@unpublished{LyTarkhanov2015, author = {Ly, Ibrahim and Tarkhanov, Nikolai Nikolaevich}, title = {A Rad{\´o} theorem for p-harmonic functions}, volume = {4}, number = {3}, publisher = {Universit{\"a}tsverlag Potsdam}, address = {Potsdam}, issn = {2193-6943}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-71492}, pages = {10}, year = {2015}, abstract = {Let A be a nonlinear differential operator on an open set X in R^n and S a closed subset of X. Given a class F of functions in X, the set S is said to be removable for F relative to A if any weak solution of A (u) = 0 in the complement of S of class F satisfies this equation weakly in all of X. For the most extensively studied classes F we show conditions on S which guarantee that S is removable for F relative to A.}, language = {en} } @unpublished{LyTarkhanov2015, author = {Ly, Ibrahim and Tarkhanov, Nikolai Nikolaevich}, title = {Asymptotic expansions at nonsymmetric cuspidal points}, volume = {4}, number = {7}, publisher = {Universit{\"a}tsverlag Potsdam}, address = {Potsdam}, issn = {2193-6943}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-78199}, pages = {11}, year = {2015}, abstract = {We study asymptotics of solutions to the Dirichlet problem in a domain whose boundary contains a nonsymmetric conical point. We establish a complete asymptotic expansion of solutions near the singular point.}, language = {en} } @phdthesis{Beinrucker2015, author = {Beinrucker, Andre}, title = {Variable selection in high dimensional data analysis with applications}, school = {Universit{\"a}t Potsdam}, pages = {VII, 107}, year = {2015}, language = {en} } @unpublished{FedosovTarkhanov2015, author = {Fedosov, Boris and Tarkhanov, Nikolai Nikolaevich}, title = {Deformation quantisation and boundary value problems}, volume = {4}, number = {5}, publisher = {Universit{\"a}tsverlag Potsdam}, address = {Potsdam}, issn = {2193-6943}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-77150}, pages = {27}, year = {2015}, abstract = {We describe a natural construction of deformation quantisation on a compact symplectic manifold with boundary. On the algebra of quantum observables a trace functional is defined which as usual annihilates the commutators. This gives rise to an index as the trace of the unity element. We formulate the index theorem as a conjecture and examine it by the classical harmonic oscillator.}, language = {en} } @unpublished{ElinShoikhetTarkhanov2015, author = {Elin, Mark and Shoikhet, David and Tarkhanov, Nikolai Nikolaevich}, title = {Analytic semigroups of holomorphic mappings and composition operators}, volume = {4}, number = {6}, publisher = {Universit{\"a}tsverlag Potsdam}, address = {Potsdam}, issn = {2193-6943}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-77914}, pages = {30}, year = {2015}, abstract = {In this paper we study the problem of analytic extension in parameter for a semigroup of holomorphic self-mappings of the unit ball in a complex Banach space and its relation to the linear continuous semigroup of composition operators. We also provide a brief review around this topic.}, language = {en} } @incollection{Petsche2015, author = {Petsche, Hans-Joachim}, title = {Einf{\"u}hrung}, series = {Raum und Zahl im Fokus der Wissenschaften : eine multidisziplin{\"a}re Vorlesungsreihe}, booktitle = {Raum und Zahl im Fokus der Wissenschaften : eine multidisziplin{\"a}re Vorlesungsreihe}, publisher = {Trafo}, address = {Berlin}, isbn = {978-3-86464-082-7}, pages = {9 -- 14}, year = {2015}, language = {de} } @article{Petsche2015, author = {Petsche, Hans-Joachim}, title = {Raum und Zahl - philosophische Kontexte}, series = {Raum und Zahl im Fokus der Wissenschaften : eine multidisziplin{\"a}re Vorlesungsreihe}, journal = {Raum und Zahl im Fokus der Wissenschaften : eine multidisziplin{\"a}re Vorlesungsreihe}, publisher = {Trafo}, address = {Berlin}, isbn = {978-3-86464-082-7}, pages = {15 -- 33}, year = {2015}, language = {de} } @article{SixtusFischer2015, author = {Sixtus, Elena and Fischer, Martin H.