bluuebunny/crossref_metadata_2025 huggingface dataset:
Application of Filtered Poisson Process in Modeling Fatigue Cracks Propagation
Authors: Śniady P. , Sieniawska R. , Żukowski S.
Published: December 2010

A stochastic model of fatigue crack propagation based on stochastic fatigue cracks growth equation is proposed. It is an extension of models given by Y. K. Lin, B. F. Spencer and K. Sobczyk. The model proposed includes the properties of both the continuous and the jump model and make possible to take into account the random disturbances in fatigue phenomenon, which are described by a nonnegative stochastic process. It is assumed that the process of disturbances can be described by a stochastic differential equation which together with the fatigue cracks growth equation builds a set of equations which can be treated as generalized Ito equations.
On initial‐boundary value problems for the inelastic material behaviour of metals
Authors: Krzysztof Chełmiński
Published: December 2010

We prove existence of strong solutions for a subclass of noncoercive, monotone constitutive equations in the theory of inelastic material behaviour of metals.
Comparison of two methods for the approximate analysis of nonlinear stochastic dynamical systems
Authors: Sobiechowski C.
Published: December 2010

Generalizations of the Gram‐Charlier series of type A and C are used to approximate the probability density function (p. d. f.) of stochastic nonlinear dynamical systems under parametrical or external white noise excitation. By means of the Fokker‐Planck equation, the expansion coefficients are obtained from a system of linear equations and a system of equations with a quadratic nonlinearity respectively. The approximations of the p. d. f. are compared and critical remarks concerning applicability are made.
Zum Korrelationskoeffizienten zweidimensionaler Zufallsgrößen mit unterschiedlichen stetigen Randverteilungen
Authors: Stich W. J. A.
Published: December 2010

Der Betrag des Pearsonschen Korrelationskoeffizienten p(X, Y) ist bekanntlich genau dann 1, wenn die Zufallsgrößen X und Y (fast überall) linear voneinander abhängen. In dieser Arbeit soll untersucht werden, wie groß p(X, Y) werden kann, wenn die Randverteilungen nicht zur gleichen Klasse gehören, z. B. wenn eine Randverteilung normal‐ und die andere gleichverteilt ist.
Effiziente Lösung einer realistischen Optimalsteuerungsaufgabe durch Transformation des Randwertproblems
Authors: Stragies R. , Chudej K. , Bulirsch R.
Published: December 2010

Wir stellen einen neuen Ansatz zur effizienten Lösung zustandsbeschränkter Optimalsteuerungsaufgaben vor. Dazu erweist sich ein Hybridansatz bestehend aus einem direkten Kollokationsverfahren [7] und einem indirekten Mehrzielalgorithmus [1,4] als zweckmäßig. Wesentliche Verbesserungen der Konditionierung des vom indirekten Verfahren zu lösenden Randwertproblems erzielen wir durch eine geschickte Transformation des Randwertproblems. Zur Vorführung dient der reichweitenmaximale Flug eines Überschallflugzeugs mit nichtlinearer Zustandsbeschränkung.
On some multicriterial problem under uncertainty
Authors: Tarakanov A.
Published: December 2010

In the communication a multicriterial variant of the “Game with Nature” is considered. It is assumed that Decision Maker (DM) is informed about situation insufficiently. In another words, he is forced to make decisions in uncertainty conditions. DM takes into account a reaction of Nature integrally. DM estimates his strategy by several criteria, which he desires to maximize.

By mathematics, the problem is formulated as multicriterial optimization problem in uncertainty conditions. It is formulated below a definition of Pareto‐optimal solution and considered a “rolled” criterion (cost function) making it possible to find all such solutions. Further, an approximating problem is formulated and proved some assertions about optimal solution character.
Numerical Solution of Flow Problems in Spherical Geometry with Spectral Methods
Authors: Tilgner A.
Published: December 2010

This contribution presents a spectral method used for solving magnetohydrodynamic problems in spherical geometry. The advantages of the method for the problem at hand are emphasized. The accuracies obtained with finite differences and a particular spectral discretization (Chebychev collocation) are compared for a one dimensional model problem.
Uniformly convergent methods for singularly perturbed problems
Authors: Uzelac Zor. , Surla Kat.
Published: December 2010

The present paper deals with boundary layer problem which represents the mathematical model for a large scale of practical problems in dynamics, fluid mechanics, chemistry and biology.

The aim of this paper is to construct the approximate solution of the given problem in the form of quadratic splines on a simple piecewise equidistant mesh of Shishkin type and on a mesh of Bakhvalov type, which is a graded mesh specially constructed a priory to fit the problem.

