Fakultät für angewandte Natur- und Geisteswissenschaften
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- Alajos Alois Unger (1814-1848) (3)
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The Unger Family from Győr: The Social Semiotics, Political Iconography and Manufacture of their 19th Century Playing Cards Mátyás (Mathias) Unger the Elder (1789–1862) and his eponymous son Mátyás (Mathias) the Younger (1824–1878) from Győr are prominent in the history of the Hungarian playing cards. Due to more recent research, new details about the family and their playing cards have surfaced. This includes the fact that another son of Mátyás Unger the Elder was Alajos (Alois) Unger (1814–1848), an academic painter trained at the Vienna Academy of Arts, particularly under Leopold Kupelwieser and Johann Ender, in late Nazarene, late Romantic style.
New findings on the Unger playing cards are presented drawing on social semiotics and its relationship to political iconography, whereby cards are considered as text and the two categories of denotation and connotation pivotal. Change in connotation and meaning is analysed to provide further explanation for how the four season cards, i.e. Tell cards (magyar kártya), today‘s standard pattern, came about with lost Unger playing cards serving as a missing link. These Unger cards reflected the art policy of the Austrian Empire of the time as image propaganda for the Casa d’Austria linked with the pietas austriaca/hungarica, in line with Alajos Unger’s oil paintings. Over time, the connotation of the Tell cards changed into a clear anti-Habsburg stance. Further reasons for why this pattern became standard in Hungary and how the four seasoned Däuser cards, popularized by the Ungers, must have become part of it are also given. Against this background, a novel bottom-up material flow simulation approach is proposed to investigate the artisanal playing card production process, output and profitability of the small workshop of the Ungers together with a research agenda for adapting it to the building and conditions of the last known production site, all on the basis of a reconstruction.
Object of our interest is an elastic body Ω ⊂ ℝ3 which we can deform by applying a tension along certain given short fibers inside the body. The deformation of the body is desribed by a hyperelastic model with polyconvex energy density and a special energy functional for the tension along the fibers. We seek to apply (possibly large) deformations to the body so that a desired shape is obtained. To this end, we formulate an optimal control problem for the fiber tension field.
Optimal control problems for finite-strain elasticity are considered. An inner pressure or an inner fiber tension is acting as a driving force. Such internal forces are typical, for instance, for the motion of heliotropic plants, and for muscle tissue. Non-standard objective functions relevant for elasticity problems are introduced. Optimality conditions are derived on a formal basis, and a limited-memory quasi-Newton algorithm for their solution is formulated in function space. Numerical experiments confirm the expected mesh-independent performance.
Discourse analysis has greatly relied on the tried and tested methods of data collection as well as on the use of traditional corpora. The question therefore arises as to how far the Internet has changed methodology in discourse analysis and to what degree it will do so in the future. A further issue that results from the possibilities the Web offers is whether traditional corpora will still be necessary to thoroughly investigate the structure and functioning of language and discourse, with regard to both native and non-native speech. In this paper the opportunities the Internet offers, the availability of tools to the researcher in using the Internet in DA but also the limits and dangers the linguist is prone to encounter will be investigated. And finally it will be discussed whether traditional empirical methods will still play any role in discourse analysis in future.
Diffusive representations of fractional differential and integral operators can provide a convenient means to construct efficient numerical algorithms for their approximate evaluation. In the current literature, many different variants of such representations have been proposed. Concentrating on Riemann-Liouville integrals whose order is in (0,1), we here present a general approach that comprises most of these variants as special cases and that allows a detailed investigation of the analytic properties of each variant. The availability of this information allows to choose concrete numerical methods for handling the representations that exploit the specific properties, thus allowing to construct very efficient overall methods.