}, title = {Eine kognitionswissenschaftliche Betrachtung der Konzepte "Raum" und "Zahl"}, series = {Raum und Zahl im Fokus der Wissenschaften : eine multidisziplin{\"a}re Vorlesungsreihe}, journal = {Raum und Zahl im Fokus der Wissenschaften : eine multidisziplin{\"a}re Vorlesungsreihe}, publisher = {Trafo}, address = {Berlin}, isbn = {978-3-86464-082-7}, pages = {35 -- 62}, year = {2015}, language = {de} } @article{Proeve2015, author = {Pr{\"o}ve, Ralf}, title = {Numerische Zeichen und die Repr{\"a}sentation von Sinn}, series = {Raum und Zahl im Fokus der Wissenschaften : eine multidisziplin{\"a}re Vorlesungsreihe}, journal = {Raum und Zahl im Fokus der Wissenschaften : eine multidisziplin{\"a}re Vorlesungsreihe}, publisher = {Trafo}, address = {Berlin}, isbn = {978-3-86464-082-7}, pages = {63 -- 76}, year = {2015}, language = {de} } @article{Heimann2015, author = {Heimann, Heinz-Dieter}, title = {Kreise - Punkte - Linien}, series = {Raum und Zahl im Fokus der Wissenschaften : eine multidisziplin{\"a}re Vorlesungsreihe}, journal = {Raum und Zahl im Fokus der Wissenschaften : eine multidisziplin{\"a}re Vorlesungsreihe}, publisher = {Trafo}, address = {Berlin}, isbn = {978-3-86464-082-7}, pages = {111 -- 127}, year = {2015}, language = {de} } @unpublished{ConfortiRoelly2015, author = {Conforti, Giovanni and Roelly, Sylvie}, title = {Reciprocal class of random walks on an Abelian group}, volume = {4}, number = {1}, publisher = {Universit{\"a}tsverlag Potsdam}, address = {Potsdam}, issn = {2193-6943}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-72604}, pages = {22}, year = {2015}, abstract = {Processes having the same bridges as a given reference Markov process constitute its reciprocal class. In this paper we study the reciprocal class of a continuous time random walk with values in a countable Abelian group, we compute explicitly its reciprocal characteristics and we present an integral characterization of it. Our main tool is a new iterated version of the celebrated Mecke's formula from the point process theory, which allows us to study, as transformation on the path space, the addition of random loops. Thanks to the lattice structure of the set of loops, we even obtain a sharp characterization. At the end, we discuss several examples to illustrate the richness of reciprocal classes. We observe how their structure depends on the algebraic properties of the underlying group.}, language = {en} } @phdthesis{Bettenbuehl2015, author = {Bettenb{\"u}hl, Mario}, title = {Microsaccades}, publisher = {Universit{\"a}tsverlag Potsdam}, address = {Potsdam}, isbn = {978-3-86956-122-6}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-72622}, school = {Universit{\"a}t Potsdam}, pages = {iv, 126}, year = {2015}, abstract = {The first thing we do upon waking is open our eyes. Rotating them in our eye sockets, we scan our surroundings and collect the information into a picture in our head. Eye movements can be split into saccades and fixational eye movements, which occur when we attempt to fixate our gaze. The latter consists of microsaccades, drift and tremor. Before we even lift our eye lids, eye movements - such as saccades and microsaccades that let the eyes jump from one to another position - have partially been prepared in the brain stem. Saccades and microsaccades are often assumed to be generated by the same mechanisms. But how saccades and microsaccades can be classified according to shape has not yet been reported in a statistical manner. Research has put more effort into the investigations of microsaccades' properties and generation only since the last decade. Consequently, we are only beginning to understand the dynamic processes governing microsaccadic eye movements. Within this thesis, the dynamics governing the generation of microsaccades is assessed and the development of a model for the underlying processes. Eye movement trajectories from different experiments