In the linear case we prove that the method is almost second order accurate, uniformly in the perturbation parameter, on the mesh of Shishkin type. Presented numerical experiments indicate the same result in the nonlinear case, while the second order of accuracy can be achieved on the mesh of Bakhvalov type.
Conservative procedure of grid functions recalculation in 2d gasdynamics
Authors: Chernigovski S. , Novac S.
Published: December 2010

Known conservative remapping procedures in 2D computational fluid dynamics use the integral formulation of conservative laws and are very expensive because of volume integral calculations on overlapping grids. We suggest in the present paper a robust and efficient grid functions recalculation algorithm which guarantees both a sufficient accuracy and conservativity for smooth and non‐smooth solutions in arbitrary regions of the grid. It consists, as in 1D case [1], of two steps. The first step is a non‐conservative interpolation. The second one is the conservative modification of the obtained data by means of solution of special functional minimization problems in order to provide the fulfillment of conservation laws, namely for mass, impulse and total energy. The numerical tests have shown the applicability of the procedure in tough regimes of 2D gasdynamical problems simulation.
Robust stability of differential delay systems
Authors: Verriest Erik I.
Published: December 2010

Based on the Lyapunov‐Krasovskii theory, a sufficient condition involving the existence of a triple of positive definite matrices satisfying a certain Riccati equation has been derived for the robust stability (independent of the delay) of linear differential delay systems. In this paper an extension for the robust stability of neutral equations is explored.
Asymptotics and exact results for some elasticity problems for beams with cracks in polygonal cross‐sections
Authors: Vlasov V. I. , Skorokhodov S. L.
Published: December 2010

By means of an analytic method the exact value of torsional rigidity for a beam with frame‐type profile and asymptotics for stress intensity factor for a beam with crack have been obtained.
Block multipole method for boundary value problems in complex‐shaped domains
Authors: Vlasov V. I. , Volkov‐Bogorodsky D. B.
Published: December 2010

New efficient analytic‐numerical method for solving elliptic boundary‐value problems in 2D and 3D complex‐shaped domains is presented. The case of domains with rounded cones is considered in detail.
Numerically efficient modeling in multibody dynamics
Authors: Schwerin Reinhold
Published: December 2010

The development of the integrator library MBSSIM [6] has shown that the efficient simulation of multibody systems such as vehicles or heavy machines in descriptor form greatly depends upon the interrelation between modeling and simulation. This subject will be studied using the scalable model of the IR‐chain [7]. It will be shown that a recursive solution of the arising linear systems in connection with a structure enhancing modeling using special natural coordinates greatly improves the performance of simulation tools.
Method of lines for the numerical simulation of heat exchangers
Authors: Wagner Yvonne
Published: December 2010

Heat exchangers are central units within a chemical engineering plant. The time‐dependent, one‐dimensional modelling of such a unit yields a coupled system of hyperbolic partial and ordinary differential equations. Commercial simulation packages need DAEs for all unit operations as input to solve the equations for the whole plant simultaneously. Thus, the method of lines is applied.

For the spatial discretization upwind difference schemes are compared with an ENO (Essentially Non‐Oscillatory) method. The latter approach is tailored to scalar conservation laws, but ENO methods also perform well on linear systems with source terms.
Selbstadaptive Gitterverfeinerung und ‐vergröberung für das Lösen der Eulergleichungen
Authors: Warendorf Katina , Rühle Roland
Published: December 2010

Partielle Differentialgleichungen müssen häufig auf sehr komplexen technischen Konfigurationen gelöst werden. Zur Lösung der Eulergleichungen wird hier die Finite Volumen Methode auf Gittern aus allgemeinen, polygonal berandeten Kontrollvolumen verwendet. In diesem Artikel wird eine selbstadaptive Strategie zur Gitterverfeinerung und ‐vergröberung dieser speziellen Gitter mit ihren Fehlerschätzern vorgestellt. Ausgangspunkt der Simulation ist ein einzelnes Kontrollvolumen, das die Grenzen des Rechengebietes darstellt. Die Gittergenerierung ist vollständig in den Simulationsprozeß integriert. Durch wiederholtes Verfeinern und Vergröbern entsteht automatisch ein lösungsangepaßtes Gitter.
Learning periodic signals with recurrent neural networks
Authors: Weiss Martin G.
Published: December 2010

We study a model for learning periodic signals in continouus time recurrent neural networks where the weight matrix has companion‐like structure. We use a model reference approach to derive a learning rule which solves the following learning problem: A network with unknown weights is running in closed loop mode giving a periodic trajectory. The output of this reference system is used as the input of a second learning network of the same structure with adjustable weights. We derive a learning rule (parameter adaptation law for the weights) which achieves the aims: Under appropriate assumptions the weights converge to the reference weights and the output tracking error goes to zero. If the learning dynamics is switched off after a sufficient period of time the learning system can approximately reproduce the reference signal when running in closed loop mode.
Error estimators for mortar finite element discretizations
Authors: Wohlmuth B.
Published: December 2010

We consider two different types of error estimators for a nonconforming domain decomposition method, the so‐called mortar finite element method. At the interfaces of the subdomains is no conformity condition enforced. An example is presented where we obtain strongly nonconforming triangulations within the adaptive refinement process.
Optimal control for elastic space constructions
Authors: Zakrzhevskii A.
Published: December 2010

The problem of optimal control is considered for elastic constructions the same as great Space constructions and rocket systems. Proper solution of the problem permits to lover or to eliminate the negative inluence of elasticity on behaviour of the construction as object of the control. Current methods used to solve the problem are based on creation of vibroisolation systems for elastic elements or of the optimal control that extinguishes one‐two of first elastic modes, that do not guarantees nonperturbation of the rest elastic modes. Adequate accounting of elastic properties of the constructions in the criterion of optimization, recommended by the author, permits to create the optimal control which damps all elastic modes of the controlled system.
Nichtlineare stetige Beobachter
Authors: Zeitz M.
Published: December 2010

Most state estimation methods for smooth nonlinear systems are also smooth and require that the Taylor linearization of the system is observable. The presented design of continuous observers can be applied if the nonlinear system is observable but not its Taylor linearization. In this case, the observability map of the system is a semi‐diffeomorphism which means that the map has only a continuous (and no smooth) inverse. A continuous observer is designed in the observability normal form coordinates and comprises a dynamic and an algebraic part. At least the algebraic part defined by the inverse observability map is continuous.

