Glosarium Matematika

273 p.; 24 cm

Analysis of gradient descents in random energies and heat baths

This thesis concerns the mathematical analysis of random gradient descent evolutions as models for rate-independent dissipative systems under the influence of thermal effects. The basic notions of the theory of gradient descents (especially rate-independent evolutions) are reviewed in chapter 2. Chapters 3 and 4 focus on the scaling regime in which the microstructure dominates the thermal effects and comprise a rigorous justification of rateindependent processes in smooth, convex energies as scaling limits of ratedependent gradient descents in energies that have rapidly-oscillating random microstructure: chapter 3 treats the one-dimensional case with quite a broad class of random microstructures; chapter 4 treats a case in which the microstructure is modeled by a sum of “dent functions” that are scattered in Rn using a suitable point process. Chapters 5 and 6 focus on the opposite scaling regime: a gradient descent system (typically a rate-independent process) is placed in contact with a heat bath. The method used to “thermalize” a gradient descent is an interior-point regularization of the Moreau–Yosida incremental problem for the original gradient descent. Chapter 5 treats the heuristics and generalities; chapter 6 treats the case of 1-homogeneous dissipation (rate independence) and shows that the heat bath destroys the rate independence in a controlled and deterministic way, and that the effective dynamics are a gradient descent in the original energetic potential but with respect to a different and non-trivial effective dissipation potential. The appendices contain some auxiliary definitions and results, most of them standard in the literature, that are used in the main text

Internationales Kolloquium über Anwendungen der Informatik und Mathematik in Architektur und Bauwesen : 20. bis 22.7. 2015, Bauhaus-Universität Weimar

The 20th International Conference on the Applications of Computer Science and Mathematics in Architecture and Civil Engineering will be held at the Bauhaus University Weimar from 20th till 22nd July 2015. Architects, computer scientists, mathematicians, and engineers from all over the world will meet in Weimar for an interdisciplinary exchange of experiences, to report on their results in research, development and practice and to discuss. The conference covers a broad range of research areas: numerical analysis, function theoretic methods, partial differential equations, continuum mechanics, engineering applications, coupled problems, computer sciences, and related topics. Several plenary lectures in aforementioned areas will take place during the conference. We invite architects, engineers, designers, computer scientists, mathematicians, planners, project managers, and software developers from business, science and research to participate in the conference

Analysis of gradient descents in random energies and heat baths

This thesis concerns the mathematical analysis of random gradient descent evolutions as models for rate-independent dissipative systems under the influence of thermal effects. The basic notions of the theory of gradient descents (especially rate-independent evolutions) are reviewed in chapter 2. Chapters 3 and 4 focus on the scaling regime in which the microstructure dominates the thermal effects and comprise a rigorous justification of rateindependent processes in smooth, convex energies as scaling limits of ratedependent gradient descents in energies that have rapidly-oscillating random microstructure: chapter 3 treats the one-dimensional case with quite a broad class of random microstructures; chapter 4 treats a case in which the microstructure is modeled by a sum of “dent functions” that are scattered in Rn using a suitable point process. Chapters 5 and 6 focus on the opposite scaling regime: a gradient descent system (typically a rate-independent process) is placed in contact with a heat bath. The method used to “thermalize” a gradient descent is an interior-point regularization of the Moreau–Yosida incremental problem for the original gradient descent. Chapter 5 treats the heuristics and generalities; chapter 6 treats the case of 1-homogeneous dissipation (rate independence) and shows that the heat bath destroys the rate independence in a controlled and deterministic way, and that the effective dynamics are a gradient descent in the original energetic potential but with respect to a different and non-trivial effective dissipation potential. The appendices contain some auxiliary definitions and results, most of them standard in the literature, that are used in the main text.EThOS - Electronic Theses Online ServiceEngineering and Physical Sciences Research Council (Great Britain) (EPSRC)University of Warwick (UoW)GBUnited Kingdo