are used, recorded with a video-based eye tracking technique, and a novel method is proposed for the scale-invariant detection of saccades (events of large amplitude) and microsaccades (events of small amplitude). Using a time-frequency approach, the method is examined with different experiments and validated against simulated data. A shape model is suggested that allows for a simple estimation of saccade- and microsaccade related properties. For sequences of microsaccades, in this thesis a time-dynamic Markov model is proposed, with a memory horizon that changes over time and which can best describe sequences of microsaccades.}, language = {en} } @unpublished{AlsaedyTarkhanov2015, author = {Alsaedy, Ammar and Tarkhanov, Nikolai Nikolaevich}, title = {Weak boundary values of solutions of Lagrangian problems}, volume = {4}, number = {2}, publisher = {Universit{\"a}tsverlag Potsdam}, address = {Potsdam}, issn = {2193-6943}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-72617}, pages = {24}, year = {2015}, abstract = {We define weak boundary values of solutions to those nonlinear differential equations which appear as Euler-Lagrange equations of variational problems. As a result we initiate the theory of Lagrangian boundary value problems in spaces of appropriate smoothness. We also analyse if the concept of mapping degree of current importance applies to the study of Lagrangian problems.}, language = {en} } @unpublished{Tarkhanov2015, author = {Tarkhanov, Nikolai Nikolaevich}, title = {A spectral theorem for deformation quantisation}, volume = {4}, number = {4}, publisher = {Universit{\"a}tsverlag Potsdam}, address = {Potsdam}, issn = {2193-6943}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-72425}, pages = {8}, year = {2015}, abstract = {We present a construction of the eigenstate at a noncritical level of the Hamiltonian function. Moreover, we evaluate the contributions of Morse critical points to the spectral decomposition.}, language = {en} } @book{VanLeeuwenChengReich2015, author = {Van Leeuwen, Peter Jan and Cheng, Yuan and Reich, Sebastian}, title = {Nonlinear data assimilation}, series = {Frontiers in applied dynamical systems: reviews and tutorials ; 2}, journal = {Frontiers in applied dynamical systems: reviews and tutorials ; 2}, publisher = {Springer}, address = {Cham}, isbn = {978-3-319-18346-6}, doi = {10.1007/978-3-319-18347-3}, pages = {xii, 118}, year = {2015}, abstract = {This book contains two review articles on nonlinear data assimilation that deal with closely related topics but were written and can be read independently. Both contributions focus on so-called particle filters. The first contribution by Jan van Leeuwen focuses on the potential of proposal densities. It discusses the issues with present-day particle filters and explorers new ideas for proposal densities to solve them, converging to particle filters that work well in systems of any dimension, closing the contribution with a high-dimensional example. The second contribution by Cheng and Reich discusses a unified framework for ensemble-transform particle filters. This allows one to bridge successful ensemble Kalman filters with fully nonlinear particle filters, and allows a proper introduction of localization in particle filters, which has been lacking up to now.}, language = {en} } @article{ConfortiPraRoelly2015, author = {Conforti, Giovanni and Pra, Paolo Dai and Roelly, Sylvie}, title = {Reciprocal Class of Jump Processes}, series = {Journal of theoretical probability}, volume = {30}, journal = {Journal of theoretical probability}, publisher = {Springer}, address = {New York}, issn = {0894-9840}, doi = {10.1007/s10959-015-0655-3}, pages = {551 -- 580}, year = {2015}, abstract = {Processes having the same bridges as a given reference Markov process constitute its reciprocal class. In this paper we study the reciprocal class of compound Poisson processes whose jumps belong to a finite set . We propose a characterization