical physics, stochastic diöerential equations with small noise.

Keywords: Semilinear parabolic equations, reaction-diöusion systems, probabilistic representations for equations of mathematical physics, stochastic diöerential equations with small noise.

MSC:

References:

File: file181.html

Abstract:The paper is devoted to the inverse problem of identifying the coeÖcient in the main term of a quasilinear elliptic diöerential equation describing the øltration of groundwater. Experience suggests that the gradient of the piezometric head, i.e., Darcy's velocity, may have discontinuities and the transmissivity coeÖcient is a piecewise constant function. For solving this problem we use a modiøcation of a direct method of G. Vainikko. Starting with a weak formulation of the problem a suitable discretization is obtained by the method of minimal error. If necessary this method can be combined with Tikhonov regularization.
The main diÖculty consists in generating distributed state observations from measurements of the ground>=water level. For this step we propose an optimized data preparation procedure using additional information such as knowledge of the sought parameter values at some points and lower and upper bounds for the parameter.
Numerical tests show that locally suÖciently many measurements provide locally satisfactory results. Two numerical examples, one with simulated data and the other with real life data, are given.

Keywords: Inverse problems, direct methods, ønite elements, linear boundary value problem.

MSC:

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File: file182.html

Abstract:A splitting ønite diöerence scheme for an initial-boundary value problem for a two-dimensional nonlinear evolutionary type equation is considered. The problem is split into nonlinear and linear parts. The linear part is also split into locally one-dimensional equations. The convergence and stability of the scheme in L2 and C norms are proved.

Keywords: evolutionary equations, ønite diöerence scheme, splitting scheme.

MSC:

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File: file187.html

Abstract:Let G = (V; E) be a simple graph and s and t be two distinct vertices of G. A path in G is called `-bounded for some ` 2 N , if it does not contain more than ` edges. We study the computational complexity of approximating the optimum value for two optimization problems of finding sets of vertex-disjoint `-bounded s; t-paths in G. First, we show that computing the maximum number of vertex-disjoint `-bounded s; t-paths is APX {complete for any fixed length bound ` >= 5.
Second, for a given number k 2 N , 1 <= k <= jV j ? 1, and non-negative weights on the edges of G, the problem of finding k vertex-disjoint `-bounded s; t-paths with minimal total weight is proven to be N PO{complete for any length bound ` >= 5. Furthermore, we show that, even if G is complete, it is N P{hard to approximate the optimal solution value of this problem within a factor of 2hÖiffl for any constant 0 < ffl < 1, where hÖi denotes the encoding size of the given problem instance Ö.
We prove that these results are tight in the sense that for lengths ` <= 4 both problems are polynomially solvable, assuming that the weights satisfy a generalized triangle inequality in the weighted problem.
All results presented also hold for directed and non-simple graphs. For the analogous problems where the path length restriction is replaced by the condition that all paths must have length equal to ` or where vertex-disjointness is replaced by edge-disjointness we obtain similar results.

Keywords: disjoint paths, length bounded paths, approximation, reducibility, completeness Mathematical Subject Classification (1991): 68Q25, 90C27, 05C38, 05C40

MSC:

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File: file189.html

Abstract:We show that all Majumdar{Papapetrou electrovacuum space{times with a non{empty black hole region and with a non{singular domain of outer communications are the standard Majumdar{Papapetrou space{ times.

References:

File: file19.html

Abstract:We extend the definition of analytic and Reidemeister torsion from closed compact Riemannian manifolds to compact Riemannian manifolds with boundary (M; @M), given a flat bundle F of A-Hilbert modules of finite type and a decomposition of the boundary @M = @?M [ @+M into disjoint components. If the system (M; @?M; @+M; F) is of determinant class we compute the quotient of the analytic and the Reidemeister torsion and prove gluing formulas for both of them. In particular we answer positively Conjecture 7.6 in [LL] Contents 0. Introduction.

