Simulations for modelling of population balance equations of particulate processes using the discrete particle model (DPM)

Magdeburg, Univ., Fak. für Mathematik, Diss., 2009

Numerical investigation of micro and macro mechanical behaviour of granular media via a discrete element approach

Magdeburg, Univ., Fak. für Mathematik, Diss., 2009

Verification of system properties of polynomial systems using discrete-time approximations and set-based analysis

Magdeburg, Univ., Fak. für Elektrotechnik und Informationstechnik, Diss., 2015

Global eriodicity and complete integrability of discrete dynamical systems

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On the applicability of mathematics : philosophical and historical perspectives

The present thesis is a contribution to the debate on the applicability of mathematics; it examines the interplay between mathematics and the world, using historical case studies. The first part of the thesis consists of four small case studies. In chapter 1, I criticize "ante rem structuralism", proposed by Stewart Shapiro, by showing that his so-called "finite cardinal structures" are in conflict with mathematical practice. In chapter 2, I discuss Leonhard Euler's solution to the Königsberg bridges problem. I propose interpreting Euler's solution both as an explanation within mathematics and as a scientific explanation. I put the insights from the historical case to work against recent philosophical accounts of the Königsberg case. In chapter 3, I analyze the predator-prey model, proposed by Lotka and Volterra. I extract some interesting philosophical lessons from Volterra's original account of the model, such as: Volterra's remarks on mathematical methodology; the relation between mathematics and idealization in the construction of the model; some relevant details in the derivation of the Third Law, and; notions of intervention that are motivated by one of Volterra's main mathematical tools, phase spaces. In chapter 4, I discuss scientific and mathematical attempts to explain the structure of the bee's honeycomb. In the first part, I discuss a candidate explanation, based on the mathematical Honeycomb Conjecture, presented in Lyon and Colyvan (2008). I argue that this explanation is not scientifically adequate. In the second part, I discuss other mathematical, physical and biological studies that could contribute to an explanation of the bee's honeycomb. The upshot is that most of the relevant mathematics is not yet sufficiently understood, and there is also an ongoing debate as to the biological details of the construction of the bee's honeycomb. The second part of the thesis is a bigger case study from physics: the genesis of GR. Chapter 5 is a short introduction to the history, physics and mathematics that is relevant to the genesis of general relativity (GR). Chapter 6 discusses the historical question as to what Marcel Grossmann contributed to the genesis of GR. I will examine the so-called "Entwurf" paper, an important joint publication by Einstein and Grossmann, containing the first tensorial formulation of GR. By comparing Grossmann's part with the mathematical theories he used, we can gain a better understanding of what is involved in the first steps of assimilating a mathematical theory to a physical question. In chapter 7, I introduce, and discuss, a recent account of the applicability of mathematics to the world, the Inferential Conception (IC), proposed by Bueno and Colyvan (2011). I give a short exposition of the IC, offer some critical remarks on the account, discuss potential philosophical objections, and I propose some extensions of the IC. In chapter 8, I put the Inferential Conception (IC) to work in the historical case study: the genesis of GR. I analyze three historical episodes, using the conceptual apparatus provided by the IC. In episode one, I investigate how the starting point of the application process, the "assumed structure", is chosen. Then I analyze two small application cycles that led to revisions of the initial assumed structure. In episode two, I examine how the application of "new" mathematics - the application of the Absolute Differential Calculus (ADC) to gravitational theory - meshes with the IC. In episode three, I take a closer look at two of Einstein's failed attempts to find a suitable differential operator for the field equations, and apply the conceptual tools provided by the IC so as to better understand why he erroneously rejected both the Ricci tensor and the November tensor in the Zurich Notebook.

The convenient calculation of some test statistics in models of discrete choice

The paper considers the use of artificial regression in calculating different types of score test when the log

Cutting edge: apoptosis of superantigen-activated T cells occurs preferentially after a discrete number of cell divisions in vivo.

