bluuebunny/crossref_metadata_2025_split huggingface dataset:
Existence theory to the equations in viscoelasticity at finite deformations
Authors: Jäpel Irg 
Published: December 2010

AbstractThe 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

AbstractThe 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

AbstractThe 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

AbstractIn 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

AbstractWhen 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

AbstractThe 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

AbstractThis 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

AbstractHäufig 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

AbstractDie 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

AbstractThe 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

AbstractEs 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

AbstractThe 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

AbstractIn 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

AbstractStochastische 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

AbstractA 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

AbstractA 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

AbstractProblem 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

AbstractThis 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

AbstractThe 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

AbstractIt 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

AbstractAuf 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.
Generalized Eigenfunctions for Half‐Plane Diffraction: Rawlins' Problem with Real Wave Numbers
Authors: Rottbrand K. 
Published: December 2010

AbstractThis 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

AbstractInitial 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

AbstractBoundary 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

AbstractFor 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

AbstractBackgroundIn 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.MethodIn 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.ResultsIn 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.ConclusionsOur 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.