References:

File: file194.html

Abstract:This paper describes a new heuristic for vehicle routing problems with narrow time windows. The problem arises in the context of the delivery of groceries to restaurants. For most of the instances the given time window distribution does not allow solutions where no time restrictions are violated. The aim is to schedule most of the customers in time building regionally bounded tours. The few remaining customers have to be scheduled manually. If the disponent decides to serve one or more of the remaining customers in time, he has to allow out-of-time deliveries for some of the automatically planned stops. The algorithm is based on a clustering procedure where a tree with multiple node weights is divided into subtrees. Upper bounds restrict the sums of the weight functions in each subtree. This problem is NP-complete for trees with a restricted number of weight functions. A greedy algorithm is developed to determine the tree partition. For our application it is extended to a version which also checks if each subtree can be routed regarding the problem specific requirements. Although the algorithm was developed for a specific real world problem, the ideas can also be applied to other vehicle routing problems - even to those with more complicated constraints.

Keywords: vehicle routing, time windows, tree partition, minimal spanning tree, greedy algorithm

MSC:

References:

File: file195.html

Abstract:We present a mathematical model for the laser surface hardening of steel. It consists of a nonlinear heat equation coupled with a system of five ordinary differential equations to describe the volume fractions of the occuring phases. Existence, regularity and stability results are discussed.
Since the resulting hardness can be estimated by the volume fraction of martensite, we formulate the problem of surface hardening in terms of an optimal control problem. To avoid surface melting, which would decrease the workpiece's quality, state constraints for the temperature are included.
We prove differentiability of the solution operator and derive necessary conditions for optimality.

References:

File: file196.html

Abstract:We consider the Dirichlet problem for equations of elliptic type in a domain G with a boundary @G: A probabilistic representation of solutions to the problem is connected with a system of stochastic differential equations (SDE). Unlike usual approximation of SDE when a time-discretization is exploited, here a space-discretization is recommended. We construct weak approximations for which an estimate of their errors contains derivatives of the required solution to the Dirichlet problem only of lower order. In particular, it is important for problems with a boundary layer. We simulate a Markov chain in G on the basis of a one-step approximation using variable step in the space. The chain should be stopped entering a sufficiently small neighborhood of the boundary @G. We estimate the average number of steps before stopping and state some convergence theorems.

Keywords: Boundary value problem, weak methods of numerical integration of SDE, random walk, boundary layer.

MSC:

References:

File: file199.html

Abstract:We extend the quasi-steady state approximation (QSSA) as well with respect to the class of diöerential systems as with respect to the order of approximation. As an application we prove that the trimolecular autocatalator can be approximated by a fast bimolecular reaction system. Finally we describe a class of singularly perturbed systems for which the ørst order QSSA can easily be obtained.

Keywords: Quasi-steady-state approximation, singularly perturbed systems, trimolecular autocatalator.

MSC:

References:

File: file2.html

Abstract:We show that one can lift locally real analytic curves from the orbit space of a compact Lie group representation, and that one can lift smooth curves
even globally, but under an assumption.

Keywords: invariants, representations.

MSC:

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File: file201.html

Abstract:The n-dimensional orthogonal knapsack problem has a wide range of practical applications, including packing, cutting and scheduling. We present a new approach for its exact solution using a two-level tree search algorithm. A key role plays a graph{theoretical characterization of packing patterns that allows us to deal with classes of packing pattern that are symmetrical in a certain sense, instead of single ones. Computational results are reported for two{dimensional test problems from literature.

References:

File: file202.html

Abstract:We consider a two-scaled diffusion system, when drift and diffusion parameters of a \slow" component are contaminated by an unobservable \ fast" one. The goal is to estimate the dynamic function which is defined by averaging the drift coefficient of the \slow" component w.r.t. the stationary distribution of the \fast" one. For estimation we use a locally linear smoother with a datadriven choice of bandwidth. A procedure proposed is fully adaptive and nearly optimal up to a log log factor.

Keywords: fast and slow components, drift and diffusion coefficients, ergodic property, nonparametric estimation, bandwidth selection.

MSC:

References:

File: file205.html

References:

File: file207.html

Abstract:We consider the Dirichlet problem for equations of elliptic type in a domain G with a boundary @G: A probabilistic representation of solutions to the problem is connected with a system of stochastic differential equations (SDE). Unlike usual approximation of SDE when a time-discretization is exploited, here a space-discretization is recommended. We construct weak approximations for which an estimate of their errors contains derivatives of the required solution to the Dirichlet problem only of lower order. In particular, it is important for problems with a boundary layer. We simulate a Markov chain in G on the basis of a one-step approximation using variable step in the space. The chain should be stopped entering a sufficiently small neighborhood of the boundary @G. We estimate the average number of steps before stopping and state some convergence theorems.