Staphylococcal enterotoxins are bacterial products that display superantigen activity in vitro as well as in vivo. For instance, staphylococcal enterotoxin B (SEB) polyclonally activates T cells that bear the Vbeta8 gene segment of the TCR. SEB-activated T cells undergo a burst of proliferation that is followed by apoptosis. Using an in vivo adaptation of a fluorescent cell division monitoring technique, we show here that SEB-activated T cells divide asynchronously, and that apoptosis of superantigen-activated T cells is preferentially restricted to cells which have undergone a discrete number of cell divisions. Collectively, our data suggest that superantigen-activated T cells are programmed to undergo a fixed number of cell divisions before undergoing apoptosis. A delayed death program may provide a mechanistic compromise between effector functions and homeostasis of activated T cells.

Regularity and mass conservation for discrete coagulation-fragmentation equations with diffusion

We present a new a-priori estimate for discrete coagulation fragmentation systems with size-dependent diffusion within a bounded, regular domain confined by homogeneous Neumann boundary conditions. Following from a duality argument, this a-priori estimate provides a global L2 bound on the mass density and was previously used, for instance, in the context of reaction-diffusion equations. In this paper we demonstrate two lines of applications for such an estimate: On the one hand, it enables to simplify parts of the known existence theory and allows to show existence of solutions for generalised models involving collision-induced, quadratic fragmentation terms for which the previous existence theory seems difficult to apply. On the other hand and most prominently, it proves mass conservation (and thus the absence of gelation) for almost all the coagulation coefficients for which mass conservation is known to hold true in the space homogeneous case.

Two weight inequalities for discrete positive operators

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Nash equilibrium strategies in discrete-time finite-horizon dynamic games with risk-and effort-averse players

The objective of this paper is to re-examine the risk-and effort attitude in the context of strategic dynamic interactions stated as a discrete-time finite-horizon Nash game. The analysis is based on the assumption that players are endogenously risk-and effort-averse. Each player is characterized by distinct risk-and effort-aversion types that are unknown to his opponent. The goal of the game is the optimal risk-and effort-sharing between the players. It generally depends on the individual strategies adopted and, implicitly, on the the players' types or characteristics.

Discrete time Non-homogeneous Semi-Markov Processes applied to Models for Disability Insurance

In this paper, we present a stochastic model for disability insurance contracts. The model is based on a discrete time non-homogeneous semi-Markov process (DTNHSMP) to which the backward recurrence time process is introduced. This permits a more exhaustive study of disability evolution and a more efficient approach to the duration problem. The use of semi-Markov reward processes facilitates the possibility of deriving equations of the prospective and retrospective mathematical reserves. The model is applied to a sample of contracts drawn at random from a mutual insurance company.

Trypanosoma cruzi strains isolated from human, vector, and animal reservoir in the same endemic region in Mexico and typed as T. cruzi I, discrete typing unit 1 exhibit considerable biological diversity

In this study, three strains of Trypanosoma cruzi were isolated at the same time and in the same endemic region in Mexico from a human patient with chronic chagasic cardiomyopathy (RyC-H); vector (Triatoma barberi) (RyC-V); and rodent reservoir (Peromyscus peromyscus) (RyC-R). The three strains were characterized by multilocus enzyme electrophoresis, random amplified polymorphic DNA, and by pathological profiles in experimental animals (biodemes). Based on the analysis of genetic markers the three parasite strains were typed as belonging to T. cruzi I major group, discrete typing unit 1. The pathological profile of RyC-H and RyC-V strains indicated medium virulence and low mortality and, accordingly, the strains should be considered as belonging to biodeme Type III. On the other hand, the parasites from RyC-R strain induced more severe inflammatory processes and high mortality (> 40%) and were considered as belonging to biodeme Type II. The relationship between genotypes and biological characteristics in T. cruzi strains is still debated and not clearly understood. An expert committee recommended in 1999 that Biodeme Type III would correspond to T. cruzi I group, whereas Biodeme Type II, to T. cruzi II group. Our findings suggest that, at least for Mexican isolates, this correlation does not stand and that biological characteristics such as pathogenicity and virulence could be determined by factors different from those identified in the genotypic characterization

A discrete forest in a continuous landscape : investigating interactions between natural resource management and sustainable development