On Multilevel Methods Based on Non-Nested Meshes

This thesis is concerned with multilevel methods for the efficient solution of partial differential equations in the field of scientific computing. Further, emphasis is put on an extensive study of the information transfer between finite element spaces associated with non-nested meshes. For the discretization of complicated geometries with a finite element method, unstructured meshes are often beneficial as they can easily be adjusted to the shape of the computational domain. Such meshes, and thus the corresponding discrete function spaces, do not allow for straightforward multilevel hierarchies that could be exploited to construct fast solvers. In the present thesis, we present a class of "semi-geometric" multilevel iterations, which are based on hierarchies of independent, non-nested meshes. This is realized by a variational approach such that the images of suitable prolongation operators in the next (finer) space recursively determine the coarse level spaces. The semi-geometric concept is of very general nature compared with other methods relying on geometric considerations. This is reflected in the relatively loose relations of the employed meshes to each other. The specific benefit of the approach based on non-nested meshes is the flexibility in the choice of the coarse meshes, which can, for instance, be generated independently by standard methods. The resolution of the boundaries of the actual computational domain in the constructed coarse level spaces is a characteristic feature of the devised class of methods. The flexible applicability and the efficiency of the presented solution methods is demonstrated in a series of numerical experiments. We also explain the practical implementation of the semi-geometric ideas and concrete transfer concepts between non-nested meshes. Moreover, an extension to a semi-geometric monotone multigrid method for the solution of variational inequalities is discussed. We carry out the analysis of the convergence and preconditioning properties, respectively, in the framework of the theory of subspace correction methods. Our technical considerations yield a quasi-optimal result, which we prove for general, shape regular meshes by local arguments. The relevant properties of the operators for the prolongation between non-nested finite element spaces are the H1-stability and an L2-approximation property as well as the locality of the transfer. This thesis is a contribution to the development of fast solvers for equations on complicated geometries with focus on geometric techniques (as opposed to algebraic ones). Connections to other approaches are carefully elaborated. In addition, we examine the actual information transfer between non-nested finite element spaces. In a novel study, we combine theoretical, practical and experimental considerations. A thourough investigation of the qualitative properties and a quantitative analysis of the differences of individual transfer concepts to each other lead to new results on the information transfer as such. Finally, by the introduction of a generalized projection operator, the pseudo-L2-projection, we obtain a significantly better approximation of the actual L2-orthogonal projection than other approaches from the literature.Nicht-geschachtelte Gitter in Multilevel-Verfahren Diese Arbeit beschäftigt sich mit Multilevel-Verfahren zur effizienten Lösung von Partiellen Differentialgleichungen im Bereich des Wissenschaftlichen Rechnens. Dabei liegt ein weiterer Schwerpunkt auf der eingehenden Untersuchung des Informationsaustauschs zwischen Finite-Elemente-Räumen zu nicht-geschachtelten Gittern. Zur Diskretisierung von komplizierten Geometrien mit einer Finite-Elemente-Methode sind unstrukturierte Gitter oft von Vorteil, weil sie der Form des Rechengebiets einfacher angepasst werden können. Solche Gitter, und somit die zugehörigen diskreten Funktionenräume, besitzen im Allgemeinen keine leicht zugängliche Multilevel-Struktur, die sich zur Konstruktion schneller Löser ausnutzen ließe. In der vorliegenden Arbeit stellen wir eine Klasse "semi-geometrischer" Multilevel-Iterationen vor, die auf Hierarchien voneinander unabhängiger, nicht-geschachtelter Gitter beruhen. Dabei bestimmen in einem variationellen Ansatz rekursiv die Bilder geeigneter Prolongationsoperatoren im jeweils folgenden (feineren) Raum die Grobgitterräume. Das semi-geometrische Konzept ist sehr allgemeiner Natur verglichen mit anderen Verfahren, die auf geometrischen Überlegungen beruhen. Dies zeigt sich in der verhältnismäßig losen Beziehung der verwendeten Gitter zueinander. Der konkrete Nutzen des Ansatzes mit nicht-geschachtelten Gittern ist die Flexibilität der Wahl der Grobgitter. Diese können beispielsweise unabhängig mit Standardverfahren generiert werden. Die Auflösung des Randes des tatsächlichen Rechengebiets in den konstruierten Grobgitterräumen ist eine Eigenschaft der entwickelten Verfahrensklasse. Die flexible Einsetzbarkeit und die Effizienz der vorgestellten Lösungsverfahren zeigt sich in einer Reihe von numerischen Experimenten. Dazu geben wir Hinweise zur praktischen Umsetzung der semi-geometrischen Ideen und konkreter Transfer-Konzepte zwischen nicht-geschachtelten Gittern. Darüber hinaus wird eine Erweiterung zu einem semi-geometrischen monotonen Mehrgitterverfahren zur Lösung von Variationsungleichungen untersucht. Wir führen die Analysis der Konvergenz- bzw. Vorkonditionierungseigenschaften im Rahmen der Theorie der Teilraumkorrekturmethoden durch. Unsere technische Ausarbeitung liefert ein quasi-optimales Resultat, das wir mithilfe lokaler Argumente für allgemeine, shape-reguläre Gitterfamilien beweisen. Als relevante Eigenschaften der Operatoren zur Prolongation zwischen nicht-geschachtelten Finite-Elemente-Räumen erweisen sich die H1-Stabilität und eine L2-Approximationseigenschaft sowie die Lokalität des Transfers. Diese Arbeit ist ein Beitrag zur Entwicklung schneller Löser für Gleichungen auf komplizierten Gebieten mit Schwerpunkt auf geometrischen Techniken (im Unterschied zu algebraischen). Verbindungen zu anderen Ansätzen werden sorgfältig aufgezeigt. Daneben untersuchen wir den Informationsaustausch zwischen nicht-geschachtelten Finite-Elemente-Räumen als solchen. In einer neuartigen Studie verbinden wir theoretische, praktische und experimentelle Überlegungen. Eine sorgfältige Prüfung der qualitativen Eigenschaften sowie eine quantitative Analyse der Unterschiede verschiedener Transfer-Konzepte zueinander führen zu neuen Ergebnissen bezüglich des Informationsaustauschs selbst. Schließlich erreichen wir durch die Einführung eines verallgemeinerten Projektionsoperators, der Pseudo-L2-Projektion, eine deutlich bessere Approximation der eigentlichen L2-orthogonalen Projektion als andere Ansätze aus der Literatur