Keywords: Boundary value problem, weak methods of numerical integration of SDE, random walk, boundary layer.

MSC:

References:

File: file212.html

Abstract:Our aim is a stochastic model for the average income of a given annuity fund. We consider a time-continous model, and therefore we regard a special kind of time-continous processes fX(t) : t >= 0g satisfying a condition of the form: E(X(t)11EtjFs) <= (ffs X(s) + fis)11Es [P ] for all 0 <= s <= t(0.1) E(X(t)11Ect jFs) >= (ffs X(s) + fis)11Ecs [P ] for all 0 <= s <= t:

Keywords: time-continous stochastic processes, disturbed martingales, income of annuity funds, P-almost sure convergence, Doob's theorem.

MSC:

References:

File: file213.html

File: file214.html

Abstract:In this paper we study an initial{boundary value Stefan{type problem with phase relaxation where the heat flux is proportional to the gradient of the inverse absolute temperature. This problem arises naturally as limiting case of the Penrose{Fife model for diffusive phase transitions with non{conserved order parameter if the coefficient of the interfacial energy is taken as zero. It is shown that the relaxed Stefan problem admits a weak solution which is obtained as limit of solutions to the Penrose{Fife phase{field equations. For a special boundary condition involving the heat exchange with the surrounding medium, also uniqueness of the solution is proved.

Keywords: Stefan problems, phase transitions, phase{field models, singular parabolic systems.

MSC:

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File: file215.html

Abstract:Linear Programming based lower bounds have been considered both for the general as well as for the symmetric quadratic assignment problem several times in the recent years. They have turned out to be quite good in practice. Investigations of the polytopes underlying the corresponding integer linear programming formulations (the non-symmetric and the symmetric quadratic assignment polytope) have been started by Rijal (1995), Padberg and Rijal (1996), and Jünger and Kaibel (1996, 1997). They have lead to basic knowledge on these polytopes concerning questions like their dimensions, affine hulls, and trivial facets. However, no large class of (facet-defining) inequalities that could be used in cutting plane procedures had been found. We present in this paper the first such class of inequalities, the box inequalities, which have an interesting origin in some well-known hypermetric inequalities for the cut polytope. Computational experiments with a cutting plane algorithm based on these inequalities show that they are very useful with respect to the goal of solving quadratic assignment problems to optimality or to compute tight lower bounds. The most effective ones among the new inequalities turn out to be indeed facet-defining for both the non-symmetric as well as for the symmetric quadratic assignment polytope. Keywords: Quadratic Assignment Problem, Polyhedral Combinatorics, QAP-Polytope, Facets, Cutting Plane Procedure
MSC Classification: 90C09, 90C10, 90C27

Keywords: Quadratic Assignment Problem, Polyhedral Combinatorics, QAP-Polytope, Facets, Cutting Plane Procedure MSC Classification: 90C09, 90C10, 90C27

MSC:

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File: file217.html

Abstract:A simple numerical argument is given that the minimal (Jones) index of an inclusion of (isomorphic) factors is strongly restricted if the square of the inclusion contains a sub-inclusion with index from the Jones series 4 cos2 ssm . As a corollary extending results of Longo, the range of the index of braided inclusions is completely computed up to the value Ind = 6. An algebraic version of the argument is outlined and is expected to generalize to braided inclusions the square of which contains an inclusion from the Hecke or Birman-Wenzl-Murakami series. This would allow to push the determination of the range of the index beyond 6.

References:

File: file218.html

Abstract:We classify all local extensions of the chiral algebra of observables for SU3 level k conformal current algebra models. Our method is based on analyzing the polynomial solutions of the corresponding Knizhnik-Zamolodchikov equations.

References:

File: file219.html

Abstract:In the theoretical description of recent experiments with dilute Bose gases confined in external potentials the Gross-Pitaevskii equation plays an important role. Its status as an approximation for the quantum mechanical many-body ground state problem has recently been rigorously clarified. A summary of this work is presented here.

References:

File: file22.html

Abstract:In this paper the behaviour of the causal variant of the ideal low-pass is investigated. It is shown that this system is not stable with respect to the energy norm. A construction of an input signal with finite energy is given in the paper such that the output signal has an infinite energy. This result solves a problem proposed by Professor Mathis.