The continuous observer approach can also be used to solve the critical observation problem if the Taylor linearization has only non‐detectable eigenvalues with a zero real part. Moreover, this approach allows an extension of the nonlinear normal form observer design because the observability rank condition is no more required. As distinct from the first presentation of continuous observers an [9], the design of nonlinear continuous observers is treated from a more applied point of view and is illustrated by examples for which smooth observers do not exist.
Reduced‐order DAE models for turbomachinery stall, surge, and flutter
Authors: Copeland George Scott
Published: December 2010

A reduced‐order model for the nonlinear dynamic behavior of flexibly‐bladed turbomachines has been developed as a system of differential‐algebraic equations. Simulations and stability analyses are presented.
A note on the volatility term structure in short rate models
Authors: Darbellay Georges A.
Published: December 2010

In finance, interest rate option models based on a stochastic process for the short rate are widely used by practitioners, yet the calibration of their volatility input is not as straightforward as it seems. One problem with these Markovian one‐factor models is that they cannot reproduce an arbitrary volatility curve. They can be made to fit any initial volatility function but the volatility curve being assumed at future times is liable to be quite different from that being assumed initially. Here, we study a lognormal process and investigate how to specify the volatility constraints in such a way that the term structure of volatility at future times, as implied by the short rate process, remains “stable”.
Simultaneous activity and attenuation emission tomography as a nonlinear ill‐posed problem
Authors: Dicken Volker
Published: December 2010

In Single Photon Emission Computed Tomography (SPECT) one is interested in reconstructing the activity distribution f of some radiopharmaceutical. Alas the data gathered suffer from attenuation described by the tissue density μ. We only have noisy sample values of the Attenuated‐Radon‐Transform

(which is nonlinear in μ) per imaged slice at hand. Traditional theory for SPECT reconstruction treats μ as a known parameter. In practical applications however μ is not known, but crudely estimated or neglected. We try to develop an algorithm that approximates both f and μ from SPECT data alone, in order to obtain quantitatively accurate SPECT images. This is done using Tikhonov regularization techniques developed for non‐linear parameter estimation problems in differential equations and an adapted Gauß‐Newton‐CG minimization algorithm.
Zur Potenziteration für schiefsymmetrische Matrizen
Authors: Dietrich G. K. P.
Published: December 2010

Die Potenziteration nach von Mises konvergiert bekanntlich nur im Falle eines dominanten Eigenwertes. Eine Ausnahme von dieser Regel bilden reell schiefsymmetrische Matrizen bzw. ‐paare.

Obgleich hier mindestens zwei betragsgleiche dominante Eigenwerte auftreten, kann eine Vektoriteration in Form eines Doppelschritt‐Algorithmus formuliert werden, die im Vergleich zur simultanen Iteration mit zwei reellen Vektoren bei gleichem Rechenaufwand etwa doppelt so schnell konvergiert. Eine alternative Formulierung als Relaxationsalgorithmus ist möglich. Die obigen Erkenntnisse sind sinngemäß auf die Methode des stärksten Anstiegs bzw. Abstiegs und der konjugierten Gradienten übertragbar und ergeben ähnliche Verbesserungen.

Für Aufgaben mit physikalischem Hintergrund lassen sich Startvektoren angeben, die Lösungen eines “verkürzten” Problems sind. Anhand einiger Vergleichsrechnungen wird die Effektivität der Algorithmen demonstriert.
Verified construction of fully symmetric cubature formulae of degree 4k‐1 with few nodes for fully symmetric planar regions using invariant theory
Authors: Dietrich S.
Published: December 2010

Traditionally, the construction of a cubature formula requires solving a large system of nonlinear equations to determine the nodes and weights. Using invariant theory this system is easy to solve due to the smart choice of an appropriate basis for the vector space spanned by the polynomials which are invariant with respect to the symmetry group of the square. The presented method for the verified construction of two‐dimensional fully symmetric cubature formulae of degree 4k ‐‐ 1 has the great advantage that even for high degrees the hardest computation to perform is solving a linear system and a system of two polynomial equations of relatively low degree in two unknowns.

Enclosures of the nodes and weights are obtained by means of interval arithmetic and verification algorithms for solving linear and nonlinear systems of equations. In order to compute enclosures of high accuracy the optimal scalar product and istaggered arithmetic are employed.

The described method constructs formulae with fewer nodes than the Gauss‐product formulae of the same degree, if existing, and it even allows one to obtain some new formulae in some particular cases.
Crystalline microstructures with finite surface energy
Authors: Dolzmann Georg
Published: December 2010

Certain alloys like In‐Tl, Ni‐Ti or Cu‐Al‐Ni undergo a solid‐solid phase transition which leads to a complicated arrangement of different phases on a microscopic scale. Many of the observed geometric patterns have been successfully modelled by minimizing the elastic energy. This approach, however, does not determine the length scale of the observed microstructures.