Nutritional enhancement of cereal milling wastes using enzymes

Wheatfeed is a low value by-product of the cereal milling industry and has potential as an ingredient of pet foods. However, it has a high fibre content and this renders it unsuitable for non-ruminants unless some means can be found to convert the fibre to more digestible substances. This work considers enzyme hydrolysis as a means for improving the nutritional value of wheatfeed. Preliminary investigations focused on evaluating mixtures of enzymes in various combinations. The extent of hydrolysis was routinely assayed by measuring the release of sugars and proteins. Further experiments were performed to establish the optimal conditions under which a mixture of enzymes, comprising cellulase, hemicellulase and pectinase, hydrolysed wheatfeed. Studies were also conducted where these enzymes were added sequentially to wheatfeed and useful information was gained on the composition of the susceptible components. Steam explosion was investigated as a pretreatment of wheatfeed to make subsequent enzyme treatment more effective. However, the results were inconclusive. Trials were carried out using commercially available enzymes to compare their effectiveness on the wheatfeed. A cellulase, was selected for further investigation into the effects of particle size, extent of agitation, and enzyme concentration on sugar release. An empirical mathematical model describing the action of this enzyme was developed. Enzyme treatment of wheatfeed was also performed under conditions of reduced water content, or 'solid state'. However, enzyme action was limited, yielding lower quantities of sugars and protein. The treatment of wheatfeed with enzymes was shown to increase digestibility of the substrate. However, the high costs of enzymes would effectively rule this out as a commercial option and alternative methods such as for example a form of composting using cellulolytic fungi might prove more economic

Plant, macrolichen and moss community structure and species richness in the coastal barrens of Nova Scotia

132 leaves : ill. (chiefly col.), col. map ; 28 cm.Includes abstract and appendices.Includes bibliographical references (leaves 112-120).Coastal barrens in Nova Scotia are an understudied habitat type characterised by short, predominantly ericaceous vegetation, sparse tree cover, exposed bedrock, areas of bog, and stressful climatic conditions. Six coastal barrens were selected along the Atlantic coast. Twenty 1 x 1 m plots at each site were sampled for vascular plants, macrolichens and mosses, and environmental factors, including substrate nutrient and moisture levels, exposure, and substrate depth. One hundred and seventy-six species were recorded over the 6 sites (105 vascular species, 43 macrolichen species, 28 moss species), 11 of which are provincially rare (S1, S2). Community composition differed among sites, and was related to distance to coast, substrate depth, substrate moisture, and vegetation height. Species richness was influenced by moisture conditions, exposure and substrate depth. Conservation efforts should protect gradients of these environmental factors in order to protect a diversity of plant types, which respond variously to these factors