MSC:

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File: file220.html

Keywords: Highway traffic, Statistical processes: Applications, Transport processes

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File: file226.html

Abstract:The application of concepts and methods of statistical mechanics to biological problems is one of the most promising frontiers of computational physics.

References:

File: file230.html

Abstract:The aim of the present paper is to extent the well known fundamental estimates (w.r.t. the L2-norm) for weak solutions of a linear elliptic system with constant coef- ficients: N

Keywords: elliptic systems, multiplicative inequality, fundamental estimate

References:

File: file232.html

Abstract:We consider a problem related to resistance spot welding. The mathematical model describes the equilibrium state of an elastic, cracked
body subjected to heat transfer and electroconductivity and can be
viewed as an extension to the classical thermistor problem.
We prove existence of a solution in Sobolev spaces.

Keywords: crack, thermistor, thermoelastic contact, spot welding

References:

File: file233.html

Abstract:In this paper is constructed an aproximate solution to P (x; D)G = H, Gj@? = F in the space of generaliaed Colombeau functions on ?. Here P is a differential operator with coefficients which are generalized functions (for example singular distributions), ? is a bounded open set, and H and F are generalized functions. Also, solutions to a class of elliptic equations with coefficients in G are obtained in somewhat different way. In the case of smooth coefficients, the consistency of the classical weak solution and the generalized solution is proved. Specially, for a class of second order elliptic equations with bounded coefficients the proposed method of finding generalized solutions produces the approximate solutions to the classical Dirichlet problem.

Keywords: generalized solutions, Dirichlet problem, elliptic second order linear PDE, singular perturbations.

MSC:

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File: file235.html

Abstract:The Novikov-Shubin numbers are defined for open manifolds with bounded geometry, the ?-trace of Atiyah being replaced by a semicontinuous semifinite trace on the C?-algebra of almost local operators. It is proved that they are invariant under quasi-isometries and, making use of the theory of singular traces for C?-algebras developed in [29], they are interpreted as asymptotic dimensions since, in analogy with what happens in Connes' noncommutative geometry, they indicate which power of the Laplacian gives rise to a singular trace. Therefore, as in geometric measure theory, these numbers furnish the order of infinitesimal giving rise to a non trivial measure. The dimensional interpretation is strenghtened in the case of the 0-th Novikov-Shubin invariant, which is shown to coincide, under suitable geometric conditions, with the asymptotic counterpart of the box dimension of a metric space. Since this asymptotic dimension coincides with the polynomial growth of a discrete group, the previous equality generalises a result by Varopoulos [52] for covering manifolds.

References:

File: file237.html

Abstract:The electric properties of monolithic microwave integrated circuits can be described in terms of their scattering matrix using Maxwellian equations. The corresponding three-dimensional boundary value problem of Maxwell's equations can be solved by means of a finite-volume scheme in the frequency domain. This results in a two-step procedure: a time and memory consuming eigenvalue problem for nonsymmetric matrices and the solution of a large-scale system of linear equations with indefinite symmetric matrices. Improved numerical solutions for these two linear algebraic problems are treated.

MSC:

References:

File: file238.html

Abstract:This is a study on the initial and boundary value problem of a symmetric hyperbolic system which is related to the conduction of heat in solids at low temperatures. The nonlinear system consists of a conservation equation for the energy density e and a balance equation for the heat AEux Qi, where e and Qi are the four basic oelds of the theory. The initial and boundary value problem that uses exclusively prescribed boundary data for the energy density e is solved by a new kinetic approach that was introduced and evaluated by Dreyer and Kunik in [1], [2] and Pertame [3]. This method includes the formation of shock fronts and the broadening of heat pulses. These eoeects cannot be observed in the linearized theory, as it is described in [4].

Keywords: Heat transfer, initial and boundary value problems for a hyperbolic system, shock waves, kinetic theory.