of the reciprocal class as the unique set of probability measures on which a family of time and space transformations induces the same density, expressed in terms of the reciprocal invariants. The geometry of plays a crucial role in the design of the transformations, and we use tools from discrete geometry to obtain an optimal characterization. We deduce explicit conditions for two Markov jump processes to belong to the same class. Finally, we provide a natural interpretation of the invariants as short-time asymptotics for the probability that the reference process makes a cycle around its current state.}, language = {en} } @article{Steup2015, author = {Steup, Martin}, title = {Raum und Zahl in der Pflanzenphysiologie}, series = {Raum und Zahl}, journal = {Raum und Zahl}, publisher = {Trafo}, address = {Berlin}, isbn = {978-3-86464-082-7}, pages = {77 -- 109}, year = {2015}, language = {de} } @incollection{KiyLuckeSass2015, author = {Kiy, Alexander and Lucke, Ulrike and Sass, K.}, title = {Gewusst was: Mit einer E-Learning-Toolbox die pers{\"o}nliche virtuelle Umgebung gestalten}, series = {DeLFI 2015 - die 13. E-Learning Fachtagung Informatik der Gesellschaft f{\"u}r Informatik e.V. : 1.-4. September 2015 M{\"u}nchen, Deutschland}, booktitle = {DeLFI 2015 - die 13. E-Learning Fachtagung Informatik der Gesellschaft f{\"u}r Informatik e.V. : 1.-4. September 2015 M{\"u}nchen, Deutschland}, number = {247}, editor = {Pongratz, Hans J. and Keil, R.}, publisher = {Gesellschaft f{\"u}r Informatik e.V.}, address = {Bonn}, isbn = {978-3-88579-641-1}, issn = {1617-5468}, publisher = {Universit{\"a}t Potsdam}, pages = {43 -- 55}, year = {2015}, language = {de} } @incollection{Guenther2015, author = {G{\"u}nther, Oliver}, title = {Zum Geleit}, series = {Raum und Zahl im Fokus der Wissenschaften : eine multidisziplin{\"a}re Vorlesungsreihe}, booktitle = {Raum und Zahl im Fokus der Wissenschaften : eine multidisziplin{\"a}re Vorlesungsreihe}, publisher = {Trafo}, address = {Berlin}, isbn = {978-3-86464-082-7}, pages = {7 -- 8}, year = {2015}, language = {de} } @book{GuentherPetscheFischeretal.2015, author = {G{\"u}nther, Oliver and Petsche, Hans-Joachim and Fischer, Martin H. and Franz, Norbert P. and Steup, Martin and Sixtus, Elena and Heimann, Heinz-Dieter and Pr{\"o}ve, Ralf}, title = {Raum und Zahl im Fokus der Wissenschaften}, series = {Studieren ++ : Konzepte, Perspektiven, Kompetenzen ; 1}, journal = {Studieren ++ : Konzepte, Perspektiven, Kompetenzen ; 1}, editor = {Petsche, Hans-Joachim}, publisher = {Trafo}, address = {Berlin}, isbn = {978-3-86464-082-7}, pages = {168}, year = {2015}, abstract = {Die nun begonnene Reihe „studieren++" resultiert aus einer von der Universit{\"a}t Potsdam angebotenen Vorlesungsreihe. Das Besondere an dieser Vorlesungsreihe ist der multidisziplin{\"a}re Anspruch und die konsequent umgesetzte Zusammenarbeit {\"u}ber Disziplingrenzen hinweg. Die nicht nur {\"u}ber Instituts-, sondern {\"u}ber Fakult{\"a}tsgrenzen praktizierte Interdisziplinarit{\"a}t erlaubt die Betrachtung eines Problems oder Sachverhalts aus unterschiedlichen Blickwinkeln. Wissenschaftliche Fragestellungen sind komplex und nicht immer auf eine Disziplin beschr{\"a}nkt. Sie in ihrer G{\"a}nze erfassen und nachhaltige L{\"o}sungsstrategien oder Konzepte entwickeln zu k{\"o}nnen gelingt oft nur durch eine multidisziplin{\"a}re Kooperation. Eine Lehrveranstaltung wie die vorliegende ist nicht nur f{\"u}r die Studierenden einer Universit{\"a}t eine hervorragende M{\"o}glichkeit, um {\"u}ber die Grenzen der eigenen Disziplin hinaus zu blicken und die Zusammenarbeit mit Wissenschaftlerinnen und Wissenschaftlern aus anderen Bereichen zu pflegen. So lernt man, sich in andere Sichtweisen hineinzuversetzen und sich zwischen den Disziplinen zu bewegen - eine Kompetenz, die in der hochkomplexen Arbeitswelt von heute von hohem Nutzen ist. Der vorliegende erste Band der Reihe hat „Raum und Zahl" zum Thema und ist aus einer Ringvorlesung