Diffusive representations of fractional derivatives have proven to be useful tools in the construction of fast and memory efficient numerical methods for solving fractional differential equations. A common challenge in many of the known variants of this approach is that they require the numerical approximation of some integrals over an unbounded integral whose integrand decays rather slowly, which implies that their numerical handling is difficult and costly. We present a novel variant of such a diffusive representation. This form also requires the numerical approximation of an integral over an unbounded domain, but the integrand decays much faster. This property allows to use well established quadrature rules with much better convergence properties.
This article concerns an analytic and numerical analysis of a class of weighted singular Cauchy integrals with exponential weights w:= exp (−Q) with finite moments and with smooth external fields Q:R→[0,∞), with varying smooth convex rate of increase for large argument. Our analysis relies in part on weighted polynomial interpolation at the zeros of orthonormal polynomials with respect to w2. We also study bounds for the first derivatives of a class of functions of the second kind for w2.
Recently, we have proposed a new diffusive representation for fractional derivatives and, based on this representation, suggested an algorithm for their numerical computation. From the construction of the algorithm, it is immediately evident that the method is fast and memory-efficient. Moreover, the method’s design is such that good convergence properties may be expected. In this paper, we commence a systematic investigation of these convergence properties.
We study fractional differential equations of Riemann–Liouville and Caputo type in Hilbert spaces. Using exponentially weighted spaces of functions defined on R, we define fractional operators by means of a functional calculus using the Fourier transform. Main tools are extrapolation- and interpolation spaces. Main results are the existence and uniqueness of solutions and the causality of solution operators for non-linear fractional differential equations.
Fractional order models have proven to be a very useful tool for the modeling of the mechanical behaviour of viscoelastic materials. Traditional numerical solution methods exhibit various undesired properties due to the non-locality of the fractional differential operators, in particular regarding the high computational complexity and the high memory requirements. The infinite state representation is an approach on which one can base numerical methods that overcome these obstacles. Such algorithms contain a number of parameters that influence the final result in nontrivial ways. Based on numerical experiments, we initiate a study leading to good choices of these parameters.
The solution of fractional-order differential problems requires in the majority of cases the use of some computational approach. In general, the numerical treatment of fractional differential equations is much more difficult than in the integer-order case, and very often non-specialist researchers are unaware of the specific difficulties. As a consequence, numerical methods are often applied in an incorrect way or unreliable methods are devised and proposed in the literature. In this paper we try to identify some common pitfalls in the use of numerical methods in fractional calculus, to explain their nature and to list some good practices that should be followed in order to obtain correct results.
As in the embedded systems domain, energy efficiency has recently become one of the main design criteria in high performance computing. The European Union Horizon 2020 project READEX (Run-time Exploitation of Application Dynamism for Energy-efficient eXascale computing) has developed a tools-aided auto-tuning methodology inspired by system scenario based design. Applying similar concepts as those presented in earlier chapters of this book, the dynamic behavior of HPC applications is exploited to achieve improved energy efficiency and performance. Driven by a consortium of European experts from academia, HPC resource providers, and industry, the READEX project has developed the first generic framework of its kind for split design-time and run-time tuning while targeting heterogeneous systems at the Exascale level. Using a real-life boundary element application, energy savings of more than 30% can be shown.
This article describes fundamental approaches for the numerical handling of problems arising in fractional calculus. This includes, in particular, methods for approximately computing fractional integrals and fractional derivatives, where the emphasis is placed on Caputo operators, as well as solvers for the associated differential and integral equations.
This article describes the fundamentals of the theory of ordinary fractional differential equations of Caputo’s type. Starting from the existence and uniqueness of solutions and the well-posedness in general, the flow of topics continues via a derivation of explicit solution formulas for certain important classes of problems and the discussion of their smoothness properties to the stability properties of these solutions. The main focus is on initial value problems, but terminal value problems are briefly considered as well. In addition to dealing with standard single-order problems, the presentation also contains a short discussion of multiterm equations and multiorder systems.