As a particular example we study a two‐dimensional model for a cubic to tetragonal phase transition. We discuss the structure of minimizers of the elastic energy and the impact of including surface energy. The mathematical analysis combines ideas from geometry and geometric measure theory. In particular we use a Liouville type theorem on sets of bounded perimeter.
A comparison of the shell theories in the sense of Kirchhoff and cosserat
Authors: Stefan Ebenfeld
Published: December 2010

We compare the different shell theories for several physical settings and give asymptotic expansions for the solutions to the respective problems.
Symmetrie elementarer Funktionen: Entscheidbarkeitsfragen und Algorithmen
Authors: Gerbracht Eberhard H. A. , Struckmann Werner
Published: December 2010

Wir zeigen, daß das Symmetrieproblem für die Klasse aller elementaren Funktionen nicht entscheidbar ist: Es gibt keinen Algorithmus, der feststellt, ob eine beliebig vorgegebene elementare Funktion punkt‐ oder achsensymmetrisch ist und der ggf. den Symmetriepunkt bzw. die Symmetrieachse ermittelt.

Das Beispiel der polynomialen Funktionen zeigt hingegen, daß es Klassen elementarer Funktionen gibt, deren Symmetrieproblem entscheidbar ist. Dieses Ergebnis läßt sich auf die Klasse der rationalen Funktionen verallgemeinern. Der hieraus resultierende Algorithmus ist als weiterer Bestandteil eines MAPLE‐Programms zur Diskussion elementarer Funktionen geplant.
On the Error of Approximation of Solutions of Operator Equations by Projective Methods
Authors: Gorbachuk M.
Published: December 2010

This paper is devoted to direct and inverse theorems of the approximation theory for solutions of operator equations of the form Au = f. The approximation is realized by variational methods, namely the Ritz method, the method of least squares, and the moment one. It is shown that the error of the approximation by these methods is completely determined by the order of smoothness of a solution with respect to a certain cognate to A operator associated with an approximation method.
Stabilization of discrete‐time bilinear systems
Authors: Grüne L. , Wirth F.
Published: December 2010

The problem of feedback stabilizing a bilinear discrete‐time system is studied. Under an accessibility condition on an associated nonlinear system on the projective space it can be shown that null controllability is equivalent to feedback stabilizability. We present a way in which a stabilizing feedback may be computed using some ideas from discounted optimal control.
Semilinear Control Systems with Symmetry
Authors: Grünvogel Stefan
Published: December 2010

If a semilinear control system possesses state space symmetry, there exist linear subspaces, which are invariant under every applied control. For the associated control system on projective space this means, that there exist invariant projective subspaces and therefore the system is not local accessible. On the first view this seems to be a disadvantage, because local accessibility is fundamental for the analysis of Lyapunov exponents, which determine the exponential stability properties. But it turns out, that we can restrict ourselves to the restricted control systems on these singular subspaces, because the whole Floquet and Morse spectrum (and therefore the Lyapunov spectrum) is attained on these subspaces.
Schranken für die positive Wurzel von Polynomen in der Finanzmathematik
Authors: Haase G. , Herzberger J.
Published: December 2010

In der Sensitivitätsanalyse bei Polynomgleichungen, die in der Finanzmathematik bei der Berechnung des Effektivzinssatzes einer Rente auftreten, werden obere und untere Schranken für die eindeutige, positive Polynomwurzel benötigt. Es werden hier solche Abschätzungen angegeben, welche es gestatten, das NEWTON‐FOURIER‐Verfahren oder etwa das intervallmäßige NEWTON‐Verfahren zu starten.
Downwind Gauß‐Seidel‐Smoothing for Convection‐Dominated Problems
Authors: Wolfgang Hackbusch , Thomas Probst
Published: December 2010

Due to the vanishing ellipticity, multigrid methods for convection‐dominated problems tend to loose their good convergence properties. With a suited discretisation, an appropriate ordering of the unknowns and, if necessary, a special block partitioning, the smoothing property of the Gauß‐Seidel iteration and therefore good convergence can be regained. This paper deals with such an ordering strategy and block partitionings.
A Contribution to the Nonparametric Statistics of Particle Systems
Authors: Heinrich L. , Werner M.
Published: December 2010

Consistency and asymptotic normality of a kernel‐type estimator for the second‐order product density of the stationary point process of exposed tangent points associated with a Boolean model are proved. This estimator is used to estimate characteristics of the typical grain. In the case of spherical grain we obtain an empirical nonparametric distribution function of the radii. This can be used to treat Wicksell's corpuscle problem even if overlapping grains are unobservable.
Analysis of a finite‐infinite element method for exterior Helmholtz problems
Authors: Ihlenburg Frank , Demkowicz Leszek
Published: December 2010

We present new analytical results on stability and convergence for infinite elements. The key idea of our analysis is to identify the infinite elements with a Dirichlet‐to‐Neumann boundary operator.
Shooting Type Methods for Solving the two point boundary value problem in the optimization of flight vehicles evolutions
Authors: Istratie V.
Published: December 2010

Briefly, a shooting method connst in the repeated solving of the Cauchy problem of the n differential equations, being correlated with a Newton procedure modified by the solving of the equations containing, as unknown, for example, parameters at the initial time resulted due to integration; the number of these equations should be equal with the number of parameters considered and equal with the number of final conditions having fixed values. The parameters are modified during the shooting process and this process is repeated (the convergence being ensured) until the final conditions are checked with a certain imposed error. One determined, the parameters at the initial final time are resulted due to integration. One may remark that the shooting method may also be applied when all the parameters (at the initial and final time) considered.

