TY - BOOK A1 - Zhuchok, Anatolii V. T1 - Relatively free doppelsemigroups N2 - A doppelalgebra is an algebra defined on a vector space with two binary linear associative operations. Doppelalgebras play a prominent role in algebraic K-theory. We consider doppelsemigroups, that is, sets with two binary associative operations satisfying the axioms of a doppelalgebra. Doppelsemigroups are a generalization of semigroups and they have relationships with such algebraic structures as interassociative semigroups, restrictive bisemigroups, dimonoids, and trioids. In the lecture notes numerous examples of doppelsemigroups and of strong doppelsemigroups are given. The independence of axioms of a strong doppelsemigroup is established. A free product in the variety of doppelsemigroups is presented. We also construct a free (strong) doppelsemigroup, a free commutative (strong) doppelsemigroup, a free n-nilpotent (strong) doppelsemigroup, a free n-dinilpotent (strong) doppelsemigroup, and a free left n-dinilpotent doppelsemigroup. Moreover, the least commutative congruence, the least n-nilpotent congruence, the least n-dinilpotent congruence on a free (strong) doppelsemigroup and the least left n-dinilpotent congruence on a free doppelsemigroup are characterized. The book addresses graduate students, post-graduate students, researchers in algebra and interested readers. N2 - Eine Doppelalgebra ist eine auf einem Vektorraum definierte Algebra mit zwei binären linearen assoziativen Operationen. Doppelalgebren spielen eine herausragende Rolle in der algebraischen K-Theorie. Wir betrachten Doppelhalbgruppen, d.h Mengen mit zwei binären assoziativen Operationen, welche die Axiome der Doppelhalbgruppe erfüllen. Doppelhalbgruppen sind Veralgemeinerungen von Halbgruppen und sie stehen in Beziehung zu solchen algebraischen Strukturen wie interassoziative Halbgruppen, restriktive Bihalbgruppen, Dimonoiden und Trioden. In dieser Lecture Notes werden eine Vielzahl von Beispielen für Doppelhalbgruppen und strong Doppelhalbgruppen gegeben. Die Unabhängigkeit der Axiome für Doppelhalbgruppen wird nachgewiesen. Ein freies Produkt in der Varietät der Doppelhalbgruppen wird vorgestellt. Wir konstruieren auch eine freie (kommutative) strong Doppelhalbgruppe, eine freie n-dinilpotent (strong) Doppelhalbgruppe und eine freie Links n-dinilpotent Doppelhalbgruppe. Darüber hinaus werden die kleinste n-nilpotente Kogruenz, die kleinste n-dinilpotente Kongruenz auf der freien (strong) Doppelhalbgruppe und die kleinste n-dinilpotente Kongruenz auf einer freien Doppelhalbgruppe charakterisiert. Das Buch richtet sich an Graduierte, Doktoranden, Forscher in Algebra und interessierte Leser. T3 - Lectures in pure and applied mathematics - 5 KW - doppelsemigroup KW - interassociativity KW - free algebra KW - semigroup KW - congruence Y1 - 2018 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-407719 SN - 978-3-86956-427-2 SN - 2199-4951 SN - 2199-496X IS - 5 PB - Universitätsverlag Potsdam CY - Potsdam ER - TY - BOOK A1 - Zass, Alexander A1 - Zagrebnov, Valentin A1 - Sukiasyan, Hayk A1 - Melkonyan, Tatev A1 - Rafler, Mathias A1 - Poghosyan, Suren A1 - Zessin, Hans A1 - Piatnitski, Andrey A1 - Zhizhina, Elena A1 - Pechersky, Eugeny A1 - Pirogov, Sergei A1 - Yambartsev, Anatoly A1 - Mazzonetto, Sara A1 - Lykov, Alexander A1 - Malyshev, Vadim A1 - Khachatryan, Linda A1 - Nahapetian, Boris A1 - Jursenas, Rytis A1 - Jansen, Sabine A1 - Tsagkarogiannis, Dimitrios A1 - Kuna, Tobias A1 - Kolesnikov, Leonid A1 - Hryniv, Ostap A1 - Wallace, Clare A1 - Houdebert, Pierre A1 - Figari, Rodolfo A1 - Teta, Alessandro A1 - Boldrighini, Carlo A1 - Frigio, Sandro A1 - Maponi, Pierluigi A1 - Pellegrinotti, Alessandro A1 - Sinai, Yakov G. ED - Roelly, Sylvie ED - Rafler, Mathias ED - Poghosyan, Suren T1 - Proceedings of the XI international conference stochastic and analytic methods in mathematical physics N2 - The XI international conference Stochastic and Analytic Methods in Mathematical Physics was held in Yerevan 2 – 7 September 2019 and was dedicated to the memory of the great mathematician Robert Adol’fovich Minlos, who passed away in January 2018. The present volume collects a large majority of the contributions presented at the conference on the following domains of contemporary