MSC:

References:

File: file240.html

Abstract:Let n-dimensional Gaussian random vector x = ? + v be observed where ? is a standard n-dimensional Gaussian vector and v 2 Rn is the unknown mean. In the papers [3, 5] there were studied minimax hypothesis testing problems: to test null - hypothesis H0 : v = 0 against two types of alternatives H1 = H1(?n) : v 2 Vn(?n). The orst one corresponds to multi-channels signal detection problem for given value b of a signal and number k of channels containing a signal, ?n = (b; k). The second one corresponds to lnq -ball of radius R1;n with the lnp -ball of radius R2;n removed, ?n = (R1;n; R2;n; p; q) 2 R4+. It was shown in [3, 5] that often there are essential dependences of the structure of asymptotically minimax tests and of the asymptotics of the minimax second kind errors on parameters ?n. These imply the problem: to construct adaptive tests having good minimax property for large enough regions ?n of parameters ?n. This problem is studied here. We describe the sets ?n such that adaptation is possible without loss of eOEciency. For other sets we present wide enough class of asymptotically exact bounds of adaptive eOEciency and construct asymptotically minimax test procedures.

Keywords: minimax hypotheses testing, adaptive hypotheses testing, asymptotics of error probabilities.

MSC:

References:

File: file242.html

Keywords: traffic simulation, combinatorial optimization, scheduling

MSC:

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File: file243.html

Abstract:This paper is devoted to the study of nonlinear geometric optics in Colombeau algebras of generalized functions in the case of Cauchy problems for semilinear hyperbolic systems in one space variable. Extending classical results, we establish a generalized variant of nonlinear geometric optics. As an application, a nonlinear superposition principle is obtained when distributional initial data are perturbed by rapid oscillations.

Keywords: Semilinear hyperbolic systems, Cauchy problems, nonlinear geometric optics, generalized solutions, delta waves.

MSC:

References:

File: file244.html

Abstract:This paper modioes the coupled mode model for semiconductor lasers, taking into account the gain dispersion of the optical waveguide. Fitting the true gain curve by a Lorentzian, we obtain a correction for the dielectric function of the waveguide. A review of the derivation of the coupled mode model from the Maxwell Equations, including the corrected dielectric function, leads to an extended set of model equations. This extended model consists of the modioed coupled mode equations and additional polarization equations and reAEects spectral selectivity due to the geometry (waveguide dispersion) as well as the material properties (material dispersion). Although it is mathematically more complex, it does not increase the computational eoeort for the dynamical simulation essentially and, thus, it should replace the original model at least for numerical calculations.

Keywords: Semiconductor laser modelling, gain dispersion of semiconductors, DFB Lasers.

References:

File: file245.html

Abstract:In this paper we study 2-dimensional Ising spin glasses on a grid with nearest neighbor and periodic boundary interactions, based on a Gaussian bond distribution, and an exterior magnetic field. We show how using a technique called branch and cut, the exact ground states of grids of sizes up to 100 ? 100 can be determined in a moderate amount of computation time, and we report on extensive computational tests. With our method we produce results based on more than 20 000 experiments on the properties of spin glasses whose errors depend only on the assumptions on the model and not on the computational process. This feature is a clear advantage of the method over other more popular ways to compute the ground state, like Monte Carlo simulation including simulated annealing, evolutionary, and genetic algorithms, that provide only approximate ground states with a degree of accuracy that cannot be determined a priori. Our ground state energy estimation at zero field is ?1:317.

References:

File: file247.html

Abstract:We consider disordered lattice spin models with finite volume Gibbs measures ??[?](doe). Here oe denotes a lattice spin-variable and ? a lattice random variable with product distribution IP describing the disorder of the model. We ask: When will the joint measures lim?"ZZd IP (d?)??[?](doe) be [non-] Gibbsian measures on the product of spin-space and disorderspace? We obtain general criteria for both Gibbsianness and non-Gibbsianness providing an interesting link between phase transitions at a fixed random configuration and Gibbsianness in product space: Loosely speaking, a phase transition can lead to non-Gibbsianness, (only) if it can be observed on the spin-observable conjugate to the independent disorder variables.

Keywords: Disordered Systems, Gibbs-measures, non-Gibbsianness, Random Field Model, Random Bond Model, Spinglass

References:

File: file248.html

Abstract:We are interested in algorithms for constructing surfaces ? of possibly small measure that separate a given domain ? into two regions of equal measure. Using the integral formula for the total gradient variation, we show that such separators can be constructed approximatively by means of sign changing eigenfunctions of the p-Laplacians, p ! 1, under homogeneous Neumann boundary conditions. These eigenfunctions are proven to be limits of a steepest descent methods applied to suitable norm quotients. Finally we use these ideas for the construction of separators on simplex grids.