The description of the shooting method, for the clarity of its presentation and of its application manner, will be made based on the concrete case of solving the two point boundary value problem related to the optimization of the hover skip, entry with final maximum velocity at a given azimuth of the space vehicle in the Earth atmosphere.
Existence theory to the equations in viscoelasticity at finite deformations
Authors: Jäpel Irg
Published: December 2010

The usual equations of motion combined with a constitutive law for a viscoelastic metal string lead us to a nonlinear, strictly hyperbolic system in one space dimension. The system under consideration is associated with a free damping boundary condition and continuously differentiable initial conditions. In the case of small initial data it is possible to prove global existence of a classical solution, whereas for large data a blow up result is obtained.
Refinement of Iterative Techniques in Topology Optimization
Authors: Kasprzak T. , Kutylowski R. , Myslecki K.
Published: December 2010

The optimal shape design of a structure is studied as a material distribution problem. The main goal of this paper is find out the optimal mass distribution for restricted mass of the construction. The analysis is carried out through FEM. The iterative procedure includes two steps. The first one leads to continues distribution of material. In other words the stiffness of the construction flows from very strong to very weak. The second iterative steps leads to discrete 0 or 1 distribution of material. The algorithm solves the problem for the same model boundary during the iterative process.
Multiscale Problems; Meshes and Solvers
Authors: Kickinger Ferdinand
Published: December 2010

The efficient solution of large scaled finite element (f. e.) equations from industrial problems is a challenging task. Typically, such problems are quite complex due to the multiscale behavior of the geometry and the data. This is the reason why standard algorithms for mesh generation and solution are inefficient or can even fail. In this context, robust methods for treating multiscale problems are needed.

The mesh generator should produce rather fine meshes catching the geometry with an asymptotically optimal complexity. Such a generator is proposed in two and tree dimensions. Usually, the meshes for geometries with microscales contain a large number of nodes. Thus, fast solvers for the f. e. equations are needed, where no hierarchical mesh structure is available. Such solvers are presented for the Potential and the Linear Elasticity Problems in two and three space dimensions within the framework of Algebraic Multigrid Methods. Together, these algorithms form an efficient tool for the Numerical Simulation of Multiscale Problems and can be easily integrated in existing f. e. codes including commercial codes.
A Note on the Global Extraction Element‐by‐Element Method
Authors: Kickinger F. , Langer U.
Published: December 2010

In the engineering literature, the so‐called Global Extraction Element‐by‐Element (GE‐EBE) Methods have been successfully used for solving real‐life mechanical problems, especially, in 3D [2], although the EBE preconditioners C haven't any asymptotically preconditioning effects on the stiffness matrix K, i. e. the spectral condition number k(C‐1K) behaves like O(h‐2), say, for elasticity problems. However, the method has quite good scaling properties. From a theoretical point of view, the GE‐EBE preconditioner is nothing else than an Additive Schwarz Method (ASM) preconditioner generated by an overlapping splitting of the finite element space into subspaces spanned by the element ansatz functions. The authors propose to use the GE‐EBE methods and their patch counterpart (GE‐PBP) either as smoothers, especially, in their multiplicative version, or as preconditioners in their multilevel additive version. In the multilevel version, such preconditioners are asymptotically optimal. The GE‐PBP smoother is especially suited for the use in Algebraic Multi‐Grid (AMG) Methods based on matrix graph coarsening strategies. The numerical results presented confirm the good smoothing properties of GE‐PBP smoothers as well as the preconditioning properties of multilevel additive GE‐PBP preconditioners. Finally, the authors discuss parallelization aspects.
Partitioning methods for the simulation of fast reactions
Authors: Kiehl M.
Published: December 2010

When solving stiff initial value problems the main computational work is related to the solution of large systems of linear equations. By partitioning the states into fast and slow variables, the dimension of these linear systems can essentially be reduced during the stationary phase. Unfortunately the transient phase and the stationary phase is different for each component, and transient components lie diagonal in the state space so that nearly all state variables behave transient. However, in reaction kinetics a different coordinate system can be used that is based on the reactions. This allows an efficient and dynamic partitioning. A similar strategy is possible in case of extremely fast reactions and then leads to differential algebraic equations.
Boundary Integral Equation Methods in the Theory of Thin Plates
Authors: Kirsch A. , Ritter S.
Published: December 2010

The bending of a thin elastic plate Ω [‐ho/2, ho/2] with bounded Ω ⊂ ℛ under transverse shear forces can be described by boundary value problems for a vector partial differential operator. The Dirichlet‐ and Neumann problems can be reformulated as a 3 × 3 system of boundary integral equations over δΩ. We study the integral operators and their singularities and investigate the Nyström method for the numerical solution of the boundary integral equations.
Asymptotic‐Induced Domain Decomposition Methods for Kinetic Equations with the Diffusion Scaling
Authors: Klar Axel
Published: December 2010

This paper deals with domain decomposition methods for kinetic and diffusion‐type macroscopic equations. As an example the radiative transfer case is treated. We consider radiative transfer equations coupled with a temperature equation. Using asymptotic analysis accurate coupling conditions at the interface between the kinetic and diffusion domain are developed. Moreover, the results of the simulation of a glass cooling process are shortly described.
Automatisierte a‐priori‐Fehlerabschätzung bei gleitkommamäßiger Ausdrucksauswertung
Authors: Krämer W.
Published: December 2010

