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Max im Comic
(2020)
Science Comics
(2021)
A New Approach to Shooting Methods for Terminal Value Problems of Fractional Differential Equations
(2023)
For terminal value problems of fractional differential equations of order α∈(0,1) that use Caputo derivatives, shooting methods are a well developed and investigated approach. Based on recently established analytic properties of such problems, we develop a new technique to select the required initial values that solves such shooting problems quickly and accurately. Numerical experiments indicate that this new proportional secting technique converges very quickly and accurately to the solution. Run time measurements indicate a speedup factor of between 4 and 10 when compared to the standard bisection method.
The present article offers new evidence on the Unger playing-card making family of Győr,Western Transdanubia, as the result of a cross-disciplinary study. Mátyás Unger the Elder (1789-1862) andhis like-named son Mátyás the Younger (1824–1878) produced various types of playing-cards from theearly to mid-19th century. In particular, their cards, their iconography, design and production process will beanalysed. The family is best known for their cards with Sopron (Oedenburg) pattern. Also discussed will bethe role of Mátyás the Elder’s second eldest son Alajos Unger as a possible designer of the later Unger cards,which were of considerably higher quality than the earlier known ones by Mátyás Unger the Elder. Thehitherto little-known Alajos Unger was trained as a draughtsman and painter first at the National DrawingSchool of his hometown and then, between 1833 and 1842, at the Vienna Academy of Fine Arts, particularlyunder Leopold Kupelwieser (1796–1862). Finally an innovative outside-in bottom-up method for gainingfurther, reliable insight into 19thcentury artisanal playing-card manufacturing will be proposed to determinethe size, output and profitability of the Unger workshop based on material-flow simulation.
Alajos (Alois) Unger, who was descended from the well-known Unger playing- card making family from Győr, is a recently rediscovered Hungarian late Nazarene and late Romanticist artist. The son and brother of the playing-card makers Mátyás (Mathias) Unger the Elder (1789-1862) and Younger (1824-78), he was originally apprenticed in this craft as well and, as could be proved for the first time, designed the family’s playing-cards. First trained at the National Drawing School of his hometown under János Hofbauer (creator of The Castle of Dévény, Hungarian National Gallery), which apprentices and journeymen of the local crafts attended, Alajos Unger enrolled at the Vienna Academy of Fine Arts first in 1833 to train there as a draughtsman and then became a pupil of Leopold Kupelwieser (1796-1862) from 1836 until 1842. Among his classmates were the famous artists Eduard von Engerth (1818-97), Franz Josef Dobiaschofsky (1818-67), Ferenc Szoldatits (1820-1916) and August von Pettenkofen (1822-1889). In an art exhibition in Győr in 1903 the quality of Unger’s genre paintings displayed there was likened to those of the latter.
It has now been possible to demonstrate how strongly his art was rooted in the late Nazarene and late Romanticist tradition of the circle around his teacher. Overall, his style not only reflects the ’’literary-musical-artistic” orientation of Kupelwieser, but also the ”fairytale-like-poetical” variety represented by Joseph von Führich and particularly Moritz von Schwind.
Alajos Unger had until recently only been known by name, but with the present article, a fuller picture of the artist’s life and work has been presented. Thus, apart from the two oil paintings, which came into the possession of the Hungarian National Gallery in the 1970s, The Recapture ofRaab (1840) and a portrait of the artist and his family (1843), a series of hitherto unknown oilworks has been discovered: a portrait of an unknown lady (1836), now part of the art collection of the University of Pennsylvania, a copy of Cesare da Sesto’s La vierge au bas-relief (date unknown), the Baptism of Vajk (1842) and a Biedermeier picture clock depicting a patriotic scene from the opera Lucia di Lammermoor set against the backdrop of a veduta of Venice (1847). The portrait of Ferenc Hergeszell, a local politician from Unger’s hometown and later member of the Hungarian Diet, from 1841, now in the collection of the Flóris Römer Museum in Győr, also bears Unger’s painterly handwriting.
Altogether, the torso of the extraordinary work of a representative of a younger generation of Nazarenes, who promoted Hungarian national art, has been unveiled in the bicentenary of his birth. In addition to this, the role of Nazarene artists and that of their networks in the development of Hungarian art generally was investigated.
This paper will deals with the Nazarene Movement and its art in Hungary
with special reference to Alajos (Alois) Unger, a recently rediscovered artist of Hungary’s Reform Era, his links to Nazarene art, the relevance of (functional) semiotics in the interpretation of Nazarene works
and the influence of the Nazarene Movement on the arts and crafts of the 19th century. This includes the design of new playing-card patterns in Hungary
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.