Ahlfors circle maps and total reality: from Riemann to Rohlin

This is a prejudiced survey on the Ahlfors (extremal) function and the weaker {\it circle maps} (Garabedian-Schiffer's translation of "Kreisabbildung"), i.e. those (branched) maps effecting the conformal representation upon the disc of a {\it compact bordered Riemann surface}. The theory in question has some well-known intersection with real algebraic geometry, especially Klein's ortho-symmetric curves via the paradigm of {\it total reality}. This leads to a gallery of pictures quite pleasant to visit of which we have attempted to trace the simplest representatives. This drifted us toward some electrodynamic motions along real circuits of dividing curves perhaps reminiscent of Kepler's planetary motions along ellipses. The ultimate origin of circle maps is of course to be traced back to Riemann's Thesis 1851 as well as his 1857 Nachlass. Apart from an abrupt claim by Teichm\"uller 1941 that everything is to be found in Klein (what we failed to assess on printed evidence), the pivotal contribution belongs to Ahlfors 1950 supplying an existence-proof of circle maps, as well as an analysis of an allied function-theoretic extremal problem. Works by Yamada 1978--2001, Gouma 1998 and Coppens 2011 suggest sharper degree controls than available in Ahlfors' era. Accordingly, our partisan belief is that much remains to be clarified regarding the foundation and optimal control of Ahlfors circle maps. The game of sharp estimation may look narrow-minded "Absch\"atzungsmathematik" alike, yet the philosophical outcome is as usual to contemplate how conformal and algebraic geometry are fighting together for the soul of Riemann surfaces. A second part explores the connection with Hilbert's 16th as envisioned by Rohlin 1978.Comment: 675 pages, 199 figures; extended version of the former text (v.1) by including now Rohlin's theory (v.2

Internationales Kolloquium über Anwendungen der Informatik und Mathematik in Architektur und Bauwesen : 20. bis 22.7. 2015, Bauhaus-Universität Weimar

The 20th International Conference on the Applications of Computer Science and Mathematics in Architecture and Civil Engineering will be held at the Bauhaus University Weimar from 20th till 22nd July 2015. Architects, computer scientists, mathematicians, and engineers from all over the world will meet in Weimar for an interdisciplinary exchange of experiences, to report on their results in research, development and practice and to discuss. The conference covers a broad range of research areas: numerical analysis, function theoretic methods, partial differential equations, continuum mechanics, engineering applications, coupled problems, computer sciences, and related topics. Several plenary lectures in aforementioned areas will take place during the conference. We invite architects, engineers, designers, computer scientists, mathematicians, planners, project managers, and software developers from business, science and research to participate in the conference

Stability Analysis of Immunogenic Gliadin Accumulation in Hard Red Spring Wheat \u3cem\u3e (Triticum Aestivum\u3c/em\u3e L.)

Misconceptions regarding plant breeding objectives have led to speculation regarding the increasing prevalence of gluten intolerance, wheat allergy, and celiac disease. It is thought that contemporary wheat cultivars accumulate more immunogenic proteins than older cultivars because of supposed genetic changes effected through plant breeding strategies. This study evaluated the stability of gliadin accumulation in 191 hard red spring wheat cultivars grown in 12 location-years. Two enzyme-linked immunosorbent assays (ELISAs) were developed. A paired t test (N = 34) failed to find a statistically significant difference between the experimental ELISAs and the commercial R5 assay measures of mean gliadin (t = 0.37, p = 0.7). A Bland-Altman analysis indicated sufficient agreement between the assays, despite a low proportion of shared variance (R2 = 0.29) and moderate correlation (r = 0.446). The experimental ELISAs overestimated gliadin by 0.412 g kg-1 flour (CI95 = -12.52, 13.34) relative to the commercial assay. Agronomic, milling quality, gluten, and baking quality traits were assessed for 154 cultivars. Correlation between gliadin and the expected predictors whole-grain protein, flour protein, and dry gluten was not significant at the α = 0.05 level. Weak correlations were observed with Falling Number score (r = 0.32), test weight (r = 0.36), shorts (r = 0.43), and flour yield (r = -0.36). Nonparametric stability analysis indicated that genotype-by-environment interaction was significant at a critical value of χ2 = 36.41 with one degree of freedom. Nonparametric stability and genotype and genotype-byenvironment (GGE) analysis identified SD4416 as one of the three the most broadly adapted cultivars. A two-sample t test of gliadin accumulated by old and new cultivars grown in the same environments did not identify statistically significant differences in gliadin accumulation. Ten D genome-specific point mutation markers were used to screen 40 cultivars chosen by rank and assigned to either the low- or high-gliadin accumulation groups. The cultivars screened showed little to no genotypic polymorphism for these markers. No conclusive evidence was found to support the hypothesis that plant breeding selection practices have increased gliadin accumulation in contemporary wheat cultivars. Environment exerted the greatest influence on gliadin accumulation in the 191 cultivars