bluuebunny/crossref_metadata_2025_split huggingface dataset:
On Infinite‐Dimensional Dynamic Systems Generated by Non‐linear Hyperbolic Equations
Authors: Shirikyan A. , Volevich L. 
Published: December 2010

AbstractWe consider high‐order non‐linear hyperbolic equations that are small perturbations of an equation with constant coefficients. It is assumed that the unperturbed equation has a characteristic polynomial whose roots with respect to the variable dual to time are outside an open strip containing the imaginary axis. We establish the property of exponential dichotomy for the equation in question. Under the additional condition that the roots of the characteristic polynomial belong to the left half‐plane we prove that the zero solution is asymptotically stable as t → + ∞.
Stochastischer Zins in der Ruintheorie
Authors: Siegl T. , Tichy R. F. 
Published: December 2010

AbstractIn den klassischen Modellen der kollektiven Ruintheorie wird keine Verzinsung des verfügbaren Kapitals angenommen. Neuere Entwicklungen auf diesem Gebiet, und die allgemeine Tendenz, finanzmathematische Methoden in der Risikotheorie anzuwenden, führen zur Anwendung stochastischer Zinssätze in der Ruintheorie. Außerdem diskutieren wir die Simulation des Problems mit hybrid Monte Carlo Verfahren.
Application of Filtered Poisson Process in Modeling Fatigue Cracks Propagation
Authors: Śniady P. , Sieniawska R. , Żukowski S. 
Published: December 2010

AbstractA 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.
Comparison of two methods for the approximate analysis of nonlinear stochastic dynamical systems
Authors: Sobiechowski C. 
Published: December 2010

AbstractGeneralizations 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

AbstractDer 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

AbstractWir 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

AbstractIn 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

AbstractThis 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

AbstractThe 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

AbstractKnown 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

AbstractBased 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.
Numerically efficient modeling in multibody dynamics
Authors: Schwerin Reinhold 
Published: December 2010

AbstractThe 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

AbstractHeat 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

AbstractPartielle 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

AbstractWe 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.
Optimal control for elastic space constructions
Authors: Zakrzhevskii A. 
Published: December 2010

AbstractThe 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

AbstractMost 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.
A note on the volatility term structure in short rate models
Authors: Darbellay Georges A. 
Published: December 2010

AbstractIn 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

AbstractIn 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

AbstractDie 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

AbstractTraditionally, 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

AbstractCertain 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.
Symmetrie elementarer Funktionen: Entscheidbarkeitsfragen und Algorithmen
Authors: Gerbracht Eberhard H. A. , Struckmann Werner 
Published: December 2010

AbstractWir 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

AbstractThis 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

AbstractThe 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

AbstractIf 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

AbstractIn 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

AbstractDue 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

AbstractConsistency 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.
Shooting Type Methods for Solving the two point boundary value problem in the optimization of flight vehicles evolutions
Authors: Istratie V. 
Published: December 2010

AbstractBriefly, 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.