Häufig stellt sich die Frage, wie weit ein auf einem Computer berechnetes Ergebnis vom exakten Ergebnis (berechnet im Körper der reellen Zahlen) entfernt ist. Die hier vorgestellten Sätze erlauben es, für die Gleitkommaauswertung eines vorgegebenen Ausdrucks eine worst‐case Fehlerschranke automatisch mit einem Computer zu berechnen. Die Bestimmung dieser relativen bzw. absoluten Fehlerschranke geschieht a‐priori. Sie ist gültig, solange die Daten (Parameter, unabhängige Variablen) des Ausdrucks innerhalb der Bereiche variieren, die bei der Fehlerabschätzung spezifiziert wurden. Alle Rundungsfehler sowie deren Fortpflanzung und Fehler, die sich aus der Nichtdarstellbarkeit von z. B. transzendenten Konstanten ergeben, werden sicher im Sinne einer worst‐case Fehleranalyse erfaßt.
Das Spektrum der Orr‐Sommerfeld‐Gleichung mit Blasius‐Strömungsprofil
Authors: Lahmann J.‐R. , Plum M.
Published: December 2010

Die Orr‐Sommerfeld‐Gleichung ist ein nichtselbstadjungiertes Eigenwertproblem der Form A[u] = λ B[u] aus der linearen Stabilitätstheorie inkompressibler, reibungsbehafteter Strömungen. wobei A und B gewöhnliche Differentialoperatoren vierter bzw. zweiter Ordnung sind:

Dabei bezeichnet α die Wellenzahl der Störung, R die Reynoldszahl der Grundströmung V und D = d/dx. In der vorliegenden Arbeit werden speziell für das Blasius‐Strömungsprofil als Grundströmung spektrale Eigenschaften ermittelt. Im ersten Teil wird das wesentliche Spektrum einer geeigneten operatortheoretischen Fassung von (1) mit störungstheoretischen Argumenten bestimmt, und im zweiten Teil mit Hilfe elementarer analytischer Mittel eine Einschließung des Gesamtspektrums. Das Blasiusprofil V ist als Ableitung der Lösung der folgenden nichtlinearen Randwertaufgabe definiert: 2fm + ffu = 0 auf (∞) mit f(0) = f' (0) = 0, limx‐∞ f'(x) = 1. Für das Blasiusprofil gilt V, V' Vn ∈ L∞, V ⩾ 0,V'⩾0.Vn⩽0.
Floquét‐Theory for Differential‐Algebraic Equations (DAE)
Authors: Lamour René
Published: December 2010

The Theorem of Lyapunov says that, in case of a periodic ODE, there exists a transformation to an ODE with constant matrices. This fact is very useful in stability investigations of nonlinear ODEs, too.

The generalization of ODE‐Floquét theory to index 1 and index 2 DAEs is given using an adapted transformation concept.
Effiziente Komponenten für Wissenschaftliches Rechnen
Authors: Lerch Michael
Published: December 2010

Es wird ein komponentenbasierter Ansatz für eine verteilte Matrix‐Bibliothek nach Karlsruher Definition [1] vorgestellt. Komponenten sind wiederverwendbare Software‐Bausteine, durch deren Einsatz man sich eine schnellere und kostengünstigere Software‐Entwicklung bei gleichzeitig gesteigerter Qualität, Sicherheit, Effizienz und Wartbarkeit erhofft. Laufzeitmessungen zeigen, daß hohes Abstraktionsniveau und Wiederverwendbarkeit nicht im Widerspruch zu Effizienz stehen.
Short‐Cut Distillation Columns: A Mathematical Approach
Authors: Lory P.
Published: December 2010

The distillation column is the basic apparatus for separation processes in chemical engineering. Mathematical models of this tool are nonlinear systems of (algebraic) equations in the steady‐state case and differential‐algebraic equations in the dynamic case. The number of equations for a single distillation columnn is N(2nc + 7), where N denotes the number of stages (trays) and nc is the number of components. In practical applications, the number of trays is within 10 × N × 100, and the number of components is less than 50. As a consequence, rigorous (tray‐by‐tray) models of distillation columns with thousands of equations are not uncommon. A realistic plant may include several distillation columns. Consequently, plant models may become very large and difficult to solve numerically. This has lead to several attempts to reduce the number of equations without sacrificing too much accuracy. The name “short‐cut distillation column” is common for a model of this type. The paper gives a mathematical approach in contrast to previous, engineering oriented attempts. For the sake of brevity it is restriced to the stationary case.
Accurate Computation of Elliptic Functions
Authors: Luther W. , Otten W.
Published: December 2010

In this note we present rapidly convergent algorithms depending on the method of arithmetic‐geometric means (AGM) for the computation of the incomplete elliptic integral of the first kind, Jacobi's Theta‐ and Zeta‐function. In particular we derive explicit a priori bounds for the error accumulation of the descending Landen transform.
Inexakte stochastische Gradientenverfahren
Authors: Marti Kurt , Stökl Gerald
Published: December 2010