Keywords: p-Laplacian, eigenfunctions, separators.

MSC:

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File: file25.html

Abstract:The electrical properties of the circuits are described in terms of their scattering matrix using Maxwellian equations. Using a finitevolume scheme a three-dimensional boundary value problem for the Maxwellian equations in the frequency domain can be solved. This results in a two-step procedure: a time and memory consuming eigenvalue problem for nonsymmetric matrices and the solution of a largescale system of linear equations with indefinite symmetric matrices. Improved numerical solutions for these two linear algebraic problems, the computation of the scattering matrix and of the used orthogonality relation are treated in this paper. The numerical effort could be reduced considerably.

MSC:

References:

File: file252.html

Abstract:We prove that the problem to get an inclusion minimal elimination ordering can be solved in linear time for planar graphs. The basic structure of the linear time algorithm is as follows. We select a vertex r as maximum and get a first approximation of a minimal elimination ordering considering a vertex x as smaller than y if x has a larger distance than y from r. Using planarity, one can determine the fill-in edges joining two vertices of the same distance from r almost immediately. The algorithm determines an O(n)-representation of these fill-in edges. To determine the final fill-in ordering, we use similar techniques as in the general parallel minimal elimination algorithm of [5].

References:

File: file253.html

Abstract:This paper is concerned with the one-dimensional stationary linear Wigner equation, a kinetic formulation of quantum mechanics. Specifically, we analyze the well-posedness of the boundary value problem on a slab of the phase-space with given inflow data for a discrete-velocity model.

References:

File: file255.html

Abstract:We show that Bourgain's estimate LK <= cn 14 log n for the isotropic con-
stant holds true for non-symmetric convex bodies as well.

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File: file257.html

Abstract:The axiomatic formulation of quantum field theory (QFT) of the 1950's in terms of fields defined as operator valued Schwartz distributions is re-examined in the light of subsequent developments. These include, on the physical side, the construction of a wealth of (2- dimensional) soluble QFT models with quadratic exchange relations, and, on the mathematical side, the introduction of the Colombeau algebras of generalized functions. Exploiting the fact that energy positivity gives rise to a natural regularization of Wightman distributions as analytic functions in a tube domain, we argue that the flexible notions of Colombeau theory which can exploit particular regularizations is better suited (than Schwartz distributions) for a mathematical formulation of QFT.

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Abstract:We study regularization methods for the integral equation of the orst kind with analytical kernel of logarithmic type. The problem is severely ill-posed. In [1] a logarithmic type convergence rate for the Tikhonov regularized solution was proved. Here we are concerned with numerical aspects of the solution. First we consider the selfregularization of the problem by using projection methods in the sense of [9].Then we will see that the Tikhonov regularization of such methods is in accordance with a discretized version of the Tikhonov regularized solution in [1]. Finally, we describe numerical experiments being in a good agreement with the theoretical results.

Keywords: regularization by discretzation, selfregularization, projection methods, Tikhonov regularization, severely ill-posed, integral equation of the orst kind, logarithmic convergence rate.

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File: file260.html

Abstract:The electric properties of monolithic microwave integrated circuits can be described in terms of their scattering matrix using Maxwellian equations. The corresponding three-dimensional boundary value problem of Maxwell's equations can be solved by means of a finite-volume scheme in the frequency domain. This results in a two-step procedure: a time and memory consuming eigenvalue problem for nonsymmetric matrices and the solution of a large-scale system of linear equations with indefinite symmetric matrices. Improved numerical solutions for these two linear algebraic problems are treated.

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File: file266.html

Abstract:The scattering matrix describes monolithic microwave integrated circuits that are connected to transmission lines in terms of their wave modes. Using a onite-volume method the corresponding boundary value problem of Maxwell's equations can be solved by means of a two-step procedure. An eigenvalue problem for non-symmetric matrices yields the wave modes. The eigenfunctions determine the boundary values at the ports of the transmission lines for the calculation of the oelds in the three dimensional structure. The electromagnetic oelds and the scattering matrix elements are achieved by the solution of large-scale systems of linear equations with indeonite symmetric matrices. Improved numerical solutions for the time and memory consuming problems are treated in this paper. The numerical eoeort could be reduced considerably.