Mathematical models based on differential operators of fractional order have proven to be very useful for describing the properties of viscoelastic materials. However, the associated differential equations can usually not be solved analytically. In this article, we provide a survey of the most important numerical methods. We restrict our attention to those types of fractional differential equations that are most important in the context of viscoelasticity, i.e., we discuss numerical methods for ordinary fractional differential equations and for certain types of time-fractional partial differential equations. Space-fractional partial differential equations are not discussed.
A note on the well-posedness of terminal value problems for fractional differential equations
(2018)
This note is intended to clarify some important points about the well-posedness of terminal value problems for fractional differential equations. It follows the recent publication of a paper by Cong and Tuan in this journal, in which a counter-example calls into question the earlier results in a paper by this note's authors. Here, we show in the light of these new insights, that a wide class of terminal value problems of fractional differential equations is well posed, and we identify those cases where the well-posedness question must be regarded as open.
Das Buch Programmieren in C++ für Elektrotechniker und Mechatroniker bietet einen Einstieg in die moderne Softwareentwicklung für Studierende der Ingenieurwissenschaften. Dabei wird ein durchgängiger Ansatz verfolgt, der, beginnend mit den Grundlagen der Programmierung, bis hin zu weiterführenden Themen, wie Hardware-nahe Programmierung, zahlreiche Themengebiete betrachtet und Studierende nicht nur für die Prüfung, sondern auch für den Arbeitsalltag vorbereitet. Da man Programmieren nur durch Üben erlernen kann, liefert das Buch einen umfangreichen Aufgabenkatalog.
Für Großunternehmen ist die Nachhaltigkeitskommunikation längst keine Nebendisziplin mehr. Was vor 20 Jahren noch als Nischenthema galt, ist heute eines der wichtigsten Strategiethemen für Unternehmen. Die Chemieindustrie steht vor der kommunikativen Herausforderung die Nachhaltigkeitsleistung aus den hoch komplexen Wertschöpfungsketten für eine breite Öffentlichkeit verständlich aufzubereiten. Eine Fokussierung auf wesentliche Kennzahlen und Themen ist dabei unerlässlich. Aufgrund der herausragenden Bedeutung des Themas für die Unternehmen, aber auch für die Gesellschaft an sich, bedarf es der Erstellung und Ausspielung von möglichst hochwertigem und zweckvollem Content seitens der Unternehmen.
The electrostatic interaction between pairs of spherical or macroscopically long, parallel cylindrical colloids trapped at fluid interfaces is studied theoretically for the case of small inter-particle separations. Starting from the effective interaction between two planar walls and by using the Derjaguin approximation, we address the issue of how the electrostatic interaction between such particles is influenced by their curvatures and by the wetting contact angle at their surfaces. Regarding the influence of curvature, our findings suggest that the discrepancies between linear and nonlinear Poisson–Boltzmann theory, which have been noticed before for planar walls, also occur for spheres and macroscopically long, parallel cylinders, though their magnitude depends on the wetting contact angle. Concerning the influence of the wetting contact angle θ simple relations are obtained for equally sized particles which indicate that the inter-particle force varies significantly with θ only within an interval around 90°. This interval depends on the Debye length of the fluids and on the size of the particles but not on their shape. For unequally sized particles, a more complicated relation is obtained for the variation of the inter-particle force with the wetting contact angle.
The behavior of a uniformly magnetized ferronematic slab is investigated numerically in a situation in which an external magnetic field is applied parallel and antiparallel, respectively, to its initial magnetization direction. The employed numerical method allows one to determine hysteresis curves from which a critical magnetic field strength (i.e., the one at which the ferronematic sample becomes distorted) as a function of the system parameters can be inferred. Two possible mechanisms of switching the magnetization by applying a magnetic field in the antiparallel direction are observed and characterized in terms of the coupling constant between the magnetization and the nematic director and in terms of the coupling strength of the nematic liquid crystal and the walls of the slab. Suitably prepared walls allow one to combine both switching mechanisms in one setup, such that one can construct a cell, the magnetization of which can be reversibly switched off.