aus dem Wintersemester 2013/2014 entstanden. Drei der f{\"u}nf Fakult{\"a}ten, insgesamt neun Institute der Universit{\"a}t Potsdam, haben sich an der Vorlesung beteiligt und sich dieses spannenden Themas angenommen. Als jemand, der sich jahrelang wissenschaftlich mit algorithmischer Geometrie sowie mit raumbezogenen Datenbanken und Navigationssystemen besch{\"a}ftigt hat, kann ich nur bekr{\"a}ftigen, dass die Bez{\"u}ge zwischen Raum und Zahl, zwischen R{\"a}umen und Zahlen, noch viel st{\"a}rker im {\"o}ffentlichen Bewusstsein verankert geh{\"o}ren. R{\"a}ume auch quantitativ zu erfassen und zu verstehen ist eine Kulturtechnik, die an Wichtigkeit eher noch zunimmt, vor allem vor dem Hintergrund, dass wir genetisch nicht allzu gut auf derartige Herausforderungen vorbereitet sind. Denn viele unserer einschl{\"a}gigen Gene entstammen noch aus der Zeit der Savanne, einer Zeit, zu der das Raumkonzept sich fast ausschließlich auf die unmittelbare r{\"a}umliche Umgebung bezog und Zahlen jenseits von 10 nur wenig Relevanz f{\"u}r das eigene {\"U}berleben hatten. Als Pr{\"a}sident der Universit{\"a}t Potsdam freut es mich ganz besonders, dass sich die hier vertretenen Wissenschaftler bereit erkl{\"a}rt haben, ihre {\"U}berlegungen mit den Studierenden und ihren Kolleginnen und Kollegen zu teilen. Herrn Kollegen Hans-Joachim Petsche m{\"o}chte ich f{\"u}r sein Engagement danken und ihm zu dieser gelungenen Reihe gratulieren. Der Geist der Wissenschaft, der nicht nur einsam im B{\"u}ro oder Labor gelebt wird, sondern gerade an einer Universit{\"a}t auch aktiv nach außen getragen werden sollte, wird hier in besonderer Weise sichtbar. Ich w{\"u}nsche Ihnen viel Freude bei der Lekt{\"u}re des Bandes und freue mich auf weitere Ver{\"o}ffentlichungen in dieser Reihe.}, subject = {Raum}, language = {de} } @phdthesis{Trump2015, author = {Trump, Stephanie Sonja}, title = {Mathematik in der Physik der Sekundarstufe II!?}, school = {Universit{\"a}t Potsdam}, pages = {214}, year = {2015}, language = {de} } @unpublished{MakhmudovMakhmudovTarkhanov2015, author = {Makhmudov, K. O. and Makhmudov, O. I. and Tarkhanov, Nikolai Nikolaevich}, title = {A nonstandard Cauchy problem for the heat equation}, volume = {4}, number = {11}, publisher = {Universit{\"a}tsverlag Potsdam}, address = {Potsdam}, issn = {2193-6943}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-83830}, pages = {14}, year = {2015}, abstract = {We consider a Cauchy problem for the heat equation in a cylinder X x (0,T) over a domain X in the n-dimensional space with data on a strip lying on the lateral surface. The strip is of the form S x (0,T), where S is an open subset of the boundary of X. The problem is ill-posed. Under natural restrictions on the configuration of S we derive an explicit formula for solutions of this problem.}, language = {en} } @phdthesis{Kaganova2015, author = {Kaganova, Ekaterina}, title = {Das Lehrpotential von Schulbuchlehrtexten im Fach Mathematik}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-80705}, school = {Universit{\"a}t Potsdam}, pages = {287}, year = {2015}, abstract = {Das Schulbuch ist ein etablierter und bedeutender Bestandteil des Mathematikunterrichts. Lehrer nutzen es, um ihren Unterricht vorzubereiten und/oder zu gestalten; Sch{\"u}ler, um in selbigem zu lernen und zu bestehen, vielleicht sogar aus eigenem Interesse; Eltern, um sich dar{\"u}ber zu informieren, was ihr Kind eigentlich k{\"o}nnen soll und wie sie ihm gegebenenfalls helfen k{\"o}nnen. Dar{\"u}ber hinaus ist das Schulbuch ein markantes gesellschaftliches Produkt, dessen Zweck es ist, das Unterrichtsgeschehen zu steuern und zu beeinflussen. Damit ist es auch ein Anzeiger daf{\"u}r, was und wie im Mathematikunterricht gelehrt werden sollte und wird. Die Lehrtexte als zentrale Bestandteile von Schulb{\"u}chern verweisen in diesem Zusammenhang insbesondere auf die Phasen der Einf{\"u}hrung neuen Lernstoffs. Daraus legitimiert sich {\"u}bergreifend die Fragestellung, was