Stochastische Gradientenverfahren haben bei sehr komplizierten Restriktionen den Nachteil, daß dann die Projektion auf den zulässigen Bereich nicht mehr numerisch einfach bestimmt werden kann. Anstatt den zulässigen Bereich nur zu vereinfachen, approximieren wir diesen durch eine konvergente Folge konvexer abgeschlossener Mengen. Dadurch entsteht ein inexaktes stochastisches Gradientenverfahren, das unter gewissen Voraussetzungen gegen eine Optimallösung des Ausgangsproblems konvergiert.
Numerical Simulation of Metalorganic Molecular Beam Epitaxy Growth over Structured Surfaces
Authors: Menke C. , Wachter M.
Published: December 2010

A mathematical model for the crystal growth over nonplanar substrates by metalorganic molecular beam epitaxy (MOMBE) is proposed. The substrate consists of crystal facets of various orientation, and of masks where no growth takes place. Surface diffusion, adsorption and desorption of atoms are taken into account. The surface diffusion processes between simultaneously growing facets are a function of the step density, which is preset by the substrate orientation. A nonlinear partial differential equation of first order in time and of fourth order in space is derived to describe the evolution of the crystal surface. Numerical simulations are presented which are in good agreement with measurements of InP crystals grown by MOMBE. In particular, experimentally observed small surface corrugations near facet edges can be explained by our model.
Multifacet Regression
Authors: Metzner Lars
Published: December 2010

A new approach in nonparametric regression is to use the signs of the residuals ri = yi ‐ θ (xi) in the regression modell yi = θ (xi) + ϵi instead of the residuals itself. It turns out, that with a suitable definition of complexity of the noise ϵi we are able to determine the minimum number of local extrema and turning points for the regression function θ, and additionally loaction intervals for each necessary extremum or turning point. With the definition of the total curvature through the derivatives of the regression function we describe the smoothest simple regression function as the solution of a constraint minimizing problem, where the constraints have no analytic expression. This method is also appliable for parametric regression, multivariate regression and nonparametric density estimation.
Some Problems of Estimation From Noisy Data
Authors: Moklyachuk M. P.
Published: December 2010

Problem of the optimal estimation is considered for transformation Aζ = Σ a (j) of the unknown values of a stationary stochastic sequence ζ(j) with density f(λ) from observations of the sequence ζ (j) + η(j), where η(j) is a stationary stochastic sequence with density g(Δ). The spectral characteristic h(f, g) and the mean square error Δ(f, g) of the optimal linear estimate of Aζ are found in the case where the spectral densities f(λ) and g(λ) are known exactly. Convex optimization methods are applied to determine the least favorable spectral densities and the minimax‐robust spectral characteristic of the optimal estimate of the transformation Aζ for various classes D = Df × Dg, of densities in the case where spectral densities f(λ) and g(λ) are not known exactly but the class D = Df × Dg of possible densities is determined.
Some Mechanisms of the Frictional Interaction in a Superconducting Cable
Authors: Naumov V. , Palmov V. , Panin A.
Published: December 2010

This work aims to understand the mechanical behaviour of the superconducting cable and the possible mechanical heat generation within the cable under cyclic mechanical loading. The purpose of the present stage is to model the mechanism of the frictional movements in the cable and estimate the impact of different factors on the frictional heat deposited in the cable. It is suppose that the heat generation in a superconducting cable follows from sliding strands (wires) with respect to each other. For both models are used the idea of semi‐consistent field. It is considered the interaction each strand with surrounding medium which formed of the rest of the strands (instead of study the frictional interaction of strands with each other).
Optimal Control System Design Using A Genetic Algorithm
Authors: Perhinschi M. G.
Published: December 2010

The purpose of this study is to investigate the use of genetic algorithms (GAs) for airvehicle control system design and optimization. The design of the controller gains for the longitudinal channel of an autonomous helicopter model is formulated and solved as a complex, constrained, nonlinear, multiple objective problem. GAs are implemented using both binary and floating point representations with associated mutation and crossover operators. Selection is based on a roulette wheel technique. Improvements of the algorithm performance are obtained by the use of selective weights in the evaluation function and elitist selection strategy.
An Inverse Sturm‐Liouville Problem by Three Spectra
Authors: Pivovarchik V.
Published: December 2010

It is well known that the equation of small transverse vibrations of a smooth string may be reduced by means of Liouville transform [1] to the Sturm‐Liouville equation. Then the inverse problem, i. e. determination of the potential, may be solved by given spectra of two boundary problems [2, 3, 4]. We consider here the inverse Sturm‐Liouville problem with the following given data: the spectrum of a boundary problem (I) on the interval [0, a] and the spectra of two‐boundary problems (II and III) on the intervals [0, 1/2a] and [1/2a, a], correspondingly. The potentials of the problems I and II (I and III) coincide on the interval [0, 1/2a] (on the interval [1/2a, a]). The conditions are found which are sufficient for three sequences of real numbers to be the spectra of the three boundary problems generated by real potential from L2 (0, a). These conditions are not much different from the necessary ones. The physical meaning of the problems is as follows. The first sequence is the spectrum of a smooth string with fixed ends. The two other sequences are the spectra of the same string clamped at the point of equilibrium.
Verifizierte Fehlerschranken und Gleichungssysteme
Authors: Rex G.
Published: December 2010