Summary Forests are key ecosystems of the earth and associated with a large range of functions. Many of these functions are beneficial to humans and are referred to as ecosystem services. Sustainable development requires that all relevant ecosystem services are quantified, managed and monitored equally. Natural resource management therefore targets the services associated with ecosystems. The main hypothesis of this thesis is that the spatial and temporal domains of relevant services do not correspond to a discrete forest ecosystem. As a consequence, the services are not quantified, managed and monitored in an equal and sustainable manner. The thesis aims were therefore to test this hypothesis, establish an improved conceptual approach and provide spatial applications for the relevant land cover and structure variables. The study was carried out in western Switzerland and based primarily on data from a countrywide landscape inventory. This inventory is part of the third Swiss national forest inventory and assesses continuous landscape variables based on a regular sampling of true colour aerial imagery. In addition, land cover variables were derived from Landsat 5 TM passive sensor data and land structure variables from active sensor data from a small footprint laserscanning system. The results confirmed the main hypothesis, as relevant services did not scale well with the forest ecosystem. Instead, a new conceptual approach for sustainable management of natural resources was described. This concept quantifies the services as a continuous function of the landscape, rather than a discrete function of the forest ecosystem. The explanatory landscape variables are therefore called continuous fields and the forest becomes a dependent and function-driven management unit. Continuous field mapping methods were established for land cover and structure variables. In conclusion, the discrete forest ecosystem is an adequate planning and management unit. However, monitoring the state of and trends in sustainability of services requires them to be quantified as a continuous function of the landscape. Sustainable natural resource management iteratively combines the ecosystem and gradient approaches. Résumé Les forêts sont des écosystèmes-clés de la terre et on leur attribue un grand nombre de fonctions. Beaucoup de ces fonctions sont bénéfiques pour l'homme et sont nommées services écosystémiques. Le développement durable exige que ces services écosystémiques soient tous quantifiés, gérés et surveillés de façon égale. La gestion des ressources naturelles a donc pour cible les services attribués aux écosystèmes. L'hypothèse principale de cette thèse est que les domaines spatiaux et temporels des services attribués à la forêt ne correspondent pas à un écosystème discret. Par conséquent, les services ne sont pas quantifiés, aménagés et surveillés d'une manière équivalente et durable. Les buts de la thèse étaient de tester cette hypothèse, d'établir une nouvelle approche conceptuelle de la gestion des ressources naturelles et de préparer des applications spatiales pour les variables paysagères et structurelles appropriées. L'étude a été menée en Suisse occidentale principalement sur la base d'un inventaire de paysage à l'échelon national. Cet inventaire fait partie du troisième inventaire forestier national suisse et mesure de façon continue des variables paysagères sur la base d'un échantillonnage régulier sur des photos aériennes couleur. En outre, des variables de couverture ? terrestre ont été dérivées des données d'un senseur passif Landsat 5 TM, ainsi que des variables structurelles, dérivées du laserscanning, un senseur actif. Les résultats confirment l'hypothèse principale, car l'échelle des services ne correspond pas à celle de l'écosystème forestier. Au lieu de cela, une nouvelle approche a été élaborée pour la gestion durable des ressources naturelles. Ce concept représente les services comme une fonction continue du paysage, plutôt qu'une fonction discrète de l'écosystème forestier. En conséquence, les variables explicatives de paysage sont dénommées continuous fields et la forêt devient une entité dépendante, définie par la fonction principale du paysage. Des méthodes correspondantes pour la couverture terrestre et la structure ont été élaborées. En conclusion, l'écosystème forestier discret est une unité adéquate pour la planification et la gestion. En revanche, la surveillance de la durabilité de l'état et de son évolution exige que les services soient quantifiés comme fonction continue du paysage. La gestion durable des ressources naturelles joint donc l'approche écosystémique avec celle du gradient de manière itérative.

Discrete and continuous compositions

This paper examines a dataset which is modeled well by thePoisson-Log Normal process and by this process mixed with LogNormal data, which are both turned into compositions. Thisgenerates compositional data that has zeros without any need forconditional models or assuming that there is missing or censoreddata that needs adjustment. It also enables us to model dependenceon covariates and within the composition