und wie (gut) Mathematikschulbuchlehrtexte lehren bzw. was und wie (gut) adressierte Sch{\"u}ler aus ihnen (selbstst{\"a}ndig) lernen, d.h. Wissen erwerben k{\"o}nnen. Angesichts der komplexen und vielf{\"a}ltigen Bedeutung von Schulbuchlehrtexten verwundert es, dass die mathematikdidaktische Forschung bislang wenig Interesse an ihnen zeigt: Es fehlen sowohl eine theoretische Konzeption der Gr{\"o}ße ‚Lehrpotential eines schulmathematischen Lehrtextes' als auch ein analytisches Verfahren, um das anhand eines Mathematikschulbuchlehrtextes Verstehbare und Lernbare zu ermitteln. Mit der vorliegenden Arbeit wird sowohl in theoretisch-methodologischer als auch in empirischer Hinsicht der Versuch unternommen, diesen Defiziten zu begegnen. Dabei wird das ‚Lehrpotential eines Mathematikschulbuchlehrtextes' auf der Grundlage der kognitionspsychologischen Schematheorie und unter Einbeziehung textlinguistischer Ans{\"a}tze als eine textimmanente und analytisch zug{\"a}ngliche Gr{\"o}ße konzipiert. Anschließend wird das Lehrpotential von f{\"u}nf Lehrtexten ausgew{\"a}hlter aktueller Schulb{\"u}cher der Jahrgangsstufen 6 und 7 zu den Inhaltsbereichen ‚Br{\"u}che' und ‚lineare Funktionen' analysiert. Es zeigt sich, dass die untersuchten Lehrtexte aus deutschen Schulb{\"u}chern f{\"u}r Sch{\"u}ler sehr schwer verst{\"a}ndlich sind, d.h. es ist kompliziert, einigen Teiltexten im Rahmen des Gesamttextes einen Sinn abzugewinnen. Die Lehrtexte sind insbesondere dann kaum sinnhaft lesbar, wenn ein Sch{\"u}ler versucht, die mitgeteilten Sachverhalte zu verstehen, d.h. Antworten auf die Fragen zu erhalten, warum ein mathematischer Sachverhalt gerade so und nicht anders ist, wozu ein neuer Sachverhalt/Begriff gebraucht wird, wie das Neue mit bereits Bekanntem zusammenh{\"a}ngt usw. Deutlich zug{\"a}nglicher und sinnhafter erscheinen die Mathematikschulbuchlehrtexte hingegen unter der Annahme, dass ihre zentrale Botschaft in der Mitteilung besteht, welche Aufgabenstellungen in der jeweiligen Lehreinheit vorkommen und wie man sie bearbeitet. Demnach k{\"o}nnen Sch{\"u}ler anhand dieser Lehrtexte im Wesentlichen lernen, wie sie mit mathematischen Zeichen, die f{\"u}r sie kaum etwas bezeichnen, umgehen sollen. Die hier vorgelegten Analyseergebnisse gewinnen in einem soziologischen Kontext an Tragweite und Brisanz. So l{\"a}sst sich aus ihnen u.a. die These ableiten, dass die analysierten Lehrtexte keine ‚ungl{\"u}cklichen' Einzelf{\"a}lle sind, sondern dass die ‚Aufgabenorientierung in einem mathematischen Gewand' ein Charakteristikum typischer (deutscher) Mathematikschulbuchlehrtexte und - noch grunds{\"a}tzlicher - einen Wesenszug typischer schulmathematischer Kommunikation darstellt.}, language = {de} } @phdthesis{AlSaedy2015, author = {Al-Saedy, Ammar Jaffar Muhesin}, title = {Normally solvable lagrangian boundary value problems}, school = {Universit{\"a}t Potsdam}, pages = {110}, year = {2015}, language = {en} } @book{PlattnerLeukert2015, author = {Plattner, Hasso and Leukert, Bernd}, title = {The in-memory revolution}, publisher = {Springer}, address = {Cham}, isbn = {978-3-319-16672-8}, pages = {275}, year = {2015}, abstract = {This book describes the next generation of business applications enabled by SAP's in-memory database, SAP HANA. In particular, the authors show the substantial changes introduced in S4/HANA by switching to SAP HANA. Using numerous examples and use cases from the authors' wealth of real-world experience, it illustrates the quantum leap in performance made possible by the new technology. The book is written by two of the most prominent actors in the area of business application systems: Hasso Plattner, co-founder of SAP and inaugurator of the Hasso Plattner Institute at the University of Potsdam, and Bernd Leukert, member of the Executive Board and the Global Managing Board of SAP. This clearly structured, highly illustrated book takes an exciting new technology and presents the practicality and success of first mover applications.