interest: classical and quantum statistical physics, mathematical methods in quantum mechanics, stochastic analysis, applications of point processes in statistical mechanics. The authors are specialists from Armenia, Czech Republic, Denmark, France, Germany, Italy, Japan, Lithuania, Russia, UK and Uzbekistan. A particular aim of this volume is to offer young scientists basic material in order to inspire their future research in the wide fields presented here. T3 - Lectures in pure and applied mathematics - 6 KW - statistical mechanics KW - random point processes KW - stochastic analysis Y1 - 2020 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-459192 SN - 978-3-86956-485-2 SN - 2199-4951 SN - 2199-496X IS - 6 PB - Universitätsverlag Potsdam CY - Potsdam ER - TY - BOOK A1 - Pilipenko, Andrey T1 - An introduction to stochastic differential equations with reflection T3 - Lectures in pure and applied mathematics N2 - These lecture notes are intended as a short introduction to diffusion processes on a domain with a reflecting boundary for graduate students, researchers in stochastic analysis and interested readers. Specific results on stochastic differential equations with reflecting boundaries such as existence and uniqueness, continuity and Markov properties, relation to partial differential equations and submartingale problems are given. An extensive list of references to current literature is included. This book has its origins in a mini-course the author gave at the University of Potsdam and at the Technical University of Berlin in Winter 2013. T3 - Lectures in pure and applied mathematics - 1 KW - Diffusionsprozess KW - Reflektierende Randbedingungen KW - stochastische Differentialgleichungen KW - diffusion process KW - reflecting boundary KW - stochastic differential equations Y1 - 2014 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-70782 SN - 978-3-86956-297-1 SN - 2199-4951 SN - 2199-496X IS - 1 PB - Universitätsverlag Potsdam CY - Potsdam ER - TY - BOOK A1 - Liero, Hannelore T1 - Estimation and testing the effect of covariates in accelerated life time models under censoring N2 - The accelerated lifetime model is considered. To test the influence of the covariate we transform the model in a regression model. Since censoring is allowed this approach leads to a goodness-of-fit problem for regression functions under censoring. So nonparametric estimation of regression functions under censoring is investigated, a limit theorem for a L2-distance is stated and a test procedure is formulated. Finally a Monte Carlo procedure is proposed. T3 - Mathematische Statistik und Wahrscheinlichkeitstheorie : Preprint - 2010, 02 KW - accelerated life time model KW - censoring KW - goodness-of-fit testing KW - nonparametric regression estimation KW - Monte Carlo testing Y1 - 2010 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-52823 ER - TY - BOOK A1 - Kulik, Alexei Michajlovič ED - Roelly, Sylvie T1 - Introduction to Ergodic rates for Markov chains and processes BT - with applications to limit theorems N2 - The present lecture notes aim for an introduction to the ergodic behaviour of Markov Processes and addresses graduate students, post-graduate students and interested readers. Different tools and methods for the study of upper bounds on uniform and weak ergodic rates of Markov Processes are introduced. These techniques are then applied to study limit theorems for functionals of Markov processes. This lecture course originates in two mini courses held at University of Potsdam, Technical University of Berlin and Humboldt University in spring 2013 and Ritsumameikan University in summer 2013. Alexei Kulik, Doctor of Sciences, is a Leading researcher at the Institute of Mathematics of Ukrainian National Academy of Sciences. T3 - Lectures in pure and applied mathematics - 2 KW - Markov processes KW - Markovprozesse KW - long-time behaviour KW - Langzeitverhalten KW - ergodic rates KW - Konvergenzrate Y1 - 2015 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-79360 SN - 978-3-86956-338-1 SN - 2199-4951 SN - 2199-496X PB - Universitätsverlag Potsdam CY - Potsdam ER - TY - BOOK A1 - Jankowski, £ukasz T1 - Modelling and simulation of light propagation in non-aged and aged step-index polymer optical fibres. - [überarb. Diss.] N2 - Kunststofflichtwellenleiter (POFs) stellen ein verhältnismäßig neues Medium zur optische Datenkommunikation über kurzen Strecken dar. Während ihrer Einsatzdauer unterliegen POFs unterschiedlichen Arten von Umweltbeanspruchungen, hauptsächlich durch hohe Temperatur, hohe Feuchtigkeit und mechanischen Belastungen. Zahlreiche experimentelle Forschungen beschäftigten sich mit der standardisierten Prüfung der Zuverlässigkeit von im Handel erhältlichen Fasern. Jedoch gab es bisher wenig Erfolg bei der Bemühung, zwei grundlegende optische Erscheinungen, Absorption und Streuung, die die Lichtausbreitung in Fasern stark beeinflussen, zu verstehen und praktisch zu modellieren: Diese beiden Effekte beschreiben nicht nur die Qualität neuer Fasern, sondern sie werden auch stark durch die Alterungsprozess beeinflusst. Der Hauptzweck dieser Doktorarbeit war es, ein praktisch verwendbares und theoretisch gut fundiertes Modell der Lichtausbreitung in nicht gealterten und gealterten POFs zu entwickeln und es durch optische Experimente zu verifizieren. Dabei wurden anwendungsorientierte Aspekte mit theoretischer POF-Modellierung kombiniert. Die Arbeit enthält die erste bekannte Anwendung der Wellenanalyse zur Untersuchung der winkelabhängigen Eigenschaften der Streuung in Lichtwellenleitern. Für die praktischen Experimente wurden mehrere POF-Proben unterschiedlicher Hersteller künstlich gealtert, indem sie bis 4500 Stunden bei 100 °C gelagert wurden (ohne Feuchtekontrolle). Die Parameter der jeweiligen Simulationen wurden mittels einer systematischen Optimierung an die gemessen optischen Eigenschaften der gealterten Proben angeglichen. Die Resultate deuten an, dass der Übertragungsverlust der gealterten Fasern in den ersten Tagen und Wochen der Alterung am stärksten durch eine wesentliche physikalische Verschlechterung der Kern-Mantel-Grenzfläche verursacht wird. Chemische Effekte des Alterungsprozesses scheinen im Faserkernmaterial zuerst nach einigen Monaten aufzutreten. N2 - This thesis discusses theoretical and practical aspects of modelling of light propagation in non-aged and aged step-index polymer optical fibres (POFs). Special attention has been paid in describing optical characteristics of non-ideal fibres, scattering and attenuation, and in combining application-oriented and theoretical approaches. The precedence has been given to practical issues, but much effort has been also spent on the theoretical analysis of basic mechanisms governing light propagation in cylindrical waveguides.As a result a practically usable general POF model based on the raytracing approach has been developed and implemented. A systematic numerical optimisation of its parameters has been performed to obtain the best fit between simulated and measured optical characteristics of numerous non-aged and aged fibre samples. The model was verified by providing good agreement, especially for the non-aged fibres. The relations found between aging time and optimal values of model parameters contribute to a better understanding of the aging mechanisms of POFs. T2 - Modelling and simulation of light propagation in non-aged and aged step-index polymer optical fibres KW - Modellierung KW - Lichtwellenleiter KW - Kunststofflichtwellenleiter KW - optische Fasern KW - POF KW - Streuung KW - Temperatur KW - Alterung KW - modelling optical fibres waveguides pof scattering temperature aging ageing Y1 - 2004 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-0001659 ER - TY - BOOK A1 - Dereudre, David A1 - Roelly, Sylvie T1 - On Gibbsianness of infinite-dimensional diffusions N2 - We analyse different Gibbsian properties of interactive Brownian diffusions X indexed by the lattice $Z^{d} : X = (X_{i}(t), i ∈ Z^{d}, t ∈ [0, T], 0 < T < +∞)$. In a first part, these processes are characterized as Gibbs states on path spaces of the form $C([0, T],R)Z^{d}$. In a second part, we study the Gibbsian character on $R^{Z}^{d}$ of $v^{t}$, the law at time t of the infinite-dimensional diffusion X(t), when the initial law $v = v^{0}$ is Gibbsian. T3 - Mathematische Statistik und Wahrscheinlichkeitstheorie : Preprint - 2004, 01 KW - infinite-dimensional Brownian diffusion KW - Gibbs field KW - cluster expansion Y1 - 2004 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-52630 ER -