Auf der Grundlage eines Theorems wird ein Algorithmus angegeben, der es erlaubt verifizierte Fehlerschranken für eine Lösung x* ϵ ℛn eines Gleichungssystems h (x) = 0 zu einer Näherungslösung x0 von x* zu berechnen. Gegebenenfalls wird die Existenz und Eindeutigkeit von x* in diesen Schranken nachgewiesen. Dazu benötigte H‐Matrix Eigenschaften können, abhängig von der Kondition des Systems, über Präkonditionierungsmatrizen erreicht werden. Im Kegel ℛ werden dann mittels eines Iterationsprozesses Schranken für x* berechnet.
Implicit Methods for Enclosing Solutions of ODEs
Authors: Rihm R.
Published: December 2010

We introduce an implicit single‐step method for enclosing solutions of initial value problems in systems of ordinary differential equations.
Linear Programming with Inexact Data is NP‐Hard
Authors: Rohn J.
Published: December 2010

We prove that the problem of checking existence of optimal solutions to all linear programming problems whose data range in prescribed intervals is NP‐hard.
Generalized Eigenfunctions for Half‐Plane Diffraction: Rawlins' Problem with Real Wave Numbers
Authors: Rottbrand K.
Published: December 2010

This paper deals with a famous diffraction problem for Σ : × < 0, y = 0 as an obstacle for some time‐harmonic plane incident wave field. RAWLINS [5] was the first to solve the corresponding mixed (D/N) b. v. p. to the scalar Helmholtzian in 1975. And he was the first to solve the equivalent pair of coupled Wiener‐Hopf equations explicitly by factoring [6] their discontinuous 2 × 2 Fourier matrix symbol in 1980. Although for real wave numbers k the factorization procedure fails it will serve as the basis: Following the lines given by ALI MEHMETI [1] in his habilitation thesis (1994) for the (D/D) b. v. p. we combine the idea of integral path deforming onto the branch cuts of ✓ζ2‐k2 in MEISTER's book [3] (1983) with the modern Wiener‐Hopf method solution derived by SPECK [9] (1989) in a H1+ϵ, ϵ 0 Sobolev space setting. The symmetry of the intermediate spaces H3, H‐5, |s| < 1/2, which is due to generalized factorization plays a key role in order to get Laplace integral representations of the generalized eigenfunctions of the problem which allow real wave numbers k. As a remarkable fact 0 < ϵ < 1/4 must hold.
Sobolev Regularity with Asymptotics for two Classes Of Integro‐Differential Equations
Authors: Schmutzler B.
Published: December 2010

Initial boundary value problems for linear integro‐differential equations of hyperbolic and parabolic type are considered, which describe linear viscoelasticity and heat conduction in materials with memory. These equations contain convolution terms with respect to time by a so‐called memory kernel. Under certain conditions of smoothness and monotonicity on the memory kernel existence, uniqueness and regularity of solutions in scales of Sobolev spaces can be proved. Furthermore, a well‐defined singularity of the memory kernel at initial time generates singularities of the solutions, which can be described by Sobolev spaces with asymptotics.
Non‐conforming Nodal‐value Discretization and Multigrid Methods for 4th,‐order Problems
Authors: Schöberl J.
Published: December 2010

Boundary value problems for 4th order PDE's arising from plate and shell models are considered. Because C1‐continuous finite elements are very expensive, usually non‐conforming elements are used, e. g. Morley's triangle. The known non‐conforming elements need Hermite‐type degrees of freedom. To build elements using just Lagrange‐type degrees of freedom, we suggest to use nodes outside of the element. Existing codes for second order equations can be extended very easily to this discretization.

The linear system is solved by a multigrid method. Because only nodal values are used, the grid transfer operations are very simple. Numerical examples verify the convergence rate of the discretization as well as the multigrid rate.
Generation of Difference and Error Formulae of Arbitrary Consistency Order on an Unstructured Grid
Authors: Schönauer W.
Published: December 2010

For the application of the finite difference method (FDM) on an unstructured finite element grid we want to generate difference formulae and corresponding error estimates of arbitrary consistency order. The problem is to find grid points with sufficient information for the determination of the interpolation polynominals, good error estimate and optimal structure of the resulting linear system of equations of the FDM. A sophisticated algorithm for the selection of good and the exclusion of bad grid points is presented. For the generation of the formulae the principle of the influence polynomials is used.
Final Pathology Findings After Immediate or Delayed Surgery in Patients with Cytologically Benign or Follicular Thyroid Nodules
Authors: Kihara Minoru , Hirokawa Mitsuyoshi , Ito Yasuhiro , Kobayashi Kaoru , Miya Akihiro , Miyauchi Akira
Published: December 2010

Background

In the present study, we reviewed our experience with thyroid cytological findings showing benign or follicular tumor and evaluated the outcomes in patients who had undergone immediate or late surgical treatment.

Method

In 2007, 445 patients underwent initial surgical therapy for benign or follicular thyroid nodules according to our criteria for surgical indication. Of these, 320 patients underwent thyroid excision immediately. In the remaining 125 patients, surgery was performed after follow‐up for more than 18 months.

Results

In this series, the frequencies of finding thyroid carcinoma pathologically were 11.6 and 6.4% in patients undergoing immediate and late surgery, respectively. In these 445 patients, there was no significant difference in age, tumor size, serum thyroglobulin, or nodule growth rate between benign and malignant thyroid nodules. There was, however, a significant difference in ultrasonographic classification.

Conclusions

Our criteria for surgical indication of nodules diagnosed as cytological benign or follicular tumors were considered appropriate. Ultrasonographic evaluation is an important and useful basis for therapeutic decision making in choosing either immediate surgery or observation for cytologically diagnosed benign or follicular tumors.