}, language = {en} } @unpublished{MeraShlapunovTarkhanov2015, author = {Mera, Azal and Shlapunov, Alexander and Tarkhanov, Nikolai Nikolaevich}, title = {Navier-Stokes equations for elliptic complexes}, volume = {4}, number = {12}, publisher = {Universit{\"a}tsverlag Potsdam}, address = {Potsdam}, issn = {2193-6943}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-85592}, pages = {27}, year = {2015}, abstract = {We continue our study of invariant forms of the classical equations of mathematical physics, such as the Maxwell equations or the Lam{\´e} system, on manifold with boundary. To this end we interpret them in terms of the de Rham complex at a certain step. On using the structure of the complex we get an insight to predict a degeneracy deeply encoded in the equations. In the present paper we develop an invariant approach to the classical Navier-Stokes equations.}, language = {en} } @unpublished{Conforti2015, author = {Conforti, Giovanni}, title = {Reciprocal classes of continuous time Markov Chains}, volume = {4}, number = {8}, publisher = {Universit{\"a}tsverlag Potsdam}, address = {Potsdam}, issn = {2193-6943}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-78234}, pages = {198}, year = {2015}, abstract = {In this work we study reciprocal classes of Markov walks on graphs. Given a continuous time reference Markov chain on a graph, its reciprocal class is the set of all probability measures which can be represented as a mixture of the bridges of the reference walks. We characterize reciprocal classes with two different approaches. With the first approach we found it as the set of solutions to duality formulae on path space, where the differential operators have the interpretation of the addition of infinitesimal random loops to the paths of the canonical process. With the second approach we look at short time asymptotics of bridges. Both approaches allow an explicit computation of reciprocal characteristics, which are divided into two families, the loop characteristics and the arc characteristics. They are those specific functionals of the generator of the reference chain which determine its reciprocal class. We look at the specific examples such as Cayley graphs, the hypercube and planar graphs. Finally we establish the first concentration of measure results for the bridges of a continuous time Markov chain based on the reciprocal characteristics.}, language = {en} } @unpublished{GibaliShoikhetTarkhanov2015, author = {Gibali, Aviv and Shoikhet, David and Tarkhanov, Nikolai Nikolaevich}, title = {On the convergence of continuous Newton method}, volume = {4}, number = {10}, publisher = {Universit{\"a}tsverlag Potsdam}, address = {Potsdam}, issn = {2193-6943}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-81537}, pages = {15}, year = {2015}, abstract = {In this paper we study the convergence of continuous Newton method for solving nonlinear equations with holomorphic mappings in complex Banach spaces. Our contribution is based on a recent progress in the geometric theory of spirallike functions. We prove convergence theorems and illustrate them by numerical simulations.}, language = {en} } @article{KiyDehneBussler2015, author = {Kiy, Alexander and Dehne, Julian and Bussler, Dirk}, title = {Aufbau einer Cloud-Speicherl{\"o}sung und Integration in bestehende IuK-Infrastrukturen am Beispiel ownCloud an der Universit{\"a}t Potsdam}, series = {Cloudspeicher im Hochschuleinsatz 2015: Proceedings der Tagung "Cloudspeicher im Hochschuleinsatz" am 07. und 08. Mai 2015 am IT-Service-Center (tubIT) der Technischen Universit{\"a}t Berlin}, journal = {Cloudspeicher im Hochschuleinsatz 2015: Proceedings der Tagung "Cloudspeicher im Hochschuleinsatz" am 07. und 08. Mai 2015 am IT-Service-Center (tubIT) der Technischen Universit{\"a}t Berlin}, publisher = {Universit{\"a}tsverlag der TU Berlin}, address = {Berlin}, isbn = {978-3-7983-2780-1}, pages = {61 -- 72}, year = {2015}, abstract = {In 2015 the second conference „Cloud Storage Deployment in Academics" took place. Interest regarding this issue was again high and topics established in 2014 like data security and scalability were complemented by new ones like federations or technical integration in existing infrastructures. This is caused by the advances in the establishment of cloud-based storage systems. This publication contains the contributions of the conference „Cloud Storage Deployment in Academics 2015", which took place in may 2015 at TU Berlin.