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File: file267.html

Abstract:We consider the problem of adaptive spatial smoothing for a time series of images. This type of data typically occurs in functional and dynamic Magnet Resonance Imaging (MRI). We propose a new method based on spatial smoothing with adaptively chosen weights. We show how this procedure can be used for eOEcient image estimation and classiocation in functional and dynamic MRI experiments. The performance of the procedure is illustrated by applications to simulated and real data.

Keywords: adaptive smoothing; spatial adaptation; functional MRI; signal detection; dynamic MRI.

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File: file268.html

Abstract:In this paper we present an overview of recent work on lattice and measure-valued models of catalytic reactions and in particular catalytic branching systems. The main phenomena exhibited by nearly critical branching systems are dimension-dependent clumping in small and large space and time scales. Special emphasis is given to the eoeects which occur when the catalyst is highly clumped and in particular when in the continuum models the catalyst is a time-dependent singular measure. Finally, the interactive model of mutually catalytic branching is described and some recent results are reviewed. >= The basic tools include log-Laplace functionals, measure-valued martingale problems, collision local times, and duality.

Keywords: Catalytic super-Brownian motion, catalytic super-random walk, catalyst, reactant, superprocess, measure-valued branching, absolute continuity, self-similarity, collision local time, glycolysis, martingale problem, segregation of types, coexistence of types, self-duality.

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File: file269.html

Abstract:The paper contains a macroscopic continuum model of adsorption in porous materials consisting of three components. We consider the AEow of a AEuid/adsorbate mixture through channels of a solid component. The AEuid serves as carrier for an adsorbate whose mass balance equation contains a source term. This term consists of two parts: orst a Langmuir contribution which is connected with bare sites on internal surfaces and describes the Langmuir isotherm in equilibrium. The second one is due to changes of the internal surface driven by the source of porosity which is a part of the balance equation for porosity. We clearly state the range of applicability of the model. A simple numerical example which describes the transport of pollutants in soils illustrates the coupling of adsorption and dioeusion. The results show that after a certain time arises a maximum in the rate of adsorption as a function of AEuid/adsorbate velocity.

Keywords: Adsorption, dioeusion, AEows in porous and granular materials.

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File: file272.html

Abstract:Recently, Barvinok, Johnson, Woeginger, and Woodroofe have shown that the Maximum TSP, i. e., the problem of finding a traveling salesman tour of maximum length, can be solved in polynomial time, provided that distances are computed according to a polyhedral norm in IRd, for some fixed d. They stated as an open problem to resolve the complexity of finding a maximum length tour under Euclidean distances in a space of fixed dimension. In this paper it is shown that the Maximum TSP under Euclidean distances in IRd for any fixed d >= 3 is NP-hard, shedding new light on the well-studied difficulties of Euclidean distances. In addition, our result implies NP-hardness of the Maximum TSP under polyhedral norms if the number k of facets of the unit ball is not fixed, and NP-hardness of the Maximum Scatter TSP for geometric instances, where the objective is to find a tour that maximizes the shortest edge.

Keywords: Traveling Salesman Problem, combinatorial optimization, geometric optimization, Euclidean norm, polyhedral norm, computational complexity.

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Abstract:Since it is unlikely that any NP-complete problem will ever be efficiently solvable, one is interested in identifying those special cases that can be solved in polynomial time. We deal with the special case of Boolean formulas where the logical implication ! is the only operator and any variable (except one) occurs at most twice. For these formulas we show that an infinite hierarchy S1 ? S2 ? ? ? exists such that we can test any formula from Si for falsifiability in time O(ni), where n is the number of variables in the formula. We describe an algorithm that finds a falsifying assignment, if one exists. Furthermore we show that the falsifiability problem for S1i=1 Si is NP-complete by reducing the SAT-Problem. In contrast to the hierarchy described by Gallo and Scutella for Boolean formulas in CNF, where the test for membership in the k-th level of the hierarchy needs time O(nk), our hierarchy permits a linear time membership test. Finally we show that S1 is neither a sub- nor a superset of some commonly known classes of Boolean formulas, for which the SAT-Problem has linear time complexity (Horn formulas, 2-SAT, nested satisfiability).

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