}, language = {de} } @unpublished{DereudreMazzonettoRoelly2015, author = {Dereudre, David and Mazzonetto, Sara and Roelly, Sylvie}, title = {An explicit representation of the transition densities of the skew Brownian motion with drift and two semipermeable barriers}, volume = {4}, number = {9}, publisher = {Universit{\"a}tsverlag Potsdam}, address = {Potsdam}, issn = {2193-6943}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-80613}, pages = {23}, year = {2015}, abstract = {In this paper we obtain an explicit representation of the transition density of the one-dimensional skew Brownian motion with (a constant drift and) two semipermeable barriers. Moreover we propose a rejection method to simulate this density in an exact way.}, language = {en} } @phdthesis{Wallenta2015, author = {Wallenta, Daniel}, title = {Sequences of compact curvature}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-87489}, school = {Universit{\"a}t Potsdam}, pages = {viii, 73}, year = {2015}, abstract = {By perturbing the differential of a (cochain-)complex by "small" operators, one obtains what is referred to as quasicomplexes, i.e. a sequence whose curvature is not equal to zero in general. In this situation the cohomology is no longer defined. Note that it depends on the structure of the underlying spaces whether or not an operator is "small." This leads to a magical mix of perturbation and regularisation theory. In the general setting of Hilbert spaces compact operators are "small." In order to develop this theory, many elements of diverse mathematical disciplines, such as functional analysis, differential geometry, partial differential equation, homological algebra and topology have to be combined. All essential basics are summarised in the first chapter of this thesis. This contains classical elements of index theory, such as Fredholm operators, elliptic pseudodifferential operators and characteristic classes. Moreover we study the de Rham complex and introduce Sobolev spaces of arbitrary order as well as the concept of operator ideals. In the second chapter, the abstract theory of (Fredholm) quasicomplexes of Hilbert spaces will be developed. From the very beginning we will consider quasicomplexes with curvature in an ideal class. We introduce the Euler characteristic, the cone of a quasiendomorphism and the Lefschetz number. In particular, we generalise Euler's identity, which will allow us to develop the Lefschetz theory on nonseparable Hilbert spaces. Finally, in the third chapter the abstract theory will be applied to elliptic quasicomplexes with pseudodifferential operators of arbitrary order. We will show that the Atiyah-Singer index formula holds true for those objects and, as an example, we will compute the Euler characteristic of the connection quasicomplex. In addition to this we introduce geometric quasiendomorphisms and prove a generalisation of the Lefschetz fixed point theorem of Atiyah and Bott.}, language = {en} } @book{Kulik2015, author = {Kulik, Alexei Michajlovič}, title = {Introduction to Ergodic rates for Markov chains and processes}, editor = {Roelly, Sylvie}, publisher = {Universit{\"a}tsverlag Potsdam}, address = {Potsdam}, isbn = {978-3-86956-338-1}, issn = {2199-4951}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-79360}, publisher = {Universit{\"a}t Potsdam}, pages = {ix, 122 S.}, year = {2015}, abstract = {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.}, language = {en} }